1Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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ME 370/570Materials Science and Engineering-I

Chapter VII

• Instructor: Dr. R. Srinivasan• Mechanical and Materials

Engineering Dept.

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Plastic Deformation• Plastic deformation in metals has been

observed to occur on specific crystallographic planes and along specific crystallographic directions

• These planes and directions are typically close-packed planes and close-packed directions– Planes with a high density of atoms– Directions along which atoms touch each other

3Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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From “Principles of Materials Science and Engineering,” 3rd Edition, by W.F. Smith McGraw-Hill, 1996

4Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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From “Principles of Materials Science and Engineering,” 3rd Edition, by W.F. Smith McGraw-Hill, 1996

5Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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• Deformation by slip occurs at a stress level much lower than is predicted by theoretical analysis of bonds breaking and reforming after planes slide over each other.

• Dislocations help explain why.• The entire plane does not slide, only parts of

the planes near dislocations do.– Inch-worm analogy– Ripple in a rug analogy

6Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

7Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

8Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

Movie “Dislocations” showing “Ripple in a Rug” analogy

9Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

10Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

11Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

12Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

For Ti, Mg, Zr, (c/a) < ideal (1.633). Therefore, there are additional planes with a high density of atomsPrism plane: and Pyramidal plane: { }0110 { }1110

13Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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When you have a large number of slip systems, the one with the highest resolved shear stress is the one on which plastic deformation (movement of dislocations) occurs.

Resolved shear force =

Area of plane =

Resolved shear stress =

Schmid Factor

λcosF

φcosA

λφτ coscosAF

R =

λφ coscos=m

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In polycrystalline metals, each grain is oriented differently, and the active slip sytem(s) may be different. When loaded, each grain deforms its own way.However, for the solid to remain as one piece, each grain must also be able to accommodate the deformation of its neighbors at the grain boundary.This requires multiple slip systems to be available at the grain boundary. Theoretically, at least 5.FCC and BCC crystals have more than 5, but HCP crystals do not.Polycrystalline HCP may be brittle.

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Equiaxed Elongated

Rolling direction

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17Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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• Slip– Orientation of crystal above and

below slip plane is the same– Displacement of atoms is multiples

of the burger’s vector– Large strain is possible

• Twinning– Crystal is reoriented– Mirror image about twin plane– Displacement increases as you go

away from the twin plane– Displacement of atoms may be

fractions of atomic spacing– Strain magnitude is small– Occurs when slip is not possible– Reorientation may activate other

slip systems

18Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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Strengthening Mechanisms

• Grain boundary strengthening• Solid solution strengthening• Cold working

19Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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20Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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)2/1(0

−+= kdy σσ

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• Pure metals are always weaker than alloys.• Solute atoms cause a distortion of the lattice.• Dislocations also cause distortion of the lattice.• Solute atoms and dislocations try to position

themselves to minimize distortion• Free movement of dislocations becomes difficult

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23Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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Increased dislocation density results in:•Increased strength•Decreased ductility

( ) 100%0

0 ×−

=AAACW d

Cold Working

Deformation at low temperatures results in Work hardening or Strain hardening

24Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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25Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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Annealing of a cold worked metal

Recovery, Recrytallization and Grain Growth

26Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

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27Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

28Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

29Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

30Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

31Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University

32Based on Materials Science and Engineering An Introduction, W.D. Callister, Jr. 5th edition, 2000, Wiley

This material is for educational used only within Wright State University