Mechanical behavior of Gamma-Met PX under uniaxial loading at elevated temperatures and high strain rates

Gamma titanium aluminides have received considerable attention over the last decade. These alloys are known to have low density, good high temperature strength retention and good oxidation and corrosion resistance. However, poor ductility and low fracture toughness have been the key limiting factors in the full utilization of these alloys. More recently, a new generation of gamma titanium aluminide alloys, commonly referred to as Gamma-Met PX, has been developed by GKSS, Germany. These alloys have been observed to have superior strength and better oxidation resistance at elevated temperatures when compared with conventional gamma titanium aluminides.The present paper discusses results of a study to understand the uniaxial mechanical behavior in both compression and tension of Gamma-Met PX at elevated temperatures and high strain rates. The compression and tensile tests are conducted using a modified Split-Hopkinson Bar apparatus at test temperatures ranging from room temperature to 900 °C and strain rates of up to 3500 s⁻¹. Under uniaxial compression, in the temperature range from room to 600 °C, the flow stress is observed to be nearly independent of test temperature. However, at temperatures higher than 600 °C thermal softening is observed at all strain rates with the rate of thermal softening increasing dramatically between 800 and 900 °C. The room temperature tensile tests show negligible strain-rate dependence on both yield stress and flow stress. With an increase in test temperature from room to 900 °C, the material shows a drop in both yield and flow stress at all levels of plastic strain. However, the measured flow stress is still higher when compared to nickel based super-alloys and other gamma titanium aluminides under similar test conditions. Also, no anomaly in yield stress is observed up to 900 °C.     

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.     

一种改进的金属材料的高温动态拉伸实验技术

在旋转盘冲击拉伸实验装置上,利用金属材料自身的导电特性,对试样施加电流.使其在电流作用下发热,实现自加热,形成了试件快速加热而波导杆温升很小的金属材料的动态高温高应变率拉伸实验技术.应用该实验技术获取了45 #钢从室温到1000℃温度范围和应变率650s-1时的材料动态拉伸应力—应变曲线.实验结果表明,45 #钢具有明显的热软化效应,其流动应力和屈服应力随温度的升高而降低.     

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。     

Inelastic stress-responses of an aluminium alloy in non-proportional deformations at elevated temperature

Some characteristics of strain-induced anisotropy and effects of strain-rate on them are experimentally investigated under non-proportional loadings at elevated temperature. By applying combined loadings of axial force and internal pressure to thin-walled tubes of an aluminium alloy at 200°C, inelastic stress-responses are observed at several constant strain-rates along bilinear strain trajectories. It is found that a softening of material and a non-coaxiality between stress and inelastic strain-increment deviators occur after the corner of bilinear strain trajectory. These phenomena appear more markedly and then decay more gradually with the increase of corner angle and/or strain-rate. Experimental results are qualitatively discussed in terms of the activation of piled-up dislocations as well as the so-called back stress and drag stress.     

Ratchetting of viscoplastic material with cyclic softening,part 1: experiments on modified 9Cr–1Mo steel

Uniaxial and multiaxial ratchetting tests were conducted at temperatures between 200 and 600 °C on modified 9Cr–1Mo steel, which exhibits both viscoplastic and cyclic softening behavior. Anomalous behavior was observed in the stress-controlled uniaxial ratchetting tests; the material exhibited outstanding ratchetting in the tensile direction under zero mean stress. Under the uniaxial conditions, the ratchetting deformation significantly depended on the loading rate and hold time in addition to parameters such as the maximum stress and stress ratio. The uniaxial ratchetting was also accelerated to a great extent when cyclic deformation was given before the ratchetting tests. Under the multiaxial conditions, the ratchetting depended on the steady stress, cyclic strain range and strain rate. The ratchetting progressed faster as the steady stress or strain range became larger, or the strain rate became smaller, as expected. Monotonic compression tests were carried out to investigate the reason for the rachetting under no mean stress. Strain range change tests were also conducted to investigate the effect of strain range on the cyclic softening behavior of the material in detail.     

Ductility of interstitial-free steel under high strain rate tension: Experiments and macroscopic modeling with a physically-based consideration

In this paper, an experimental investigation and a constitutive modeling of the mechanical response of an interstitial-free (IF) steel over a wide range of strain rates (from 0.001/s to 750/s) are presented. Tensile tests at relatively high strain rates, exceeding 100/s, are performed at an initial room temperature, using the so-called one bar technique developed on the basis of the Hopkinson bar method. At a high strain rate, a distinct upper yield limit is observed, and the subsequent flow stress increases remarkably. Furthermore, the ductility is reduced significantly in comparison to the case of low strain rate tension. In order to express such a complicated material response of IF steel, we develop a new constitutive model that takes into account effects of a change in the mobile dislocation density and thermal softening. The model can be easily applicable to large-scale engineering computations, because it is macroscopically formulated. We try to reproduce the tensile response including a diffuse neck formation at high strain rates, using the proposed constitutive model and finite element method. The results indicate that a change in the mobile dislocation density, together with thermal softening, has substantial effects on apparent work hardening behavior at high strain rates, although the change in the mobile dislocation density is transcribed at macroscopic scale in the model. Finally, we discuss characteristics of true stress–true strain curves at various strain rates, and their correlation with the plastic instability behavior.     

Brittle fracture of precompressed steel as affected by hydrostatic pressure,temperature and strain concentration

Highly precompressed 1020 HR steel, 0.65 prestrain at 400°F (204°C), tested in nominally uniform tension at ?80°F (?62°C) fractures at about 110,000 psi (760 MN/m²) with less than 0.02 plastic strain. Yet the addition of a hydrostatic pressure of less than 7000 psi (48 MN/m²) converts this visually brittle fracture to a ductile one with appreciable necking. The explanation of this surprising experimental result is shown to follow directly and simply from the combination of a tensile stress criterion of fracture, strain concentration and the low tangent modulus of the stress-strain curve in tension beyond the Bauschinger transition region of a few percent of plastic strain. Temperature dependence and strain-rate dependence of brittle fracture similarly are predictable in an almost trivial manner from the appropriate stress-strain curves for different amounts of precompression. So also is the amazingly high ductility or fracture toughness of the most complex of perforated or notched statically loaded structures of mild steel in an undamaged or fully annealed state.     

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.     

Influence of Molecular Conformation on the Constitutive Response of Polyethylene: A Comparison of HDPE, UHMWPE, and PEX

The current work presents the characterization and comparison of the mechanical response of three different industrial forms of polyethylene. Specifically, high-density polyethylene (HDPE), ultra high molecular weight polyethylene (UHMWPE), and cross-linked polyethylene (PEX) were tested in compression as a function of temperature (−75 to 100°C) and strain-rate (10⁻⁴ to 2,600 s⁻¹). The responses of UHMWPE and PEX are very similar, whereas HDPE exhibits some differences. The HDPE samples display a significantly higher yield stress followed by a flat flow behavior. Conversely UHMWPE and PEX both exhibit significant strain hardening after yield. The temperature and strain-rate dependence are captured by simple linear and logarithmic fits over the full range of conditions investigated. The yield behavior is presented in terms of an empirical mapping function that is extended to analytically solve for the mapping constant. The power-law dependence on strain-rate observed in some polymers is explained using this mapping function.     

A numerical study on the rate sensitivity of cellular metals

Metallic foams have non-linear deformation behavior, which make them attractive in many applications. Many experimental researches on the dynamic behavior and rate sensitivity of cellular metals have been reported in the literature, but they contain conflicting, and sometimes confusing, conclusions on the strain-rate and inertia effect of cellular metals. In this paper, the dynamic crushing behavior of 2D Voronoi honeycomb is studied by finite element method. The influences of inertia, strain hardening and strain-rate hardening of metal matrix on the deformation mode and plateau stress of the honeycomb are investigated. Three deformation modes are found in different velocity ranges. According to the numerical results, it is found that the plateau stress increases significantly with the increase of impact velocity due to non-uniform deformation induced by inertia. The strain-hardening effect is slight in our numerical tests and the rate effect of the honeycomb is obviously weaker than that of the cell wall material.     

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.     

高强混凝土动态压缩试验分析

准确测量混凝土动态压缩性能及其应变率强化效应一直是冲击动力学研究领域的重点和难点之一。针对混凝土大口径SHPB实验，分析探讨了其中几个主要问题:应力均匀性问题、恒应变率问题和端面接触问题。研究表明:对于此次试验中混凝土试件而言，应力均匀性假设限制试验最大应变率小于166 s?1；杆和试件端面接触不平和接触不良使得测算出的杨氏模量和屈服强度明显小于实际值；在此基础上，给出了五步测试法和预应力法；利用复合整形技术实现了近似恒应变率加载。利用以上所发展和改进的技术得到了C110混凝土动静态应力应变曲线，结果显示，在试验范围内混凝土杨氏模量并没有应变率效应，其单轴压缩屈服强度与应变率对数呈线性正比关系，其唯象应变率强化因子为0.10。理论分析表明，大口径SHPB试验所得混凝土应变率效应是一种唯象效应，对于混凝土类压力敏感屈服材料而言，应该根据其屈服面方程对其进行校正，从而得到其本构方程中材料的应变率强化因子，分别利用Tresca屈服准则和K&C本构中屈服面方程对其进行校正，得到C110材料的真实应变率强化因子分别为0.015和0.038。     

Dynamic pre-strain and inertia effects on the fracture of metals

A combined experimental and theoretical study is described which examines the influence of strain-rate and dynamic pre-strain on the ductile fracture of thin cylinders. The thin-cylinder configuration is particularly important in this case because it allows inertia terms to be directly incorporated into the theory of plastic instability. A series of quasi-static and dynamic tests is conducted on three materials with differing degrees of strain-rate sensitivity and strain-hardening. The experimental observation that fracture is inhibited at high strain-rates is in accord with the theory when inertia can no longer be considered insignificant. It is also shown that dynamic pre-strain has little or no effect on the flow stress or the strain at fracture in materials which-are essentially strain-rate insensitive, but does reduce the fracture strain in the strain-rate sensitive materials.     

PLASTIC BEHAVIOR AND CONSTITUTIVE MODELING OF ARMOR STEEL OVER WIDE TEMPERATURE AND STRAIN RATE RANGES

Plastic behavior of 603 armor steel is studied at strain rates ranging from 0.001 s-1 to 4500 s-1 , and temperature from 288 K to 873 K. Emphasis is placed on the effects of temperature, strain rate, and plastic strain on flow stress. Based on experimental results, the JC and the KHL models are used to simulate flow stress of this material. By comparing the model prediction and the experimental results of strain rate jump tests, the KHL model is shown to have a better prediction of plastic behavior under complex loading conditions for this material, especially in the dynamic region.     

High-rate decremental-strain-rate test

A modified torsional split-Hopkinson bar is intoduced and used to study material response associated with a sudden reduction of stain rate during high-rate plastic deformation. In tests on 1100-0 aluminum iniial deformation at a strain rate of approximately 2400 s⁻¹ is reduced by a factor of 15 after 200 μs of high-rate deformation. After the reduction, the deformation continues at the low rate for additional 550 μs. The change in the strain rate is obtained by using a stepped input bar. The results for 1100-0 aluminum show a decrease in the flow stress following the reduction in the strain rate. A short delay exists between the beginning of the strain-rate reduction and the response of the stress. The magnitude of the drop in the stress agrees with the difference in flow stress expected in constant-strain-rate tests in the corresponding high- and low-strain rates. Following the stress reduction. The stress remains essentially constant with no hardening during the subsequent deformation at the low rate.     

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.     

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。     

Time-dependent ratchetting experiments of SS304 stainless steel

The time-dependent strain cyclic characteristics and ratchetting behaviours of SS304 stainless steel were investigated by uniaxial/multiaxial cyclic loading tests at room and elevated temperatures (350 and 700 °C). The effects of loading rate, peak/valley strain or stress holds, ambient temperature and non-proportional loading path on the cyclic softening/hardening and ratchetting behaviours of the material were discussed. It is shown that: the cyclic deformation of the material presents remarkable time-dependence at room temperature and 700 °C; the cyclic hardening feature and ratchetting strain depend significantly on straining or stressing rate, hold-time, ambient temperature and the non-proportionality of loading path; the time-dependent ratchetting is resulted from the slight opening of hysteresis loop and visco-plasticity together, and the viscosity is a dominating factor at 700 °C; at 350 °C, abnormal rate-dependence and quick shakedown of ratchetting are observed due to the dynamic strain aging of the material at this temperature. Some significant conclusions are obtained, which are useful to construct a constitutive model to describe the time-dependent ratchetting behaviour of the material. It is also stated that the unified visco-plastic constitutive model discussed here cannot provide reasonable simulation to the time-dependent ratchetting at 700 °C, especially to that with certain peak/valley stress hold, since the effect of the high viscosity on time-dependent ratchetting cannot be properly described by using a unified visco-plastic flow rule.