1 ME383 Modern 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

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

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

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

9 Shear Stress & Strain Shear Stress Shear Strain F F

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

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

12 Engineering Stress-Strain Curve X Neck Fracture PlasticElastic E Offset, 0.2%

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

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 ?