Stress Variational Analysis Of Composite Laminates With Matrix Defects

The matrix cracks of laminates are often induced when the laminates are used in engineering,because the cracks can make reduction of the stiffness of laminates,the stiffness can be used to evaluate the damage status of material.At present,the research for the laminates assumes that distribution of the in-plane stresses in each thin layer is uniform across the thicknesses,but the finite element results show that the distribution is generally non-uniform.Therefore,there are some deviations between theoretical and experimental results when the assumption of the uniform distribution is used to analyze the overall mechanical properties of the laminatesBy means of an general expression of series function for the normal stress at the boundary of damage element of laminates with matrix cracks,the general expressions of the stress components of laminate satisfying the equilibrium differential equation of elastomer,the stress boundary condition and the interlaminar stress continuity condition are established in this paper.Based on the principle of minimum complementary energy,the general expressions of the governing equation are derived.Solving the governing equation,the effective elastic modulus of the laminates with matrix cracks is calculated and analyzed by truncating a finite number of terms.Based on analysis of the stresses in the orthogonal laminates and the elastic modulus of the laminates with matrix cracks,the results of stiffness obtained by the non-uniform distribution of normal stress across the thickness is closer to the experimental results than those obtained by uniform distribution.Meanwhile,it is very little difference,not only to evaluate the stress components when the linear distribution of normal stress is replaced by the parabolic distribution,but also to evaluate the effective elastic modulus..