Constitutive equations for high temperature flow stress prediction of 6063 Al alloy considering compensation of strain

In order to develop the appropriate constitutive equation which can precisely model high temperature flow stress of 6063 Al alloy, a series of isothermal hot compression tests were performed at temperatures from 573 to 773 K and strain rates from 0.5 to 50 s?1 on a Gleeble?1500 thermo-simulation machine. Zener–Hollomon parameter in an exponent-type equation was used to describe the combined effects of temperature and strain rate on hot deformation behaviour of 6063 Al alloy, whereas the influence of strain was incorporated in the developed constitutive equation by considering material constants (α,n,Q andA) to be 4th order polynomial functions of strain. The results show that the developed constitutive equation can accurately predict high temperature flow stress of 6063 Al alloy, which demonstrates that it can be suitable for simulating hot deformation processes such as extrusion and forging, and for properly designing the deformation parameters in engineering practice.

Constitutive relationship of IN690 superalloy by using uniaxial compression tests

The hot deformation behavior of IN690 superalloy was characterized in a temperature range of 1273-1473 K and a strain rate range of 0.01-10 s^-1 using uniaxial compression tests on process annealed material.The constitutive relations between flow stress and effective strain,effective strain rate as well as deformation temperature were studied.It can be concluded that the flow stress significantly reduces with the deformation temperature of IN690 superalloy increasing.Whereas,there is a significant increase of flow stress when the strain rate increases from 0.1 s^-1 to 10 s^-1.Based on the hyperbolic-sine Arrhenius-type equation,a constitutive equation considering compensation of strain was developed.The activation energy and the material constants（Q,n and ln A） decrease as the deformation strain increases.The strain dependent term is successfully incorporated in the constitutive equation through a quartic equation.A good agreement between the experimental data and the predicted results has been achieved,indicating that the proposed constitutive equation and the methods of determing the material constants are suitable to model the high temperature deformation behavior of IN690 superalloy.

Microstructural evolution,flow stress and constitutive modeling of Al−1.88Mg−0.18Sc−0.084Er alloy during hot compression

To explore the hot compression behavior and microstructural evolution,fine-grained Al−1.88Mg−0.18Sc−0.084Er(wt.%)aluminum alloy wires were fabricated with Castex(continuous casting−extrusion)and ECAP-Conform,and their hot compression behavior was investigated at temperatures of 673−793 K and strain rates of 0.001−10 s−1;the microstructures were characterized by optical microscope,X-ray diffractometer,transmission electron microscope,and electron backscattered diffractometer,and the flow stresses were obtained by thermal compression simulator.Microstructural evolution and flow curves reveal that dynamic recovery is the dominant softening mechanism.Continuous dynamic recrystallization followed by dynamic grain growth takes place at a temperature of 773 K and a strain rate of 0.001 s−1;the yielding drop phenomenon was discovered.Hyperbolic sine constitutive equation incorporating dislocation variables was presented,and a power law constitutive equation was established.The stress exponent is 3.262,and the activation energy for deformation is 154.465 kJ/mol,indicating that dislocation viscous glide is the dominant deformation mechanism.

The Complete Stress-strain Curve of Recycled Aggregate Concrete under Uniaxial Compression Loading

The mechanical performance of recycled aggregate concrete （RAC） is investigated. An experiment on the complete stress-strain curve under uniaxial compression loading of RAC is carried out. The experimental results indicate that the peak stress, peak strain, secant modulus of the peak point and original point increase with the strength grade of RAC enhanced. On the contrary, the residual stress of RAC decreases with the strength grade enhancing, and the failure of RAC is often broken at the interface between the recycled aggregate and the mortar matrix. Finally, the constitutive model of stress-strain model of RAC has been constituted, and the results from the constitutive model of stress-strain meet the experiment results very well.

Prediction of flow stress of Mg-Nd-Zn-Zr alloy during hot compression

Isothermal hot compression tests were carried out on Mg-3.0Nd-0.2Zn-0.4Zr （mass fraction, %, NZ30K） alloy using a Gleeble-3500 thermo-simulation machine at temperatures ranging from 350 to 500 ℃and strain rates from 0.001 to 1 s^-1. A correction of flow stress for deformation heating at a high strain rate was carried out. Based on the corrected data for deformation heating, a hyperbolic sine constitutive equation was established. The constants in the constitutive equation of the hyperbolic sine form were determined as a function of strain. The flow stresses predicted by the developed equation agree well with the experimental results, which confirms that the developed constitutive equations can be used to predict the flow stress of NZ30K alloy during hot deformation.

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale,as a kind of brittle rock,often exhibits different nonlinear stress-strain behavior,failure and timedependent behavior under different strain rates.To capture these features,this work conducted triaxial compression tests under axial strain rates ranging from 5×10-6 s-1 to 1×10-3 s-1.The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates.These strain rate-dependent mechanical behaviors of shale are originated from damage growth,which is described by a damage parameter.When axial strain is the same,the damage parameter is positively correlated with strain rate.When strain rate is the same,with an increase of axial strain,the damage parameter decreases firstly from an initial value(about 0.1 to 0.2),soon reaches its minimum(about 0.1),and then increases to an asymptotic value of 0.8.Based on the experimental results,taking yield stress as the cut-off point and considering damage variable evolution,a new measure of micro-mechanical strength is proposed.Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength,a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established.Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.

Study on the Constitutive Model of Marble Based on the Conventional Triaxial Compression Test

The RMB-150B rock mechanics test system was employed to obtain the complete stress-strain test curves under confining pressures of 0-30MPa for marble samples from Ya'an ,Sichuan province. On the basis of former study and the convention triaxial pressure test results ,the complete procedures curves which described the relationships between yielding strength、 peak strength、 residual strength and confining pressure was obtained. Taking the strain softening of rock into account, the bilinear elastic-linear softening-residual perfect plasticity four-linear model was put forward in this paper on the basis of the test results and theory of plasticity. This model was adopted to describe the behaviors of marble in different phases under triaxial compression with the constitutive equation of strain softening phase as focus. The results indicated that the theoretic model fitted in well with the test results.

MODELLING OF TENSILE STRESS-STRAIN CURVE OF WOVEN FABRICS

A general shape of tensile stress-strain curves of woven fabrics is first recognised by puttingtested and predicted results together.An exponential function with two parameters is then selectedfor the prediction of tensile stress-strain relationship.The predicted results by using the proposedfunction show excellent agreement with experimental data.

TC4钛合金电致塑性本构方程建立

采用自行设计的绝缘夹具对TC4钛合金板材进行了电致塑性单向拉伸试验。基于对照试验的方法,以无脉冲电流且不同温度条件作为参照,与同等温度条件下脉冲电流加热情况进行对比,以探索电流参数对TC4钛合金电致塑性效应和力学性能的影响规律。结果表明:在试验研究范围内,脉冲电流的占空比主要影响材料的温度变化,脉冲电流密度对TC4钛合金的电致塑性起主导地位,脉冲电流作用下的TC4钛合金材料抗拉强度大幅下降,塑性提高。基于Johnson-Cook模型和Arrhenius方程建立了耦合温度和脉冲电流密度的TC4钛合金电致塑性本构方程,并进行了验证。

土工格室加筋正常固结粉质黏土应力应变响应

土工格室加筋正常固结粉质黏土对工程建设意义重大。基于土工格室与填土的相互作用机制和增量法,采用弹塑性理论、邓肯-张双曲线模型、修正剑桥屈服函数以及剪胀方程,推导了土工格室加筋正常固结黏土的应力应变响应计算模型,进行了土工格室加筋正常固结黏土的三轴固结排水剪切试验,实测不同围压下的应力应变关系,采用三轴试验结果验证了所提理论模型的正确性和可靠性。此外,采用所提理论模型进行了参数敏感分析,研究了填土的力学性质参数、格室的网格尺寸和力学性质参数对于加筋土应力应变响应的影响。研究结论表明,与砂砾料相似,土工格室约束作用对于正常固结黏土的内摩擦角影响较小,而黏聚力有所增加;随着轴向应变的增加或围压的减小,加筋效果逐渐明显;加筋正常固结黏土的强度和刚度随着非线性弹性常数k的增加、强度参数φ的增加和Rf的减小而增大,常数n对于加筋土应力应变响应影响较小。本研究成果可为工程建设提供理论借鉴。

铸态Mg-6Zn合金的半固态压缩变形行为及本构模型的建立

利用Gleeble-3500型热力模拟试验机对铸态Mg-6Zn合金在变形温度500,520,540℃,应变速率0.1,1,5 s^(-1)下进行半固态压缩试验,得到了真应力-真应变曲线;基于真应力和真应变试验数据及Arrhenius模型,建立该合金的半固态压缩本构模型,并进行试验验证。结果表明:Mg-6Zn合金的半固态压缩变形过程主要分为类弹性变形、应变硬化变形和流变黏塑性变形3个阶段;峰值应力随变形温度的升高或应变速率的减小而降低。利用建立的本构模型计算得到的真应力与试验结果之间的相关性很好,相关系数为0.947,平均相对误差为5.57%,说明该本构模型能够较准确地预测铸态Mg-6Zn合金的半固态压缩变形行为。

基于Hoek-Brown准则的岩体高温-荷载耦合损伤模型及其验证

针对隧道岩体在高温和荷载共同作用下产生的耦合损伤问题,基于连续损伤力学理论,引入高温-荷载耦合损伤因子,建立了考虑高温作用的广义Hoek-Brown(H-B)准则的弹塑性损伤本构模型,解决了模型在数值积分过程中的奇异点问题,并利用Fortran语言编写了模型的有限元程序。结果表明:模型计算的应力-应变曲线与试验所得到的曲线趋势一致且计算结果误差在5%以内,温度作用下隧洞围岩损伤逐渐加剧,验证了模型的准确性和程序的稳健性,可为火灾作用下隧道围岩安全稳定性评价提供一种有效计算方法。

粉煤灰再生混凝土力学性能试验研究

利用试验检测机构废弃的混凝土试块作为再生粗骨料的原材料,配制不同粗骨料取代率的混凝土,再加入适量粉煤灰,制成试件(取代率分别为0、30%、60%和100%),用于混凝土立方体抗压、劈裂抗拉、轴心抗压和弹性模量试验,通过观察其破坏过程和破坏形态,获取荷载-位移全过程曲线,研究并提出了本构方程。试验结果表明,粉煤灰再生骨料混凝土与天然骨料混凝土相比,各项力学指标随着再生骨料取代率的增大先是呈现增长趋势,当达到峰值后,各项力学指标均下降;两者的应力-应变曲线具有相似的形状,在上升阶段,再生混凝土与天然混凝土的应力-应变曲线变化不大,但在下降段再生混凝土的应力-应变曲线急剧下降。

藏式毛石砌体受压力学性能试验与数值模拟研究

通过试验和PFC2D二维数值计算对2组共计8个典型藏式毛石棱柱体试件进行单轴压缩性能分析,获得了棱柱体压缩破坏全过程、应力-应变全曲线和弹性模量等基本力学参数。发现藏式毛石砌体受压过程呈现出阶段性和明显的非线性行为,得到了PFC2D二维数值模拟能较好地再现毛石砌体的压缩破坏形态和裂缝开展情况,黏土中增添碎石能提高约23%的承载力,且能有效改善试件失稳破坏形态,石材抗拉强度和黏土弹性模量是影响试件初裂强度和峰值强度的关键。为工程中评估藏式毛石砌体抗压承载力提供了一种新方法。

022Cr22Ni5Mo3N双相不锈钢高温热变形行为

利用JMatPro11.0热力模拟软件、Gleeble-3500热力模拟试验机研究了022Cr22Ni5Mo3N双相不锈钢的高温热变形行为,揭示了其在1000~1150℃,0.01~5 s^(-1)下的热变形特征。结果表明:022Cr22Ni5Mo3N双相不锈钢的热变形温度应大于脆性σ相的溶解温度,即980℃;其次,材料的流变应力随变形温度的升高和应变速率的降低而减小。基于动态材料模型构筑了材料的热加工图,并结合微观组织进行了验证。其最佳热加工窗口为1090~1125℃、0.01~0.03 s^(-1),该区域对应的组织特征为:两相组织均匀,奥氏体相发生充分动态再结晶且组织中不存在σ相;在失稳参数1100℃、5 s^(-1)条件下,组织中两相晶粒被明显拉长且再结晶比例低,相界处的析出物易诱发裂纹。因此实际加工参数应接近最佳热加工工艺窗口,避免失稳区参数及σ相的应变析出。

石粉-钢渣混凝土单轴受压应力-应变全曲线实验研究

为了探究单轴受压下石粉-钢渣混凝土的本构关系,根据正交试验方案配制了不同掺量钢渣砂(30%、40%、50%)、钢渣石(30%、40%、50%)、石粉(0%、7.5%、15%)的石粉-钢渣混凝土,对石粉-钢渣混凝土的应力-应变关系进行了实验研究,建立了单轴受压下石粉-钢渣混凝土的本构关系模型。实验结果表明:当受到单轴压力时,石粉-钢渣混凝土的破坏模式与普通混凝土相似,表现出斜剪切的特征。石粉-钢渣混凝土峰值应力、峰值应变及弹性模量随着钢渣骨料掺量的增加而提高。为了更好地模拟无量纲应力-应变曲线,本工作采用了Carreira and Chu模型的上升段和过镇海模型的下降段进行了分段拟合。结果表明,实验曲线与分段模型曲线吻合较好。

温度⁃应力耦合下聚四氟乙烯压缩蠕变行为及本构描述

聚四氟乙烯(Polytetrafluoroethylene,PTFE)具有耐高低温、耐化学腐蚀和高热稳定性等优点,已成为工业领域中不可或缺的密封材料,其压缩性能对密封结构的安全服役至关重要。通过对PTFE开展压缩试验和压缩蠕变试验,研究PTFE在不同温度下的压缩性能,探究应力、温度对蠕变行为的耦合影响规律。研究结果表明,PTFE的压缩屈服强度和压缩模量随温度的升高而降低。压缩蠕变性能受到温度和应力的耦合影响,在相同温度下,随着应力的增加,PTFE的瞬时应变和蠕变速率增加。在相同应力下,随着温度的增加,压缩模量降低,分子能量和自由体积增大,从而PTFE的瞬时应变和蠕变量增大,总应变也增大。最后,采用Burgers模型、Findley模型和时间硬化模型对PTFE在不同加载工况下的蠕变行为进行了分析,发现Burgers模型和Findley模型可以较好地描述PTFE在不同温度下的蠕变行为。本研究可以为PTFE压缩蠕变性能的密封结构设计及工程应用提供理论指导和数据支撑。

新型Cr-Mo-V型热作模具钢高温流变应力模型

通过热压缩实验,获得实验钢在变形温度为950~1200℃、应变速率为0.001~5 s^(-1)和最大真应变为0.916条件下的真应力-真应变曲线。结果表明:在本实验选取的变形条件下,新型Cr-Mo-V钢呈现出典型的动态再结晶特征,变形温度高于1050℃且应变速率低于0.1 s^(-1)时,动态再结晶特征更明显;同一变形温度下,峰值应力和峰值应变随应变速率的提高呈增大趋势;同一应变速率下,峰值应力和稳态应力随变形温度的升高逐渐降低。采用多元线性回归法获得与峰值应力对应的Arrhenius方程模型参数,基于此建立了实验钢的高温流变应力本构模型。利用创建的不同应变下本构方程材料常数的八次多项式对实验钢的流变应力进行计算,应变补偿相关系数R和平均绝对相对误差e AARE分别为0.98902和3.21%,计算数据与实验数据吻合良好。

06Cr23Ni13不锈钢的热压缩本构方程及热加工图

利用Gleeble-3500热模拟试验机研究了06Cr23Ni13不锈钢在变形温度为850~1250℃及应变速率为0.01~10 s-1条件下的热变形软化行为。结果表明:当应变速率相同时,随着变形温度的升高,06Cr23Ni13不锈钢的流变应力减小;而当变形温度相同时,流变应力值随着应变速率的增大而增大。根据Arrhenius模型构建并验证了06Cr23Ni13不锈钢的本构方程。基于动态材料模型理论绘制了06Cr23Ni13不锈钢在大变形量(ε=0.6)下的热加工图。由06Cr23Ni13不锈钢的热加工图可知在变形温度为1100~1250℃、应变速率为0.01~0.05 s-1的高温低应变区域内,能量耗散率η值可高达0.37~0.44,属于易加工区域,是最佳的热加工窗口。

Ti60合金热变形行为与应变补偿型本构模型

目的确定Ti60合金在高温下的应变行为,促进材料性能的优化和工程应用的发展。方法在变形温度为900、950、990、1020、1050℃,应变速率为0.001、0.01、0.1、1、5 s^(-1),最大变形量为60%条件下,利用Gleeble-3800热模拟实验机对Ti60试样进行不同应变速率的热压缩实验。结果Ti60合金的高温流变应力-应变规律如下:当温度一定时,随着应变速率的升高,峰值应力上升,当温度和应变速率一定时,随着应变的升高,应力表现为先上升后下降的趋势,而在1020℃、0.01 s^(-1)条件下,表现反常,这可能与第二相的动态析出有关。不同真应变下的变形激活能Q=838.9962019 kJ/mol,相应的本构方程相关系数n=2.889582,α=0.013182009,A=1.3357×10^(33),建立了Ti60合金热变形Arrhenius本构关系模型Z=εexp(838.996×10^(3))=1.3357×10^(3)[sinh(1.3182×10^(-2)σ_(p))]^(2.889582),用于预测和优化Ti60合金在高温条件下的峰值应力。采用应变补偿方法计算了五次多项式的各个系数和其他应变对应的应力。通过比较由模型计算得到的流变应力结果和实际热模拟实验数据,发现实验结果与计算结果一致,不仅验证了应变补偿方法的合理性,而且为数值模拟等相关研究提供了数据支撑。结论通过实验和模拟,对Ti60合金的高温变形行为有了更全面和更准确的认识。