A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral

Applied Solid Mechanics Section, Battelle's Columbus Laboratories, Columbus, OH 43201, U.S.A.
Engineering Fracture Mechanics (Impact Factor: 1.77). 01/1977; 9(4):931-938. DOI: 10.1016/0013-7944(77)90013-3


An efficient technique for evaluating stress intensity factors is presented. The method, based on the crack closure integral, can be used with a constant strain finite element stress analysis and a coarse grid. The technique also permits evaluation of both Mode I and Mode II stress intensity factors from the results of a single analysis. Example computations are performed for a double cantilever beam test specimen, a finite width strip with a central crack, and a pin loaded circular hole with radial cracks. Close agreement between numerical results given by this approach and reference solutions were found in all cases.

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    • "A finite element mesh of 8-node, isoparametric quadrilateral elements is constructed in ABAQUS to represent the center-cracked SMA specimen with a finer mesh density in the crack growth path in front of the the crack-tip. The VCCT capability of ABAQUS, which is an extension of the classical crack-closure technique based on Irwin's crack closure integral [22] [34] [23] [39], is employed to calculate the crack-tip energy release rate. "
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    ABSTRACT: A finite element analysis of crack growth is carried out in shape memory alloys subjected to thermal variations under plane strain, mode I, constant applied loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate which is modeled using the virtual crack closure technique. The load level, applied at a high temperature at which the austenite phase is stable, is assumed sufficiently low so that the resulting crack-tip energy release rate is smaller than the critical value but sufficiently high so that the critical value is reached during cooling, initiating crack growth [Baxevanis and Lagoudas, 2015. Int. J. Fract. 191, 191–213]. Stable crack growth is observed, mainly associated with the shielding effect of the transformed material left in the wake of the advancing crack. Results pertaining to the near-tip mechanical fields and fracture toughness are presented and their sensitivity to phase transformation metrics and bias load levels is investigated.
    Full-text · Article · Jan 2016
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    • "The incremental response of the material inside the fully transformed zone surrounding the crack tip at all times is linear elastic, and the fields are characterized by an unknown crack-tip energy release rate, G I . The VCCT is employed in the analysis for computing G I [33] [34] [35]. VCCT is an extension of the classical crack closure method based on the Irwin's crack closure integral [36]. "
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    ABSTRACT: The effect of thermomechanically-induced phase transformation on the driving force for crack growth in polycrystalline shape memory alloys is analyzed in an infinite center-cracked plate subjected to a thermal actuation cycle under mechanical load in plain strain. Finite element calculations are carried out to determine the mechanical fields near the static crack and the crack-tip energy release rate using the virtual crack closure technique. A substantial increase of the energy release rate–an order of magnitude for some material systems–is observed during the thermal cycle due to the stress redistribution induced by large scale phase transformation. Thus, phase transformation occurring due to thermal variations under mechanical load may result in crack growth if the crack-tip energy release rate reaches a material specific critical value.
    Full-text · Article · Jan 2016 · Journal of the Mechanics and Physics of Solids
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    • "Traditionally, the study of delaminations is split into two distinct phenomena: the initiation of the crack and the ensuing propagation, where the latter is based on formulae of a pre-existing crack. The virtual crack closure technique (VCCT) proposed by Rybicki and Kanninen [4] is often used for predicting delamination growth. However, in the finite element method (FEM), VCCT results are dependent on the mesh in front of the crack tip and a pre-defined location of a crack is required. "
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    ABSTRACT: The Refined Zigzag Theory is applied to the modeling of delaminations in laminated composites. The commonly used cohesive zone approach is adapted for use within a continuum mechanics model, and then used to predict the onset and propagation of delamination in five cross-ply composite beams. The resin-rich area between individual composite plies is modeled explicitly using thin, discrete layers with isotropic material properties. A damage model is applied to these resinrich layers to enable tracking of delamination propagation. The displacement jump across the damaged interfacial resin layer is captured using the zigzag function of the Refined Zigzag Theory. The overall model predicts the initiation of delamination to within 8% compared to experimental results and the load drop after propagation is represented accurately.
    Full-text · Technical Report · Oct 2015
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