S.K. Choi

Stress intensity factors for semi-circular specimens under three-point bending

Abstract The semi-circular specimen under three-point bending technique is a versatile, cost-effective and reliable method for determining the mixed-mode (I and II) fracture toughness envelope of rocks. However, existing numerical results on the stress intensity factor variation with specimen geometry are very limited. This study extends previous numerical work to cover a wide range of possible specimen geometries of experimental interest. From this, a number of observations relevant to the practical use of this technique are discussed. Analytical functions are then provided as an approximation to the mode I variation of the stress intensity factors.

Comparison between various displacement-based stress intensity factor computation techniques

The computation of the stress intensity factor at a crack tip can be determined from the nodal displacements along the crack face. Amongst the existing techniques available are the Displacement Correlation Technique (DCT), the Quarter-Point Displacement Technique (QPDT) and the Displacement Extrapolation Technique (DET). As each of these techniques are popular in general LEFM analysis, an evaluation of their relative performances would seem appropriate. Previously, only limited comparisons have been made. In this paper the comparison is made on the basis of extensive numerical analysis. In addition two new variants to the DET are introduced and shown to be more efficient computationally.The results indicate that the QPDT is generally more accurate and consistent in performance than the DCT. The DET, however, exhibited some erratic characteristics. Detailed examinations revealed that the linear regression analysis employed in the DET for the extrapolation is highly sensitive to the nodal displacement distribution. Both the new variant DETs exhibited much more consistent behaviour.

A finite element code for fracture propagation analysis within elasto-plastic continuum

A new code for the simulation of mixed-mode fracture propagation within a body deforming elasto-plastically is presented in this paper. The analysis is fully automated in that it requires no user interaction. An automatic local remeshing technique is developed based on the window remeshing technique of Murti [Numerical fracture mechanics using finite element methods. Ph.D.Thesis, University of New South Wales (1986)]. This algorithm ensures that proper element geometries are maintained in the crack tip vicinity and that reasonable shaped elements are preserved further away from the crack tip. A new approach was developed to predict the fracture trajectory under load or displacement control. This new approach is particularly suited to applications where the applied loads or displacements are the controlling factors rather than the crack extension. The code incorporates recently developed profile reduction and mesh rezoning techniques for increased efficiency. The capability of this new code is demonstrated by application to a number of practical problems.

An improved numerical inverse isoparametric mapping technique for 2D mesh rezoning

Abstract Mesh rezoning is essential in some finite element analyses. Of the existing techniques, inverse isoparametric mapping ( x, y ) → ( eη ) is a mathematically sound and accurate approach. A survey of existing techniques reveals that the predefined line technique proposed by Murti and Valliappan [Comput. Structures22, 1011–1021 (1986)] is the most efficient for quadratic elements. A new, robust and more efficient implementation of the predefined line technique is presented in tins paper. Extensions of the technique to encompass triangles and collapsed quadrilaterals are described. A detailed examination of its solution convergence rate and its dependence on element distortion is conducted to better understand the techniques performance. Its implementation for other than quadratic elements is also outlined. A numerical example is included to demonstrate the efficiency and effectiveness of this improved technique.

The use of transition elements

Abstract Since the introduction of transition elements for crack tip singularity modelling, a number of opinions have been expressed regarding their application and performance. In particular, conflicting proposals concerning optimal transition element size have been suggested. In order to resolve the anomaly, a critical examination of these proposals was made. Consequently, several inconsistencies with regard to the derivation of the mid-node location of these transition elements were revealed. The effects of these inconsistencies were examined numerically and the accuracy of the computed stress intensity factors was compared with the original formulation of Lynn and Ingraffea. The results of the numerical analyses appear to show no discernible optimal transition element size.

A comparison of algorithms for profile reduction of sparse matrices

A comparison is undertaken of a number of algorithms for profile reduction of sparse symmetric banded positive definite matrices based on results reported in the literature, with regard to the profile reduction and the execution time. A simple methodology is also proposed to facilitate the selection of appropriate profile reduction algorithms for a given application. This methodology takes into account the computational time required by the algorithm and the estimated time required for factorization of the global stiffness matrix based on the resulting root-mean-square wavefront. A number of conclusions pertaining to the performance of these algorithms and to their appropriate applications are discussed. In the context of discrete crack propagation analyses, it can be concluded that the MPG algorithm is preferred, followed by the Sloan algorithm.