fatigue 2009 v8
TRANSCRIPT
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 112
Overview
Fatigue is the most common cause of catastrophic failure in metals and can occur in othermaterials as well SolidWorksreg software provides a as reliable and cos-effecive way o
predic and resolve aigue-relaed problems beore hey happen
PREVENTING MECHANICAL FATIGUE
T E C H N I C A L P A P E R
wwwsolidworkscom
8132019 Fatigue 2009 v8
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IntroductionIn 1954 wo crashes involving he worldrsquos firs commercial je airliner he deHavilland Come brough he words ldquomeal aiguerdquo o newspaper headlines andino long-lasing public consciousness The aircraf also one o he firs o havea pressurized cabin had square windows Pressurizaion combined wih repeaedfligh loads caused cracks o orm in he corners o he windows and hose crackswidened over ime unil he cabins ell apar during fligh1 As well as being a humanragedy in which 68 people died he Come disasers were a wake-up call o engi-neers rying o creae sae srong designs
The imporance o analyzing aigue coninues o grow as companies srive o bemore efficien Saving maerial saves money afer all Reducing he hickness o awaer botle he slighes amoun can mean huge maerial savings hrough massproducion Bu prevening mechanical aigue is even more vial
Forunaely a ool o address his complicaed issuemdashand address i quicklymdashis available SolidWorks Simulaion is a as reliable and cos-effecive way orengineers o predic and resolve problems wih aigue
What is FatigueDesigners consider he mos imporan saey consideraion o be he overallsrengh o he componen assembly or produc To accommodae his you creae
a design ha will sand up o he probable ulimae load and add a saey acor oha or insurance In operaion however he design is very unlikely o experiencea consan load I is likely ha he design will experience load variaions and evenundergo muliple applicaions o hese load variaions which may lead o ailureover ime
Faigue is defined as ailure under a repeaed or oherwise varying load whichnever reaches a level sufficien o cause ailure in a single applicaion I is he moscommon cause o ailure among meals and i ofen occurs in oher maerials aswell2 Faigue happens in hree sages
983089 Crack initiation
983090 Crack propagation
983091 Final fracture
The firs sage o aigue is cracks resuling rom plasic sresses in localizedareas Such sresses are usually caused by sress concenraion sies on hesurace o a componen or a pre-exising deec on or jus below he surace
While i may be difficul or even impossible o model such deecs in CAD hevariabiliy in maerials is much easier o accoun or SolidWorks Simulaion canpredic sress concenraion areas and can help design engineers predic how longheir designs are likely o las beore experiencing he onse o aigue This paperocuses on predicing he oal aigue lie o a componen and onprevening cracks in he firs place so he las wo sages are beyondhe scope o his discussion3
A SCUBA ank is one example o a device ha is prone o aigue ailure wihouproper design Divers do no ofen go o dephs where overloading he meal ankbecomes a problem Ye a ank will experience many sress cycles hroughou islieime mos o all when adding pressurized oxygen This paper reers o heSCUBA ank in Figure 1 below in subsequen discussions
Fatigue is defined as ldquofailure under a
repeated or otherwise varying load which
never reaches a level sufficient to cause
failure in a single applicationrdquo
2 | Preventing Mechanical Fatigue | wwwsolidworkscom
1 Akinson R J Winkworh W J amp Norris G M (1960) Behaviour o skin aigue cracks a he corners o windows in a come uselage
2 Calliser W D (2007) Maerials Science and Engineering An Inroducion John Wiley amp Sons
3 Adams V Faigue Analysis in Produc Design - An Overview o Technologies and Techniques
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 312
Figure 1 The SCUBA ank used or a aigue sudy
Crack GrowthTwo physical mechanisms drive he process o aigue crack growh Under a cyclingload slip planes in he microsrucure o he maerial grain move back and orhcausing micro exrusions and inrusions on he surace o he componen These arear oo small o seemdashmeasuring beween one and 10 microns in heighmdashbu canbe considered o be embryonic cracks (Sage One)
When he Sage One crack reaches he grain boundary he mechanism ransers o
he adjacen grain Sage One cracks grow in he direcion o he maximum shear45 degrees o he direcion o loading
A approximaely hree grains in size he crack behavior changes because he crackhas become large enough o orm a geomerical sress concenraion (Sage OneI)Sage OneI cracks creae a ensile plasic zone a he ip and afer his poin hecrack grows perpendicular o he direcion o he applied load
When considering componen sress levels or aigue iniiaion and propagaionhe von Mises sress levels may be good or crack iniiaion predicion bu he maxprinciple sress will propagae he crack
The advancing crack effecively reduces a componenrsquos local cross secional areaso ha he componen rupures When examining ailed componens one sees ha
aigue racures have a characerisic appearance which reflecs he iniiaion sieand he progressive developmen o he crack ron culminaing in an area o finaloverload racure
3 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 412
How to Analyze FatigueTwo principal acors govern he amoun o ime i akes or a crack o sar andgrow sufficienly o cause componen ailure he componen maerial and sressfield Three main ways o calculae aigue lie exis Sress Lie (SN) Srain Lie(EN) and Linear Elasic Fracure Mechanics (LEFM)
1 SN Method The Sress Lie approach predics he componenrsquos aiguelie based upon sandard maerial es o ailure I gives resuls basedupon he whole aigue lie and as such does no break he process downino he hree sages The sress lie approach is based upon he
calculaion o varying elasic sresses which means i canno be appliedo low cycle aigue (ailures wih 10000 load cycles) However i is veryaccurae or high cycle aigue which is he realm o mos indusrialapplicaions and considerable maerial daa has been published ormaerials esed using his mehod
2 EN Method The Srain Lie echnique can calculae plasic sresses andcan be used or boh crack predicion and oal lie calculaions I can beused or boh low cycle aigue or sudying aigue in plasics Howeverhere is much less daa ou here or maerials based on his mehod
3 LEFM Method Linear Elasic Fracure Mechanics is used o calculaecrack growh raes I assumes ha a crack is already presen andpredics crack growh wih respec o he sress inensiy a hecrack ip
SolidWorks Simulaion aims o help people make designs ha will no aigue inhe firs place For hese casesmdashwhere sresses are low (elasic) and may repeaor hundreds o housands o cycles or moremdashhe Sress Lie and he Srain Lieapproaches are boh very accurae Wih his specific goal hough he addedaccuracy o he EN mehod in low-cycle aigue is a moo poin SolidWorksSimulaion ocuses solely on he likelihood o high cycle aigue
One major advanage o he SN mehod over he EN mehod is daa availabiliy Farmore maerial experimens have been conduced wih Sress Lie han wih srainlie For his reason SolidWorks Simulaion relies on he SN approach insead o
he EN approach
In ac he primary inpu o he SN mehodmdashhe S-N curvemdashwas he firseffecive approach o ackling aigue analysis This graph was esablished byAugus Woumlhler who in he 19h cenury se up and conduced he firs sysemaicaigue invesigaion Sandard laboraory ess applied cyclical loads such asroaing bends canilever bends axial push-pulls and orsion The daa comparedhe number o load cycles o ailure (N) o he sresses induced (S) hence hename ldquoS-N curverdquo Today scieniss and engineers produce S-N curves o show herelaionship o each ype o sress o he number o cycles o repeiion leading oailure Engineers can derive he sress level a maerial can endure or a specificnumber o cycles rom hese curves
SolidWorks Simulation aims to help people
make designs that will not fatigue in the
first place
4 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 512
A mock S-N curve or carbon seel is shown in Figure 2 below
Figure 2 A sample S-N curve
Any S-N curve can be broken down ino a ew imporan parameers and regionsFirs is here an endurance limi In oher words is here some sress level hawill never cause he maerial o ail regardless o he number o cycles For seelhe answer is yes bu or many oher maerials he answer is no We see anendurance limi in Figure 2 I appears as a horizonal line saring a abou 106
cycles denoed Se
Anoher key eaure is he disincion beween high cycle and low cycle aigueHigh cycle aigue begins when he genly sloping line owards he lef o he graphsuddenly dives This o course is easier o define in some maerials han inohers bu 10000 is generally regarded as a ypical ransiion value Designersand engineers have o prioriize beween high cycle and low cycle aigue or heirsubsequen analyses
5 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 612
The S-N curve provides valuable inormaion abou a maerialrsquos abiliy o endurevarious sresses However i ails o accoun or differen load scenarios as shownin Figure 3 below
Figure 3 Alernaing posiive mean and non-uniorm sress disribuions
The blue curve in Figure 3 is classified as an alernaing load scenario The sressescycle evenly beween posiive and negaive values cenered abou zero sress TheS-N curve is developed assuming his ype o loading sequence
However he oher cases are also common Many devices operae enirely inension like he yellow curve Ohers are non-uniorm like he red curvemdashar rom
he alernaing case In hese complicaed loading scenarios a crucial parameeris he mean sress Sudies have shown ha a nonzero mean sress significanlyaffecs aigue lie Afer all crack propagaion only occurs under ensile loadsso a device should crack more quickly i is enire cycle is in ension insead ohaving some compression In shor he higher he mean sress he more damagehe device will usually experience
6 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 712
Forunaely hree popular mehods o mean sress adjusmen have beendeveloped as shown in Figure 4 below
Figure 4 The Gerber Goodman and Soderberg lines orm he bases o classic mean
correcion echniques
The Gerber Goodman and Soderberg mehods denoe he prediced ailure
behavior according o he mean correcion lines shown wih he same names inFigure 4 The Gerber mehod uses a quadraic non-conservaive approach relaed ohe endurance limi (Se) and ulimae ensile srengh (Su) ha is generallyapplicable o ducile maerials The Goodman approach relies on a conservaivelinear relaionship beween he same parameers The Soderberg line is he mosconservaive o all relaionships as i links Se o he ensile yield srengh (Sy) Theinersecion o he alernaing and mean sresses (Sa and Sm respecively) canprovide some sense o he likelihood o ailure according o he differensandard lines
All hree o hese mehods apply only when all associaed S-N curves are based onully reversed loading Moreover hese correcions only become significan i heapplied aigue load cycles have large mean sresses compared o he sress rangeTesing has shown ha aigue ailure generally occurs somewhere in he regionbeween he Goodman line and he Gerber line Thus o give some leewayin a design i is mos pracical o use he more conservaive o he wo ashe upper bound
7 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 212
IntroductionIn 1954 wo crashes involving he worldrsquos firs commercial je airliner he deHavilland Come brough he words ldquomeal aiguerdquo o newspaper headlines andino long-lasing public consciousness The aircraf also one o he firs o havea pressurized cabin had square windows Pressurizaion combined wih repeaedfligh loads caused cracks o orm in he corners o he windows and hose crackswidened over ime unil he cabins ell apar during fligh1 As well as being a humanragedy in which 68 people died he Come disasers were a wake-up call o engi-neers rying o creae sae srong designs
The imporance o analyzing aigue coninues o grow as companies srive o bemore efficien Saving maerial saves money afer all Reducing he hickness o awaer botle he slighes amoun can mean huge maerial savings hrough massproducion Bu prevening mechanical aigue is even more vial
Forunaely a ool o address his complicaed issuemdashand address i quicklymdashis available SolidWorks Simulaion is a as reliable and cos-effecive way orengineers o predic and resolve problems wih aigue
What is FatigueDesigners consider he mos imporan saey consideraion o be he overallsrengh o he componen assembly or produc To accommodae his you creae
a design ha will sand up o he probable ulimae load and add a saey acor oha or insurance In operaion however he design is very unlikely o experiencea consan load I is likely ha he design will experience load variaions and evenundergo muliple applicaions o hese load variaions which may lead o ailureover ime
Faigue is defined as ailure under a repeaed or oherwise varying load whichnever reaches a level sufficien o cause ailure in a single applicaion I is he moscommon cause o ailure among meals and i ofen occurs in oher maerials aswell2 Faigue happens in hree sages
983089 Crack initiation
983090 Crack propagation
983091 Final fracture
The firs sage o aigue is cracks resuling rom plasic sresses in localizedareas Such sresses are usually caused by sress concenraion sies on hesurace o a componen or a pre-exising deec on or jus below he surace
While i may be difficul or even impossible o model such deecs in CAD hevariabiliy in maerials is much easier o accoun or SolidWorks Simulaion canpredic sress concenraion areas and can help design engineers predic how longheir designs are likely o las beore experiencing he onse o aigue This paperocuses on predicing he oal aigue lie o a componen and onprevening cracks in he firs place so he las wo sages are beyondhe scope o his discussion3
A SCUBA ank is one example o a device ha is prone o aigue ailure wihouproper design Divers do no ofen go o dephs where overloading he meal ankbecomes a problem Ye a ank will experience many sress cycles hroughou islieime mos o all when adding pressurized oxygen This paper reers o heSCUBA ank in Figure 1 below in subsequen discussions
Fatigue is defined as ldquofailure under a
repeated or otherwise varying load which
never reaches a level sufficient to cause
failure in a single applicationrdquo
2 | Preventing Mechanical Fatigue | wwwsolidworkscom
1 Akinson R J Winkworh W J amp Norris G M (1960) Behaviour o skin aigue cracks a he corners o windows in a come uselage
2 Calliser W D (2007) Maerials Science and Engineering An Inroducion John Wiley amp Sons
3 Adams V Faigue Analysis in Produc Design - An Overview o Technologies and Techniques
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 312
Figure 1 The SCUBA ank used or a aigue sudy
Crack GrowthTwo physical mechanisms drive he process o aigue crack growh Under a cyclingload slip planes in he microsrucure o he maerial grain move back and orhcausing micro exrusions and inrusions on he surace o he componen These arear oo small o seemdashmeasuring beween one and 10 microns in heighmdashbu canbe considered o be embryonic cracks (Sage One)
When he Sage One crack reaches he grain boundary he mechanism ransers o
he adjacen grain Sage One cracks grow in he direcion o he maximum shear45 degrees o he direcion o loading
A approximaely hree grains in size he crack behavior changes because he crackhas become large enough o orm a geomerical sress concenraion (Sage OneI)Sage OneI cracks creae a ensile plasic zone a he ip and afer his poin hecrack grows perpendicular o he direcion o he applied load
When considering componen sress levels or aigue iniiaion and propagaionhe von Mises sress levels may be good or crack iniiaion predicion bu he maxprinciple sress will propagae he crack
The advancing crack effecively reduces a componenrsquos local cross secional areaso ha he componen rupures When examining ailed componens one sees ha
aigue racures have a characerisic appearance which reflecs he iniiaion sieand he progressive developmen o he crack ron culminaing in an area o finaloverload racure
3 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 412
How to Analyze FatigueTwo principal acors govern he amoun o ime i akes or a crack o sar andgrow sufficienly o cause componen ailure he componen maerial and sressfield Three main ways o calculae aigue lie exis Sress Lie (SN) Srain Lie(EN) and Linear Elasic Fracure Mechanics (LEFM)
1 SN Method The Sress Lie approach predics he componenrsquos aiguelie based upon sandard maerial es o ailure I gives resuls basedupon he whole aigue lie and as such does no break he process downino he hree sages The sress lie approach is based upon he
calculaion o varying elasic sresses which means i canno be appliedo low cycle aigue (ailures wih 10000 load cycles) However i is veryaccurae or high cycle aigue which is he realm o mos indusrialapplicaions and considerable maerial daa has been published ormaerials esed using his mehod
2 EN Method The Srain Lie echnique can calculae plasic sresses andcan be used or boh crack predicion and oal lie calculaions I can beused or boh low cycle aigue or sudying aigue in plasics Howeverhere is much less daa ou here or maerials based on his mehod
3 LEFM Method Linear Elasic Fracure Mechanics is used o calculaecrack growh raes I assumes ha a crack is already presen andpredics crack growh wih respec o he sress inensiy a hecrack ip
SolidWorks Simulaion aims o help people make designs ha will no aigue inhe firs place For hese casesmdashwhere sresses are low (elasic) and may repeaor hundreds o housands o cycles or moremdashhe Sress Lie and he Srain Lieapproaches are boh very accurae Wih his specific goal hough he addedaccuracy o he EN mehod in low-cycle aigue is a moo poin SolidWorksSimulaion ocuses solely on he likelihood o high cycle aigue
One major advanage o he SN mehod over he EN mehod is daa availabiliy Farmore maerial experimens have been conduced wih Sress Lie han wih srainlie For his reason SolidWorks Simulaion relies on he SN approach insead o
he EN approach
In ac he primary inpu o he SN mehodmdashhe S-N curvemdashwas he firseffecive approach o ackling aigue analysis This graph was esablished byAugus Woumlhler who in he 19h cenury se up and conduced he firs sysemaicaigue invesigaion Sandard laboraory ess applied cyclical loads such asroaing bends canilever bends axial push-pulls and orsion The daa comparedhe number o load cycles o ailure (N) o he sresses induced (S) hence hename ldquoS-N curverdquo Today scieniss and engineers produce S-N curves o show herelaionship o each ype o sress o he number o cycles o repeiion leading oailure Engineers can derive he sress level a maerial can endure or a specificnumber o cycles rom hese curves
SolidWorks Simulation aims to help people
make designs that will not fatigue in the
first place
4 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 512
A mock S-N curve or carbon seel is shown in Figure 2 below
Figure 2 A sample S-N curve
Any S-N curve can be broken down ino a ew imporan parameers and regionsFirs is here an endurance limi In oher words is here some sress level hawill never cause he maerial o ail regardless o he number o cycles For seelhe answer is yes bu or many oher maerials he answer is no We see anendurance limi in Figure 2 I appears as a horizonal line saring a abou 106
cycles denoed Se
Anoher key eaure is he disincion beween high cycle and low cycle aigueHigh cycle aigue begins when he genly sloping line owards he lef o he graphsuddenly dives This o course is easier o define in some maerials han inohers bu 10000 is generally regarded as a ypical ransiion value Designersand engineers have o prioriize beween high cycle and low cycle aigue or heirsubsequen analyses
5 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 612
The S-N curve provides valuable inormaion abou a maerialrsquos abiliy o endurevarious sresses However i ails o accoun or differen load scenarios as shownin Figure 3 below
Figure 3 Alernaing posiive mean and non-uniorm sress disribuions
The blue curve in Figure 3 is classified as an alernaing load scenario The sressescycle evenly beween posiive and negaive values cenered abou zero sress TheS-N curve is developed assuming his ype o loading sequence
However he oher cases are also common Many devices operae enirely inension like he yellow curve Ohers are non-uniorm like he red curvemdashar rom
he alernaing case In hese complicaed loading scenarios a crucial parameeris he mean sress Sudies have shown ha a nonzero mean sress significanlyaffecs aigue lie Afer all crack propagaion only occurs under ensile loadsso a device should crack more quickly i is enire cycle is in ension insead ohaving some compression In shor he higher he mean sress he more damagehe device will usually experience
6 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 712
Forunaely hree popular mehods o mean sress adjusmen have beendeveloped as shown in Figure 4 below
Figure 4 The Gerber Goodman and Soderberg lines orm he bases o classic mean
correcion echniques
The Gerber Goodman and Soderberg mehods denoe he prediced ailure
behavior according o he mean correcion lines shown wih he same names inFigure 4 The Gerber mehod uses a quadraic non-conservaive approach relaed ohe endurance limi (Se) and ulimae ensile srengh (Su) ha is generallyapplicable o ducile maerials The Goodman approach relies on a conservaivelinear relaionship beween he same parameers The Soderberg line is he mosconservaive o all relaionships as i links Se o he ensile yield srengh (Sy) Theinersecion o he alernaing and mean sresses (Sa and Sm respecively) canprovide some sense o he likelihood o ailure according o he differensandard lines
All hree o hese mehods apply only when all associaed S-N curves are based onully reversed loading Moreover hese correcions only become significan i heapplied aigue load cycles have large mean sresses compared o he sress rangeTesing has shown ha aigue ailure generally occurs somewhere in he regionbeween he Goodman line and he Gerber line Thus o give some leewayin a design i is mos pracical o use he more conservaive o he wo ashe upper bound
7 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 312
Figure 1 The SCUBA ank used or a aigue sudy
Crack GrowthTwo physical mechanisms drive he process o aigue crack growh Under a cyclingload slip planes in he microsrucure o he maerial grain move back and orhcausing micro exrusions and inrusions on he surace o he componen These arear oo small o seemdashmeasuring beween one and 10 microns in heighmdashbu canbe considered o be embryonic cracks (Sage One)
When he Sage One crack reaches he grain boundary he mechanism ransers o
he adjacen grain Sage One cracks grow in he direcion o he maximum shear45 degrees o he direcion o loading
A approximaely hree grains in size he crack behavior changes because he crackhas become large enough o orm a geomerical sress concenraion (Sage OneI)Sage OneI cracks creae a ensile plasic zone a he ip and afer his poin hecrack grows perpendicular o he direcion o he applied load
When considering componen sress levels or aigue iniiaion and propagaionhe von Mises sress levels may be good or crack iniiaion predicion bu he maxprinciple sress will propagae he crack
The advancing crack effecively reduces a componenrsquos local cross secional areaso ha he componen rupures When examining ailed componens one sees ha
aigue racures have a characerisic appearance which reflecs he iniiaion sieand he progressive developmen o he crack ron culminaing in an area o finaloverload racure
3 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 412
How to Analyze FatigueTwo principal acors govern he amoun o ime i akes or a crack o sar andgrow sufficienly o cause componen ailure he componen maerial and sressfield Three main ways o calculae aigue lie exis Sress Lie (SN) Srain Lie(EN) and Linear Elasic Fracure Mechanics (LEFM)
1 SN Method The Sress Lie approach predics he componenrsquos aiguelie based upon sandard maerial es o ailure I gives resuls basedupon he whole aigue lie and as such does no break he process downino he hree sages The sress lie approach is based upon he
calculaion o varying elasic sresses which means i canno be appliedo low cycle aigue (ailures wih 10000 load cycles) However i is veryaccurae or high cycle aigue which is he realm o mos indusrialapplicaions and considerable maerial daa has been published ormaerials esed using his mehod
2 EN Method The Srain Lie echnique can calculae plasic sresses andcan be used or boh crack predicion and oal lie calculaions I can beused or boh low cycle aigue or sudying aigue in plasics Howeverhere is much less daa ou here or maerials based on his mehod
3 LEFM Method Linear Elasic Fracure Mechanics is used o calculaecrack growh raes I assumes ha a crack is already presen andpredics crack growh wih respec o he sress inensiy a hecrack ip
SolidWorks Simulaion aims o help people make designs ha will no aigue inhe firs place For hese casesmdashwhere sresses are low (elasic) and may repeaor hundreds o housands o cycles or moremdashhe Sress Lie and he Srain Lieapproaches are boh very accurae Wih his specific goal hough he addedaccuracy o he EN mehod in low-cycle aigue is a moo poin SolidWorksSimulaion ocuses solely on he likelihood o high cycle aigue
One major advanage o he SN mehod over he EN mehod is daa availabiliy Farmore maerial experimens have been conduced wih Sress Lie han wih srainlie For his reason SolidWorks Simulaion relies on he SN approach insead o
he EN approach
In ac he primary inpu o he SN mehodmdashhe S-N curvemdashwas he firseffecive approach o ackling aigue analysis This graph was esablished byAugus Woumlhler who in he 19h cenury se up and conduced he firs sysemaicaigue invesigaion Sandard laboraory ess applied cyclical loads such asroaing bends canilever bends axial push-pulls and orsion The daa comparedhe number o load cycles o ailure (N) o he sresses induced (S) hence hename ldquoS-N curverdquo Today scieniss and engineers produce S-N curves o show herelaionship o each ype o sress o he number o cycles o repeiion leading oailure Engineers can derive he sress level a maerial can endure or a specificnumber o cycles rom hese curves
SolidWorks Simulation aims to help people
make designs that will not fatigue in the
first place
4 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 512
A mock S-N curve or carbon seel is shown in Figure 2 below
Figure 2 A sample S-N curve
Any S-N curve can be broken down ino a ew imporan parameers and regionsFirs is here an endurance limi In oher words is here some sress level hawill never cause he maerial o ail regardless o he number o cycles For seelhe answer is yes bu or many oher maerials he answer is no We see anendurance limi in Figure 2 I appears as a horizonal line saring a abou 106
cycles denoed Se
Anoher key eaure is he disincion beween high cycle and low cycle aigueHigh cycle aigue begins when he genly sloping line owards he lef o he graphsuddenly dives This o course is easier o define in some maerials han inohers bu 10000 is generally regarded as a ypical ransiion value Designersand engineers have o prioriize beween high cycle and low cycle aigue or heirsubsequen analyses
5 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 612
The S-N curve provides valuable inormaion abou a maerialrsquos abiliy o endurevarious sresses However i ails o accoun or differen load scenarios as shownin Figure 3 below
Figure 3 Alernaing posiive mean and non-uniorm sress disribuions
The blue curve in Figure 3 is classified as an alernaing load scenario The sressescycle evenly beween posiive and negaive values cenered abou zero sress TheS-N curve is developed assuming his ype o loading sequence
However he oher cases are also common Many devices operae enirely inension like he yellow curve Ohers are non-uniorm like he red curvemdashar rom
he alernaing case In hese complicaed loading scenarios a crucial parameeris he mean sress Sudies have shown ha a nonzero mean sress significanlyaffecs aigue lie Afer all crack propagaion only occurs under ensile loadsso a device should crack more quickly i is enire cycle is in ension insead ohaving some compression In shor he higher he mean sress he more damagehe device will usually experience
6 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 712
Forunaely hree popular mehods o mean sress adjusmen have beendeveloped as shown in Figure 4 below
Figure 4 The Gerber Goodman and Soderberg lines orm he bases o classic mean
correcion echniques
The Gerber Goodman and Soderberg mehods denoe he prediced ailure
behavior according o he mean correcion lines shown wih he same names inFigure 4 The Gerber mehod uses a quadraic non-conservaive approach relaed ohe endurance limi (Se) and ulimae ensile srengh (Su) ha is generallyapplicable o ducile maerials The Goodman approach relies on a conservaivelinear relaionship beween he same parameers The Soderberg line is he mosconservaive o all relaionships as i links Se o he ensile yield srengh (Sy) Theinersecion o he alernaing and mean sresses (Sa and Sm respecively) canprovide some sense o he likelihood o ailure according o he differensandard lines
All hree o hese mehods apply only when all associaed S-N curves are based onully reversed loading Moreover hese correcions only become significan i heapplied aigue load cycles have large mean sresses compared o he sress rangeTesing has shown ha aigue ailure generally occurs somewhere in he regionbeween he Goodman line and he Gerber line Thus o give some leewayin a design i is mos pracical o use he more conservaive o he wo ashe upper bound
7 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 412
How to Analyze FatigueTwo principal acors govern he amoun o ime i akes or a crack o sar andgrow sufficienly o cause componen ailure he componen maerial and sressfield Three main ways o calculae aigue lie exis Sress Lie (SN) Srain Lie(EN) and Linear Elasic Fracure Mechanics (LEFM)
1 SN Method The Sress Lie approach predics he componenrsquos aiguelie based upon sandard maerial es o ailure I gives resuls basedupon he whole aigue lie and as such does no break he process downino he hree sages The sress lie approach is based upon he
calculaion o varying elasic sresses which means i canno be appliedo low cycle aigue (ailures wih 10000 load cycles) However i is veryaccurae or high cycle aigue which is he realm o mos indusrialapplicaions and considerable maerial daa has been published ormaerials esed using his mehod
2 EN Method The Srain Lie echnique can calculae plasic sresses andcan be used or boh crack predicion and oal lie calculaions I can beused or boh low cycle aigue or sudying aigue in plasics Howeverhere is much less daa ou here or maerials based on his mehod
3 LEFM Method Linear Elasic Fracure Mechanics is used o calculaecrack growh raes I assumes ha a crack is already presen andpredics crack growh wih respec o he sress inensiy a hecrack ip
SolidWorks Simulaion aims o help people make designs ha will no aigue inhe firs place For hese casesmdashwhere sresses are low (elasic) and may repeaor hundreds o housands o cycles or moremdashhe Sress Lie and he Srain Lieapproaches are boh very accurae Wih his specific goal hough he addedaccuracy o he EN mehod in low-cycle aigue is a moo poin SolidWorksSimulaion ocuses solely on he likelihood o high cycle aigue
One major advanage o he SN mehod over he EN mehod is daa availabiliy Farmore maerial experimens have been conduced wih Sress Lie han wih srainlie For his reason SolidWorks Simulaion relies on he SN approach insead o
he EN approach
In ac he primary inpu o he SN mehodmdashhe S-N curvemdashwas he firseffecive approach o ackling aigue analysis This graph was esablished byAugus Woumlhler who in he 19h cenury se up and conduced he firs sysemaicaigue invesigaion Sandard laboraory ess applied cyclical loads such asroaing bends canilever bends axial push-pulls and orsion The daa comparedhe number o load cycles o ailure (N) o he sresses induced (S) hence hename ldquoS-N curverdquo Today scieniss and engineers produce S-N curves o show herelaionship o each ype o sress o he number o cycles o repeiion leading oailure Engineers can derive he sress level a maerial can endure or a specificnumber o cycles rom hese curves
SolidWorks Simulation aims to help people
make designs that will not fatigue in the
first place
4 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 512
A mock S-N curve or carbon seel is shown in Figure 2 below
Figure 2 A sample S-N curve
Any S-N curve can be broken down ino a ew imporan parameers and regionsFirs is here an endurance limi In oher words is here some sress level hawill never cause he maerial o ail regardless o he number o cycles For seelhe answer is yes bu or many oher maerials he answer is no We see anendurance limi in Figure 2 I appears as a horizonal line saring a abou 106
cycles denoed Se
Anoher key eaure is he disincion beween high cycle and low cycle aigueHigh cycle aigue begins when he genly sloping line owards he lef o he graphsuddenly dives This o course is easier o define in some maerials han inohers bu 10000 is generally regarded as a ypical ransiion value Designersand engineers have o prioriize beween high cycle and low cycle aigue or heirsubsequen analyses
5 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 612
The S-N curve provides valuable inormaion abou a maerialrsquos abiliy o endurevarious sresses However i ails o accoun or differen load scenarios as shownin Figure 3 below
Figure 3 Alernaing posiive mean and non-uniorm sress disribuions
The blue curve in Figure 3 is classified as an alernaing load scenario The sressescycle evenly beween posiive and negaive values cenered abou zero sress TheS-N curve is developed assuming his ype o loading sequence
However he oher cases are also common Many devices operae enirely inension like he yellow curve Ohers are non-uniorm like he red curvemdashar rom
he alernaing case In hese complicaed loading scenarios a crucial parameeris he mean sress Sudies have shown ha a nonzero mean sress significanlyaffecs aigue lie Afer all crack propagaion only occurs under ensile loadsso a device should crack more quickly i is enire cycle is in ension insead ohaving some compression In shor he higher he mean sress he more damagehe device will usually experience
6 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 712
Forunaely hree popular mehods o mean sress adjusmen have beendeveloped as shown in Figure 4 below
Figure 4 The Gerber Goodman and Soderberg lines orm he bases o classic mean
correcion echniques
The Gerber Goodman and Soderberg mehods denoe he prediced ailure
behavior according o he mean correcion lines shown wih he same names inFigure 4 The Gerber mehod uses a quadraic non-conservaive approach relaed ohe endurance limi (Se) and ulimae ensile srengh (Su) ha is generallyapplicable o ducile maerials The Goodman approach relies on a conservaivelinear relaionship beween he same parameers The Soderberg line is he mosconservaive o all relaionships as i links Se o he ensile yield srengh (Sy) Theinersecion o he alernaing and mean sresses (Sa and Sm respecively) canprovide some sense o he likelihood o ailure according o he differensandard lines
All hree o hese mehods apply only when all associaed S-N curves are based onully reversed loading Moreover hese correcions only become significan i heapplied aigue load cycles have large mean sresses compared o he sress rangeTesing has shown ha aigue ailure generally occurs somewhere in he regionbeween he Goodman line and he Gerber line Thus o give some leewayin a design i is mos pracical o use he more conservaive o he wo ashe upper bound
7 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 512
A mock S-N curve or carbon seel is shown in Figure 2 below
Figure 2 A sample S-N curve
Any S-N curve can be broken down ino a ew imporan parameers and regionsFirs is here an endurance limi In oher words is here some sress level hawill never cause he maerial o ail regardless o he number o cycles For seelhe answer is yes bu or many oher maerials he answer is no We see anendurance limi in Figure 2 I appears as a horizonal line saring a abou 106
cycles denoed Se
Anoher key eaure is he disincion beween high cycle and low cycle aigueHigh cycle aigue begins when he genly sloping line owards he lef o he graphsuddenly dives This o course is easier o define in some maerials han inohers bu 10000 is generally regarded as a ypical ransiion value Designersand engineers have o prioriize beween high cycle and low cycle aigue or heirsubsequen analyses
5 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 612
The S-N curve provides valuable inormaion abou a maerialrsquos abiliy o endurevarious sresses However i ails o accoun or differen load scenarios as shownin Figure 3 below
Figure 3 Alernaing posiive mean and non-uniorm sress disribuions
The blue curve in Figure 3 is classified as an alernaing load scenario The sressescycle evenly beween posiive and negaive values cenered abou zero sress TheS-N curve is developed assuming his ype o loading sequence
However he oher cases are also common Many devices operae enirely inension like he yellow curve Ohers are non-uniorm like he red curvemdashar rom
he alernaing case In hese complicaed loading scenarios a crucial parameeris he mean sress Sudies have shown ha a nonzero mean sress significanlyaffecs aigue lie Afer all crack propagaion only occurs under ensile loadsso a device should crack more quickly i is enire cycle is in ension insead ohaving some compression In shor he higher he mean sress he more damagehe device will usually experience
6 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 712
Forunaely hree popular mehods o mean sress adjusmen have beendeveloped as shown in Figure 4 below
Figure 4 The Gerber Goodman and Soderberg lines orm he bases o classic mean
correcion echniques
The Gerber Goodman and Soderberg mehods denoe he prediced ailure
behavior according o he mean correcion lines shown wih he same names inFigure 4 The Gerber mehod uses a quadraic non-conservaive approach relaed ohe endurance limi (Se) and ulimae ensile srengh (Su) ha is generallyapplicable o ducile maerials The Goodman approach relies on a conservaivelinear relaionship beween he same parameers The Soderberg line is he mosconservaive o all relaionships as i links Se o he ensile yield srengh (Sy) Theinersecion o he alernaing and mean sresses (Sa and Sm respecively) canprovide some sense o he likelihood o ailure according o he differensandard lines
All hree o hese mehods apply only when all associaed S-N curves are based onully reversed loading Moreover hese correcions only become significan i heapplied aigue load cycles have large mean sresses compared o he sress rangeTesing has shown ha aigue ailure generally occurs somewhere in he regionbeween he Goodman line and he Gerber line Thus o give some leewayin a design i is mos pracical o use he more conservaive o he wo ashe upper bound
7 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 612
The S-N curve provides valuable inormaion abou a maerialrsquos abiliy o endurevarious sresses However i ails o accoun or differen load scenarios as shownin Figure 3 below
Figure 3 Alernaing posiive mean and non-uniorm sress disribuions
The blue curve in Figure 3 is classified as an alernaing load scenario The sressescycle evenly beween posiive and negaive values cenered abou zero sress TheS-N curve is developed assuming his ype o loading sequence
However he oher cases are also common Many devices operae enirely inension like he yellow curve Ohers are non-uniorm like he red curvemdashar rom
he alernaing case In hese complicaed loading scenarios a crucial parameeris he mean sress Sudies have shown ha a nonzero mean sress significanlyaffecs aigue lie Afer all crack propagaion only occurs under ensile loadsso a device should crack more quickly i is enire cycle is in ension insead ohaving some compression In shor he higher he mean sress he more damagehe device will usually experience
6 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 712
Forunaely hree popular mehods o mean sress adjusmen have beendeveloped as shown in Figure 4 below
Figure 4 The Gerber Goodman and Soderberg lines orm he bases o classic mean
correcion echniques
The Gerber Goodman and Soderberg mehods denoe he prediced ailure
behavior according o he mean correcion lines shown wih he same names inFigure 4 The Gerber mehod uses a quadraic non-conservaive approach relaed ohe endurance limi (Se) and ulimae ensile srengh (Su) ha is generallyapplicable o ducile maerials The Goodman approach relies on a conservaivelinear relaionship beween he same parameers The Soderberg line is he mosconservaive o all relaionships as i links Se o he ensile yield srengh (Sy) Theinersecion o he alernaing and mean sresses (Sa and Sm respecively) canprovide some sense o he likelihood o ailure according o he differensandard lines
All hree o hese mehods apply only when all associaed S-N curves are based onully reversed loading Moreover hese correcions only become significan i heapplied aigue load cycles have large mean sresses compared o he sress rangeTesing has shown ha aigue ailure generally occurs somewhere in he regionbeween he Goodman line and he Gerber line Thus o give some leewayin a design i is mos pracical o use he more conservaive o he wo ashe upper bound
7 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 712
Forunaely hree popular mehods o mean sress adjusmen have beendeveloped as shown in Figure 4 below
Figure 4 The Gerber Goodman and Soderberg lines orm he bases o classic mean
correcion echniques
The Gerber Goodman and Soderberg mehods denoe he prediced ailure
behavior according o he mean correcion lines shown wih he same names inFigure 4 The Gerber mehod uses a quadraic non-conservaive approach relaed ohe endurance limi (Se) and ulimae ensile srengh (Su) ha is generallyapplicable o ducile maerials The Goodman approach relies on a conservaivelinear relaionship beween he same parameers The Soderberg line is he mosconservaive o all relaionships as i links Se o he ensile yield srengh (Sy) Theinersecion o he alernaing and mean sresses (Sa and Sm respecively) canprovide some sense o he likelihood o ailure according o he differensandard lines
All hree o hese mehods apply only when all associaed S-N curves are based onully reversed loading Moreover hese correcions only become significan i heapplied aigue load cycles have large mean sresses compared o he sress rangeTesing has shown ha aigue ailure generally occurs somewhere in he regionbeween he Goodman line and he Gerber line Thus o give some leewayin a design i is mos pracical o use he more conservaive o he wo ashe upper bound
7 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 812
Following a saic analysis sudy aigue is ofen sudied hrough wo classic ormso analysis called Minerrsquos Rule and ldquoRainflow Couningrdquo Minerrsquos rule assumes hai an objec can endure N cycles o S sress levels hen each cycle removes a rac-ion o he objecrsquos aigue lie ha equals 1N For example i a seel bar ails aferbeing subjeced o 90000 cycles a 200 MPa each cycle ook 190000 o is lie(The rule also allows muliple loads o be aken ino accoun hrough a weighedaverage which only requires sligh modificaions) Minerrsquos rule has wo majorlimiaions I canno ake he probabiliy o aigue iniiaion ino accoun and idoes no consider he order o sresses reached in any way However is resuls
are generally consisen wih esing so i has become a sandard orm o analysisMos componens undergo a varying load hisory in real lie condiions in ermso boh ampliude and mean sress Thereore a ar more general and realisicapproach considers variable ampliude loading in which he sresses alhoughrepeiive over ime have varying ampliude making i possible o spli hem inoload ldquoblocksrdquo Rainflow couning eners he picure in order o find he sresses andhe requency ha hose sresses occur on a par or Minerrsquos rule calculaions Anexample o rainflow couning is shown in Figure 5 below
Figure 5 An example o rainflow couning Sofware sars wih a filled region (lef) and ldquodrainsrdquo he graph
in pieces leaving one secion behind afer he firs ieraion (righ)
The sress range and is associaed mean sress is deermined rom he load hisoryshown in he graph The load hisory is ldquofilled wih rainrdquo Afer he sress range andmean have been deermined he ldquorainrdquo is drained rom he lowes poin The rangeand mean or each remaining porion o rapped ldquorainrdquo is hen deermined From heresuls Minerrsquos rule can be applied and he aigue lie calculaed
Imagine ha Figure 5 is a segmen o an S-N curve ha shows a combinaion oensile sresses wih he zero line locaed a he botom o he graph as shown in
Figure 5 Saring a he highes poin on he lef he graph is ldquodrainedrdquo Imagine he jagged line as a roo urned sideways and drain o he righmdashyou should see i alloff as shown The region on he righ in Figure 5 remains afer he firs ieraion Forhis secion he range and mean are aken ino accoun or Minerrsquos rule The effecso each region can be combined via superposiion5
8 | Preventing Mechanical Fatigue | wwwsolidworkscom
5 Poter J M amp Waanabe R T (1989) Developmen o Faigue Loading Specra ASTM Inernaional
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 912
Naurally mos objecs do no always experience he same loads The ypical SCUBAank or example may be loaded wih differen pressures a differen imes ordifferen duraions Rainflow couning is a graphical way o average hese meansresses during a producrsquos lie and Minerrsquos rule can combine he effecs o hesesresses ogeher
SolidWorks Simulaion provides excellen ools or sudying aigue wih he SNapproach because he inpu consiss o a linear elasic sress field and Analysisallows you o consider he possible ineracions o muliple load cases I se ocalculae he wors case load environmen a ypical approach he sysem can
provide a number o differen aigue compuaion resuls including lie plosdamage plos and acor o saey plos In addiion SolidWorks Simulaion canprovide plos o he raio o he smaller alernaing principal sress divided by helarger alernaing principal sress called a biaxialiy indicaor plo as well as aRainflow Marix char The later is a 3D hisogram in which he X and Y axesrepresen he alernaing and mean sresses and he Z axis represens he numbero cycles couned or each bin
Simple Loading ScenariosMuliple acors are used o deermine he saey o he SCUBA ank he acor osaey a he operaing pressure he burs pressure and he anks lie expecancyThe roo o a aigue analysis is a saic sudy o calculae he elasic sress fielddue o an inernal pressure The firs check a designer will make is o ensure ha he
sress acor o saey is greaer han he required minimum I he design passes hesrengh es hen he aigue check plo will indicae he regions o he maerial indanger o aigue ailure
The resuls o he pressure simulaion are shown below The acor o saey reporsa minimum value o 15 which in many cases would be oo low which indicaes hanone o he maerial o he ank is above yield In he aigue check plo we havespecified a minimum aigue acor o saey o 4 The red regions in Figure 6 belowindicae he areas or which he sresses all ouside o he saey zone in Figure 4The value o his plo is ha i gives you a place o sar wih more in-deph aigueanalysis Raher han conducing an exhausive sudy o he enire ank ocusing onhese poenial ho spos may be a more producive use o ime and resources
Figure 6 Resuls o he SCUBA ank pressure simulaion Maerial Facor o Saey (lef)
and Faigue Check plos (righ)
Rainflow counting is a graphical way to
average mean stresses during a productrsquos
life and Minerrsquos rule can combine the effects
of these stresses together
9 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1012
The pressure es simulaion indicaes he need or a ull aigue analysis A ullaigue analysis will no only provide a Faigue Facor o Saey plos bu alsoDamage and Toal Lie plos The damage plo shows how much o he aigue lieo he maerial has given up due o he applied load cycles Once he damagepercenage is greaer han 100 one can assume ha ha porion o he maerialhas a crack hrough i The Toal Lie plo shows how many load cycles have o beapplied o ully aigue any porion o he maerial In his case we can see ha heSCUBA ank can be filled a maximum o 149000 imes beore aigue will be anissue This value mus be seen as an upper bound and he aigue acor o saey
would reduce his o well below 100000
Figure 7 Resuls o he Scuba ank pressure simulaion Damage Percenage (lef)
and Toal Lie plos (righ)
Advanced Loading ScenariosUnorunaely many real-lie scenarios involve more complicaed orces han hoseexperienced by he SCUBA ank case sudy A combinaion o differen ypes oloads is imporan when analyzing he aigue o many devices in operaion Forexample loads can be classified as ldquodead loadsrdquo and ldquolive loadsrdquo A dead load isconsan I a deunc rain is simply siting on racks ha rainrsquos weigh exers adead load on he racks In conras a live loadmdashlike ha exered by a rainpassing over some lengh o rackmdashchanges wih ime
SolidWorks Simulaion provides he ools necessary o examine simulaneousloading bu sequenial loading is sill a ldquoblack boxrdquo o some degree Two casesudiesmdasha unicular rain and a wind urbinemdashdemonsrae he roles o aigueanalysis in unique siuaions
SolidWorks Simulation provides the tools
necessary to examine simultaneous loading
10 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1112
Funicular You wan o deermine he likelihood o aigue in he rame o a unicular The carrepeaedly ollows a course where he loads on he rame rom he wind he urnsin he rack and he passengers are known This sudy showcases a se o loads hacan be analyzed wih SolidWorks Simulaion
Figure 8 A unicular on a rack The combined loads acing on
he rame can be combined or aigue analysis
These loads occur simulaneously in real lie Passengers are sanding wihin heunicular carrsquos rame while he wind blows and he car urns along he rail Bu heloads can be discreized Each orce can be reaed as a separae ldquoevenrdquo wihin hesimulaion sofware The loads a each node can hen be summed ogeher and hasummaion can be repeaed over ime By knowing he sresses on he unicularrsquosrame and he number o cycles a which each sress level occurs he sofware usesMinerrsquos rule o esimae he srucurersquos lie SolidWorks Simulaion works very effec-ively wih hese combined simulaneous loading scenarios and i can save a lo oime compared wih hand calculaions or mechanical esing
SolidWorks Simulation works very
effectively with combined simultaneous
loading scenarios and it can save a lot
of time compared with hand calculations
or mechanical testing
11 | Preventing Mechanical Fatigue | wwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom
8132019 Fatigue 2009 v8
httpslidepdfcomreaderfullfatigue-2009-v8 1212
S lidW k i i d d k D l S egrave S lidW k C All h d d d k
Wind TurbineImagine a designer would like o analyze he likelihood o aigue or his windurbine design He has recorded en-minue samples o he loads experienced byhe srucure in sarup sopping and sandard operaing mode He wans o see ihe srucure can wihsand 10000 sars and sops over 20 years oworking condiions This scenario is one ha canno be analyzed hroughSolidWorks Simulaion
The firs issue is he ime span No mater how many minues or even hours osresses he user recorded i would be difficul o generalize hose resuls over
years o operaion Assuming consan wind is sufficien or a unicular or whichhe wind is a minor acor Bu i is one o he major sresses on a wind urbineRandom changes in wind paterns are crucial and consan ampliude is no anadequae approximaion The wind blows a hurricane srengh one day says idlehe nexmdashand in no orderly patern
Wih respec o he sofware his is a undamenally differen case ha cannobe analyzed effecively SolidWorks Simulaion defines ldquoevensrdquo ha can beinsananeously combined as described wih he unicular Bu differen evens haare ordered sequenially canno be grouped ogeher Again one o helimiaions o Minerrsquos rule is ha i neglecs he effec o he order o evenson a srucure I can only work wih repeaed cycles a random
The bes possible esimae o dae is o use analysis and sudy hese evens inparallel The column o sresses a each node over ime can hen be placed inoa large spreadshee Then he designer would have o manually combine hesesresses and atemp o sum hem wih Minerrsquos rule Bu his process is airlyime-consuming and error prone so a aigue sudy like his sill remainseffecively unsolvable
ConclusionSriking he balance beween saving maerials and preserving design lie isbecoming more imporan every day The moivaion o sudy aigue in mechanicaldesign goes hand-in-hand wih his growing need SolidWorks Simulaion providesmany differen ools or you o accoun or aigue bu saving ime is our mossignifican conribuion You can do many o hese calculaions by hand bu helikelihood o compuaional error and he inense ime commimen are significan
drawbacks compared wih SolidWorks Simulaion And while experimenal esingis he only way o acquire compleely accurae daa he coss and ime associaedwih hese ess can be humongous The analysis ools ha SolidWorks providescan help your eam go a long way owards designing beter producs
Addiional ideas and help are available on he SolidWorks websiea wwwsolidworkscom
Dassaul SysegravemesSolidWorks Corp300 Baker AvenueConcord MA 983088983089983095983092 983090 USAPhone 983089 983096983088983088 983094983097983091 983097983088983088983088Ouside he US +983089 983097983095983096 983091983095983089 983093983088983089983089Email inosolidworkscomwwwsolidworkscom