Ronald Krueger

Virtual crack closure technique: History, approach, and applications

Abstract : An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.

A summary of benchmark examples to assess the performance of quasi-static delamination propagation prediction capabilities in finite element codes

The development and application of benchmark examples for the assessment of quasi-static delamination propagation capabilities is demonstrated. The methodology proposed, based on fracture mechanics, is used to develop benchmarks for the double cantilever beam, end-notched flexure, single leg bending as well as mixed-mode bending specimens for 20%, 50% and 80% mode II. The methodology proposed for the development of quasi-static benchmark results is discussed in detail, and will be presented using the double cantilever beam specimen as an example. The practical application of the benchmarks generated is illustrated by using the double cantilever beam and mixed-mode bending (50% mode II) benchmarks to assess the automated procedure implemented in Abaqus/Standard®. This assessment proved to be valuable by highlighting the issues (e.g. overshooting, saw-tooth behavior, non-convergence) associated with choosing the input parameters unique to the Virtual Crack Closure Technique implementation in Abaqus/Standard®. Additional studies should include the assessment of the propagation capabilities in more complex specimens and on a structural level.

Mode mixity analysis of face/core debonds in a single cantilever beam sandwich specimen

The single cantilever beam sandwich specimen has been proposed, as a fracture test standard for mode I peel loading. Critical parameters, including specimen dimensions, determine whether the crack propagates along the face/core interface in mode I during the fracture test. This paper outlines a parametric study based on a numerical method to examine local mode mixity conditions for a wide array of sandwich systems by varying several geometrical and material parameters. The thickness and modulus of the face sheet were seen to influence the mode mixity for most sandwich systems. Core Poisson’s ratio was shown to influence the local mode mixity and has the capability of driving the crack along the interface or into the core. The effect of the intact specimen length was analyzed and presented from a mode mixity perspective based on various elastic foundation modulus expressions. Reinforcement of the single cantilever beam specimen with stiff layers was also investigated numerically and compared with a similar analysis in the literature. The analysis presented in this paper shows that, despite reducing the global shear component, the local mode mixity condition deviated away from the mode I regime for several sandwich specimens. An appropriate foundation model along with a minimum loading rod length was one of the recommendations provided from the analyses, which may supplement the ASTM International standardization efforts.