Constitutive modeling for strain rate-dependent behaviors of nanocrystalline materials based on dislocation density evolution and strain gradient

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Articles

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INTRODUCTION

Nanocrystalline (NC) materials, which are single or multiphase polycrystals with grain size ranging from 1 to 100 nm, have received more and more attention over the past two decades, because of their outstanding physical and mechanical properties in comparison with conventional coarse-grain polycrystalline materials.^1-5A good knowledge of NC materials might enable new materials with enhanced properties to be processed, such as ultrahigh yield and fracture strength, superior wear resistance, and enhanced super plastic formability.¹Among the possible amelioration, the increase of flow stress has been intensively studied. As such, these materials have become more and more important in designing lighter and stronger structures. However, it should be noted that the strength increases simultaneously with a decrease of tensile strain.^6,7The limited ductility has been a major obstacle in the development and application of metals. While it was previously attributed to pre-existed flaws, such as impurities and porosities,⁸recent samples of high quality still showed a little ductility in tension tests.^9,10Therefore, the ductility issue remains an important subject of present research.

It has been well established that the macroscopic properties of metallic materials are significantly grain size dependent. Strong grain size effects on the mechanical behaviors of metal material during nonuniform plastic deformation have been investigated by researchers from different countries in various kinds of experiments. For example, the experiment of thin copper (Cu) wires twisting¹¹revealed that the scaled shear increases with the decreasing wire diameter. Subsequently, the experiment of ultrathin beams bending¹²showed that bending hardening increases as the beam thickness decreases and data from simple tension displayed size-independent phenomena. Besides, the increasing experimental phenomena of size-dependence of NC material behavior at the micrometer or nanometer level have been observed in microindentation or nanoindentation tests.^13,14It is accepted¹⁵that the grain size effects are due to the presence of spatial gradients of strain in each single grain. These gradients are associated with the plastic inhomogeneity of slip and are expected to be particularly significant near grain boundaries (GBs).¹⁶

To study the effects of grain size on mechanical behaviors of NC materials, several theoretical and experimental investigations have been conducted. It is evident that...