Kinematic Waves and Nonuniform Damage Development in Composite Laminates

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Abstract
When subjected to fatigue loading, the off-axis plies of some polymer matrix laminates undergo a transverse cracking whose density is maximum close to the free edges and decreases toward the specimen center; moreover, this damage distribution evolves as the number of cycles increases. The "kinematic wave" concept is applied to the principle of conservation of number of crack tips, along with suitable assumptions concerning the velocity of a crack tip propagating into a material whose damage state is characterized by a local crack density. This principle gives a nonlinear wave equation governing damage as a function of both distance x from a free edge and number N of cycles. Experimental results pertaining to a cross-ply carbon/epoxy laminate whose 90° layers are thin compared to the longitudinal layers are obtained in the form of successive X-ray pictures taken at different times in the specimen life. Plotting the contour lines of damage in the (x,N) plane results in a family of straight lines which can be interpreted as the characteristic curves of a simple wave solution for the above wave equation. Measuring the slope of each curve of this family, along which damage is constant, allows the coefficient of the wave equation to be determined as a function of damage. A power law is found to fit well with the corresponding curve, which assesses the consistency of the model with the experimental results for the laminate investigated. The damage growth law obtained in this manner is the first step toward the future construction of a more general model which could be used to predict the service life of a composite structural part.