**Guidelines for Selecting a Failure Criterion**

Guidelines for selecting the appropriate Failure Criterion to calculate the Factor of Safety of your design.

Theoretical predictions for failure of lamina are compared with experiments by comparing failure envelopes (outside the envelope, lamina failure occurs) under various biaxial states of stress. A lamina is assumed to be under a state of plane stress with non-zero stress components being σ_{1}, σ_{2} and τ_{12}. Directions 1 and 2 represent ply orientation direction and transverse to ply orientation direction respectively.

A schematic of failure envelope for a particular failure theory is shown, for example, Tsai-Wu failure criterion. X and S are normal and shear strengths of the lamina respectively. t and c represent tensile and compressive loadings. The open circles in the second plot show some sample experimental results for τ_{12} > 0.

Failure envelopes for the other failure criteria (Tsai-Hill and Maximum Stress criteria) are superimposed and accuracy of predictions evaluated against experimental results for selecting the best failure criterion.

The graph is not representative of any material system. It is shown for understanding how a failure criterion is evaluated.

For multi-directional laminates, it is difficult to evaluate which failure theory to use. Similar failure envelopes are constructed for laminates. However, for FPF (first ply failure), which the program uses, there is a wide variation between theoretical predictions and experimental observations due to several reasons.

Based on such observations some recommendations are made to help you select among the different failure theories.

In general, it is difficult to determine which theory to use due to the lack of comprehensive experimental results. Whenever possible, you should use all three failure theories and select the worst case for a relatively conservative design.

For matrix dominated failure, the maximum stress criterion is best applied to a lamina when cross-fiber stress σ_{2} > 0. You can check this stress for each ply using Composite Options in the Stress Plot PropertyManager.

The Tsai-Hill criterion is best applied to a lamina when strengths are equal in tension and compression. For matrix dominated failure, the Tsai-Hill criterion is best applied to a lamina when cross-fiber stress σ_{2} < 0.

The Tsai-Wu criterion is best applied for unequal strengths in tension and compression. For matrix dominated failure, the Tsai-Wu criterion is best applied to a lamina when cross-fiber stress σ_{2} < 0.

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