Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling

The elastic–plastic behaviors of three body-centered cubic metals, tantalum, tantalum alloy with 2.5% tungsten, and AerMet 100 steel, are presented over a wide range of strains (15%), strain rates (10⁻⁶–10⁴ s⁻¹) and temperatures (77–600°F). Johnson-Cook and Zerilli-Armstrong models were found inadequate to describe the observations. A new viscoplastic model is proposed based on these experimental results. The proposed constitutive model gives good correlations with these experimental results and strain-rate jump experiments. In the next paper (Liang, R., Khan A.S., 2000. Behaviors of three BCC metals during non-proportional multi-axial loadings and predictions using a recently proposed model. International Journal of Plasticity, in press), multi-axial loading results on these materials and comparison with the proposed model will be presented.     

5083H111铝合金宽应变率拉伸动态本构模型

结合5083H111铝合金较宽应变率范围2×10-4 ~ 4×102s-1内的拉伸实验数据,揭示该铝合金的拉伸“V”型率效应特征,分析对数应变率敏感系数λ和切线模量Et的应变率和应变相关性,进而通过对Johnson-Cook模型的修正来建立合理描述5083H111铝合金较宽应变率范围内的动态拉伸本构模型。建立的动态本构模型中,流动应力包括应变率相关和应变相关两部分。该模型合理描述了5083H111铝合金的拉伸“V”型率效应特征,预测结果与实验结果较为一致。另外,结合破坏应变的对数应变率敏感系数β,得到了拉伸破坏应变预测方程,其预测结果也与实验结果基本一致。     

Mechanics of very fine-grained nanocrystalline materials with contributions from grain interior, GB zone, and grain-boundary sliding

In this paper, we formulated an atomically-equivalent continuum model to study the viscoplastic behavior of nanocrystalline materials with special reference to the low end of grain size that is typically examined by molecular dynamic (MD) simulations. Based on the morphology disclosed in MD simulations, a two-phase composite model is construed, in which three distinct inelastic deformation mechanisms disclosed from MD simulations are incorporated to build a general micromechanics-based homogenization scheme. These three mechanisms include the dislocation-related plastic flow inside the grain interior, the uncorrelated atomic motions inside the grain-boundary region (the GB zone), and the grain-boundary sliding at the interface between the grain and GB zone. The viscoplastic behavior of the grain interior is modeled by a grain-size dependent unified constitutive equation whereas the GB zone is modeled by a size-independent unified law. The GB sliding at the interface is represented by the Newtonian flow. The development of the rate-dependent, work-hardening homogenization scheme is based on a unified approach starting from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity through replacement of the Maxwell viscosity of the constituent phases by their respective secant viscosity. The developed theory is then applied to examine the grain size- and strain rate-dependent behavior of nanocrystalline Cu over a wide range of grain size. Within the grain-size range from 5.21 to 3.28 nm, and the strain rate range from 2.5 × 10⁸ to 1.0 × 10⁹/s, the calculated results show significant grain-size softening as well as strain-rate hardening that are in quantitative accord with MD simulations [Schiotz, J., Vegge, T., Di Tolla, F.D., Jacobsen, K.W., 1999. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60, 11971–11983]. We have also applied the theory to investigate the flow stress, strain-rate sensitivity, and activation volume over the wider grain size range from 40 nm to as low as 2 nm under these high strain rate loading, and found that the flow stress initially displays a positive slope and then a negative one in the Hall–Petch plot, that the strain-rate sensitivity first increases and then decreases, and that the activation volume first decreases and then increases. This suggests that the maximum strain rate sensitivity and the lowest activation volume do not occur at the smallest grain size but, like the maximum yield strength (or hardness), they occur at a finite grain size. These calculated results also confirm the theoretical prediction of Rodriguez and Armstrong [Rodriguez, P., Armstrong, R.W., 2006. Strength and strain rate sensitivity for hcp and fcc nanopolycrystal metals. Bull. Mater. Sci. 29, 717–720] on the basis of grain boundary weakening and the report of Trelewicz and Schuh [Trelewicz, J.R., Schuh, C.A., 2007. The Hall–Petch breakdown in nanocrystalline metals: a crossover to glass-like deformation. Acta Mater. 55, 5948–5958] on the basis of hardness tests. In general the higher yield strength, higher strain rate sensitivity, and lower activation volume on the positive side of the Hall–Petch plot are associated with the improved yield strength of the grain interior, but the opposite trends displayed on the negative side of the plot are associated with the characteristics of the GB zone which is close to the amorphous state.     

5A06铝合金的动态本构关系实验

运用材料试验机和分离式霍普金森压杆装置(SHPB)对3种不同加工及热处理状态的5A06铝合金在常温~500 C、应变率为10-4~103 s-1 下的力学行为进行了实验研究。基于Johnson-Cook (JC) 本构模型,通过实验数据拟合得到了每种状态下材料的本构模型参量。对Johnson-Cook本构模型中的应变率强化项作了修正,修正后的Johnson-Cook本构模型与实验数据基本吻合,从而确立了3种状态下5A06铝合金的动态本构关系。     

A thermoviscoelastic model for amorphous shape memory polymers: Incorporating structural and stress relaxation

A thermoviscoelastic constitutive model is developed for amorphous shape memory polymers (SMP) based on the hypothesis that structural and stress relaxation are the primary molecular mechanisms of the shape memory effect and its time-dependence. This work represents a new and fundamentally different approach to modeling amorphous SMPs. A principal feature of the constitutive model is the incorporation of the nonlinear Adam–Gibbs model of structural relaxation and a modified Eyring model of viscous flow into a continuum finite–deformation thermoviscoelastic framework. Comparisons with experiments show that the model can reproduce the strain–temperature response, the temperature and strain-rate dependent stress–strain response, and important features of the temperature dependence of the shape memory response. Because the model includes structural relaxation, the shape memory response also exhibits a dependence on the cooling and heating rates.     

Anisotropic responses, constitutive modeling and the effects of strain-rate and temperature on the formability of an aluminum alloy

Finite deformation anisotropic responses of AA5182-O, over a wide range of strain-rates (10⁻⁴ to 10⁰ s⁻¹) and temperatures (293-473 K) are presented. The plastic anisotropy parameters were experimentally determined from tensile experiments using specimens from sheet material. Using the experimental results under plane stress conditions, the anisotropy coefficients for Barlat’s yield function (YLD96) were calculated at different strain-rates and temperatures. The correlations obtained from YLD96 are in good agreement with the observed experimental results. The strain-rate sensitivity of AA5182-O alloy changed from negative at 293 K to positive at 473 K. Khan-Huang-Liang (KHL) constitutive model is shown to correlate the observed strain-rate and temperature dependent responses reasonably well. The material parameters were obtained from the experimental responses along the rolling direction (RD) of the sheet. Marciniak and Kuckzinsky (M-K) theory was used to obtain the theoretical strain and stress-based forming limit curves (FLCs) at different strain-rates and temperatures. The experimental result from the published literature is compared with the FLCs from the current study.     

Deformation behavior of tantalum and a tantalum tungsten alloy

A comparative study of the deformation behavior of tantalum and a tantalum 2.5 wt.% tungsten alloy is carried out. High strain-rate experimental data are used to develop phenomenological constitutive relations. The temperature and the strain-rate sensitivity of the flow stresses are compared. It is observed that although the flow stress for the Ta–2.5%W alloy is greater than that of Ta, the corresponding temperature and strain-rate sensitivity is less pronounced. Ta–2.5%W experiences a solid-solution softening, wherein the athermal stress component has increased, while the thermal component has decreased by the alloying.     

A secant-viscosity composite model for the strain-rate sensitivity of nanocrystalline materials

In order to address the strain-rate sensitivity of nanocrystalline solids, a secant-viscosity composite model is developed in this article. The microgeometry of the composite is taken to consist of the grain-interior phase and the grain-boundary affected zone (GBAZ) as suggested by Schwaiger et al. [Schwaiger, R., Moser, B., Dao, M., Chollacoop, N., Suresh, S., 2003. Some critical experiments on the strain-rate sensitivity of nanocrystalline nickel. Acta Mater. 51, 5159–5172], while the constituent properties are modeled by a unified viscoplastic constitutive law. The drag stress of the grain interior is assumed to follow the Hall–Petch relation, but that of the GBAZ is independent of grain size, d. Then in terms of the secant viscosity of the constituent phases, the strain-rate sensitivity of the nanocrystalline solid is determined with the help of a linear viscous comparison composite and a field-fluctuation approach. To test the applicability of the developed model, it is applied to predict the strain-rate effect of a nanocrystalline Ni, and the grain-size dependence of its stress–strain relations. Our theoretical calculations indicate that the tensile strength of a nanocrystalline Ni with d = 40 nm is about five times that of a microcrystalline one with d = 10 μm under the same strain rate of , and that the nanocrystalline Ni exhibits a much stronger strain-rate effect. These predictions are found to be consistent with the experimental data of Schwaiger et al. Possible grain-size softening with further grain-size reduction such as reported in molecular dynamic simulations is also demonstrated.     

Experimental investigation and modeling of the tension behavior of polycarbonate with temperature effects from low to high strain rates

The effects of strain rate and temperature on the tension stress–strain responses of polycarbonate are experimentally investigated over a wide range of strain rates (0.001–1700 s⁻¹) and temperatures (0–120 °C). A modified split Hopkinson tension bar is used for high-rate uniaxial tension tests. Experimental results indicate that the stress–strain responses of polycarbonate at high strain rates exhibit the nonlinear characteristics including the obvious yielding and strain softening. The tension behavior is strongly dependent on the strain rate and temperature. The values of yield stress and strain at yield present a dramatic increase at higher strain rates and decrease with the increase in temperature. Moreover, there exists a significant rate-sensitivity transition in the polycarbonate tension yield behavior. Based on the experimental investigation, a physically based three-dimensional elastoplastic constitutive model for the finite deformation of glassy polymers is used to characterize the rate-temperature dependent yield and post-yield behavior of polycarbonate when subjected to tension loading. The model results are shown close to the experimental data within the investigated strain-rate and temperature ranges.     

DH36钢拉伸塑性流动特性及本构关系

对DH36钢在温度从293~800 K、应变率为0.001和0.1 s-1的拉伸塑性流动特性进行实验研究,通过端口形貌图对变形前后的试样进行了微观分析,结果表明:(1)在实验温度范围内,0.001和0.1 s-1的应变率下,第三型应变时效现象出现,随应变率的增加,时效发生的温度区域移向更高温度;(2)第三型应变时效的发生与合金原子在晶界和晶粒中大量的第二相析出强化有关联;(3)建立包含第三型应变时效现象的统一本构模型,通过比较该模型能够较好的预测DH36的塑性拉伸流动应力。