ME 383 Modern Manufacturing Practices

1. ME 383Modern Manufacturing Practices Lecture Note #3 Stress-Strain & Yield Criteria Dr. Y.B. Guo Mechanical Engineering The University of Alabama

2. Today’s Lecture • Engineering Stress & Strain • True Stress & Strain • Engineering Stress/Strain vs. True Stress/Strain • Stress – Strain Curves

3. Deformation Mode • Basic Deformation Mode Tension or Compression Torsion

4. Tensile Test Simulation

5. Tensile Test Simulation

6. P y P x Engineering Stress & Strain - Tension • Engineering Stress • Engineering Strain (compression vs. tension)

7. P y P x Engineering Stress & Strain - Tension • Elongation • Ductility (Reduction of Area)

8. P y P x Engineering Stress & Strain - Tension • Poisson’s Ratio ( ~ 0.3)

9. F F Shear Stress & Strain • Shear Stress • Shear Strain

10. P y P x True Stress & Strain • More Accurate Measurement • True Stress • True Strain

11. Engineering Stress/Strain vs. True Stress/Strain • True Stress & Engineering Stress (Up to necking) • True Strain & Engineering Strain (Up to necking)

12. Elastic Plastic X Fracture E Offset, 0.2% Neck Engineering Stress-Strain Curve

13. Engineering Stress-Strain Curve (Cont’d) • Young’s Modulus : slope of the of the elastic range • Yield Strength : stress required to generate permanent deformation • Tensile Strength : maximum stress • Flow Stress: stress causes continuous deformation after yielding • Failure Stress: stress when the material fractures

14. True Eng. True Stress-Strain Curve • Constitutive Eq. (plastic range) • :strength coefficient (true stress at unit true strain) • :strain hardening exponent

15. True Stress-Strain Curve (Cont’d) • True Strain Equals to the “n” Value at Necking, i.e., Max Load (only occurs in tension) • Proof P

16. Example 1 • A strip of metal of 1.5m long is stretched in three steps: to length of 2.0m, then to 2.5m, finally to 3.0m. Calculate engineering and true strain. • Solution: Engineering Strain

17. Example 1 (Cont’d) • True Strain

18. Example 2 • Calculate True and Engineering • at necking

19. End • Questions ?

20. Today’s Lecture • Stress-Strain State: • Hooke’s Law • Yield Criteria: 1) Tresca 2) von Mises • Effective Stress and Strain • Work of Deformation and Temperature • Case Studies

21. Stress State - Triaxial Stress • Equilibrium: • Principal Stress

22. Strain State - Triaxial Strain • Principal Strain

23. Stress-Strain Relationship in Triaxial State • Generalized Hooke’s Law • Example: In Tension,

24. Yield Criteria • Tresca • von Mises • Difference < 15% • Ductile Mat’s Breaks at Max. Shear Stress, while Brittle at Max. Normal Stress

25. Effective Stress and Effective Strain • Convenient Way of Expressing the Stress State • Effective Stress - based on principal stress • Effective Stress - based on normal stress

26. Effective Stress and Effective Strain • Convenient Way of Expressing the Strain State • Effective Strain(Tresca) (von Mises)

27. Work of Deformation & Temp. • Specific Energy (deformation work per unit volume) • Work • Temperature

28. Example 1 - Stress State & yield Q: P? Tresca: Von Mises:

29. Example 2 - Stress State & yield Q: P? Tresca: Von Mises:

30. Example 3 - Work and Temp. Q: W and T?

31. Example 3 - Work and Temp.

32. End • Questions ?