W.L. Zang

An analytic model for thermoelastic properties of composite laminates containing transverse matrix cracks

An analytical model for the prediction of the thermoelastic properties of composite laminates containing matrix cracks is presented. In particular, transverse matrix cracks with their crack surfaces parallel to the fibre direction and perpendicular to the laminate plane are treated. Two- and three-dimensional laminates of arbitrary layup configurations are covered by the model. The presented expressions for stiffnesses, thermal expansion coefficients, strain contributions from release of residual stresses and local average ply stresses and strains do solely contain known ply property data and matrix crack densities. The key to the model is the judicious use of a known analytical solution for a row of cracks in an infinite isotropic medium. The model has been verified against numerically determined stiffnesses, thermal expansion coefficients and local average ply stresses for matrix cracked angle-ply and cross-ply laminates. Comparisons to experimental data for cross-ply laminates are also presented. It is shown that the present model to a very good accuracy can predict thermoelastic properties of matrix cracked composite laminates at varying matrix crack densities and layup configurations.

Damage Evolution and Thermoelastic Properties of Composite Laminates

An analytic model for the prediction of the thermoelastic properties of micro cracked composite laminates is presented. The expression for the calculation of en ergy release rates due to growth of micro cracks is also provided. Numerical results are presented that show that the present method, to a very good accuracy, can predict ther moelastic properties of micro cracked laminates at varying crack densities and layup con figurations. In addition, a resistance curve behavior of the energy release rate is observed for both carbon/epoxy and glass/epoxy composite laminates. The reasons for this R-curve behavior are discussed. Criteria that govern the initiation and growth of micro cracks in composite laminates are discussed and compared to experimental data.

Kinked cracks in an anisotropic plane modeled by an integral equation method

A boundary integral method for cracks in an anisotropic material is presented. The method is based on the integral equation for the resultant forces along the cracks. The integral kernels contain only a weak logarithmic singularity, which simplifies the numerical implementation. Crack closure is also taken into account in the numerical formulation. Numerical tests are presented to illustrate the efficiency and the reliability of the proposed method.

An integral equation method for piece-wise smooth cracks in an elastic half-plane

A boundary integral equation method for piece-wise smooth cracks in an elastic half-plane is presented. Both internal and surface cracks have been considered. The numerical formulation is based on an element description of the unknown dislocation densities along the crack line. Crack line kinks are treated by an introduction of double nodes at each kink. Numerical test examples are presented and compared, either to existing solutions, or to own finite element calculations. Excellent agreements were obtained for all cases.

On modelling of piece-wise smooth cracks in two-dimensional finite bodies

An integral equation method for the solution to problems of piece-wise smooth cracks in two-dimensional finite bodies is presented. The method is based on an integral equation for the resultant forces along the crack line, coupling to an integral equation for the displacements on the outer boundary. Two kinds of integral kernels have been derived. One is based on the fundamental solutions for an infinite plane and the other is based on the fundamental solutions for a half-plane. The latter can be directly applied to both internal crack problems and surface crack problems. Four numerical examples are presented and compared either to existing results or to the authors FEM calculations.

Kinked cracks in bonded half-planes modeled by an integral equation method

Based on the integral equation for resultant forces along a crack, a boundary integral equation method for the solution of kinked cracks in bonded half-planes is presented. The equation only contains a weak logarithmic singularity and is valid for every point along the crack lines. Numerical results are presented to illustrate the efficiency and reliability of the method.

Local Stresses and Thermoelastic Properties of Composite Laminates Containing Micro Cracks

A model for prediction of effective stiffnesses, thermal expansion coefficients as well as average ply stresses in micro cracked laminates is presented. The theory for determination of ply stresses is a new development of a procedure for prediction of stiffness and thermal expansion coefficients previously developed by the authors. The model is based on asymptotic solutions for two extreme cases, dilute and infinite micro crack densities respectively. In the present paper, explicit expressions are given for the coefficients appearing in the theory. Theoretical predictions of stiffnesses, thermal expansion coefficients and average ply stresses of micro cracked cross ply and angle ply laminates are compared to FE- calculations. It is found out that the present theory is both quick and easy to use and also gives reliable estimations of mechanical properties in micro cracked laminates.

An Integral Equation Method Based on Resultant Forces on a Piece-wise Smooth Crack in a Finite Plate

ABSTRACT Integral equations for the resultant forces on a piece–wise smooth crack line are formulated and coupled to the standard BEM equations for the outer boundary of a finite plane. The resulting equations are a generalization of the equations for infinite geometries (Cheung and Chen, 1987). The integrals along the crack line, with the dislocation densities as unknowns, contain only a weak logarithmic singularity. An improvement of the numerical formulation at a kink of the crack line is introduced. Two numerical experiments are presented and compared with alternative numerical calculations.