A damage related thermo-viscoplastic constitutive model of metallic materials under high rate deformation

Abstract

A constitutive model considering the effects of strain hardening, strain rate hardening, thermal softening and material damage softening is suggested. In order to take the effect of material damage into account, a strain softening term is added in Johnson–Cook flow stress law. The model can predict the overall deformation process of metallic materials at high strain rates and a simple way is provided to determine the coefficients of softening term.     

Applicability of Kocks–Mecking approach for tensile work hardening in P9 steel

Abstract

Work hardening behaviour of P9 steel in the temperature range 300–873 K has been examined in the framework of Kocks–Mecking (K–M) approach. At all temperatures, P9 steel exhibited two-stage work hardening behaviour characterised by a rapid decrease in instantaneous work hardening rate (i.e. θ?=?dσ/d?, where σ is the true stress and ? is the true plastic strain) with stress at low stresses (transient stage) followed by a gradual decrease at high stresses (stage III). Stage III work hardening of P9 steel was adequately described by K–M approach. The variations of work hardening parameters associated with K–M approach for stage III with temperature indicated three distinct temperature regimes. At all temperatures, good correlations between the respective work hardening parameters evaluated using K–M approach and from Voce equation and its derivative have been obtained for P9 steel.     

Modeling high-temperature tensile deformation behavior of AZ31B magnesium alloy considering strain effects

The hot tensile deformation behaviors of AZ31B magnesium alloy are investigated over wide ranges of forming temperature and strain rate. Considering the effects of strain on material constants, a comprehensive constitutive model is applied to describe the relationships of flow stress, strain rate and forming temperature for AZ31B magnesium alloy. The results show that: (1) The effects of forming temperature and strain rate on the flow behaviors of AZ31B magnesium alloy are significant. The true stress–true strain curves exhibit a peak stress at small strains, after which the flow stress decreases until large strain, showing an obvious dynamic softening behavior. A considerable strain hardening stage with a uniform macroscopic deformation appears under the temperatures of 523 and 573 K. The strain hardening exponent (n) increases with the increase of strain rate or the decrease of forming temperature. There are not obvious strain-hardening stages when the forming temperature is relatively high, which indicates that the dynamic recrystallization (DRX) occurs under the high forming temperature, and the balance of strain hardening and DRX softening is easy to obtain. (2) The predicted stress–strain values by the established model well agree with experimental results, which confirm that the established constitutive equation can give an accurate and precise estimate of the flow stress for AZ31B magnesium alloy.     

Strain-rate effect on high temperature low-cycle fatigue deformation of AISI 304L stainless steel

The effect of strain rate on the behaviour of high temperature low-cycle fatigue is investigated for AISI 304L stainless steel. Regardless of the test temperature of 873 or 973 K, the fatigue life is saturated in the strain-rate range of slower than 4 × 10^–3 sec^–1. Also it is interesting to note that serrated flow, which is evidence of the occurrence of dynamic strain ageing, is clearly observed in the load-elongation hysteresis loops for strain rates that are slower (at 873 K) and faster (at 973 K) than 4 × 10^–3 sec^–1. Since the combination of temperature and strain rate is concerned with the phenomenon of dynamic strain ageing, it is considered that the above-mentioned saturated fatigue life at 873 K is caused by dynamic strain ageing and that the hardening effect due to dynamic strain ageing abnormally increases the fatigue life. However, even though the behaviour of fatigue life under strain rates slower than 4 × 10^–3 sec^–1 at 973 K has nothing to do with the dynamic strain ageing, it has been found that the failure life is also saturated in this slower strain-rate range. This behaviour is considered to be caused by the effect of creep, because the deformation under the low strain-rate activates the recovery process and as a result it causes saturation of the inelastic strain range.     

Flow stress and ductility of AA7075-T6 aluminum alloy at low deformation temperatures

The present investigation has been conducted in order to develop a rational approach able to describe the changes in flow stress of AA7075-T6 aluminum alloy with deformation temperature and strain rate, when this material is deformed at temperatures in the range of 123-298 K at strain rates in the range of 4 × 10⁻⁴ to 5 × 10⁻² s⁻¹. The constitutive formulation that has been advanced to accomplish these objectives represents a simplified form of the mechanical threshold stress (flow stress at 0 K) model developed at Los Alamos National Laboratory (Los Alamos, New Mexico, USA). Thus, it is assumed that the current flow stress of the material arises from both athermal and thermal barriers to dislocation motion. In the present case, the effect of three thermal barriers has been considered: solid solution, precipitation hardening and work-hardening. The first two effects do not evolve during plastic deformation, whereas the last one is considered as an evolutionary component of the flow stress. Such an evolution is described by means of the hardening law earlier advanced by Estrin and Mecking (1984) [20]. The law is implemented in differential form and is integrated numerically in order to update the changes in strain rate that occur during tensile tests carried out both at constant and variable crosshead speed. The extrapolation of the hardening components from 0 K to finite temperatures is accomplished by means of the model earlier advanced by Kocks (1976) [19]. The results illustrate that the constitutive formulation developed in this way is able to describe quite accurately both the flow stress and work-hardening rate of the material, as well as temperature and strain rate history effects that are present when deformation conditions change in the course of plastic deformation. The evaluation of the ductility of the alloy indicates that the changes in this property are mainly determined by deformation temperature rather by strain rate. When deformation temperature decreases from 298 to 123 K, ductility also decreases from ∼35 to 24%. However, despite these relatively small variations, significant changes in the fracture morphology could be observed on the fracture surfaces of the examined specimens, with the predominance of a mixed ductile-brittle mechanism at lower temperatures.     

Constitutive models for high-temperature flow behaviors of a Ni-based superalloy

The high-temperature deformation behaviors of a typical Ni-based superalloy are investigated by hot compression tests under the strain rate of 0.001–1 s⁻¹and temperature of 920–1040 °C. The experimental results show that the deformation behaviors of the studied superalloy are significantly affected by the deformation temperature, strain rate and strain. The flow stress increases with the increase of strain rate or the decrease of deformation temperature. The flow stress firstly increases with the strain to a peak value, showing the obvious work hardening behaviors. Then, the stress decreases with the further straining, indicating the dynamic flow softening behaviors. Considering the coupled effects of deformation temperature, strain rate and strain on the hot deformation behaviors of the studied Ni-based superalloy, the phenomenological constitutive models are established to describe the work hardening-dynamic recovery and dynamic softening behaviors. In the established models, the material constants are expressed as functions of the Zener–Hollomon parameter. The established constitutive models can give good correlations with the experimental results, which confirm an accurate and precise estimation of the flow stress for the studied Ni-based superalloy.     

Effect of carbon content on plastic flow behaviour of plain carbon steels at elevated temperature

Abstract

In the present study the effect of carbon composition on the hot flow behaviour of two different plain carbon steels is analysed. For this purpose the constitutive equations describing the stress–strain (σ–?) relationships at a given strain rate ? and temperature T were determined for each steel. Uniaxial hot compression tests were performed to characterise the mechanical behaviour of the alloys. It was observed that irrespective of the test conditions, the low carbon steel displayed similar flow stresses to the high carbon steel. Comparison of the characteristic parameters of the constitutive equations describing the high temperature flow behaviour of these steels, together with values reported in the literature enabled determination of the effect of carbon content on flow behaviour. It has been found that flow stresses can be rationalised as a balance between work hardening and softening processes (basically dynamic recovery). At high temperatures and small strain rates, the high carbon steel showed lower hardening rates and slower dynamic recovery kinetics than the low carbon steel. In contrast, at low temperatures and large strain rates, the high carbon steel displayed higher hardening rates and recovery rates than the low carbon steel.     

Effect of temperature and strain rate on tensile flow and work hardening behaviour of a Ti modified austenitic stainless steel

Abstract

The tensile flow stress data for a 15Cr - 15Ni - 2.2Mo - Ti modified austenitic stainless steel in the temperature range 300 - 1023 K and in the strain rate range 6.3 × 10^-5- 1.3 × 10^-2 s^-1 was analysed in terms of the Ludwigson and Voce equations. It was found that the Ludwigson equation described the flow behaviour adequately up to the test temperature of 923 K, whereas the Voce equation could be employed over the full temperature range. The peaks/ plateaus observed in the variation of these parameters as a function of temperature and strain rate in the intermediate temperature range have been identified as one of the manifestations of dynamic strain aging (DSA). Also the variation of these parameters with temperature and strain rate could clearly bring out the different domains of DSA observed in this alloy. The work hardening analysis of the flow stress data revealed that, in the DSA regime, the onset of stage III hardening is athermal.     

Superplastic behaviour of annealed AA 8090 Al-Li alloy

Abstract

High temperature flow behaviour and microstructural evolution were investigated in an annealed AA 8090 Al - Li alloy over the temperature range 623 - 803 K and strain rate range ~ 6 × 10⁶ - 3 × 10² s^-1. Stress - strain rate data, obtained using a differential strain rate test technique and plotted in log - log scale, exhibited three regions I, II, and III, with increasing strain rate. In these regions, the values of strain rate sensitivity index m and the activation energy for deformation were determined to be 0.17, 0.43, and 0.17; and 758.8, 93.3, and 184.3 kJ mol^-1, respectively. The stress - strain curves obtained from constant strain rate tests exhibited flow hardening at lower strain rates and higher temperatures whereas flow softening occurred at higher strain rates and lower temperatures. The microstructural evolution revealed the dominance of grain growth under the former conditions and dynamic recrystallisation under the latter conditions. Ductility and m were found to increase with temperature, with the maximum values of 402% and 0.55, respectively, at a temperature 803 K and strain rate 2 × 10^-4 s^-1.     

GH5188合金板材高温拉伸变形流动行为与本构方程研究

目的 研究GH5188合金板材高温拉伸变形流动行为,为高温合金板材高温成形工艺的制定和优化提供指导。方法 基于GH5188合金板材高温拉伸试验,分析了变形工艺参数对GH5188合金板材高温拉伸变形时真应力、应变速率敏感性指数和应变硬化指数的影响规律,建立了本构模型对其流动行为进行描述和预测。结果 GH5188合金板材高温拉伸变形流动行为受应变硬化、流动软化和应变速率硬化的共同影响,其变形过程分为弹性变形、加工硬化、稳态流动和断裂4个阶段。随变形温度的升高和应变速率的降低,真应力减小。变形温度、应变速率和真应变对GH5188合金板材的应变速率敏感性指数和应变硬化指数具有显著影响。基于Johnson-Cook和Hensel-Spittel模型,建立了考虑应变硬化效应、流动软化效应和应变速率硬化效应耦合影响的GH5188合金板材高温拉伸变形本构模型(JC-HS模型),采用该模型预测的真应力与试验值的平均相对误差为6.02%。结论 建立的JC-HS模型能够较好地描述和预测GH5188合金板材的高温拉伸流动行为。     

Dynamic strain-rate effect on uniaxial tension deformation of Ti5Al2.5Sn α-titanium alloy at various temperatures

The uniaxial tensile experiments for Ti5Al2.5Sn alloy were performed at strain rates ranging from 10^?3–10⁺³ s^?1 and test temperatures of 153–873 K. Experimentally measured stress-strain responses indicate the yield strength exhibits positive strain-rate dependency, while the yield strength increases as the test temperature is decreased. To understand the thermomechanical coupling of dynamic plastic deformation, a specially developed single-tensile-pulse loading technique was used, and the isothermal stress-strain curves for the rates of 180 and 450 s^?1 were obtained at temperatures of 203, 298 and 573 K. The plastic strain hardening measurements obtained here are essentially athermal and largely independent of strain rate, consistent with titanium and its alloys being bcc-structure-like in mechanical behaviour. Based on the experimentally obtained plastic deformation features of the alloy, the physically based Voyiadjis-Abed constitutive relationship was modified to model the dynamic tensile deformation of the Ti5Al2.5Sn alloy at low and high temperatures.     

Constitutive modeling of the mechanical behavior of high strength ferritic steels for static and dynamic applications

A constitutive relation is presented in this paper to describe the plastic behavior of ferritic steel over a broad range of temperatures and strain rates. The thermo-mechanical behavior of high strength low alloy (HSLA-65) and DH-63 naval structural steels is considered in this study at strains over 40%. The temperatures and strain rates are considered in the range where dynamic strain aging is not effective. The concept of thermal activation analysis as well as the dislocation interaction mechanism is used in developing the flow model for both the isothermal and adiabatic viscoplastic deformation. The flow stresses of the two steels are very sensitive to temperature and strain rate, the yield stresses increase with decreasing temperatures and increasing strain rates. That is, the thermal flow stress is mainly captured by the yield stresses while the hardening stresses are totally pertained to the athermal component of the flow stress. The proposed constitutive model predicts results that compare very well with the measured ones at initial temperature range of 77 K to 1000 K and strain rates between 0.001 s⁻¹ and 8500 s⁻¹ for both steels.     

Zirlo锆合金高温变形行为及本构关系EI北大核心CSCD

采用Gleeble-3800型热模拟试验机,对Zirlo合金进行等温恒应变速率压缩实验,研究其在变形温度550~700℃,应变速率0.01~10 s^(-1)范围内的热变形行为;并在Arrhenius型双曲正弦函数方程基础上引入应变量,构建了基于应变补偿的Arrhenius本构模型,同时构建了基于位错密度演化加工硬化模型和基于唯象型的软化模型的分段唯象型本构模型。结果表明:Zirlo合金的流变应力随着温度的降低和应变速率的提高而升高,低应变速率下流变应力呈现更高的温度敏感性,流变应力曲线在不同变形条件下分别呈现加工硬化、动态回复、动态再结晶特征。经过误差分析可知,基于应变补偿的Arrhenius本构模型大部分预测值的误差均在15%以内,具有较高的准确性,而分段唯象型本构模型相对平均绝对误差最大值不超过3%,具有97%以上的准确率,可以很好地预测合金的应力-应变曲线,具有良好的拓展性,并且可初步判断曲线类型,具有良好的实用性。     

Microstructural changes occurring during superplastic deformation of Ti-6AI-6V-2Sn alloy

Abstract

Microstructural changes occurring during superplastic deformation of Ti-6Al-6V-2Sn alloy with an initial microstructure consisting of mixed fine lamellar and equiaxed α grains were investigated. Uniaxial tensile tests with constant strain rate were conducted at temperatures ranging from 775 to 925°C and at strain rates rangingfrom 7 × 10^-5 to 1 × 10^-3 S^-l. To investigate the microstructural changes occurring during deformation, some of the tests were terminated at preprogrammed true strains of 0.5, 0.9, and 1.5 for subsequent metallographic investigation. The effects of high temperature exposure on the microstructural changes and on the superplastic deformation behaviour were also evaluated. It was found that both static and dynamic recrystallisation were initiated under certain test conditions and could be related to the flow stress behaviour during the superplastic deformation tests. For tests at low temperature and high strain rate, the flow stress increased quickly at the very beginning of the deformation without significant microstructural change. After the flow stress reached its maximum value, dynamic recrystallisation occurred at a lamellae accompanied by a decrease of the flow stress, known as strain softening. Raising the test temperature or decreasing the deformation strain rate provided the opportunity for thermal energy to initiate static or semidynamic recrystallisation. Thereafter, the flow stress behaviour at the beginning of the test changed to a slow strain hardening type. There also existed a transition temperature; soaking before tensile testing above this temperature would result in static recrystallisation, and the superplastic deformation characteristics would be affected.