Calibration of a probabilistic cohesive zone model for generating a fracture nomograph

Abstract

ABSTRACTIn the recent years, Cohesive Zone Models (CZMs) have gained increasing popularity for modelling the fracture process [1] and also in other applications like composite de‐lamination [2] solder failures [3] in circuits, etc. This can be attributed to the ability of the CZM to adapt to the nonlinearities in the process it represents by adjusting the model parameters. These parameters that are selected to represent the material behaviour in the vicinity of the crack or a damage zone are non‐deterministic in nature resulting in random fracture strength estimates. Currently, there are no standardized tests for measuring the CZM parameters and their random scatter. Numerous researchers in the literature suggest values for the CZM parameters based on their experience from limited test data. Traditionally, fracture toughness is determined through coupon tests for any material system that is being analysed using Linear Elastic Fracture Mechanics to determine the fracture strength of a specimen. Since data for fracture toughness are available, this research is aimed at determining the probability density functions (PDFs) for the cohesive zone parameters that would give the same scatter in fracture strength as that obtained from the test statistics. Correlations between the model parameters were introduced to improve the accuracy of the fracture strength PDF. A finite width cracked plate was selected as a test case to demonstrate the process. This paper also presents evidence that material scatter can be isolated from the geometric effects to determine a normalized PDF of fracture strength for a given material. This normalized PDF can then be scaled, using mean fracture strength, to any crack configuration to develop a nomograph that can be used to rapidly assess risk without the need for a probabilistic fracture analysis.