8 mechanical behavior of metals elastic deformation plastic deformation yield strengthnotes
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7/31/2019 8 Mechanical Behavior of Metals Elastic Deformation Plastic Deformation Yield Strengthnotes
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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