Showing papers in "Journal of Strain Analysis for Engineering Design in 2004"

Identification of the parameters of a non-linear continuum damage mechanics model for ductile failure in metals

Abstract: Damage modelling in ductile metal has received a lot of attention in the last thirty years. Since 1969, many models have been proposed in the literature even though, in most of the cases, the exper...

A simple model to predict crack growth in bonded joints and laminates under variable-amplitude fatigue

Abstract: It is now well established that adhesives and fibre-reinforced polymers (FRPs) can fail at far lower loads under fatigue loading than under quasi-static loading. Most of the work on the fatigue of these materials has been under constant amplitude (CA); however, recent work has shown that fatigue crack growth acceleration and unstable crack growth can be seen under conditions of variable-amplitude (VA) fatigue. In this paper, further evidence of this effect is given. This phenomenon is attributed to the influence of VA fatigue on the evolution of a damage zone ahead of the main crack front and results from the characterization of these damage zones are also presented. Finally, a simple fracture mechanics-based model for predicting crack growth under VA fatigue is proposed. This is shown to be entirely consistent with the experimental observations.

Unusual strain rate sensitive behaviour of AISI 316L austenitic stainless steel

Abstract: This paper presents the results of quasi-static and dynamic tensile tests on 2, 3 and 4 mm thick 316L austenitic stainless steel. It details the test conditions and discusses the results, particularly focusing on strain rate sensitivity and methods of employing the tensile properties in the finite element package, ABAQUS. The results show that the stainless steel is moderately strain rate sensitive in the region of yield. At the ultimate tensile strength (UTS), some negative strain rate sensitivity was observed, which previous researchers for this grade of steel have not reported. Two main conclusions were drawn, namely (a) the strain rate sensitivity was too complex to be modelled accurately by a constitutive equation such as the Cowper-Symonds relation and (b) the properties of the tested materials could be accurately described by a few (true stress, logarithmic strain) coordinate pairs, as linear strain hardening was observed, for a given strain rate.

An ultrasonic approach for contact stress mapping in machine joints and concentrated contacts

Abstract: The measurement of pressure at a contact in a machine part is important because contact stresses frequently lead to failure by seizure, wear or fatigue. While the interface might appear smooth on a macroscale, it consists of regions of asperity contact and air gaps on a microscale. The reflection of an ultrasonic pulse at such a rough contact can be used to give information about the contact conditions. The more conformal the contact, the smaller is the proportion of an incident wave amplitude that will be reflected. In this paper, this phenomenon has been used to produce maps of contact pressure at machine element interfaces. An ultrasonic pulse is generated and reflected at the interface, to be received by the same piezoelectric transducer. The transducer is scanned across the interface and a map of reflected ultrasound (a c-scan) is recorded. The proportion of the wave reflected can be used to determine the stiffness of the interface. Stiffness correlates qualitatively with contact pressure, but unfortunately there is no unique relationship. In this work, two approaches have been used to obtain contact pressure: firstly by using an independent calibration experiment, and secondly by using experimental observations that stiffness and pressure are linearly related. The approach has been used in three example cases: a series of press fitted joints, a wheel/rail contact and a bolted joint.

Stress concentration at crossholes in thick cylindrical vessels

Abstract: Elastic stress concentration factors (SCFs) for internally pressurized thick cylindrical vessels with radial and offset circular and elliptical crossholes are presented. Three forms of intersection between the crosshole and main bore are considered: plain, chamfered and blend radiused. The minimum SCF was found to occur for the plain intersection configuration, with the peak stress at the crotch corner between the main bore and crosshole on the longitudinal plane of symmetry. Incorporating a chamfer or blend radius at the intersection reduces the stress concentration at the main bore but introduces higher peak stress elsewhere in the chamfer or blend region.

Numerical evaluation of residual stress relaxation by cyclic load

Abstract: The aim of this work is to evaluate by numerical simulation the real stress state of a welded component subjected to a sinusoidal external load. In particular, the relaxation process of the residual stress, due to the application of a cyclic external load, has been studied. Longitudinal welded joints, laser welded and 3 mm thick, are analysed in this work following the residual stress evolution during a fatigue test. A numerical procedure, implemented by the ABAQUS code, carries out the residual stress field originated by a welding process and it is taken as a pre-stress condition in the present ABAQUS simulations. In order to evaluate the influence of the amplitude level on the residual stress relaxation, eight different sinusoidal loads at the load ratio R ¼ 0:1 are applied to the model. The results show a significant reduction in the initial residual stress level, even after the first load cycle. They offer a very precise explanation of the fatigue behaviour of this kind of welded joints, confirming the behaviour experimentally observed.

Limit load solutions for thin-walled cylinders with circumferential cracks under combined internal pressure, axial tension and bending:

Abstract: Limit load solutions for thin-walled cylinders with circumferential cracks under combined axial tension, bending and pressure are developed, considering the effect of pressure-induced hoop stress v...

Elastic strains around cracked cold-expanded fastener holes measured using the synchrotron X-ray diffraction technique

Abstract: In this work, the capability of the synchrotron X-ray diffraction technique to measure changes in the residual strains caused by fatigue crack growth from cold-expanded holes in an aluminium alloy plate has been investigated. The measurement technique was validated by comparing the synchrotron measurements around uncracked holes with those obtained on similar specimens using the neutron diffraction and Sachs' techniques. Measurements were performed with and without superimposed tensile mechanical loading and the results compared with analytical results. The improved spatial resolution of the synchrotron technique relative to the other methods has allowed the strain fields around a fatigue crack growing from a cold-expanded hole to be evaluated in the unloaded state and at two loading levels. Only at the higher load does the crack appear to open along its full length.

Interaction of arbitrary multiple cracks in an infinite plate

Abstract: In this article, the interaction of arbitrary multiple cracks in an infinite plate is examined by means of a boundary element method consisting of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements proposed by the present author. In the boundary element implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The present numerical results of stress intensity factors (SIFs) for some typical multiple crack problems show that the numerical approach is simple yet very accurate for analysing the interaction of arbitrary multiple cracks in an infinite plate.

Measurement and prediction of fatigue crack growth from cold expanded holes Part 1: The effect of fatigue crack growth on cold expansion residual stresses

Abstract: Cold expansion of holes introduces beneficial compressive residual stresses that retard cracking in fatigue loaded material. Using X-ray diffraction measurements, it was found that when the fatigue protection was exceeded and crack initiation and growth occurred, the original residual stress distribution was significantly modified. The change of residual stresses due to fatigue crack growth was investigated by considering the geometrical discontinuity in the material and the small-scale plasticity accompanying fatigue crack propagation. Fatigue crack growth simulation by cutting a slot using electrodischarge machining showed that the cold expansion residual stresses were affected much more by a slot than by an actual fatigue crack.

Computer simulation of strain accumulation and hardening for pearlitic rail steel undergoing repeated contact

Abstract: This paper presents a validated model of plastic strain accumulation in railway rail steel under repeated wheel-rail contact.Such contacts subject the rails to severe stresses, taking the material local to the contact beyond yield, and leading to the incremental accumulation of plastic deformation (ratcheting) as wheels pass.This process is at the root of several rail wear and rolling contact fatigue crack growth mechanisms.Existing plasticity models are inadequate for modelling the strain accumulation taking place in this material, which is under high hydrostatic compression (of the order of 1 GPa) and is severely anisotropic.The model described here is based on a ratcheting law derived from small-scale twin-disc rolling-sliding contact experiments and simulates tens of thousands of ratcheting cycles and the corresponding strain hardening in a few minutes on a personal computer.Results indicate that, to model these processes successfully, and to represent correctly the high levels of ductility seen in rail steels under compressive load, stress-strain data generated under high hydrostatic compression are required.

Finite element bending behaviour of composite hyperbolic paraboloidal shells with various edge conditions

Abstract: A general finite element procedure with an eight-noded isoparametric curved quadratic element is presented to investigate the static behaviour of laminated composite hyperbolic paraboloidal shells bounded by straight edges (commonly called hypar shells). Numerical results are obtained for uniformly loaded laminated composite hypar shells with six practical boundary conditions, where the edges are differently restrained. Eight different types of lamination including single layered and multi-layered, cross-ply and angle-ply, symmetric and antisymmetric stacking orders are chosen. The numerical results of different shell actions of 48 combinations are furnished to estimate their relative performances. The authors further propose typical comparative performance matrix to study the relative efficiencies of different stacking combinations, which will be a great help in design.

Rail behaviour during cooling after hot rolling

Abstract: Rails are manufactured from bloom by hot rolling. Subsequently, they are cooled to ambient temperature. At the end of the cooling process, the rails bend almost in the form of circular ares. They are then straightened in the roller-straightening machine. Knowledge of the shape of the bent rail and the magnitude of residual stress at the end of the cooling process is useful for proper computation of the straightness and residual stress in the rails after the straightening operation. The present paper describes a simulated model developed for the investigation of the behaviour of the rail during the entire cooling process. The analysis has been carried out as a decoupled thermomechanical transient problem using the general-purpose finite element software ANSYS. Histories of the temperature distribution and deformation of the rail have been obtained by the method. The results are in good agreement with the observed behaviour of the rails in the real-life environment. The model has also evaluated the generate...

An integrated approach for measuring near-surface and subsurface residual stress in engineering components

Abstract: This paper presents measurements performed using an integrated centre hole drilling-deep hole drilling technique on two components: a butt-welded plate and a rail. The results were compared with th...

Measurement and prediction of fatigue crack growth from cold expanded holes Part 2: Prediction of fatigue crack growth from cold expanded holes

Abstract: In this paper a linear elastic fracture mechanics approach was used to predict fatigue crack growth from an open cold expanded hole. Predictions were made for two cases: by using the initial cold expansion residual stress distribution, assumed to be unaffected by fatigue crack growth, and by using the residual stress distribution corresponding to each crack length. The estimated fatigue crack growth rates were compared with experimental results and it was found that taking into account the residual stress change due to fatigue crack growth significantly improved the prediction accuracy.

Thickness and multi-axial stress creep rupture criteria of the Type IV component of a ferritic steel weld:

Abstract: The paper summarizes previously derived constitutive parameters for temperatures of 575, 590, 600, 620 and 640°C. Values of the multi-axial stress rupture parameter, v, are reviewed and recorded. This constitutive parameter set is used to determine the thickness of the Type IV material zone (0.7 mm). Values of Type IV multi-axial stress rupture parameter v are determined for a wide range of butt-welded pipe and cross-welded uni-axial specimens, and an interpolation equation is derived in terms of temperatures and stress level. Finally, continuum damage mechanics (CDM) analyses are performed for pipes and cross-welded testpieces, which include a coarse-grained heat-affected zone (CG-HAZ). It is shown that the constitutive parameter set, which corresponds to a minimum creep rate ratio of 1/2.5, with respect to the parent material, gives accurate predictions of lifetimes and damage distributions.

Effect of local induction heat treatment on the induced residual stresses in the web region of a welded rail

Abstract: Rails are often joined by welding and about 80–90 per cent of tracks are welded using the flash-butt welding method. As the result of the welding process, high tensile residual stresses are induced in the web region of the rail, at and near the welded zone. Since the main part of the welded zone is coarse grained and has porosities and inclusions, the web part of the rail is susceptible to failure. The magnitude of the induced stresses may be reduced by stress-relieving heat treatment, but in practice the heat treatment process is not used as it is very time consuming and adds to overall project costs. In this paper, microscopic studies were performed on the welded zone in the head, the web and the base parts of the rail. The effects of local induction heat treatments on the microstructure and on the resultant tensile residual stresses in the web region were studied. To do this, firstly, dilatometery specimens were prepared from the base metal of the rail. These were heat-treated under different induction...

Optimal free-form shapes for holes in flat plates under uniaxial and biaxial loading:

Abstract: This paper presents new and transferable design data defining precise optimal free-form shapes for holes in large and finite width plates under biaxial and uniaxial loading conditions respectively. An iterative two-dimensional finite element gradientless shape optimization procedure was used to obtain the optimal shapes, which offer the lowest possible stress concentration, subject to geometric constraints. Precise non-dimensional coordinates are given for a range of hole aspect ratios and are presented in tabular form that allows them to be easily used by designers. The optimal shapes were determined both with and without minimum radius of curvature constraints. Optimal shapes in large plates were found to provide up to a 28 per cent reduction in peak local stress over elliptical shapes of the same aspect ratio. For finite width plates the reduction in peak local stress was as high as 44 per cent. The results obtained are applicable to both the initial design of components with cut-outs and the shape rew...

Critical plane modelling of fatigue initiation under rolling and sliding contact

Abstract: Contact fatigue is a phenomenon of important practical significance for engineering applications involving localized contacts, such as gears, rail wheel system and rolling bearings. The service lifetime of such components is related to damage, which results from the contact fatigue. The process in the material structure that causes this kind of failure is quite complicated. The aim of the present paper is to describe a contact fatigue initiation criterion, based on the critical plane approach for the general contact problem. On the basis of contact stress analysis with modified Hertzian boundary conditions, the loading cycle of characteristic material points in the contact area is determined. The Dang Van damage initiation criterion is based on the critical plane approach, which combines the largest allowable shearing and hydrostatic stresses (tensile and compressive), with an assumed elastic shakedown behaviour and it is used in this work. The material point of initial fatigue damage is then determined at the transition of the loading cycle stresses over the critical plane. The model assumed a homogeneous and elastic material model, without any imperfections or residual stresses, and elastic shakedown is considered. A proper determination of loading cycles and their characteristic values is of significance for contact fatigue initiation analysis. Finally, determination of the most critical material point on or under the contact surface and related number of loading cycles required for fatigue damage initiation is calculated with the strain-life (▫$epsilon$▫-N) method.

A review of asymptotic procedures in stress analysis: Known solutions and their applications:

Abstract: A comprehensive review is given of the origins of asymptotic procedures in stress analysis. Specifically, attention is focused on the use of fracture mechanics to characterize the elastic stress state ahead of a crack tip. Analogies are then drawn between this configuration and the stress state adjacent to the apex of a sharp V-notch. Extensions of these asymptotic procedures to bonded and slipping contacts are then considered and it is shown that although power order singularities may be obtained, the solutions are more complicated. Lastly, the use of nested asymptotic procedures are considered in order to account for a small but finite radius at the tip of cracks and notches or at the edge of slipping contacts.

Relaxation of residual stresses induced by turning and shot peening on steels

Abstract: Experiments on the relaxation of residual stresses in steels by fatigue loading are described. This question is of interest because it is well known that compressive residual stresses are often induced by special surface treatments (such as shot peening) to improve the fatigue life of metal parts; however, if cyclic relaxation occurs, the beneficial effects can, in part, vanish during service. Two hardened and tempered steels of grade C45 and 39NiCrMo3 were used in the tests. For both materials, different specimens were given two surface treatments: simple turning without successive surface treatment, inducing on the surface a moderate tensile residual stress state, and shot peening, inducing high residual compressive stresses. The specimens were submitted to constant-amplitude tension-compression fatigue loading, and the surface residual stresses were measured after 0, 1, 10 cycles and more. Results show that relaxation occurs from the very first cycle; the amount of residual stress relaxation depends on...

Frictionally excited thermoelastic instability in the presence of contact resistance

Abstract: In sliding systems, frictional heating generates a well-known instability above a certain critical speed Vcr, which is a function of geometrical and material properties only. Similar instabilities are known to occur in the static problem, driven by temperature differences, in the presence of thermal contact resistance. Thermal contact resistance at the interface has seldom been considered and gives rise to full coupling of the problem. Generally, the resistance decreases non-linearly when pressure is increased. Here, the critical condition (in terms of heat flux and sliding speed) for the stability of the uniform pressure solution for a half-plane in frictional contact with a rigid wall at fixed temperature is studied for a general resistance function R(p). It is found that the heat flux direction increases the instability as in the case of zero speed, i.e. when directed into the half-plane (which is the only distortive material), whereas frictional heating can have also a stabilizing effect, for a given ...

Re-examination on thermal stresses of bonded structures:

Abstract: To the authors' best knowledge this is the first time that the photoelastic method has been used to determine experimentally the whole-field state of thermal stresses of bonded structures. Except for the immediate vicinity of the interfacial edges, the photoelastic results were confirmed through the finite element method (FEM). Theoretical solutions provided by both Timoshenko and Suhir were then re-examined and compared with the photoelastic and FEM results. A comparison of those results indicated that the current theoretical solutions are oversimplified and need to be improved.

Determination of the bending stiffness for a spiral strand

Abstract: Owing to their peculiar construction, axially preloaded spiral strands undergo plane-section bending only for sufficiently small maximum lateral deflection/span ratios. Beyond a certain limit of this ratio, plane sections do not remain plane and, depending on the level of axial tension and imposed radius of curvature, interlayer slippage takes place, starting from the outer layer and spreading towards the centre of the strand. On the theoretical side, apart from one publication in the mid-1980s and some fairly recent publications by the first author and his associates, all other theoreticians have previously assumed either plane-section bending or, in many cases, have totally ignored the ever-present interwire friction, assuming that the individual helical wires act as simple helical springs. Previously reported experimental techniques, aimed at measuring the effective bending stiffness of helically wound cables, also largely suffer from major shortcomings. In the present paper, a novel experimental method is reported for obtaining reliable measurements of the effective bending stiffness of axially loaded spiral strands. It is very simple and relatively inexpensive to use in practice, for even very large (greater than, say, 100mm outside diameter) spiral strands. Effective bending stiffness measurements, based on this approach, are reported here for a 164mm outside diameter spiral strand (with axial loads of up to 3 MN), with these supported by a detailed theoretical analysis, which reinforces the generally sound nature of the proposed method.

What level of friction guarantees adhesion in a complete contact

Abstract: The Williams' solution for the state of stress near the apex of an elastic wedge is used to study the traction distribution adjacent to the tip of a complete contact. Assuming that the surfaces remain in contact during loading, the coefficient of friction needed to ensure local adhesion is found. This is compared with that predicted by an analysis of an elastic rectangle clamped between elastic half- planes and is shown to be consistent. The results are appropriate to all complete contacts between elastically similar components.

On the influence of the initial tension of a strip with a rectangular hole on the stress concentration caused by additional loading

Abstract: The influence of the initial stretching of a simply supported plate strip containing a rectangular hole with rounded-off corners on the stress concentration around the hole caused by the bending of the strip under the action of uniformly distributed normal forces on the plane of its upper face is studied within the framework of the three-dimensional theory of elasticity under a plane-strain state. The mathematical formulation of the corresponding boundary value problems is presented. For the solution to these problems the finite element method is employed and for this purpose the validity of the constructed functional is proven. The material of the plate strip is selected as linear elastic, homogeneous and orthotropic. The numerical results are presented for the composite consisting of two alternating layers made from isotropic linear elastic materials.

Strains in steel bars of reinforced concrete elements subjected to repeated loads

Abstract: To evaluate the strains in a steel bar of a reinforced concrete structure under repeated loads, a mechanical model is proposed. More precisely, a reinforcing bar embedded in a concrete cylinder subjected to uniaxial actions is modelled. In the proposed one-dimensional approach, both the nonlinear fracture mechanics of concrete and the bond-slip between the two materials are taken into account, since they affect the structural response of several reinforced concrete structures in the serviceability conditions and in the ultimate limit state. When cyclic actions are applied and previous cracks close up again, the interaction between the fictitious crack model of concrete in tension and the bond-slip near the crack is investigated. During the unloading phase of each cycle, only through refinement of the damage effects, with regard to the classical bond and cohesive models, can the hysteretic behaviour of the reinforced concrete structures be modelled. The strains in the bar, computed with the proposed model,...

Optimal notch shapes for loaded plates

Abstract: This paper presents design data defining optimal freeform notch shapes for use in tensile loading conditions for a range of geometries, notably the notch aspect ratio and plate widths. Here, an ite...

Stresses in rotating cross-ply laminated hollow cylinders with arbitrary thickness

Abstract: The stress analysis of a rotating finite cross-ply laminated composite hollow cylinder with two ends simply supported is conducted with the Coriolis acceleration effect involved. The state-space approach is employed together with the layerwise method as well as the Fourier expansion technique. The analysis is completely based on the exact elasticity equations so that hollow cylinders with arbitrary thickness can be readily dealt with. Numerical comparison with exact solution of a rotating infinite hollow cylinder without the Coriolis effect shows good agreement.

A comparison of failure prediction methods for an adhesively bonded composite beam

Abstract: In this paper, three different techniques are proposed to predict the failure load in two adhesively bonded composite I-beams. These methods are analytical solutions, finite element analyses (FEAs) and hybrid methods (combination of FEA and closed-form solutions). The two I-beams were tested in the three-point bending and four-point bending configurations. In the analytical solutions, simple stress analysis and fracture mechanics, based on beam theory, are used. Failure in the adhesive layer as well as failure in the skin or spar caps is considered. In the finite element (FE) approach a submodelling technique is adopted, in which a coarse model and a submodel are required. A circular flaw of 6mm radius is initiated in the adhesive layer and the strain energy release rates are extracted from the FEA results using a modified crack closure technique. In the hybrid method, a global FE model is constructed and the stresses are calculated; then an analytical solution for a circular crack is applied. Comparison ...