Cross-scale indentation scaling relationships of strain gradient plastic solids: Influence of inclusions near the indenter tip应变梯度塑性材料的跨尺度压痕标度律: 压尖附近异构夹杂的影响

The indentation test is a localized testing technique; therefore, the role of the material size-effect and local non-uniformity is of much importance. The influence of the heterogeneity in size-independent materials has been studied previously. The present work detailedly investigated the influence of the material size-effect and heterogeneity (inclusions near the indenter tip) on the indentation hardness using a size-dependent strain gradient plastic theory. And it was found that when considering the material size-effect, shallow hard inclusions in the heterogeneous materials more significantly enhance the material indentation hardness compared with the size-independent materials which are based on the conventional plastic theory. This hardening effect is believed to be related to the elevation of the load and local constraints of large deformation. The effect of material inhomogeneity mainly comes from the non-uniformity of the structure rather than the inclusion modulus itself especially when the size-effect is involved, and the transition range of the inclusion modulus’ influence is pretty narrow. The effect of non-uniformity becomes negligible after the initial inclusion depth is larger than its diameter. The horizontal offset of the indenter from the inclusion is also of much sensitivity to the influence of the heterogeneous indentation. This paper focuses on the scaling relationships in micro- and nanoindentation, the influence of non-uniformity in microscopic materials is studied and supplemented as well.