Failure criteria for laminated composites

1. Failure criteria for laminated composites • Defining “failure” is a matter of purpose. • Failure may be defined as the first event that damages the structure or the point of structural collapse. • For composite laminates we distinguish between “first ply failure” when the first ply is damaged and “ultimate failure” when the laminate fails to carry the load. • Ultimate failure requires “progressive failure” analysis where we reduce the stiffness of failed plies and redistribute the load.

2. Failure criteria for isotropic layers • Failure is yielding for ductile materials and fracture for brittle materials. • Every direction has same properties so we prefer to define the failure based on principal stresses. Why? • We will deal only with the plane stress condition, which will simplify the failure criteria. Then principal stresses are • What about the third principal stress?

3. Maximum normal stress criterion • For ductile materials strength is same in tension and compression so criterion for safety is • However, criterion is rarely suitable for ductile materials. • For brittle materials the ultimate limits are different in tension and compression

4. Maximum strain criterion • Similar to maximum normal stress criterion but applied to strain. • Applicable to brittle materials so tension and compression are different. What is wrong with the figure?

5. Maximum shear stress (Tresca) criterion • Henri Tresca (1814-1885) French ME • Material yields when maximum shear stress reaches the value attained in tensile test. • Maximum shear stress is one half of the difference between the maximum and minimum principal stress. • In simple tensile test it is one half of the applied stress. So criterion is

6. Distortional Energy (von Mises) criterion • Richard Edler von Mises (1883 Lviv, 1953 Boston). • Distortion energy (shape but not volume change) controls failure. • Safe condition • For plane stress reduces to

7. Comparison between criteria • Largest differences when principal strains have opposite signs

8. Maximum difference between Tresca and von Mises • Define stresses as . For what do we get the maximum ratio between the two predictions of critical value of ? Can assume 1. Why? • Positive . Tresca gives . Von Mises leads to . Maximum for =0.5, • Negative . Tresca leads to . Von Mises still same equation. Maximum ratio for =-1. • Check!