On stress intensity factor computation from the quarter‐point element displacements

Abstract

SUMMARYIn conjunction with the quarter-point element, a wide range of stress intensity factor computation techniques may be employed. Of these, the displacement correlation technique (DCT) and the quarterpoint displacement technique (QPDT) have been in common use. It has been suggested by various investigators that the DCT is more rational in formulation and should therefore be more accurate than the QPDT. However, published numerical studies provide conflicting results on the relative performance of either technique. To resolve this anomaly, this study provides a detailed investigation on the DCT and QPDT performance. On the basis of considering the second term in Westergaard's expression and supported by numerical experiments, it is concluded that the QPDT would generally perform better than the DCT.

Patch repair design optimisation for fracture and fatigue improvements of cracked plates

“…In the present study the SIFs for Mode I and Mode II are evaluated by using the displacements correlation technique (Lim et al, 1992) applied to quarter point finite elements nodal results. By writing the displacement fields for a crack under Mode I or Mode II loading (Lim et al, 1992):…”

Generalized displacement correlation method for estimating stress intensity factors

“…For infinitesimal elements, this mechanism can eliminate the error induced by the second source of error, but not the first. A similar phenomenon exist for the original displacement-based methods: Numerous studies have observed that errors of these methods do not converge to zero as the near-tip mesh is refined [12,13,18,19,22] and an explanation was offered by Harrop [24].…”

“…This limitation of the quarter-point method was described by Tracey [10] but has largely been neglected, as it does not apply to the typical loading conditions in mechanical engineering, where crack surface tractions are absent. Although this limitation of the quarter-point displacement method does not lead to inaccuracies in many studies comparing these two methods in the context of mechanical engineering [12,13,19,22], it is highly deleterious if the method is to be used for hydraulic fracturing modeling or similar problems. The displacement extrapolation method suffers similarly since the loading scenario shown in case (c) of Figure 1 is not supported in the assumptions underlying that method.…”

“…These methods and others have been compared in a number of studies [e.g. 5,[11][12][13][14]. One of the most significant advantages of the displacement-based methods is the simple formulation.…”

Numerical buckling analysis of compressed or tensioned cracked thin plates

“…In the latter theoretical cracked configuration, the mode I (K I ) and mode II (K II ) SIFs can be expressed as [25] K I = σ 0 · cos 2 θ · √ πa, In the present study both mode I and mode II SIFs are evaluated by using the displacement correlation technique [26] applied to quarter-point finite element nodal results (evaluated by linear analyses). Nevertheless, better accuracy can be achieved by considering the mean value of the displacements measured at points near the crack tip (i.e.…”