Prediction of the constitutive equation for uniaxial creep of power-law materials through instrumented indentation testing and modeling

对一种模型材料进行了压痕蠕变试验和有限元模拟，结果表明，采用仪器压痕试验技术可以推导出常规单轴蠕变的本构方程。当压痕压力和压痕蠕变率分别保持Ps和α恒定值时，锥形压痕下区域的等效应力和等效塑性应变轮廓随着压痕位移的增加而扩大，同时保持几何自相似性。这些结果表明，压头尖端周围发生了伪稳态变形。在实际决定压头速度的有限区域内表现出蠕变行为的代表性点被定义为等效应力= Ps/3的位置。当蠕变应力指数为n=3.0时，对应点的等效塑性应变率为α/3.6。从Al-5.3mol% mg固溶合金和mg基双相合金压痕试验结果中提取的应力指数和蠕变活化能与文献报道的拉伸蠕变试验结果非常吻合。此外，〓和〓的值与相同温度下拉伸蠕变试验的施加应力值和相应的蠕变速率值吻合良好。上述结果表明，通过精心设计的压痕蠕变试验，不仅可以获得少量或小体积试样的高级材料的蠕变特性，而且可以通过压痕蠕变试验结果以足够的精度预测拉伸蠕变的本构方程。

Indentation creep tests and finite element simulations were performed on a model material to show that a constitutive equation for conventional uniaxial creep can be derived using the instrumented indentation testing technique. Whenthe indentation pressure and the indentation creep rate maintain constant values of Ps and α, respectively, the contours of the equivalent stress and the equivalent plastic strainrate in the region beneath the conical indenter expand according to the increase in the indenter displacement while maintaining the geometrical self-similarity. These findings indicate that a pseudo-steady state deformation takes place around the indenter tip. The representative points exhibiting the creep behavior within the limited region, which actually determines the indenter velocity,is defined as the location where the equivalentstress 〓 is equal to Ps/3.The equivalent plastic strain rate at the correspondingpoint is found to α/3.6 in the case that the creep stress exponent is n=3.0.The stressexponent and the activation energy for creep extracted from the results of Al-5.3mol%Mgsolid-solution alloy and Mg-based dual phase alloy indentation tests are in close agreementwith those of tensile creep tests reported in the literature. In addition, the values for〓and〓 agree well with the values for the applied stress and the corresponding creep ratein tensile creep tests at the same temperature. The above results show not only that thecreep characteristics of advanced materials, which are often available in minute quantities or as small-volume specimens, can be obtained from carefully designed indentation creep tests, but also that the constitutive equation for tensile creep can be predicted with sufficient precision through indentation creep test results.