: 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.

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Virtual crack closure technique: History, approach, and applications

An investigation was performed to study the delamination growth in two different cross-ply laminated three-point bending specimens. A two dimensional (2D) finite element (FE) analysis was firstly carried out to determine the strain energy release rates during the delamination of the beams. Contact elements were used to prevent the material interpenetration on the crack surfaces. To study three dimensional (3D) effects on the crack growth in the composite beams, 3D FE analysis was developed. The 3D results showed that the distribution of the energy release rates along the delamination front are not constant. At the free surface a coupling between mode II and mode III energy release rates was also observed, and it was further noticed that the dominating deformation mode is different for distinct laminate lay-ups even under a pure mode I loading condition. Comparison of the 2D and 3D FE analyses suggested that the critical delamination toughness obtained from 2D computations be conservative. INTRODUCTION Laminated composites have demonstrated their usefulness and potential increases in many structural applications. These materials must be designed to meet various engineering requirements and to withstand the service loads. Delamination is the major failure mode of laminated composites and is now widely investigated by static and/or low velocity impact loading tests. Delamination is initiated by two types of cracks: shear cracks in matrix and normal tension cracks perpendicular to fibres. These interlaminar cracks immediately propagate into ply interface and the associated stress concentration may then initiate delamination cracks. The initiation and growth of delamination is governed by the interlaminar fracture toughness of the material. For most of the specimen geometries used in laminate testings it is possible to obtain analytical solutions using beam theory [1,2,3,4], A general method for calculating the total energy release rates Gj from the local values of forces and * Dept. of Matr. Sci and Eng., Oregon Grad. Inst, P.O. Box 91000, Portland, OR 97291-1000, USA. * Dept. of Strength of Materials, Riga Tech. University, Kalku St. 1, LV 1047, Riga, LATVIA. Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533 252 Localized Damage bending moments in a cracked laminates has been suggested by Williams [5]. These formulas [5] are the same as well known formulas for Double Cantilever Beam (DCB), End Notched Flexure (ENF) and other specimens developed previously by other methods. Formulas are simple only for the case of isotropic layers. Fig. la shows a laminated cross ply beam with a central edge notch or edge crack in the bottom layer. In this case delamination crack with length a runs into the ply interface normal to the notch. This case of delamination growth due to bending in graphite/epoxy laminates was investigated by Sun [6]. A formula to calculate the total energy release rate was also given as Here D = /4,, •/),, -B^, where AH, EH and D%% are beam stiffnesses, and subscripts 1 and 2 denote values in section 1 and 2 respectively (see Fig. Ib). |2P |2P

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F.-G. Buchholz

Papers

Delamination Analysis For 2D- AndSB-models Of A Cross-ply LaminatedThree-point Bending Specimen