Inverse Method for the Analysis of Instrumented Impact Tests of Polymers

VALERIA PETTARIN; PATRICIA FRONTINI; GUILLERMO ELICABE

Les Diablerets, Switzerland

Conferencia; Fracture of Polymers, Composites and Adhesives – 3rd ESIS TC4 Conference on Polymers and Composites; 2002

European Structural Integrity Society

There is a considerable interest in dynamic fracture as reflected in substantial literature. Nevertheless, it is one of the least well-understood aspects of fracture. This is due, in large part, to the very complicated nature of dynamic phenomena in fracture arising from the temporal degree of freedom. The important consequence of these dynamic effects is that the bending forces and associated stored strain energy actually acting in the specimen may be incorrectly deduced because the force transducer is mounted on the striker. Also, severe oscillations and even multiple zero values may be observed in the measured force-time relationship. The experimental results, when expressed as critical stress intensity factor Kc or critical energy release rate Gc versus notch length a, often show considerable scatter and the vital issue of the uniqueness in such a relationship remains largely unresolved (Williams et al, 1987). In this work, a simple mass-spring-dashpot (one dimensional) model from literature (Pavan et al, 1999) sufficiently detailed to represent all dynamic effects was used to represent the experimental response of a RTPMMA polymer subjected to impact loading in three-point bending configuration. The recovery of the bending force acting in the specimen (responsible of the fracture of the sample) from impact force measurements is reported. The mathematical resolution of the model that represents the event required the use an inverse resolution method. A discrete model was developed from the differential equations of the model, which transforms the problem of obtaining the bending force acting in the specimen from impact measurements into a linear algebraic problem. Estimations of the bending force may, in principle, be obtained by the direct inversion of the linear equation. Although this solution appeared to be straightforward, small errors (i.e. quadrature and experimental errors) resulted in large errors in the estimated bending force. However, by constraining the least-squares solution by means of a penalty function (regularization technique), approximate useful solutions were obtained. Regularization techniques require the selection of a constraining parameter known as the regularization parameter g. The results demonstrate that this technique yields adequate recoveries of the bending force. Through this work the regularization technique appears as a useful tool for the analysis of the transient response of instrumented impact testers, which allows extracting the true dynamic parameters values in routine material testing.