The effect of time-dependent twinning on low temperature (<0.25 ∗ Tm) creep of an alpha-titanium alloy

The low-temperature (less than one-fourth of the melting temperature) creep deformation behavior of hexagonally close-packed (HCP) α-Ti–1.6 wt.% V was investigated. Creep tests were performed at various temperatures between room temperature and 205 °C at 95% of the respective yield stress at the different temperatures. The creep strain rate was found to increase with increasing temperature. Scanning and transmission electron microscopy revealed that slip and unusually slow twin growth, or time-dependent twinning, are active deformation mechanisms for the entire temperature range of this investigation. The activation energy for creep of this alloy was calculated to identify the rate-controlling deformation mechanism, and was found to increase with increasing creep strain. At low strain, the activation energy for creep was found to be close to the previously calculated activation energy for slip. At high strain, the calculated activation energy indicates that both slip and twinning are significant deformation mechanisms. The appearance of twinning at high strains is explained by a model for twin nucleation by dislocation pileups.     

A combined isotropic-kinematic hardening model for the simulation of warm forming and subsequent loading at room temperature

A coupled isotropic-kinematic hardening material model was developed based on phenomenological observations of performed two stage experiments on a medium carbon steel – SAE 1144, where the first deformation is performed at elevated temperatures and the second deformation at room temperature. Above all, deformations with orthogonal loading at various temperatures were investigated in order to determine the influence of the loading direction as well as of the temperature. Bergström’s theory of work hardening as well as the nonlinear kinematic hardening of an Armstrong–Frederick type were used as a basis for the model development. In the proposed model a relationship between material coefficients of the classical Bergström model and temperature was investigated. The aim of the new material model was to introduce the least possible amount of new parameters as well as to facilitate the mathematical determination of parameters during the fitting of the model with experimental data. The developed model was implemented in an in-house FE-Code in order to simulate the material behavior due to the dynamic strain aging and the hardening behavior after the dynamic strain aging process. Representative simulation results were compared with the experimental data in order to validate the efficiency and the application range of the model.     

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。     

Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers

The inelastic deformation behaviors of metals and polymers are discussed with the aim of finding a common base that would simplify academic and engineering analyses. Only monotonic loading conditions at room temperature are considered. For loading at different rates, nonlinear relations between loading rate and stress level, creep stress level and creep strain, and relaxation rate and stress were common to both type of materials. There are, of course, significant differences in elastic properties, strength levels and the strains involved. Special properties such as relaxation behaviors and creep anomalies can be qualitatively and quantitatively reproduced by the state variable model VBO (viscoplasticity theory based on overstress). Since experimental investigations typically concentrate on one particular aspect of inelastic deformation behavior such as creep or strain-rate dependence, it is often difficult to gather a comprehensive data set for a given material. In spite of this, considerable similitude in the deformation behavior of metals and polymers in various test conditions has nevertheless been established.     

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.     

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.     

96.5Sn-3.5Ag钎料合金的时相关单轴应变循环变形行为及其本构关系研究

在室温下对96.5Sn-3.5Ag钎料合金进行了不同加载波形下的单轴应变循环实验。研究了在具有不同保持时间、不同应变率、不同应变幅值及其历史对材料的循环变形行为的影响。基于材料时相关变形行为,提出了统一粘塑性本构模型,并对该材料的变形行为进行本构模拟。实验结果表明:该钎料合金单轴变形行为具有应变率、保持时间以及应变幅值依赖性。本构关系的预言结果与实验结果吻合得一致性说明该种模型能够很好地描述材料的单轴应变循环变形行为。     

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.     

Stress–strain behaviour of poly(ethylene terephthalate) (PET) during large plastic deformation by plane strain compression: the relation between stress–strain curve and thermal history, temperature and strain rate

This study presents an experimental investigation of the large plastic deformation of poly(ethylene terephthalate) (PET) submitted to plane strain compression. PET samples, obtained by injection moulding, annealed and non-annealed, were deformed using a specific compression device developed for this purpose. The obtained stress–strain curves at different temperatures and strain rates are useful for engineering applications and show a significant temperature dependence and a minor dependence on the strain rate. A softening temperature as a minimum temperature necessary to initiate deformation when a minimum, almost zero, stress is applied is introduced. This temperature, at the zero stress and strain limit, we denominate “Stress–Strain independent softening Temperature (T _SOF)”. The T _SOF values, 104 and 113°C for non-annealed and annealed PET, respectively, have been obtained using three different strain rates, indicating that the property is sensitive to the thermal history of the material.     

The solid–fluid transition in a yield stress shear thinning physical gel

We present an experimental investigation of the solid–fluid transition in a yield stress shear thinning physical gel (Carbopol^® 940) under shear. Upon a gradual increase of the external forcing, we observe three distinct deformation regimes: an elastic solid-like regime (characterized by a linear stress–strain dependence), a solid–fluid phase coexistence regime (characterized by a competition between destruction and reformation of the gel), and a purely viscous regime (characterized by a power law stress-rate of strain dependence). The competition between destruction and reformation of the gel is investigated via both systematic measurements of the dynamic elastic moduli (as a function of stress, the amplitude, and temperature) and unsteady flow ramps. The transition from solid behavior to fluid behavior displays a clear hysteresis upon increasing and decreasing values of the external forcing. We find that the deformation power corresponding to the hysteresis region scales linearly with the rate at which the material is being forced (the degree of flow unsteadiness). In the asymptotic limit of small forcing rates, our results agree well with previous steady state investigations of the yielding transition. Based on these experimental findings, we suggest an analogy between the solid–fluid transition and a first-order phase transition, e.g., the magnetization of a ferro-magnet where irreversibility and hysteresis emerge as a consequence of a phase coexistence regime. In order to get further insight into the solid–fluid transition, our experimental findings are complemented by a simple kinetic model that qualitatively describes the structural hysteresis observed in our rheological experiments. The model is fairly well validated against oscillatory flow data by a partial reconstruction of the Pipkin space of the material’s response and its nonlinear spectral behavior.     

HTPB复合底排药压缩屈服应力模型研究

目前广泛应用于底排增程技术的 HTPB 复合底排药 (composite base bleed grain,CBBG) 是一种颗粒填充含能材料,战场环境中将承受冲击、温度等载荷作用. 为研究 HTPB CBBG 冲击压缩力学性能,进行了不同温度 (233$\sim$323 K) 和应变率 (1100$\sim$7900 s$^{-1}$) 下的分离式霍普金森压杆实验. 实验结果表明,各工况下,应力应变曲线均呈现屈服-$\!$-应变硬化特征,HTPB CBBG 保持高韧性. 提高应变率和降低温度均导致相同应变下的应力幅值上升,但温度较应变率对HTPB CBBG 冲击压缩力学性能的影响更为显著. 基于所研究温度范围高于 HTPB CBBG 玻璃化转变温度,通过将水平、垂直移位因子与温度的关系表示为 WLF 方程的形式,将时温等效原理引入协同模型,并计及内应力的应变率增强效应,提出了一种新的屈服应力模型.选取参考温度,利用水平、垂直移位因子-$\!$-温度曲线和屈服应力主曲线拟合模型参数.模型预测值与实验数据对比结果表明:该模型可准确表征 233$\sim$323 K 时 HTPB CBBG 屈服应力的双线性应变率相关性,明确了较低和较高应变率时,应变率效应分别主要由内应力和驱动力贡献.      

A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers

The stress response of amorphous polymers exhibits tremendous change during the glass transition region, from soft viscoelastic response to stiff viscoplastic response. In order to describe the temperature-dependent and rate-dependent stress response of amorphous polymers, we extend the one-dimensional small strain fractional Zener model to the three-dimensional finite deformation model. The Eyring model is adopted to represent the stress-activated viscous flow. A phenomenological evolution equation of yield strength is used to describe the strain softening behaviors. We demonstrate that the stress response predicted by the three-dimensional model is consistent with that of one-dimensional model under uniaxial deformation, which confirms the validity of the extension. The model is then applied to describe the stress response of an amorphous thermoset at various temperatures and strain rates, which shows good agreement between experiments and simulation. We further perform a parameter study to investigate the influence of the model parameters on the stress response. The results show that a smaller fractional order results in a larger yield strain while has little effect on the yield stress when the temperature is below the glass transition temperature. For the stress relaxation tests, a smaller fractional order leads to a slower relaxation rate.     

Modeling deformation behavior of polymers with viscoplasticity theory based on overstress

The nonlinear strain rate sensitivity, multiple creep and recovery behavior of polyphenylene oxide (PPO), which were explored through strain rate-controlled experiments at ambient temperature by Khan [The deformation behavior of solid polymers and modeling with the viscoplasticity theory based overstress, Ph.D. Thesis, Rensselaer Polytechnic Institute, New York], are modeled using the modified viscoplasticity theory based on overstress (VBO). In addition, VBO used by Krempl and Ho [An overstress model for solid polymer deformation behavior applied to Nylon 66, ASTM STP 1357, 2000, p. 118] and the classical VBO are used to demonstrate the improved modeling capabilities of VBO for solid polymer deformation. The unified model (VBO) has two tensor valued state variables, the equilibrium and kinematic stresses and two scalar valued states variables, drag and isotropic stresses. The simulations include monotonic loading and unloading at various strain rates, multiple creep and recovery at zero stress. Since creep behavior has been found to be profoundly influenced by the level of the stress, the tests are performed at different stresses above and below the yield point. Numerical results are compared to experimental data. It is shown that nonlinear rate sensitivity, nonlinear unloading, creep and recovery at zero stress can be reproduced using the modified viscoplasticity theory based on overstress.     

Deformation rate effects on failure modes of open-cell Al foams and textile cellular materials

The compressive behavior of open-cell aluminum alloy foam and stainless steel woven textile core materials have been investigated at three different deformation rate regimes. Quasi-static compressive tests were performed using a miniature loading frame, intermediate rates were achieved using a stored energy Kolsky bar, and high strain rate tests were performed using a light gas gun.In agreement with previous studies on foam materials, the strain rate was not found to have a significant effect on the plateau stress of metallic foams. For all the tests, real time imaging of the specimen combined with digital image correlation analysis allowed the determination of local deformation fields and failure modes. For the Kolsky bar tests, the deformations in the foam specimen were found to be more distributed than for the quasi-static test, which is attributed to moderate inertia effects. The differences in failure mode are more dramatic for the gas gun experiments, where a full compaction shock wave is generated at the impact surface. The stresses in front and behind the shock wave front were determined by means of direct and reverse gas gun impact tests, i.e., stationary and launched specimen, respectively. A one-dimensional shock wave model based on an idealized foam behavior is employed to gain insight into the stress history measurements. We show that the predictions of the model are consistent with the experimental observations. Woven textile materials exhibited moderate dependence of strength on the deformation rate in comparison with open-cell foam materials.     

Temperature evolution associated with phase transition from quasi static to dynamic loading

Thermo-mechanical coupling is an intrinsic property of first order martensitic transformation. In this paper, we study the temperature evolution during phase transition at a wider strain rates from quasi static to impact loading to reveal the thermodynamic nature of the strain rate effect of phase transition materials. Based on the laws of thermodynamics and the principle of maximum dissipated energy, a thermal-mechanically coupled model was proposed. The model shows that, in the quasi static case, the temperature profile grades around the moving phase boundary, while for the dynamic case, thermal response of the specimen can be reached homogeneously due to random nucleation. The predicted results of the model are in good agreement with the experimental results, suggesting that the interaction between the self-heating effect and the temperature dependence of phase transition behavior plays a leading role in the process of the transformation deformation mechanism associated with the loading rate.

     

Micromechanical modelling of the static and cyclic loading of an Al 2124-SiC MMC

The objective of this study was to use micromechanical finite element models to simulate both the static and cyclic mechanical behaviour of a metal matrix composite: a forged Al 2124 alloy reinforced with 17% SiC particles, at two different temperatures: room temperature and 150°C. In the simulations, periodic unit cell models incorporating the explicit representation of the matrix and the reinforcing particles in both 2D and 3D, were used. Micromechanical models with both idealised and realistic reinforcing particle shapes and distributions were generated. The realistic particle shapes and distributions were inferred from experimental SEM micrographs. The pattern and intensity of the plastic deformation within the matrix was studied and the macroscale behaviour of the composite was inferred from average stress and strain values. In order to include the effects of residual stresses due to the processing of the material, a quenching simulation was performed, prior to the mechanical loading, and its effects on the macroscopic tensile behaviour of the MMC was assessed. The effects of removing the periodicity constraint on the models by using a cell embedding technique was investigated. In order to try and model the deformation behaviour of the matrix more accurately, crystal plasticity models, which included the explicit representation of individual grains were examined for different matrix grain morphologies. The results of the simulations were compared with experimental results for the MMC in terms of macroscopic tensile stress–strain curves. Finally, the effects of different matrix strain hardening models were examined in order to investigate the cyclic behaviour of the MMC.     

A model for high temperature creep of single crystal superalloys based on nonlocal damage and viscoplastic material behavior

A model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity. It is based on a variational formulation, employing potentials for free energy, and dissipation originating from plasticity and damage. Evolution equations for plastic strain and damage variables are derived from the well-established minimum principle for the dissipation potential. The model is capable of describing the different stages of creep in a unified way. Plastic deformation in superalloys incorporates the evolution of dislocation densities of the different phases present. It results in a time dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage. Herein, the nonlocal one is included in order to model strain localization as well as to remove mesh dependence of finite element calculations. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown.     

聚脲弹性体力学性能与本构关系研究进展

聚脲是一种由异氰酸酯组分和氨基组分反应生成的新型弹性体高聚物.由于聚脲具有断裂伸长率高、应变率强化、高耗能等一系列优异的力学性能,其在国防、能源、交通等领域显示出广阔的应用前景.目前,国内外学者针对聚脲在不同温度、不同应变率下的静动态力学性能开展了大量研究,在此基础上提出了多种本构模型,对温度、应变率等因素相关的力学行为进行了描述和预测.这些工作为深刻理解聚脲抗冲击机理及材料的进一步应用奠定了基础.文章首先简要介绍了聚脲弹性体的微相分离结构及特点;然后从小变形线性黏弹性和大变形非线性黏弹性两个方面概述了关于聚脲力学性能的研究,包括相应测试技术的发展和聚脲黏弹性影响因素的研究;进一步从变形梯度乘法分解法、遗传积分法、应变-时间解耦法等不同建模方法出发对已建立的聚脲本构模型进行综述,并从应变率范围、温度范围、压力相关性、软化行为表征及模型参数数量的角度对比了不同类型模型的区别;最后针对聚脲力学性能与本构关系下一步研究值得重点关注的问题提出了几点建议.     

应力作用下NiTi形状记忆合金微结构演化的相场模拟及其本征应变率敏感性

基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型,实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度,从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为,并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.000 5～15 s-1）力学行为的本征应变率敏感性。研究结果表明,单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生,未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象,在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中,NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积,拥有更优的超弹性变形能力。计算结果显示,在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性,应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。     

Mechanical and optical characterization of cellulose acetate

To obtain the basic relations for photo-viscoelastoplastic stress analysis using cellulose acetate, the effect of strain rate as well as room temperature on mechanical and optical properties was precisely investigated by the uniaxial tension test. As a result, the nonlinear stress-strain, the non-linear-stress-fringe order and the nonlinear-fringe-order strain relations were uniquely reoresented in their nondimensional forms regardless of strain rate and room temperature. Young's modulus, yield stress and the yield fringe order were linearly related both to room temperature and to logarithm of strain rate. The effect of strain rate on these relations has caused great difficulties in experimental stress analysis with respect to photoplasticity. However, it was found in this work that the value of the strain rate at any points in the model can be determined by the fringe-order rate measured. Therefore, it is possible to estimate not only the distribution of strain rate but that of stress or strain in the photo-viscoelastoplastic model with cellulose acetate.