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。     

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。     

一种新形式的钢纤维混凝土冲击动态本构关系及材料参数的确定

采用?75 mm大口径SHPB系统进行了钢纤维体积率为0%、0.75%、1.5%三种混凝土材料动态性能实验,得出了不同钢纤维含量、不同应变率下的材料应力-应变关系曲线,实验结果表明:随着纤维含量及应变率的增加,钢纤维混凝土材料的峰值应变、峰值应力都随之提高,并在峰值应力之后出现应力的应变软化现象。以此实验结果为基础,提出了一种依赖于应变和应变率相关函数的新型非线性黏塑性动态本构关系,并通过对实验曲线的三步逐次最小二乘优选模拟,得到了相应的材料参数。结果表明,该本构关系对实验数据的模拟效果较好。     

A micromechanical model of hardening, rate sensitivity and thermal softening in BCC single crystals

The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model, we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cross-slip; and dislocation pair annihilation. The model is found to capture salient features of the behavior of Ta crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.     

Constitutive modelling of the high strain rate behaviour of interstitial-free steel

A physically based modelling and experimental investigation of the work hardening behaviour of IF steel covering a wide range of strain rates including complex strain path and/or strain rate changes are presented. In order to obtain isothermal stress–strain curves at high strain rates, a procedure has been proposed with the aid of finite element analysis. The result reveals that the apparent excess of the flow stress after a jump in strain rate, which is frequently observed in bcc metals, is in fact due to the thermal softening at large strains, and that the flow stress after a jump in strain rate tends asymptotically to the values corresponding to the curve at the new strain rate. The strain rate affects not only the short-range stress but also the long-range stress via the strain-rate dependant evolution of dislocation structures. The proposed model is based on the dislocation model of intragranular hardening proposed by Teodosiu and Hu [Teodosiu, C., Hu, Z., 1995. Evolution of the intragranular microstructure at moderate and large strains: modelling and computational significance. In: Shen, S., Dawson, P. R., (Eds.), Proceedings of Numiform'95 on Simulation of Materials Processing: Theory, Methods and Applications. Balkema, Rotterdam, pp. 173–182] and extended to strain rate sensitive one with applying the results of the thermal activation analysis. A satisfactory agreement has been achieved between model predictions and experimental results.     

Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

Time dependent damage in half-plane part 1: Displacement loading

Analyzed in this study is the time dependent damage of a half-plane subjected to a normal surface displacement over a segment at 0.5 mm/s. The material is made of 4340 steel and dissipates energy in an irreversible manner such that the stress and strain response in each local element can be different and change with time. The inherent coupling between mechanical and thermal effects are accounted for without letting the rate change of volume with surface for the element to vanish. This is in contrast to the assumption made in the classical theories of continuum mechanics.Results obtained from the more refined theory of surface/volume energy density differed qualitatively and quantitatively from those of plasticity. The differences are particularly significant in the vicinity of load application and/or boundary. Stress and strain behavior in the local elements exhibited both hardening and softening behavior while plasticity pre-fixes the monotonic behavior for every element at all times. Uniaxial data are related uniquely to those under multiaxial conditions by invoking the concept of a plane of homogeneity. This is done in general without making the restrictive assumptions in plasticity that the effective stress and effective strain coincide with the uniaxial data. By including the change of local strain rates and strain rate history, local elements are found to undergo cooling and heating during the initial stage of loading. Such non-equilibrium phenomenon has also been observed experimentally in uniaxial and pre-cracked specimens.     

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.     

Dynamic Tensile Characterization of a 4330-V Steel with Kolsky Bar Techniques

Dynamic tensile experimental techniques of high-strength alloys using a Kolsky tension bar implemented with pulse shaping and advanced analytical and diagnostic techniques have been developed. The issues that include minimizing abnormal stress peak, determining strain in specimen gage section, evaluating uniform deformation, as well as developing pulse shaping for constant strain rate and stress equilibrium have been addressed in this study to ensure valid experimental conditions and obtainment of reliable high-rate tensile stress–strain response of alloys with a Kolsky tension bar. The techniques were applied to characterize the tensile stress–strain response of a 4330-V steel at two high strain rates. Comparing these high-rate results with quasi-static data, the strain rate effect on the tensile stress–strain response of the 4330-V steel was determined. The 4330-V steel exhibits slight work-hardening behavior in tension and the tensile flow stress is significantly sensitive to strain rate.     

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.     

Stress–strain behaviour of aluminium alloys at a wide range of strain rates

The stress–strain behaviour of extruded AA6xxx and AA7xxx aluminium alloys in T6 temper was studied at a wide range of strain rates. Tensile tests at low to medium strain rates were performed in a standard tensile test machine, while a split-Hopkinson tension bar was used to carry out tests at high rates of strain. Extruded aluminium alloys have anisotropic mechanical properties, and tests were therefore done in three directions with respect to the extrusion direction. It is found that the AA6xxx alloys exhibit no significant rate sensitivity in the stress–strain behaviour, while moderate rate sensitivity was found for the AA7xxx alloys. There seems to be no significant difference between the rate sensitivity in the three tensile directions. The experimental data were used to identify the parameters of a thermo-viscoplastic constitutive relation for the extruded alloys, which includes the effects of strain hardening, strain-rate hardening, thermal softening and plastic anisotropy.     

Constitutive equations for thermomechanical deformations of glassy polymers

Poly-Carbonate (PC) and Poly-Methyl-Methacrylate (PMMA) are lightweight and mechanically tough transparent glassy polymers. Their mechanical behavior at low to moderate strain rates has been well characterized; however, that at high strain rates needs additional work. We propose two modifications to existing pressure-dependent viscoplastic constitutive equations that enable one to simulate better mechanical deformations of PC and PMMA at high strain rates. First, the elastic moduli are taken to depend upon the current temperature and the current effective strain rate. Second, two internal variables are introduced to better characterize the strain softening of the material at high strain rates. A technique to find values of newly introduced material parameters is described. We compute the local temperature rise due to energy dissipated during plastic deformations. The true axial stress vs. the true axial strain curves in uniaxial compression from numerical simulations of the test configurations at high strain rates using the proposed constitutive equations are found to agree well with the experimental results available in the literature.     

Dynamic limit analysis formulation for impact simulation of structural members

This paper introduces an extended concept of limit analysis to deal with the dynamic equilibrium condition considering the inertia and strain-rate effect for dynamic behavior of structures. The conventional limit analysis method has been applied to only static collapse analysis of structures without consideration of dynamic effects in the structural behavior. A dynamic formulation for the limit analysis has been derived for incremental analysis dealing with time integration, strain and stress evaluation, strain hardening, strain-rate hardening and thermal softening. The time dependent term in the governing equation is integrated with the WBZ-α method. The dynamic material behavior is described by the Johnson–Cook model in order to consider strain-rate hardening and thermal softening as well as strain hardening. Simulations have been carried out for impact analysis of a Taylor bar and an S-rail and their numerical results are compared with elasto-plastic explicit analysis results by LS-DYNA3D. Comparison demonstrates that the dynamic finite element limit analysis can predict the crashworthiness of structural members effectively with less effort and computing time than the commercial code compared. The crashworthiness of a structure with the rate-dependent constitutive model is also compared to that with the quasi-static constitutive relation in order to investigate the dynamic effect on deformation of structures.     

冲击载荷下HTPB推进剂的热耗散

为了研究HTPB推进剂在冲击载荷下的能量耗散规律,结合分离式霍普金森压杆(SHPB)搭建了红外测温系统。该系统响应速度快,可同步获取冲击实验中HTPB推进剂表面的温度变化。结果表明,HTPB推进剂受载后表现出黏-超弹特性,并且在高速变形中试件经历了温度的显著升高。在黏-超弹性本构模型的基础上引入温度项,考虑了热软化效应,更加准确地描述了HTPB推进剂在高应变率变形下的热力学响应,可对复合固体推进剂在冲击载荷下的热力耦合分析提供参考。     

Time dependent damage in half-plane part 2: Traction loading

Transient time dependent stress and strain distribution are obtained for a half-plane made of 4340 steel. A traction load is applied dynamically at a global strain rate of 5·10² s⁻¹. Unlike the classical theory of incremental plasticity, that assumes the same constitutive relation for all elements, the surface/volume energy density theory derives the uniaxial constitutive equation for each element individually according to the local strain rate and strain rate history. Meterial elements are shown to undergo cooling and heating as a result of thermal/mechanical interaction. The equivalent uniaxial response for the traction boundary condition therefore differed from that of the displacement boundary condition considered in Part 1 [1] of this communication. Effective stress and effective strain variations for the local elements next to the applied load exhibited considerable softening after hardening while the plasticity solution increased monotonically. These differences are attributed to the neglect of dilatational and change in local strain rate effects in plasticity in addition to assuming that unloading is parallel to the load path. Damage of the material elements is also discussed in connection with the surface and volume energy density when they reach their respective critical values.     

DYNAMIC MECHANICAL BEHAVIOR OF 6061 AL ALLOY AT ELEVATED TEMPERATURES AND DIFFERENT STRAIN RATES

The compressive stress-strain relationships of 6061Al alloy over wide temperatures and strain rates are investigated. The dynamic impact experiments are performed using an improved high temperature split Hopkinson pressure bar apparatus. The experimental results are compared with those obtained by the modified Johnson-Cook constitutive model. It is found that the dynamic mechanical behavior depends sensitively on temperature under relatively low strain rates or on strain rate at relatively high temperatures. The good agreement indicates that it is valid to adopt the parameter identification method and the constitutive model to describe and predict the mechanical response of materials.     

NEPE推进剂低高应变率下改进的黏-超弹本构模型

为研究低高应变率条件下NEPE推进剂的力学特性,通过电子万能试验机和分离式霍普金森杆装置,对NEPE推进剂进行了准静态和冲击实验,得到了不同应变率下（1.667×10?4～4 500 s?1）的应力-应变曲线。实验结果表明NEPE推进剂具有明显的非线性弹性和应变率敏感性,随着应变率的增加,材料的强度、屈服应力和弹性模量显著增加,与低应变率相比,高应变率条件下材料的应变率敏感性更高。在高速冲击下材料内部瞬间产生大量热量无法及时散发出去,使得材料内部温度升高,导致材料出现软化效应,力学性能降低。本文建立了一个非线性黏超弹本构模型,其中采用Rivlin应变能函数来描述稳态超弹响应部分,采用积分型本构模型来描述材料的动态黏弹性响应部分,考虑到松弛时间具有应变率相关性,本文采用了一个率相关松弛函数来替代传统的Prony级数形式。使用极慢速压缩实验数据对本构模型中的超弹部分进行拟合获得超弹参数,然后用准静态和动态实验数据对本构模型进行拟合得出其他参数。不同应变率下的预测曲线与实验曲线具有较好的重合度,证明了该模型可以很好地描述低高应变率下NEPE推进剂的力学特性。     

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10^?3 and 10⁰/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.     

A constitutive model of cyclic plasticity

This paper addresses a constitutive model of cyclic plasticity with special emphasis on the yield-point phenomena. In order to point out the deformation characteristics of a mild steel, four types of experiments were conducted, i.e. uniaxial tension at several crosshead speeds, cyclic straining, and stress- and strain-controlled ratchetting. A viscoplastic constitutive model of cyclic plasticity is proposed on the premise that the phenomena of sharp yield point and the subsequent abrupt yield drop result from rapid dislocation multiplication and the stress-dependence of dislocation velocity. Besides, cyclic plasticity behavior, such as the Bauschinger effect, cyclic hardening/softening characteristics and ratchet-strain accumulation, is described by some kinematic and isotropic hardening rules. The cyclic stress–strain responses predicted by this model agree well with the corresponding experimental results.     

Cyclic plastic deformation and cyclic hardening/softening behavior in 304LN stainless steel

Low cycle fatigue experiments have been conducted on 304LN stainless steel in ambient air at room temperature. Uniaxial ratcheting behavior has also been studied on this material and in both engineering and true stress controlling modes. It is shown that material’s cyclic hardening/softening behavior in low cycle fatigue and in ratcheting is dependent not only on material but also on the loading condition. Improvement of ratcheting life and mean stress dependent hardening are observed in the presence of mean stress. A method based on the strain energy density (SED) is used to represent cyclic hardening/softening behavior of the material in this work. The decrease of SED with cycles is an indication that the life in low cycle fatigue and in ratcheting is improved. The SED represents the area of the hysteresis loops.