Fracture behavior of reconstructed acetabular cement sheath with microporous microcracks
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https://www.eduzhai.net International Journal of M aterials Engineering 2012, 2(6): 90-104 DOI: 10.5923/j.ijme.20120206.04 Fracture Behavior of the Cement Mantle of Reconstructed Acetabulum in the Presence of a Microcrack Emanating from a Microvoid D. Ouinas1,*, A.Flliti1, M. Sahnoun1, S. Benbarek2, N. Taghezout3 1Laboratoire de modélisation numérique et expérimentale des phénomènes mécaniques, Department of M echanical Engineering, University Abdelhamid Ibn Badis, M ostaganem, 27000, Algeria 2LECM , Department of M echanics, Faculty of Engineering, University of Sidi-BelAbbes, 22000, Algeria 3Department of Computer Science, University of Es-Senia Oran, BP 1524, El-M ' Naouer, 31000, Oran, Algeria Abstract In this work, the fin ite element method is used to analyze the behavior of the crack emanating fro m a microvoid in acetabular cement mantle by co mputing the stress intensity factor. A simple 2D mu ltilayer model developed by Benbarek et al. to reproduce the stress distributions in the cement mantle has been used. To provide the place of birth of the crac k, the stress distribution around the microvoid is determined in several positions for three different loads. The effect of axial an d radial d isplacement of the microvoid in the cement is highlighted. The results indicate that the stress distribution xx , yy and xy induced in the cement around the microvoid are not ho mogeneous and this, whatever its position. In addit ion, there is a large birth risk of crac ks in several radial directions depending on the position of the mic rovoid in the cement mantle. The crack can be triggered in several d irect ions in mode I or mode II, while the mixed mode is dominant. The KI and KII SIF varies according to the position of the microcrack and the microvoid in the cement. They increase proportionally with the increase of the weight of the patient. It should be noted that the KI SIF are t wo t imes higher than the SIF KII. The maxima of the KI SIF are obtained for the position of the microvoid α = 100° and θ = 45° of the microcrack and the risk of the propagation of the microcrack is very important for this orientation. Keywords Bone cement, Acetabulum, Microvoid, Microcracks, Stress Intensity Factors , Fin ite Element Analysis 1. Introduction Although the Polymethylmethacrylate has long been known as a fixat ive in orthopedics dental prostheses, its first use in hip arthroplasty in 1962. Despite the various disadvantages of PMMA, improved techniques of preparation and implementation of cement and implementation methods contributes to the survival of cemented arthroplasties. In addition, the function of fixing the implant, the bone cement is responsible for transferring the loads of the joint to the bone. Face loads transmitted, which can reach in some circu mstances eight times the weight of the patient[3,4], bio-co mpetence cement mus t be good. Thus, the mechanical and physical properties of cement are determin ing in the service life of the imp lant[6,7]. These properties are strongly affected by the size and number of pores in cement. Indeed, the porosity can cause crack * Corresponding author: firstname.lastname@example.org (D. Ouinas) Published online at https://www.eduzhai.net Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved initiat ion by fat igue, by creating irregular areas[9,10]. Thus, surgeons tend to reduce the porosity to ensure greater resistance to fatigue. Go ld, that this trend is directly related to the chosen method of mixing during the preparation of cement. For example, the conventional method of mixing leads to a porosity ranging from 5 to 16% depending on the type of cement, while the method of "vacuum mixing" generates a porosity of 0.1 to 1%[12,13]. So me authors assume that the latter method, increases the mechanical properties largely due to the decrease in micropores and macropores [14, 15], thus improving the life of the cement[16,17]. The effect of the position and orientation of a crack in the cement in three loads using the finite element method has been studied by Serier et al. and Bachir Bouiad jra et al.. They indicate that, fo r the third case load, the risk of crack p ropagation is higher when the crack is in the horizontal position for both failure modes. Achour et al. presented a study on the mechanical behavior of the damage (failure) of the interface between the cement / bone and cement / stem in total h ip prosthesis. They conclude that interfacial crack (cement / bone) in the distal region can spread by opening and shear; it can cause a risk of brutal 91 International Journal of M aterials Engineering 2012, 2(6): 90-104 fracture if the crack length exceeds 0.6 mm. The risk of failure of the interface cement/bone or cement/stem in the pro ximal area is less important compared with medial and distal areas. Flitti et al. studied the effect of the position of a microcrack on mechanical behavior out of a total hip prosthesis under the effect of a 90kg patient's weight. They concluded that the initiat ion of a c rack in the ce ment area distal fe mu r gro ws in mixed mode, unlike init iated in the pro ximal zone which can propagate in mode II. Bouziane et al. examined the behavior of microvoids located in the cement of a model of the hip prosthesis simp lified three -dimensional. They show that when the microvoid is located at the proximal and distal areas, the static charge causes a higher stress field that the dynamic load. Un like the work of Benbarak et al.  and [18-20] (microcrack constant), wh ich showed that the effect of the position of the microcrack constant emanating from the microvoid ; in this paper we have shown the variation KI and KII factors as a function of the length of the microcrack emanating fro m the microvoid and for a plurality o f positions in the cement. These positions are chosen according to the critical amplification Von Mises determined fro m the microvoid on along the circu mference and on the depth of the thickness of the cement (P1-P9). To co mp lete this study, we evaluated the principal stresses at the two interfaces of the cement (upper and lower). Also, the presence of two microcracks fro m of the microvoid is highlighted. The objective of this study are expected to shed light on the influence of the presence of microvoid and a crack emanating fro m the microvoid on the fracture behavior of bone cement, by using finite element method. The effect of the position of the microvoid in cement and effect of the size of the microcrack on the fracture behavior are h ighlighted. The stress intensity factor to the microcrack-tip is used like criterion of rupture. The analysis of the distribution of the Von Mises stresses in the various components of the acetabular part and the implant is made to a zero angle between the necks of the imp lant relat ive to the axis of the cup. We are required to develop a fin ite element model to analyze the p resence of a microvoid on the behavior and strength of bone cement 2. Geometrical Model The geometrical model is generated fro m a roentgenogram of a 4mm slice normal to the acetabulum through the pubic and iliu m. The cup has an outer diameter of 54 mm and an inner diameter of 28 mm. It is sealed with the bone cement mantle to uniform thickness of 2 mm. The inside diameter of the UHMWPE cup is 54 mm. The interfaces between the cup-cement and cement-subchondral bone are assumed to be fully bonded. In this work two cases were analyzed: the first is to take the presence of a microvoid in different positions in cement. The stress concentrations are determined. In the second case we assume init ially the propagation of a microcrack emanating fro m the microvoid in the determined position and characterized by a high stress concentration gradient; and another time it is assumed that the microcrack emanating fro m the microvoid in different positions. The stress intensity factors are evaluated. The model was div ided in seven different reg ions (Figure 1) according to the different elastic constants with isotropic properties considered in each region. The main areas are: cortical bone, subchondral bone and spongious bone [24-28]. The femo ral head was modeled as a spherical surface that was attached to the spherical acetabular cavity. The acetabular cavity is located on the outside of the hip bone at the junction of its three co mponents (Figure 1): iliu m, ischium and pubic bone. Table 1 su mmarizes the material properties of cement mantle, cup and all sub-regions of acetabulum bone. Table 1. Mechanical propert ies of materials [28,29] Mat ériaux Coryical bone Sub-chondral bone Spongious bone 1 Spongious bone 2 Spongious bone 3 Cup UHMWPE Cement PMMA Module de Young Coefficient de Poisson 17 000 0.30 2 000 0.30 132 0.20 70 0.20 2 0.20 690 0.35 2 300 0.30 Cement Cortical bone Cup Sub chondral bone Spongious bone 1 Spongious bone 2 Spongious bone 3 Figure 1. Composition of the acetabulum 3. Finite Element Modelling The acetabulum was modeled using the finite element code Abaqus 6.11.1. To simp lify the study, the 2D model of the acetabulum was considered. This representation was used to be representative of a section taken through the transverse plane of the acetabulum. Berg mann found that the variation of the resultant forces acting on the acetabulum is larger in the transverse plane. A very fine discretizat ion was used to represent all possible, and to be closer to reality, and special mesh type ¼ was used near a microcrack tip. Figure 2 shows the mesh of the geometrical model. The geometrical model consists of 20611 ele ments in total, 13564 quadratic elements of type CPS4R and 7047 triangular elements of type CPS3. We opted for an orientation defined by an angle of 0°between the implant neck and the axis of the cup. The latter reflects a posture of the human body. D. Ouinas et al.: Fracture Behavior of the Cement M antle of Reconstructed Acetabulum 92 in the Presence of a M icrocrack Emanating from a M icrovoid Figure 2. Geometrical model Mesh y α Cement Cup Bone x Figure 3. Load model A limited amount of research has been done on the distribution of the loads acting on the acetabulum caused by the transfer of the force inducted by the femoral head. In a study Bergmann et al. have measured maximu m values of the resultant of the forces applied to the hip o f 584% of the body weight for jogging at 7 km/h for a man of 82 years (height: 1.68 m, we ight 650 N) and 870% of body weight for stumbling a wo man of 69 years (height 1.60 m, 470 N). For reasons to be in the worst case, we chose a zero inclination angle between the neck of the imp lant and the axis of the cup (see Fig. 3) which was used by Benbarek et al. whose they indicate that they present more stress concentration. The considered Body weight is 70, 140 and 210 kg. The sacroiliac jo int was co mpletely stationary while the pubic joint was free in the sagittal plane. The boundary conditions considered are shown in the configuration of Figure 3, pubic nodes are blocked in all directions, on the wing o f the iliu m the nodes are blocked along the x axis and a uniformly distributed load applied on the implant. The contact between the bone and cement and between the cement and the cup was taken as fully bound, and between femora l head and the cup was assumed to be without frict ion under small slip. 4. Results and Analysis 4.1. Variation of Von Mises Before analyzing the stress intensity factor at the microcrack tip, it is necessary to analyze the stress distribution around the microvoid to predict the microcrack initiat ion. In Figures 4-1, 4-27, we plotted the variation of Von Mises stresses as a function of the standardized size of 93 International Journal of M aterials Engineering 2012, 2(6): 90-104 the contour of the microvoid located in different positions in the bone cement. The positions of the angle are taken at 0°, 20°, 40°, 70°, 90°, 100°, 120°, 150°and 170°. For each angle of the microvoid nine axial positions are taken fro m the cup-cement interface head to the cement-bone interface-subchondral bone (compact bone beneath the cartilage resistant). The Von Mises stresses are plotted for three load cases, a weight of 70kg, 140kg and 210kg. The normal weight of the patient can be multiplied according to these activities, in walk state, rising and descending stairs. In Figures 4.1-4.3 we see that the maximu m Von M ises stresses are obtained in the middle positions of the cavity. They are becoming increasingly important with the importance of patient weight. It is clear that the stress distribution is not uniform around the microvoid. We note several peaks in each rad ial position of the microvoid. All these stresses are due to the compression effect produced by the weight of the patient. At the radial position corresponds to 0 the maximu m stress at the interface is cup-cement of the order o f 20M Pa and the bone-cement interface subchondral is of the order of 35M Pa. The first interface to the second interface stress changes from single to double, this shows that when the microvoid is close to the bone-cement interface subchondral interaction effect is much larger than when it is close to the interface head cup-cement. The maximu m stresses in the microvoid near the interface cement / bone sub-chonral into position 0 are of the order of 35M Pa, 70MPa and 140MPa, respectively for the weight of 70kg, 140kg and 210kg. Th is shows the effect of the interaction between the microvoid and the interface. In these three cases the maximu m stress exceeds the tensile failure, which shows the severity of the defect position in the cement. In addition, depending on the axial position of the microvoid, the constraints become important. Fro m the position P1 where the cavity is close to the cup-cement interface, the maximu m stress increases progressively to approach the interface cement-subchondral bone. This finding is significant regardless of the radial position of the microvoid. The stress levels at the radial position of microvoid 0 are respectively 7, 3, 5.2, 1.75, 3, 9, 30 times higher than the radial positions 20,40,70,90,100,120,150 and 170 respectively. This shows that if the microvoid is in positions 0,40,90,100,120 it presents a high risk compared to other radial positions Except for the rad ial position at 0 , the curves show four zones of stress concentration. The areas characterized by the highest concentrations are obtained at positions 0 and 180 , that is to say the bottom of the microvoid. The other two zones are at positions 90 and 270 . It should be noted that when the microvoid is in rad ial positions at 120 , the Von Mises stresses are very low co mpared to other positions. At the radial position 0 the maximu m stresses are very important and this is the fact that the microvoid is located between the cup and the cortical bone. 4.2. Stress Variation xx on the Contour of the Microvoi d In addition, it is necessary to analyze numerically by the fin ite element method the levels and distribution of the main constraints on the contour of the microvoid. Figures 5.1-5.3 show the intensity and the stress distribution around this defect for several positions in the cement and a position of the implant. It should be noted that in the positions 0°and 180°, the stresses xx are null whatever the applied load (70kg, 140kg and 210kg). The curves are antisymmetric with respect to the x axis of the cavity that is to say with respect 180 °. The maximu m stresses are obtained for the position of the cavity at 100°. At 120°, the stresses are similar to those marked 100°. The two peaks maximu m stress positive are at 60 °and 240 °and the two peaks of the compressive stress are in 120 °and 300 °.The maximu m co mpression stresses are important for the position of the microvoid null, this is due to the edge effect. Such a position of the microvoid in cement, fact of increasing strongly the risk of damage. Thus, when the patient's weight exceeds 100kg, any position of the microvoid can lead to rupture of the cement in the first cycles of activity and therefore to the destruction of the hip p ro s th es is . 4.3. Stress Variation yy on the Contour of the Microvoi d In Figures 6.1-6.3, we show the evolution of the stress yy on the contour of the microvoid for different positions in ce ment. It is c lear that gaits are antisymmetric with respect to 180°. For all cases, the tensile stresses in the near vicinity of the microvoid are s mall co mpared with the co mpressive stresses at the position 0. When the weight P=70 kg, the maximu m co mpressive stress yy is about four times lower of the compression fracture limit, while the traction is three times lower, wh ich shows that they are relatively low. By against, a weight of 140kg and the position of the microvoid to 100°, the constraints tend to the tensile strength limit to angles 30° and 210°. The stress yy greatly exceeds the strength in tension and co mpression. In this case, the cement is almost frag mented in tension or compression depending on the position of the microvoid in the binder. 4.4. Stress Variation xy on the Contour of the Microvoi d Figures 7.1-7.3 show the variat ion of the shear stress on the contour of the microvoid for different positions in the cement. We note that the positions of the cavity to 100 °and 120 °have four peaks of co mpression. The positions 0 °and 40 ° have four peaks of tension. However, the highest D. Ouinas et al.: Fracture Behavior of the Cement M antle of Reconstructed Acetabulum 94 in the Presence of a M icrocrack Emanating from a M icrovoid compression stresses are obtained for the position of the cavity to 100 °and are of the order of 8 MPa, 15 MPa and 30 MPa, respectively for the applied loads 70kg, 140kg and 210kg. The tangential stresses are increasingly important with the importance of the applied load. The positive shear stresses are maximu m for the position of the cavity at 0°; they reach 12 MPa. In this case, the risk of birth of microcrack in mode II can occur in one area, whereas the position of the cavity at 100 °can be in four positions if the load is large, wh ich increases the likelihood of damage to the cement. The lower stresses are obtained for the positions 40 ° and 120°. In co mparison with the stresses xx and yy the tangential stresses are low to create a microcrack mode II. 4.5. Stress Variation in the Contour of the Cement In Figures 8.1 and 8.2 we plot the variation of stresses in the interfaces cement/bone subchondral and cement-cup in the presence of a microvoid of 0.02mm d iameter in the radial positions at 0°, 40°, 100°and 120°and in middle of the cement. The applied load is of the o rder of 70 kg. It should be noted that the presence of the cavity has an effect on the change in the stress at the two interfaces. By against, the Von Mises stress is greatest in areas well clear in contours interfacials. The areas most stressed are in the position 0 and in the interval varying fro m 90°to 120°in both in terfaces . The first peak is obtained at 0°and the second at 100°for the two interfaces of the cement. In this case, the Von Mises stresses are almost three times less to tensile strength stress. It should be noted that if a microvoid is in these two areas of peak stress, the defect will quadruplicate the stress and therefore present a high risk of microcrack init iation, and the likelihood of its spread is high. The Von Mises stresses are higher in the cup/cement interface that in the cement interface-subchondral bone and it exp lains that the cement is a stress absorber. If a cav ity is close to the interface, the stresses in the interface and the cavity will be increased as a result of interaction and therefore the risk of damage is major. This behavior shows that the existence of the microvoid is a source of increasing stress concentrations and consequently the risk of loosening of the prosthesis 5. Variation of SIF of Microcrack Emanating from the Microvoid In this section we have studied the evolution of the stress intensity factor KI and KII as a function of the length of the microcrack emanating fro m the microvoid located in the bone cement. This latter is taken in the most unfavorable radial positions previously established. Three patient's weight loads are considered, 70kg, 210kg and 140kg. In addition, we chose the radial positions with the concentrations of Von M ises stresses are maximu m for angles 0,40,100 and 120. The positions of the maximu m stresses on the contour of the microvoid whose a microcrack is susceptible to propagate are the angles 45,94,11 and 142 respectively 0,40,100 and 120. According to figures 9.1-9.6, we find that the stress intensity factors KI and KII will vary as a function of the increase in the length of the microcrack emanating fro m the microvoid. This variat ion is more marked with increasing of patient weight. The stress intensity factors KI for the positions of the microvoid 40°are positive and for positions 0°are negative. While KII SIF are negatives whatever the microvoid position. We note that the SIF KI and KII obtained for the position 0 of the microvoid are much larger in absolute value compared to other positions, showing that the birth of a microcrack emanating fro m a cavity at an angle 0 constitute a high risk of rupture co mpared with other positions. This is due to the edge effect. The KII SIF is almost ten times s maller than the KI except for the case of load 70kg, where it is almost neglig ible for large microcracks. In position 100 , the KI SIF shows significant positive values that can cause rupture of the cement easily. This microvoid position affects significantly the bone-cement fracture toughness, which controls the failure process at the in terfaces . In Figure 10 we present the Von M ises stress levels for four different orientations 0,40,100 and 120 the microvoid in cement. It shows the mapping stress of the microcrack tip emanating fro m the microvoid located in the bone cement. It is clear that stresses vary depending on the microvoid position. In Figures 11.1-11.6 we plotted the variation of KI and KII SIF as a function of the microcrack length in the second position containing the maximu m stresses on the Von M ises contour of the microvoid to the angles 195,144 and 323 respectively 40,100 and 120. It is clear that the SIF of oriented microcrack in the second position are low co mpared to the first position. In this case the KII SIF changes sign, it is positive for 40,100. 6. Influence of the Orientation of the Microcracks from the Microvoid on the SIF In Figures 12.1-12.6, we have shown the variation of the stress intensity factor KI and KII as a function of the microcrack orientation emanating fro m a microvoid located in the cement. The microvoid takes several critica l positions, 0°, 40°, 100°and 120°for three different loads of the patient. The SIF KI and KII vary as function of the microcrack and the microvoid positions in the cement. They increas eproportion ally with the increase of the weight of the patient. It should be noted that the SIF KI are two times h igher than the SIF KII. The maximu m values of KI FIC are obtained for the position of the microvoid α = 100° and of the microcrack θ = 45°. The risk of p ropagation of the microcrack is very important for this orientation. The minimu m values are respectively θ = 135 ° and θ = 310°. The maximu m values for SIF KII are obtained for the position of the microvoid α = 100° 95 International Journal of M aterials Engineering 2012, 2(6): 90-104 and θ = 90°, θ = 290° respectively of the microcrack. The minimu m value is at θ = 160°. It should be noted that there is a position for which the SIF KI and KII are null, this corresponds to the interval 220 270 . The same behavior has been marked when the microvoid is at the position α = 120°. If the microvoid is at the position α = 40°, the mic rocrack is susceptible to propagate in pure mode I at θ = 135° or at θ = 335° or pure mode II at θ = 20° or θ = 170°. And if it is at 0°, the SIF KI reaches its maximu m negative at 0 °and 335 °for the SIF KII. 35 Microvoid Position Angle =0 30 P1 P2 P3 25 P4 P5 P6 20 P7 P8 P9 15 Charge P=70 Kg 10 5 0 0,00 0,13 0,25 0,38 0,50 0,63 0,75 0,88 1,00 Microvoid Position Angle =20 5 P1 P2 P3 P4 4 P5 P6 P7 P8 P9 3 Charge P=75 Kg 2 1 0 0,00 0,20 0,40 0,60 0,80 1,00 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0,00 0,20 Microvoid Position Angle =40 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=70 Kg 0,40 0,60 0,80 1,00 8 Microvoid Position Angle =70 P1 P2 P3 6 P4 P5 P6 P7 P8 4 P9 Charge P=70 Kg 2 0 0,00 0,20 0,40 0,60 0,80 1,00 70 Microvoid Position Angle =0 60 P1 P2 P3 50 P4 P5 P6 40 P7 P8 P9 30 Charge P=140 Kg 20 10 0 0,00 0,13 0,25 0,38 0,50 0,63 0,75 0,88 1,00 140 Microvoid Position Angle =0 120 P1 P2 P3 100 P4 P5 P6 P7 80 P8 P9 Charge P=120 Kg 60 40 20 0 0,00 0,13 0,25 0,38 0,50 0,63 0,75 0,88 1,00 11 10 9 8 7 6 5 4 3 2 1 0 0,00 22 20 18 16 14 12 10 8 6 4 2 0 0,00 0,20 0,20 22 Microvoid Position 20 Angle =20 P1 18 P2 P3 16 P4 P5 14 P6 P7 12 P8 P9 10 Charge P=140 Kg 8 6 4 2 0 0,40 0,60 0,80 1,00 0,00 0,20 Microvoid Position Angle =40 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=140 Kg 0,40 0,60 0,80 1,00 40 35 30 25 20 15 10 5 0 0,00 0,20 Microvoid Position Angle =20 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=210 Kg 0,40 0,60 0,80 Microvoid Position Angle =40 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=210 Kg 0,40 0,60 0,80 1,00 1,00 14 Microvoid Position Angle =70 12 P1 P2 P3 10 P4 P5 P6 8 P7 P8 P9 6 Charge P=140 Kg 4 2 0 0,00 0,20 0,40 0,60 0,80 1,00 26 Microvoid Position 24 Angle =70 P1 22 P2 20 P3 P4 18 P5 16 P6 P7 14 P8 P9 12 Charge P=210 Kg 10 8 6 4 2 0 0,00 0,20 0,40 0,60 0,80 1,00 D. Ouinas et al.: Fracture Behavior of the Cement M antle of Reconstructed Acetabulum 96 in the Presence of a M icrocrack Emanating from a M icrovoid 18 16 14 12 10 Microvoid Position 30 Angle =90 P1 P2 P3 25 P4 P5 P6 20 P7 P8 P9 Charge P=70 Kg 15 Microvoid Position Angle =70 50 P1 P2 P3 45 P4 P5 40 P6 P7 35 P8 P9 Charge P=140 Kg 30 Microvoid Position Angle =90 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=210 Kg 8 25 6 10 20 4 2 0,00 0,20 0,40 0,60 0,80 1,00 5 0 0,00 0,20 0,40 0,60 0,80 1,00 15 10 5 0,00 0,20 0,40 0,60 0,80 1,00 20 18 16 14 12 10 8 6 4 2 0,00 0,20 0,40 12 10 8 6 4 2 0,00 0,20 0,40 0,60 0,60 35 Microvoid Position Angle =100 P1 P2 30 P3 P4 P5 25 P6 P7 P8 P9 20 Charge P=70 Kg 15 10 0,80 1,00 5 0,00 25 Microvoid Position Angle =120 P1 P2 P3 20 P4 P5 P6 P7 P8 15 P9 Charge P=70 Kg 10 0,80 1,00 5 0,00 Microvoid Position 70 Angle =100 P1 P2 60 P3 P4 P5 P6 50 P7 P8 P9 40 Charge P=140 Kg 30 Microvoid Position Angle =100 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=210 Kg 20 0,20 0,40 0,60 0,80 1,00 10 0,000 0,013 0,026 0,039 0,052 0,065 50 Microvoid Position Angle =120 45 P1 P2 P3 40 P4 P5 35 P6 P7 30 P8 P9 25 Charge P=140 Kg 20 Microvoid Position Angle =120 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=210 Kg 15 10 0,20 0,40 0,60 0,80 1,00 5 0,00 0,20 0,40 0,60 0,80 1,00 4,0 3,5 3,0 2,5 2,0 Microvoid Position 9 Angle =150 P1 8 P2 P3 P4 7 P5 P6 6 P7 P8 P9 5 Microvoid Position 18 Angle =150 P1 P2 16 P3 P4 14 P5 P6 P7 12 P8 P9 10 Charge P=140 Kg Microvoid Position Angle =150 P1 P2 P3 P4 P5 P6 P7 P8 P9 Charge P=210 Kg Charge P=70 Kg 4 8 1,5 3 6 1,0 2 4 0,5 0,00 0,20 0,40 0,60 0,80 1,00 1 0,00 0,20 0,40 0,60 0,80 1,00 2 0,00 0,20 0,40 0,60 0,80 1,00 1,2 3,0 Microvoid Position 9 Microvoid Position Angle =170 Angle =170 Microvoid Position P1 P1 8 Angle =170 1,0 P2 2,5 P2 P1 P3 P3 7 P2 P4 P4 P3 0,8 P5 P6 2,0 P5 P4 P6 6 P5 P7 P7 P6 P8 P8 5 P7 0,6 P9 Charge P=70 Kg1,5 P9 Charge P=140 Kg P8 P9 4 Charge P=210 Kg 0,4 1,0 3 0,2 0,00 0,20 0,40 0,60 0,80 1,00 0,5 0,00 0,20 0,40 0,60 0,80 1,00 2 1 0,00 0,20 0,40 0,60 0,80 1,00 Figure 4. Variation of Von Mises stress on the microvoid contour located in the bone cement in different positions and different loads. 97 International Journal of M aterials Engineering 2012, 2(6): 90-104 Figure 5. Variation in the xx stress on the microvoid contour Figure 6. Variation in the yy stress on the microvoid contour D. Ouinas et al.: Fracture Behavior of the Cement M antle of Reconstructed Acetabulum 98 in the Presence of a M icrocrack Emanating from a M icrovoid Figure 7. Variation in the xy stress on the microvoid contour Figure 8. Variation of Von Mises stress contours on the bone cement 99 International Journal of M aterials Engineering 2012, 2(6): 90-104 KI[MPa(mm)1/2] KI[MPa(mm)1/2] 0,10 0,05 0,00 -0,05 -0,10 -0,15 -0,20 -0,25 Radial Position of Microvoid 0 40 100 120 Charge P=70 Kg -0,30 0,0 0,2 0,4 0,6 0,8 1,0 KII[MPa(mm)1/2] 0,01 0,00 -0,01 -0,02 -0,03 -0,04 Radial Position of Microvoid 0 40 100 120 Charge P=70 Kg -0,05 0,0 0,2 0,4 0,6 0,8 1,0 0,2 0,0 -0,2 -0,4 -0,6 Radial Position of Microvoid 0 40 100 -0,8 120 Charge P=140 Kg -1,0 0,0 0,2 0,4 0,6 0,8 1,0 0,2 0,0 -0,2 -0,4 -0,6 -0,8 -1,0 -1,2 Position radiale de la cavit -1,4 0 40 -1,6 100 120 -1,8 Charge P=210 Kg -2,0 0,0 0,2 0,4 0,6 0,8 1,0 KII[MPa(mm)1/2] KII[MPa(mm)1/2] 0,01 0,00 -0,01 -0,02 -0,03 -0,04 -0,05 -0,06 -0,07 -0,08 -0,09 -0,10 -0,11 Radial Position of Microvoid 0 40 100 120 Charge P=210 Kg -0,12 0,0 0,2 0,4 0,6 0,8 1,0 -0,01 -0,02 -0,03 -0,04 -0,05 -0,06 -0,07 -0,08 -0,09 -0,10 -0,11 -0,12 -0,13 -0,14 -0,15 -0,16 -0,17 Radial Position of Microvoid 0 40 100 120 Charge P=210 Kg -0,18 0,0 0,2 0,4 0,6 0,8 1,0 Figure 9. Variation of KI and KII SIF vs. microcrack length emanating from the microcavity in the bone cement (position 1) KI[MPa(mm)1/2]
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