Identification and Modeling of the Crack Development Behavior in the Fracture Mechanics of Polymer Materials

Examining the mechanical properties of polymer materials has particular importance due to the increasing usage of these materials. In this paper, the crack development process was identified using the experimental data obtained from the tensile tests of polyvinyl chloride polymer (PVC) to reduce the experimental test number. Some pre-cracks were created on the experimental samples by slotting and broaching methods and the experimental results of force versus displacement were recorded for each sample. In the next step, some mathematical pre-processing operations including equating the sampling intervals using interpolation and integration using trapezoidal methods were performed on the experimental data. In the third stage, by using the pre-processed data and the Least Squares (LS) identification method, the mathematical model of the system, the frequency domain discrete transfer function of the crack development process, was obtained. Finally, after evaluating and verifying the obtained mathematical model with other experimental results, it was proposed to predict the crack development process. The obtained results showed that by identifying the crack development process for limited samples, it is possible to avoid the number of experimental tests that are time-consuming and costly. In addition, the second-order two-stage least squares method with five unknown parameters was promisingly able to estimate crack development dynamics with acceptable accuracy, particularly in the first half of the development process.