Finite Element Simulation of Dry Wear of Prosthesis Made of UHMWPE and 316LVM Stainless Steel

Abstract

The study of wear is currently one of the most important aspects of applied mechanics. The damage caused by this phenomenon involves the total replacement of parts in devices ranging from industrial machinery to biomedical implants. The focus of these work is aimed at the analysis and prediction of mechanical wear in prostheses manufactured using UHMWPE materials and 316 LVM stainless steel by means of the finite element method using Abaqus^® software V. 2020. The wear mechanism between the surfaces of the UHMWPE material specimen and a 316 LVM stainless steel specimen was modeled using Archard’s wear theory to determine the parameters of damage, plastic deformation, and fatigue. The attrition process was discretized into several steps, including developing a program in Fortran code, and integrating a pre-established subroutine known as UMESHMOTION, followed by a Mesh update whenever contact nodes were deformed. For the simulation process, the variables of the thermal properties of conductivity, specific heat, and the parameters of the Johnson-Cook plastic model were taken into account. The simulation results were validated by laboratory tests.

1. Introduction

Within classical mechanics, one of the most relevant phenomena is wear and tear. The studies that have been carried out in recent years still leave many questions to be answered. In this sense, engineering highlights the importance of the loads to which mechanical components are subjected and the reduced margin of tolerances during manufacturing, which is a challenge for the tribological aspect.

Damage caused by wear and tear on the components of a piece of equipment requires its replacement, which triggers a negative economic impact depending on the application. Because of this, it is important to establish appropriate working methods during the analysis that allow for predicting future equipment failures and maintaining productivity, guaranteeing the safety and integrity of operators, and, above all, reducing the costs generated by this phenomenon [1].

Yonggang Meng points out that research activities in the field of tribology have been too far-reaching in the areas of physics, chemistry, surface science, nanotechnology, materials science, biomedical engineering, mechanical engineering, and manufacturing. However, an area that is still relatively not given the necessary importance due to is the phenomenon of wear and tear and how to avoid it [2]. From a medical point of view, in orthopedics, the total replacement of an affected joint returns the patient’s mobility and quality of life by, improving the motor capacity of the joint hip, knee, spinal column or elbow. The replacement of a damaged joint with prostheses requires some effective surgical techniques to restore mobility. In this sense, technological advances have been reflected in the design and materials of these implants, giving rise to a constant search for systems that minimize the maximum wear and tear of surfaces and increase their useful life.

The most widely used material in orthopedics for the replacement of damaged joints is UHMWPE due to its excellent mechanical properties, such as its self-lubrication, impact resistance, resistance to high loads, abrasion resistance, and a low coefficient of friction (0.04–0.05) in surface contact with metal alloys such as 316 LVM stainless steel and Ti6Al4V alloy [3]. However, wear and tear of the UHMWPE material insert is the most common cause of patients having to undergo revision surgery, leading to total replacement of the prosthesis. Therefore, it is of great importance to understand the scope and limitations of the biomaterials used in orthopedics to increase their life cycle, improve their tribological performance and thus increase the quality of life of patients with joint replacements [4].

The innovation and application of the materials and design of prostheses are not of the present. In 1959, John Charnley proposed the use of acetabular cups made of polytetrafluo roethylene and femoral rods of stainless steel for a hip prosthesis. However, it presented a high rate of wear and penetration of the metal component in the wall of the acetabular cup, which motivated subsequent work to improve the femoral components [5].

On the other hand, in 1951 Walldius developed the first knee prosthesis from acrylic resin and a steel stem, which was replaced by cobalt-chromium due to the low resistance it presented [6].

Today, scientific and technological development has allowed the emergence of biomedical applications and the introduction of different materials previously considered incompatible or dangerous to the human body. To analyze the applicability of a material in biomedical implants, its most important properties must be determined from laboratory tests under ideal conditions and it must be considered that they often differ or do not adjust to the real conditions of the phenomenon, which results in them failing when tested in vitro. Experimental tests in the laboratory to know the main mechanical properties of materials are essential for their characterization. However, a necessary complement is wear tests to allow for better decisions making regarding their use. Bortoleto, for example, describes a bolt-on-disc test using a numerical analysis tool for dry contact between surfaces; using cylindrical bolts of 5 mm diameter by 22 mm height and, discs of 60 mm diameter by 5 mm height of AISI 4140 and AISI H13 materials from which it was possible to obtain their chemical compositions [6].

On the other hand, studies carried out by Yahong Xue in 2018 show that experimental tests of wear due to pin-on-disc sliding were carried out on a model of self-lubricating spherical bearing with the aim of determining the mechanical properties of the materials and estimating the wear using the Archard’s equation. The tests were carried out under three different load conditions (50, 75, and 100 MPa) and sliding speeds (1896, 2528, and 3160 mm/s) in a friction and wear testing machine [7].

However, Rodríguez Cañizo, through experimental analysis reported an estimation of wear between UHMWPE and stainless steel in coxofemoral prostheses using a tribological machine with a bolt-on-disc, mainly parameterizing the annual wear rate and the amount of material removed during surface contact from three operating conditions between the components: dry, lubricated with distilled water and lubricated with bovine serum [8].

Previous research showed results on wear rate and mechanisms without giving importance to the phenomenon caused by the temperature gradient due to friction. But researchers such as Selim Gürgen, in order to consider the effects of temperature, fabricated UHMWPE-based composite materials with silicon carbobium (SiC) filling. Bolt-on-disc tests were performed using a tungsten carbide ball under an applied load of 10 N, heating the specimens to 40 and 60 °C. He used different particle sizes and concluded that fine particle fillers are more likely to detach from the polymer matrix at elevated temperatures. This results in an accelerated wear characteristic in composite materials with adhesive-abrasive wear characteristics [9].

Sara K. Young used a knee simulator to analyze the wear of tibial inserts of UHMWPE material sterilized with gamma rays in the air and with a high level of oxidation. The tests were performed at 5 million cycles, showing wear scars and, indicating that tests with knee simulators are a valid method to produce burns, cracks, and delamination similar to those observed in vivo [10].

A characteristic that slows down the development of research in tribology is the scarcity of certified equipment to perform wear tests, which is why finite element simulation (FEM) has been popularized in recent years as an optional tool for the prediction, analysis and characterization of materials in a virtual laboratory.

Sun Changning developed a finite element analysis method to understand the mechanics of wear and material loss in knee tumor prostheses. The relevant parameters within the research detail a maximum deformation of the femur of 0.59 mm, and a contact pressure of 44.88 MPa, which causes an uneven distribution of stresses in the femur and, consequently, a loosening and detachment of material. These data have not only, contributed to the optimized design of the prostheses, but above all to the development of a specific rehabilitation program to prolong the useful life of the prostheses. The displacement obtained results for contact pressure and von Mises stress without taking into account the thermal properties of the material [11].

A common problem for the useful life of joint prostheses is the wear of the UHMWPE. This phenomenon occurs mainly due to three wear mechanisms: adhesive, abrasive, and fatigue, the latter being the cause of failure of these components [12].

Recent research on knee prostheses regarding the tribological analysis of UHMWPE implanted in people over 60 years of age, indicates that the patient’s life expectancy is less than the useful life of the prosthesis, which is around 10 to 15 years. Recent statistics show a worldwide increase in cases of osteoarthritis in young adults under 40 years of age requiring TKR (total knee replacement) prostheses with materials that meet the demands of a more active lifestyle [13].

The correct choice of biomaterials for biomedical applications depends significantly on their properties. However, the cost of the prosthesis is significant. Materials such as 316 LVM-UHMWPE stainless steel have been introduced. They are inexpensive and widely available but are of great concern due to the high coefficient of friction and the detrimental effects they can have. Therefore, the objective of this research is to evaluate the wear of the polyethylene insert in the absence of lubrication by performing reciprocating motion tests in order to analyze the type of wear of the UHMWPE and determine its failure characteristics using scanning electron microscopy (SEM). A numerical model was also developed in Fortran language, applied to finite element, Abaqus^® software V. 2020 (FEM). The model includes temperature conditions generated by the friction of the surfaces, and can be used as a virtual tribological testing tool to obtain a more detailed analysis of the stages of the wear mechanism of the parts and is also able to predict and reliably correlate the evolution measured experimentally with the wear recorded in laboratory tests. This approach can be applied in future research on the deterioration of surfaces by friction [14,15].

The literature review shows research on tribological characterization in laboratory tests and FEM applications. However, the contribution of thise work is the development of a mathematical wear model in Fortran language and the inclusion of temperature in reciprocating virtual tests because it is a determining variable that accelerates the transfer of material by adhesion to abrasive wear.

Laboratory reciprocating motion wear tests were performed using a UHMWPE specimen and a 316 LVM stainless steel ball, and the results werw analyzed using SEM to determine the type and, damage caused by wear. A program in Fortran language was also developed using Archard’s wear equation by means of a subroutine integrated into the software Abaqus^® V. 2020 called UMESHMOTION. Laboratory results such as wear mechanism type, wear track width amplitude, damage and stages depending on the sliding distance were compared with the virtual runs in order to determine the validation of the program.

2. Materials and Methods

To obtain the coefficient of friction, the alternative sliding method was used using a 316-LVM stainless steel sphere from the REDHILL^® brand and a cylindrical specimen of UHMWPE material type GUR 1020 supplied by a knee prosthesis manufacturer in Mexico. The specimens used in the wear tests were obtained from a cylindrical bar 0.03 m in diameter. Cross-sectional cuts were made to the 0.0008 m thick bar by means of a diamond disc cutter using coolant at low revolutions to avoid overheating. The preparation of the specimens was performed through a grinding process with abrasive paper, using a standard grain size of 320, 400, 600, 800, 1200, and 1500, to finally obtain a surface finish with 1 μm diamond paste. The roughness obtained for the specimens was Ra −0.177 ± 0.03 μm. The cleaning of the specimens consisted of washing them with detergent and distilled water in an ultrasonic container for subsequent drying at room temperature and, finally, cleaning them with isopropyl alcohol.

For reciprocating tests in the laboratory, a low-frequency (1 Hz) tribometer without lubrication was used, where the variables of interest were the coefficient of friction of the material of the flat surface in contact and the volume of wear generated by the steel ball. Figure 1 shows the methodology of the experimental part.

For the development of the test, the circular section specimen shown in Figure 2A-1 was used. The 0.01 m diameter sphere, see Figure 2B, slides over the upper face of the specimen at a speed of 30 rpm, coupled to the reciprocating sliding machine as shown in Figure 1; the test was carried out under the American Society for Testing Materials, ASTM G133-05 and normal loads of 10 N were applied on the surface, see Figure 2A-3. A stroke of 30 mm and a test temperature of 26 ± 2 °C, were used [16].

The force used during the reciprocating motion test is the result of the maximum contact pressure P_max, in the gait cycle, in the position when the femur with respect to the tibia forms an angle of 15° on the transverse area of the weakest area of the knee prosthesis of the UHMWPE piece which has a value of A_T = 2.22 mm [17].

The equation of Normal Force was used.

$${\mathrm{F}}_{\mathrm{N}}={\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{A}}_{\mathrm{T}}$$

(1)

Substituting values gives us an average strength of FN = 11.5 N. The tribometer handles loads of 5, 10, 15, 20, 25, etc., so it was decided to use the 10 N load for the experimental part.

The conditions used during the reciprocating test are given in

Table 1. Conditions used during the reciprocating test.

Test Tube	Applied Load (N)	Race (mm)	Speed (rev/min)	Test Time (seconds)	Tests Performed
1	10	30	30	1800	3
2	10
3	10

.

Scanning electron microscopy (SEM), using a JEOL JSM-IT100 SEM model, was used to observe the wear test specimens used in the laboratory.

2.1. Geometric Model in FEM

Using computer-aided design software, the parts that make up the physical test were modeled in the laboratory. The 316 LVM stainless steel ball was modeled as a solid of the discrete rigid type, which means that the sphere adopts the characteristics of being very rigid (high hardness) compared to the parts of the model, so its deformation and wear does not matter for the analysis, so it was not necessary to assign any of the material properties. It was drawn with a geometry of 0.01 m in diameter with a hemispherical shape, applying a mesh with hexahedral elements of standard-linear quadratic, rigid element, three-dimensional four nodes (R3D4) and a size of 0.00128 m for each element that composes it and with a total of 394 elements. The UHMWPE specimen has a cylindrical geometry of 0.03 m in diameter and 0.008 m in height. However, only a bar of 0.003 m by 0.017 m with a thickness of 0.0008 m was modeled, as shown in Figure 3. It was decided to draw the hemisphere and the specimen bar with these geometries to save computational memory and time in the iterations. A meshing control was applied to the bar with a size of 0.00034 m and 14000 elements in the upper layer of the specimen and 6000 elements with a mesh size of 0.00050 m in the lower part of the specimen. Explicit-linear elements coupled with the temperature-displacement of eight nodes (C3D8T) were used to observe the effect of temperature. The analysis of the assembly was carried out through a scheme of explicit elements. To determine the appropriate element size in the upper layer of the specimen, a convergence analysis was performed [18].

The values of the elastic properties (Young’s and Poisson’s modulus) of the UHMWPE were obtained using by nanoindentation tests, and the density and thermal properties were obtained from bibliographic references [17,19,20].

Table 2. Mechanical properties [17,19,20].

Material	Young’s Modulus (MPa) [17]	Poisson’s Coefficient [17]	Density (ton/mm3) [19]	Thermal Properties [20]
				Conductivity (W/(mm °C))	Specific Heat (J/(Ton °C))
UHMWPE	1080	0.4	9.7 × 10−10	0.00041	8,164,000,000

shows the characteristics of the UHMWPE, to be used in the simulation. A mentioned above, the semisphere was not placed in a certain way because it was handled as a rigid body.

UHMWPE is vulnerable to plastic deformation due to the speed and temperature generated in each to-and-fro movement caused by friction between components; therefore, it is important to consider the parameters of the Johnson–Cook plastic model under these conditions. These parameters include (yield strength (A), the coefficient and rate of hardening by strain (B, n), the temperature sensitivity coefficient (m), and melting and transition temperature as shown in

Table 3. Jonhson–Cook properties [21].

A (MPa)	B (MPa)	n	m	Melting Temperature °C	Transition Temperature °C
16.11	39.29	0.57	1	18	−150

) and are necessary for finite element simulation [21].

The reciprocating motion test is subjected to contact pressure, so the conditions of the Johnson–Cook plastic model of the UHMWPE specimen are important for modeling in the simulation.

For the boundary conditions, the interaction between surfaces of the pieces in contact was of the surface-to-surface type. A concentrated force of 10 N was placed in the central part of the hemisphere on the z-axis in the negative direction. The hemisphere was selected as the master surface (hardest material). The UHMWPE bar was assigned as a slave surface (soft material), and the lower face was fixed with the embedded-in condition, preventing movement due to the sliding of the ball in the direction of the positive z-axis, as shown in Figure 4.

In the interaction section, the contact properties Tangential Behavior were placed with a coefficient of friction value of 0.3 obtained from the experimental part, and the option of Normal Behavior was added with a Pressure Overclosure of the type Hard Contac and Heat generation to get the fraction of the energy dissipated by friction that is converted into heat Tangential Behavior.

Figure 5 shows the sliding motion conditions of the 316 LVM stainless steel ball describing a reciprocating linear displacement on the z-axis of 0.017 m and a depth of 0.002 m on the specimen.

2.2. Wear Model

The most widely used mathematical model for calculating the rate of attrition is the Archard’s model [22]. Authors such as Molinari, Podra, Cantizano, Hegadekatte, etc., [23,24,25,26] among others, have used Archard’s wear equation to simulate wear due to friction in the contact between surfaces, which is given by

$${\mathrm{W}}_{\mathrm{v}}={\mathrm{K}}_{\mathrm{w}}\mathrm{F}\mathrm{S}$$

(2)

where W_v represents the volumetric wear of the surface of the worn specimen, K_w is the wear coefficient obtained experimentally, F is the contact load, and S is the sliding distance between the contact surfaces. The linear wear equation at any point on the sliding surface would be as follows:

$${\mathrm{W}}_{\mathrm{L}}=\mathrm{K}\mathrm{P}{\mathrm{S}}_{\mathrm{w}\mathrm{i}\mathrm{i}}\left(\mathrm{i}=\mathrm{1,2},3,\dots ..\mathrm{n}\right)$$

(3)

where, “n” represents the total number of intervals in the alternative slip test.

Wear coefficient data were obtained from experimental data from laboratory micro-abrasion tests using a 316 LVM stainless steel ball and a UHMWPE specimen [17].

Table 4. Results of the micro-abrasion test.

Testing	Wear Coefficient (mm3/N)
5N-1000	2.51 × 10−9
5N-2000	1.19 × 10−9
5N-4000	3.92 × 10−9

shows results obtained from three specimens at 1000, 2000, and 4000 cycles.

In Fortran programming language, the Archard’s wear equation was introduced as follows.

$$\mathrm{W}=(\mathrm{K}\times \mathrm{C}\mathrm{S}\mathrm{L}\mathrm{I}\mathrm{P}\times \mathrm{C}\mathrm{P}\mathrm{R}\mathrm{E}\mathrm{S}\mathrm{S}\times {\mathsf{\Delta }\mathrm{n}}_{\mathrm{i}})$$

(4)

Wear was calculated for the central part of the UHMWPE material specimen with the CSLIP (contact slip variable) and CPRESS (contact pressure variable) values obtained from the polyethylene surface nodes. And Δn_i is the number of cycle numbers with a value for each jump of 1000 cycles.

2.3. Program in Fortran Language

An interface of the UMESHMOTION subroutine integrated into the finite element software for mathematical modeling was used. The subroutine is mainly used to assess wear problems [18].

In this subroutine, the variables K = 3.92 × 10⁻⁹ which is the wear coefficient (mm³/N) obtained experimentally, and delta n = 1 × 10³, which is the step of each cycle, were integrated. Therefore, the computational function of wear at the position of a given node is given by Equation (3).

Figure 6 shows the flow chart of the programming process for the wear test simulation model.

3. Results

From the laboratory tests with the reciprocating sliding machine, the coefficient of friction (COF) was obtained, and data was used in the simulation by MEF. The conditions of three different loads shown in

Table 5. Valores COF.

Applied Load (Newton)	Coefficient of Friction (mm3/N)
10	0.10 ± 0.09
20	0.10 ± 0.04
30	0.099 ± 0.003

were used.

The tests were carried out dry under all three conditions, and a very similar COF was obtained between the sliding surfaces of the UHMWPE vs 316 LVM stainless steel. Figure 7 illustrates the variations in the COF recorded over 1800 s, showing that the value of the coefficient of friction stabilizes at approximately 0.1, regardless of the load and under dry conditions.

The results of the laboratory tests with the 10 N load show a central groove on the UHMWPE surface due to plastic deformation in specimens 2 and 3, (Figure 8B and C, respectively), due to the load, exceeding the shear strength of the material. Tearing or fragmentation of the polyethylene (pitting) can also be observed in the three specimens (Figure 8A–C).

The sliding of the surface of the 316 LVM stainless steel ball on the UHMWPE surface generates a visible wear footprint, as shown in Figure 9. This increases with each slide of the ball on the surface, and this imprint is caused by the tangential behavior and the coefficient of friction of 0.1 obtained during the experimental part between both surfaces, favoring a hard contact

Figure 10 shows the elastoplastic deformation folds on the soft surface of UHMWPE due to the increase in the temperature gradient at a scale of 500 μm and a sliding distance of 4000 cycles.

After 4000 cycles, the detachment of polyethylene is observed in the specimens, improving the shear resistance of the material and creating multiple cracks due to fatigue

Finite Element Contact Pressure Analysis

The simulation was performed using numerical methods software (Abaqus^® CAE 2020). With this tool, the maximum contact pressures (CPRESS) and the plastic equivalent strain (PEEQ) were obtained, which represents a measure of material deformation, which represents the proximity of the material to failure due to the contact between the surfaces of the UHMWPE Vs 316 LVM stainless steel [16].To corroborate the PEEQ applied to the specimen in the laboratory, wear tests and observation of the characteristics of the wear mechanism and hysteresis formation during simulation were performed.

Figure 11 shows that the CPRESS value generated by the 316 LVM stainless steel ball is 38.029 MPa.

The increase in the equivalent elastoplastic strain (PEEQ) shown in Figure 12A indicates that there is a maximum plastic strain of 0.845 located in the zone of the central part of the wear footprint. This value indicates the inelastic deformation of the material. If this variable is more significant than zero, it means that the material has given way [18]. Figure 12B yields the von Mises value of 24.478 MPa.

At the beginning of the contact of the hemisphere with the polyethylene, the displacement of the material moves towards the top, forming the lip of the material and the plastic deformation. Figure 13 shows the plastic deformation without exceeding the yield strength of the material since it does not show detachment.

For the analysis of the wear stages, the cycles were divided into 0, 800, 1600, 2400, 3600, and 4000 cycles.

Figure 14 shows the wear stages in the specimen during the different sliding cycles. It can be observed that in none of the stages, is there wear on the surface of the specimen. At 3200 and 4000 cycles, plastic deformation occurs, causing the material to have a lateral and frontal displacement, and at 4000 cycles, cracks occur due to material fatigue.

Figure 12 also shows the depth caused by the ball as it moved the material with a total depth at 4000 cycles of 52.870 μm.

In the Abaqus^® software, the width of the wear track was determined, with a measurement of 0.60 mm, shown in Figure 15.

In the experimental part, the width of the footprint generated from the specimen wear tests due to the 10 N load is shown in Figure 16. Imaging was obtained via MEB to determine the width measured along the entire length of the groove.

Eight measurements were made to determine the thickness of the groove obtained at 4000 cycles using the Image J tool, giving the following results shown in

Table 6. Amplitudes in mm obtained by Image J.

Measurement Number	Distance (mm)
1	0.791
2	0.662
3	0.741
4	0.733
4	0.720
6	0.583
7	0.604
8	0.629

below.

Measurements of the width of the groove of the wear track were taken by MEB, obtaining an average distance of 0.772 mm.

4. Discussion

UHMWPE is mainly used for the manufacture of inserts in joint prostheses, specifically in the knee prosthesis, which supports 3.5 times the patient’s weight during the walking cycle in a position when the femur forms a 15° angle with respect to the tibia. Under this condition, a 10 N load was obtained to be applied during simulated and laboratory reciprocating slip tests.

Tests performed on the reciprocating machine indicate that the material stabilizes at a value of COF = 0.105 ± 0.0036, with loads of 10, 20 and 30 Newtons. The result of the dynamic coefficient of friction of the UHMWPE presents a low value for all tests in dry conditions in contact with the surface of the 316 LVM stainless steel ball, demonstrating that regardless of the load conditions the tests reached a stable state of friction, corroborating the results obtained by the author Fatima Zivic [27]. The COF value obtained in the laboratory was used as data for the numerical simulation of the test.

The MEB analysis at a magnification of 100 μm of the worn surfaces in the specimen of the UHMWPE type GUR 1020 under the conditions described above is observed in Figure 8A–C. It does not show macroscopic undulations typical of slip tests under high load conditions [28] However, the predominant wear mechanisms were adhesion and thermal fatigue, developed at microscopic levels as a result of the short sliding time (1800 s), where ductility and maximum shear stress are observed, shown by the presence of grooves and pitting, which induces that the type of wear mechanism is adhesive and abrasive. In Figure 8B,C, apart from pitting as a result of fatigue wear, a more aggressive wear effect can be seen due to the generation of a groove in the middle of the wear footprint.

Figure 10A shows a groove in the central part at a magnification of 400 μm. This is due to the effect of displacement of the material to the sides and the largest amount is displaced to the front, at 1500 μm (Figure 10B) near the central area of the specimens used in the laboratory. The effect of cracking in the material with small tears of the polymer, known as pitting, is shown. This leads us to conclude that at short sliding times, microscopic damage to the material already occurs, which could result in the dissemination of polymer remains into the surrounding tissue, causing toxicity and lowering the performance of the implant and a probable total replacement of the joint prosthesis.

In the numerical simulation, the presence of grooves in cycles greater than 3200 was observed in the UHMWPE sample, which provided relevant information on the mechanics of thermal fatigue wear during sliding as a function of time. Figure 12 shows the evolution of wear. The loss of material from 2400 cycles by the adhesion mechanism can be observed. During the simulation tests, an early loss of material was evidenced after a few adhesion wear cycles, despite the fact that a surface finish was given to the polyethylene specimen of Ra −0.177 ± 0.03 μm. At 3200 and 4000 cycles fatigue wear is generated by cracks in the surface of the polyethylene. Due to the spherical-shaped geometric configuration of the sliding pin, the loss of the material is entirely due to the adhesion mechanism, and the absence of cutting angles is due to the more challenging material. The micrographs obtained through the MEB do not show grooves made by amorphous abrasive particles, but rather a central groove created by the surface contact between the sphere and the specimen as a result of the sliding speed and the applied load. Due to the surface finish of the polyethylene specimen, no ridges that acted as surface roughness were modeled in the simulation, so there were no characteristic folds of plastic deformation at macroscopic levels.

With the use of the thermal properties of conductivity and specific heat added to the simulation data, they transmitted the effect of plastic deformation, due to the increase in temperature due to friction, which causes the material to deform, causing microscopic ripples followed by fatigue cracks.

On the other hand, the plastic deformations in the simulations present the same behavior in the displacement of material for the formation of folds and lips, leaving similar characteristics in terms of shape and volume displaced by the sliding sphere.

The von Mises value of 24.448 MPa is below the ultimate yield stress of the material, which is 28 MPa [29]. The von Mises value indicates that the plastic deformation does not exceed the elastic limit of the polymeric material, and consequently there is no release of burrs or abrasive particles up to 4000 cycles.

The limitations of the project in terms of the simulation is the mesh tuning capacity due to the demand of computational memory required. For this reason, the cracks generated by the wear tests in the laboratory are not replicated in the results of the last stages of the cycles in the simulation.

5. Conclusions

The value of the coefficient of friction during the laboratory tests stabilized at a value of COF = 0.105 ± 0.0036 with the loading conditions of 10, 20, and 30 N.

For the wear simulations in the UHMWPE, the thermal properties of the material are significant. The parameters of the Johnson-Cook model are also important because the tests are subject to a linear velocity and the generation of plastic deformation temperatures, in order to represent the thermo-mechanical wear of the contact surface between the materials involved.

The load value of 10 N used for the simulation was obtained due to the weight-bearing condition of the insert in a knee joint prosthesis, which is 3.5 times the weight of the patient at an angle of 15° formed between the femur and the tibia.

The predominant wear mechanism in laboratory tests after analyzing the surfaces in SEM, is due to adhesion. As a consequence of the sliding speed and the applied load, cracks occur due to fatigue of the material.

Observing the wear mechanics in the simulation at each of the sliding stages, detachment in any cycle. The groove generated in the central part of the specimens is due to the displacement of the material as an effect of plastic deformation caused by the increase in temperature as a result of friction between surfaces.

The plastic deformation value (PEEQ) indicates that the material presents large displacements. This is shown in the micrographs taken from the laboratory tests, and corroborated with the simulations of the replica in the reciprocating test. The plasticity data of the material and the, Johnson—Cook plastic and damage values with a melting temperature of 148 °C were obtained from bibliographic reference.

As a consequence of the load and the linear speed of the 316 LVM stainless steel sphere, the material was displaced towards the front part to generate the formation of lips. It was in this part, together with the central groove, that the highest concentration of tension and trapped energy occurred, which was released via plastic deformation and lateral folds without detachment of the indicated material because there was no cadence. This occurrence can generate residual stresses, causing cracks or, in critical situations, fatigue failures in the material.

The von Mises stress value of 24.448 is below the ultimate yield stress of the material, so there was no particle detachment in the sliding distance tested in the laboratory.

The width of the footprint was compared with laboratory tests, obtaining a distance of 0.604–0.791 mm in both scenarios. In conclusion, regarding the analysis of the wear mechanics of UHMWPE, the numerical model can be used as a tool to analyze wear mechanics in articulated prosthesis.

Figure 12, shows, the increase in the depth of material displacement from 41,377 µm at 800 cycles to 52,870 µm at 4000 cycles, presenting only the fatigue wear mechanism.

The percentage error of the wear track amplitudes between laboratory and, virtual tests was 13.8%, most probably due to the mesh quality presented on the contact surface.