3. Mechanical Properties of Materials
3.1 Stress-Strain Relationships3.2 Hardness3.3 Effect of Temperature on Properties3.4 Fluid Properties3.5 Viscoelastic Properties
Importance of Mechanical Properties
Mechanical properties determine a material’s behavior when subjected to mechanical stresses
Properties include elastic modulus, ductility, hardness, and various measures of strength
Mechanical properties desirable to the designer, such as high strength, usually make manufacturing more difficult Integration of design and manufacturingTension, Compression and Shear tests
3.1 Stress-Strain RelationshipsTensile Properties
Elastic modulus ductility hardnessvarious measures of strength
Proportional limitElastic limitYield strengthOffset yield strengthUltimate Tensile strengthFailure Strength
Elongation (EL)=(Lf-Lo)/Lo
Area Reduction(AR)=(Ao-Af)/Ao
oAFTS max=
ASTM StandardASTM (American Society for Testing and Materials)
specifies preparation of test specimen
Elastic Plastic Deformation FractureP
P
neckingGauge Length
Measuring Displacement; extensometer, strain gaugeMeasuring Force; Transducer
Tensile Test
Engineering Stress & StrainOriginal Area, Ao
True Stress and StrainInstantaneous Current Area, A
ooe L
eAF δσ == ,
LL
AF 0ln, == εσ
Stress and Strain Diagram
Su
Sy
Sf
Slope=E
Unloading
Reloading
stress
strain
nK εσ =log σ
log ε10-3 10-2 10-1
ε=n
At neckingσ=K
Slope=n=a/b
1
Flow Curve:
Flow CurveThe straight line in a log-log plot shows the relationship between true stress and true strain in the plastic region as
where K = strength coefficient; and n = strain hardening exponentstrain hardening - true stress increases continuously in the plastic region until necking.
nKεσ =
Ultimate Tensile Strength
σσσ
AddAdPAP
+==
0=dP
AdAd
−=σσ
At Maximum load (necking),
For a constant volume process
εdldl
AdA
ldAAdlAl
==−
=+=
0constant
1
εσσdd
=
nK εσ =Flow Curve:
Eq. (1) can be manipulated
With the flow curve,
nKnK nn
=∴= −
εεε 1
Ductile and Brittle Perfectly elastic: σ=EεPerfectly plastic: σ=YElastic and Perfectly Plastic
Flow curve: K = Y, n = 0
Elastic and Strain hardeningFlow curve: K > Y, n > 0
NonlinearTemperature-dependent
Characteristics
Compression Properties
Engineering stress, Engineering strain,
oe A
F=σ
o
o
hhhe −
=
Barreling due to the frictionAt the contact surfaces.
nK εσ =
Use K and n from tensile tests
Bending and Testing of Brittle Materials
Brittle Materials deform elastically until fracture Failure occurs at the outer fibers of specimen when tensile strength are exceeded. Cleavage - separation rather than slip occurs along certain crystallographic planes
Three Point Bend Test(Four Point Bend Test)Transverse Rupture Strength (TRS)
2
5.1btFLTRS =
F
L bt
Shear Properties
b
δ
AF
=τ bδγ =
tRT
22πτ =
LRαγ =
γτ G=•For most materials, G ≅ 0.4E
HardnessBrinell Hardness Test: 10mm diameter ball
with a load of 500, 1000 or 3000kg
Rockwell Hardness Test: A cone shape indenter; the depth of penetration is measured.Vickers Hardness Test: Pyramid shape indenter
( )( )22
2
ibbb DDDDFHB
−−=π
2854.1DFHV =
Shear Plastic Stress-Strain Relationship
Relationship similar to flow curve Shear stress at fracture = shear strength S
Shear strength can be estimated from tensile strength: S ≅ 0.7(TS)
Since cross-sectional area of test specimen in torsion test does not change, the engineering stress-strain curve for shear is similar to true stress-strain curve
HardnessKnoop hardness Test: Pyramid shape indenter
Scleroscope: rebound heightDurometer: The resistance to penetration (elastic deformation)Relationship between Hardness and Strength
22.14DFHK =
( )MPa45.3lb/in500 2
ininKwhereHBKTS hh
===
Temperature EffectEffect the all propertiesHot hardnessRecrystallization (0.5Tm)
RecrystallizationMost metals strain harden at room temperature Upon heating to sufficiently high temperature, strain hardening does not occur
recrystallization - Formation of new grains that are free of strainRecrystallization temperature of a given metal = 0.5 Tm measured on an absolute scale
Recrystallization above the recrystallizationtemperature takes time.In manufacturing - recrystallization reduces forces and power. Hot working -Forming metals above recrystallization temperature
Fluid Flow in ManufacturingIn many processes, materials converted from solid to liquid by heating.
Metals are cast in molten state Glass is formed in a heated and highly fluid state Polymers are almost always shaped as thick fluids
Flow is a defining characteristic of fluidsViscosity (the resistance to flow) is a measure of the internal friction when velocity gradients are present in the fluidReciprocal of viscosity is fluidity - the easiness of a fluid flows
Relation between Shear Stress and Strain rate
Viscosity can be defined using two parallel plates separated by a distance d Shear viscosity is the fluid property that defines the relationship between F/A and dv/dy (shear rate);
where η = a constant of proportionality called the coefficient of viscosity, Pa-s
• For Newtonian fluids, viscosity is a constant • For non-Newtonian fluids, it is not
γηητ &===dydv
AF γητ &=or
dvdyd
Some Viscosity Data
0.0003Water@100C
0.1Machine Oil
0.001Water@20C
103Glass @1095C
55Polymer@205C
105Glass @815C
115Polymer@151C
1012Glass @540C
ViscosityPa-s
MaterialsViscosityPa-s
Materials
Viscous behaviorsA thermoplastic polymer melt is non-Newtonian
A fluid that exhibits this decreasing viscosity with increasing shear rate is called pseudoplastic
This complicates analysis of polymer shaping processes such as injection molding
Viscoelastic Behavior
PolymersThe property of a material that determines the strain subjected to combination of stress and temperature over time.
( ) ( )εσ tft =
Viscoelastic Behavior of Polymers
• Viscoelastic -Combination of viscosity and elasticity• Die swell - In extrusion of polymers, the profile of extruded material grows in size after being squeezed through the smaller die opening
−It “remembers”(Shape memory)
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