To understand the high strain rate deformation mechanism and determine the grain size,strain rate and porosity dependent yield strength of nanocrystalline materials,a new mechanical model based on the deformation mechanism of nanocrystalline materials under high strain rate loading was developed.As a first step of the research,the yield behavior of the nanocrystalline materials under high strain rate loading was mainly concerned in the model and uniform deformation was assumed for simplification.Nanocrystalline materials were treated as composites consisting of grain interior phase and grain boundary phase,and grain interior and grain boundary deformation mechanisms under high strain rate loading were analyzed,then Voigt model was applied to coupling grain boundary constitutive relation with mechanical model for grain interior phase to describe the overall yield mechanical behavior of nanocrystalline materials.The predictions by the developed model on the yield strength of nanocrysatlline materials at high strain rates show good agreements with various experimental data.Further discussion was presented for calculation results and relative experimental observations.
To completely understand the rate-dependent stress-strain behavior of the porous nanocrystalline materials,it is necessary to formulate a constitutive model that can reflect the complicated experimentally observed stress-strain relations of nanocrystalline materials.The nanocrystalline materials consisting grain interior and grain boundary are considered as viscoplastic and porous materials for the reasons that their mechanical deformation is commonly governed by both dislocation glide and diffusion,and pores commonly exist in the nanocrystalline materials.A constitutive law of the unified theory reflecting the stress-strain relations was established and verified by experimental data of bulk nanocrystalline Ni prepared by hydrogen direct current arc plasma evaporation method and hot compression.The effect of the evolution of porosity on stress-strain relations was taken into account to make that the predicted results can keep good agreements with the corresponding experimental results.
To determine the time-independent constitutive modeling for porous and multi- phase nanocrystalline materials and understand the effects of grain size and porosity on their mechanical behavior, each phase was treated as a mixture of grain interior and grain bound- ary, and pores were taken as a single phase, then Budiansky＇s self-consistent method was used to calculate the Young＇s modulus of porous, possible multi-phase, nanocrystalline materials, the prediction being in good agreement with the results in the literature. Further, the established method is extended to simulate the constitutive relations of porous and possible multi-phase nanocrystalline materials with small plastic deformation in conjunction with the secant-moduli approach and iso-strain assumption. Comparisons between the experimental grain size and porosity dependent mechanical data and the corresponding predictions using the established model show that it appears to be capable of describing the time-independent mechanical behaviors for porous and multi-phase nanocrystalline materials in a small plastic strain range. Further discussion on the modification factor, the advantages and limitations of the model developed were present.
As a model bee metal, tantalum and its alloys have wide applications in defense-related fields. The KHL （Khan, Huang, Liang, 1999） model and the constitutive model proposed by Nemat-Nasser et al （Nemat-Nasser and Kapoor, 2001） for tantalum and its alloys were analyzed and compared with each other. A set of published data recorded during elastic-plastic deformations of tantalum, tantalum alloy containing tungsten of 2.5% （Ta-2.5W）, over a wide range of strains, strain rates, and temperatures were used to correlate the two models. Overall, it can be concluded that KHL model correlates much better with the data than the model used by Nemat-Nasser et al.
