Showing papers in "Journal of Strain Analysis for Engineering Design in 2001"

Moiré interferometry for engineering mechanics: Current practices and future developments

Abstract: In the past decade, the optical method called moire interferometry has matured rapidly to emerge as an invaluable tool, proved by many industrial and scientific applications. It has been applied to numerous problems in engineering mechanics. It measures in-plane displacement fields with high sensitivity and high spatial resolution. This paper reviews current practices of moire interferometry and its extensions. Applications in diverse fields are addressed to demonstrate the wide applicability of the method, especially the recent applications for thermal deformation analyses of microelectronics devices. Speculation on future developments and practices is presented.

Elasto-plastic stress and strain behaviour at notch roots under monotonic and cyclic loadings:

Abstract: Notch deformation behaviour under monotonic and cyclic loading conditions was investigated using circumferentially notched round bar and double-notched flat plate geometries, each with two different notch concentration factors. Notch strains for the double-notched plate geometry were measured with the use of miniature strain gauges bonded to specimens made of a vanadium-based microalloyed steel. Elastic as well as elasto-plastic finite element analyses of the two geometries were performed. Notch root strains and stresses were predicted by employing the linear rule, Neuber's rule and Glinka's rule relationships under both monotonic and cyclic loading conditions. The predicted results are compared with those from elastic-plastic finite element analyses and strain gauge measurements. Effects of notch constraint and the material stress-strain curve on the notch root stress and strain predictions are also discussed.

Synchrotron X-ray residual strain scanning of a friction stir weld

Abstract: Synchrotron X-ray strain scanning has been used to determine the residual stress distribution over the cross-sectional area of a friction stir weld across an I-section made of extruded aluminium al...

Slip initiation and progression in helical armouring layers of unbonded flexible pipes and its effect on pipe bending behaviour

Abstract: Comparatively straightforward analytical formulations are given for determining the bending moment-curvature relationship for a helical layer in unbonded flexible pipes. The approach takes into account the non-linearity of the layer caused by sliding of individual helical elements between the surrounding layers. Bending stiffness of a helical layer is found to be a function of bending curvature, interlayer friction coefficients and interlayer contact pressures. The analysis presented here is based on the Coulomb friction model and is derived using the principle of virtual work. Theoretical results for a typical unbonded flexible pipe using the non-linear formulation for helical layers are compared with experimental data.

Macroscopic fretting variables in a splined coupling under combined torque and axial load

Abstract: A three-dimensional study of frictional contact in a helical splined coupling for the assessment of macroscopic fretting variables is presented. The study is based on an experimentally validated finite element model of the coupling under combined torque and axial loads. The effect of axial profile modification for reduced contact stresses in spline teeth and the effect of friction coefficient are considered. The motivation for the work is the need for representative information about fretting variable distributions in splined couplings for the development and application of simplified fretting test configurations.

Mechanical behaviour prediction in plain weave composites

Abstract: The correct application of woven fabric composites requires an accurate knowledge of their mechanical behaviour, in terms of both global stiffness and strength. The aim of this paper is the development of a finite element (FE) approach to the description of the mechanical response starting from the actual mesostructure of the material. Experimental observations identified the unit cell on the basis of symmetry considerations. Different stacking configurations of the unit cell were considered. A global-local procedure was used to reduce the computational effort without losing computational accuracy. A damage model of the material under tensile load was defined and implemented in the FE code. A comparison with experimental stress-strain curves validates the approach proposed.

Thermal effects on the development of plastic zones in thin axisymmetric plates

Abstract: A simple thermoelastic-plastic problem is solved analytically to show a thermal effect on the development of plastic zones in thin plates. The temperature field is assumed to be uniform but monotonically varying with the time. The material of the plate obeys the von Mises yield criterion with a constant yield stress. It is shown that a negligible rise of temperature may lead to a significant growth of the plastic zone. Even though stress analysis only is needed in the plastic zone to illustrate this effect, a complete closed-form solution to the problem is given.

Modelling of rotors with three-dimensional solid finite elements:

Abstract: A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in c...

Vibratory stress relief - an investigation of the torsional stress effect in welded shafts

Abstract: In this study the effect of torsional vibration on residual stresses was investigated. Three types of shaft specimen were processed, namely (a) a homogeneous shaft, (b) a shaft welded on a circumferential line and (c) a spot-welded shaft. The first two types of shaft showed some redistribution in the residual stresses under applied torsional loads. On the spot-welded shafts the residual stresses were found to decrease significantly at a very low level of vibration induced stress.

An assessment of ASME III and CEN TC54 methods of determining plastic and limit loads for pressure system components

Abstract: The paper considers three different pressure system components—a nozzle in a torisphere subjected to moment loading, a piping branch junction subjected to out-of-plane moment loading and an unpierced torispherical head under pressure loading. The results from non-linear, finite element, stress analyses are used to compare the limit and plastic loads obtained using the ASME III twice-elastic-slope and the CEN TC54 tangent intersection definitions. The results highlight the difficulties involved in quantifying limit loads and plastic loads for such components.

Tubular bonded joint under torsion: Theoretical analysis and optimization for uniform torsional strength:

Abstract: The paper analyses the problem of torsion in an adhesive bonded tubular joint. The constitutive, equilibrium and compatibility equations were used to obtain the stress field in the adhesive. The analysis confirms that the maximum stresses are attained at the ends of the adhesive and that the peak of maximum stress is reached at the end of the stiffer tube and does not tend to zero as the adhesive length approaches infinity.A special type of tubular joint can be produced by modifying the joint profile, thus ensuring that the stress field in the adhesive is constant and thereby optimizing the tubular joint for uniform torsional strength. This result is of considerable practical utility and makes it possible to produce adhesive bonded joints which are both lighter and stronger under torsion. Finally, some suggestions for the joint design are presented.

Determination of the stress distribution in foam-cored sandwich construction composite tee joints

Abstract: The stresses in sandwich construction tee joints are determined using both experimental and numerical techniques. The features of interest in the tee joint are the use of a boundary angle laminate which reinforces the connection between the two component parts of the tee joint, the use of a fillet at the connection and the effect of any gap at the join. The experimental approach is thermoelastic stress analysis (TSA) based on the use of the SPATE (stress pattern analysis by thermal emissions) equipment. Techniques for calibrating the constituent parts of the joint are described so that quantitative stress values can be obtained from the TSA. A detailed finite element study of the tee joints is also carried out, the results of which are compared with the experimental data.

Buckling of a spherical shell embedded in an elastic medium loaded by a far-field hydrostatic pressure

Abstract: Elastic buckling of a spherical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure is analysed using the energy method together with a Rayleigh—Ritz trial function. For simplicity, only axisymmetric deformations are considered and inextensional buckling is assumed. The strains within the structure that are pre-critical are assumed to be small for the linear theory to be applicable. An expression is derived relating the pressure load to the buckling mode number, from which the upper-bound critical load can be determined. It is found that the presence of the surrounding elastic medium increases the critical load of the shell and the corresponding buckling mode number. However, the results also show that the strain of the shell at the point of instability may not be small for typical values of material and geometric constants.

High-speed fracture studies on bimaterial interfaces using photoelasticity—a review:

Abstract: Dynamic photoelasticity and high-speed photography have been combined to study fracture of bimaterial interfaces in the subsonic and intersonic regimes. The response of isochromatic fringes to various interface fracture parameters is investigated. Next, a series of experiments is conducted with specially designed specimen geometries under different loading conditions to encompass the whole range of interfacial crack propagation behaviours. The photoelastic data obtained from these experiments is carefully analysed to obtain the crack velocity, complex stress intensity factor, mode mixity and dynamic energy release rate. Finally a fracture criterion in the subsonic regime is proposed and validated with the experimental results.

Development of new inverse boundary element techniques in photoelasticity

Abstract: This paper presents a number of possible algorithms for inverse boundary element (BE) techniques applied to photoelastic analysis. The BE technique is shown to be an ideal companion to photoelastic analysis since, unlike the finite element (FE) method, the interior solutions can be represented by unconnected points rather than by discretized elements. From the photoelastic principal stress information obtained at a sufficient number of internal points, the unknown boundary conditions can be reconstructed using the inverse boundary element method (BEM). The inverse BE theory and numerical formulation are presented for problems involving Cartesian stress components and are then extended to photoelastic stress analysis. The inverse BE approach follows two stages. In stage 1, the photoelastic stress measurements of the differences in principal stresses and their directions at the interior points are used to compute the unknown boundary conditions on the surface. In stage 2, the individual stress components are calculated by the forward BEM using the computed boundary conditions from stage 1. The effect of scatter of the experimental results is also included in the analysis. A number of examples are presented in this paper and are shown to be in excellent agreement with other solutions.

The influence of punch blunting on the elastic indentation response

Abstract: Elastic solutions of a family of axisymmetric problems concerning frictionless contact between a rigid punch and a semi-infinite substrate are considered using the method of Green and Zerna and of Collins. The analysis is relevant to the interpretation of experimental results in materials indentation testing, e.g. when substrate properties need to be determined from load-displacement traces, and precise information about the indenter tip shape is crucial. Commonly used solutions for ideal punch shapes, e.g. those having spherical or conical tips, may only be viewed as approximations since, in practice, indenter tips are neither perfectly round nor infinitely sharp. In oder to illustrate the influence that small variations in punch shape may have on the contact behaviour, analytical solutions for a blunted Hertzian indenter and a rounded cone are obtained in parametric form, and their asymptotic behaviour at the extremes of low and high loads is investigated. A smooth punch is then considered of a general shape, given by a power series, and the resulting general solution is used as a basis for developing an inverse problem formulation of the tip share calibration procedure. The method allows the best match between the measured and predicted load-displacement dependencies to be established. An example of the application of this procedure to the analysis of some nanoindentation data is presented.

Analysis of residual stresses generated by progressive induction hardening of steel cylinders

Abstract: The internal stresses generated during quenching can produce warping and even cracking of a steel body and, therefore, the prediction of such stresses is an important task. Phenomenological aspects of quenching involve couplings between different physical processes occurring in the phenomena. The present contribution is concerned with modelling and simulation of quenching, presenting an anisothermal model formulated within the framework of continuum mechanics and the thermodynamics of irreversible processes. A numerical procedure is developed based on an operator split technique associated with an iterative numerical scheme in order to deal with non-linearities in the formulation. With this assumption, the coupled governing equations are solved involving four uncoupled problems: thermal, phase transformation, thermoelastic and elastoplastic behaviours. The proposed general formulation is applied to analyse progressive induction hardening of steel cylinders. Numerical results suggest that the proposed model is capable of capturing the main behaviour observed in experimental data.

Wire failures in ropes and their influence on local wire strain behaviour in tension-tension fatigue:

Abstract: Experimental work using multiple strain gauges has investigated the take-up of load by a wire at either side of a break and how this is affected by fatigue cycling. In addition the effect of a wire break on other wires at the same cross-section has been investigated. The results indicate that a significant amount of slippage can occur for up to 20 000 cycles after a wire has broken, causing the load transfer length to change from two strand lay lengths to around three. The transfer length was found to be much lower for Lang's lay rope than ordinary lay and this was attributed to the greater interlayer forces in Lang's lay ropes. With respect to the effect of wire breaks on other wires at the same cross-section it was found that the primary increase is in the strains in wires in the same strand, although wire strains in adjacent strands also increase to some extent. Wires on the opposite side of the rope construction were found to show a decrease in surface strain after the break which may be attributed to local bending effects.

A photoelastic analysis of crescent-shaped cracks in bolts

Abstract: Three-dimensional photoelasticity was used to analyse the effect of crack shape on the stress intensity factors (SIFs) at the tips of cracks in threaded connectors under axial and eccentric loads. The results show that the shape of the crack does not affect the maximum SIF occurring at the middle of the crack front. However, it does influence the distribution around the crack front, with the KI/ Ko values decreasing more rapidly towards the end of the crack front for more crescent-shaped cracks. Despite the complexity of the geometry, the SIFs were found to be predominantly mode I. Eccentric loading was found to increase the SIFs at the centre of the crack front slightly. The crack shape employed in this study was different from those used by earlier investigators but was based on evidence from fatigue tests.

A force field superposition approach to plane elastic stress and strain analysis

Abstract: The force field superposition method for linear elastic problems of stress and strain analysis involves representing the stress and displacement fields in a given solution domain as a superposition of fields generated by a number of point forces. These forces are located outside the solution domain, and in the case of two-dimensional, singly connected finite domain problems can be uniformly distributed around the perimeter of a circle enclosing the physical domain. Doubly connected and infinite domain problems can also be treated. The results of some simple test problems show that remarkable accuracy can be achieved with very little computational effort relative to other numerical methods. More complex problems require the solution domain to be divided into several subdomains, each of which may be subjected to superposition analysis.

Numerical methods to predict failure during the in-service welding of gas pipelines

Abstract: It is evident that numerical methods have a useful role in the assessment of welding conditions for the safe in-service welding of high-pressure gas pipelines No published work has considered the direct calculation of burn-through using a combination of thermal and stress analysis Using empirical relationships between welding process parameters and weld bead size and shape is an appropriate way of defining the weldment geometry and the heat-source coordinates With this approach, adequate agreement between predicted weld penetration, weld cooling times and heat-affected zone hardness has been made Following the prediction of a thermal field a full thermo-elastic plastic model can be used to predict the conditions likely to cause burn-throughIn this paper two significant research aspects of in-service welding have been addressed, as follows:1A new mathematical description of a heat source to represent the common in-service welding process, ie vertically up and vertically down manual metal arc welding

A review and detailed examination of non-layered conformal contact by finite element analysis

Abstract: This is the first of two papers concerned with conformal contact and considers the fundamental conditions arising in non-layered configurations. This work was part of a research programme concerned with the development of a water-lubricated axial piston pump, in which the combination of contacting materials and contact conditions are critical. Finite element analysis was used to study cylindrical and spherical conformal contacts, with the models being validated by comparison with known analytical solutions. The models are shown to be extremely accurate and both types of contact are thoroughly investigated in this paper. The same models are then developed further to examine the contact conditions in conformal layered contacts, which to date has received very little attention, and this is the subject of the second paper.

New forming limit diagram of laser tailored blank

Abstract: The new forming limit diagram (FLD) of a laser tailored blank, which includes independent forming limit curves (FLCs) of a welded zone and constituent base metals, is introduced. To obtain the form...

The dynamic analysis of piping systems using pseudo-dynamic techniques

Abstract: This paper describes an application of pseudo-dynamic techniques to the dynamic analysis of piping structures. Essentially it consists in coupling a direct time integration algorithm, such as the Newmark method, to an experimental step. At each time step the integration algorithm generates a displacement vector of the structure, which is prescribed for the test specimen. This is mounted in a rigid test rig fitted with a set of displacement actuators and load cells at the level of the structure degrees of freedom. The load cells allow the reading of the internal restoring force vector, which is fed back to the direct time integration algorithm in an actual time step. Further calculations for the velocity and acceleration vectors will define a new structure configuration by evaluating a new displacement vector referred to the next time step. This procedure makes it possible to assess experimentally a realistic stress distribution at sections of complex shape piping parts. The method is a precise tool in dynamic analysis and, on being carried out in a quasi-static procedure, it operates with less expensive equipment than is necessary in real dynamic test.

Wire strain variations in normal and overloaded ropes in tension-tension fatigue and their effect on endurance

Abstract: This paper investigates wire strain variations in tension-tension fatigue for two six-strand rope constructions under normal and overloaded conditions. It has been found that for ropes in tension there is a considerable variation in wire strains both on different wires at the same cross-section and to a marginally lesser extent along the length of the same wire. It has also been found that a Lang's lay rope has a wider variation of strains than the identical ordinary lay rope. Load cycling has been found to reduce the distribution slightly for an initial period, around 8 per cent of the rope's life (for the load range used), after which the variations in wire strains do not change significantly for the rest of the life of the rope. Tests involving initial overload have shown a considerable reduction in wire strain variation. By way of an example for an ordinary lay rope an initial overload caused the wire strain standard deviation to decrease from 22 per cent of mean to 11 per cent of mean and was accompa...

Grid pattern for in-plane strain measurements by digital image processing

Abstract: This paper presents a non-contact and non-destructive method for full-field in-plane strain measurements. Digital image processing is employed for monitoring the deformations of grid lines marked on a planar surface of a component or a specimen. Full-field in-plane strain distributions are obtained by processing the geometrical characteristics of the grid with computer graphics algorithms. The strain field determined in the necking zone of a tensile specimen has demonstrated the benefit of the method.

Localization of plastic deformation during high strain rate torsion testing of rolled homogeneous armour

Abstract: A recently developed technique which allows a study of the localization of plastic flow during high-speed torsion testing is briefly described. High-speed photographs showing successive stages in the deformation of three rolled homogeneous armour (RHA) steel specimens are presented. Three stages are identified corresponding to uniform shear, localized shear and the propagation of ductile failure. The results are analysed to estimate the conditions under which localization and subsequent ductile fracture are initiated. The results are compared with a previous study on a soft iron.

Twisted impregnated yarns: Transverse tensile strength

Abstract: Twisted yarns are normally used for increasing the lateral cohesion of filaments and also for ease of handling. In this paper, an analytical method is presented for predicting the effective transverse tensile strength of the twisted impregnated yarns made of continuous filaments. In the analysis, a varying degree of twist in filaments at different radii of the yarn is considered. The effect of the twist angle on the transverse tensile strength properties of the twisted impregnated yarns is presented. It is seen that there can be an increase in transverse tensile strength of the twisted impregnated yarns compared with that of the corresponding impregnated strands.

Flexural behaviour of a curved orthotropic beam on an elastic foundation

Abstract: This paper is concerned with the mechanical behaviour of a curved orthotropic beam on an elastic foundation under flexural loading. The differential equation in this case is derived from force-moment equilibrium consideratios and classical laminated orthotropic plate theory. General solutions for various loading conditions are derived using a stress function approach. Finally, the effects of various parameters such as the anisotropy ratio, foundation modulus and radius of the beam on stresses are presented from a design perspective.

Analysis of a resin socket termination for a wire rope

Abstract: A finite element model to determine the socket strains and resin pressures in a resin socket termination for a wire rope has been developed. This model takes account of the relative movement between the socket and the resin cone that occurs when a termination is under load. To verify the accuracy of the model, computed socket strains were compared with strain measurements both on a full-scale termination and on a laboratory-scale model. As a result of these comparisons, modifications were made to the finite element model to improve its accuracy. It was concluded that the wires were held in the socket by frictional forces which were effective only in the resin section between 10 and 50 per cent of the socket basket length (measured from the front of the socket). This conclusion was verified by further laboratory tests.It was therefore deduced that manufacturing defects in the back half of the socket would not reduce the strength of the termination, while defects in the front half are much more significant....