Minimizing Stress Concentrations in the Femoral Heads of Hip Joint Prostheses: Effect of Borehole Shapes

This paper presents a stress analysis of the ceramic femoral heads of hip joint prostheses with different borehole shapes to evaluate their mechanical reliability in terms of stress concentration. Under the ideal loading conditions used for ceramic rupture tests specified by the ISO 7206-5 standard, a finite element (FE) modeling is performed to determine the tensile and hoop stress distributions in the ceramic femoral heads. Two borehole shapes that are currently used in the manufacturing industry for hip joint prostheses, namely the flat bottom and keyhole, were first studied. Two new borehole shapes, dome arc and dome ellipse, were then introduced by the authors in the paper to minimize the stress concentration. It was found that while the currently used borehole shapes lead to high tensile notch stresses at their critical corners causing possible fracture failure of ceramic heads, the authors’ borehole designs can improve the mechanical reliability significantly. In addition, the effects of taper-bore contact length and their interface friction are investigated and discussed. Introduction Because of their excellent mechanical properties and good biocompatibility, ceramic balls for total hip replacements (THR) have been widely used [1]. In THR, a ceramic ball head is mounted on a metallic stem by frictional fitting, and the system is then pivoted in ceramic or polyethylene cups. Although ceramic femoral ball heads have proved their exceptional mechanical reliability, recent clinical studies do show their fracture failure due to a number of causes [2, 3]. Among the possible causes to failure, improper assembly and contamination of the contact surfaces between the stem and the taper-borehole of a ceramic ball head during surgery are reportedly significant [4]. While these causes are, to some extent, unavoidable, the mechanical reliability of the ceramic ball heads has to be continuously raised by increasing the strength of component itself. One way to improve this is to optimize the design of the ceramic femoral heads. In order to hold a ceramic head firmly, a metallic stem is fitted into the taper-borehole of the ceramic ball head. Depending on the preference of manufacturers and the ease of manufacturing, currently two types of taper borehole shapes are used in THR. One is the flat bottom shape with a filet at the corner of a ceramic taper-borehole, where a stress concentration occurs at the filet corner [5]. The other is the keyhole shape which has an undercut at the corner of the taper-borehole [6]. The surface with such an undercut shape is difficult to machine, which often leaves a low surface finish and causes further stress concentration sites. As ceramic is brittle and prone to fracture under a critical tensile stress, these currently used borehole shapes can actually reduce the mechanical reliability of ceramic femoral heads in THR. This paper aims to study the stress distributions in the ceramic femoral heads, by analyzing both the existing taper-borehole shapes and some new designs of the authors to understand the effect of borehole shapes on the variation of stresses and hence to provide some useful guidelines for improving the mechanical reliability of the femoral heads. The finite element method will be used Key Engineering Materials Vol. 443 (2010) pp 736-741 Online available since 2010/Jun/02 at www.scientific.net © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.443.736 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 129.94.206.15-29/03/11,03:14:26) for the stress analysis. The loading conditions will follow the specification by the ISO7206-5 standard. Borehole Designs There are two existing designs of borehole which have widely been used for the ceramic femoral heads in THR. One is a flat bottom shape which is designed for easy production as shown in Fig. 1(a) [5]. Ceramic femoral heads with such a flat bottom are produced by drilling, creating a small fillet at the corner. This small fillet can cause local stress concentration, and often leads to the fracture failure of the ceramic heads. Another existing borehole design is a keyhole shaped internal geometry at the bottom of a ceramic taper-bore, as illustrated in Figure 1 (b), which is designed to avoid a possible impingement of the stem taper onto the bottom of the borehole under any unexpected loading or loosing of the stem taper assembly [6, 7]. The shape with an undercut in this design, however, is quite difficult to form during pre-sintering (Green Ceramic), and its surface is difficult to be finished by grinding or polishing, leaving a lower surface quality in such a critical area where local stress concentrations always occur. (a) Flat bottom (b) Keyhole (c) Dome arc (d) Dome ellipse Fig. 1 Shapes of borehole in ceramic femoral head In order to minimize the stress concentrations, this paper introduces the following new borehole designs for stress evaluation: (1) dome arc, and (2) dome ellipse on the bottom of the ceramic taperbore, as shown in Figure 1(c) and 1(d) respectively. In the case of the dome arc, a spherical dome is formed at the bottom of taper-bore, while for the dome ellipse, the taper-bore’s bottom surface is a half of an ellipsoid. The radii of the dome arc and dome ellipse can be chosen such that the transition between the taper-bore and the bottom dome is smooth (tangent to each other) to avoid the local stress concentration. Since the geometric shapes of these new designs are simple, they are easy to fabricate in the pre-sintering stage of the ceramic heads to achieve a surface finish. Finite Element Modeling As the in-vivo (physiological) loading situation against the actual hip joint prosthesis is quite complex, the ISO 7206-5 standard proposes a simple test procedure to determine the rupture strength of a ceramic femoral head, which is considered to be able to approximately simulate the clinical performance of a ceramic femoral head used in hip joint prosthesis [8]. In this paper, as a first attempt, we consider only the static loading conditions specified by ISO 7206-5 to test the mechanical strength of ceramic femoral heads with the borehole designs described above. In the test configuration, as shown in Fig. 2, a ceramic femoral head with a taper stem is placed onto a 100 ̊ cone support under an axial load F. In this paper, the ceramic femoral head is considered to be of pure alumina, the taper stem is made of a titanium-aluminium-venadium alloy, and the 100 ̊ cone support is of stainless steel. Their Young’s modulus (E) and Poison’s ratio (υ) used in the calculations are (a) alumina: E = 380 GPa and υ = 0.245, (b) titanium-aluminium-venadium alloy: E = 105 GPA and υ = 0.3, and (c) stainless steel: E = 210 GPa and υ = 0.3, respectively. Throughout Key Engineering Materials Vol. 443 737