The Journal of Strain Analysis for Engineering Design

This paper presents an efficient numerical weight function technique, based on the boundary element method, for the determination of stress intensity factors of curved crack fronts in three-dimensional finite bodies. The weight functions are based on the notion of fundamental fields, which are defined from point loads acting at the crack front. A regularization procedure that incorporates the fundamental fields of the penny-shaped crack in an infinite elastic body is used to obtain weight functions for a penny-shaped edge crack in a cylindrical bar. Stress intensity factors for elliptical crack fronts can be generated by employing the properties of the fundamental fields at the load points on the crack front.

Stress intensity factor variations along the crack-fronts are presented when these finite cracked geometries are subjected to various loads that produce mode I deformation of the crack faces. Wherever possible, solutions are compared with values published in the literature and are found to be in good agreement.

The theory of an automated fringe pattern analysis using the spatial-carrier phase shifting method for moiré interferometry is presented. The automated method is shown to provide a fast and accurate strain measurement over the whole field. Measurements on a brass specimen and a tapered laminated composite specimen are shown to highlight the efficiency and the capability of this technique for moiré interferometry. The filtering technique used to remove noise from the required displacement function is also presented.

A thermo-elastic-plastic model in conjunction with an experimental flow stress-strain curve, is applied to a cold extrusion process. The flow stress is considered as a function of strain, strain rate, and temperature to simulate a more realistic situation. A modified iteration method is proposed to a linear piecewise continuous model to increase the accuracy and avoid divergence. The strain is calculated by Taylor's series expansion and is associated with its corresponding convergence criteria; an available scheme for the calculation of the strain rate is thus involved. In addition, a least squared method is proposed to check loading or unloading situations. An extrusion experiment is then made and the simulated loading force compared with the experimental loading force is very satisfactory.

The creep rupture behaviour and the accuracy of the measured strains for the uniaxial tensile testpiece with extensomenter ridges have been studied by use of the Continuum Damage Mechanics (CDM)-based creep finite element solver, DAMAGE XX. Multi-axial creep constitutive equations with multi-damage state variables were used in the computer modelling process. The procedure models the development of failed regions of the testpiece due to the stress concentration in the transition regions from the parallel portion to the extensometer ridges. The accuracy of the creep strain measurement for the testpiece was investigated with the variation of time, gauge length, and stress levels. The computer modelling results show that although the error of the creep strain measurement is a fuction of time, it is dependent upon the stress sensitivity of the material law. For power-law material the maximum error is invariant of the normalized stress, but dependent upon the value of n; and for the sinh-based material law the maximum error is dependent upon the magnitude of the applied stress.

The stress intensity factor along the front of a semi-elliptical surface flaw subjected to tension or bending loading is calculated by means of a finite element analysis carried out with twenty node isoparametric three-dimensional elements. The stress and strain singular behaviour in the vicinity of the defect is modelled by moving the finite element midside nodes near the crack front to quarter-point positions. An extensive analysis is carried out by assuming different values of the flaw aspect ratio (0.2., 0.4, 0.6, 0.8, and 1.0), while the relative depth of the crack's deepest point is varied from 0.1 to 0.4. As regards the crack configurations previously tackled in the literature, the agreement between the results of the present study and those obtained by other authors is quite satisfactory, especially for small relative crack depths.

A simplified treatment is presented for the analysis of tubular specimens subject to in-phase tension-torsion loads in the elasto-plastic regime. Use is made of a hardening function readily obtainable from the uniaxial cyclic stress-strain curve and hysteresis loops. Expressions are given for incremental as well as deformation theories of plasticity. The reversals of loading are modelled by referring the flow equations to the point of reversal and calculating distances from the point of reversal using a yield critertion. The method has been used to predict the deformation response of in-phase tests on an En15R steel, and comparisons with experimental data are provided. The material exhibited a non-Masing type behaviour. A power law rule is developed for predicting multiaxial cyclic response from uniaxial data by incorporating a hysteretic strain hardening exponent.

The paper presents an effective method for achieving the optimum design of composite structures subjected to multiple displacement constraints. Based on the optimality criterion method and some approximate engineering assumptions, this paper introduces a simplified expression relating the design variables to Lagrange multipliers, which correspond to displacement constraints. Therefore, the optimal design variables are derived from a smaller number of unknown coefficients. Thus the computational efficiency is greatly enhanced. Furthermore, the multilevel optimization technique is adopted. The optimum design variables are obtained in system level optimization. For more detailed design the ply thicknesses of a composite plate are adjusted in component level optimization by using the maximum strain energy criterion. A cantilever composite beam, subjected to strength and multiple displacement constraints, is studied as the illustrative example. The computational results indicate the efficiency of the method.