Benchmark solution for degradation of elastic properties due to transverse matrix cracking in laminated composites

Degradation of laminate moduli and laminate coefficients of thermal expansion, as well as degradation of the cracked lamina moduli and lamina coefficients of thermal expansion, are predicted as a function of crack density for laminated composites with intralaminar matrix cracks. The methodology assumes linear elastic behavior and periodicity of the transverse cracks. The representative volume element is discretized into finite elements. Stress free conditions on the crack surfaces are enforced. Periodic boundary conditions are applied so that any state of applied far-field strain can be simulated. An averaging procedure is used to yield the average stress field. Three uniaxial states of strain and a null state of strain coupled with a unit increment of temperature are used to obtain the degraded stiffness and coefficients of thermal expansion. Results are presented for a number of laminates and materials systems that are customarily used in the literature for experimentation. The modeling approach and results can be used to assess the quality of approximate models. Comparisons are presented to the predictions of one such model and to experimental data. Also, comparisons are presented to classical lamination theory for asymptotic values of crack density.