Plane strain crack toughness testing of high strength metallic materials.

It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.

Crack tip finite elements are unnecessary

The plane strain elastic-plastic state at a crack tip is determined for compact tension, bend, double edge-cracked and centre-cracked specimens using a finite element method with triangular constant-strain elements. The solutions are found to differ by 10 to 30 per cent at the ASTM-limit as regards fracture surface displacement, normal stress and plastic zone size. In order to bring the boundary layer solution for the crack problem into agreement with the solution for a specific specimen one has to modify this solution. The modification consists of an addition to the boundary tractions for the boundary layer problem of tractions corresponding to the non-singular, constant second term in a series expansion of the normal stress parallel to the crack plane.

Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials

A finite element technique for determination of elastic crack tip stress intensity factors is presented. The method, based on the energy release rate, requires no special crack tip elements. Further, the solution for only a single crack length is required, and the crack is 'advanced' by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis. The promising straightforward extension of the method to general three-dimensional crack configurations is presented and contrasted with the practical impossibility of conventional energy methods.

A stiffness derivative finite element technique for determination of crack tip stress intensity factors

A multidomain boundary element formulation for the analysis of general two-dimensional plane strain/stress crack problems is presented. The numerical results were accurate and efficient. The analyses were performed using traction singular quater-point boundary elements on each side of the crack tip(s) with and without transition elements. Traction singular quarter-point boundary elements contain the correct √r displacement and 1/√r traction variations at the crack tip. Transition elements are appended to the traction singular elements to model the √r displacement variation. The 1/√r traction singularity is not represented with these elements. Current research studies for the crack propagation analysis of quasi-static and fatigue fracture problems are discussed.

Two‐dimensional stress intensity factor computations using the boundary element method

Rectangular Tensile Sheet With Symmetric Edge Cracks

A technique combining the advantages of conformal mapping and boundary collocation arguments for calculating stress intensity factors for cracks in plane problems is described. The difficulty of finding the mapping function on a rigidly prescribed parameter region is avoided at the expense of using boundary collocation methods on part of the boundary. Conventional collocation arguments are modified by prescribing stress, force, and moment conditions in a least-square collocation sense. These pseudo-redundant conditions provide a reasonable basis for estimation of the effects of inaccuracy of the boundary conditions. The technique is applied to the problem of a circular disk with an internal crack under a loading of external hydrostatic tension.

A modified mapping-collocation technique for accurate calculation of stress intensity factors

: The stress intensity factors for single edge cracks in rectangular tensile sheet are studied by using a complex variable form of analysis. The results for deep cracks show a considerable increase in the intensity factors as compared to the case of symmetric edge cracks. Accurate numerical values of the stress intensity factors for the appropriate range of parameters are included. (Author)

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Single Edge Crack in Rectangular Tensile Sheet

The rate of change of the elastic strain energy with respect to notch depth is considered for edge notches or slots with a finite constant radius, ρ, at the tip. Numerical results are obtained for an edge slot in a semi-infinite sheet under tension. It is found that the slot can be considered as a crack of length L + 1.18 ρ for this purpose. In finite sheet, this result is valid for small L/ρ ratios.

Oscar L. Bowie

Papers

Rectangular Tensile Sheet With Symmetric Edge Cracks

A modified mapping-collocation technique for accurate calculation of stress intensity factors

Single Edge Crack in Rectangular Tensile Sheet

The effective crack length of an edge slot in a semi-infinite sheet under tension

Symmetric Edge Cracks in Tensile Sheet With Constrained Ends