Elastic recovery of a scratch in a polymeric surface: experiments and analysis

A scratch may be regarded as a tangential indentation. Hence standard indentation laws can be used to analyse the geometry of the scratches left by a moving tip on the surface of a viscoelastic viscoplastic body such as a commercial grade of cast polymethylmethacrylate (PMMA). This paper presents experimental results and an analysis of the elastic recovery of a scratch after contact with a tip. The experimental data were obtained with a new scratch apparatus fitted with a built-in microscope, which allows in situ analysis of the contact area and the groove left on the surface. The elastic plastic total penetration depth h_ep is split into its plastic part h_p and elastic part h_e. In the case of full plasticity around the tip during scratching, which for an elastic plastic material implies a sufficiently high value of the contact strain, the elastic law describes the depth relaxation and experimental data agree with the analysis. In the case of a purely elastic response of the material, corresponding to low values of the contact strain, the rear contact radius is equal to the front contact radius. At intermediate levels of strain, an analysis of the elastic recovery must take into account the contribution of the plastic term to the elastic plastic response of the material.     

Study of plowing and friction at the surfaces of plastic deformed metals

Experimental and analytical investigations of plowing and friction were conducted at the surfaces of well-polished lead, aluminum, copper, nickel, molybdenum, and tungsten to study the mechanism of the load/penetration dependency. The experimental tests were performed with a Nano-Indenter XP of MTS and a Scanning Probe Microscope (SPM), Nanoscope IIIa of Digital Instruments. In addition to make indentation and measure the hardness and Young’s modulus, the indenter was used to make scratches at the surface of metals under different normal load while the penetration depth and frictional force encountered during the scratching were recorded. The SPM, operated mostly in the contact mode, was used to examine the scratch profile. Under the test conditions, plastic deformation dominated at the surfaces of the metals. An analytical model was established to express plastically deformed contacts, based on plowing of a conical-shaped indenter with a hemispherical tip at a plastic deformed surface. Penetration depth and scratched volume were calculated, which is in good agreement with experimental observation. The frictional coefficient μ was also calculated with the model, which accounted for plowing as well as the adhesion force between the indenter and surface. Beside fair agreement of experimental data and calculated values on μ under the loads applied, the model indicated a dramatic rise in friction coefficient under very low loads, which was not observed in the tests. The discrepancy was discussed, and it was believed that the dramatic increase in μ is for the calculated μ and may be due to the assumed dominant contribution of adhesion force in actual contact load with decreasing external load, and it appears only the adhesion energy Δγ is significant. The actual adhesion energy Δγ between our diamond indenter and metal surface in our test condition might be smaller than the value used in calculation.     

Influence of porosity on cavitation instability predictions for elastic–plastic solids

Cavitation instabilities have been found for a single void in a ductile metal stressed under high triaxiality conditions. Here, the possibility of unstable cavity growth is studied for a metal containing many voids. The central cavity is discretely represented, while the surrounding voids are represented by a porous ductile material model in terms of a field quantity that specifies the variation of the void volume fraction in the surrounding metal. As the central void grows, the surrounding void volume fractions increase in nonuniform fields, where the strains grow very large near the void surface, while the high stress levels are reached at some distance from the void, and the interaction of these stress and strain fields determines the porosity evolution. In some cases analysed, the porosity is present initially in the metal matrix, while in other cases voids nucleate gradually during the deformation process. It is found that interaction with the neighbouring voids reduces the critical stress for unstable cavity growth.     

Numerical study of scratch velocity effect on recovery of viscoelastic-viscoplastic solids

The scratch test is a classical way to investigate the abrasive resistance of coatings and substrates. Because of the complex phenomena involved, the use of refined finite element analysis is often required to analyze the influence of specific parameters. In this paper, the influence of the tip velocity on the scratch recovery of polymer-like time-dependent solids is qualitatively investigated. More precisely the response of three constitutive models is analyzed: an elastic-viscoplastic model, a linear viscoelastic model and finally a viscoelastic-viscoplastic model. This last model is an original assembly based on the connection in series of the elastic-viscoplastic model and the linear viscoelastic model. For that, a new method allowing the connection in series of two different rheological models in a FE code is presented. To analyze the numerical results, the concept of representative stress and representative strain rate of a scratch test is introduced.     

Dynamic asymmetrical instability of elastic–plastic beams

Dynamic instability of elastic–plastic beam is investigated by employing a three-degree-of-freedom (3-DoF) beam model. Especially, asymmetrical instability induced by symmetrical load is discussed. The asymmetrical instability is considered as a second-order buckling mode. Four types of perturbations, i.e., geometrical misalignment, material property mismatch, unsymmetry of applied load and disturbance of boundary conditions, are introduced to activate the asymmetrical responses. The asymmetrical response is characterized by a modal participation factor α₂ which corresponds to an asymmetrical mode shape. Phase plane trajectories and Poincaré map are used to illustrate the chaotic characteristics of the beam response. Results show that if the perturbations are small enough, the perturbation type has negligible influence on the critical load for the occurrence of the asymmetrical instability, which implies that the asymmetrical instability is an intrinsic feature of the beam system. However, with the increase of the magnitude of the perturbations, the influence of the asymmetrical vibration is expanded to a large extension of loading parameter.     

Instabilities generated by friction in a pad–disc system during the braking process

This paper presents a numerical and experimental study of a pad–disc tribometer. The explicit dynamic finite element software PLAST 3 in 3-D is used to simulate the behaviour of the two bodies involved. Coulomb's friction law is used at the contact surface with a constant coefficient. For this application, temporal simulations show that separation occurs between surfaces, proof of instabilities. This unstable state is characterized by a stick–slip–separation wave. We show that instabilities describe a periodic shock phenomenon at the contact interface. Consequently, the acceleration spectrum recorded on the surface of the pad reveals periodicity in the frequency domain. It shows also that, in this case, the vibrations responsible for the instability are localized in the pad. The mode responsible for squealing can be obtained by a modal analysis of the pad–disc system by assuming that the interface is stuck. We highlight the importance of the pad Poisson's ratio in the occurrence of this unstable state. A numerical/experimental comparison has been performed and the fundamental frequency of squeal obtained experimentally and its magnitude agree with those calculated numerically with PLAST 3.     

Three-parameter approach for elastic–plastic fracture of the semi-elliptical surface crack under tension

Systematic three-dimensional elastic–plastic finite element analyses are carried out for a semi-elliptical surface crack in plates under tension. Various aspect ratios (a/c) of three-dimensional fields are analyzed near the semi-elliptical surface crack front. It is shown that the developed J–Q annulus can effectively describe the influence of the in-plane stress parameters as the radial distances (r/(J/σ₀)) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/σ₀) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σ_e, the hydrostatic stress σ_m and the stress triaxiality R_σ, the three-parameter J–Q_T–T_z approach is proposed based on the numerical analysis as well as a critical discussion on the previous studies. By introducing the out-of-plane stress constraint factor T_z and the Q_T term, which is determined by matching the finite element analysis results, the J–Q_T–T_z solution can predict the corresponding three-dimensional stress state parameters and the equivalent strain effectively in the whole plastic zone. Furthermore, it is exciting to find that the values of J-integral are independent of n under small-scale yielding condition when the stress-free boundary conditions at the side and back surfaces of the plate have negligible effect on the stress state along the crack front, and the normalized J tends to a same value when φ equals about 31.5° for different a/c and n. Finally, the empirical formula of T_z and the stress components are provided to predict the stress state parameters effectively.     

Three-dimensional finite element modelling of the scratch test for a TiN coated titanium alloy substrate

A three-dimensional (3D) finite element (FE) simulation of a rigid Rockwell C indenter scratching a TiN/Ti-6Al-4V coating/substrate system is presented. Coulomb friction between the indenter and the surface of the coating/substrate system was considered. The material properties of the coating and substrate were assumed to be elastic–plastic following a bilinear law with isotropic strain hardening. The von Mises yield criteria was used to determine the onset of plastic deformations. The scratch depth profiles at different moving distances were studied. The distributions of the stress field at the contact surface, in the coating, and at the interface of the coating/substrate system were investigated. The finite element results can be used to explain the failure modes of coated materials at the scratch test.     

Strain and Stress Fields During Scratch Tests on Amorphous Polymers: Influence of the Local Friction

In this paper, we present results deduced from three-dimensional finite element simulations of scratching, with spherical indenter geometry at different imposed ratios, a/R in the range of 0.1–0.9. For each simulated ratio a/R, the local friction has been increased from 0 to 1. The paper aims at studying the tangential scratch behaviour of homogeneous polymeric substrates, considered in first approximation as elastic linear-hardening plastic material. For only elastic–plastic contacts, without any strain rate or temperature effects, it focuses on studying some characteristic response due to spherical scratching process as a function of scratching conditions (a/R, μ _loc ) such as the stress and plastic strain fields, including the plastic zone dimension and the definition of an volume average plastic strain.     

Safety and collapse of elastic–plastic beams against dynamic loads

The dynamic load-bearing capacity of elastic–plastic beam structures is analysed by the apparatus of shakedown theory. The reduced kinematic formulation for bending beams, which is equivalently deduced from Koiter’s kinematic theorem, combined with the plastic collapse’s method of hinge mechanisms appears effective in solving practical problems. The safety limits on the quasiperiodic dynamic loads as well as respective collapse mechanisms for a number of practical beams are determined.     

Analysis of wheel and rail adhesion under wet condition by using elastic–plastic microcontact model

This paper presents a numerical model to investigate the adhesion characteristics of the wheel/rail contact with consideration of surface roughness under wet conditions. The elastohydrodynamic lubrication theory is used to obtain the load carried by water, and the statistical elastic–plastic microcontact model presented by Zhao–Maietta–Chang is applied to calculate the load carried by asperities contact. Meanwhile, the thermal influencing reduction factor is used to consider the inlet heating effects on the film thickness, and the change of water viscosity is also taken into consideration due to the flash temperature generated by the moving rough surfaces. Furthermore, the present work investigates the dependence of the wheel/rail adhesion coefficient on train speed, surface roughness amplitude, the initial temperature, the plasticity index and the maximum contact pressure under wet condition. Copyright © 2014 John Wiley & Sons, Ltd.     

Plane strain elastic–plastic bending of a strain-hardening curved beam

Elastic–plastic analysis of plane strain pure bending of a strain-hardening curved beam has been presented. Only a linear hardening case has been analyzed as the nonlinear equations for a general hardening case could not be solved analytically. A numerical scheme for the computation of stresses and displacements in different stages of deformation has been given and limited FEM verifications have been presented.     

A new stress-based model of friction behavior in machining and its significant impact on residual stresses computed by finite element method

Friction modeling in metal cutting has been recognized as one of the most important and challenging tasks facing researchers engaged in modeling of machining operations. To address this issue from the perspective of predicting machining induced residual stresses, a new stress-based polynomial model of friction behavior in machining is proposed. The feasibility of this methodology is demonstrated by performing finite element analyses. A sensitivity study is performed by comparing the cutting force and residual stress predicted based on this new model with those based on a model using an average coefficient of friction deduced from cutting forces and a model using an average coefficient of friction deduced from stresses. The average coefficient of friction computed based on the measured cutting forces is the conventional approach and is still widely used. The average coefficient of friction due to stresses can be considered as a simplified version of the proposed model. Simulation results show significant difference among the predicted residual stresses. As the proposed model is able to capture the relationship between the normal stress and shear stress on the tool rake face better than the conventional approach can, it has a potential for improving the quality of the prediction of the residual stresses induced by machining.     

From local failure toward global collapse of elastic–plastic structures in fluctuating fields

Application of shakedown theory to study the load-bearing capacity of truss structures subjected to varying loads is presented. Inadaptation may cause local fractures not leading to the global collapse (the loss of load-bearing capacity) of a structure. A full analysis requires a step-by-step application of the reduced kinematic formulae constructed recently by the author to check the occurrence of a local fracture by alternating plasticity and a possible spreading of the fracture zone until the critical state of global incremental (or instantaneous) collapse is reached. This basic phenomenon, in somehow more sophisticated appearance, might be observed in many more general structures and in inhomogeneous materials working in changing fields, as in some fiber bundle models presented. The solution procedure could also help to improve the design of a structure for particular working conditions.     

Subsurface deformation and damage accumulation in aluminum–silicon alloys subjected to sliding contact

The study of plastic deformation and damage accumulation below the contact surfaces is important in order to understand the dry sliding wear behaviour of aluminum alloys. Experimental evidence exists for the nucleation of voids and microcracks around second phase particles in the material layers adjacent to the contact surface. Propagation of these cracks at a certain depth below the surface may lead to the creation of long, thin plate-like wear debris particles. This work studied the deformation processes during sliding wear by means of metallographic observations of subsurface layers in an Al–7% Si (A356 Al) alloy and by finite element analyses. Specifically, the accumulation of subsurface stresses and strains was investigated, using a coupled structural-thermal finite element model based on the Voce-type exponential stress–strain relationship obtained from the sliding wear tests. Additionally, temperature and strain rate effects were taken into account using a constitutive equation based on Johnson–Cook and Cowper–Symonds models.Accordingly during sliding, the flow stress in subsurface layers increased rapidly and reached a saturation stress after a finite number of sliding contacts. The variation of hydrostatic pressure for different loading conditions was also determined as a function of sliding passes: as the sliding process progressed from the first to the seventh contacts, the hydrostatic pressure at the surface increased from 1150 to 1300 MPa. A total temperature increase of 45 K occurred at the surface after the seventh sliding contact. A debris formation model was proposed in which the presence of a maximum damage gradient at critical depth was considered. The model showed that, with a sliding velocity of 10 m/s, and a normal load of 150 N per unit thickness in mm, the material location where the maximum rate of damage occurred corresponded to a normalized depth (depth/counterface diameter) of 0.060. Increasing the load to 250 N/mm caused an increase in the critical depth of damage (a normalized depth of 0.085). Comparisons with the experimental subsurface crack observations indicate that the proposed damage rate calculations provide a good estimation of the subsurface crack propagation depth.     

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.     

Material behaviors and mechanical features in friction stir welding process

This paper presents the 3D material flows and mechanical features under different process parameters by using the finite element method based on solid mechanics. Experimental results are also given to study the effect of process parameters on joining properties of the friction stir welds. Numerical results indicate that the tangent flow constitutes the major part in the material flow. The shoulder can accelerate the material flow on the top half of the friction stir weld. The distribution of the equivalent plastic strain can correlate well with the microstructure zones. Increasing the angular velocity of the pin, the material in the nugget zone can be more fully mixed, which improves the joining quality of the two welding plates. The increase of speeds, including the rotational speed and the translational speed, can both accelerate the material flow, especially in front of the pin on the retreating side where the fastest material flow occurs. The contact pressure on the pin-plate interface is decreased with the increase of the angular velocity. An erratum to this article can be found at     

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.     

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.