Mixed-mode Strain Energy Release Research Articles

Validation and enhancements for the localised experimental–numerical technique

Over many years the use of composite structures in aerospace and automobile applications has been expanding. Thus, the study of weaknesses associated with composite materials has become paramount. Delamination is a fundamental concern with these structures, and mixed mode strain energy release rates are valuable information for analysing delamination cracks. The localised experimental–numerical technique (LENT), which measures local test displacement data and combines this with local finite element analysis to evaluate the mixed mode strain energy release rates, is examined via extensive experimental testing and analysis to provide validation for the technique. Additionally, a sensitivity analysis is presented to assess the influence of pixel size on the strain energy release rate results determined using LENT. Enhancements to the method are presented focusing on reducing the pixel size and improving post-processing techniques for increased accuracy. Variations in the local area analysed with LENT are also investigated. The results demonstrate that the localised experimental–numerical technique has potential for the evaluation of mixed mode strain energy release rates using localised test data.

A localised experimental–numerical technique for determining mixed mode strain energy release rates

Composite structures are being used increasingly in the aerospace industry due to their superior specific stiffness and strength. One key issue associated with such structures is delamination, and how to effectively predict this. A new method which is derived from localised test displacement data is presented to determine the mixed mode strain energy release rates of layered structures with a pre-existing crack. Images taken during experimentation of the vicinity of the crack tip are analysed at low load and high load to determine the displacement changes across the load variation. These displacements are applied as boundary conditions to a simple local numerical model including a constraint at the crack tip. The forces and displacements at the crack tip are taken as output data and combined with the Virtual Crack Closure Technique to predict strain energy release rates. Initial validation of the localised experimental–numerical technique (LENT) shows that applying experimental data to a numerical model does give reasonable agreement thus far in the established trends, and hence LENT is promising for use in determining mixed mode strain energy release rates and mode mixity ratios.

A shell/3D modeling technique for the analysis of delaminated composite laminates

A shell/3D modeling technique was developed for which a local solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local 3D model and the global structural model which has been meshed with shell finite elements. Double Cantilever Beam, End Notched Flexure, and Single Leg Bending specimens were analyzed first using full 3D finite element models to obtain reference solutions. Mixed mode strain energy release rate distributions were computed using the virtual crack closure technique. The analyses were repeated using the shell/3D technique to study the feasibility for pure mode I, mode II and mixed mode I/II cases. Specimens with a unidirectional layup and with a multidirectional layup were simulated. For a local 3D model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Generalized modified crack closure integral (GMCCI) and its application to interface crack problems

It is well known that at an interface crack tip, mode mixity exists even under single mode loading situations. The modified crack closure integral (MCCI) technique together with finite element analysis has been extensively used in the past to estimate the mixed mode strain energy release rate (SERR) components at these crack tips. One of the aspects which attracted considerable attention in these problems is the convergence of SERR components as the virtual crack extension size is progressively decreased to zero. Such studies have proved to be computationally expensive as the problem has to be solved each time for various sizes of virtual crack extension. Also it was not possible to estimate the effect of preventing the crack face interpenetration on SERR estimates for large sizes of virtual crack extension greater than the contact zone size. To overcome these in this paper, a generalized modified crack closure integral (GMCCI) algorithm is proposed for four and eight-noded isoparametric quadrilateral elements, which can estimate the SERR components for several sizes of virtual crack extension through a single finite element analysis. This is achieved through a numerical integration of the crack closure integral (CCI) and for various sizes of virtual crack extension covering a large number of equal or unequal size elements ahead and behind the crack tip. The procedure developed is demonstrated with application to typical interface crack problems under remote tension and shear.

Strain Energy Release Rates in Finite Graphite/Epoxy Plates with a Crack under Mixed Mode Deformation

This paper investigates the mixed mode problem numerically and experi mentally for the finite orthotropic plate where an inclined crack parallel to the fiber direc tion is centrally placed. The mixed mode correction factors of strain energy release rate are calculated by using the modified mapping collocation method and those of graphite/ epoxy plates are presented as functions of the crack length for various aspect ratios, crack angles and boundary conditions. To confirm the validity of these results, the mixed mode fracture test for graphite/epoxy specimens is performed for selected combinations of crack length and angle. Mixed mode strain energy release rates for various crack angles and crack lengths are obtained.

Prediction of Tensile Matrix Failure in Composite Laminates

A conceptually simple mixed mode fracture analysis method is presented for the prediction of tensile matrix failure in composite laminates. The analysis technique, which makes use of a mixed mode strain energy release rate fracture criteria in con junction with an approximate two-dimensional shear-lag model, is cast in terms of a tensile matrix strength criterion. In contrast to presently available point stress tech niques, surprisingly accurate predctions of mode I matrix failure in the 90° lamina of (±θ/90 n) s and mixed mode matrix failure in the θ° lamina of (02/θ) s T300/934 com posite laminates are observed.