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Objectives1. Explain the microscopic process for

elastic behavior (modulus).2. Explain the microscopic process for

plastic deformation

3. Explain the difference betweenengineering and true stress and strain.

4. Convert between engineering and true

stress or strain5. Know the modulus of selected

representative engineering materials

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Elastic Deformation

 ___________of bonds

Will be almost the same in

tension as in compression.

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Plastic DeformationExperiment: Mg Crystal

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Deformed Single Crystal

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Magnesium Single Crystal

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Sliding Mechanism

One closed packed plane slides pastneighbor

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Estimate Stress

At Saddle

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Stress for Slip

Hooke’s Law: 

= G  

For Mg; G = 17.2 GPa

So

 estimated = 8.6 x 10^3 MPa

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Actual Sy = 0.7 MPa

Estimated y = 8.6 x 10 ^3 Pa

Error > 10,000 times!!

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When your model produces

erroneous predictions

 – it is wrong.

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Actual Process

Dislocation ____ or _____

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Crystal Deformation Due to Slip

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The “Carpet-Ruck” Analogy of 

an Edge Dislocation:

Sli H Sli

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Slip Happens on Slip

Systems” 

Close Packed PlanesClose Packed Directions

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Summary

Elastic Deformation is due to ______. Volume is not constant.

Plastic deformation is due to ______.

Volume will be constant. (m = 0.5)

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Symmetry of Properties

Modulus is bondstretching/compression – should besame in compression and tension.

Yield behavior is caused by shearstress – which only changes directionwith switch from compression totension.

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Symmetry in the elastic & plastic deformation mechanisms

Materials should have samestress-strain behavior incompression and tension.

But: It is not so !

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 Actual Stress-Strain Behavior 

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Problem:

Changing Area

During Test

Thus:

Stresses based on

Ao are inaccurate.

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Remaining Problem Is In StrainDefinition:

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For Another Increment of 10%

Strain:

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Solution: TRUE STRAIN

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Corrected Tensile Curve

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Stress-Strain Conversions

Convert betweentrue andengineering

quantities:

)1ln()1(ees

 

  

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Stress-Strain Curves are

measures of _____storageand dissipation.

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This applies for non-linear curves as well.

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Ductile vs. Brittle

Callister, Materials Science and Engineering

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 Anelasticity/Hysteresis

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Reduction of Area

Analogous to strain to failure

Will give ultimate value when strainmeasurement doesn’t go to failure. 

100)(0

0

 A

 A A ROA

f 

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Hardness• Resistance to permanently indenting the surface. 

• Large hardness means: --resistance to plastic deformation or cracking in

compression.

--better wear properties.

10 mm sphere

apply known force measure size 

of indent after  removing load

d  D  

Smaller indentsmean larger hardness. 

increasing hardness 

mostplastics 

brasses Al alloys 

easy to machinesteels  file hard 

cuttingtools 

nitridedsteels  diamond 

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Hardness: Measurement

Rockwell• No major sample damage

• Each scale runs to 130 but only useful in

range 20-100.• Minor load 10 kg

• Major load 60 (A), 100 (B) & 150 (C) kg

A = diamond, B = 1/16 in. ball, C = diamond

HB = Brinell Hardness• TS (psia) = 500 x HB

• TS (MPa) = 3.45 x HB