Generalized displacement correlation method for estimating stress intensity factors

Abstract

Summary:Conventional displacement-based methods for estimating stress intensity factors require special quarter-point finite elements in the first layer of elements around the fracture tip and substantial near-tip region mesh refinement. This paper presents a generalized form of the displacement correlation method (the GDC method), which can use any linear or quadratic finite element type with homogeneous meshing without local refinement. These two features are critical for modeling dynamic fracture propagation problems where locations of fractures are not known a priori. Because regular finite elements' shape functions do not include the square-root terms, which are required for accurately representing the near-tip displacement field, the GDC method is enriched via a correction multiplier term. This paper develops the formulation of the GDC method and includes a number of numerical examples, especially those consisting of multiple interacting fractures. We find that the proposed method using quadratic elements is accurate for mode-I and mode-II fracturing, including for very coarse meshes. An alternative formulation using linear elements is also demonstrated to be accurate for mode-I fracturing, and acceptable mode-II results for most engineering applications can be obtained with appropriate mesh refinement, which remains considerably less than that required by most other methods for estimating stress intensities.

A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

“…• The Generalized Displacement Correlation method, recently developed by Fu et al (2012) for the FEM, uses the displacement solution at crack surfaces for an explicit calculation of the mixed mode SIF.…”

Stress intensity factors for circumferential through‐wall cracks in thin‐walled cylindrical shells subjected to tension and torsion

“…Because of the discrepancy observed in Figure , an assessment of the two methods for obtaining the stress intensity factor is required. When quarter‐point elements are used at the crack tip, several authors advocate the use of the quarter‐point displacement technique (QPDT) or the DCT instead of the displacement extrapolation technique . These techniques use simple mathematical expressions to estimate the stress intensity factor directly from the displacement of the quarter‐point node, or as an extrapolation from the two first nodes away from the crack tip only.…”

“…When quarter-point elements 44,45 are used at the crack tip, several authors advocate the use of the quarter-point displacement technique (QPDT) 45,48 or the DCT 48 instead of the displacement extrapolation technique. 43,[48][49][50][51] These techniques use simple mathematical expressions to estimate the stress intensity factor directly from the displacement of the quarterpoint node, or as an extrapolation from the two first nodes away from the crack tip only. For the case of R m /t = 40 and θ = 40°, the three techniques are compared for a mesh with very small quarterpoint elements (radial length = a/160) at the crack tip in Figure 11 and for a mesh with larger quarter-point elements (radial length = a/12) in Figure 12.…”

Simulation of Hydraulic Fracture Networks in Three Dimensions Utilizing Massively Parallel Computing Resources

“…In the case of field scale studies, the mesh resolution required to resolve the stress field near the tip of a fracture is unattainable without some form of automatic mesh refinement near the tip. In cases where this is the case, methods may be used to estimate the stress field as given in [7]. If no such method is utilized, then a stress criteria for face rupture will likely be a compressive stress, as the unbounded stress field is dramatically underestimated by the resolution.…”