A Phenomenological Constitutive Model for Describing Thermo-Viscoplastic Behavior of Al-Zn-Mg-Cu Alloy Under Hot Working Condition

In order to predict the high-temperature deformation behavior of Al-Zn-Mg-Cu alloy, the hot compression tests were conducted in the strain rate range of (0.001–0.1)s⁻¹ and the forming temperature range of (573–723) K. Based on the experimental results, Johnson-Cook model was found inadequate to describe the high-temperature deformation behavior of Al-Zn-Mg-Cu alloy. Therefore, a new phenomenological constitutive model is proposed, considering the coupled effects of strain, strain rate and forming temperature on the material flow behavior of Al-Zn-Mg-Cu alloy. In the proposed model, the material constants are presented as functions of strain rate. The proposed constitutive model correlates well with the experimental results confirming that the proposed model can give an accurate and precise estimate of flow stress for the Al-Zn-Mg-Cu alloy investigated in this study.     

Mechanically alloyed nanocrystalline iron and copper mixture: behavior and constitutive modeling over a wide range of strain rates

A comprehensive study on the response of a nanocrystalline iron and copper mixture (80% Fe and 20% Cu) to quasi-static and dynamic loading is performed. The constitutive model developed earlier by Khan, Huang & Liang (KHL) is extended to include the responses of nanocrystalline metallic materials. The strain rate and grain size dependent behaviors of porous nanocrystalline iron-copper mixture were determined experimentally for both static and dynamic loading. A viscoplastic model is formulated by associating the modified KHL model (representing the fully dense matrix behavior), and Gurson's plastic potential which provides the yield criteria for porous material. Simulations of uniaxial compressive deformations of iron-copper mixture with different initial porosity, grain size and at a wide range of strain rate (10⁻⁴ to 10³ s⁻¹) are made. The numerical results correlate well with the experimental observations.     

Pressure-shear waves in 6061-T6 aluminum and alpha-titanium

Thepressure-shear plate impact technique is used to study material behavior at high rates of deformation. In this technique, plastic waves of combined pressure and shear stresses are produced by impact of parallel plates skewed relative to their direction of approach. Commercially pure alpha-titanium and 6061-T6 aluminum are tested under a variety of pressure and shear tractions by using different combinations of impact velocities and angles of inclination. A laser interferometer system is used to monitor simultaneously the normal and transverse components of motion of a point at the rear surface of the target plate. The experimental results are compared with numerical solutions based on an elastic/viscoplastic model of the material. Both isotropic and kinematic strain hardening models are used in the computations. The results indicate that unlike the normal velocity profiles, the transverse velocity profiles are sensitive to the dynamic plastic response and, thus, can be used to study material behavior at high strain rates. For the materials tested the results suggest that the flow stress required for plastic straining increases markedly with increasing strain rate at strain rates above 10⁴s^?1. Hydrostatic pressure of the order that exists in the tests (up to 2 GPa) does not affect the plastic flow in 6061-T6 aluminum and appears to have at most a minor effect on the deformation of the titanium.     

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.     

Artificial neural network prediction to the hot compressive deformation behavior of Al–Cu–Mg–Ag heat-resistant aluminum alloy

The behavior of the flow stress of Al-Cu-Mg-Ag heat-resistant aluminum alloys during hot compression deformation was studied by thermal simulation test. The temperature and the strain rate during hot compression were 340-500 °C, 0.001 s⁻¹ to 10 s⁻¹, respectively. Constitutive equations and an artificial neural network (ANN) model were developed for the analysis and simulation of the flow behavior of the Al-Cu-Mg-Ag alloys. The inputs of the model are temperature, strain rate and strain. The output of the model is the flow stress. Comparison between constitutive equations and ANN results shows that ANN model has a better prediction power than the constitutive equations.     

高氮奥氏体不锈钢高温动态响应特性及本构关系

在293~873 K的环境下,采用分离式霍普金森杆装置对高氮钢试样进行了102~103 s-1应变率下的动态加载实验。结合准静态实验结果,分析了应变率和温度对材料塑性流动特性的影响。结果表明:高氮钢的动态力学行为具有很强的应变率敏感性和温度敏感性。当应变率达到400 s-1或更高时,流动应力随应变率的增加显著升高;在同一应变率下,流动应力随温度的降低明显升高。研究了温度和应变率耦合效应对材料塑性行为的影响,得出温度软化效应在高氮钢高温动态塑性变形中起主导作用。基于经典的Johnson-Cook（J-C）模型,通过对实验数据的分析,得出了高氮钢材料的修正J-C本构方程,经验证修正J-C方程预测结果与实验结果吻合。     

微纳米晶金属的应变率敏感性及应变硬化行为分析

基于亚微米、纳米晶粒组织塑性变形过程中多种变形机制(位错机制、扩散机制及晶界滑动机制)共存,建立了理论模型,用于定量研究亚微米、纳米晶粒组织的塑性变形行为.以铜为模型材料,计算分析了晶粒尺度、应变率以及温度对亚微米、纳米晶粒组织塑性变形行为的影响.结果表明:相比粗晶铜,亚微米晶铜表现出明显的应变率敏感性,并且应变率敏感系数随晶粒尺度及变形速率的减小而增大;同时,增大变形速率或降低变形温度都能提高材料的应变硬化能力,延缓颈缩发生,进而提高材料的延性.计算分析结果与实验报道吻合.     

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Previous investigations on the effects of strain-rate and temperature histories on the mechanical behavior of steel are briefly reviewed. A study is presented on the influence of strain rate and strain-rate history on the shear behavior of a mild steel, over a wide range of temperature Experiments were performed on thin-walled tubular specimens of short gage length, using a torsional split-Hopkinson-bar apparatus adapted to permit quasi-static as well as dynamic straining at different temperatures. The constant-rate behavior was first measured at nominal strain rates of 10^?3 and 10³ s^?1 for ?150, ?100, ?50, 20, 200 and 400°C. Tests were then carried out, at the same temperatures, in which the strain rate was suddenly increased during deformation from the lower to the higher rate at various large values of plastic strain. The increase in rate occurred in a time of the order of 20 μs so that relatively little change of strain took place during the jump. The low strain-rate results show a well-defined elastic limit but no yield drop, a small yield plateau is found at room temperature. The subsequent strain hardening shows a maximum at 200°C, when serrated flow occurs and the ductility is reduced. The high strain-rate results show a considerable drop of stress at yield. The post-yield flow stress decreases steadily with increasing temperature, throughout the temperature range investigated. At room temperature and below, the strain-hardening rate becomes negative at large strains. The adiabatic temperature rise in the dynamic tests was computed on the assumption that the plastic work is entirely converted to heat. This enabled the isothermal dynamic stress-strain curves to be calculated, and showed that considerable thermal softening took place. The initial response to a strain-rate jump is approximately elastic, and has a magnitude which increases with decrease of testing temperature; it is little affected by the amount of prestrain. At 200 and 400° C, a yield drop occurs after the initial stress increment. The post-jump flow stress is always greater than that for the same strain in a constant-rate dynamic test, the strain-hardening rate becoming negative at large strains or low testing temperature. This observed effect of strain-rate history cannot be explained by the thermal softening accompanying dynamic deformation. These and other results concerning total ductility under various strain-rate and temperature conditions show that strain-rate history strongly affects the mechanical behavior of the mild steel tested and, hence, should be taken into account in the formulation of constitutive equations for that material.     

Relationship between Local Strain Jumps and Temperature Bursts Due to the Portevin-Le Chatelier Effect in an Al-Mg Alloy

Local strain and temperature of an AA5754-O aluminum alloy sheet have been full-field measured during monotonous tensile tests carried out at room temperature. Sharp strain increases and temperature bursts which are locally generated by the Portevin-Le Chatelier phenomenon have been measured at the same point for two strain rates: V2?=?1.9?×?10^?3?s^?1 and V10?=?9.7?×?10^?3?s^?1. A relationship, which is based on the underlying physical mechanisms, has been established between the strain and the temperature and experimentally verified for the highest strain rate V10. The discrepancy between the theoretical and experimental results for the lowest strain rate V2 suggests that the localized plastic deformations do not follow an adiabatic transformation. Such a set-up seems to offer a direct and experimental method to check the adiabatic character of localized plastic deformations.     

Finite deformation of a polymer: experiments and modeling

The response of a polymer (polytetrafluoroethylene) to quasi-static and dynamic loading is determined and modeled. The polytetrafluoroethylene is extremely ductile and highly nonlinear in elastic as well as plastic behaviors including elastic unloading. Constitutive model developed earlier by Khan, Huang and Liang (KHL) is extended to include the responses of polymeric materials. The strain rate hardening, creep, and relaxation behaviors of polytetrafluoroethylene were determined through extensive experimental study. Based on the observation that both viscoelastic and viscoplastic deformation of polytetrafluoroethylene are time dependent and nonlinear, a phenomenalogical viscoelasto–plastic constitutive model is presented by a series connection of a viscoelastic deformation module (represented by three elements standard solid spring dashpot model), and a viscoplastic deformation module represented by KHL model. The KHL module is affected only when the stress exceeds the initial yield stress. The comparison between the predictions from the extended model and experimental data for uniaxial static and dynamic compression, creep and relaxation demonstrate that the proposed constitutive model is able to represent the observed time dependent mechanical behavior of polytetrafluoroethylene polytetrafluoroethylene qualitatively and quantitatively.     

Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of bcc and fcc mechanisms of metals

Combination of physically based constitutive models for body centered cubic (bcc) and face centered cubic (fcc) metals developed recently by the authors [Voyiadjis, G.Z., Abed, F.H., 2005. Microstructural based models for bcc and fcc metals with temperature and strain rate dependency. Mech. Mater. 37, 355–378] are used in modeling the plastic deformation of AL-6XN stainless steel over a wide range of strain rates between 0.001 and 8300 s⁻¹ at temperatures from 77 to 1000 K. The concept of thermal activation analysis as well as the dislocation interaction mechanism is used in developing the plastic flow model for both the isothermal and adiabatic plastic deformation. In addition, the experimental observations of AL-6XN conducted by Nemat-Nasser et al. [Nemat-Nasser, S., Guo, W., Kihl, D., 2001. Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures, J. Mech. Phys. Solids 49, 1823–1846] are utilized in understanding the underlying deformation mechanisms. The plastic flow is considered in the range of temperatures and strain rates where diffusion and creep are not dominant, i.e., the plastic deformation is attributed to the motion of dislocations only. The modeling of the true stress–true strain curves for AL-6XN stainless steel is achieved using the classical secant modulus for the case of unidirectional deformation. The model parameters are obtained using the experimental results of three strain rates (0.001, 0.1, and 3500 s⁻¹). Good agreement is obtained between the experimental results and the model predictions. Moreover, the independency of the present model to the experiments used in the modeling is verified by comparing the theoretical results to an independent set of experimental data at the strain rate of 8300 s⁻¹ and various initial temperatures. Good correlation is observed between the model predictions and the experimental observations.     

Grain size,strain rate,and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: Synthesis,experiment, and constitutive modeling

For the first time, high quality bulk nanocrystalline (nc) fcc metals, with least amounts of imperfections, exhibiting high strength and ductility at room and different temperatures, under quasi-static and dynamic types of loading, were prepared and a comprehensive study on their post-yield mechanical properties was performed. This investigation included study of the effect of temperature on stress–strain responses of mechanically milled bulk nc Cu and Al. The samples after preparation through mechanical milling and consolidation processes were subjected to uniaxial compressive loading at quasi-static and dynamic strain rates of 10⁻² s⁻¹ and 1840–3105 s⁻¹, respectively, at temperatures ranging from 223 to 523 K. In both materials strong dependency of flow stress to temperature was observed; this dependency was rather more pronounced when the materials were tested at the quasi-static strain rate. Further, a new grain size and temperature dependent viscoplastic phenomenological constitutive equation, Khan–Liang–Farrokh (KLF) model was developed based on the Khan–Huang–Liang (KHL) constitutive equation. The model was featured to correlate different characteristic behaviors of polycrystalline materials in the plastic regime, as the result of grain refinement. In addition, the viscoplastic responses of bulk Cu and Al of different grain sizes (from sub-micron to nanometer range), and those from bulk nc Cu and Al at different strain rates (quasi-static to dynamic), recently published (21 and 22), were simulated using the newly developed equation. The results confirmed reasonable capability of the developed model to correlate a wide spectrum of the viscoplastic responses of these fcc metals.     

304不锈钢室温和高温单轴循环塑性的实验研究

对304不锈钢进行了室温和高温单轴应变控制和应力控制下的系统循环试验。揭示和分析了循环应变幅值、平均应变及其历史和温度历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史以及温度对循环棘轮行为的影响。也讨论了应变循环和应力循环间交互作用对材料循环塑性行为的影响。研究表明,无益单轴应变循环特性还是非对称单轴应力循环下的棘轮效应不仅取决于当前温度和加载状态,而且强烈依赖于其加载历史。研究得到了一些有助于304不锈钢室温和高温单轴循环行为本构描述的结果。     

Constitutive relation of viscoelastic dielectric elastomer

In this paper, we present a modified model describing the constitutive relation of viscoelastic dielectric elastomer (DE). The uniform uniaxial tension-recovery experiment was carried out at different stretching rates. Based on Yeoh hyper-elastic model, model-fitting approach is put forward to obtain the relationship between parameters of Yeoh model and stretching rate, thus the modified model was obtained. From the approximate relationship between harmonic motion and uniform reciprocating motion, the stress–strain curve in the recovery process was also identified through the hysteresis between stress and strain. The modified model, with concise form and evident physical concept, can describe the strong nonlinear behavior between deformation and mechanical stress of the material in a common stretching rate range (from 0.01s^?1 to 0.8s^?1 at least). The accuracy and reliability of the modified model was examined.     

超高强度钢AF1410塑性流动特性及其本构关系

在本文中,为揭示超高强度钢AF1410的塑性流动性,并研究其塑性流动本构关系,利用CSS4410电子万能试验机和改进的Hopkinson拉压杆技术,对AF1410钢在温度从100K到600K,应变率从0.001/s到2000/s,塑性应变超过20%的塑性流动特性进行了试验研究。结果表明,拉伸加载下AF1410钢屈服强度低于压缩屈服强度,且随应变率增加,拉压屈服强度差值越来越大;该材料塑性流动应力对应变率敏感性低,而对温度较为敏感;随应变率的提高,该材料拉伸失效应变减小,但温度对失效应变无明显影响。最后基于位错的运动学关系,借助试验数据,获得了AF1410钢的塑性流动物理概念本构模型,并通过与经典J-C模型的结果对比对该物理概念本构模型进行了评估分析,表明该物理概念本构模型在较宽温度和应变率范围能较好的预测AF1410钢的塑性流动应力。     

不锈钢材料的动态力学性能及本构模型

利用带有温度调控系统的SHPB实验装置测定了0Cr17Mn5Ni4Mo3Al不锈钢在3种应变率(300、1 000、2 700 s-1)、4种环境温度（25、300、500和700 ℃）下的应力应变关系;在液压伺服材料试验机(MTS)上进行了3种温度下的准静态（0.0005 s-1）压缩实验。实验结果表明:该不锈钢有明显的应变率强化效应和温度软化效应,并且随着环境温度的升高,应变率强化效应减弱。对Johnson-Cook模型进行了修正,考虑了冲击过程中绝热温升引起的软化效应。修正后的Johnson-Cook模型与实验结果吻合较好。     

Flow stress behavior of porous FVS0812 aluminum alloy during hot-compression

The hot deformation behavior of porous FVS0812 aluminum alloy prepared by spray deposition was studied by means of compression tests on a Gleeble 1500 machine. The samples were hot compressed at temperatures ranging from 573 K to 773 K under various true strain rates of 10⁻⁴–10⁰ s⁻¹. The deformation behaviors are characterized by a significant strain hardening during hot-compression due to the progressive compaction of the pores with increasing compressive strain. A revised formula describing the relationships of the flow stress, strain rate and temperature of the porous alloy at elevated temperatures is proposed by compensation of strain. The theoretical predictions are compared with experimental results, which show good agreement.     

An experimental and numerical study of the localization behavior of tantalum and stainless steel

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic–plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material’s local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length is 870–890 μm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8–25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 × 10⁴ s⁻¹ in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the shear section. The numerical results for stainless steel suggest that melting temperature was reached throughout the shear band shortly after peak load. Due to sample geometry, the stress state in the shear zone was not pure shear; a significant normal stress relative to the shear zone basis line was developed.     

Finite element micromechanics model of impact compression of closed-cell polymer foams

Finite element analysis, of regular Kelvin foam models with all the material in uniform-thickness faces, was used to predict the compressive impact response of low-density closed-cell polyethylene and polystyrene foams. Cell air compression was analysed, treating cells as surface-based fluid cavities. For a typical 1 mm cell size and 50 s^?1 impact strain rate, the elastic buckling of cell faces, and pop-in shape inversion of some buckled square faces, caused a non-linear stress strain response before yield. Pairs of plastic hinges formed across hexagonal faces, then yield occurred when trios of faces concertinaed. The predicted compressive yield stresses were close to experimental data, for a range of foam densities. Air compression was the hardening mechanism for engineering strains <0.6, with face-to-face contact also contributing for strains >0.7. Predictions of lateral expansion and residual strains after impact were reasonable. There were no significant changes in the predicted behavior at a compressive strain rate of 500 s^?1.     

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。