摘要
由于颗粒增强有机树脂基复合材料(Particulate reinforced resin matrix composite)良好的综合性能和魅力的外观,已经逐步取代传统的银汞合金,成为现代口腔医学牙齿修复材料的首选。然而,作为牙齿修复的复合材料在修复早期会出现聚合收缩现象,由此而产生的收缩应力将引起修复材料与天然牙齿之间脱胶,形成微空洞,甚至修复材料与牙齿完全脱落导致修复失败。另一方面,复合材料处于口腔湿润的环境中,会吸湿膨胀,复合材料内水分比的变化将会改变材料的应力状态,从而对材料的物理、力学性能产生不利影响,会造成材料的不可逆损伤。针对聚合收缩和吸湿膨胀耦合作用对复合材料性能及修复牙齿结构力学特性的影响问题,传统的研究主要采用试验方法。
为了模拟在聚合收缩和吸湿膨胀耦合作用下的复合材料性能变化及修复牙齿结构力学行为,从而为牙齿修复选择合适的材料提供力学依据,基于三维单胞模型和有限元技术,本文进行了如下主要研究工作:
1、假设口腔中水分扩散满足著名的Fick第二定律,导出了湿扩散有限元方程,进一步实现湿-力耦合有限元分析,拓展了有限元方法的应用范围。
2、从材料的角度分析了牙齿填充修复材料性能影响因素。用立方体单胞模型对颗粒增强复合材料的性能进行了深入的探讨,研究发现:(1)充填颗粒体积分数是复合材料弹性模量的重要影响因素,复合材料的弹性模量随颗粒的体积分数增加而增大;(2)当基体与充填颗粒粘结良好时,颗粒的强度决定了复合材料的强度;(3)界面层性能对复合材料性能有很大的影响。
3、考虑界面脱胶损伤效应,采用三种立方单胞模型,通过有限元法研究了吸湿率对颗粒增强复合材料力学行为的影响。得到如下结论:(1)相同的吸湿性,在30%PVF(颗粒体积分数:Particle volume fraction,PVF)前增加PVF,层间脱胶损伤值显著增加;此后损伤值的增加趋于平缓;(2)保持层间强度和PVF不变,层间脱胶损伤随吸湿率的增加而接近线性增加;(3)FCC(面心立方:Face-centred cubic,FCC)模型层间脱胶损伤的预测结果和实验数据基本吻合;同时此模型可以用于预测牙齿填充材料三点弯曲实验的临界载荷。
4、建立理想牙齿修复结构,利用有限元方法研究了同时考虑聚合收缩和吸湿膨胀耦合作用下的填充修复材料和粘结界面层材料性能对牙齿修复结构的力学行为的影响,得到如下结论:(1)低弹性模量的牙齿填充修复材料能限制天然牙组织的位移,但天然牙组织的位移与粘结界面层的弹性模量无关。减小粘结界面层弹性模量会对牙尖弯曲产生影响,而改变修复材料的弹性模量则不会;(2)低弹性模量的填充修复材料会导致牙齿修复结构相对低的应力场和位移场。高的粘结界面层材料弹性模量会引起修复材料中的高应力,但不会引起天然牙中的高应力;(3)在三种不同吸湿率:超吸水率、等吸水率和次吸水率的条件下,牙齿修复结构的应力场基本上相同,但位移场却差别很大。
5、考虑聚合收缩作用下,粘结界面层的性能对牙齿修复结构力学性能的影响,将聚合收缩过程简化为粘弹性模型,通过有限元计算分析得出如下结论:(1)应用较低弹性模量和较大厚度的粘结界面层可以一定程度的缓解粘结界面层顶端与牙釉质交接处的应力集中。然而,粘结界面层厚度的增加会导致牙齿修复腔底部粘结界面层和修复材料连接处的应力增大;(2)敏感度分析表明,粘结界面层的弹性模量和厚度都对修复牙齿结构的残余应力都有较大影响。
Composites with particulate reinforced resin matrix are now increasingly applied for replacing traditional restorative materials, such as silver amalgam, because of their advantage mechanical properties and good aesthetic. However, polymerization shrinkage of the resin-based materials is of concern because the resulting shrinkage stresses can lead to failure of the interfacial bonds, which results in marginal leakage, premature failure of the restoration, and in some cases micro-cracking of the tooth. In addition, the composite resin appears to be capable of uptaking water in aqueous environment of oral, which exerts an obviously detrimental effect on the physical/mechanical properties, and even results in irreversible damage to the dental composite. To determine the properties of composite and restoration-tooth structure under polymerization shrinkage and water diffusion, the previous studies of others were based on trial-and error methods.
As a numerical method, the finite element technology can be used to solve complex engineering problems. There are currently no options in commercial finite element programs specifically designed to address the issue which take into consideration both polymerization shrinkage and water sorption due to its difficulty.
To simulate the behavior of the restoration-tooth under polymerization shrinkage and water diffusion, the following investigations have been done based on the three-dimensional unit cell model and the finite element analysis:
1 Moisture distribution in the restoration-tooth structure which expose to oral environment can be evaluated by assuming that moisture diffusion is described by a Fickian process. The strain analysis and moisture diffusive finite element formulations were obtained, respectively. The finite element formulation applicable for hygro-mechanical problem was derived by coupling solution.
2 Impact factors about the performance of restorative material were analyzed considering varying material properties. The performance of the particulate reinforced composites (PRC) was studied deeply using the cubic unit cell model. It was found: (1) The stiffness of the PRC increase as the PVF increase. (2)The strength of the PRC depended on the strength of the particulate. (3)The interphase property has the strong effect on the property of the PRC.
3 Damage effects of water sorption on mechanical properties of the PRC have been predicted using 3D finite cell models. The results were found as following: (1) The damage value increases more significantly with the increase in PVF before 30% PVF, beyond which the increasing trend becomes gradually gentle. (2)Keeping the interphase strength and PVF unchanged, the damage increase with increasing moisture concentration in a nearly linear relation. (3)The results generated from the FCC model with consideration of the interphase debonding are in good agreement with the experimental data, meanwhile, the FCC model is also capable of predicting the critical load for the damaged and the undamaged dental composite subject too the 3-point flexural test.
4 A 3D-fmite element analysis has been successfully exploited to examine the mechanical behavior of the restoration-tooth structure under the polymerization shrinkage and water sorption. It was found: (1) The low stiffness of the composite has the effect to limit the displacement occurring in the remaining tooth tissue. For lower interphase, the cuspal flexures are litter higher. The high interphase modulus acts as a 'shielding effect' for stress transfer. (2)The mildest composite results in the lowest tooth stress and displacement. The stiffest restoration-tooth interphase leads to the lowest displacement and highest stress in composite. The stresses generated in the models increased with the stiffness of the composite. The stress and displacement are reduced due to the compensation action of water sorption. (3)The hyper-water sorption results in maximum stress and displacement within the models, while the equi-water sorption lead to minimum value.
5 The effect of properties of the interphase on the mechanical behavior of the restoration-tooth structure under the polymerization shrinkage was discussed. The behavior of polymerization shrinkage was described using the model of viscoplasticity. Some results were got using the FEM method: (1) The low stiffness and thick interphase can release the high residual stresses which are located at the occlusal surface along the tooth-composite joint, but the thick interphase can result in the stress concentration in the angle surrounding the pulp wall. (2)Sensitivity analysis indicated that the modulus and thickness of the adhesive have the strong effect on the residual stresses of the restoration-tooth, a thin interphase of a more flexible adhesive exhibits the same mechanical performance as a thick interphase of a less flexible adhesive for the restoration-tooth within limits.
引文
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