Analysis of fatigue crack growth behaviour in polymers and their composites based on ordinary differential equations parameter estimation

Traditionally, the fatigue behaviour of polymers and polymer composites is analyzed by performing Wohler experiments, a well-known technique for the i nvestigation of metals. These experiments are very expensive and time consu ming. The application of fracture mechanics provides a much faster way to a nalyze the fatigue crack growth behaviour of polymers and polymer composite s, This analysis is based on the Paris-Erdogan equation describing a stable phase of crack growth. With this method the fatigue crack growth diagram i s derived simultaneously with the reading of the measurements. Care must be taken however, to minimize error arising from variations in initial crack length, the uncertainty in the determination of the elastic modulus and est imation of the region of stable crack growth. To overcome some of the syste matic problems mentioned above, the following procedure is applied: The fra cture mechanical parameter estimation problem is mapped onto a nonlinear le ast squares problem restricted by a differential equation. This problem is numerically solved by a boundary value problem approach which consists of a multiple shooting technique combined with a damped Gauss-Newton procedure. In this procedure, the only data to be measured is the compliance as a fun ction of time or number of cycles. After the problem of least squares is so lved and the material parameters determined, the distribution of residuals of the fit is used to estimate the region of stable crack growth. Since the analysis is based on well defined statistical foundations (maximum likelih ood estimation), we gain a methodological advantage of the increased object ivity of the analysis. Considering the increasing importance of lifespan pr ognoses for plastic components based on fatigue crack propagation experimen ts, this method is preferred to the conventional, rather subjective procedu re. (C) 1999 Elsevier Science Ltd. All rights reserved.