The modified temperature term on Johnson-Cook constitutive model of AZ31 magnesium alloy with {0002} texture

The dynamic compression experiments with Split-Hopkinson Pressure Bar(SHPB)were performed on AZ31 magnesium alloy rolled sheet specimens in the normal direction(AZ31-ND)with{0002}texture at the temperature of 293-523 K and the strain rate of 0.001-2200 s^−1.The temperature term in Johnson-Cook(JC)constitutive model had been reasonably modified.This advantage made constitutive model promising for decribing the dynamic deformation behavior of AZ31-ND with{0002}texture more accurately.The obtained true stress-true plastic strain curves agreed well with the measured results in a wide range of strain rates and temperatures.The thermal softeninging,strain and strain rate hardening effect on the AZ31-ND with{0002}texture were discussed.The adiabatic shear band(ASB)of AZ31-ND with{0002}texture hat shaped specimen was successfully predicted by combining modified JC constitutive model and numerical simulation,which was also validated by Electron Back-Scattered Diffraction(EBSD)map under the same boundary condition.

A modified Johnson–Cook model for 7N01 aluminum alloy under dynamic condition

Tensile tests at different strain rates(0.0002, 0.002, 0.02, 1000 and 3000 s^(-1)) were carried out for 7N01 aluminum alloy. Low strain rate experiments(0.0002, 0.002 and 0.02 s^(-1)) were conducted using an electronic mechanical universal testing machine, while high strain rate experiments(1000, 3000 s^(-1)) were carried out through a split Hopkinson tensile bar. The experimental results showed that 7N01 aluminum alloy is strain rate sensitive. By introducing a correction scheme of the strain rate hardening coefficient, a modified Johnson–Cook model was proposed to describe the flow behaviors of 7N01 aluminum alloy. The proposed model fitted the experimental data better than the original Johnson–Cook model in plastic flow under dynamic condition. Numerical simulations of the dynamic tensile tests were performed using ABAQUS with the modified Johnson–Cook model. Digital image correlation was used together with high-speed photography to study the mechanical characters of specimen at high strain rate. Good correlations between the experiments results, numerical predictions and DIC results are achieved. High accuracy of the modified Johnson-Cook model was validated.

New constitutive equation utilizing grain size for modeling of hot deformation behavior of AA1070 aluminum

A new phenomenological and empirically-based constitutive model was proposed to modify the term in the original Johnson−Cook constitutive model.The new model can be used to describe and predict the flow stress of AA1070 aluminum with different initial grain sizes in the hot working process.This developed model considers thermal softening,strain-rate hardening,strain hardening,initial grain size,and interactions with each other and can correctly model the behavior of AA1070 at elevated temperature with different strains,strain rates,and initial grain sizes.The hot flow behavior of AA1070 was investigated through compression tests over wide ranges of temperature from 623 to 773 K,strain rate from 0.005 to 0.5 s−1 and initial grain size from 50 to 450μm.Results show that the initial grain size has a significant effect on the flow behavior of AA1070.Then,correlation coefficient(R),average absolute relative error(AARE),and relative error were examined for comparative predictability of the model.Results show that flow stresses for different initial grain sizes calculated by the new proposed model perfectly correlate with experimental ones,with a mean relative error of 1.19%,which confirms that the new modified Johnson−Cook relation can give a precise estimation of the hot flow stress of AA1070 aluminum by considering the initial grain size.

Constitutive models in stability analysis of rock slope

Equivalent Mohr-Coulomb yield criterion was established,and the relationship between different constitutive models was studied.The application of equivalent Mohr-Coulomb yield criterion in Ansys was achieved by means of transforming material parameters.The stability research aiming at the most common rock slope without conspicuous slide surface was accomplished,the methods of measurably assessing the stability of rock slope without conspicuous slide surface were explored,and the disadvantages of method of minimum slide-resisted reserve as dangerous slide path were pointed out.The results show that through the calculation and analysis of cases,the conception that measurable assessment of the stability of rock slope without conspicuous slide surface can be achieved under condition that equivalent Mohr-Coulomb yield criterion is validated.Its safety parameter formula is explicit in theory and credible in results.The results obtained are approximate to those obtained by using finite element intensity reducing method.

Constitutive modeling of compression behavior of TC4 tube based on modified Arrhenius and artificial neural network models

Warm rotary draw bending provides a feasible method to form the large-diameter thin-walled（LDTW）TC4 bent tubes, which are widely used in the pneumatic system of aircrafts. An accurate prediction of flow behavior of TC4 tubes considering the couple effects of temperature,strain rate and strain is critical for understanding the deformation behavior of metals and optimizing the processing parameters in warm rotary draw bending of TC4 tubes. In this study, isothermal compression tests of TC4 tube alloy were performed from 573 to 873 K with an interval of 100 K and strain rates of 0.001, 0.010 and0.100 s^（-1）. The prediction of flow behavior was done using two constitutive models, namely modified Arrhenius model and artificial neural network（ANN） model. The predictions of these constitutive models were compared using statistical measures like correlation coefficient（R）, average absolute relative error（AARE） and its variation with the deformation parameters（temperature, strain rate and strain）. Analysis of statistical measures reveals that the two models show high predicted accuracy in terms of R and AARE. Comparatively speaking, the ANN model presents higher predicted accuracy than the modified Arrhenius model. In addition, the predicted accuracy of ANN model presents high stability at the whole deformation parameter ranges, whereas the predictability of the modified Arrhenius model has some fluctuation at different deformation conditions. It presents higher predicted accuracy at temperatures of 573-773 K, strain rates of 0.010-0.100 s^（-1）and strain of 0.04-0.32, while low accuracy at temperature of 873 K, strain rates of 0.001 s^（-1）and strain of 0.36-0.48.Thus, the application of modified Arrhenius model is limited by its relatively low predicted accuracy at some deformation conditions, while the ANN model presents very high predicted accuracy at all deformation conditions,which can be used to study the compression behavior of TC4 tube at the temperature range of 573-873 K and the strain rate of 0.001-0.100 s^（-1）. It can provide guideline for the design of processing parameters in warm rotary draw bending of LDTW TC4 tubes.

基于修正Mohr-Coulomb准则的弹塑性本构模型及其数值实施

针对Mohr-Coulomb准则高估岩土体抗拉性能的局限性,建立考虑最大拉应力准则的修正Mohr-Coulomb模型;系统地论述隐式本构积分算法的主要内容,推导相应的一致性刚度矩阵。以ABAQUS软件为平台,采用向后欧拉隐式应力积分算法编制了UMAT本构程序,对单轴拉伸试验和三轴压缩试验进行数值模拟,对比分析ABAQUS自带模型和自编模型的优劣,结果表明编写的修正Mohr-Coulomb模型能够有效地反映岩土介质的抗拉性能,弥补了ABAQUS自带模型的不足。

Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory.An SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables together.The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model.Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough.However,they are too slight to be necessarily considered when the dimensionless height is large enough.The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam are.The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam.The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.

修正的Mohr-Coulomb准则在重力坝建基面抗滑稳定分析中的应用

针对有限单元法在重力坝建基面抗滑稳定控制中量化标准缺失的问题,采用自适应隐式本构积分算法推导了修正的Mohr-Coulomb准则,通过ABAQUS编写成UMAT子程序,用于重力坝建基面抗滑稳定分析,并针对典型重力坝坝型选取常见下游坝坡率,应用强度折减系数法分析了同一网格尺寸下不同坝高对建基面屈服区的影响。结果表明,在对应建基面屈服区贯通率达到15%时的强度折减系数随坝高增加而降低,且在强度折减系数小于1.8时建基面的屈服范围与坝高呈正相关,强度折减系数为1.6时具有明显的线性关系,并结合工程实例验证了结论的可靠性。

退火态增材制造AZ91D镁合金在极端条件下的力学行为

本研究使用激光选区熔化技术(Selective laser melting,SLM)制备了AZ91D镁合金(SLM-AZ91D),并对其进行去应力退火处理,采用微观组织表征与力学特性测试研究了退火态SLM-AZ91D镁合金在不同温度与应变速率等极端条件下的力学行为。结果表明:退火态SLM-AZ91D试样中主要包含α-Mg基体、β-Mg_(17)Al_(12)等相,不同区域的蜂窝结构存在明显差异,平均晶粒尺寸非常细小,仅为1.82μm,无明显织构;相较于打印态试样,退火态试样的平均显微硬度值提升了约26.7%;退火态试样的压缩流变应力在173~293 K时对温度不敏感,而在373~573 K时则表现出显著的温度软化效应;随着温度的升高,流变应力呈现下降趋势。尽管应变速率强化效应较弱,但退火态试样的流变应力仍随着应变速率的增大而逐渐增大。基于实验结果拟合了修正Johnson-Cook本构模型,该模型的计算结果与实验结果吻合较好。

渗碳热处理后18CrNiMo7–6合金钢表面变质层J–C损伤失效参数研究

合金钢在经过渗碳热处理后会在表面形成变质层。在表面变质层内,材料的力学性能沿深度方向发生变化。针对渗碳热处理后的18CrNiMo7-6合金钢的表面变质层,提出了确定Johnson-Cook损伤参数分层测试方法。通过对材料变质层进行分层线切割,得到不同变质层深度下的薄板试样;为获得不同应力三轴度下的拉伸结果,预制了不同断裂方向的拉伸剪切试样,通过试验与仿真相结合的方法,确定了考虑应变累积效应的应力三轴度并测定了材料失效应变与应力三轴度的关系;采用宽脉冲拉伸系统测定了拉伸试样的失效应变与应变率的关系。研究结果表明,同一层材料的失效应变随应力三轴度的增大而减小,在同一应力三轴度水平下,失效应变随层深增大而增大;不同层深处的试样均具有明显的应变率弱化效应,且在同一应变率水平下,失效应变随层深增大而增大;基于测量参数的拉伸过程数值仿真与试验数据的对比验证了所测定参数的准确性。

Constitutive Models for Compressive Deformation of AZ80Magnesium Alloy under Multiple Loading Directions and Strain Rates

Two constitutive models,the modified Johnson-Cook model and the logarithm linear relation model based on empirical approach and data analysis,were presented to illustrate compressive deformation of magnesium alloys AZ80 under multiple loading directions and strain rates.The results of stress-strain curve analysis and sensitivity index analysis suggested that the stress held large fluctuations in loading direction of 90°.Model testing signified that the logarithm linear relation model was more proper than the modified Johnson-Cook model in view of relative mean square error and correlation coefficients.Moreover,numerical simulation building on established models also indicated that the logarithm linear model is more precise than the modified Johnson-Cook model.

Microstructural evolution and constitutive models of 9CrMoCoB heatresistant steel during high-temperature deformation

In order to research the hot deformation behavior of 9CrMoCoB heat-resistant steel,hot compression tests were performed over a wide range of temperatures from 850 to 1150℃ and strain rates from 0.01 to 10.00 s^-1.The flow stress appears to increase with the decrease in deformation temperature and the increase in strain rate.The relationship between microstructural evolution and deformation parameters was studied,indicating that both low strain rate and high deformation temperature appear to promote the dynamic recrystallization,while excessively high temperature with low strain rate would result in the high non-uniformity of grain size.The experimental stress-strain data was applied to calculate the material constants involved in the Arrhenius-type constitutive model and the modified Zerilli-Armstrong(MZA)model,and feasibility of these two models was evaluated.The results show that the MZA model is more accurate to predict the high-temperature flow behavior of the experimental steel than the Arrhenius-type constitutive equation.

基于Arrhenius改进模型的无取向电工钢高温变形本构关系

建立无取向电工钢热轧高温行为的统一本构关系模型。基于大型工业轧机取样的无取向电工钢连续冷却转变图分析测定,采用Gleeble热模拟试验机在750~1 120℃温度范围和0.05~10 s^(-1)应变速率范围进行热模拟试验。随着温度的降低,在1 120~975℃的奥氏体区,应力随之增加;975~875℃的奥氏体-铁素体两相区内,应力随之降低;875~750℃铁素体区内,应力随之增加;铁素体区以动态回复软化机制为主,而奥氏体区以动态再结晶为主,而且变形速率越大,动态再结晶越不明显,直至仅呈现动态回复型。基于Arrhenius改进模型框架,建立描述该钢种热连轧机粗轧机组和精轧机组完整轧制过程加工硬化与软化机制的统一本构关系,可精确地预测加工材料的属性。

面板堆石坝应力变形计算中考虑土的各向异性

土体本构模型一般都将土体作为各向同性材料,应用于混凝土面板堆石坝应力变形计算时常会带来不小的误差,本文以双曲线模型为例剖析了计算中存在的问题。该模型假定从大主应力方向加荷与从小主应力方向加荷弹性模量和泊松比都相同,但真三轴仪试验表明两者有显著差异。混凝土面板中的应力是水荷载引起的,而水荷载沿坝体的小主应力方向施加,无论弹性模量还是泊松比,与荷载从大主应力方向施加都有很大的不同。各向同性的本构模型忽略了它们的差异,仅仅用大主应力方向加荷的方法来确定弹性模量和泊松比,必然会有较大误差,对混凝土面板来说就可能是不能容许的误差。文中提出了一种考虑各向异性的本构模型,它是以E-ν模型为基础,作了某些修正处理。用其对面板坝进行计算,面板应力有明显改善。

岩石损伤软化的修正本构模型

利用服从Weibull分布的岩石微元强度表示方法,基于Drucker-Prager破坏准则,通过引入损伤变量的修正系数,利用应力-应变关系曲线峰值点处的应力、应变确定Weibull分布参数的关系式,建立不同围压下的损伤软化本构模型。该模型参数较少且易于确定,其参数的确定方法揭示了模型参数的物理意义。与前人的研究成果进行对比分析,结果表明该模型比未修正前有着明显的优越性,且与实测结果吻合较好,分析结果显示出该模型的合理性。

复合改性双基推进剂黏弹性-黏塑性-黏损伤本构模型研究

为描述复合改性双基(CMDB)推进剂复杂的力学性能,推导出黏弹性-黏塑性-黏损伤本构模型。进行一系列蠕变-回复试验,获得了本构模型参数。通过不同应力水平和不同加载时间下的蠕变-回复试验和恒加载率-回复试验,验证了本构模型的有效性。结果表明:黏弹性-黏塑性-黏损伤本构模型能够预测CMDB推进剂的蠕变-回复响应和恒加载率-回复响应;与黏弹性-黏塑性本构模型相比,黏弹性-黏塑性-黏损伤模型对CMDB推进剂力学性能的预测能力明显提高;损伤变量随着应变增大,在经过缓慢增大和快速增大后逐渐趋于稳定,应变变化越慢,损伤变量越大,黏弹性-黏塑性-黏损伤模型和黏弹性-黏塑性模型的预测结果差别就越大。

修正剑桥模型的隐式积分算法在ABAQUS中的数值实施

利用大型有限元软件ABAQUS所提供的用户材料子程序UMAT接口,针对修正的剑桥本构模型开发了隐式积分算法,并且与自动选择时间步长的增量有限元方程迭代解法相结合,对正常固结土与超固结土的三轴排水与不排水试验进行了数值模拟。结果表明,所发展的隐式本构积分算法与时间步长自动选择方法具有较好的稳定性和较高的计算精度,能够得到比较合理的数值分析结果。

含气水合物沉积物弹塑性损伤本构模型探讨

天然气水合物的开采会带来一系列的岩土工程问题,为了保障相关工程设施的安全,有必要建立一个合理的水合物沉积物本构模型。通过深入分析水合物沉积物力学特点,从颗粒间的作用机制出发,认为水合物沉积物的力学响应是沉积物中土体颗粒间摩擦与水合物胶结二者共同作用的结果;考虑到摩擦与接触特性不同的力学机制,分别采用修正剑桥模型和弹性损伤模型对土体骨架及水合物胶结的应力-应变关系进行描述;通过假定水合物胶结的损伤演化规律,并认为在受力变形过程中二者的应变始终相等,初步建立了一个水合物沉积物的弹塑性损伤本构模型。不同水合物饱和度沉积物应力-应变曲线的模型预测结果与室内三轴排水试验结果吻合良好,表明了所建模型的可行性和合理性。

温度周期作用下大理岩三轴蠕变试验与理论模型研究

为了解温度周期作用对大理岩蠕变力学特性的影响,采用温度-应力-渗流耦合的岩石力学三轴流变试验系统对大理岩进行了不同温度及温度周期变化下三轴压缩蠕变试验。基于试验结果,研究了大理岩试样在不同温度及温度周期变化下轴向应变随时间的变化规律,分析了不同温度及温度周期变化下蠕变的变形机制,掌握了温度对大理岩三轴蠕变影响的基本规律,并且建立了考虑温度及温度周期变化影响的改进的Burgers模型。理论值与试验结果非常接近,表明考虑温度及温度周期变化的改进Burgers模型适合描述大理岩的黏弹性蠕变特征。为长期暴露于外部环境下的岩质边坡的长期稳定性分析提供了重要的参考依据。

金属铍的压缩变形行为

利用材料试验机及Hopkinson杆装置系统开展热等静压金属铍在不同温度下的静动态压缩力学行为研究,获得了温度、应变率对金属铍屈服强度和加工硬化行为的影响规律。结果表明:金属铍在压缩应力状态下呈现出良好的塑性,同时其力学性能具有显著的应变率敏感性与热软化效应,屈服强度和流动应力随应变率提高呈明显增大趋势,随着温度升高逐渐降低。同时,室温下其加工硬化行为随着应变增大表现为分段硬化特征,随温度升高则趋于理想塑性。最后,采用修正的Johnson-Cook本构模型对实验结果进行了拟合,模型计算结果与实验结果吻合较好。