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Indentation tests have been used to measuring the strength and hardness of materials. Moreover, micro and nanoindentation have become major tools for investigating the micromechanical properties of small scale volumes. However, it is well-known that the micro and nanoindentation hardness of materials shows the strong size effect. But the classical continuum plasticity can’t predict these size effects in micro/nano scale, since the constitutive equation of the classical mechanics doesn’t include the internal length as a parameter for the deformation. In this paper, modified strain gradient theory is proposed based on the nonhomogeneity of polycrystalline metallic materials. When the grains of crystalline metals deform, overlaps and voids appear at the grain boundary. These overlaps and voids can be corrected by the GNDs. By taking into account the nonhomogeneity of polycrystalline materials, the density of the GNDs due to the deformation is calculated. Consideration of the GNDs on the grain boundary gives a relationship between the size effect and the hardness. This relationship can explain the indentation size effects in micro/nano scale. Using the proposed model, analysis of the effect of indent size and grain size under the nanoindentation test of polycrystalline materials is
carried out.
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