De Groot R, Peters M C, De Haan Y M, Dop G J, Plasschaert A J
Department of Cariology and Endodontology, University of Nijmegen, The Netherlands.
J Dent Res. 1987 Dec;66(12):1748-52. doi: 10.1177/00220345870660121001.
In previous work (Peters and Poort, 1983), the stress distribution in axisymmetric models of restored teeth was analyzed by finite element analysis (FEA). To compare the tri-axial stress state at different sites, they calculated the Von Mises equivalent stress and used it as an indication for weak sites. However, the use of Von Mises' theory for material failure requires that the compressive and tensile strengths be equal, whereas for composite resin the compressive strength values are, on the average, eight times larger than the tensile strength values. The objective of this study was to investigate the applicability of a modified Von Mises and the Drücker-Prager criterion to describe mechanical failure of composite resin. In these criteria, the difference between compressive and tensile strength is accounted for. The stress criteria applied to an uni-axial tensile stress state are compared with those applied to a tri-axial tensile stress state. The uni-axial state is obtained in a Rectangular Bar (RB) specimen and the tri-axial state in a Single-edge Notched Bend (SENB) specimen with a chevron notch at midspan. Both types of specimens, made of light-cured composite, were fractured in a three-point bend test. The size of the specimens was limited to 16 mm x 2 mm x 2 mm (span, 12 mm). Load-deflection curves were recorded and used for linear elastic FEA. The results showed that the Drücker-Prager criterion is a more suitable criterion for describing failure of composite resins due to multi-axial stress states than are the Von Mises criterion and the modified Von Mises criterion.
在之前的研究工作中（彼得斯和波特，1983年），通过有限元分析（FEA）对修复后牙齿的轴对称模型中的应力分布进行了分析。为了比较不同部位的三轴应力状态，他们计算了冯·米塞斯等效应力，并将其用作薄弱部位的指标。然而，使用冯·米塞斯材料失效理论要求抗压强度和抗拉强度相等，而对于复合树脂来说，抗压强度值平均比抗拉强度值大八倍。本研究的目的是探讨修正的冯·米塞斯准则和德鲁克-普拉格准则在描述复合树脂机械失效方面的适用性。在这些准则中，考虑了抗压强度和抗拉强度之间存在差异的情况。将应用于单轴拉伸应力状态的应力准则与应用于三轴拉伸应力状态的应力准则进行了比较。单轴状态在矩形棒（RB）试样中获得，三轴状态在跨中带有人字形切口的单边切口弯曲（SENB）试样中获得。两种由光固化复合材料制成的试样均在三点弯曲试验中发生断裂。试样尺寸限制为16毫米×2毫米×2毫米（跨度为12毫米）。记录了载荷-挠度曲线，并将其用于线弹性有限元分析。结果表明，与冯·米塞斯准则和修正的冯·米塞斯准则相比，德鲁克-普拉格准则更适合描述复合树脂在多轴应力状态下的失效情况。
