磨牙烤瓷熔附金属全冠的有限元分析
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摘要
烤瓷熔附金属全冠(PFM全冠)，是目前后牙缺损常见的修复类型。因其美观、强度高、边缘适合性和生物相容性好，广泛应用于临床固定修复。PFM冠是由金属基底冠和陶瓷烧结而成的复合材料，并通过粘结剂固定在基牙上。因此其应力状况和其各组分的力学性质和厚度有密切关系。
有限元分析法是一种借助电子计算机求解连续介质力学问题的应力分析方法。自有限元分析法应用于口腔医学领域以来，该方法被广泛应用于口腔医学各个领域，显示出了巨大的优越性。本文采用螺旋CT扫描及三维有限元分析方法建立了下颌第一磨牙PFM冠修复模型，据此探讨了不同基底冠与瓷层厚度比例、不同基底冠材料和厚度、不同瓷层厚度、不同粘结剂材料和厚度对PFM冠应力分布的影响，得出了以下结果：
1．临床常规咬合面备牙量2.0mm，当基底冠厚度与瓷层厚度比例分别设为0.2：1.7、0.4：1.5、0.6：1.3、0.8：1.1，粘结剂为0.1mm时，随着基底冠厚度从0.2mm增大到0.8mm，基底冠和瓷上的压应力峰值与Mises应力峰值有增大的趋势，拉应力峰值则呈降低趋势。且当基底冠厚度为0.2时，拉应力峰值远远大于基底冠厚度为0.4mm、0.6mm、0.8mm时的拉应力峰值，而后三种基底冠厚度之间的拉应力峰值变化不显著。可见，基底冠与瓷层厚度比例对PFM冠应力有影响，综合考虑应力变化趋势及峰值大小的变化量，本文认为选基底冠与瓷层厚度比例0.4：1.5较合理。
2．当瓷层厚度一定(1.1mm)，基底冠厚度分别设为0.2mm、0.4mm、0.6mm、0.8m时，粘结剂为0.1mm，随着基底冠厚度从0.2mm增大到0.8mm，基底冠和瓷上的压应力峰值与Mises应力峰值有增大的趋势，拉应力峰值则呈降低的趋
第四军医大学硕士学位论文
势。但是，当基底冠厚度为0.2时，拉应力峰值远远大于基底冠厚度为0.4llun、
0.6"un、0.Slnm时的拉应力峰值，而后三种厚度基底冠之间的拉应力峰值变化
不明显。可见基底冠厚度对PFM冠应力有影响，综合考虑应力变化趋势及峰
值大小的变化量，本文认为选基底冠0.4nun较合理。
3.当基底冠厚度一定(0.4~)，瓷层厚度分别设为0.3llnn、0.6llun、0.glnln、
1.Zlnln、1.Slnm，粘结剂为0.Inun，当瓷层厚度从0.3llun一0.6Inln一0.glnln时，
瓷层上的拉应力有显著减小的趋势，虽然其压应力有增大，但趋势并不明显。
当瓷层厚度从0.glnln一1 .Zllun一1.Slnln时，瓷层上的拉应力减小趋势和压应力
增大趋势变缓，这说明瓷层厚度的变化对瓷层上的拉应力峰值影响较大，而
对压应力峰值影响较小。可见瓷层厚度对PFM冠应力有影响，综合考虑应力
变化趋势及峰值大小的变化量，本文认为瓷层厚度为不应小于0.glnln。
4.当基底冠厚度为0.4Inln、粘结剂厚度设定为0.lmm、粘结剂材料为聚梭酸
锌、瓷层厚度设定为1.snun时，基底冠材料分别为Au--Pd、Ni一Cr、In一ceram
alumina，随着基底冠材料弹性模量的增大，基底冠与瓷上的拉应力峰值虽
有减小，但变化不大，而基底冠与瓷上的压应力峰值、Von Mises应力峰值
则不断增大，且压应力升幅大于拉应力降幅，因此改变基底冠材料的弹性模
量可明显改变P阳冠的应力峰值。本文认为基底冠为Au一Pd合金应力值比较
合理。
5.当粘结剂材料分别为磷酸锌、复合树脂、玻璃离子、聚梭酸锌时，随着粘
结剂材料弹性模量的增大，基底冠、瓷层上的拉应力峰值、压应力峰值、Von
Mi ses应力峰值有减小趋势，而粘结剂上的拉应力峰值、压应力峰值、Von
Mises应力峰值有增大趋势，但应力峰值变化趋势均不明显。本文认为不同
粘结剂对PFM冠应力影响小。
6.当粘结剂厚度分别为0.O25Inln、0.050Inln、0.075llun、0.100Inln时，随着粘
结剂厚度的增大，基底冠、瓷层上的拉应力峰值、压应力峰值、Von Mi ses
应力峰值有增大的趋势，而粘结剂上的拉应力峰值、压应力峰值、Von Mises
应力峰值有减小的趋势，但应力峰值变化趋势均不明显。本文认为粘结剂的
厚度对瓷冠应力影响小。
第四军医大学硕士学位论文
7.在本实验的垂直载荷作用下，瓷层、基底冠、粘结剂上拉应力峰值、压应
力峰值、Von Mises应力峰值均出现在加载处，同时在颈缘处也存在较大的
应力集中。
Because the porcelain fused to metal crown(PFM) has many advantages such as aesthetic perception , high strength , excellent seal and excellent biocompatability, it is widely used for teeth restorations on clinical application now. Because PFM crown is made by the method of sintered with metal and porcelain and it is integrated with teeth by the cement, the stress distribution of PFM crown under the force is related with the property and thickness of its components.
The three dimensional finite element analysis is a method using computer to solve mechanical question about continuous medium. This method is widely used in medical field. In this paper, the PFM crown of the first molar of mandibular was built by the method of three dimensional finite element analysis and it having different rate of the thickness of metal base and porcelain different material and thickness of metal base , different thickness of porcelain, different material and thickness of cement were analyzed. The results are as following:
1. While the overall occlusal thickness of 2.0mm was maintained and the thickness of cement is 0.1mm, the rate of the thickness of metal base and porcelain is 0.2:17, 0.4:1.5, 0.6:1.3, 0.8:1.1 respectively, the peak compress stress and the peak Mises stress are increased and the peak tensile stress is
reduced as the thickness of metal base is increased from 0.2mm to 0.8mm. But the peak tensile stress is larger than that of the thickness 0.4mm , 0.6mm, 0.8mm of metal base as the thickness of metal base is 0.2mm and there are no obvious difference on the peak tensile stress between these crown with 0.4mm, 0.6mm, 0.8mm thickness of metal base . Then concerning with the trend of the changing stress and the magnitude of stress, the rate 0.4:1.5 of the thickness of metal base and porcelain is reasonable.
2. While the thickness of porcelain and is 1.1mm and the thickness of cement is 0.1 mm, the thickness of metal base is 0.2mm , 0.4mm , 0.6mm, 0.8mm respectively, as the thickness of metal base is increased from 0.2mm to 0.8mm, the peak compress stress and the peak Mises stress on the metal base and the porcelain are increased and the peak tensile stress is reduced. But as the thickness of metal base is 0.2mm, the peak tensile stress are larger than that of the metal base and the porcelain with the thickness 0.4mm, 0.6mm, 0.8mm and there are no obvious difference on the peak tensile stress between these metal base s and the porcelains with the thickness of 0.4mm, 0.6mm, 0.8mm. Then it is concluded that the thickness of 0.4mm of metal base is reasonable.
3. While the thickness of metal base is 0.4mm and the thickness of cement is 0.1mm, the thickness of porcelain is 0.3mm, 0.6mm, 0.9mm 1.2mm, 1.5mm respectively, as the thickness of porcelain is increased from 0.3mm to 0.6mm and 0.6mm to 0.9mm, the peak tensile stress is reduced obviously and the peak compress stress is increased indistinctively and as the thickness of porcelain is increased from 0.9mm to 1.2mm and 1.2mm to 1.5mm, the peak tensile stress is reduced indistinctively and the peak compress stress is increased indistinctively. It show that the change of the thickness of porcelain has obvious effect on the peak tensile stress and indistinctive effect on the peak compress stress. Then it is concluded that the thickness of porcelain is not less than 0.9mm.
4. While the thickness of metal base is 0.4mm and the material of cement is zinc polycarboxylate, the material of metal base is Au-Pd alloy , Ni-Cr alloy ,
In-ceram alumina porcelain respectively, as the Yang's modulus of the metal base is increased, the peak tensile stress is reduced slightly and the peak compress stress and the peak Mises stress are increased obviously, it show that the change of the Yang's modulus has obvious effect on the stress of crown. Then it is concluded that the magnitude of stress on Au-Pd alloy of metal base is reasonable.
5. While the material of cement is zinc phosphate - composite resin- glass ionomer- zinc polycarboxylate respectively, a
有限元分析法是一种借助电子计算机求解连续介质力学问题的应力分析方法。自有限元分析法应用于口腔医学领域以来，该方法被广泛应用于口腔医学各个领域，显示出了巨大的优越性。本文采用螺旋CT扫描及三维有限元分析方法建立了下颌第一磨牙PFM冠修复模型，据此探讨了不同基底冠与瓷层厚度比例、不同基底冠材料和厚度、不同瓷层厚度、不同粘结剂材料和厚度对PFM冠应力分布的影响，得出了以下结果：
1．临床常规咬合面备牙量2.0mm，当基底冠厚度与瓷层厚度比例分别设为0.2：1.7、0.4：1.5、0.6：1.3、0.8：1.1，粘结剂为0.1mm时，随着基底冠厚度从0.2mm增大到0.8mm，基底冠和瓷上的压应力峰值与Mises应力峰值有增大的趋势，拉应力峰值则呈降低趋势。且当基底冠厚度为0.2时，拉应力峰值远远大于基底冠厚度为0.4mm、0.6mm、0.8mm时的拉应力峰值，而后三种基底冠厚度之间的拉应力峰值变化不显著。可见，基底冠与瓷层厚度比例对PFM冠应力有影响，综合考虑应力变化趋势及峰值大小的变化量，本文认为选基底冠与瓷层厚度比例0.4：1.5较合理。
2．当瓷层厚度一定(1.1mm)，基底冠厚度分别设为0.2mm、0.4mm、0.6mm、0.8m时，粘结剂为0.1mm，随着基底冠厚度从0.2mm增大到0.8mm，基底冠和瓷上的压应力峰值与Mises应力峰值有增大的趋势，拉应力峰值则呈降低的趋
第四军医大学硕士学位论文
势。但是，当基底冠厚度为0.2时，拉应力峰值远远大于基底冠厚度为0.4llun、
0.6"un、0.Slnm时的拉应力峰值，而后三种厚度基底冠之间的拉应力峰值变化
不明显。可见基底冠厚度对PFM冠应力有影响，综合考虑应力变化趋势及峰
值大小的变化量，本文认为选基底冠0.4nun较合理。
3.当基底冠厚度一定(0.4~)，瓷层厚度分别设为0.3llnn、0.6llun、0.glnln、
1.Zlnln、1.Slnm，粘结剂为0.Inun，当瓷层厚度从0.3llun一0.6Inln一0.glnln时，
瓷层上的拉应力有显著减小的趋势，虽然其压应力有增大，但趋势并不明显。
当瓷层厚度从0.glnln一1 .Zllun一1.Slnln时，瓷层上的拉应力减小趋势和压应力
增大趋势变缓，这说明瓷层厚度的变化对瓷层上的拉应力峰值影响较大，而
对压应力峰值影响较小。可见瓷层厚度对PFM冠应力有影响，综合考虑应力
变化趋势及峰值大小的变化量，本文认为瓷层厚度为不应小于0.glnln。
4.当基底冠厚度为0.4Inln、粘结剂厚度设定为0.lmm、粘结剂材料为聚梭酸
锌、瓷层厚度设定为1.snun时，基底冠材料分别为Au--Pd、Ni一Cr、In一ceram
alumina，随着基底冠材料弹性模量的增大，基底冠与瓷上的拉应力峰值虽
有减小，但变化不大，而基底冠与瓷上的压应力峰值、Von Mises应力峰值
则不断增大，且压应力升幅大于拉应力降幅，因此改变基底冠材料的弹性模
量可明显改变P阳冠的应力峰值。本文认为基底冠为Au一Pd合金应力值比较
合理。
5.当粘结剂材料分别为磷酸锌、复合树脂、玻璃离子、聚梭酸锌时，随着粘
结剂材料弹性模量的增大，基底冠、瓷层上的拉应力峰值、压应力峰值、Von
Mi ses应力峰值有减小趋势，而粘结剂上的拉应力峰值、压应力峰值、Von
Mises应力峰值有增大趋势，但应力峰值变化趋势均不明显。本文认为不同
粘结剂对PFM冠应力影响小。
6.当粘结剂厚度分别为0.O25Inln、0.050Inln、0.075llun、0.100Inln时，随着粘
结剂厚度的增大，基底冠、瓷层上的拉应力峰值、压应力峰值、Von Mi ses
应力峰值有增大的趋势，而粘结剂上的拉应力峰值、压应力峰值、Von Mises
应力峰值有减小的趋势，但应力峰值变化趋势均不明显。本文认为粘结剂的
厚度对瓷冠应力影响小。
第四军医大学硕士学位论文
7.在本实验的垂直载荷作用下，瓷层、基底冠、粘结剂上拉应力峰值、压应
力峰值、Von Mises应力峰值均出现在加载处，同时在颈缘处也存在较大的
应力集中。
Because the porcelain fused to metal crown(PFM) has many advantages such as aesthetic perception , high strength , excellent seal and excellent biocompatability, it is widely used for teeth restorations on clinical application now. Because PFM crown is made by the method of sintered with metal and porcelain and it is integrated with teeth by the cement, the stress distribution of PFM crown under the force is related with the property and thickness of its components.
The three dimensional finite element analysis is a method using computer to solve mechanical question about continuous medium. This method is widely used in medical field. In this paper, the PFM crown of the first molar of mandibular was built by the method of three dimensional finite element analysis and it having different rate of the thickness of metal base and porcelain different material and thickness of metal base , different thickness of porcelain, different material and thickness of cement were analyzed. The results are as following:
1. While the overall occlusal thickness of 2.0mm was maintained and the thickness of cement is 0.1mm, the rate of the thickness of metal base and porcelain is 0.2:17, 0.4:1.5, 0.6:1.3, 0.8:1.1 respectively, the peak compress stress and the peak Mises stress are increased and the peak tensile stress is
reduced as the thickness of metal base is increased from 0.2mm to 0.8mm. But the peak tensile stress is larger than that of the thickness 0.4mm , 0.6mm, 0.8mm of metal base as the thickness of metal base is 0.2mm and there are no obvious difference on the peak tensile stress between these crown with 0.4mm, 0.6mm, 0.8mm thickness of metal base . Then concerning with the trend of the changing stress and the magnitude of stress, the rate 0.4:1.5 of the thickness of metal base and porcelain is reasonable.
2. While the thickness of porcelain and is 1.1mm and the thickness of cement is 0.1 mm, the thickness of metal base is 0.2mm , 0.4mm , 0.6mm, 0.8mm respectively, as the thickness of metal base is increased from 0.2mm to 0.8mm, the peak compress stress and the peak Mises stress on the metal base and the porcelain are increased and the peak tensile stress is reduced. But as the thickness of metal base is 0.2mm, the peak tensile stress are larger than that of the metal base and the porcelain with the thickness 0.4mm, 0.6mm, 0.8mm and there are no obvious difference on the peak tensile stress between these metal base s and the porcelains with the thickness of 0.4mm, 0.6mm, 0.8mm. Then it is concluded that the thickness of 0.4mm of metal base is reasonable.
3. While the thickness of metal base is 0.4mm and the thickness of cement is 0.1mm, the thickness of porcelain is 0.3mm, 0.6mm, 0.9mm 1.2mm, 1.5mm respectively, as the thickness of porcelain is increased from 0.3mm to 0.6mm and 0.6mm to 0.9mm, the peak tensile stress is reduced obviously and the peak compress stress is increased indistinctively and as the thickness of porcelain is increased from 0.9mm to 1.2mm and 1.2mm to 1.5mm, the peak tensile stress is reduced indistinctively and the peak compress stress is increased indistinctively. It show that the change of the thickness of porcelain has obvious effect on the peak tensile stress and indistinctive effect on the peak compress stress. Then it is concluded that the thickness of porcelain is not less than 0.9mm.
4. While the thickness of metal base is 0.4mm and the material of cement is zinc polycarboxylate, the material of metal base is Au-Pd alloy , Ni-Cr alloy ,
In-ceram alumina porcelain respectively, as the Yang's modulus of the metal base is increased, the peak tensile stress is reduced slightly and the peak compress stress and the peak Mises stress are increased obviously, it show that the change of the Yang's modulus has obvious effect on the stress of crown. Then it is concluded that the magnitude of stress on Au-Pd alloy of metal base is reasonable.
5. While the material of cement is zinc phosphate - composite resin- glass ionomer- zinc polycarboxylate respectively, a
引文
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27．任卫红，郭天文，张艺权，王保成．粘结剂对钛瓷结合性能的影响．第四军医大学学报，2002，23(9)：780～782．
28．张春元，何邕江，黄红园．钛金属烤瓷修复的临床性能评价．华西口腔医学杂志，2002年，20(2)：131～133．
29．叶剑涛，常少海，潘朝斌，蔡华雄．余艳崧含钛镍铬合金烤瓷冠临床应用效果观察，广东牙病防治，2003年，11(2)：137～138．
30．王坚，施斌．In-Ceram全瓷冠的临床疗效评价．江西医学院学报，2002，42(4)：99～100．
31．孙凤，魏克立，张晓，林野，邱立新，黄凌．曹佳种植体的全瓷修复．现代口腔医学杂志，2003，16(7)：518～519．
32. Yoshinari M, Kim S, Derand T. Properties of glass infiltrated alumina porcelain. 齿科材料器械,1994,13: 170.
33. Kaarel A, Michael V, Jim Ironside. Finite element analysis studies of a metal-ceramci crown on a first premolar tooth. The International J of prosthodontics, 2002,15(6):551～527.
34. H. aykul, M. toparli, M. dalkiz. A calculation of stress distribution in metal-porcelain crowns by using three dimensional finite element method. J of Oral Reh, 2002, 29:381～386.
35. Anusavice KJ, Hojjatie B, Dehoff PH. Influnce of metal thickness on stress distribution in metal-ceramic crowns. J Dent
Res, 1986,65(9): 1173～1178.
36．姚蔚，陈新民，赖锐．金属与瓷层厚度对PFM力学性质的影响．临床口腔医学杂志，2003，19(7)：427～430．
37. Aykul H, Toparli M, Dalkiz M. A calculation of stress distribution in metal-porcelain crowns by using three dimensional finite element method[J]. J Oral Reha, 2002, 29:381～386.
38．林江红，谢斌，张富强．不同瓷层和金属厚度的金属烤瓷应力的三维有限元分析．广东牙病防治，2003，11(1)：33～34．
39．文志红，杜传诗，杜莉．金—瓷修复体瓷折裂及剥脱原因分析．华西口腔医学杂志，1998，16(1)：62～64．
40. YmamotoM. Metal-Ceramic. Chicago: Quintessence Publishing Co Inc.1985:93.
41．杜传诗，魏治统，李宁．CW-PA型烤瓷Ni-Cr合金的研制及临床应用．华西口腔医学杂志，1989，7(3)：138．
42．雷亚超，魏治统，杜传诗．金属与陶瓷热膨胀差对金属烤瓷冠热稳定性的影响．中华口腔医学杂志，1991，20(6)：329．
43．朱梓园，张保卫，张修银．烤瓷熔附金属制作工艺与金瓷结合强度的研究进展．口腔材料器械杂志，2001，10(1)：37～39．
44. Anusavice KJ, Hojjatie B, Dehoff PH. Influence of metal thickness on stress distribution in metal-ceramic crowns. J Dent Res, 1986,65(9):1173～1178.
45．徐君伍(主编)．口腔修复学．人民卫生出版社，1996，第四版：149～150．
46. Smith DC. Dental cement-Current status and future prospects. Dent Clin North Am 1983,6:763～792.
47. Magne P, Versluis A, Douglas WH. Effect of luting composite shrinkage and thermal loads on the stress distribution in porcelain laminate veneers. J Prosthet Dent, 1999,81:335～344.
48. Uctasli S, Wilson HJ. Influence of layer and stain firing on the fracture strength of heat-pressed ceramics. J Oral Rehabil, 1996, 23:170～174.
49. Smith DC. Dental cements-Current status and future prospects. Dent Clin North Am, 1983,6:763～792.
50. Leevailoj C, Platt JA. In vitro study of fracture incidence and compressive fracture load of all-ceramic crowns cemented with resin-modified glass ionomer and other luting agents. J Prosther Dent 1998,(80):699～707.
51. Kamposiora P, Papavasilious G. Finite element analysis estimates of cement microfracture under complete veeer crowns. J Prosthet Dent. 1994(71):435～441.
52. Anusavice KJ, Hojjatie B.Tensile stress in glass ceramic crowns: Effect of flaws and cement voids.Int J Prosthodent, 1992(5):351～358.
53. Kaarel A, Michael V, Jim Ironside. Influence of cement on a restored crown of a first premolar using finite element analysis. The international journal of prosthodontics, 2003(16): 82～89.
54. Mccormick JY, Rowland W. Effect of luting media on the compressive strengths of two types of all-ceramic crown. Quintessence Int, 1993 (24):405～408.
55．于淑湘，陈吉华．不同粘结材料对玻璃瓷冠修复体抗碎裂载荷影响的研究．实用口腔医学杂志，18(3)：232～235．
56．张建中，高法章，阎俏梅．陶瓷的特性与崩瓷．中华口腔医学杂志，1999，34(5)：313～314．
57．白天玺主编．现在口腔烤瓷铸造支架修复学．人民军医出版社，2002：70～74．
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