Numerical modelling of cyclic plasticity and fatigue damage in cold-forging tools

Industrial cold-forging tools with complex geometry are very likely to be exposed to local plastic deformation near stress concentrating details. The accumulation of plastic deformation resulting from the cyclic loading conditions leads to fatigue damage and eventually to generation of a crack in the surface of the die. To study the effect of die prestressing on fatigue damage development, a plane strain finite element model of a cold-forging die is analysed. A complex material model, combining kinematic and isotropic hardening with continuum damage mechanics, is used to simulate the elastic–plastic material behaviour and damage development. Furthermore, a range of uncoupled damage measures are applied in the comparison of conventional and new prestressing concepts.     

A surface flow line model of a scratching tip: apparent and true local friction coefficients

The apparent friction coefficient is the ratio between the tangential force and the normal load applied to a moving scratching tip. It includes a so-called “true local” friction coefficient, which is the scission at the interface between the tip and the surface being scratched, and a “geometrical” friction coefficient, which is the plough effect due to the wave front created ahead of the moving tip and depends on the shape of the tip. Like in any mechanical test, three basic types of behaviour of the material at the interface are observed: purely elastic, elastic–plastic and fully plastic. As is usual in polymers, the material behaviour is time and temperature dependent and may exhibit strain hardening. A surface flow line model is developed here to deduce the geometrical and true friction coefficients at the interface between a moving scratching tip and a surface from the apparent friction coefficient. Using this model, several situations may be simulated to predict the influence of the geometry of the tip on the scratch resistance of the material.     

Thermomechanical analysis of elastoplastic medium in sliding contact with fractal surface

The effects of mechanical and thermal surface loadings on deformation of elastic–plastic semi-infinite medium were analyzed simultaneously by using the finite element method. Rigid rough surface of a magnetic head and smooth surface of an elastic–plastic hard disk were chosen to perform a comprehensive thermo-elastic–plastic contact analysis at the head–disk interface (HDI). A two-dimensional finite element model of a rigid rough surface characterized by fractal geometry sliding over an elastic–plastic medium was then developed. The evolution of deformation in the semi-infinite medium due to thermomechanical surface loading is interpreted in terms of temperature, von Mises equivalent stress, and equivalent plastic strain. In addition to this, the effects of friction coefficient, sliding, and interference distance on deformation behavior were also analyzed. It is shown that frictional heating increases not only the contact area but also the contact pressure and stresses.     

Pulse loading shape effects on pressure–impulse diagram of an elastic–plastic, single-degree-of-freedom structural model

Pulse loading shape effects on the dynamical response of an elastic–plastic, single-degree-of-freedom (SDOF) structural model are studied in the present paper. Two dimensionless parameters are introduced to classify the studied problem into elastic, elastic–plastic and rigid–plastic structural responses. When structural damage is controlled by maximum structural deflection, a characteristic curve in loading parameter space can be used to define an isodamage curve, i.e., pressure–impulse diagram, which is generally loading-shape-dependent. Dimensionless loading parameters, termed as effective loading parameters, are introduced in the present paper to give unique loading-shape-independent pressure–impulse diagram for each response category.     

Stress distributions in energy generating two-layer tubes subjected to free and radially constrained boundary conditions

Analytical solutions are obtained for thermally induced axisymmetric elastic and elastic–plastic deformations in heat generating composite tubes having a free inner and a radially constrained outer boundaries. Tresca's yield condition and its associated flow rule are used to determine the elastic–plastic response of the assembly. Depending on the physical properties of the materials used, eight different plastic regions with different mathematical forms of the yield condition may occur in the assembly. The closed form solutions for these plastic regions are obtained by assuming linearly hardening material behavior. Various numerical examples are handled using thermal and mechanical properties of real engineering materials.     

Investigation of sharp contact at rigid–plastic conditions

Sharp contact problems are examined theoretically and numerically. The analysis is focused on elastic–plastic material behaviour and in particular the case when the local plastic zone arising at contact is so large that elastic effects on the mean contact pressure will be small or negligible. It is shown that, save for the particular case of a rigid–plastic power-law material, at such conditions, there is no single representative value on the uniaxial stress-strain curve that can be used in order to evaluate the global parameters at contact. However, the present numerical results indicate that good accuracy predictions for the mean contact pressure can be achieved when this variable is described by two parameters corresponding to the stress levels at, approximately, 2 and 35% plastic strain. Regarding the size of the contact area, it is shown that this quantity is very sensitive to elastic effects and any general correlation with material properties is complicated at best. The numerical analysis is performed by using the finite element method and the theoretical as well as the numerical results are compared with relevant experimental ones taken from the literature. From a practical point of view, the presented results are directly applicable to material characterization or measurements of residual mechanical fields by sharp indentation tests, but also for situations such as contact in gears or in electronic devices.     

Numerical simulation of the localization behavior of hydrostatic-stress-sensitive metals

The present paper deals with the numerical simulation of the elastic–plastic deformation and localization behavior of solids which are plastically dilatant and sensitive to hydrostatic stresses. The model is based on a generalized macroscopic theory taking into account macroscopic as well as microscopic experimental data obtained from tests with iron-based metals. It shows that hydrostatic components may have a significant effect on the onset of localization and the associated deformation modes, and that they generally lead to a notable decrease in ductility. The continuum formulation relies on a generalized I₁–J₂–J₃ yield criterion to describe the effect of the hydrostatic stress on the plastic flow properties of metals. In contrast to classical theories of metal plasticity, the evolution of the plastic part of the strain rate tensor is determined by a non-associated flow rule based on a plastic potential function which is expressed in terms of stress invariants and kinematic parameters. Numerical simulations of the elastic–plastic deformation behavior of hydrostatic-stress-sensitive metals show the physical effects of the model parameters and also demonstrate the efficiency of the formulation. Their results are in excellent agreement with available experimental data. A variety of large-strain elastic–plastic problems involving pronounced localizations is presented, and the influence of various model parameters on the deformation and localization behavior of hydrostatic-stress-sensitive metals is discussed.     

Numerical study of the flange earring of deep-drawing sheets with stronger anisotropy

A Barlat–Lian anisotropy yield function is introduced into a quasi-flow corner theory of elastic–plastic finite deformation and the elastic–plastic large deformation finite element formulation based on the principle of virtual velocity and the discrete Kirchhoff triangle plate shell element model. The focus of the present researches is on the numerical simulation of the flange earring of deep-drawing process of circular sheets with stronger anisotropy, based on which, the schemes for controlling the flange earring are proposed.     

Simulation of thermal stresses due to grinding

An efficient finite element procedure has been developed to calculate the temperatures and stresses arising due to a moving source of heat. The procedure is applied to calculate the thermal stresses produced in hardened steels during grinding. The thermal load during grinding is modeled as a uniformly or triangularly distributed, 2D heat source moving across the surface of a half-space, which is insulated or subjected to convective cooling. The grinding of elastic and elastic–plastic workpiece materials has been simulated. The calculated transient stresses and temperatures in an elastic solid are found to be in good agreement with prior analytical and numerical results. In an elastic–plastic workpiece material, for which no analytical solution is available for the residual stress distributions, the finite element calculations show that the near surface residual stress is predominantly tensile and that the magnitude of this stress increases with increasing heat flux values. Based on an analysis of the effects of workpiece velocity, heat flux magnitude and convective cooling, on the residual stress distributions in an elastic–plastic solid, it is seen that the calculated thermal stress distributions are consistent with experimentally measured residual stresses on ground surfaces. Furthermore, the results explain often cited observations pertaining to thermally induced grinding stresses in metals.     

Elastic–plastic deformations of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions

Analytical solutions for the elastic–plastic stress distribution in rotating variable thickness annular disks are obtained under plane stress assumption. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. The thickness of the disk is assumed to vary in parabolic form in radial direction which leads to hypergeometric differential equations for the solution. It is shown that, depending on the boundary conditions used, the plastic core may contain one, two or three different plastic regions governed by different mathematical forms of the yield criterion. The expansion of these plastic regions with increasing angular velocity is obtained together with the distributions of stress, displacement and plastic strain. It is also shown mathematically that in the limiting case the variable thickness disk solution reduces to the solution of rotating uniform thickness disk.     

Contact Fatigue Analysis of a Dented Surface in a Dry Elastic–Plastic Circular Point Contact

The present article proposes a methodology for the computational analysis of damage induced in the vicinity of dents in a dry circular point contact under repeated rolling. The failure risk is evaluated through the use of the Dang Van multiaxial fatigue criterion. The dent is a typical surface defect encountered in rolling element bearings when operating in contaminated environments. It is usually created by a solid particle not removed by seals or filters when passing through an EHL conjunction. Since local plasticity occurs when the debris is first entrapped between the contacting surfaces, and later when the resulting dents are subjected to moving contact load, the elastic–plastic behavior of the material should be captured by the model. First, the dent shape and the subsurface stress and strain fields produced by the presence of a spherical particle are obtained by the finite element method. Second, the rolling of the load over the surface defect is simulated using a semi-analytical elastic–plastic code. The simulations are carried out for two different debris materials, both ductile but one significantly softer than the contacting surfaces, i.e., made of stainless steel 316L, the other one being made of bearing steel AISI 52100 similar to the contacting surfaces. The dent shape and initial stress and strain states are first presented. Subsequent stress and strain states after a few rolling cycles are then presented. Finally the effects of the coefficient of friction, presence of residual stress, and contact load magnitude are highlighted.     

On the rotating elastic–plastic solid disks of variable thickness having concave profiles

In this paper, an analytical solution for the elastic–plastic stress distribution in rotating variable thickness solid disks is presented. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. It is shown that depending on the shape of the disk profile, the radial stress in the central region may exceed the circumferential stress. The plastic zone which develops away from the axis of the disk consists of three annular regions governed by different mathematical forms of the yield criterion. The propagation of these plastic regions with increasing angular velocity is obtained together with the distributions of stresses and deformations in nondimensional forms.     

A Generalised Asperity-Based Friction Model

Despite considerable research effort, the use of physics-based modelling to predict frictional behaviour is still a debatable question in modern tribological research. This article presents a dry-friction model, based on physical phenomena such as adhesion, elastic–plastic contact and deformation. This contribution offers a means to simulate all kinds of frictional behaviour that is observed in experimental research. The contact of two bodies through their surfaces is transformed into the contact of a body that is provided with asperities and containing material and geometrical information of both of the mating surfaces, and a counter profile, holding solely geometrical information. The local adhesion between the asperity tips and the counter profile, together with the elastic–plastic behaviour of the asperities themselves, form the basis for this model. The simulation results show qualitatively good agreement with experimental study. Friction and contact phenomena such as normal creep, increasing static coefficient of friction with increasing dwell time, pre-sliding hysteresis with nonlocal memory, Stribeck and viscous effect, frictional lag, stick–slip and dynamical oscillations are revealed by this model. Furthermore, future improvement and refinement of the model is possible (and ongoing) so as to incorporate lubrication and asperity wear.     

Plastic deformation and contact area of an elastic–plastic contact of ellipsoid bodies after unloading

This paper presents theoretical and experimental results of the residual or plastic deformation and the plastic contact area of an elastic–plastic contact of ellipsoid bodies after unloading. There are three regime responses of the deformation and contact area: elastic, elastic–plastic and fully plastic. Experimental investigation is presented in order to validate the proposed model. A new technique is introduced to measure the plastic deformation and plastic contact area. Very good correlation is found between the theoretical prediction and the experimental results.     

Preliminary assessment of sandwich plates subject to blast loads

The question motivating the present study is whether metal sandwich plates with sufficiently strong cores are able to sustain substantially larger blast loads than monolithic solid plates of the same material and total mass. Circular plates clamped at their edges are considered under blast loads large enough to produce substantial deflections. The material is elastic–perfectly plastic. Material strain-rate dependence and fracture are neglected. A dynamic finite element formulation for elastic–plastic solids is employed to analyze the plate response. Uniformly distributed blast impulses are considered. As a basis for comparison, complete results are obtained for solid plates for both zero-period and finite-period impulses. Similar computations are carried out for a set of sandwich plates having tetragonal truss cores. The potential for superior strength and energy absorbing capacity of the sandwich plates is demonstrated compared with solid plates having the same mass. The importance of both the strength and energy absorbing capacity of the core are highlighted for superior blast resistance. Proposals for further research are made.     

Application of crystal plasticity to plastic behavior at notched plate and crack propagation

Strain concentration characteristics of ductile polycrystalline materials are studied experimentally and numerically by considering a notched square segment of material. The micromechanical modeling is performed using the finite element method based on crystal plasticity, while the material sample is taken to be FCC polycrystallline copper segment. The constitutive behavior is taken to be large-strain strain-rate-dependent elastic–plastic material. To effectively simulate polycrystalline behavior, the grain shape is generated from Voronoi tessellation, bearing a different lattice orientation in each grain. Strain concentration patterns around the notched bottom are observed experimentally and numerically, which are enlarged near the notch by accompanying a formation of localized strain accumulation toward an oblique direction. For the sample analyzed, with a relatively small macroscopic strain of 0.10, the notched bottom region experiences plastic strains as large as 1.00, and provides a strong indication that failure will initiate from the corner. Implications of this modeling study to microcracking failure are discussed by considering two fundamental modes of shear and cleavage to provide plausible microcracking examples.     

Modeling and estimation of deformation behavior of particle-reinforced metal–matrix composite

In order to estimate the characteristic feature of the deformation behavior of materials with a length scale, the strain gradient plasticity theories, corresponding variational principle and a finite element method are given. Then the finite element method is applied to the estimation of the mechanical characteristics of the particle reinforced metal–matrix composites modeled under plane strain conditions. The effects of the volume fraction, size and distribution pattern of the reinforcement particles on the macroscopic mechanical property of the composite are discussed. It has been clarified that the deformation resistance of the composite is substantially increased with decreasing particle size under a constant volume fraction of the reinforcement material. The main cause of the increase of the deformation resistance in the plastic range is the high strain gradient appearing in the matrix material, which increases with the reduction of the distance between particles.     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

Elastic–plastic adhesive contact of rough surfaces based on plastic asperity concept

The paper describes an analysis of adhesive contact between rough surfaces with small-scale surface asperities using an elastic–plastic model of contact deformation based on fictitious plastic asperity concept developed by Abdo and Farhang [Int. J. Non-Linear Mech. 40 (2005) 495]. The model considers simultaneous occurrence of elastic and plastic behaviours for an asperity. The well-established elastic adhesion index and plasticity index are used to consider the different contact conditions that arise as a result of varying load and material parameters. The load-separation behaviour for different combinations of these parameters is obtained. Comparison with previous elastic–plastic model that was based on elastic-then-plastic assumption is made showing significant differences.     

Viscoelastic and elastic–plastic behaviors of amorphous polymeric surfaces during scratch

In this study, we propose an analysis of the residual groove after contact between a spherical indenter and an amorphous polymeric surface (polymethylmethacrylate, PMMA) in scratch experiments. The geometrical shape of the residual groove was mathematically described using an exponential decay law. Finite element modeling (FEM) of scratch tests was compared to the corresponding experimental results. Assuming a two-segment simplified constitutive law with linear elastic behavior followed by linear strain hardening, the friction at the interface between the indenter and the material was modeled with a Coulomb's friction coefficient varying from 0 to 0.4, for computed ratios a/R between 0.1 and 0.4. The FEM results for elastic–plastic contact indicate that the shape of the residual groove is directly related to the plastic strain field in the deformation beneath the indenter during scratching. It is shown that the dimensions of the plastically deformed volume and the plastic strain gradient both depend on the ratio a/R and also on the friction coefficient.