Martyn J Pavier

Determination of T-stress from finite element analysis for mode I and mixed mode I/II loading

The elastic T-stress has been recognised as a measure of constraint around the tip of a crack in contained yielding problems. A review of the literature indicates that most methods for obtaining T are confined to simple geometry and loading configurations. This paper explores direct use of finite element analysis for calculating T. It is shown that for mode I more reliable results with less mesh refinement can be achieved if crack flank nodal displacements are used. Methods are also suggested for calculating T for any mixed mode I/II loading without having to calculate stress intensity factors. There is good agreement between the results from the proposed methods and analytical results. T-stress is determined for a test configuration designed to investigate brittle and ductile fracture in mixed mode loading. It is shown that in shear loading of a cracked specimen T vanishes only when a truly antisymmetric field of deformation is provided. However this rarely happens in practice and the presence of T in shear is often inevitable. It is shown that for some cases the magnitude of T in shear is much more than that for tension. The effect of crack length is also investigated.

Finite element micromechanical modelling of yield and collapse behaviour of metal matrix composites

The initial yield and collapse behaviour of fibre reinforced metal matrix composites (MMCs) have been investigated using finite element micro-mechanical models. Initial yield occurs as the loading on the MMC is increased until the most heavily loaded point within the matrix reaches the yield stress. Collapse occurs when the MMC is unable to support a higher load. The results of this work show that loads to cause collapse of MMCs are higher than those to cause first yield, particularly when the effect of residual stress arising from manufacture is included in the analysis. Initial yield and collapse envelopes have been generated for a Silicon Carbide-Titanium MMC for biaxial and shear loading. These envelopes include the effect of residual stress and also various interface conditions between the fibre and matrix: either perfectly bonded or de-bonded, with and without friction. An analytical micro-mechanical model has been developed using the method of cells to predict the collapse behaviour. The results of the analytical model compare reasonably well with those of the finite element method. Using the analytical model the effect of varying the fibre volume fraction on the collapse behaviour has been studied.

Experimental Techniques for the Investigation of the Effects of Impact Damage on Carbon-Fibre Composites

Abstract Low-velocity impact damage to composite laminates causes a complicated pattern of matrix cracks, fibre cracks and delamination. A significant effect of this damage is to reduce the strength of the laminate, particularly in compression; however, owing to the complexity of the damage the precise mechanisms controlling the strength reduction are unclear. In this paper a technique is described for replicating impact damage artificially by including PTFE film delaminants and cut plies during lay-up. Comparisons between real and artificially reproduced damage are made to demonstrate the validity of the technique. Experimental methods of X-radiography and resin injection are developed to allow the mechanisms controlling strength reduction to be assessed, both under tensile and compressive loading. Under tensile load the reduction in strength caused by impact damage is found to be entirely due to fibre cracks and may be estimated by using a net-section calculation. Meanwhile under compression, strength reduction is largely caused by the redistribution of stress resulting from buckling of delaminated plies and may be predicted by calculating stresses in the undelaminated part of the laminate.

Effect of residual stress around cold worked holes on fracture under superimposed mechanical load

Abstract Cold working is one method used to enhance the fatigue life of holes in aerospace structures. The method introduces a compressive stress field in the material around the hole and this reduces the tendency for fatigue cracks to initiate and grow under superimposed cyclic mechanical load. To include the benefit of cold working in design the stress intensity factors must be evaluated for cracks growing from the hole edge. Two-dimensional (2D) finite element analyses have been carried out to quantify the residual stresses surrounding the cold worked hole. These residual stresses have been used in a finite element calculation of the effective stress intensity factor for cracks emanating from the hole edge normal to the loading direction. The results of the 2D analysis have been compared with those derived using a weight function method. The weight function results have been shown always to underestimate the stress intensity factor. A three-dimensional (3D) FEA has been carried out using the same technique for stress intensity factor evaluation to investigate the effect of through thickness variation of residual stress. Stress intensity factors calculated with the 3D analysis are generally higher than those calculated using the 2D analysis.

A finite element simulation of the cold working process for fastener holes

Two-dimensional axisymmetric finite element simulations have been conducted for the cold working of a fastener hole in an aluminium plate. The simulation models the actual cold working process where an oversize mandrel is pulled through the fastener hole. The results of the simulation are compared with a simplified finite element model where the cold working process is reduced to applying a uniform radial expansion to the hole edge. It is shown that substantial differences exist between the finite element simulations; specifically, the simulation of the actual process shows tensile residual radial stresses on the surface of the plate after cold working whereas the simplified simulation shows only compressive ones. Further comparisons are made for the axial deformation of the plate by using the results of an experimental measurement of the surface profile around a cold worked hole. There is good agreement between the finite element and experimental results. The results of this work show that accurate simulations of cold working are necessary if predicted residual stresses are to be used to assess fatigue life.

On the consequences of T-stress in elastic brittle fracture

By using a generalized maximum tensile stress (MTS) criterion to predict onset of brittle fracture, it is shown that the presence of T-stress can have a significant effect on mode I and mode II toughness. The most prominent influence of T-stress on toughness occurs for mode II conditions. However, earlier tests concentrated on near mode I and results were masked by scatter. New experiments, using combinations of mode II loading and T-stress, support conclusively the generalized MTS criterion. This criterion is shown to be very robust and applicable to predicting probability of brittle failure. The criterion is also relevant to other experimental results where combinations of mode II loading with high values of T-stress can lead to values of mode II toughness that are greater than mode I toughness.

Mode I cracks subjected to large T-stresses

There are several criteria for predicting brittle fracture in mode I and mixed mode loading. In this paper, the modified maximum tangential stress criterion originally proposed for mixed mode loading, is employed to study theoretically brittle fracture for mode I cracks. In particular, the effect of the non-singular term of stress, often known as the T-stress, on the angle of initiation of fracture and the onset of crack growth is explored. The T-stress component of the tangential stress vanishes along the crack line. Therefore, it is often postulated for linear elastic materials that the effect of T-stress on mode I brittle fracture can be ignored. However, it is shown here that the maximum tangential stress is no longer along the line of initial crack when the T-stress exceeds a critical value. Thus, a deviation in the angle of initiation of fracture can be expected for specimens having a large T-stress. It is shown that the deviation angle increases for larger values of T-stress. Theoretical results show that the apparent fracture toughness decreases significantly when a deviation in angle occurs. Earlier experimental results are used to corroborate the findings. The effect of large T-stresses is also explored for a crack specimen undergoing moderate scale yielding. The elastic-plastic investigation is conducted using finite element analysis. The finite element results reveal a similar deviation in the angle of maximum tangential stress for small to moderate scale yielding.

The effect of delamination geometry on the compressive failure of composite laminates

One of the causes of a reduction in the compressive strength of a composite material containing delaminations is the buckling of the delaminated plies. To understand the effect of delamination geometry on the compressive behaviour of laminated composite materials, compression tests were carried out on glass-fibre-reinforced plastic (GRP) test specimens containing artificial delaminations of various geometry, created by inserting PTFE film into the laminate during lay-up. Finite-element modelling was also carried out to gain further understanding of the mechanisms of compressive failure. Good agreement between finite-element predictions and experimental measurements were found for the whole range of delamination geometries that were tested. Finite-element and simple closed-form models were also developed for delaminated panels with isotropic properties. This enabled a study of the effect of delamination geometry on compressive failure without the complicating effects of orthotropic material properties. The results of this study can be used to derive a graph of non-dimensional failure load versus non-dimensional failure stress, where the results for any one delamination geometry superimpose on those for all others.

Fatigue crack growth from plain and cold expanded holes in aluminium alloys

Fatigue crack growth in open holes in aluminium alloys 2024-T351 and 2650 was investigated. Tests were carried out using plates containing plain holes and cold expanded holes in aluminium. The tests explored the influence of the applied stress, the ratio of the minimum to the maximum applied stress, R, and crack closure. Longer fatigue lives of specimens with cold expanded holes were obtained provided that the applied load ratio was less than 0.7, and the maximum applied stress was less than 0.5 of the yield strength. The decrease in fatigue crack growth in cold-expanded specimens was related to higher crack opening stresses which is a consequence of the presence of compressive residual stresses arising from cold expansion. Fatigue crack growth rates were described as a function of an effective stress intensity factor, which was determined using measured crack opening stress. Measured crack opening stress was also compared with opening stress determined from fatigue crack growth rates.

Analytical and finite element predictions of residual stresses in cold worked fastener holes

Abstract Two-dimensional finite element (FE) studies, for plane stress, plane strain and axisymmetric conditions, were conducted to simulate 4 per cent cold working of a 6.35 mm diameter hole in a 6 mm thick plate of 2024 T 351 aluminium alloy. The simulations were used to assess the influence of strain hardening, the role of reversed yielding and through-thickness residual stress distributions. Experiments were also conducted to determine the tensile and compressive stress-strain response of the aluminium alloy, revealing a pronounced Bauschinger effect and non-linear strain hardening in compression. The FE simulations and results from several earlier analytical models were compared and substantial differnces found in the region of reversed yielding. Approximations used to model the compressive deformation behaviour of the material overestimate the compressive residual stresses at the hole edge. From the axisymmetric FE model a residual stress gradient through the plate thickness was found. The plane stress and plane strain assumptions used in the earlier analytical models did not satisfactorily approximate the three-dimensional residual stress fields obtained from the FE simulations.