Finite element analysis of rough surfaces based on ultimate‐stress asperity concept

Elastoplastic contact mechanics model of rough surface based on fractal theory

The determination of the elastoplastic deformation regime arising at the microcontact of a deformable ellipsoid and a rigid smooth flat was the main purpose of this study. One-eighth of an ellipsoid and a flat plate were taken as the contact bodies in the finite element analysis, and a mesh scheme of multisize elements was applied. Two observed phenomena regarding the contact pressures and the equivalent von Mises stresses formed at the contact area are given in order to identify the inception of the fully plastic deformation regime of an ellipsoid with an ellipticity ke. If the ellipticity (k) of an elliptical contact area is defined as the length ratio of the minor axis to the major axis, it is asymptotic to the ke value when the interference is sufficiently increased, irrespective of the ke value. The dimensionless interference regime associated with the elastoplastic deformation regime is narrowed by increasing the ellipticity of the ellipsoid (ke). Significant differences in the microcontact parameters such as the contact pressure, the contact area, and the contact load were found to be a function of the interference and the ke parameter of an ellipsoid. The interferences corresponding to the inceptions of the elastoplastic and fully plastic deformation regimes are both increased if the ke value is lowered. The interference, the contact area, and the contact load predicted by the present model for the behavior demonstrated at the inception of the elastoplastic deformation regime are lower than those obtained from the Horng model (Horng, J. H., 1998, “An Elliptical Elastic-Plastic Asperity Microcontact Model for Rough Surfaces,” ASME J. Tribol., 120, pp. 82–88) and the Jeng-Wang model (Jeng, Y. R., and Wang, P. Y., 2003, “An Elliptical Microcontact Model Considering Elastic, Elastoplastic, and Plastic Deformation,” ASME J. Tribol., 125, pp. 232–240). Big differences in the results of the average contact pressure, the contact area, and the contact load among the above microcontact models are discussed. The discrepancies are also explained from the developments of these models and boundary conditions set for the elastoplastic deformation regime.

The present work deals with the computation of surface stresses and deformation in the presence of friction. The evaluation of the elastic-plastic contact is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. Several factors of sliding friction model are discussed: surface roughness, mechanical properties and contact load and areas that have strong effect on the friction force. The critical interference that marks the transition from elastic to elastic- plastic and plastic deformation is found out and its connection with plasticity index. A finite element program for determination contact analysis of the assembled details and due to details of deformation that arose a normal and tangencial stress is used.

Cadaveric validation of a finite element modeling approach for studying scapular notching in reverse shoulder arthroplasty

Due to inherent nonlinear stiffness and damping characteristics, dry friction interfaces have a significant impact on the dynamics of jointed structures. When two surfaces are brought into purely normal contact, contact pressure distribution is of high concern. This work focused on the statistics of the contact pressure distribution between a rough surface and a smooth rigid plane, which provides new insight into the interface contact behaviour. First, the fractal rough surface is generated using the Weierstrass–Mandelbrot function with measured roughness parameters. With meshed rough surfaces, an elastic–plastic finite element contact analysis is performed to determine the contact pressure distribution. Then, the results of contact pressure are statistically analysed. The effects of roughness and contact load on contact area, contact stiffness and mean contact pressure are thoroughly investigated. The probability distribution of contact pressure is determined by fitting a continuous function using a twofold Weibull mixture model. The proposed probability distribution function is found to be capable of describing contact pressure. The contact pressure distribution is affected by the surface fractal characteristics and evolves with the contact load.

In a mechanical interface, the contact surface topography has an important influence on the contact stiffness. In the contact processes of asperities, elastic-plastic change can lead to discontinuity and lack of smoothness at a critical contact point. The result is a large difference between the elastic-plastic deformation and the actual asperity deformation. Based on Hertz contact theory, the heights of asperities on a rough surface obey a Gaussian distribution. To take into consideration the continuity of elastic-plastic asperity deformation, we divide the elastic-plastic deformation into three stages: pre-elastic-plastic, mid-elastic-plastic, and post-elastic-plastic deformation. This establishes an elastic-plastic contact model of asperity at a continuous critical point. The contact model of a single asperity fits well with the Kogut–Etsion model and the Zhao–Maietta–Chang model, and the variation trend is consistent. At a lower plastic index, the present model coincides with classical models of contact area and contact load. At a higher plastic index, the simulation results of the present model differ from the Greenwood–Williamson model and the Chang–Etsion–Bogy model but are similar to results from the Kogut–Etsion and Zhao–Maietta–Chang models. This study provides a more accurate microscopic contact model for rough surfaces and a theoretical framework for interface design and analysis.

Contact temperature under three-body dry friction conditions

A new model of surface breaking rolling contact fatigue (RCF) crack driven by a coupled action of a squeeze oil film built up in the crack interior and a pressure exerted at the external contact interface was developed. The model can be applied to the ‘nominally dry’ contact couples with an occasional presence of liquid in the crack interior (wheel/rail contact) as well as to the elastohydrodynamic lubrication (EHL) conditions. In the first case, the contact load is a result of solid/solid interaction and can be determined by solving the FE contact problem, but the liquid contained in the crack interior forms a thin film between the crack faces changing their interaction into the type of liquid/solid. This liquid is being periodically squeezed under contact load and acts as a ‘squeeze film’ known from the lubrication theory. In the second case, the liquid (lubricating oil) is permanently present in the contact area and consequently in the vicinity of the crack mouth. This creates conditions for filling the crack with oil. Similarly as in the first case, the ‘squeeze oil film’ is built between the crack faces. The contact load in this case results from a liquid/solid interaction and can be approximated by the pressure and traction distributions obtained from the numerical solution of the elastohydrodynamic contact problem. In both cases the model can be used to determine the Linear Elastic Fracture Mechanics (LEFM) crack tip stress intensity histories during cyclic loading and consequently to predict the crack growth rate and direction.An example of applying the model to the EHL case is given to explain the mechanisms and phenomena leading to the crack front loading. The cycle of rolling a roller over the crack was numerically simulated to obtain the mixed mode (I and II) SIF histories. In the analysis, the EHD pressure and traction were determined through the full solution of the EHD line contact problem accounting for the presence of a crack, whilst the pressure in the crack was found with the use of the wedge shaped squeeze oil film (SOF) model. Possible effects of the mode I and mode II stress intensity cycles on crack growth rate and direction are discussed. The solution indicates high pressure in the neighbourhood of the crack tip, exerted on the crack faces by the squeeze oil film. This leads to the ranges of the mode I and mode II SIF variations, which are larger than for the ‘dry’ and ‘fluid entrapment’ models, and can be an explanation for the crack growth rate observed in practice

Influence of surface roughness and contact load on friction coefficient and scratch behavior of thermoplastic olefins

Clayey soils with swelling and shrinkage characteristics have been major causes for many problems in roads, buildings and other civil engineering infrastructure in various areas of Pakistan, particularly where there are several patches of such soils on either side of Indus River. As the consistency characteristics are directly related with the variation of moisture content; therefore, this study was explicitly focused to investigate the effect of lime and wheat straw on the consistency characteristics of clayey soils with relatively high swelling and shrinkage characteristics. The consistency test results indicate that by the increase in lime content there is a decrease in the plasticity index of soil; for instance, 10% lime content resulted to 59% decrease in the plasticity index value. On the other hand; the addition of wheat straw resulted in a significant increase in the plasticity index; for instance, 10% wheat straw content resulted to a 120% increase in the plasticity index. This study has further shown that the shrinkage and swelling of clayey soils which resulting to several problems in the civil engineering infrastructures may adequately be managed through mixing an appropriate amount of lime and wheat straw as soil stabilizing agent for both immediate and long-term effects.

As a result of increase in population and socioeconomic activities, the rate of production of wastes over the years has been on the rise. A major approach towards managing these wastes is to consider the possibility of waste recycle and minimization. This study assesses the effects of Snail Shell Ash (SSA), a product of snail shell-which itself is a waste product, on lime stabilized lateritic soil. Preliminary tests such as; specific gravity, Atterberg limits and particle size distribution tests were carried out on natural soil sample, for the purposes of identification and classification. The soil sample based on AASHTO classification was classified as A-7-5. Hydrated lime was added to the soil sample at varying proportions of 2, 4, 6, 8 and 10% by weight of soil, thereafter, each of the mixes was subjected to Atterberg limits tests to get the optimal amount of lime required, which was 10% lime because it was at this amount of lime that the least value of plasticity index was gotten. The Snail Shell Ash was later added to the lime-treated lateritic soil at proportions of 2, 4, 6, 8 and 10%. Each of the mixes was subjected to compaction, California bearing ratio (CBR), Atterberg limits and unconfined compressive strength (UCS) tests. Results from these tests showed improvement in soil properties, also, the values of the CBR and UCS increased considerably. At soil natural states, CBR values of 9.5% and 5.5% increased to 67.20% and 53.60% at 6% SSA at unsoaked and soaked states respectively. Also, UCS value of 190 kN/m2 at soil natural increased to 380kN/m2 at 6% SSA. It can be concluded that the SSA performs satisfactorily as a cheap complement for lime in stabilizing lateritic soil.

In this research, the potential use of recycled concrete aggregate (RCA) and CG as a base course construction material was investigated. A laboratory test involving the mechanical stabilization of RCA and CG was conducted to examine their physical properties. Eight samples of RCA blended with CG in varying proportions from 0% to 100 % with 10 % variation were studied. The laboratory test results indicate that 100 % CG yields specific gravity (SG), aggregate crushing value (ACV), aggregate impact value (AIV), Los Angeles abrasion (LAA), flakiness index (FI), elongation index (EI), plasticity index (PI), water absorption, soundness, and California bearing ratio (CBR) values of 2,54 %, 38,37 %, 20,10 %, 33,17 %, 5,59 %, 12,09 %, 0,90 %, 3,52 %, 10,60 %, and 38,08 %, respectively. The results for 100% RCA show SG, ACV, AIV, LAA, FI, EI, PI, water absorption, soundness, and CBR values of 2,70 %, 9,56 %, 5,30 %, 9,20 %, 15,30 %, 15,84 %, NP, 0,23 %, 1,49 %, and 105,87 %, respectively. These results also fail to meet the gradation requirements based on ERA standard specifications. Therefore, mechanical stabilization was adopted to improve the physical properties of the samples. Blending 60 % RCA with 40 % CG resulted in SG, ACV, AIV, LAA, FI, EI, PI, water absorption, soundness, and CBR values of 2,65 %, 19,46 %, 10,70 %, 10,88 %, 16,15 %, 22,01 %, NP, 0,26 %, 2,09 %, and 101,98 %, respectively. At this proportion, the gradation aligns with the required ERA standard specifications for GB2 and GB3 materials. Therefore, CG up to 40 % by weight with 60 % RCA is viable for road base course construction, especially when readily available or nearby.

The repeated normal elastic plastic contact problem of a deformable sphere against a rigid flat under full stick contact condition is investigated with a commercial finite element software ANSYS. Emphasis is placed on the effect of strain hardening and hardening model with the maximum interference of load ranging from elastic to fully plastic, which has not yet been reported. Different values of tangent modulus coupled with isotropic and kinematic hardening models are considered to study their influence on contact parameters. Up to ten normal loading-unloading cycles are applied with a maximum interference of 200 times the interference required to initiate yielding. Results for the variation of mean contact pressure, contact load, residual interference, and contact area with the increasing number of loading unloading cycles at high hardening parameter as well as for low tangent modulus with two different hardening models are presented. Results are compared with available finite element simulations and in situ results reported in the literature. It is found that small variation of tangent modulus results in same shakedown behavior and similar interfacial parameters in repeated loading-unloading with both the hardening rules. However at high tangent modulus, the strain hardening and hardening rules have strong influence on contact parameters.

<div class="htmlview paragraph">Numerous human cadaver impact studies have shown that acute injury to the knee, femoral shaft, and hip may be significantly reduced by increasing the contact area over the anterior surface of the knee. Such impact events are common in frontal crashes when the knee strikes the instrument panel (IP). The cadaveric studies show that the injury threshold of the knee-thigh-hip complex increases as the contact area over the knee is likewise increased. Unfortunately, no prior methodology exists to record the spatial and temporal contact pressure distributions in dummy (or cadaver) experiments. Previous efforts have been limited to the use of pressure sensitive film, which only yields a cumulative record of contact. These studies assumed that the cumulative pressure sensitive film image correlated with the peak load, although this has never been validated. A temporal record of the varying contact pressures would thus be helpful in validating models studying high-speed contact events (i.e. knee impact) incurred during automotive crashes. Thus, the aim of the current study was to present a new methodology to study the contact mechanics of the knee-IP impact event. This was achieved by using specially designed electronic pressure mats capable of transducing the corresponding contact area and pressure magnitudes at a sampling frequency of 1,340 Hz. Sled tests were performed at different delta-V’s using a Hybrid III, 5<sup>th</sup> percentile female dummy. The instrument panels were simulated with blocks of different padding materials of varying stiffness. This produced a variety of contact pressures, areas, and femur loads. The impact load values as recorded by the load cell in the femoral shaft of the dummy, were correlated with the corresponding contact area and contact pressure values to investigate if the peak load at the knee also corresponds with the cumulative pressure distribution. The current study showed that the center of pressure migrated approximately 13 mm suggesting that the temporal pressure distribution is a better measurement than a cumulative image if the true contact area is needed.</div>

The main purpose of the present investigation was to determine the damages generated by the low velocities with the help of the experimental method (Impact by a drop test) and the finite element method. The commercial transient finite element package LS-dyna used to model the effect of slug impactor and circular notch induced damage in composite material subjected to low velocity impact. The studied composite material was T800S/M21 made of carbon/epoxy. The effect of circular notch was examined. The composite material was subjected to stainless steel slug impactor in the transverse direction dropping the composite laminate at the center with three different velocities (2.85 m/s, 3.47 m/s and 4.17 m/s). The analysis was carried out using the model MAT59 for laminate and a rigid body model MAT20 for the slug impactor. The automatic_surface to_surface has been used to model the contact between the impactor and the laminate and the contact_automatic_surface_to_surface_tiebreak to simulate delamination between layers. A good agreement had been shown between the finite element results and the experimental values obtained from the drop tower test. The impact load, impact energy, displacements and the maximal were reported as function of the impact time. The delamination area and the layer impact energy were represented as function of layer orientations. By increasing the impact velocity, the displacement, the delamination area, the contact load and the impact energy increases respectively. The circular notch had an effect on the displacement values; this values increases in respect of the impact velocities. At the reverse, the contact load decreases respectively in function of the velocities. The main purpose of the present investigation was to determine the damages generated by the low velocities with the help of the experimental method (Impact by a drop test) and the finite element method. The commercial transient finite element package LS-dyna used to model the effect of slug impactor and circular notch induced damage in composite material subjected to low velocity impact. The studied composite material was T800S/M21 made of carbon/epoxy. The effect of circular notch was examined. The composite material was subjected to stainless steel slug impactor in the transverse direction dropping the composite laminate at the center with three different velocities (2.85 m/s, 3.47 m/s and 4.17 m/s). The analysis was carried out using the model MAT59 for laminate and a rigid body model MAT20 for the slug impactor. The automatic_surface to_surface has been used to model the contact between the impactor and the laminate and the contact_automatic_surface_to_surface_tiebreak to simulate delamination between layers. A good agreement had been shown between the finite element results and the experimental values obtained from the drop tower test. The impact load, impact energy, displacements and the maximal were reported as function of the impact time. The delamination area and the layer impact energy were represented as function of layer orientations. By increasing the impact velocity, the displacement, the delamination area, the contact load and the impact energy increases respectively. The circular notch had an effect on the displacement values; this values increases in respect of the impact velocities. At the reverse, the contact load decreases respectively in function of the velocities.