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)