4 - Failure criteria and margins of safety

Abstract

This chapter addresses failure of unidirectional composites and laminates by determining the load at which allowables are first exceeded at some point in the composite. Stress and strain allowables (for either effective ply materials or constituent materials) quantify limits on the stress and strain components, below which the material can be expected to safely operate (with no loss of structural integrity). The maximum stress, maximum strain, Tsai-Hill, and Tsai-Wu failure criteria are employed to assess failure, at the ply level in laminates, at the constituent scale in unidirectional composites, and at the constituent scale within laminates. The equations enabling calculation of margins of safety (MoS) for each of these criteria are presented, both in the case of pure mechanical loading and in the case of thermomechanical loading, wherein the thermal loading is treated as a preload. The MATLAB implementation is then presented enabling calculation of the laminate or composite allowable loads by proportionally scaling the applied loading to the point at which failure would first occur somewhere within the laminate or composite. Code is also provided that generates multiaxial failure envelopes. Finally, example problems are presented that illustrate the ability to assess failure of laminates and unidirectional composites based on effective ply material allowables and constituent allowables.