## LSU Historical Dissertations and Theses

1993

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Anne B. Doucet

S. Acharya

#### Abstract

Two analytical shear lag models have been developed for the progressive damage and final failure of epoxy matrix, fiber-reinforced composites under biaxial loading. The first is a three layer model for laminates of the type ($\pm\theta$,90n) s under general biaxial loading. It gives matrix cracking predictions for the central 90$\sp\circ$ ply group. The second model is a five-layer model for laminates of the type (90n/0m/90p) s under biaxial loading, but it does not include in-plane shear. The five-layer model predicts matrix cracking in all ply groups. The amount of damage in terms of modulus decrease and number of matrix cracks is determined for each layer under increasing static loads. This is done by assuming that a crack occurs, calculating the energy dissipated due to the crack formation, dividing by the critical crack size, and comparing the result with the critical strain energy re!ease rate. When a layer cracks, the other layers must take additional load. Final failure occurs when the primary load carrying plies reach their ultimate strength. The models incorporate an algorithm for the effect of small, initial local delaminations on matrix cracking. The three-layer model has been verified experimentally using literature data and in-house experimental data. The five-layer model has also been experimentally verified in this work. Experimental verification was performed by statically loading uniaxial glass-epoxy tension specimens and measuring damage accumulation in terms of crack density and the decrease of Young's modulus. The present study shows that the models developed can be used for initial predictions of damage and failure of epoxy matrix, fiber-reinforced composites.

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