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.

Effects of constitutive parameters on adiabatic shear localization for ductile metal based on JOHNSON-COOK and gradient plasticity models

By using the widely used JOHNSON-COOK model and the gradient-dependent plasticity to consider microstructural effect beyond the occurrence of shear strain localization,the distributions of local plastic shear strain and deformation in adiabatic shear band(ASB)were analyzed.The peak local plastic shear strain is proportional to the average plastic shear strain,while it is inversely proportional to the critical plastic shear strain corresponding to the peak flow shear stress.The relative plastic shear deformation between the top and base of ASB depends on the thickness of ASB and the average plastic shear strain.A parametric study was carried out to study the influence of constitutive parameters on shear strain localization.Higher values of static shear strength and work to heat conversion factor lead to lower critical plastic shear strain so that the shear localization is more apparent at the same average plastic shear strain.Higher values of strain-hardening exponent,strain rate sensitive coefficient,melting point,thermal capacity and mass density result in higher critical plastic shear strain,leading to less apparent shear localization at the same average plastic shear strain.The strain rate sensitive coefficient has a minor influence on the critical plastic shear strain,the distributions of local plastic shear strain and deformation in ASB.The effect of strain-hardening modulus on the critical plastic shear strain is not monotonous.When the maximum critical plastic shear strain is reached,the least apparent shear localization occurs.

Identification of constitutive model parameters for nickel aluminum bronze in machining

The material of nickel aluminum bronze (NAB) presents superior properties such as high strength, excellent wear resistance and stress corrosion resistance and is extensively used for marine propellers. In order to establish the constitutive relation of NAB under high strain rate condition, a new methodology was proposed to accurately identify the constitutive parameters of Johnson?Cook model in machining, combining SHPB tests, predictive cutting force model and orthogonal cutting experiment. Firstly, SHPB tests were carried out to obtain the true stress?strain curves at various temperatures and strain rates. Then, an objective function of the predictive and experimental flow stresses was set up, which put the identified parameters of SHPB tests as the initial value, and utilized the PSO algorithm to identify the constitutive parameters of NAB in machining. Finally, the identified parameters were verified to be sufficiently accurate by comparing the values of cutting forces calculated from the predictive model and FEM simulation.

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.

Flow stress behavior and constitutive modeling of 20MnNiMo low carbon alloy

The hot deformation behavior of 20 Mn Ni Mo low carbon alloy was investigated by isothermal compression tests over wide ranges of temperature(1223-1523 K) and strain rate(0.01-10 s^(-1)). According to the experimental true stress-true strain data, the constitutive relationships were comparatively studied based on the Arrhenius-type model, Johnson-Cook(JC) model and artificial neural network(ANN), respectively. Furthermore, the predictability of the developed models was evaluated by calculating the correlation coefficient(R) and mean absolute relative error(AARE). The results indicate that the flow stress behavior of 20 Mn NiM o low carbon alloy is significantly influenced by the strain rate and deformation temperature. Compared with the Arrhenius-type model and Johnson-Cook(JC) model, the ANN model is more efficient and has much higher accuracy in describing the flow stress behavior during hot compressing deformation for 20 Mn Ni Mo low carbon alloy.

Dynamic Constitutive Model of Physical Simulation in High-Speed Blanking for C5191 Phosphor Bronze

Strain hardening,strain rate strengthening and thermal softening data of C5191 phosphor bronze at highspeed blanking are not easy to be obtained with a general measure method,therefore,it is quite difficult to establish the dynamic constitutive model.To solve this problem,the tensile properties at a strain rate of 1 s^(-1) by GLEEBLE-3500,and dynamic tensile conditions at strain rates of 500,1 000 and 1 500 s^(-1) by split Hopkinson tensile bar (SHTB) apparatus are studied.According to these test data,the classic Johnson-Cook equation is modified.Furthermore,the modified Johnson-Cook equation is validated in the physical simulation model of high-speed blanking.The results show that the strength of C5191 phosphor bronze maintains a certain degree of increase as the strain rate increasing and presents a clear sensitivity to strain rate.The modified Johnson-Cook equation,which has better description accuracy than the classical Johnson-Cook equation,can provide important material parameters for physical simulation models of its high-speed blanking process.

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Johnson-Cook模型的C5191-H磷青铜高速冲裁本构关系

针对高速冲裁过程中材料的应变硬化、应变速率强化、热软化效应数据难以获取,无法建立物理仿真动态模型的问题,利用Gleeble-3500热模拟试验机和分离式Hopkinson拉杆装置对C5191-H磷青铜分别进行应变速率为1、500、1000和1500 s-1、温度为20~400℃的拉伸试验,利用试验数据拟合并修正了经典的Johnson-Cook动态方程,并在高速冲裁数值模拟中验证了修正后的本构方程的有效性。结果表明:C5191-H磷青铜拉伸变形时呈现出明显的应变硬化和应变速率敏感性;利用试验数据拟合并修正应变强化项的Johnson-Cook动态本构模型,此模型具有较高的大应变、高速率、热效应本构关系描述精度,并能较好地描述该材料的高速冲裁物理仿真过程。

基于修正Johnson-Cook模型和再结晶模型的A356铝合金高温流变行为

为研究A356铝合金的高温流变行为和组织演变,构建能准确描述其高温流变行为的本构模型,在变形温度分别为450、475、500和525℃,应变速率分别为0.001、0.01、0.1、1.0和10 s^(-1)条件下对A356铝合金进行热压缩实验。结果表明,A356铝合金高温流变应力曲线表现出典型的动态回复和动态再结晶特征;随变形温度的升高和应变速率的增加,α-Al变形程度先增加后减弱。利用修正Johnson-Cook本构模型和再结晶模型建立了可以准确描述A356铝合金高温流变行为的分段模型,并引入相关系数R和平均相对误差AARE对模型的准确性进行了分析,验证了模型的可行性。

基于修正Johnson-Cook本构模型的BFe10-1.6-1白铜合金高温流变行为

为了研究BFe10-1.6-1白铜合金的高温流变行为,采用Gleeble-3800热模拟试验机在变形温度分别为1023、1073、1123、1173、1123和1273 K,应变速率分别为0.001、0.01、0.1、1.0和10 s^(-1)的条件下对BFe10-1.6-1白铜合金进行了热压缩试验,建立了BFe10-1.6-1铜合金的Johnson-Cook本构模型。利用试验应力-应变数据建立了Johnson-Cook本构方程和修正Johnson-Cook本构方程。将所建立的方程预测的流变应力与试验数据进行了对比。引入相关系数R和平均绝对相对误差e_(AARE)验证了修正Johnson-Cook本构方程的准确性。R和e_(AARE)值分别为0.985和6.57%。结果表明,修正Johnson-Cook本构模型能够精确预测大多数变形条件下的流变应力。BFe10-1.6-1白铜合金的主要高温软化机制为动态回复。

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.

基于修正Johnson-Cook本构模型的奥氏体不锈钢高温流变行为

文章研究了修正的Johnson-Cook(m-JC)本构模型对304奥氏体不锈钢高温流变行为的表征能力。利用不同温度、应变和应变速率等温热压缩试验的试验真应力-应变数据来计算本构模型的材料常数,建立了关于304奥氏体不锈钢的m-JC本构模型。通过比较预测结果的相关系数、平均相对误差以及均方差,评估了模型的适用性。结果表明,修正的JC模型预测结果和试验结果之间的平均相对误差绝对值为6.77%,相关系数为0.987,均方差为11.2 MPa,m-JC本构模型可以较为准确的描述304奥氏体不锈钢的流变行为。

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。

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。