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Is 7206 ISO standard enough to prove the endurance of femoral components of hip prostheses?
Engineering Failure Analysis 15 (2008) 83–89 www.elsevier.com/locate/engfailanal
Is 7206 ISO standard enough to prove the endurance of femoral components of hip prostheses? Jesu´s Chao Centro Nacional de Investigaciones Metalu´rgicas (CSIC), Avda. Gregorio del Amo, 8, 28040 Madrid, Spain Received 20 November 2006; accepted 20 November 2006 Available online 16 January 2007
Abstract The design of a cementless femoral stem that fractured at the neck–shoulder junction was analysed with reference to parts 4 and 8 of ISO standard 7206. The stresses in the section where fracturing occurred were calculated assuming the 2300 N loading specified in ISO 7206-8. The results show that the prosthesis met ISO standard requirements regarding fatigue behaviour. However, this feature does not occur when a load of 4000 N, corresponding to a patient with a body weight of 1000 N, is applied. It is therefore suggested that patient body weight should be taken into account when designing and choosing the appropriate stem size. 2006 Elsevier Ltd. All rights reserved. Keywords: 7206 ISO standard; Fatigue design; Cementless Hip prosthesis; Ti6Al4V alloy
1. Introduction Total hip arthroplasty (THA) has proven to be a successful method for the relief of pain and the restoration of normal daily activities in patients with hip disablement. The long-term success of this operation depends on a variety of factors, such as the surgical technique employed, the positioning and alignment of the stem, the stability of the intramedullary fixation, the patient weight, and the implant design. A recent study on a population of 7695 hip prostheses (implanted during the period 1990–2000) [1] revealed that 24.8% of these prostheses had been revised, i.e. one or both of the prosthesis components had required replacement. The studied prosthesis population consisted of: 17% cemented, 54% cementless, 28.6% with cementless cup and cemented stem, and 0.4% with cemented cup and cementless stem. Stem fracture was the reason for 1.7% of the implant revisions, while the most frequently observed cause (86.5%) was loosening. On the basis of these figures, it may be thought that mechanical failure of the femoral component is a rare complication in THA. However, the author considers that this is not an unimportant problem, above all when the retrieval of the stem is extremely difficult and necessitates deliberate damage to the femur [2,3]. Case reports of in vivo fracture of cementless hip prosthesis have attributed this event to: a weak junction between the madreporic corrugations and the smooth E-mail address: [email protected] 1350-6307/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2006.11.017
84
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
plate [4]; the smelting technology used and cracking of the porous layer [5]; the narrowness of the antero-posterior dimensions of the proximal region of the stem [2]; a galvanic corrosion–fatigue process at the tapered interface between the neck and the head of modular femoral components [6,7]; a lack of support in the proximal region of the stem and the distal stem fixation [8]; and the machining induced residual stresses on the surface of the stress concentration at the neck–shoulder junction [3]. The second last failure mode [8] may be justifiable because the stem fracture is preceded of loosening of the proximal part of the implant [9], and the loosening issue is still a topic subjected to investigation. The other failure modes are the result of mistakes in the design and/or control method of the femoral component. In a previous paper, it was analysed the fractographic features and metallurgical factors of the in vivo fatigue failure at the neck–shoulder junction of a cementless Ti6Al4V femoral stem (Fig. 1) [3]. This paper analyses whether this stem model would pass the endurance test according to ISO 7206 standard. Because the test
Fig. 1. Photograph of broken prosthesis (the arrow indicates the fracture initiation point). Remnants of bone tissue may be seen in the stem proximal area, indicating good osseointegration.
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
85
load specified in ISO standard seems, on the basis of previous works, unsuitable to test the endurance of stems to be implanted in patients of 1000 N body weight (BW), it is also considered an applied load of 4000 N instead of the 2300 N specified in ISO standard. 2. Background Three patients of about 60 years old and a body mass index above 30 kg/m2 underwent THA in different hospitals with different surgeons. A cementless Ti6Al4V femoral stem of the same model was used for all patients. The stem was coated in the proximal third with a beaded porous coating of Ti6Al4V. Fractures occurred in vivo suddenly after about four years of implantation without any preliminary pain. The three patients underwent a revision surgery with replacement of the fractured stems, during which great difficulty was experienced in removing the well fixed fragment of the broken stems. The proximal third of the stems was covered with remains of bony tissue, confirming osseointegration of the stem by bony ingrowth (Fig. 1). Fortuitous mechanical failure of the implants was ruled out because very similar fractures were observed in all cases. Recently it was shown that fracture of these prostheses was produced by a fatigue process initiated at the neck–shoulder junction [3]. The fracture was initiated in the lateral region of the neck, propagating through the cross section in the latero-medial direction, and ended in overload failure of the remaining cross section accompanied with gross plastic deformation. No superficial marks attributable to physical damage during implantation or extraction were visible on the neck. No microstructural defects were observed in cross sections of the stem near the fracture or in the fracture surface. 3. Analysis method The parts 4 and 8 of 7206 ISO standard [10,11] constitute a laboratory procedure to determine the endurance of femoral components of hip prostheses. According to this standard a compression load between 300 and 2300 N has to be applied on the head of the prosthesis at an angle of 10 in abduction and 9 in flexion to the stem axis. Since the hip prostheses here analysed were manufactured before the year 2002, subsequent modifications to ISO standard have not been considered. Therefore, the stem was constrained in a distance of 80 mm below the centre of the head of the prosthesis. In accordance with previous work, the experimental constraint of the stem defined by the ISO standard was simulated with a couple of bearing points on the frontal and sagittal planes located at 80 and 160 mm from the centre of the femoral head and fixing the distal tip against rotation [12]. The maximum stresses on the cross section where the break occurred (A–A 0 section in Fig. 2) and the corresponding to 80 mm from the centre of the head (B–B 0 section in Fig. 2) were calculated according to the methods used in the material strength handbooks, e.g. [12]. It was assumed that the displacements upon loading are small. From the analysis of the literature, the hip joint forces obtained using telemetric hip prostheses ranged from 2.8 to 5.2 times the BW, depending of the kind of physical activities [13–16]. Assuming an average value of 4 times the BW, the specified maximum load in ISO standard (2300 N) should be adequate to a BW of about 575 N, which is accordance with previous theoretical predictions [17]. Evidently for BW here considered of about 1000 N it seems more suitable to apply a test load of 4000 N instead of that of 2300 N specified by ISO standard irrespective of the patient BW. A load of 2300 N was chosen to calculate the maximum equivalent stress at the above mentioned cross sections. Fig. 2 presents a sketch of the stem showing the dimensions and parameters necessary for the calculation of stresses at A–A 0 and B–B 0 sections according to the following formulation. Section A–A 0 . The hip force F was resolved into F1(=Fcos9) and F2 (=Fsin9) components: the former was obtained from the projection of F on the plane defined by the neck and distal axes of the stem, whereas F2 component is normal to this plane. The component F1 is further resolved into the parallel F3(=F1cos55) and normal F4 (=F1sin55) components to the A–A 0 section. The normal load component (F4) gives rise to a compression stress state. The in-plane components (F2 and F3) give rise to My = F2d and Mx = F3d bending moments and to the corresponding shear stresses.
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J. Chao / Engineering Failure Analysis 15 (2008) 83–89
Fig. 2. Scheme showing both the geometrical details of the femoral component and the arrangements for fatigue test according to parts 4 and 8 of 7206 ISO Standard. The dimensions and the values of the parameters necessary to calculate the stresses at AA’ and BB’ cross sections are also shown. The hollow arrows in the AA’ and BB’ cross sections indicate the location of the maximum equivalent stress (a) medial view and (b) posterior view.
The net axial stress in a generic (x, y) point of the cross section is given by: 4F 4 M x My rz ¼ þ y x Ix Iy pD2 In this equation, the inertia moments (Ix and Iy) are given by: pD4 Ix ¼ Iy ¼ 64 in which D is the neck diameter. The shear stresses in a (x, y) generic point are given by: Qy F 2 Q F3 szx ¼ and szy ¼ x IyD I xD in which 3 3 1 1 ðD2 4y2 Þ2 and Qy ¼ ðD2 4x2 Þ2 12 12 are the first order moments of the area.
Qx ¼
ð1Þ
ð2Þ
ð3Þ
ð4Þ
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
87
The Von Mises criterion was used to calculate the equivalent stress corresponding to the combination of the above stresses, which is expressed by: req ¼ ½r2z þ 3ðs2zx þ s2zy Þ1=2
ð5Þ
Section B–B 0 . The hip force F was resolved into F1 and F2 components as in the case of A–A 0 section. However, F1 component was resolved into components normal F5( = F1cos10) and parallel F6(=F1sin10) to B–B 0 plane. The load component F5 gives rise to a compression stress state and a pure Mx=F5d1 bending moment. The components F2 and F6 produce My = F2d2 and Mx = F6d2 bending moments, and the corresponding shear stresses. The expression of the net axial stress (rz) is that of Eq. (1) but with the corresponding values of the load components, cross section area and inertia moments to B–B 0 section. The expressions of the inertia moments of this particular cross section are given by [18]: h3 3 2 2 I x ¼ 0:25b 0:055b þ 0:7854bð0:17977b þ 0:848bh þ h Þ þ ð6Þ 3 Iy ¼
b3 ð16h þ 3pbÞ 192
ð7Þ
The shear stresses for a (x, y) generic point are given by: szx ¼
Qy F 2 bI y
and
szy ¼
Qx F 6 ðb þ hÞI x
ð8Þ
in which Qx was obtained by numerical integration and Qy is given by: 1 h 1 Qy ¼ ðb2 4x2 Þ þ ðb2 4x2 Þ2 8 3
ð9Þ
In addition, F2 component produces a T = F2d1 torsion moment which induces for a generic (x, y) point the following shear stresses: szx ¼
T T y; szy ¼ x 2I x 2I y
ð10Þ
The equivalent stress is given by Eq. (5). The obtained equivalent stress was compared with the endurance limit to assess whether or not this stress could cause fatigue fracture. The endurance limit of the prosthesis neck (A–A 0 section) was estimated as the able stress to withstand 5 · 106 cycles without failure of a notched specimen with a stress concentration factor (k = 1.95) identical to that introduced at the prosthesis neck by the design of stem. In an identical way the endurance limit of the B–B 0 section was estimated on smooth specimens. Such values have previously been obtained with specimens machined from bars of Ti6Al4V ELI surgical alloy with a microstructure similar to that of the fractured stem [3]. The tests were performed at room temperature in laboratory air under tension–tension loading conditions with a minimum-to-maximum stress ratio of 0.1. The frequency used in these tests was 20 Hz. 4. Results and discussion Table 1 shows the values of the maximum equivalent stress normalised by the endurance limit in the A–A 0 and B–B 0 sections. In both cross sections the maximum stress is located in the antero-lateral region of the cross
Table 1 Maximum equivalent stresses, requiv; coordinates (x, y) of the location of maximum equivalent stress; endurance limit, rfatigue; and the ratio of maximum equivalent stress to endurance limit of AA 0 and BB 0 cross sections Cross section A–A B–B 0
0
requiv (MPa)
(x, y) (mm)
rfatigue (MPa)
requiv/rfatigue
184 206
(0.6, 6.5) (3.4,6.9)
210 536
0.876 0.384
88
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
section. The normalisation procedure used involves that the fracture of the prosthesis occurs when the ratio is higher than or equal to one. The results show that the prosthesis fulfils the endurance test in accordance with parts 4 and 8 of ISO standard 7206 since the value of the equivalent stress to fatigue strength ratio for 2300 N load is less than 1. However, the value of 0.876 obtained at the neck is far from being conservative, especially when it is considered that the fatigue strength was overestimated since the tests were performed in the laboratory atmosphere at a frequency of 20 Hz and not in the more realistic conditions of a frequency of 1 Hz at a saline environment. Moreover, if the angle of flexion of the stem were supposed to be 3 instead of the 10 specified by the standard, the above calculations would predict the failure of the prosthesis at the neck. The fracture occurred in patients with a BW of about 1000 N. Having into account that the hip joint force is about 4 times BW, the maximum equivalent stress is 1.74 times higher than that of 2300 N. Thus, failure at the neck of the femoral component is predicted even when their activity was limited to slow walking. To prevent stem fracture it is necessary to increase the neck cross section and the radius of the neck–shoulder junction in order to decrease both the stress and the stress concentration factor at the neck. These modifications would not affect either the flexibility of the stem and in turn to the osseointegration of the implant. 5. Conclusions The prostheses can fulfil the requirements specified in parts 4 and 8 of ISO standard 7206. The ISO standard 7206 is found to be unsuitable for patients of a weight of nearly 1000 N. It is necessary to consider the patient weight in order to properly design and to choose the more appropriate stem.
Acknowledgements The author likes to thank Ms. Carmen Pen˜a for the assistance with the prosthesis drawing and Dr. J.L. Gonzalez-Carrasco for reviewing the manuscript. References [1] Stea S, Bordini B, Sudanese A, Toni A. Registration of hip prosthesis at the Rizzoli institute, 11 years’ experience. Acta Orthop Scand 2002(Suppl 305):40–4. [2] Wilson LF, Nolan JF, Waddington MBH. Fracture of the femoral stem of the Ring TCH. J Bone Joint Surg 1992;74-B:725–8. [3] Chao J, Lo´pez V. Failure analysis of a Ti6Al4V cementless HIP prosthesis. Eng Fail Anal 2007;14:822–30. [4] Lord G, Bancel P. The madreporic cementless total hip arthroplasty. Clin Orthop 1983;176:67–76. [5] Lord G, Bancel P, Marotte JH, Guillamon JL, Blanchard JP. Cementless revisions of failed aseptic cemented and cementless total hip arthroplasties. 284 cases. Clin Orthop 1988;235:67–74. [6] Collier JP, Surprenant VA, Jensen RE, Mayor MB, Surprenant HP. Corrosion between the components of modular femoral hip prosthesis. J Bone Joint Surg 1992;74-B:511–7. [7] Gilbert JL, Buckley CA, Jacobs JJ, Bertin KC, Zernich MR. Intergranular corrosion–fatigue failure of cobalt alloy femoral stems. A failure analysis of two implants. J Bone Joint Surg 1994;76-A:110–5. [8] Kishida Y, Sugano N, Ohzono K, Sakai T, Nishii T, Yoshikawa H. Stem fracture of the cementless spongy metal Lu¨beck hip prosthesis. J Arthroplasty 2002;17:1021–7. [9] Paul JP. Strength requirements for internal and external prostheses. J Biomech 1999;32:381–93. [10] ISO 7206 Implants for Surgery: Partial and Total Hip Prostheses. Part 4: Determination of endurance properties of stemmed femoral components with application of torsion. 1989. Switzerland. International Organization for Standardization. [11] ISO 7206 Implants for Surgery: Partial and Total Hip Prostheses. Part 8: Endurance performance of stemmed femoral components with application of torsion. Switzerland. International Organization for Standardization. [12] Berrocal LO. In: Resistencia de Materiales, 1980, Chapters 4-6. Madrid: Universidad Polite´cnica de Madrid. E.T.S.I. Industriales. [13] Kotzar GM, Davy DT, Goldberg VM, Heiple KG, Berilia J, Brown RH, et al. Telemetrized in vivo hip joint force data: a report on two patients alter total hip arthroplasty. J Orthop Res 1991;9:621–33. [14] Bergmann G, Graichen F, Rohlman A. Hip joint loading during walking and running, measured in two patients. J Biomech 1993;26:969–90. [15] Bergmann G, Graichen F, Rohlman A. Is staircase walking a risk for the fixation of hip implants? J Biomech 1995;28:535–53.
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[16] Taylor SJG, Perry JS, Meswania JM, Donaldson N, Walker PS, Cannon SR. Telemetry of forces from proximal femoral replacements and relevance to fixation. J Biomech 1997;30:225–34. [17] Baleani M, Cristofolini L, Viceconti M. Endurance hip prostheses: a comparison between the load fixed in ISO 7206 standard and the physiological loads. Clin Biomech 1999;14:339–45. [18] Sanjua´n JR. In: Elementos de la teorı´a de momentos de inercia y ca´lculo de los mismos. (Editorial Labor. Madrid) 1955, pp.172–73.
Is 7206 ISO standard enough to prove the endurance of femoral components of hip prostheses? Jesu´s Chao Centro Nacional de Investigaciones Metalu´rgicas (CSIC), Avda. Gregorio del Amo, 8, 28040 Madrid, Spain Received 20 November 2006; accepted 20 November 2006 Available online 16 January 2007
Abstract The design of a cementless femoral stem that fractured at the neck–shoulder junction was analysed with reference to parts 4 and 8 of ISO standard 7206. The stresses in the section where fracturing occurred were calculated assuming the 2300 N loading specified in ISO 7206-8. The results show that the prosthesis met ISO standard requirements regarding fatigue behaviour. However, this feature does not occur when a load of 4000 N, corresponding to a patient with a body weight of 1000 N, is applied. It is therefore suggested that patient body weight should be taken into account when designing and choosing the appropriate stem size. 2006 Elsevier Ltd. All rights reserved. Keywords: 7206 ISO standard; Fatigue design; Cementless Hip prosthesis; Ti6Al4V alloy
1. Introduction Total hip arthroplasty (THA) has proven to be a successful method for the relief of pain and the restoration of normal daily activities in patients with hip disablement. The long-term success of this operation depends on a variety of factors, such as the surgical technique employed, the positioning and alignment of the stem, the stability of the intramedullary fixation, the patient weight, and the implant design. A recent study on a population of 7695 hip prostheses (implanted during the period 1990–2000) [1] revealed that 24.8% of these prostheses had been revised, i.e. one or both of the prosthesis components had required replacement. The studied prosthesis population consisted of: 17% cemented, 54% cementless, 28.6% with cementless cup and cemented stem, and 0.4% with cemented cup and cementless stem. Stem fracture was the reason for 1.7% of the implant revisions, while the most frequently observed cause (86.5%) was loosening. On the basis of these figures, it may be thought that mechanical failure of the femoral component is a rare complication in THA. However, the author considers that this is not an unimportant problem, above all when the retrieval of the stem is extremely difficult and necessitates deliberate damage to the femur [2,3]. Case reports of in vivo fracture of cementless hip prosthesis have attributed this event to: a weak junction between the madreporic corrugations and the smooth E-mail address: [email protected] 1350-6307/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2006.11.017
84
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
plate [4]; the smelting technology used and cracking of the porous layer [5]; the narrowness of the antero-posterior dimensions of the proximal region of the stem [2]; a galvanic corrosion–fatigue process at the tapered interface between the neck and the head of modular femoral components [6,7]; a lack of support in the proximal region of the stem and the distal stem fixation [8]; and the machining induced residual stresses on the surface of the stress concentration at the neck–shoulder junction [3]. The second last failure mode [8] may be justifiable because the stem fracture is preceded of loosening of the proximal part of the implant [9], and the loosening issue is still a topic subjected to investigation. The other failure modes are the result of mistakes in the design and/or control method of the femoral component. In a previous paper, it was analysed the fractographic features and metallurgical factors of the in vivo fatigue failure at the neck–shoulder junction of a cementless Ti6Al4V femoral stem (Fig. 1) [3]. This paper analyses whether this stem model would pass the endurance test according to ISO 7206 standard. Because the test
Fig. 1. Photograph of broken prosthesis (the arrow indicates the fracture initiation point). Remnants of bone tissue may be seen in the stem proximal area, indicating good osseointegration.
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
85
load specified in ISO standard seems, on the basis of previous works, unsuitable to test the endurance of stems to be implanted in patients of 1000 N body weight (BW), it is also considered an applied load of 4000 N instead of the 2300 N specified in ISO standard. 2. Background Three patients of about 60 years old and a body mass index above 30 kg/m2 underwent THA in different hospitals with different surgeons. A cementless Ti6Al4V femoral stem of the same model was used for all patients. The stem was coated in the proximal third with a beaded porous coating of Ti6Al4V. Fractures occurred in vivo suddenly after about four years of implantation without any preliminary pain. The three patients underwent a revision surgery with replacement of the fractured stems, during which great difficulty was experienced in removing the well fixed fragment of the broken stems. The proximal third of the stems was covered with remains of bony tissue, confirming osseointegration of the stem by bony ingrowth (Fig. 1). Fortuitous mechanical failure of the implants was ruled out because very similar fractures were observed in all cases. Recently it was shown that fracture of these prostheses was produced by a fatigue process initiated at the neck–shoulder junction [3]. The fracture was initiated in the lateral region of the neck, propagating through the cross section in the latero-medial direction, and ended in overload failure of the remaining cross section accompanied with gross plastic deformation. No superficial marks attributable to physical damage during implantation or extraction were visible on the neck. No microstructural defects were observed in cross sections of the stem near the fracture or in the fracture surface. 3. Analysis method The parts 4 and 8 of 7206 ISO standard [10,11] constitute a laboratory procedure to determine the endurance of femoral components of hip prostheses. According to this standard a compression load between 300 and 2300 N has to be applied on the head of the prosthesis at an angle of 10 in abduction and 9 in flexion to the stem axis. Since the hip prostheses here analysed were manufactured before the year 2002, subsequent modifications to ISO standard have not been considered. Therefore, the stem was constrained in a distance of 80 mm below the centre of the head of the prosthesis. In accordance with previous work, the experimental constraint of the stem defined by the ISO standard was simulated with a couple of bearing points on the frontal and sagittal planes located at 80 and 160 mm from the centre of the femoral head and fixing the distal tip against rotation [12]. The maximum stresses on the cross section where the break occurred (A–A 0 section in Fig. 2) and the corresponding to 80 mm from the centre of the head (B–B 0 section in Fig. 2) were calculated according to the methods used in the material strength handbooks, e.g. [12]. It was assumed that the displacements upon loading are small. From the analysis of the literature, the hip joint forces obtained using telemetric hip prostheses ranged from 2.8 to 5.2 times the BW, depending of the kind of physical activities [13–16]. Assuming an average value of 4 times the BW, the specified maximum load in ISO standard (2300 N) should be adequate to a BW of about 575 N, which is accordance with previous theoretical predictions [17]. Evidently for BW here considered of about 1000 N it seems more suitable to apply a test load of 4000 N instead of that of 2300 N specified by ISO standard irrespective of the patient BW. A load of 2300 N was chosen to calculate the maximum equivalent stress at the above mentioned cross sections. Fig. 2 presents a sketch of the stem showing the dimensions and parameters necessary for the calculation of stresses at A–A 0 and B–B 0 sections according to the following formulation. Section A–A 0 . The hip force F was resolved into F1(=Fcos9) and F2 (=Fsin9) components: the former was obtained from the projection of F on the plane defined by the neck and distal axes of the stem, whereas F2 component is normal to this plane. The component F1 is further resolved into the parallel F3(=F1cos55) and normal F4 (=F1sin55) components to the A–A 0 section. The normal load component (F4) gives rise to a compression stress state. The in-plane components (F2 and F3) give rise to My = F2d and Mx = F3d bending moments and to the corresponding shear stresses.
86
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
Fig. 2. Scheme showing both the geometrical details of the femoral component and the arrangements for fatigue test according to parts 4 and 8 of 7206 ISO Standard. The dimensions and the values of the parameters necessary to calculate the stresses at AA’ and BB’ cross sections are also shown. The hollow arrows in the AA’ and BB’ cross sections indicate the location of the maximum equivalent stress (a) medial view and (b) posterior view.
The net axial stress in a generic (x, y) point of the cross section is given by: 4F 4 M x My rz ¼ þ y x Ix Iy pD2 In this equation, the inertia moments (Ix and Iy) are given by: pD4 Ix ¼ Iy ¼ 64 in which D is the neck diameter. The shear stresses in a (x, y) generic point are given by: Qy F 2 Q F3 szx ¼ and szy ¼ x IyD I xD in which 3 3 1 1 ðD2 4y2 Þ2 and Qy ¼ ðD2 4x2 Þ2 12 12 are the first order moments of the area.
Qx ¼
ð1Þ
ð2Þ
ð3Þ
ð4Þ
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
87
The Von Mises criterion was used to calculate the equivalent stress corresponding to the combination of the above stresses, which is expressed by: req ¼ ½r2z þ 3ðs2zx þ s2zy Þ1=2
ð5Þ
Section B–B 0 . The hip force F was resolved into F1 and F2 components as in the case of A–A 0 section. However, F1 component was resolved into components normal F5( = F1cos10) and parallel F6(=F1sin10) to B–B 0 plane. The load component F5 gives rise to a compression stress state and a pure Mx=F5d1 bending moment. The components F2 and F6 produce My = F2d2 and Mx = F6d2 bending moments, and the corresponding shear stresses. The expression of the net axial stress (rz) is that of Eq. (1) but with the corresponding values of the load components, cross section area and inertia moments to B–B 0 section. The expressions of the inertia moments of this particular cross section are given by [18]: h3 3 2 2 I x ¼ 0:25b 0:055b þ 0:7854bð0:17977b þ 0:848bh þ h Þ þ ð6Þ 3 Iy ¼
b3 ð16h þ 3pbÞ 192
ð7Þ
The shear stresses for a (x, y) generic point are given by: szx ¼
Qy F 2 bI y
and
szy ¼
Qx F 6 ðb þ hÞI x
ð8Þ
in which Qx was obtained by numerical integration and Qy is given by: 1 h 1 Qy ¼ ðb2 4x2 Þ þ ðb2 4x2 Þ2 8 3
ð9Þ
In addition, F2 component produces a T = F2d1 torsion moment which induces for a generic (x, y) point the following shear stresses: szx ¼
T T y; szy ¼ x 2I x 2I y
ð10Þ
The equivalent stress is given by Eq. (5). The obtained equivalent stress was compared with the endurance limit to assess whether or not this stress could cause fatigue fracture. The endurance limit of the prosthesis neck (A–A 0 section) was estimated as the able stress to withstand 5 · 106 cycles without failure of a notched specimen with a stress concentration factor (k = 1.95) identical to that introduced at the prosthesis neck by the design of stem. In an identical way the endurance limit of the B–B 0 section was estimated on smooth specimens. Such values have previously been obtained with specimens machined from bars of Ti6Al4V ELI surgical alloy with a microstructure similar to that of the fractured stem [3]. The tests were performed at room temperature in laboratory air under tension–tension loading conditions with a minimum-to-maximum stress ratio of 0.1. The frequency used in these tests was 20 Hz. 4. Results and discussion Table 1 shows the values of the maximum equivalent stress normalised by the endurance limit in the A–A 0 and B–B 0 sections. In both cross sections the maximum stress is located in the antero-lateral region of the cross
Table 1 Maximum equivalent stresses, requiv; coordinates (x, y) of the location of maximum equivalent stress; endurance limit, rfatigue; and the ratio of maximum equivalent stress to endurance limit of AA 0 and BB 0 cross sections Cross section A–A B–B 0
0
requiv (MPa)
(x, y) (mm)
rfatigue (MPa)
requiv/rfatigue
184 206
(0.6, 6.5) (3.4,6.9)
210 536
0.876 0.384
88
J. Chao / Engineering Failure Analysis 15 (2008) 83–89
section. The normalisation procedure used involves that the fracture of the prosthesis occurs when the ratio is higher than or equal to one. The results show that the prosthesis fulfils the endurance test in accordance with parts 4 and 8 of ISO standard 7206 since the value of the equivalent stress to fatigue strength ratio for 2300 N load is less than 1. However, the value of 0.876 obtained at the neck is far from being conservative, especially when it is considered that the fatigue strength was overestimated since the tests were performed in the laboratory atmosphere at a frequency of 20 Hz and not in the more realistic conditions of a frequency of 1 Hz at a saline environment. Moreover, if the angle of flexion of the stem were supposed to be 3 instead of the 10 specified by the standard, the above calculations would predict the failure of the prosthesis at the neck. The fracture occurred in patients with a BW of about 1000 N. Having into account that the hip joint force is about 4 times BW, the maximum equivalent stress is 1.74 times higher than that of 2300 N. Thus, failure at the neck of the femoral component is predicted even when their activity was limited to slow walking. To prevent stem fracture it is necessary to increase the neck cross section and the radius of the neck–shoulder junction in order to decrease both the stress and the stress concentration factor at the neck. These modifications would not affect either the flexibility of the stem and in turn to the osseointegration of the implant. 5. Conclusions The prostheses can fulfil the requirements specified in parts 4 and 8 of ISO standard 7206. The ISO standard 7206 is found to be unsuitable for patients of a weight of nearly 1000 N. It is necessary to consider the patient weight in order to properly design and to choose the more appropriate stem.
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