Numerical simulation and experimental evaluation of the corrosion susceptibility of degradable magnesium-based bone implants
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摘要: 镁基合金作为"第三代生物医用材料"，以其优异的生物相容性和可降解性吸引了众多学者的关注。在传统医疗骨植入器械难以降解的背景下，展现出了其独特的潜力。然而，由于植入后在人体体液环境的应力和腐蚀作用下腐蚀损伤和退化速率的未知性，难以预测其在临床应用中的性能。因此，为防止因退化过快而导致过早地断裂失效，本研究建立了一种应用于金属腐蚀性能预测的数值模型，该模型被用于研究镁基合金的腐蚀行为预测。通过体外腐蚀试验评估其对不同程度应力腐蚀的敏感性并校准模型参数。为测试模型的准确性，对骨植入物的腐蚀行为进行了预测。结果表明，该模型可以可靠地预测各种应力条件下植入物的腐蚀损伤、降解率和相关的机械性能退化。因此，应力腐蚀模型作为一种数值模拟工具，具备准确预测腐蚀行为的同时优化植入物的退化速率的潜力。此外，提出的模型程序和方法适用于不同合金成分、多种应用场景接骨板的应力腐蚀预测，有助于实现植入材料退化速率的精确调节。Abstract: Magnesium-based alloys, as "third-generation biomedical materials", have attracted the attention of many scholars for their excellent biocompatibility and degradability. In the context of traditional medical bone implant devices, which are difficult to degrade, it shows its unique potential. However, it is difficult to predict its performance in clinical applications due to the unknown rate of corrosion damage and degradation under the stress and corrosive effects of the human body fluid environment after implantation. Therefore, in order to prevent premature fracture failure due to excessive degradation, a numerical model applied to the prediction of corrosion performance of metals was developed in this study to investigate the in vitro corrosion behaviour of AZ31B magnesium alloy splints, and the stress-corrosion susceptibility of the splints was assessed by in vitro corrosion tests, and several sets of tests were conducted to obtain data to calibrate the model parameters. The results show that the established model can accurately predict the corrosion damage, degradation rate, and mechanical property damage of implants under different stress loads. Therefore, the stress corrosion model has the potential as a numerical simulation tool to accurately predict corrosion behaviour while optimising the degradation rate of implants. In addition, the procedures and methods of the proposed model are applicable to the stress corrosion prediction of splints with different alloy compositions and mul- tiple application scenarios, which can help to achieve an accurate regulation of the degradation rate of implant materials.
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图 1 腐蚀模拟算法流程图
Figure 1. Flowchart of corrosion simulation algorithm
D, Dc, Dh, Dc-1 and Dh-1 are the damage field, pitting damage, stress corrosion damage, pitting damage at the last time step, and stress corrosion damage at the last time step, respectively; δU and δSC are the critical thickness of the corrosion product film and the width of the corrosion cracks; Le and KU are the length of the characteristic finite element and material kinetic related parameters of the corrosion process; S and R are corrosion process and pH related parameters; Δt and α are numerically calculated time increments and time amplification constants; λe,t is the dimensionless pitting corrosion parameter of cell e at time t; σ*e is the maximum effective stress (i.e. Mises stress) of the load
图 2 (a)用于试验测试的样品；(b)(a)中测试样品的加载模型；(c)接骨板的有限元模型；(d)接骨板的结构，接骨板中螺纹孔的放大视图
Figure 2. (a) Sample used for experimental testing; (b) Loading model of the test sample in (a); (c) Finite element model of the splint; (d) Structure of the splint, enlarged view of the threaded holes in the splint
图 4 恒定载荷浸泡腐蚀设备示意图
Figure 4. Schematic diagram of constant load immersion corrosion equipment
图 5 镁合金在静载荷条件下的腐蚀过程示意图
Figure 5. Schematic diagram of the corrosion process of magnesium alloy under loaded conditions
图 6 腐蚀过程中AZ31B镁合金的质量损失率与析氢增量
Figure 6. Mass loss rate and hydrogen precipitation increment of AZ31B magnesium alloys during corrosion
图 7 AZ31B镁合金接骨板样品损伤程度随模拟时间的变化图，左下角插入的图片显示了螺纹孔附近腐蚀程度随时间的演化(点蚀与应力腐蚀协同作用)
Figure 7. Plot of the extent of damage to a sample of AZ31B magnesium alloy splints over simulation time, with the image inserted in the lower left corner showing the evolution of the extent of corrosion near the threaded holes over time (pitting corrosion in synergy with stress corrosion)
图 8 模型预测AZ31B镁合金的屈服强度在不同时间节点的损伤程度以及损伤后的屈服强度
Figure 8. Model prediction of yield strength of AZ31B magnesium alloy at different time points of damage and yield strength after damage
图 9 相同时间下，不同载荷AZ31B镁合金接骨板的损伤，插入的图片展示了关键腐蚀位置
Figure 9. Damage to AZ31B magnesium alloy splints with different loads at the same time, inserted image enlarged Critical corrosion locations
图 10 AZ31B镁合金接骨板在不同静载荷条件下(0、0.5、0.65、0.8 MPa)浸泡30 h后的宏观腐蚀形貌与模型预测结果
Figure 10. Macroscopic corrosion morphology and model prediction of AZ31B magnesium alloy splints after 30 h immersion under different static load conditions (0, 0.5, 0.65, 0.8 MPa)
图 11 模型预测AZ31B镁合金的质量损失与体外试验测得质量损失的对比图。条带表示试验中质量损失的最大值和最小值的范围，而误差线表示模型预测的质量损失的平均值±标准差
Figure 11. Plot of model-predicted mass loss of AZ31B magnesium alloy against mass loss measured in in vitro tests. The bars indicate the range of maximum and minimum values of mass loss in the test, while the error line indicates the mean ± standard deviation of the model-predicted mass loss
表 1 AZ31B的化学成分(wt%)
Table 1. Chemical composition of AZ31B (wt%)
Al Zn Mn Si Ca Fe Ni Cu Other Mg 2.74 1.27 0.361 0.0161 0.0078 0.0152 0.0016 0.0008 0.08 Bal 
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表 2 Hank's溶液的化学成分(g·L−1)
Table 2. Chemical composition of Hank's solution (g·L−1)
NaCl KCl KH2PO4 MgSO4•7 H2O NaHCO3 CaCl2 Na2HPO4•H2O Glucose 8.00 0.40 0.06 0.20 0.35 0.14 0.06 1.00
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表 3 AZ31B合金的腐蚀性能参数
Table 3. Corrosion performance parameters of AZ31B alloy
Load/MPa δU/mm δSC/mm KU S R $\Upsilon $ ψ α 0.5/0.65/0.8 0.17 0.07 0.026 0.02 3.2 0.6 5 103 Notes: δU and δSC are the critical thickness of the corrosion product film and the width of the corrosion cracks; KU is a parameter related to the corrosion process and material dynamics; S and R are corrosion process and pH related parameters; $\Upsilon $ and ψ are the shape and scaling parameters of the Weibull distribution, respectively; α is the time amplification constant in the numerical calculation.
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