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Engineering Materials
Springer-Verlag Berlin Heidelberg GmbH
Engineering ONLINE LIBRARY
http://www.springer.de/engine/
Wolfgang Grellmann· Sabine Seidler (Eds.)
Deformation and Fracture Behaviour of Polymers
With 447 Illustrations and 51 Tables
" Springer
Prof. Dr. Wolfgang Grellmann Department of Engineering Science Martin-Luther-University of Halle-Wittenberg D-06099 Halle, Germany http://www.kunststoffdiagnostik.de
Prof. Dr. Sabine Seidler Institute of Materials Science and Testing Vienna University of Technology FavoritenstraEe 9-11 A-I040 Vienna, Austria http://www.tuwien.ac.atlE308
Lectures of a discussion conference took place at the Institute of Polymer Materials e.¥., MartinLuther-University of Halle-Wittenberg under the direction of Prof. Dr. W. Grellmann, Merseburg. The respective articles of the participants in the seminar were published unchanged in content in that version provided by the authors. Because of overall impression a uniform textual and graphical layout of the contributions was widely realized by the editors.
Library of Congress Cataloging-in-Publication Data Deformation and fracture behaviour of polymers 1 Wolfgang Grellmann, Sabine Seidler, eds. p. cm. -- (Engineering materials) Includes index. ISBN 978-3-642-07453-0 ISBN 978-3-662-04556-5 (eBook) DOI 10.1007/978-3-662-04556-5 1. Polymers--Fracture. 2. Deformations (Mechanics) I. Grellmann, Wolfgang, 1949-II. Seidler, Sabine, 1961- III. Series.
ISBN 978-3-642-07453-0
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© Springer-Verlag Berlin Heidelberg 2001 Originally published by Springer-Verlag Berlin Heidelberg New York in 2001 Softcover reprint ofthe hardcover 1st edition 2001 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
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Preface
The application of fracture mechanics to polymers and composites allows the quantitative description of the toughness behaviour by means of fracture mechanics parameters and enables preventive failure analysis. In recent years this young scientific discipline has developed rapidly, and now the experimental results are looking for more applications in industrial practice. However, the practical applications of fracture mechanics parameters to structural-integrity assessment are severely restricted owing to their limited transferability from specimens to components. Indeed, geometry-independent fracture mechanics parameters are very important for the reliable functioning of polymers and components in nearly all industrial application fields.
These application fields include the polymer development, quality control, construction and polymer-specific design of reliable components in the motor industry, the electrical industry and the manufacture of household appliances, as well as applications in information technology and medical applications.
The present status report on the deformation and fracture behaviour of polymer materials was composed on the basis of revised lectures presented at the Merseburg discussion conference entitled 'Deformation and Fracture Behaviour of Polymers' and additional single contributions.
The editors and authors have tried hard to present information about the applied fracture mechanics of polymers and composites in the light of their current research work.
The aim was to express the present standard of knowledge as comprehensively as possible by inclusion of additional contributions referring to sets of problems such as the assessment of toughness properties with fracture mechanics parameters, approximate methods, quantification of morphology-property correlations, and limits of application.
These discussion conferences take place every two years with the intention of demonstrating the progress of basic and applied research in the deformation and fracture behaviour of polymers, homopolymers, blends, copolymers, composites and biocompatible materials. For this purpose, plenary lectures, short reports, discussions and an exhibition of instruments in the field of destructive and nondestructive material testing are organized.
Particular topics of these conferences are
- toughness characterization of polymers with fracture mechanics concepts - morphology-property correlations - hybrid methods of polymer testing and polymer diagnostics - technological test methods for testing of components and structures - biocompatible materials and medical prostheses
examples and limits of the application of polymers.
VI Preface
It is hoped that these conferences will make a contribution to the current understanding of problems in this field by specialists from universities/colleges and the polymer industry.
We want to thank sincerely all co-authors and collaborators from the Institute of Materials Science and Polymer Materials e.V. of the Department of Material Sciences of the Martin-Luther-University of Halle-Wittenberg and all collaborators from the Institute of Materials Science and Testing of the Vienna University of Technology, who made possible the publication ofthis book by their readiness for duty and their willing cooperation.
The editors sincerely thank Dr. Christian Bierligel from the Institute of Material Sciences for the comprehensive cooperation and advice that he gave.
We also thank Dipl.-Ing. Katrin Reincke for the technical preparation of the manuscript, as well as Springer for their forthcoming cooperation.
Merseburg, Vienna Wolfgang Grellmann
October 2000 Sabine Seidler
Contents
List of Authors.............................................................................. XIII
Nomenclature............................................................................... XV
Terminology............... ................................................................... xxv
A Characterization of Toughness Using Fracture Mechanics Methods
A 1 State of the Art and Development Trends
A 1.1 New Developments in Toughness Evaluation of Polymers and Compounds by Fracture Mechanics W Grellmann................................. ............ ................................... 3
A 1.2 Concepts of Fracture Mechanics for Polymers F. Ramsteiner, W Schuster, S. Forster......................................... 27
A 2 Experimental Methods
A 2.1 Influence of Specimen Geometry and Loading Conditions on the Crack Resistance Behaviour ofPoly(vinyl chloride) and Polypropylene W Grellmann, S. Seidler, K. Jung, M Che, 1. Kotter...................... 51
A 2.2 Procedure for Determining the Crack Resistance Behaviour Using the Instrumented Charpy Impact Test W Grellmann, S. Seidler, W Hesse................................................. 71
A 2.3 Possibilities and Limits of Standards and Drafts for J-R Curve Determination of Polymers S. Seidler, W Grellmann........................... ...................................... 87
A 2.4 The Relationship Between the Fracture Behaviour and Structural Parameters ofPE-HD E. Nezbedowi, J. Kucera, Z. Salajka................................................ 95
VIII Contents
A 3 Alternative Methods
A 3.1 Application of Single-Specimen Testing Methods for Determining J-R Curves of Polymers S. Seidler.......................................................................................... 105
A 3.2 Application of Normalization Method for Determining J-R Curves in the Amorphous Polymer PVC M Che, W. Grellmann, S. Seidler.................................................... 121
A 3.3 Calculation of J-R Curves Based on Load-Deflection Diagrams Using the Hinge Model Test Specimen R. Steiner, W. Grellmann................................................................. 133
A 3.4 An Alternative Method Based on J-TJ and ~T6 Stability Assessment Diagrams to Determine Instability Values from Crack Resistance Curves R. Lach, W. Grellmann.................................................................... 141
B Morphology-Property Correlations
B 1 Homopolymers
B 1.1 Supermolecular Structure and Mechanical Behaviour of Isotactic Polypropylene M Raab, J. Kotek, J. Baldrian, W. Grellmann.......... ...................... 153
B 1.2 Correlation Between Structure and Toughness Behaviour of High-Density Polyethylene under Impact Load H. Beerbaum, W. Grellmann, S. Seidler.......................................... 161
B 1.3 Toughness and Relaxation Behaviour ofPMMA, PS and PC W. Grellmann, R. Lach................ .................................................... 181
B 1.4 Crazing in Amorphous Polymers - Formation of Fibrillated Crazes Near the Glass Transition Temperature G. H. Michler. ........ .......................................................................... 193
B 1.5 Influence of Temperature and Moisture on Toughness Behaviour of Polyamide B. Langer, S. Seidler, W. Grellmann..... ................................... ....... 209
Contents IX
B 2 Blends
B 2.1 Relationship Between Fracture Behaviour and Morphology in PE/PP Blends U. Niebergall, J. Bohse, H Sturm, S. Seidler, W Grellmann.......... 229
B 2.2 Influence of Modifier Content and Temperature on Toughness Behaviour of Polyamide I Bethge, K. Reincke, S. Seidler, W Grellmann.............................. 243
B 2.3 Morphology and Toughness ofPP/EPR Blends T. Koch, S. Seidler, K. Jung, W Grellmann.................................... 257
B 2.4 Morphology and Micro-Mechanics of Phase-Separated Polyethylene Blends R. Godehardt, W Lebek, G. H Michler.......................................... 267
B 3 Copolymers
B 3.1 Toughness Optimization of Multi-Phase Polymer Materials Based on a PP Matrix Using Fracture Mechanics Parameters S. Seidler, W Grellmann................................................................. 281
B 3.2 Crack Toughness Behaviour of ABS Materials R. Lach, W Grellmann, P. Kruger.................................................. 301
B 3.3 Fracture Mechanics Characterization of ABS Materials - Influence of Morphology and Temperature R. Lach, W. Grellmann, Y. Han, P. Kruger..................................... 317
B 3.4 Brittle Fracture of ABS - Investigation of the Morphology-Failure Relationship B. Moginger, G. H Michler, H-C. Ludwig..................................... 335
C Hybrid Methods of Polymer Testing and Polymer Diagnostics
C.I Defect-Selective Imaging A. Dillenz, N. Krohn, R. StOj3el, G. Busse........................................ 355
C.2 Determination of Local Deformation Behaviour of Polymers by Means of Laser Extensometry C. Bierogel, W. Grellmann............................................... ............... 365
X Contents
C.3 Damage Analysis of Composite Materials by Acoustic-Emission Examination J. Bohse, T. Krietsch........................................................................ 385
D Technological Test Methods
0.1 Polymer-Based Composites for Friction and Wear Applications K Friedrich, P. Reinicke, J. Hoffmann........................................... 405
0.2 Modification of Polymers by Means of Amorphous Carbon for Optimization ofTribological Properties /. Hyla, J. Myalski, W. Grellmann...................................... ............. 419
0.3 Mechanical Vibration Behaviour of a Compressor Blade Made from a High-Performance Composite W. Grellmann, R. Steiner, /. Kotter, M Neitzel, M Maier, K. von Diest..................................................................................... 429
E Biocompatible Materials and Medical Prostheses
E.l Polymer Materials in Joint Surgery J. Brandt, W. Hein................................................... ........................ 441
E.2 Material Parameters and ESEM Characterization of Functional ENT Prostheses During Ongoing Degradation E.-J. Haberland, A. Berghaus, M Fating, /. Bethge, W. Grellmann.. .................................. ..................... ......... 451
E.3 Microbial Corrosion of Pharyngo-Tracheal Shunt Valves (,Voice Prostheses') /. 8ebowl, E.-J. Haberland, A. Stiefel.............................................. 461
E.4 Deformation Behaviour of Voice Prostheses - Sensitivity of Mechanical Test Methods C. Bierogel, /. Bethge, W. Grellmann, E.-J. Haberland................. 471
F Special Materials
F.l Crack Initiation, Wear and Molecular Structure of Filled Vulcanized Materials W. Grellmann, G. Heinrich, T. Casar.............................................. 479
F.2 Investigation of Crack Propagation Behaviour of Unfilled and Filled Vulcanizates
Contents XI
K. Reincke, R. Lach, W. Grellmann, G. Heinrich............................ 493
F.3 Characterization of Deformation Behaviour of Modified Polymer Concrete H Wehner, W. Grellmann, T. Hildebrandt...................................... 505
F.4 Fracture Mechanics Testing of Modified Epoxy Resins with Mini-Compact Tension (CT) Specimens H Walter, C. Bierogel, W. Grellmann, M Fedtke, B. Michel......... 519
G Examples and Limits of Application
G.l Modelling of the Mechanical Behaviour of Non-Linear Viscoelastic Materials under a Multi-Dimensional State of Stress E. Schmachtenberg, M Wanders, N. M Yazici............................... 533
G.2 Detergent Resistance ofPP/GF Composites W. Grellmann, S. Seidler, C. Bierogel, R. Bischoff................ .......... 549
G.3 Material Optimization of Polypropylene-Short-Glass-Fibre Composites
B. Langer, C. Bierogel, W. Grellmann, J. Fiebig, G. Aumayr.......... 561
G.4 Influence of Exposure on the Impact Behaviour of Glass-Fibre-Reinforced Polymer Composites H. Waiter, C. Bierogel, W. Grellmann, B. Rufke............................. 571
G.5 Physical Ageing and Post-Crystallization of Polypropylene J. Fiebig, M Gahleitner..... ....................... ....... ................................ 581
Subject Index................................................................................... 593
Author Index.................................................................................... 599
List of Authors
Aumayr, Gilnther, Dipl.-Ing., Linz (Austria) Baldrian, Josef, Dr., Prague (Czech Republic) Beerbaum, Heike, Dr.-Ing., Halle (Germany) Berghaus, Alexander, Prof. Dr. med. habil., Halle (Germany) Bethge, Ines, Dipl.-Ing., Halle (Germany) Bier6gel, Christian, Dr.-Ing., Halle (Germany) Bischoff, Reinhard, Dr.-Ing., Berlin (Germany) Bohse, Jilrgen, PO Dr.-Ing. habil., Berlin (Germany) Brandt, JOrg, Dr. med., Halle (Germany) Busse, Gerd, Prof. Dr. rer. nat. habil., Stuttgart (Germany) Cisar, Thomas, Dipl.-Ing., Halle (Germany) Che, Mingcheng, Dr.-Ing., Geilenkirchen (Germany) von Diest, Konstantin, Dr.-Ing., Kaiserslautern (Germany) Dillenz, Alexander, Dipl.-Phys., Stuttgart (Germany) Fedtke, Manfred, Prof. Dr. rer. nat. habil., Merseburg (Germany) Fiebig, Joachim, Dipl.-Phys., Linz (Austria) Forster, Stephan, Ludwigshafen (Germany) Friedrich, Klaus, Prof. Dr.-Ing., Kaiserslautern (Germany) Fiiting, Manfred, Dr., Halle (Germany) Gahleitner, Markus, Dr. techn., Linz (Austria) Godehardt, Reinhold, Dr. rer. nat., Halle (Germany) Grellmann, Wolfgang, Prof. Dr. rer. nat. habil., Halle (Germany) Haberland, Ernst-Jilrgen, PO Dr. rer. nat. habil., Halle (Germany) Han, Yanchun, Dr., Changchun (China) Hein, Werner, Prof. Dr. med. habil., Halle (Germany) Heinrich, Gert, Dr. rer. nat. habil., Hannover (Germany) Hesse, Wolfgang, Dipl.-Phys., Halle (Germany) Hildebrandt, Thomas, Dipl.-Ing., Rendsburg (Germany) Hoffmann, JUrgen, Dipl.-Ing., Kaiserslautern (Germany) Hyla, lzabella, Prof. Dr.-Ing. habil., Katowice (Poland) Jung, Kerstin, Dr.-Ing., Merseburg (Germany) Koch, Thomas, Dipl.-Ing., Vienna (Austria)
XIV List of Authors
Kotek, Jiri, Dr.-Ing., Prague (Czech Republic) Kotter, Ines, Dipl.-Ing., Merseburg (Germany)
Krietsch, Torsten, Dr., Berlin (Germany)
Krohn, Nils, Dipl.-Phys., Stuttgart (Germany)
Kruger, Peter, Dr., Leverkusen (Germany)
Kucera, Jaroslav, Dr., Bmo (Czech Republic)
Lach, Ralf, Dr.-Ing., Halle (Germany)
Langer, Beate, Dr.-Ing., Merseburg (Germany)
Lebek, Werner, Dipl.-Phys., Halle (Germany)
Ludwig, Hans-Christian, Dipl.-Ing., Stuttgart, (Germany)
Maier, Martin, Prof. Dr., Kaiserslautem (Germany)
Michel, Bernd, Prof. Dr. rer. nat. habil., Berlin (Germany)
Michler, Goerg Hannes, Prof. Dr. rer. nat. habil., Halle (Germany) Mliginger, Bernhard, Dr.-Ing., Stuttgart (Germany)
Myalski, Jerzy, Dr.-Ing., Katowice (Poland)
Neitzel, Manfred, Prof. Dr., Kaiserslautem (Germany)
Nezbedova, Eva, Dr.-Ing., Bmo (Czech Republic)
Niebergall, Ute, Dr.-Ing., Berlin (Germany)
Raab, Miroslav, Dr.-Ing. Associate Prof., Prague (Czech Republic)
Ramsteiner, Falko, Dr. rer. nat., Ludwigshafen (Germany)
Reincke, Katrin, Dipl.-Ing., Halle (Germany) Reinicke, Petra, Dipl.-Ing., Kaiserslautem (Germany)
Rutke, Bruno, Dr.-Ing., Schkopau (Germany)
Salajka, Zdenik, Dr., Bmo (Czech Republic) Schmachtenberg, Ernst, Prof. Dr.-Ing., Essen (Germany)
Schuster, Werner, Ludwigshafen (Germany)
Sebova, Irina, Dr. med., Halle (Germany)
Seidler, Sabine, Prof. Dr.-Ing. habil., Vienna (Austria)
Steiner, Ralf, Dr.-log., Merseburg (Germany)
Stiefel, Amd, Prof. Dr., Halle (Germany)
StoDel, Rainer, Dipl.-Ing., Stuttgart (Germany)
Sturm, Heinz, Dr. rer. nat., Berlin (Germany)
Walter, Hans, Dipl.-Ing., Merseburg (Germany)
Wanders, Martin, Dr.-Ing., Essen (Germany)
Wehner, Heidrun, Dipl.-Ing., Merseburg (Germany)
Yazici, NazifMehmet, Dipl.-Ing., Essen (Germany)
Nomenclature
Only those symbols that are used in several passages are listed here. Because of the fmite size of the alphabets used and because of mUltiple application in scientific usage, double use of symbols and indices was not avoidable.
a (mm) initial crack length (i.e. machined notch plus razor-sharpened tip), the physical crack size at the start of testing
aBS (mm) physical crack length augmented to account for crack tip plastic deformation (fracture mirror length)
acN (kJ/m2) Charpy impact strength of notched specimen according to ISO 179
acu (kJ/m2) Charpy impact strength of unnotched specimen according to ISO 179
aeII (mm) effective crack length
ar (mm) final crack length used in the normalization method
a/W ratio of initial crack length to specimen width
A (J.1m) average interparticle distance
Al first amplitude considered for the calculation of the logarithmic decrement
Ac (Nmm) complementary deformation energy used in the J-integral evaluation method of Merkle and Corten
Acrit (J.1m) critical particle distance for brittle-to-tough transition
Ad (J.1m) average interparticle distance, measured between centres
Ael (Nmm) elastic part of AG AG (Nmm) general deformation energy of test specimen
computed from the area under the load-deflection diagram up to F max
AH (Nmm) nominal impact energy of pendulum hammer
An nth amplitude considered for the calculation of the logarithmic decrement
XVI Nomenclature
ApI (Nmm) plastic part of Ao
AR (Nmm) crack propagation energy
Atot (Nmm) area under the load-deflection diagram used in the approximate method of Schindler
b statistical segment length
B (mm) specimen thickness
C (mmIN) compliance
C), ... ,9 constants of the power law for describing R-curves
Cel (mmIN) elastic compliance
CD (~m) average interparticle distance (mid point distance)
d (~m) average particle diameter
do average distance between ends of a chain segment
D maximum grain size
Do (nm) distance of fibrils
DI ,2 geometrical functions in the J-integral evaluation method of Merkle and Corten (MC)
E (MPa) Young's modulus (modulus of elasticity)
Es (MPa) flexural modulus
Ed (MPa) dynamic flexural modulus
Edis (Nmm) dissipated energy
Ec (MPa) flexural modulus according to ISO 178
Epot (Nmm) potential energy
Espec (MPa/(kgldm3» specific modulus of elasticity
Et (MPa) modulus of elasticity in tension
Eli (MPa) integral modulus of elasticity in tension (tensile modulus)
Ell (MPa) local modulus of elasticity in tension
/ (mm) deflection
Is (mm) deflection of an unnotched specimen
/gy (mm) deflection at the transition from elastic to elastic-plastic material behaviour
!K (mm) maximum deflection/max excluding the component/s
/max (mm) deflection at maximum load F max
/PI (mm) plastic component of maximum deflection
Nomenclature XVII
ipl (mm) plastic component of maximum deflection of V -notched specimens used for the key curve method
F (N) load (force)
Fl (N) inertial load, which arises from the inertia of the part of the test specimen accelerated after the first contact with the striker
Fgy (N) characteristic load value corresponding to the transition from elastic to elastic-plastic material behaviour
FID1JX (N) maximum load
FQ' (N) pseudo-elastic load
G (MPa) shear modulus
G (N/mm) energy release rate
G1 (N/mm) energy release rate in mode I . (MPa) dynamic modulus G
H heterogeneity
He heterogeneity at tensile strength
HK (N/mm2) ball indentation hardness
I intensity
J (N/mm) J-integral; a mathematical expression, a line or surface integral that encloses the crack front from one surface to the other, used to characterize the local stress-strain field around the crack front; fracture mechanics parameters are calculated using methods of evaluation of this integral
JO.2 (N/mm) technical crack initiation value for an amount of crack growth of /),.a = 0.2 mm
~ (N/mm) J value in mode I (the index I is only used in the case of geometry independence)
'" Me Id (N/mm) critical J value at the point of unstable crack growth, for dynamic loading, in the geometry-independent J-integral evaluation method of Merkle and Corten
'" ST Id (N/mm) critical J value at the point of unstable crack growth, for dynamic loading, in the geometry-independent J-integral evaluation method of Sumpter and Turner
Jdapp (N/mm) critical Jvalue at the point of unstable crack growth determined from J-TJ stability assessment diagram, for dynamic loading
XVIII Nomenclature
JlL (N/mm) critical Jvalue at the point of unstable crack growth, for dynamic loading, in the geometry-independent J-integral evaluation method of Begley and Landes
Jdc (N/mm) crack initiation value used in the key curve method
J/ (N/mm) crack initiation value used in the approximate method of Kobayashi and Moskala
Jl (N/mm) crack initiation value used in the approximate method of Schindler
Jg (N/mm) fracture resistance at upper limit of J-controlled crack growth
~ (N/mm) physical crack initiation value determined from intersection of stretch zone width and J-R curve
Jrn (N/mm) maximum available J value used in the approximate method of Schindler
Jmax (N/mm) validity limit for J
JTJ (N/mm) energy absorption capacity of a material during stable crack growth
leo" (mm3/Nm) wear resistance factor
K (MPamm/2) stress intensity factor
KI (MPamm I/2) stress intensity factor in mode I (the index I is only used in the case of geometry independence)
K lc (MPammIl2) fracture toughness, critical parameter at the point of unstable crack growth; static loading, geometry-independent
KId (MPammI12) fracture toughness, critical parameter at the point of unstable crack growth; dynamic loading, geometry-independent
K CTOD lc,ld (MPamm/2) K Ic and KId, calculated from C(T)OD
E KIc,ld
(MPammI/2) K Ic and KId, calculated from equivalent-energy concept
J Klc,Id
(MPamm1/2) K Ic and KId, calculated from J-integral
KLEFM lc,ld (MPamm/2) K Ic and KId, calculated from LEFM
Ie contour length of polymer chain between two adjacent entanglements
L (mm) specimen length
Nomenclature XIX
Lo (mm) initial gauge length
La (run) thickness of amorphous interlayer determined by means of Lpexp
Latbeo (run) thickness of amorphous interlayer determined by means of Letbeo
Le (run) thickness of lamellae determined by means of Lp
Letbeo (run) thickness of lamellae calculated from melting
temperature Ts~
Lp (run) long period from small-angle X-ray diffraction scattering
m constraint factor in relation between J and Sconcepts
mH (kg) weight of pendulum hammer
Mo molecular weight of a monomer unit
Me molecular weight of a chain network
Mn (kg/mol) molecular weight, number average
Mw (kg/mol) molecular weight, weight average
MFR (g/10 min) melt mass-flow rate
n rotational factor
n work-hardening factor
Ne number of statistical segments of a chain
Oi surface area of craze fibrils
p (MPa) pressure
poo (MPa) Vogel pressure used in WLF equation
Q (J) quantity of heat
rK (!lm) notch radius of razor blade
Re average final distance of a chain net between two chemical crosslinks
Re average fmal distance of a chain net between two elastic active entanglements
Rr average final distance of a chain net between two filler particles
s (mm) support span
s, (N/mm2) slope of blunting line used in the approximate method of Schindler
xx Nomenclature
S2 (N/mm2) slope of crack propagation line used in the approximate method of Schindler
Smax maximum of scattering
S (wt. %) percentage of fractions up to maximum particle diameter of one fraction of the total mixture
t (s) time
tb (ms) time to brittle fracture
tB (ms) time to fracture
tan 0 mechanical loss factor
T eC) temperature
To (J/m3) threshold tearing energy
TaJ eC) Vogel temperature used in the WLF equation
TBn eC) brittle-to-tough transition temperature
Tg eC) glass transition temperature
TJ tearing modulus
TI2 tearing modulus determined from J-f1a curve at f1a= 0.2 mm
Tm eC) melting point
Tmo (K) equilibrium melting temperature
TSOE (K) melting temperature determined from DSC according toOIN 53765
Tv eC) Vicat heat resistance temperature
T/jO.2 tearing modulus determined from O-f1a curve at f1a= 0.2 mm
U (Nmm) deformation energy
v (mm) crack-mouth-opening displacement
Vo (lis) strain rate
VF volume of fibrils in a craze
VH (mls) pendulum hammer speed
VI. (mm) load-line displacement
vp (mm) plastic component of the crack-mouth-opening displacement
Vr (mmlmin); (mls) crosshead speed
Ws (mm3/Nm) specific wear rate
Nomenclature XXI
Wt (Jlmlh) wear rate
W (rrun) specimen width
z (rrun) distance of knife-edge from specimen surface
al (%) degree of crystallinity obtained from density
a2 (%) degree of crystallinity obtained from melting enthalpy
a3 (%) degree of crystallinity obtained from X-ray diffraction
/3 proportionality constant of geometrical size criterion for LEFM
/3J slope of line through origin used for determination of
J;pp; the point of unstable crack growth is the
intersection between the line through the origin and the J-TJ curve
/30 slope of line through origin used for determination of
o;PP; the point of unstable crack growth is the
intersection between the line through the origin and the 8-To curve
(rrun) crack-(tip )-opening displacement describing the local strain field in front of the crack tip, calculated with the help of the plastic-hinge model
. (mm/s) crack-opening-displacement rate 0
00.2 (rrun) technical crack-opening displacement calculated at Ila = 0.2 rrun
0, (rrun) crack-(tip)-opening displacement in mode I (the index I is only used in the case of geometry independence)
Ole (rrun) critical ovalue for unstable crack growth, quasi-static loading, geometry-independent
Old (rrun) critical ovalue for unstable crack growth, dynamic loading, geometry-independent
OIdll (rrun) critical ovalue for unstable crack growth obtained by using advanced plastic-hinge model, dynamic loading, geometry-independent
Og (rrun) ovalue at upper limit of O-controlled crack growth
~ (rrun) crack-tip-opening displacement at physical crack initiation
XXII Nomenclature
~ (mm) validity limit for 0 value
l1a (mm) amount of stable crack growth, distance between original crack size and crack front after loading
11a", (mm) amount of stable crack growth at maximum of the load-deflection diagram used in the approximate method of Schindler
l1amax (mm) upper validity limit of l1a
l1amin (mm) lower validity limit of l1a
I1C (mm/N) variation of compliance
111 (mm) change in length
. (mmls) rate of change of length M
!lJ (s) time difference
I1v (m/s) velocity change of pendulum hammer during the test
11(1' (MPa) excess increase of local stress
& proportionality constant of geometrical size criterion in J-integral concept
& (%) strain
& (lIs); (o/o/min) .
strain rate ( & = d& / dt)
&8 (%) tensile strain at break according to ISO 527
&ce (%) normal flexural strain
&01 (%) amount of uniform elongation without necking
bj (%) integral strain
&i (1/s) integral strain rate
&, (%) local strain
&, (lis) local strain rate
limax (%) maximum local strain
bimin (%) minimum local strain
&M (%) strain at tensile strength according to ISO 527
&Mi (%) integral strain at tensile strength according to ISO 527
&q (%) lateral (transverse) strain
ESE (%) critical strain at acoustic onset
Nomenclature XXIII
&y (%) yield strain according to ISO 527
GZM (%) tensile strain at maximum load according to DIN 53455
&zR (%) breaking elongation
87S (%) yield strain according to DIN 53455
T/ geometrical function
T/el;pl geometrical functions for assessment of elastic (el) and plastic (pI) parts of deformation energy used in the J-integral evaluation method of Sumpter and Turner
e logarithmic decrement
e (0) scattering angle
It yield ratio of polymer chain at formation of fibrils
A.craze stretching at fracture
Amax maximum stretching
Ar relative index of damping
J.l coefficient of friction
J.l Poisson's ratio
J1c chemical-chain-knot density
f.L;. integral Poisson's ratio
J.lI local Poisson's ratio
v Poisson's ratio
; proportionality constant of geometrical size criterion forCTOD
p (kg/m3) density
Pk density of crystalline phase at the melting point
(i (MPa) stress
(i (S/m) conductivity
(i (MPals) stress rate
OhM (MPa) flexural strength according to DIN 53452
(is (MPa) tensile stress at break according to ISO 527
(id (MPa) yield stress determined from Charpy impact test at specific rate
(if (MPa) flexural stress according to ISO 178
XXIV Nomenclature
O"o.s (MPa) flexural strength at peripheral strain of3.5 %
O"tM (MPa) flexural strength according to ISO 178
OJ: (MPa) yield stress: either oy or O"p = 112 ( oy +aW OJ (MPa) integral stress
OJ (MPa) local stress
O"M (MPa) tensile strength according to ISO 527
OSpec (MPaI(kgldm3» specific flexural strength
O"SE (MPa) critical stress at onset of acoustic emission
oy (MPa) yield stress (yield point) according to ISO 527
O"zM (MPa) tensile strength according to DIN 53455
O"zR (MPa) tensile stress at break according to DIN 53455
O"zS (MPa) yield stress (yield point) according to DIN 53455
T oscillation period
qJv filler or fibre content
f/J geometrical factor
'1/ (Hz) frequency
'I/o (Hz) reference frequency used in WLF equation
tV non-dimensional constant for characterizing J-controlled crack growth
n (Hz) upper frequency limit used in WLF equation
Terminology
ABS AE ASA BA BR BTT CCT CF CFRP CT CTOA C(T)OD DCB DDENT DENB DENT DMA DMTA DSC EIP EP EPDM EPFM EPM EPR EVAC ESCC ESEM FEM GF GPC HDT HVEM ICIT IFWIT ITIT LEFM MC MOPE MSM NDT
acrylonitrile-butadiene-styrene acoustic emission acrylonitrile-styrene-acrylate butyl-acrylate copolymer butadiene rubber brittle-to-tough transition centre-cracked tension specimen carbon fibre carbon-fibre-reinforced polymer compact tension specimen crack-tip-opening angle crack-(tip )-opening displacement double-cantilever beam deeply double-edge-notched tension specimen double-edge-notched bend specimen double-edge-notched tension specimen dynamic-mechanical analysis dynamic-mechanical-thermal analysis differential scanning calorimetry ethylene-propylene epoxide; epoxy ethylene-propylene-diene rubber elastic-plastic fracture mechanics ethylene-propylene copolymer ethylene-propylene rubber ethylene-vinyl acetate copolymer environmental stress corrosion cracking environmental scanning electron microscope finite-element method glass fibre gel permeation chromatography heat distortion temperature high-voltage transmission electron microscope instrumented Charpy impact test instrumented falling-weight impact test instrumented tensile impact test linear elastic fracture mechanics J-integral evaluation method of Merkle and Corten medium-density polyethylene mUltiple-specimen R-curve method non-destructive testing
XXVI Terminology
NMR NPT NR PA PBI PBT PC PE PE-HD PEEK PEEKK PENT PET PI PMMA PP PS PS-HI PTFE PUR PVC R-curve RPM RT SAN SAXS SB SBR SBS SCB SEM SENB SENT SFM SIF SIS SSM ST SZH SZW TDCB TEM TFA TPU UD UHMWPE WAXS WLF
nuclear magnetic resonance notch-pipe test natural rubber polyamide (nylon) poly-bis-maleinimide poly(butylene terephthalate) polycarbonate polyethylene high-density polyethylene polyetheretherketone polyetheretherketoneketone polyethylene notch test poly(ethylene terephthalate) polyimide poly(methyl methacrylate) polypropylene polystyrene high-impact modified polystyrene polytetrafluoroethylene polyurethane poly(vinyl chloride) crack resistance curve J-integral evaluation method of Rice, Paris and Merkle room temperature styrene-acrylonitrile small-angle X-ray scattering styrene-butadiene block copolymer styrene-butadiene rubber styrene-butadiene-styrene short-chain branching scanning electron microscope single-edge-notched bend specimen single-edge-notched tension specimen scanning force microscope stress intensity factor stepwise isothermal segregation single-specimen R-curve method J-integral evaluation method of Sumpter and Turner stretch zone height stretch zone width tapered double-cantilever beam specimen transmission electron microscope tear and fatigue analyser thermoplastic urethane unidirectional ultra-high-molecular-weight polyethylene wide-angle X-ray scattering Williams-Landel~Ferry equation