Finite Element Analysis of Fretting Wear between the Cortical Suspension Device and the Cortical Bone
-
摘要:
研究了皮质悬吊装置的钛板和股骨表面的皮质骨承受交变载荷发生的微动行为. 基于钛/皮质骨材料建立了球/平面微动磨损有限元模型，通过与Hertz接触理论和已有试验结果进行对比，验证了有限元方法的正确性；同时研究了位移幅值、摩擦系数和法向力对钛球/皮质骨接触面间微动磨损行为的影响. 最后把已验证的模型和方法用于研究前交叉韧带(ACL)重建手术中的皮质悬吊装置和股骨间的微动磨损情况. 发现随着微动位移幅值从2 μm增大至10 μm，磨损状态由部分滑移向完全滑移转变，最大磨损深度由0.195 μm逐渐增大至14.13 μm，磨损体积由5.69×104 μm3增大至1.41×106 μm3；在位移幅值为5和10 μm时，磨损深度、磨损面积和磨损体积都表现出随摩擦系数增大而减小的趋势；在位移幅值为5 μm时，磨损深度随法向力的增加逐渐减小，在位移幅值为10 μm时，磨损深度随法向力的增加逐渐增大. 通过研究交变载荷下皮质悬吊装置/皮质骨微动磨损模型的微动磨损行为发现：磨损深度最大值在皮质骨隧道孔边缘的应力最大值处，并且与球/平面微动磨损模型预测趋势相同，可以通过增加皮质悬吊装置和皮质骨隧道孔边缘接触面间的摩擦系数来提高皮质骨的抗微动磨损能力，提高ACL重建手术成功率.
-
关键词:
- 皮质悬吊装置 /
- 微动磨损 /
- 皮质骨 /
- Archard磨损方程 /
- 有限元分析
Abstract:Anterior cruciate ligament (ACL) requires ACL reconstruction after rupture because of its inability to regenerate. Cortical suspension device is one of the most common fixation devices for ACL reconstruction at the femoral. The purpose of this paper was to study the fretting wear behavior of the cortical suspension device. Considering the fretting behavior of contact surfaces between the titanium plate in the cortical suspension device and the cortical bone of the femur due to the alternating load, the finite element method for the fretting wear of titanium/cortical bone was proposed, and the fretting wear behavior between the cortical suspension device and the femoral surface was predicted by this method. Firstly, the ALE adaptive mesh and the UMESHMOTION subroutine in the ABAQUS finite element software and the Archard model were used to establish a ball/plane fretting wear model of titanium/cortical bone material. And the correctness of the finite element method had been verified by comparing with results of Hertz contact theory and experiment. The effects of displacement amplitude, friction coefficient and normal force on the fretting wear were researched. Finally, a titanium plate/cortical bone fretting wear model was established using validated models and methods to study the fretting wear behavior between the cortical suspension device and the femur. By studying the fretting wear behavior of the ball/plane fretting wear model, it was found that with the increase of fretting displacement amplitude from 2 μm to 10 μm, the wear state gradually changed from partial slip to complete slip; the wear depth increased from 0.195 μm to 14.13 μm and the wear volume increased from 5.69×104 μm3 to 1.4×106 μm3. The wear depth decreased from 8.38 μm to 2.17 μm and the wear state changed from complete slip to partial slip with the increase of the friction coefficient from 0.3 to 0.7 when the displacement amplitude was 5 μm; the wear depth decreased from 15.25 μm to 10.96 μm and the wear state was in complete slip when the displacement amplitude was 10 μm. With the increase of the normal force from 40 N to 120 N, the wear depth decreased from 6.06 μm to 2.71 μm and the wear state changed from complete slip to partial slip when the displacement amplitude was 5 μm. However, the wear depth increased from 10.9 μm to 15.2 μm and the wear state was in complete slip when the displacement amplitude was 10 μm. By studying the fretting wear behavior of the titanium/cortical bone fretting wear model under alternating load, it was found that the wear was at the edge of cortical bone tunnel hole and the maximum CPRESS stress was. As the friction coefficient increases from 0.3 to 0.7, the wear depth gradually decreased from 12.6 μm to 4.4 μm, which was the same as the prediction trend of ball/plane fretting wear model. By increasing the friction coefficient between the cortical suspension device/cortical bone tunnel hole edge contact surface, the anti-fretting capacities of cortical bone could be improved, which could improve the success rate of ACL reconstruction.
-
Keywords:
- cortical suspension device /
- fretting wear /
- cortical bone /
- Archard model /
- FEA
-
![]()
图 2 ALE网格自适应技术和微动磨损实现流程
Figure 2. ALE adaptive meshing and simulation process of fretting wear
![]()
图 5 A组工况下：(a) Ft-D曲线；(b) Path-X接触节点的接触切应力和最大静摩擦力比值(Ratio)；(c)不同位移幅值的接触状态；(d) Path-X的磨损深度；(e)接触区域S的磨损深度以及(f)磨损面积和磨损体积
Figure 5. Group A working condition: (a) Ft-D curve; (b) ratio of contact shear stress and maximum static friction at contact nodes on path-X; (c) contact state with different displacement amplitude of each model contact area S; (d) wear depth on each model Path-X; (e) wear depth of each model contact area S; (f) wear area and wear volume at different displacement amplitudes
![]()
图 6 B组工况下(a) Ft-D曲线(D = 5 μm)，(b) Path-X的磨损深度(D = 5 μm)，(c) Ft-D曲线(D = 10 μm)，(d) Path-X的磨损深度(D = 10 μm)，(e)接触区域S的磨损体积与磨损面积(D = 5 μm)以及(f)接触区域S的磨损体积与磨损面积(D = 10 μm)
Figure 6. Group B working condition: (a) Ft-D curve (D = 5 μm); (b) wear depth on each model Path-X (D = 5 μm); (c) Ft-D curve (D = 10 μm); (d) wear depth on each model Path-X (D = 10 μm); (e) wear volume and wear area of contact area S (D = 5 μm); (f) wear volume and wear area of contact area S (D = 10 μm)
![]()
图 8 皮质悬吊装置和股骨模型简化过程
Figure 8. Simplified process of cortical suspension device and femoral model
![]()
图 9 皮质悬吊装置和股骨接触有限元模型
Figure 9. Finite element model of the cortical suspension device/cortical bone contact
![]()
图 10 接触区域M的(a)磨损深度和(b)接触应力图
Figure 10. (a) Wear depth and (b) contact pressure of contact area M
![]()
图 11 接触区域M的(a)不同摩擦系数下的磨损深度以及(b)磨损深度和磨损体积
Figure 11. (a) Wear depth at different friction coefficients and (b) wear depth and wear volume of contact area M
表 2 各工况载荷设置
Table 2 Load setting for each working condition
Group
numberNormal force,
FN/NFriction
coefficient, μDisplacement, D/μm A 80 0.5 2, 4, 5, 6, 8, 10 B 80 0.3, 0.4, 0.5, 0.6, 0.7 5, 10 C 40, 60, 80, 100, 120 0.5 5, 10 
下载: 导出CSV
-
[1] Berthier Y, Vincent L, Godet M. Velocity accommodation in fretting[J]. Wear, 1988, 125(1-2): 25–38. doi: 10.1016/0043-1648(88)90191-3.
[2] Sharp J W, Kani K K, Gee A, et al. Anterior cruciate ligament fixation devices: ex0pected imaging appearance and common complications[J]. European Journal of Radiology, 2018, 99: 17–27. doi: 10.1016/j.ejrad.2017.12.006.
[3] Mahapatra P, Horriat S, Anand B S. Anterior cruciate ligament repair–past, present and future[J]. Journal of Experimental Orthopaedics, 2018, 5: 20. doi: 10.1186/s40634-018-0136-6.
[4] Persson A, Gifstad T, Lind M, et al. Graft fixation influences revision risk after ACL reconstruction with hamstring tendon autografts[J]. Acta Orthopaedica, 2018, 89(2): 204–210. doi: 10.1080/17453674.2017.1406243.
[5] Rony L, Lancigu R, Hubert L. Intraosseous metal implants in orthopedics: a review[J]. Morphologie, 2018, 102(339): 231–242. doi: 10.1016/j.morpho.2018.09.003.
[6] Riviș M, Roi C, Roi A, et al. The implications of titanium alloys applied in maxillofacial osteosynthesis[J]. Applied Sciences, 2020, 10(9): 3203. doi: 10.3390/app10093203.
[7] Zhang Xiaogang, Zhang Yali, Jin Zhongmin. A review of the bio-tribology of medical devices[J]. Friction, 2022, 10(1): 4–30. doi: 10.1007/s40544-021-0512-6.
[8] Ortega P C, Medeiros W B, Moré A D O, et al. Failure analysis of a modular revision total HIP arthroplasty femoral stem fractured in vivo[J]. Engineering Failure Analysis, 2020, 114: 104591. doi: 10.1016/j.engfailanal.2020.104591.
[9] Li Junlei, Qin Ling, Yang Ke, et al. Materials evolution of bone plates for internal fixation of bone fractures: a review[J]. Journal of Materials Science & Technology, 2020, 36: 190–208. doi: 10.1016/j.jmst.2019.07.024.
[10] 于海洋, 蔡振兵, 朱旻昊, 等. 人股骨密质骨横断面的微动磨损特性研究[J]. 摩擦学学报, 2004, 24(5): 448–452]. doi: 10.3321/j.issn:1004-0595.2004.05.014. Yu Haiyang, Cai Zhenbing, Zhu Minhao, et al. Fretting behavior of the cross section of human femur cortical bone[J]. Tribology, 2004, 24(5): 448–452 doi: 10.3321/j.issn:1004-0595.2004.05.014
[11] Fu Yongqing, Batchelor A W, Wang Ying, et al. Fretting wear behaviors of thermal sprayed hydroxyapatite (HA) coating under unlubricated conditions[J]. Wear, 1998, 217(1): 132–139. doi: 10.1016/S0043-1648(98)00142-2.
[12] 崔文, 张亚丽, 王志强, 等. 人工髋、膝关节磨损测试标准及模拟试验机研究进展[J]. 摩擦学学报, 2019, 39(2): 248–258]. doi: 10.16078/j.tribology.2018152. Cui Wen, Zhang Yali, Wang Zhiqiang, et al. Review of the artificial hip and knee wear testing standards and simulation testing machines[J]. Tribology, 2019, 39(2): 248–258 doi: 10.16078/j.tribology.2018152
[13] Yu H Y, Cai Z B, Zhou Z R, et al. Fretting damage of human cortical bone in transverse orientation against titanium[J]. Key Engineering Materials, 2005, 288–289: 607–610. doi: 10.4028/www.scientific.net/kem.288-289.607.
[14] Yu H Y, Quan H X, Cai Z B, et al. Radial fretting behavior of cortical bone against titanium[J]. Tribology Letters, 2008, 31(2): 69–76. doi: 10.1007/s11249-008-9339-9.
[15] Gao Shanshan, Cai Zhenbing, Quan Huixin, et al. Comparison between radial fretting and dual-motion fretting features of cortical bone[J]. Tribology International, 2010, 43(1–2): 440–446. doi: 10.1016/j.triboint.2009.07.008.
[16] Wang Chenchen, Zhang Gangqiang, Li Zhipeng, et al. Tribological behavior of Ti-6Al-4V against cortical bone in different biolubricants[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2019, 90: 460–471. doi: 10.1016/j.jmbbm.2018.10.031.
[17] 冯存傲, 张德坤, 陈凯, 等. 钛珠涂层和羟基磷灰石涂层与皮质骨界面的切向微动损伤研究[J]. 摩擦学学报, 2022, 42(6): 1148–1160]. doi: 10.16078/j.tribology.2021236. Feng Cunao, Zhang Dekun, Chen Kai, et al. Tangential fretting wear of cortical bone interface between titanium bead coating and hydroxyapatite coating[J]. Tribology, 2022, 42(6): 1148–1160 doi: 10.16078/j.tribology.2021236
[18] Fallahnezhad K, Oskouei R H, Badnava H, et al. An adaptive finite element simulation of fretting wear damage at the head-neck taper junction of total hip replacement: the role of taper angle mismatch[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2017, 75: 58–67. doi: 10.1016/j.jmbbm.2017.07.003.
[19] Bitter T, Khan I, Marriott T, et al. Finite element wear prediction using adaptive meshing at the modular taper interface of hip implants[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 77: 616–623. doi: 10.1016/j.jmbbm.2017.10.032.
[20] McColl I R, Ding J, Leen S B. Finite element simulation and experimental validation of fretting wear[J]. Wear, 2004, 256(11–12): 1114–1127. doi: 10.1016/j.wear.2003.07.001.
[21] Öqvist M. Numerical simulations of mild wear using updated geometry with different step size approaches[J]. Wear, 2001, 249(1-2): 6–11. doi: 10.1016/S0043-1648(00)00548-2.
[22] Zhang Le, Ma Songyun, Liu Dongxu, et al. Fretting wear modelling incorporating cyclic ratcheting deformations and the debris evolution for Ti-6Al-4V[J]. Tribology International, 2019, 136: 317–331. doi: 10.1016/j.triboint.2019.03.056.
[23] Fouvry S, Paulin C, Liskiewicz T. Application of an energy wear approach to quantify fretting contact durability: introduction of a wear energy capacity concept[J]. Tribology International, 2007, 40(10–12): 1428–1440. doi: 10.1016/j.triboint.2007.02.011.
[24] Cai Mingxin, Zhang Po, Xiong Qiwen, et al. Finite element simulation of fretting wear behaviors under the ball-on-flat contact configuration[J]. Tribology International, 2023, 177: 107930. doi: 10.1016/j.triboint.2022.107930.
[25] Liu Juan, Shen Huoming, Yang Yiren, et al. Finite element and experimental investigation of human femur cortical bone microdamage during radial fretting[J]. Advanced Materials Research, 2012, 486: 313–320. doi: 10.4028/www.scientific.net/amr.486.313.
[26] Nagentrau M, Tobi A L M, Jamian S, et al. Delamination-fretting wear failure evaluation at HAp-Ti-6Al–4V interface of uncemented artificial hip implant[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2021, 122: 104657. doi: 10.1016/j.jmbbm.2021.104657.
[27] Archard J F. Contact and rubbing of flat surfaces[J]. Journal of Applied Physics, 1953, 24(8): 981–988. doi: 10.1063/1.1721448.
[28] Cruzado A, Urchegui M A, Gómez X. Finite element modeling and experimental validation of fretting wear scars in thin steel wires[J]. Wear, 2012, 289: 26–38. doi: 10.1016/j.wear.2012.04.018.
[29] Zhou Binbin, Zhou Changyu, Chang Le, et al. Investigation on fatigue crack growth behavior of Zr702/TA2/Q345R explosive welding composite plate with a through-wall crack[J]. Composite Structures, 2020, 236: 111845. doi: 10.1016/j.compstruct.2019.111845.
[30] Dorogoy A, Rittel D, Shemtov-Yona K, et al. Modeling dental implant insertion[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2017, 68: 42–50. doi: 10.1016/j.jmbbm.2017.01.021.
[31] 李玲, 麻诗韵, 阮晓光, 等. 加载相位差对微动磨损影响的数值模拟研究[J]. 表面技术, 2018, 47(9): 93–100]. doi: 10.16490/j.cnki.issn.1001-3660.2018.09.013. Li Ling, Ma Shiyun, Ruan Xiaoguang, et al. Numerical simulation of the effect of loading phase difference on fretting wear[J]. Surface Technology, 2018, 47(9): 93–100 doi: 10.16490/j.cnki.issn.1001-3660.2018.09.013
[32] Onggo J R, Nambiar M, Pai V. Fixed- versus adjustable-loop devices for femoral fixation in anterior cruciate ligament reconstruction: a systematic review[J]. Arthroscopy: the Journal of Arthroscopic & Related Surgery, 2019, 35(8): 2484–2498. doi: 10.1016/j.arthro.2019.02.029.
计量
- 文章访问数: 0
- HTML全文浏览量: 0
- PDF下载量: 0
