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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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Standard Test Methods
• 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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Standard Test Methods
Mechanical Behaviour of Materials, N. E. Dowling
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Standard Test Methods
• 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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Uniaxial Tension Test
• 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)
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Uniaxial Tension Test
• 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
Localized deformationnecking
Uniformdeformation
Localized deformationnecking
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
Mechanical Behaviour of Materials, N. E. Dowling
Offset yield Upper yieldLower yield
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Tension Test-criteria for yielding
• 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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Tension Test-criteria for yielding
• 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-criteria for yielding
Mechanical Behaviour of Materials, N. E. Dowling
36
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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Tension Test-Measures of Ductility
• 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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Tension Test-Measures of Ductility
• 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
Mechanical Behaviour of Materials, N. E. Dowling
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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
Mechanical Behaviour of Materials, N. E. Dowling
60
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
Mechanical Behaviour of Materials, N. E. Dowling
63
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
http://www.gordonengland.co.uk/hardness/
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Indentation Hardness Test
• Rockwell hardness test: measures the depth of indentation
HR = E - e
http://www.gordonengland.co.uk/hardness/
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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
http://www.gordonengland.co.uk/hardness/
69
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
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
Mechanical Behaviour of Materials, N. E. Dowling
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