Analysis of laminates with transverse cracks and induced delaminations: stress distribution, effective properties and energy release rate
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Vladimir VINOGRADOV (UNITED KINGDOM)Abstract :
Delamination cracks within fiber-reinforced composite laminates can form at different stages during the laminate service life and often serve as the main mechanism of laminate failure. Whether these delamination cracks occur due to monotonous, cyclic, or thermal loading, understanding their impact on the mechanical properties of the cracked laminate, stress distribution, and energy release rate associated with propagating delaminations is of high importance.
This paper introduces a robust methodology to estimate the stress field and thermoelastic constants of a laminate with parallel matrix cracks and delaminations. The approach is based on the principle of minimum complementary energy. The admissible in-plane stresses are assumed to be piece-wise linear functions of laminate depth. Zero traction conditions at the free surfaces of the laminate and delamination cracks are introduced as (differential) constraints and integrated into the energy minimization formulation using Lagrange multipliers. It is demonstrated that minimizing the complementary energy reduces to Euler-Lagrange equations in the form of a system of fourth-order non-homogeneous ordinary differential equations for the unknown stress functions.
The proposed approach yields a concise matrix-form solution for the effective thermoelastic properties, including the effective ABD matrix of the cracked laminate, thermal expansion coefficients, temperature-induced curvatures and specific heat. Notably, this method is versatile and applicable to various layups, numbers of cracks, and cracking patterns. Through suitable boundary conditions, different crack patterns such as parallel or staggered matrix cracks, symmetric or antisymmetric (Z-type) delaminations, and multiple and/or migrating delaminations can be addressed. Comparisons between predictions and experimental results demonstrate excellent agreement for Young's modulus, Poisson's ratio, shear modulus, flexural rigidity, and thermal expansion as functions of matrix crack density across different laminates. The numerical implementation of this method demands negligible computational efforts compared to finite element analysis.
Results depicting stress distribution perturbations and variations in effective laminate properties due to delamination cracks are presented for symmetric and non-symmetric crack patterns with varying delamination lengths. Additionally, the energy release rate for a growing delamination is derived and discussed, revealing a notable dependence on the evolving delamination location and geometry.
This paper introduces a robust methodology to estimate the stress field and thermoelastic constants of a laminate with parallel matrix cracks and delaminations. The approach is based on the principle of minimum complementary energy. The admissible in-plane stresses are assumed to be piece-wise linear functions of laminate depth. Zero traction conditions at the free surfaces of the laminate and delamination cracks are introduced as (differential) constraints and integrated into the energy minimization formulation using Lagrange multipliers. It is demonstrated that minimizing the complementary energy reduces to Euler-Lagrange equations in the form of a system of fourth-order non-homogeneous ordinary differential equations for the unknown stress functions.
The proposed approach yields a concise matrix-form solution for the effective thermoelastic properties, including the effective ABD matrix of the cracked laminate, thermal expansion coefficients, temperature-induced curvatures and specific heat. Notably, this method is versatile and applicable to various layups, numbers of cracks, and cracking patterns. Through suitable boundary conditions, different crack patterns such as parallel or staggered matrix cracks, symmetric or antisymmetric (Z-type) delaminations, and multiple and/or migrating delaminations can be addressed. Comparisons between predictions and experimental results demonstrate excellent agreement for Young's modulus, Poisson's ratio, shear modulus, flexural rigidity, and thermal expansion as functions of matrix crack density across different laminates. The numerical implementation of this method demands negligible computational efforts compared to finite element analysis.
Results depicting stress distribution perturbations and variations in effective laminate properties due to delamination cracks are presented for symmetric and non-symmetric crack patterns with varying delamination lengths. Additionally, the energy release rate for a growing delamination is derived and discussed, revealing a notable dependence on the evolving delamination location and geometry.