Determination of Probability Density Functions of the Cohesive Zone Parameters

Abstract

In the recent years Cohesive Zone Models (CZM) have gained increasing popularity for modeling the fracture process and also in other applications like composite de-lamination, solder failures 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 behavior 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 analyzed using Linear Elastic Fracture Mechanics (LEFM) to determine the fracture strength of a specimen. Since data for fracture toughness is available, this research is aimed at determining the probability density functions for the cohesive zone parameters that would give the same scatter in fracture strength as that obtained from the linear elastic fracture mechanics. This approach was selected to be able to use the existing test data to calibrate cohesive zone model parameters and their probability distributions in situations where the assumptions of LEFM are valid. This research is based on the premise that when LEFM assumptions are satis ed both CZM and LEFM provide the same fracture strength estimates. This paper presents the details of the CZM parameters used to represent the fracture process zone and also an algorithm to determine the Probability Distribution Functions (PDF) of those parameters.