Failure criteria for laminated composites Defining failure is

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.

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?

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

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?

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

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

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

Maximum difference between Tresca and von Mises •