### STP1242: A Coulomb-Mohr Type Criterion for Matrix Mode Failure in a Lamina

Chatterjee, SN

*Staff scientist, Material Sciences Corporation, Fort Washington, PA*

Pages: 20 Published: Jan 1997

**Abstract**

Failure of laminated composites under in-plane and/or through the thickness stresses is a complex phenomenon. Ply failure is often predicted based on the maximum value (or values) of one or more functionals, such as the maximum stress (strain) or polynomials involving the stress components. Some researchers have pointed out that it is necessary to distinguish between two types of failure, namely, (1) fiber-dominated mechanisms (tension or compression in the fiber direction), and (2) matrix mode failures. Failures in the second mode are expected to occur on planes parallel to fibers, and they can be predicted by seeking a plane on which a functional involving the normal and two shear stress components acting on the plane attain a maximum value. Two such functionals are chosen, one for tensile and the other for compressive matrix failure, and they involve three matrix-dominated strengths, namely, the transverse tensile and shear strengths and the longitudinal shear strength of the ply.

In this work, it is shown that a Coulomb-Mohr type criterion or a combination of such pyramidal failure surfaces, which is physically appealing and is widely used for many brittle materials, such as rock and concrete, can be utilized for predicting matrix mode compressive failures in a lamina. A simple modification is introduced to account for the fact that the transverse shear strength of a ply may be different from its longitudinal shear strength. Predictions are compared with results from other failure theories as well as test data from tension and compression tests on angle ply (± θ)^{ns} and off-axis unidirectional coupons reported in literature. For tensile failure, the criterion has to be modified by introduction of tension cutoffs, which are usually needed for all brittle materials. Use of the criterion under more complex conditions, such as thick composites under three-dimensional stress states is explored and advantages and disadvantages of the criterion are discussed.

**Keywords:**

unidirectional composite, matrix mode compression failure, tension cutoffs, damage surface, failure surface, multiaxial stress state, interaction, pyramidal failure surfaces

**Paper ID:** STP18279S

**Committee/Subcommittee:** D30.04

**DOI:** 10.1520/STP18279S

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