b. weisse(% u. loher/% w. rieger^, w. weber^ ^mgrox/rag ...€¦ · bilinear and incompatible modes...

FEM simulations of prosthesis hip joint

implants

B. Weisse(% U. Loher/% W. Rieger , W. Weber^

^ Department of Strength/Technology, EMPA, Uberlandstrasse 129,

Email: [email protected]^Mgrox/rAG, CH-8240rAayngEmail: [email protected]

Abstract

The scope of this report is to present the non-linear finite element method (FEM)calculations for two artificial hip joint implants (system composed of a spigot,head and cup). For the implants the influence of the boundary conditions, thevariation of the taper angle difference, the coefficient of friction between thespigot and the head and also the material of spigot and head on the stressdistribution in the system are determined.For each of the two implants, based on the designs of the producer Metoxit AG,an axisymmetric FE model was generated. Note that the head of the two implantspossesses different bore depths. The geometry of the spigot and cup are similarin both models. The calculations were carried out with ABAQUS/Standard.The results of the analyses show that the boundary conditions of the implant andthe variation of the taper angle difference have a strong influence on the tensilehoop stress distribution in the head. In addition, it was found that the variation ofcoefficient of friction determined by measurements and the different materialsconsidered for the spigot and head have a small effect on the stresses. Moreover,the stresses in the head of the system with the deeper head bore do notnecessarily have to be higher than those in the head with the shallow head bore,since the resulting stresses depend on the support conditions and the taper angledifference.The dominant influence of the boundary conditions on the stress distribution inthe head raises doubts as to the correctness of the ISO 7206-5 standard; while thein vivo circumstances of the implant are not completely simulated by the testspecified in this guideline.

Transactions on Engineering Sciences vol 24, © 1999 WIT Press, www.witpress.com, ISSN 1743-3533

322 Computational Methods in Contact Mechanics

The FE simulations confirm the test results and the experience observed onhuman implants.

1 Introduction

This paper documents a parametric stress analysis of a hip joint implant whichundergoes an axisymmetric loading. The chief aim of the study is to determinethe effects on the stress level of the following five parameters, namely (1) thedepth of the head bore, (2) the boundary conditions respectively the outersupport conditions of the head, (3) the taper angle difference, (4) the coefficientof friction at the taper press fit and (5) the materials of spigot and head.This paper represents the outgrowth of the work by Dragoni & Andrisano*,whereby more parameters are considered for the implant for which the FEmethod is adopted for its unpaired flexibility in coping with model changes.Because of the need to control such subtle parameters, the versatility provedinvaluable in the present case.Although in contrast with the in vivo circumstances of a deviation of the loadfrom the joint axis, the axisymmetric assumptions are well representative of therelevant stress response in the head. In fact, the transverse component of the totalhip load has a negligible effect on magnitude and distribution of taper hoopstresses which embody the major structural hazard of this component, Fessler &FrickerThe models chosen for the implant are examined in the following sections. In themodels true unilateral contact at both spigot-head and head-cup interfaces isaccounted for.

2 FE models

Based on the designs of a spigot, of two heads with a nominal diameter of28 mm - possessing different bore depth - and of a cup of the producer MetoxitAG, two implant geometries were considered: one with a long bore depth (IL)and one with a short bore depth (IS). For each of the geometries, twoaxisymmetric models with two distinctive taper angle differences between thespigot and the head, taking into account the tolerances, are generated with the aidof the pre-processor MSC/PATRAN. The biggest difference of the half taperangle amounts to A(p=4'58.5" and the smallest to A(p=029.5". In total fourgeometry models are produced. After the assembly of the spigot with the head,the remaining distance from the head taper ground to the spigot end is 1.2 mmfor the two IL models and 2.25 mm for the two IS models.The geometry models are meshed with two-dimensional axisymmetric, 4 nodebilinear and incompatible modes elements CAX4I, ABAQUS^. Twelve multiplepoint constraints (small circles) are used to obtain a homogenous load input onthe spigot (Figure 1).As the half taper angle difference of 4'58.5" compared to 0*29.5" is small, onlythe models with the highest taper angle will be shown.


Computational Methods in Contact Mechanics 323

Note that the radius of the inner surface of the cup is larger than that of the outersurface of the head. Mean values of the dimensions given in the drawing weretaken considered.

cupcup """""

distance fiBBHB^ distancehead cone ground |ffl|HBB head cone ground

spigot end 'P'S* end

head

head

Figure 1: FE models (left: IL, right: IS)

3 Load cases

Three load cases are taken into account. In all cases the spigot is loaded with aforce of 14.4 kN over the bottom cross section. To avoid interaction betweenapplied load and taper stresses, the loaded section was placed more than onediameter away from the conical opening. Individual axial constrainings of spigotand head are ensured by interfacial forces arising at the contacts. Only the loadcases for the IL model with A(p=4'58.5" will be shown in the figures.In the Load case 1 the cup is restrained in the direction of loading by setting tozero the axial displacement of the nodes located on the upper surface of the cup.In addition, the central node on the rotational axis is restrained in the radialdirection.In Load case 2 the cup is fixed on the side. This means that all degrees offreedom of the lateral nodes of the cup are restrained.The Load case 3 simulates the boundary conditions used in the static load testaccording to the ISO 7206-5 standard: the head is restrained in a 100° cone. Overa distance of 2.5 mm, corresponding to the width of a copper ring for the loadtransfer in the bearing, the degree of freedom of each of the six nearest nodes arerestrained in normal direction of the head's outside surface.Note that these test conditions do not exactly reproduce the in vivocircumstances of the implant. The first and second load cases simulate more



realistically the in vivo circumstances of the hip joint implant than the third one(Figure 2).

Figure 2: IL FE model (left: Load case 1, center: Load case 2, right: Load case 3)

4 Description of contact

The interactions between the three deformable components are defined with afinite sliding model (this allows a large displacement more than a typical elementdimension) between the contacting surfaces, ABAQUS^. It consists of twocomponents: one normal to the surfaces and one tangential to the surfaces(frictional shear stress). The model uses a hard surface behaviour, this means thatwhen the opposite surfaces separate the contact pressure between them becomeszero or negative and the constraint is removed (clearance concept). In order todetermine whether contact has occurred at a particular point, the analysis alsomust calculate the relative sliding of the two surfaces.The limiting frictional shear stress is defined by u/p (Coulomb Law), where ji isthe static coefficient of friction and p the contact pressure between the twosurfaces. The contacting surfaces will not slip until the shear stress across theirinterface is smaller or equals the limiting frictional shear stress (sticking).Modelling the ideal friction behaviour can result in convergence problems duringthe simulation, therefore ABAQUS uses a penalty friction formulation withallowable "elastic slip", small amount of relative motion between the surfacesthat occurs when the surfaces should be sticking. This stick-slip frictionalbehaviour and a possible opening of contact interfaces makes the probleminherently non-linear.



For the sake of simplicity, no friction is assumed at the head-cup interface, sincethe relative tangential movements between these two parts are always found tobe small. This simplification is believed not to have altered the taper stresses.The coefficient of friction between the spigot and the head amounts 0.425,corresponding to a mean value of measured coefficients of friction betweenTiA16V4 and

5 Materials

in tribology tests made by Op de Hipt

The materials of the three components were assumed elastic and were assignedthe following properties, Rieger^ (Table 1):

Component

cup

spigot

head

Material

ALOg

TiA16V4

stainless

steel

AlzOg

ZrO:

Young's

modulus £

[MPa]

420'000

105'000

210'000

420'000

2 10' 000

Poisson's

ratio v

0.3

0.3

0.3

0.3

0.3

Compression

strength

[MPa]

3' 800

860

750

3 '800

2'000

Bending

strength

[MPa]

400

860

750

400

900

Table 1: Properties of the materials used for the three components

6 Results

The FEM simulations were carried out with ABAQUS/Standard, version 5.7.The fringe plots are visualised with the postprocessor MSC/PATRAN.In the following discussion of the results, attention will be given only to thetensile hoop stress (0%) developing in the head. The reason for taking intoaccount the mentioned stress is that the main part of the principal stress, whichembodies the major structural hazard of the head, is coming from thecircumferential stress component: the tensile hoop stress. This dominant stress isspotted in the spigot, head and cup, but needs to be considered carefully at thehead bore crown and along the head bore generator.

7.1 Influence of the depth of the head bore

In load case 1 and 2, the tensile hoop stresses are smaller in the IS implant modelwith A(p=4'58.5" than those of the IL model in the bore crown, near the rotationalaxis (Figure 3). For load case 3 the tensile hoop stresses are approximately thesame in the mentioned region (Figure 4).



In load case 1, the tensile hoop stresses are still smaller in the IS implant withAcp=029.5" than those for the IL model in the bore crown; but in load case 2, thetensile hoop stresses are higher in the IS implant than those for the IL model inthe mentioned region. In load case 3 the tensile hoop stresses are stillapproximately the same for both models.Moreover, in the three load cases, independent of the taper angle difference, thestress progression along the bore generator seems to rise differently in the IL andIS models. Outgoing from the flat head side, the tensile hoop stress magnitude atthe beginning of the cone is higher in the IS model than that in the IL model;although the gradient of the stress progression is smaller. However, themaximum resulting tensile hoop stress, occurring approximately in the middle ofthe bore depth, is higher in the IL model. Figures 3 and 4 illustrate that the lowerlimit of the 30.17 N/mm"-isoline at the taper, outgoing from the flat head side, isreached closer to the cone beginning in the IS model, even when the maximumstress is lower in this model.Only the models with A(p=4'58.5" will be shown in the next two figures.

Figure 3: Tensile hoop stress (a, [N/mm2]) distribution of load case 1 in themodel with A(p=4'58.5"(left: IL model, right: IS model)



#

Figure 4: Tensile hoop stress (0% [N/mm2]) distribution of load case 3 in themodel with A(p=4'58.5"(left: IL model, right: IS model)

7.2 Influence of the boundary conditions

The results of the analyses show that the boundary conditions of the implanthave a strong influence on the stress distribution in the head. Figures 5 and 6show that the tensile hoop stress magnitude and distribution in the IL and ISmodels with A(p=029.5" of load case 1, 2 and 3 are different. This influence isless dominant in the models with Acp=4'58.5", not shown in the figures.The in vivo circumstances of the implant are a combination of load case 1 and 2,while load case 3 simulates the test configuration of the ISO 7206-5 standard. Itis clearly shown in the fringe plots that this influence raises doubts as to thecorrectness of the guidance, because it is not realistically simulating theboundary conditions of the human application.



Figure 5: Tensile hoop stress (<?% [N/mm2]) distribution in the IL model withA(p=029.5" (left: load case 1, center: load case 2, right: load case 3)

Figure 6: Tensile hoop stress (o% [N/mm2]) distribution in the IS model withA<p=029.5" (left: load case 1, center: load case 2, right: load case 3)



7.3 Influence of the taper angle difference

The variation of the taper angle difference has a strong influence on the stressdistribution in the head. Figure 7 shows, with the IL model of load case 2, thatthe tensile hoop stress distribution and magnitude vary with the taper angledifference. In this figure the tensile hoop stresses of the IL model withA(p=029.5" are smaller than those in the model with A(p=4'58.5". Note, that in another model and load case an increase of the taper angle difference could alsohave an opposite effect on the stress value and distribution. In the IS model ofload case 3, the taper hoop stresses are higher in the model with A(p=029.5" thanin that with Acp=4'58.5" (Figure 8).

Figure 7: Tensile hoop stress (0% [N/mm2]) distribution in the IL model for loadcase 2 (left: A(p=4'58.5", right: A(p=029.5")



Figure 8: Tensile hoop stress (0% [N/mm2]) distribution in the IS model forload case 3 (left: A(p=4'58.5", right: A(p=029.5")

7.4 Influence of coefficient of friction

The coefficient of friction has an strong influence on the stresses in both the ILand IS implant for all load cases. According to the tribology tests performed byOp de Hipr% the static coefficients of friction between A^Og and TiA6V4 varyfrom 0.366 to 0.477. The mean value is to 0.425. The variation in the coefficientof friction is not sufficient to have a significant effect on the tensile hoop stressdistribution and amount. Figure 9 illustrates this effect on the IS model withA(p=029.5" of load case 2.



i

Figure 9: Tensile hoop stress (0% [N/mm2]) distribution in the IS model withA(p=029.5"(left: =0.366, center: u=0.425, right: =0.477)

7.5 Influence of the materials

The different materials considered for the spigot and head have a small effect onthe stresses in the head. Only the tensile hoop stresses near to the bore generatorare slightly affected (Figure 10).



Figure 10: Tensile hoop stress (0% [N/mm2]) distribution in the IS model withAcp=4'58.5" (left: TiA16V4-spigot, AliOg-head; center: stainlesssteel-spigot, A^C^-head, right: TiA16V4-spigot, ZrO2-head)

7 Conclusion

Non-linear FE simulations of the stress state within prosthesis hip joint implantshave been performed for various parameters.The results of the investigation can be summarised as follows. (1) The depth ofthe bore does not have an important influence on the tensile hoop stress value inthe head. The effect of a deeper bore can lead to a stress reduction or increase,depending on load case and taper angle difference. (2) The boundary conditionsof the implant have a strong influence on the stress distribution in the head. Thein vivo circumstances of the implant are rather a mix of load case 1 and 2, whileload case 3 simulates the test configuration of the ISO 7206-5 standard. Theresults show, that this influence raises doubts as to the correctness of theguidance, because it is not simulating the real application conditions. (3) Thevariation of the taper angle difference has a strong influence on the stressdistribution in the head. This depends also on the load case considered and thedepth of the head's bore. A clear dependence could not be found. (4) The higherthe taper friction, the lower the tensile hoop stresses in the head. For the ISmodel with A<p=0*29.5"in load case 3 this effect is so strong that, in comparisonwith frictionless situation, frictional coefficients of 0.366, 0.425 and 0.477produce a stress decrease of 10, 12 and 14 times, respectively. Note that thedifference of stress magnitude between the three considered coefficients offriction is small. (5) The stiffer the spigot, the lower the tensile hoop stresses.



This influence is perceivable but not strong. The stiffer the head, the lower arealso the stresses. This influence is as well small.Finally, the FE simulations confirm the laboratory test results for the case of thedesigned parameters under point (1) and (5) and the experience observed onhuman implants (information of W. Rieger, Metoxit AG). Tests were notavailable for the designed parameters discussed under point (2), (3) and (4).

8 References

1. Dragoni, E.; Andrisano, A. O., Stresses in ceramic prosthetic heads

under axisymmetric loading: effect of taper friction, support conditions

and spigot elasticity, 8^ SIMCER Intl Symposium on Ceramics, Rimini

1992.

2. Fessler, H.; Fricker, D. C, Friction in femoral prosthesis and photo-

elastic model cone taper joints, Proc. Instn Mech. Engrs, Part H, 203, 1-

14, 1997.

3. ABAQUS/Standard V. 5.7, User's manual, Volume I, //, ///, Hibbit;

Karlsson & Sorensen, Inc. 1997.

4. ABAQUS/Standard, Getting started with ABAQUS/Standard, chapter

11: Contact, Hibbit; Karlsson & Sorensen, Inc. 1996.

5. Op de Hipt, M., Tribology Test Report, Messungen zur Ermittlung von

statischen Reibungskoeffizienten, Nr. M/72-98, CSEM Tribo-Coatings,

Neuchatel 1997.

6. Rieger, W., Materials and Properties, homepage of Metoxit:

www.metoxit.com, Metoxit AG, 1998.


b. weisse(% u. loher/% w. rieger^, w. weber^ ^mgrox/rag ...€¦ · bilinear and incompatible modes...

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