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Failure of fiber reinforced orthotropic layers. • Failure often controlled by the complex interaction of fibers and matrix. • Still, the ideal was to come up with failure criteria that are small generalization of those used for isotropic materials. (a,b) fiber microbuckling; (c) kink band; (d) shear failure on 45-deg plane.
How many experiments? • Unlike isotropic materials properties are different in fiber and matrix directions. • Brittleness and matrix-fiber interaction mean that properties are different in tension, compression and shear. • Consequently at least five failure stresses
Max stress and max strain criteria • Max stress (note that these are no longer principal stresses) • Max strain
Example 6.2.1 • Boron Epoxy with . • Strengths: • What order of magnitude strains can it take? • Calculate maximum for varying ply angles. • Then consider also cases with , for r=0.05, and r=0.15.
Solution procedure • Transform loading stresses and to material coordinates get • Then compare each to the limit and find the maximum value.
Tensile strength • Need to look at failure envelope. • Does the envelope make sense? • Anything surprising?
Comparing tensile to compressive strength • What changed about the envelope?
Biaxial loading • Anything remarkable?
Tsai-Hill Criterion • Rodney Hill (1921-2011) Cambridge Prof. • Hill sought quadratic criterion for anisotropic materials with equal tensile and compression propertiesof the form • Stephen Tsai, Stanford Prof. applied to composites. • You find coefficients by applying five test conditions . For example, tensile test in fiber direction gives • Altogether get
Hoffman criterion • Oscar Hoffman, Lockheed 1967 • To account for difference in tension and compression need to have linear terms • Derivation as homework. • Criterion is no longer homogeneous. What does that mean? • Implication for safety factors. Have a paper on that with A. Groenwold of U. Stellenbosch.