Objective

The aim of this paper is to investigate the effects on shrinkage strain/stress development of the lateral constraints at the bonded surfaces of resin composite specimens used in laboratory measurement.

Methods

Using three-dimensional (3D) Hooke’s law, a recently developed shrinkage stress theory is extended to 3D to include the additional out-of-plane strain/stress induced by the lateral constraints at the bonded surfaces through the Poisson’s ratio effect. The model contains a parameter that defines the relative thickness of the boundary layers, adjacent to the bonded surfaces, that are under such multiaxial stresses. The resulting differential equation is solved for the shrinkage stress under different boundary conditions. The accuracy of the model is assessed by comparing the numerical solutions with a wide range of experimental data, which include those from both shrinkage strain and shrinkage stress measurements.

Results

There is good agreement between theory and experiments. The model correctly predicts the different instrument-dependent effects that a specimen’s configuration factor (C-factor) has on shrinkage stress. That is, for noncompliant stress-measuring instruments, shrinkage stress increases with the C-factor of the cylindrical specimen; while the opposite is true for compliant instruments. The model also provides a correction factor, which is a function of the C-factor, Poisson’s ratio and boundary layer thickness of the specimen, for shrinkage strain measured using the bonded-disc method. For the resin composite examined, the boundary layers have a combined thickness that is ∼11.5% of the specimen’s diameter.

Significance

The theory provides a physical and mechanical basis for the C-factor using principles of engineering mechanics. The correction factor it provides allows the linear shrinkage strain of a resin composite to be obtained more accurately from the bonded-disc method.

中文翻译：

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C因子的两侧

客观的

本文的目的是研究在实验室测量中使用的树脂复合材料试样粘结表面对横向约束的收缩应变/应力发展的影响。

方法

使用三维（3D）胡克定律，最近开发的收缩应力理论已扩展到3D，以包括通过泊松比效应在粘结表面受到侧向约束所引起的额外平面外应变/应力。该模型包含一个参数，该参数定义了在此类多轴应力下与粘结表面相邻的边界层的相对厚度。对于不同边界条件下的收缩应力，求解所得的微分方程。通过将数值解与大量实验数据（包括来自收缩应变和收缩应力测量的数据）进行比较，可以评估模型的准确性。

结果

理论和实验之间有很好的一致性。该模型可以正确预测样品的构型因子（C因子）对收缩应力的不同仪器依赖性影响。也就是说，对于非顺应性的应力测量仪器，收缩应力随着圆柱试样的C因子而增加；而对于兼容的仪器则相反。该模型还提供了校正系数，该校正系数是C系数，泊松比和样品边界层厚度的函数，用于使用粘合圆盘法测量的收缩应变。对于所检查的树脂复合材料，边界层的总厚度约为样品直径的11.5％。

意义

该理论使用工程力学原理为C因子提供了物理和机械基础。它提供的校正因子使树脂复合物的线性收缩应变可以通过粘合圆盘法更准确地获得。