mat 307 composite materials - sabancı...

Instructor: Melih Papila

Mechanical Testing

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Quiz• What features/properties you think mechanical and thermal

characterization can determine for you?• Why would you need mechanical and thermal characterization if

– You are a material supplier– You are involved in designing an engineering system.

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Material Selection• Procedure

– Analysis of problem regarding material application– Translation of the material application requirements to material

property values– Selection of candidate materials– Evaluation of candidate materials– Decision making

• Properties– Mechanical, thermal, chemical, electrical

• Constraints– Existing facilities– Compatibility– Marketability– Availability– Disposability and recyclability

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Factors Affecting MaterialPerformance

• Structure, property, processing relationships processing• Imperfections (e.g. number of dislocations) • Crystal structures: Crystalline versus amorphous• Residual stresses• Strengthening• Toughening Inclusions• Heat treatment (such as annealing, normalizing, and

quenching)

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Things Related to MechanicalBehavior

• Material nature Material nature• Ductile versus brittle fracture • Static versus cyclic loading • Deformation mechanisms Deformation mechanisms• Creep deformation (stress and temperature effects) • Fatigue fracture (high cycle vs. low cycle) • Notch sensitivity and loading directions

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Mechanical Testing of Materials

• Test type/loading– Tension– Compression– Hardness– Bending– Torsion

• Environmental conditions– Test ambient– Specimen

• Test specimen– Un-notched– Notched

• Any stress raiser: Notch, hole, groove, cracks …

• Test standards– Industry– Company

• Test Equipment

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Mechanical Testing of Materials

• Universal Testing Machines– Go back to early

1900s– Mechanical-screw-

driven machine (electromechanical)

– Servo-hydraulic machine

• Static or dynamic?• Strain gage based

– Load cells– Extensometer

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Standard Test Methods

• Mechanical testing– Material properties as input for design procedure– Quality control

• Test standards provide consistency, user-producer communication

• Professional societies: – American Society for Testing and Materials - ASTM– International Organization for Standardization –

ISO– European Norms- EN– TSE

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• Annual Book of ASTM standards covers significant number of standards for mechanical testing-about 10 volumes

• Test standards organized by class of material– Metals, concrete, plastics, rubber, glass...

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Mechanical Behaviour of Materials, N. E. Dowling

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• Provide procedures to be followed in detail– Specimen description– Loading conditions– Values to report– Statistical analysis

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Mechanical Testing

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Uniaxial Tension Test

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Uniaxial Tension Test• Pulling a sample of material in tension until

fracture• Specimens designed to avoid break where

gripped

gauge length

PPDia d

Frictiongrips

Pin end

Strip

UTAS

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Are the load and elongation answering our questions?

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These definitions of stress and strain allow one to compare test results for specimens of different cross-sectional area A0 and of different length l0.

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Uni-axial Tension Test

• Strain or load controlled– Usually constant Crosshead speed, mm/min

• Report stress-strain curve until failure• Ideally recorded by dedicated transducers

– Extensometer– Strain gages bonded on the specimen

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Uniaxial Tension Test• Elastic constants

– Elastic or Young’s modulus-slope of initial elastic line, E=(σB- σA)/(εB-εB)

– Tangent modulus-tangent at the origin (if there is no well-defined linear region)

B

A

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Hooke’s law

• In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law:

σ = E ε

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Other elastic constants

– Poisson’s ratio

– Shear Modulus

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• Material properties are based on– Mostly engineering stress-strain

– Some true stress-strain

σdef Load

Original area=ε

def Change in lengthOriginal length=

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Load versus Extension Curves

• Load vs extension curves do not allow comparison of materials

• Need to plot Engineering stress vs Engineering strain curves

Load

Extension

Linear

Non linearX

Failure

Uniformdeformation

Localized deformationnecking

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Uniaxial Tensile Testhttp://www.msm.cam.ac.uk/doitpoms/tlplib/mechanical-

testing/index.php

Method

Results2

Video (ref. Callister resources)

http://www.msm.cam.ac.uk/doitpoms/tlplib/mechanical-testing/index.php

http://www.msm.cam.ac.uk/doitpoms/tlplib/mechanical-testing/index.php

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• Stress-strain behavior varies widely– Brittle behavior: without extensive

deformation-gray cast iron, some polymers (PMMA), glass

– Ductile behavior: failure following extensive deformation-metals

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Typical Stress Strain Curves

Linear

XFailure

Linear

XFailureLower

UpperYieldPoint

E

1

E

1

Uniformdeformation


Uniformdeformation


Non linear Non linear

Low C steelLow C steel AlloyAlloy SteelSteelStrain εStrain ε

Stress σ Stress σ

Does the resistance of the material decrease after necking?

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Tension Test

• Strength– Ultimate-highest engineering stress prior to fracture– Fracture strength-stress at fracture– Yield strength-stress where departure from elastic

behavior happens and contribution of plastic strain begins resulting in rapidly increasing deformation

• Tensile strength at yield• Tensile strength at break• Usual priority- assure that stresses are

sufficiently small that yielding does not occur

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Tension Test-criteria for yielding

• First departure from linearity-proportional limit, – Difficult to precisely locate- depends on judgment– Some material with gradually decreasing slope, no

proportional limit identified

• Elastic limit-highest stress without permanent deformation– Difficult to determine, periodic unloading to check

for permanent deformation

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Tension Test-criteria for yielding• Some metals exhibit nonlinearity followed by a dramatic drop in load

(fig 4.11)– Upper yield point, σou -prior to the drop– Lower yield point, σol -prior to the subsequent increase


Offset yield Upper yieldLower yield

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• Offset Method-offset yield strength– Intersection of the stress-strain curve and

the straight line parallel to elastic slope E or Et, that is offset by an arbitrary amount

– Offset amount for metals 0.2% strain

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Offset Yield Strength

Locate C at 0.2%(or Locate C at 0.2%(or 0.1%) strain0.1%) strain

Draw CD // to ABDraw CD // to AB

The Proof Strength is The Proof Strength is stress at Dstress at D

Proof Strength is Proof Strength is sometimes called the sometimes called the 0.2% (or 0.1%) offset 0.2% (or 0.1%) offset Yield strengthYield strength

Only Only req’dreq’d when well when well defined yield cannot be defined yield cannot be determineddetermined

0.002 strain

Strain

Stress

A

B

C

D

Proof Strength

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• For polymers offset yield strength also used

• Yield is at dσ/dε=0, if there is early relative maximum σou, usually followed by substantial plastic deformation (fig 4.10),

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Tension Test-Measures of Ductility

• Definition: Ability of a material to accommodate inelastic deformation without breaking

• Measured by– Engineering fracture strain or percent elongation,

corresponds to the engineering fracture strength point

εf=(Lf-Li)/Li

% elongation =100 εf

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• Recall: ductility is A measure of the ability of materials to withstand deformation without failure

• Elongation is the value at fracture– For polymers (ASTM standard): strain εf at the instant of

fracture from stress-strain curve– For metals (ASTM standard): measured after it is broken

using marks placed at a known distance apart prior to the test – plastic component of the strain or elongation εpf (~ εf for ductile metals)

– For metals of limited ductility, difficult to measure plastic portion of the elongation, instead

εpf= εf- σf/E

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• Also measured by percent reduction in area

%RA=100(Ai-Af)/Ai

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Tension Test-Necking and Ductility

• If ductile, necking usually occurs (fig 4.12)– Deformation begins to concentrate in one region,

area reduction higher than elsewhere– Strain becomes non-uniform

• With necking involved, percent elongation is sensitive to L/d or L/t as it is an average over a gage length, thus reduction in area is considered as more fundamental

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Engineering Measures of Energy Capacity

• Work done by the applied tensile load is equal to energy absorbed by the material, area under the stress-strain curve work done per unit volume

u=∫σdεCalled tensile toughness of the material

(ability of the material to absorb energy without fracture)

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Tension Energy Capacity

• Within the region of elastic deformation, potential energy released upon unloading

• At the proportional limit, resilience (ability of the material to store elastic energy)

ur= σp2/2E

Usually use offset yield strength more practicalur= σo

2/2E

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If the stress-strain curve flat beyond yielding, sufficient to approximate the area

⎟⎠

⎞⎜⎝

⎛ +≈

2uo

ffuσσ

ε

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Mechanical properties

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Strength, Ductility Toughness

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Strain Hardening

• Increase in mechanical resistance with increasing strain following the yielding

• A measure of the strain hardening σu/ σo

Range considered average for metals 1.2-1.4

Dowling example 4.1

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Work or Strain Hardening

Consider the Stress Strain curve for low C steelConsider the Stress Strain curve for low C steelArrows indicate the load pathArrows indicate the load path

We have increased the linear range of the stress strain curveWe have increased the linear range of the stress strain curve

XFailure

YieldPoint

E

1

E

1A

B

C

D

Work (or strain)hardening

Residual strain

StrainStrain

StressStress

Note AB is // to DC

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Trends inTensile Behavior

• Materials vary widely regarding their strength and ductility

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Effect of Temperature and Strain Rate• In a temperature range where creep-related effects

occur, strain rate temperature interaction exists• Polymers of low Tg, for instance (larger creep effects

occur even around RT), strain rate draws attention– Lower strain rate provides more time for creep related

deformation/strain accumulate– Not uncommon to evaluate tensile behavior at more than one

rate• Metals and Ceramics: significant around 0.3-0.6 TM• Generally speaking-for a given material at T range

where creep-related strain-rate effects occur-– At a given T, increasing strain rate increases the

strength, but decreases ductility– For a given strain rate, decreasing temperature

increases strength, but decreases ductility

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Effect of Temperature• Many components are subjected to

high temperatures during service- expect some change to properties

Increasing Temperature

Stre

ss

Strain

Typical Material in TensionTypical Material in Tension

Temperature Temperature ↑↑⇓⇓

ductility ductility ↑↑toughness toughness ↑↑E E ↓↓yield strength yield strength ↓↓tensile strength tensile strength ↓↓

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Effect of Temperature and Strain Rate


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True Stress & True Strain

• Eng stress & strain are based on original areas and lengths

• True stress & strain are based on actual areas and lengths

• Fig.4.19 (Dowling)

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True Stress-Strain

• Engineering stress and strain appropriate when the changes in specimen dimensions are small, area for instance

• For ductile materials, in particular, true stress-strain differs from engineering stress-strain

( )εε

σσ

+=

⎟⎠⎞

⎜⎝⎛=

1ln~

~AAi

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True Strain• Suppose we use number of smaller gage

lengths Lj rather than a standard engineering approach (L=Σ Lj). And corresponsding length changes Δ Lj

• If Lj are infinitesimal (Li initial total gage length)

∑Δ

=j

j

LL

ε~

)1ln(lnln~ εε +=Δ+

=== ∫i

i

i

L

LL

LLLL

LdL

i

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True Stress and Strain ctd• No practical difference between eng

stress & true stress and eng strain & true strain in the linear region

• (1% difference between ε and εt at an eng strain of 0.002 - [400 MPa in steel])

• Note that engineering stress-strain are most appropriate for small strains where the changes in area and length are specifically considered.

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True Strain• Neither plastic nor creep strain

contributes to volume change• Beyond yielding, reasonable to

approximate the volume as constant (volume change in a tension test is limited to small maount associated with elastic strain)

i

i

i

i

i

i

LL

AA

LLL

LL

AA

lnln~

1

==

+=Δ+

==

ε

ε

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True stress-strain

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True stress-strain

TT

nTT

nKK

εσεσ

lnlnln +==

K, n : material constants (n: strain hardening exponent)

For many Metals and alloys

Utrueσ

Fσ

Yσ

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Tension Test


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Example

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Compression

• Behavior in compression may be substantially different– Concrete

• Similar test arrangement except the direction of loading

• Specimen dimensions– Too small: end effects– Too long: buckling– L/d=3 for ductile materials– L/d=1.5-2 for brittle

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Compression


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Hardness Test• Hardness is the property of a material that enables it to

resist plastic deformation, usually by penetration. However, the term hardness may also refer to resistance to scratching, abrasion or cutting.

• Several types, usually for metals– Indentation hardness: pressing of a hard indenter against the

sample with a known force – Scleroscope hardness test: rebound of a hammer with

diamond tip. A modified version is also for polymers– Mohs hardness: used in mineralogy. Scratching, matter of

judgment, scaled between 1-10, (soft mineral talc –diamond, respectively). In comparative tests, harder scratces the softer

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Indentation Hardness Test• Surface resistance to indentation/penetration that results

from plastic deformation beneath the indenter• Differ by type and geometry of indenter, amount of force,

but measure the size/depth of an indentation– Brinell harness test: sphere indenter of 10 mm in dia,, varying load,

measure the size of indentation– Rockwell hardness test: using different scale (various sized indenter,

different loads)– Vickers hardness test: diamond pyramid used as indenter– Shore Durometer hardness test (polimers, rubber)

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Indentation Hardness Test

• Brinell harness test: sphere indenter of D, load F, measure the size of indentation Di

http://www.gordonengland.co.uk/hardness/

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Indentation Hardness Test• Vickers harness test: square

based pyramid diamond indenter, load F, measure the size of indentation Di


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Indentation Hardness Test

• Rockwell hardness test: measures the depth of indentation

HR = E - e


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Indentation Hardness Test• Microhardness test: very similar to that of the standard

Vickers hardness test, except that it is done on a microscopic scale with higher precision instruments. Vickers diamond pyramid or the Knoop elongated diamond pyramid. Use projected area A, KHN = F/A


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Indentation Hardness Test• Shore Durometer hardness Test: to determine the relative

hardness of soft materials, usually plastic or rubber

http://www.ptli.com/testlopedia/tests/DurometerShore-d2240.asp

http://www.ptli.com/testlopedia/subs/zwick_shore.asp

70

Notch-impact Tests• Measure the resistance of a

material to sudden fracture in the presence of stress raiser or flaw

• Energy required to break the sample is determined from an indicator measuring how high the pendulum swings after breaking the sample

• Simple, quickly compare materials, William F. Smith:

Foundations of Materials Science and Engineering

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Notch-impact Tests

http://www.matweb.com/reference/izod-impact.asp

For polymers and plastics

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Bending (Flexure) Tests

• Tensile strength of brittle materials that are difficult to grip without cracking, glass…

• Laminated materials: interlaminar strength

• Meaningful for materials of linear stress-strain behavior until fracture

IMc

=σ

ffb PtcL

283

=σ

The force necessary to break a specimen of specified width and thickness

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Bending (Flexure) Tests

• Elastic modulus may also be obtained

• Maximum deflection using linear-elastic analysis

EIPLv

48

3

=

⎟⎠⎞

⎜⎝⎛=

dvdP

ILE

48

3


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