Virtual crack closure technique: History, approach, and applications

TLDR

Cracks and delaminations between dissimilar materials pose significant challenges, prompting interest in fracture‑mechanics–based methods to evaluate damage tolerance of composite components during design and certification. The paper provides an overview of the virtual crack closure technique, summarizing its history, approach, and applications. The authors detail the virtual crack closure technique for two‑dimensional quadrilateral finite elements with linear and quadratic shape functions, extend it to three‑dimensional solids and plate/shell elements, and discuss necessary modifications for geometrically nonlinear analysis and tip‑element corrections for varying crack lengths and widths.

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 finite elements with linear and quadratic shape functions are given. Formulas for applying the technique in conjunction 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.