Micro-mechanical damage model accounting for composite material nonlinearity due to matrix-cracking of unidirectional composite laminates

A new micromechanical damage model for predicting the effect of matrix-cracking on the mechanical behavior of the composite material is proposed. The model is based on the volumetric change that occurred due to the presence of cracks in a composite lamina due to uniaxial off-axis loading. It determines the volumetric crack-density (VCD) by combining the macro-mechanical and micro-mechanical principles. A representative volume-element is proposed that determines the material mechanical properties (E1, E2, G12 and ν12) in terms of crack-density, fiber and matrix properties and initial volume-fraction of fibers. The rule-of-mixture in combination with Halpin-Tsai model is used to determine the mechanical properties of a cracked composite lamina. It has been shown that, matrix-cracking is the main cause for composite-material nonlinearity. Moreover, the model has been shown to give a reliable and reasonable predictions of the VCD and the tangential damage-factor (TDF) for various fiber/matrix systems using the corresponding available data from literature. An alternative secant damage-factor is being proposed, which has a linear relationship with the VCD. In order to validate the model, two composite materials; Boron/Epoxy (Narmco-5505) and Graphite/Epoxy (4617/Modmor-II), have been considered using laminates at different fiber-orientation angles. The maximum volume-crack-density (MVCD) and maximum secant damage-factor (MSDF) are obtained using equations that depend on the fiber-orientation angle and the initial material mechanical properties.