Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

In this paper, the fatigue crack growth in helical gear tooth root has been simulated using linear elastic fracture mechanics. The extended finite element method has been used to simulate 3D fatigue crack growth and obtain growth path. Paris equation has been used to calculate the fatigue life of the gear. The modelling time has reduced considerably compared to previous works carried out on 3D crack growth in gears. Some verifications have been carried out to ensure the reliability of the results.     

Three‐dimensional magnetostatic problem

The paper is devoted to an approximation of the solution of Maxwell's equations in three‐dimensional space. We present two methods which couple a finite element method inside the magnetic materials with a boundary integral method which uses Poincaré–Steklov's operator to describe the exterior domain. A computer code has been implemented for each method and a number of numerical experiments have been performed to validate each proposed methodology. Namely, we present numerical results concerning a non‐linear magnetostatic problem in ℝ³. Copyright © 1999 John Wiley & Sons, Ltd.     

Gradient‐enhanced damage modelling of high‐cycle fatigue

Continuum damage mechanics can be used to model the initiation and growth of fatigue cracks. However, finite element analyses using standard fatigue damage formulations exhibit an extreme sensitivity to the spatial discretisation of the problem. The mesh sensitivity is caused by the fact that the underlying continuum model predicts instantaneous, perfectly brittle crack growth as soon as a crack has been initiated. The growth of damage localizes in a vanishing volume during this instantaneous growth. This localization is not so much due to loss of ellipticity of the problem, but is caused by the fact that the damage rate is singular at the crack tip. The damage rate singularity can be removed by the introduction of higher‐order deformation gradients in the constitutive modelling. As a result, crack growth at a finite rate and with a positive amount of energy dissipation is predicted. Finite element analyses converge to this solution and are thus no longer pathologically dependent on the spatial discretization. Copyright © 2000 John Wiley & Sons, Ltd.     

Physics‐based multiscale damage criterion for fatigue crack prediction in aluminium alloy

In this paper, a physics‐based multiscale approach is introduced to predict the fatigue life of crystalline metallic materials. An energy‐based and slip‐based damage criterion is developed to model two important stages of fatigue crack initiation: the nucleation and the coalescence of microcracks. At the microscale, a damage index is developed on the basis of plastic strain energy to represent the growing rate of a nucleated microcrack. A statistical volume element model with high computational efficiency is developed at the mesoscale to represent the microstructure of the material. Also, the formation of a major crack is captured by a coalescence criterion at mesoscale. At the macroscale, a finite element analysis of selected test articles including lug joint and cruciform is conducted with the statistical volume element model bridging two scale meshes. A comparison between experimental and simulation results shows that the multiscale damage criterion is capable of capturing crack initiation and predicting fatigue life.     

Microstructure‐sensitive fatigue modelling of medical‐grade fine wire

This work presents a modelling methodology to assess the sensitivity to microstructure in high‐cycle fatigue performance of fine wires made from MP35N alloy (35Ni‐35Co‐20Cr‐10Mo in wt%) used as conductors in cardiac leads. The model consists of a microstructure generator that creates a mesh of a statistically representative microstructure, a finite element analysis using a crystal plasticity constitutive model to determine the local response behaviour of the microstructure, and a postprocesser using fatigue indicating parameters to assess the likelihood of fatigue crack initiation. The fatigue crack initiation potency for selected microstructure attributes, boundary and interface conditions, and loading profiles is determined by computing the Fatemi‐Socie fatigue indicating parameter over a physically relevant volume of scale. Case studies are used to investigate (1) the influence of nonmetallic inclusion proximity to the wire surface on fatigue potency and (2) the transition life demarcating lives primarily controlled by fatigue crack initiation versus microcrack fatigue growth.     

Three‐dimensional modelling and simulation of magnetorheological fluids

A magnetorheological fluid (MR fluid) is a type of smart fluid composed of micrometer‐sized magnetizable particles suspended in a carrier fluid. The rheological properties of an MR fluid can be greatly altered upon application of an external magnetic field. This paper presents a computational framework for the numerical study of MR fluids, in which a two‐stage modelling and simulation strategy is proposed to achieve reasonable accuracy and computational efficiency. At the first stage for simulating the particle chain formation, the particle dynamics plays a major role whereas the hydrodynamics of the fluid flow is of secondary importance. Thus an MR fluid is modelled in the context of the discrete element method and the simple Stokes formula is adopted for the hydrodynamic interaction. At the second stage, the formulated particle chains are applied as the initial configuration for simulating the rheological properties of the fluid under different shear loading conditions. A combined lattice Boltzmann and discrete element approach is employed to fully resolve the fluid field and the hydrodynamic interactions between the fluid and the particles. Some relevant magnetic models are comprehensively reviewed and the mutual dipole model is employed in this work to account for the magnetic interactions between the particles. The proposed solution procedure is illustrated via a set of numerical simulations for a representative volume element of an MR fluid. Copyright © 2010 John Wiley & Sons, Ltd.     

A crystal plasticity based methodology for fatigue crack initiation life prediction in polycrystalline copper

Fatigue failure is the dominant mechanism that governs the failure of components and structures in many engineering applications. In conventional engineering applications due to the design specifications, a significant proportion of the fatigue life is spent in the crack initiation phase. In spite of the large number of works addressing fatigue life modelling, the problem of modelling crack initiation life still remains a major challenge in the scientific and engineering community. In the present work, we present a methodology for estimating fatigue crack initiation life using macroscale loading conditions and the microstructural phenomenon causing crack initiation. Microstructure sensitive modelling is used for predicting potential crack initiation life by employing randomly generated representative microstructures. The microstructural parameters contributing to crack initiation life are identified and accounted for by computing lattice level energy dissipation during fatigue crack initiation. This model is coupled with experimental results to improve the predictive capabilities and identification of potentially damaging weak points in the microstructures. The estimated values for crack initiation life were found to be in good agreement with the experimentally observed values of initiation life. The results have shown that this kind of approach could be successfully used to predict crack initiation life in polycrystalline materials. This work successfully provides an approach for estimating crack initiation life based upon numerical computations accounting for the microstructural phenomenon.     

Three‐dimensional analysis of fatigue tests on bituminous mixtures

A tension–compression test on cylindrical specimens was used to study the three‐dimensional behaviour of bituminous mixtures during fatigue tests. The tests were carried out at 10 °C, 10 Hz at constant strain amplitude mode. The axial strain, radial strain and axial stress were measured using a prototype apparatus developed at the University of Lyon/“Ecole Nationale des TPE” (ENTPE). In addition to axial stress and strain analysis, the measurements of the radial strain made it possible to obtain the complex Poisson ratio and the volumetric strains during the tests. The results showed good correlations between the volumetric strains and global damage. The effects of the change of temperature due to viscous dissipation on the volumetric strain and on the complex modulus were also analysed.     

Numerical modelling and experimental investigation on welding residual stresses in large‐scale tubular K‐joints

This paper is devoted to the experimental and numerical assessment of residual stresses created by welding in the region surrounding the weld toe of tubular K‐shaped joints (i.e. region most sensitive to fatigue cracking). Neutron‐diffraction measurements were carried out on K‐joints cut from large‐scale truss beams previously subjected to high cycle fatigue. Tri‐axial residual stresses in the transverse, longitudinal and radial direction were obtained from the weld toe as a function of the depth in the thickness of the tube wall. In addition, thermomechanical analyses were performed in three‐dimensional using ABAQUS and MORFEO finite element codes. Experimental and numerical results show that, at and near the weld‐toe surface, the highest residual stresses are critically oriented perpendicularly to the weld direction, and combined with the highest externally applied stresses. Based on a systematic study on geometric parameters, analytical residual stress distribution equations with depth are proposed.     

Quantitative assessment of preferential fatigue initiation sites in a multi‐phase aluminium alloy

Complex multi‐phase Al–Sn–Si alloys are commonly employed in the manufacture of small automotive plain bearings. The fundamental fatigue initiation behaviour of this class of alloys is currently not well understood. A range of analytical techniques were applied to investigate preferential initiation site location and to attempt to identify critical microstructural features. It was apparent from experimental studies that points of fatigue crack initiation are associated with the Si secondary phase. Using tessellation approaches and subsequently both adaptive numerical modelling and micro‐scale finite element modelling allowed the identification of features affecting the probability that a given Si phase would initiate a fatigue crack.     

Three‐dimensional measurement and cohesive element modelling of deformation and damage in a 2.5‐dimensional woven ceramic matrix composite

A cohesive element numerical model, which reproduces the three‐dimensional microstructure of a 2.5‐dimensional silicon‐nitrogen‐oxide fibre/fabric‐reinforced boron nitride ceramic matrix composite (SiNO/BN) is applied to simulate the failure of specimens that are observed in situ during diametral compression testing. Measurements of deformation by image correlation of two‐dimensional optical surface observations and three‐dimensional X‐ray computed tomographs are used to fit the simulation's elastic properties for the matrix and fibre tows. The observed patterns of damage nucleation and propagation are correctly simulated using a local tensile strain criterion.     

A low‐order,hexahedral finite element for modelling shells

A thin, eight‐node, tri‐linear displacement, hexahedral finite element is the starting point for the derivation of a constant membrane stress resultant, constant bending stress resultant shell finite element. The derivation begins by introducing a Taylor series expansion for the stress distribution in the isoparametric co‐ordinates of the element. The effect of the Taylor series expansion for the stress distribution is to explicitly identify those strain modes of the element that are conjugate to the mean or average stress and the linear variation in stress. The constant membrane stress resultants are identified with the mean stress components, and the constant bending stress resultants are identified with the linear variation in stress through the thickness along with in‐plane linear variations of selected components of the transverse shear stress. Further, a plane‐stress constitutive assumption is introduced, and an explicit treatment of the finite element's thickness is introduced. A number of elastic simulations show the useful results that can be obtained (tip‐loaded twisted beam, point‐loaded hemisphere, point‐loaded sphere, tip‐loaded Raasch hook, and a beam bent into a ring). All of the gradient/divergence operators are evaluated in closed form providing unequivocal evaluations of membrane and bending strain rates along with the appropriate divergence calculations involving the membrane stress and bending stress resultants. The fact that a hexahedral shell finite element has two distinct surfaces aids sliding interface algorithms when a shell folds back on itself when subjected to large deformations. Published in 2004 by John Wiley & Sons, Ltd.     

Three‐dimensional superconvergent gradient recovery on tetrahedral meshes

In this paper, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three‐dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have superconvergence in the l₂ norm at nodes of a CVDT mesh for an arbitrary three‐dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method. Copyright © 2016 John Wiley & Sons, Ltd.     

Low cycle fatigue life prediction in shot‐peened components of different geometries – part II: life prediction

This study investigates the effects of shot peening on the low‐cycle fatigue performance of a low‐pressure steam turbine blade material. The finite element model incorporating shot‐peening effects, which has been introduced in part I, has been used to predict the stabilised stress/strain state in shot‐peened samples during fatigue loading. The application of this model has been extended to different notched geometries in this study. Based on the modelling results, both the Smith–Watson–Topper and Fatemi–Socie critical plane fatigue criteria have been used to predict the fatigue life of shot‐peened samples (treated with two different peening intensities) with varying notched geometries. A good agreement between experiments and predictions was obtained. The application of a critical distance method considering the stress and strain hardening gradients near the shot‐peened surface has been found to improve the life prediction results. The effects of surface defects on the accuracy of life predictions using the proposed method were also discussed.     

Prediction of fretting fatigue crack initiation in double lap bolted joint using Continuum Damage Mechanics

In fretting fatigue, the combination of small oscillatory motion, normal pressure and cyclic axial loading develops a noticeable stress concentration at the contact zone leading to accumulation of damage in fretted region, which produces micro cracks, and consequently forms a leading crack that can lead to failure. In fretting fatigue experiments, it is very difficult to detect the crack initiation phase. Damages and cracks are always hidden between the counterpart surfaces. Therefore, numerical modeling techniques for analyzing fretting fatigue crack initiation provide a precious tool to study this phenomenon. This article gives an insight in fretting fatigue crack initiation. This is done by means of an experimental set up and numerical models developed with the Finite Element Analysis (FEA) software package ABAQUS. Using Continuum Damage Mechanics (CDM) approach in conjunction with FEA, an uncoupled damage evolution law is used to model fretting fatigue crack initiation lifetime of Double Bolted Lap Joint (DBLJ). The predicted fatigue lifetimes are in good agreement with the experimentally measured ones. This comparison provides insight to the contribution of damage initiation and crack propagation in the total fatigue lifetime of DBLJ test specimens.     

High cycle fatigue mechanisms of aluminum self‐piercing riveted joints

A study examining the fatigue failure mechanism of self‐piercing riveted (SPR) joints between aluminum alloy 6111‐T4 and 5754‐O is presented in this paper. In particular, the high‐cycle fatigue behavior of the SPR joints in the lap‐shear configuration is characterized. Experimental fatigue testing revealed that failure of SPR joints occurred because of cracks propagating through the sheet thickness at locations away from the rivet. In‐depth postmortem analysis showed that significant fretting wear occurred at the location of the fatigue crack initiation. Energy dispersive X‐ray of the fretting debris revealed the presence of aluminum oxide that is consistent with fretting initiated fatigue damage. High‐fidelity finite element analysis of the SPR process revealed high surface contact pressure at the location of fretting‐initiated fatigue determined by postmortem analysis of failed coupons. Furthermore, fatigue modeling predictions of the number of cycles to failure based on linear elastic fracture mechanics supports the conclusion that fretting‐initiated fatigue occurred at regions of high surface contact pressure and not at locations of nominal high‐stress concentration at the rivet.     

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

The spring‐layer interface model is widely used in describing some imperfect interfaces frequently involved in materials and structures. Typically, it is appropriate for modelling a thin soft interphase layer between two relatively stiff bulk media. According to the spring‐layer interface model, the displacement vector suffers a jump across an interface whereas the traction vector is continuous across the same interface and is, in the linear case, proportional to the displacement vector jump. In the present work, an efficient three‐dimensional numerical approach based on the extended finite element method is first proposed to model linear spring‐layer curved imperfect interfaces and then applied to predict the effective elastic moduli of composites in which such imperfect interfaces intervene. In particular, a rigorous derivation of the linear spring‐layer interface model is provided to clarify its domain of validity. The accuracy and convergence rate of the elaborated numerical approach are assessed via benchmark tests for which exact analytical solutions are available. The computated effective elastic moduli of composites are compared with the relevant analytical lower and upper bounds. Copyright © 2011 John Wiley & Sons, Ltd.     

Fretting fatigue failure mechanism of automotive shock absorber valve

Fretting fatigue is a complex mechanical failure phenomenon, in which two contact surfaces undergo a small relative oscillatory motion due to cyclic loading. This study proposes a methodology to analyze the fretting fatigue failure mechanism of automotive shock absorber valve by means of experimental and numerical approaches. A servo hydraulic test set-up is used to simulate fretting fatigue under real working conditions. Moreover, a 3-D finite element model is developed to analyze the contact status and stress distribution at contact interface between connected components, i.e. washer-disc contact. The experimental test results depict that fretting damage appears at contact interface between washer and disc, which causes the initial crack nucleation and advancing the crack up to the final fracture of valve disc. Stress field, obtained by numerical simulation, is used to monitor some fretting fatigue features such as the distribution of relative slip amplitude, contact pressure and different stress fields at contact interfaces. Eventually, the crack initiation site is estimated by monitoring variation of equivalent multiaxial damage stress at contact interface.     

Three‐dimensional stress concentrations at circular pin holes in clearance‐fit lugs

The influences of thickness and bonding clearance on stress concentration factors (SCFs) at circular holes in pin‐loaded straight lugs are systematically investigated using the finite element method. The three‐dimensional effect on stress concentration at pin hole is strong when the thickness B of lug is higher than the radius R of pin hole. The maximum tensional SCF K_max normalized by its corresponding plane stress solution K_p–σ increases with increasing B/R when B/R is higher than 2 for all of r/R (the radius of pin to that of lug), and also increases with decreasing r/R for a given B/R. It is also found that the plane stress SCF K_p–σ nearly remains a constant when r/R < 0.98, but is strongly sensitive to r/R and increases by 30% with r/R changing from 0.98 to 1. On the other hand, the friction coefficient, Young's modulus and the load level have also influences on stress concentrations, which should not be neglected in design of structures. An empirical formula of the maximum SCF is obtained for convenience of engineering applications.     

Three‐dimensional numerical solution for wear prediction using a mortar contact algorithm

A finite element formulation to compute the wear between three‐dimensional flexible bodies that are in contact with each other is presented. The contact pressure and the bodies displacements are calculated using an augmented Lagrangian approach in combination with a mortar method, which defines the contact kinematics. The objective of this study is to characterize the wear rate coefficients for bimetallic pairs and to numerically predict the wear depths in new component designs. The proposed method is first validated with the classical pin‐on‐disc problem. Then, experimental results of wear for the metallic pairs used in internal combustion engine valves and inserts are presented and are taken as a reference solution. An example is provided that shows agreement of the numerical and experimental solution. Finally, the proposed algorithm is used to predict the wear in an application example: the wear in an internal combustion engine valve. Copyright © 2013 John Wiley & Sons, Ltd.