A model of one-surface cyclic plasticity and its application to springback prediction

This paper presents an elasto-plastic constitutive model based on one-surface plasticity, which can capture the Bauschinger effect, transient behavior, permanent softening, and yield anisotropy. The combined isotropic-kinematic hardening law was used to model the hardening behavior, and the non-quadratic anisotropic yield function, Yld2000-2d, was chosen to describe the anisotropy. This model is closely related to the anisotropic non-linear kinematic hardening model of Chun et al. [2002. Modeling the Bauschinger effect for sheet metals, part I: theory. International Journal of Plasticity 18, 571-95.]. Different with the model, the current model captures in particular permanent softening with a constant stress offset as well as the Bauschinger effect and transient behavior under strain path reversal. Inverse identification was carried out to fit the material parameters of hardening model by using uni-axial tension/compression data. Springback predicted by the resulting material model was compared with experiments and with material models that do not account for permanent softening. The results show that the resulting material model has a good capability to predict springback.     

Creep of brazed plate-fin structures in high temperature compact heat exchangers

In recent years, the need for high temperature heat exchangers to improve the efficiency of power and chemical conversion systems has been growing. However, the creep design of the high temperature compact heat exchangers has been a primary concern because the working temperature can be well above the creep limit of the materials. To establish the high temperature design criterion for compact heat exchangers, creep behavior of the plate-fin structures and brazed joints are investigated in this paper. The time-dependent deformation and bending stress of the plate-fin structures are obtained analytically by simplifying the fins to elastic springs. The creep damage evolution inside the brazed joint is studied by coupling the finite element method with a damage constitutive equation. The significant effect of creep property mismatch in the brazed joint on the creep strength is demonstrated.     

Creep of brazed plate-fin structures in high temperature compact heat exchangers

In recent years, the need for high temperature heat exchangers to improve the efficiency of power and chemical conversion systems has been growing. However, the creep design of the high temperature compact heat exchangers has been a primary concern because the working temperature can be well above the creep limit of the materials. To establish the high temperature design criterion for compact heat exchangers, creep behavior of the plate-fin structures and brazed joints are investigated in this paper. The time-dependent deformation and bending stress of the plate-fin structures are obtained analytically by simplifying the fins to elastic springs. The creep damage evolution inside the brazed joint is studied by coupling the finite element method with a damage constitutive equation. The significant effect of creep property mismatch in the brazed joint on the creep strength is demonstrated.     

Numerical modeling of nonlinear deformation of polymer composites based on hyperelastic constitutive law

Fiber reinforced polymer (FRP) composites exhibit nonlinear and hyperelastic characteristics under finite deformation. This paper investigates the macroscopic hyperelastic behavior of fiber reinforced polymer composites using a micromechanical model and finite deformation theory based on the hyperelastic constitutive law. The local stress and deformation of a representative volume element are calculated by the nonlinear finite element method. Then, an averaging procedure is used to find the homogenized stress and strain, and the macroscopic stressstrain curves are obtained. Numerical examples are given to demonstrate hyperelastic behavior and deformation of the composites, and the effects of the distribution pattern of fibers are also investigated to model the mechanical behavior of FRP composites.     

基于虚拟制备的金属橡胶各向异性本构特性研究

金属橡胶是一种各向异性的多孔材料,其本构特性常靠人工经验或试验获得,内部复杂的螺旋网状结构无法通过测试手段弄清机理。为此,运用虚拟制备技术与数值动态重构等手段,深入探究金属橡胶内部空间几何拓扑结构和弹簧微元间接触摩擦机理,结合扫描电子显微镜（Scanning electron microscope,SEM）中材料的微观形态进一步解释金属橡胶在宏观上的各向异性力学行为。通过引入弹簧微元组合概率分布以及空间局域性孔隙分布的概念,有效表征金属橡胶材料内部弹簧微元无序式网格互穿结构。充分考虑金属橡胶细观上的空间拓扑结构与微观摩擦机理参量,以及包含了材料形状、相对密度、金属丝直径、螺旋卷螺距、金属丝弹性模量等宏观制备参数,构建能够反映金属橡胶细观结构特征与宏观性能相一致的各向异性本构模型。通过与材料准静态压缩试验结果对比分析,采用残差分析定量验证。结果表明,提出的金属橡胶各向异性的本构模型,能够有效地反映与预测金属橡胶材料的复杂各向异性力学行为,为材料的深入研究与应用普及提供一定的理论指导。     

A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels)

The determination of residual stresses induced by welding or heat treatment operations requires the use of complex models taking into account thermal, metallurgical and mechanical phenomena. In this paper, we propose a mechanical model in which each phase can follow its own constitutive law. This model also takes into account phase transformation plasticity, which is treated independently of the behavior of each phase. This model has been implemented into the French FEM code Castem 2000. The interest of the proposed method is that it allows one to mix any type of nonlinear behavior using Taylor homogenization hypothesis. There is no need to develop a theory to get the equations of the homogenized material law. Two numerical examples demonstrate the efficiency and the flexibility of this approach. The results obtained are compared to experimental values for a typical welding situation and a high-temperature response. This comparison seems to indicate that viscous effects in the materials have a significative influence on the residual stresses produced by welding.     

板翅式热管散热器充液率、倾角对冷板温度场的影响

动车牵引变流器用板翅式热管散热器由于结构的特殊性,在倾斜时充液率、倾角对空腔冷板温度场的分布影响较大,试验难以实现对此的研究。因此,本文通过建立数学模型,采用ICEPAK数值模拟软件,以实际模型的板翅式热管散热器为例,分析了充液率,倾斜角度对散热器有效传热面积比,冷板温度场分布的影响,得到该散热器的最佳充液率范围为0.5~0.6。     

Modeling and free vibration behavior of rotating composite thin-walled closed-section beams with SMA fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy(SMA) fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton’s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin’s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.     

槽道板结构的应力分析方法

分析板翅式换热器和微换热器的基本结构,通过引入小挠度薄板理论和弹性支承结构模型,解析计算槽道板结构的弯曲变形和弯曲应力,然后将这种分析法拓展到多层槽道板结构,进而利用有限元方法对其进行对比验证分析.结果表明,应用小挠度薄板理论和弹性支承结构模型分析槽道板结构的变形和应力具有较好的精度,为微小型装置或具有槽道结构设备的应力分析提供一种有效的方法和依据.     

压电复合悬臂梁非线性模型及求解

基于功能材料的复合悬臂梁涉及多物理场耦合,其本构关系的非线性影响悬臂梁的输出及控制精度,采用Helmholtz Gibbs自由能关系建立压电材料的非线性本构模型。基于Boltzmann原理,该模型的内核函数由热能和Gibbs能量平衡决定。将模型与悬臂梁结构进行耦合,利用边界和初始条件导出压电复合悬臂梁的强解形式,并对强解进行弱化,采用Galerkin法对弱解进行离散化,利用三次B样条函数得到悬臂梁的数值解。研究结果表明,与已有文献的实验进行比较,所建立的压电材料非线性本构模型能够较好地预测复合悬臂梁的行为。     

Prediction of anisotropic material behavior based on multiresolution continuum mechanics in consideration of a characteristic length scale

New advanced materials have received more attention from many scientists and engineers because of their outstanding chemical, electrical, thermal, optical, and mechanical properties. Since the design of advanced material by experiments requires high cost and time, numerical approaches have always been of great interest. In this paper, finite element analysis of anisotropic material behavior has been carried out based on a multiresolution continuum theory. Gurson-Tvergaard-Needleman (GTN) damage model has been applied as a constitutive model at macroscale. Effects of plastic anisotropy on deformation behavior are assessed using Hill??s 48 yield function for anisotropic material and von Mises yield function for isotropic material, respectively. The material parameters for both isotropic and anisotropic damage models have systematically been determined from microstructure through unit cell modeling. The newly proposed linear approximation of local velocity gradient resolved the underdetermined problem of the previous homogenization process. Anisotropic material behaviors of a tensile specimen have been investigated by the proposed multiresolution continuum theory.     

柔性立管内衬层的非线性力学行为分析

由于聚合物材料的黏弹性,柔性立管内衬层易发生蠕变而"嵌入"至骨架层沟槽中,这一现象可能造成立管结构完整性缺失和骨架层撕裂等安全隐患,但现有的分析理论及有限元模型中,对材料的性质均是做了简单的线性假设,并未考虑聚合物材料的非线性黏弹性特性。基于PA11的试验测试结果,分别采用时间硬化非线性本构模型和考虑时温影响的多重积分非线性本构模型来表征材料性质,并对比两种模型与试验数据拟合情况。根据内衬层与骨架层的真实结构建立二维有限元数值模型,采用两种理论模型进行结构的非线性蠕变行为分析及对比。结果表明：非线性蠕变本构模型能够在在非稳态阶段和存在温度梯度的条件下,更加准确地预测的结构关键部位应变和应力,可为柔性立管内衬层的设计及评估提供借鉴和参考。     

CrMnFeCoNi高熵合金拉伸断裂的晶体塑性有限元模拟

CrMnFeCoNi高熵合金的优异力学性能使其具有广阔的工程应用前景。材料力学行为的本构描述对其工程服役行为的安全评估至关重要,但是描述CrMnFeCoNi高熵合金拉伸断裂行为的本构模型少见报道。基于晶体塑性本构模型,利用Cohesive单元在多晶代表性体积单元内部植入含损伤破坏机制的晶界,模拟了CrMnFeCoNi高熵合金在单轴拉伸下的晶间断裂过程。模拟结果与试验所得的应力-应变曲线吻合较好,且能准确描述断裂发生时的应力下降过程,说明采用晶体塑性本构模型与Cohesive本构模型可以有效描述材料的宏观响应行为和断裂失效行为。进一步分析表明：裂纹从应力集中处开始萌生;随着应变的持续增加,裂纹沿着晶界扩展,最终造成断裂;晶粒随机取向对裂纹萌生位置与扩展路径有显著影响,但对宏观拉伸应力-应变曲线几乎没有影响。     

A thermal design method for the performance optimization of multi-stream plate-fin heat exchangers

An optimization design method based on field synergy principle is developed for Multi-stream plate-fin heat exchangers (MPHEs) with a segmented differential model. The heat exchanger is divided into a number of sub-exchangers along the main stream, and each sub-exchanger consists of N passages along the height of the exchanger. Compared with the traditional heat exchanger design, this method allows temperature and pressure fields to be obtained via coupling calculation with consideration of variable physical properties and the axial heat loss of the heat exchanger. Finally, the heat exchanger is optimally designed using a temperature-difference uniformity optimization factor based on field synergy principle. This design model can provide an accurate temperature field and pressure field, because the stream properties are determined by the mean temperature and pressure of each local sub-exchanger. Optimum results indicate that the temperature distribution on the cross section of the heat exchanger is relatively uniform and that the temperature difference of heat transfer for each stream is always a small value. These characteristics prove the feasibility and effectiveness of this design model. In this paper, a case of five stream plate-fin heat exchangers for an ethylene plant is designed under a practical cold box operating condition with the proposed model, the structure and heat transfer of which are optimally determined. The design model and optimization method proposed in this work can provide theoretical and technical support to the optimization design of MPHEs.

     

A new hardening rule for metallic foam plasticity

Metallic foams are a class of porous materials widely used in the industry because of their advantages. In recent years, extensive studies on the behavior of these materials have been conducted. Several constitutive equations have also been presented and applied. This study proposes a new constitutive equation that predicts metallic foam behavior using the stress–strain curve in uniaxial compression. The proposed model offers a new functionality for work hardening and is evaluated for both isotropic and combined hardening. The constitutive equations are implemented in MATLAB and integrated using return mapping algorithm. The material parameters are identified using genetic algorithm and through a comparison of the experimental and numerical results. The aluminum foams discussed in this paper are the commercially available types, Foaminal and Alporas. The comparison of numerical and experimental results indicate that this new constitutive equation predicts foam behavior in a reasonable manner. Moreover, a good agreement is observed between the experimental and computational curves.     

Inelastic constitutive models for the simulation of a cyclic softening behavior of modified 9Cr-lMo steel at elevated temperatures

In this paper, the inelastic constitutive models for the simulations of the cyclic softening behavior of the modified 9Cr-1Mo steel, which has a significant cyclic softening characteristic especially in elevated temperature regions, are investigated in detail. To do this, the plastic modulus, which primarily governs the calculation scheme of the plasticity, is formulated for the inelastic constitutive models such as the Armstrong-Frederick model, Chaboche model, and Ohno-Wang model. By implementing the extracted plastic modulus and the consistency conditions into the computer program, the inelastic constitutive parameters are identified to present the best fit of the uniaxial cyclic test data by strain-controlled simulations. From the computer simulations by using the obtained constitutive parameters, it is found that the Armstrong-Frederick model is simple to use but it causes significant overestimated strain results when compared with the Chaboche and the Ohno-Wang models. And from the ratcheting simulation results, it is found that the cyclic softening behavior of the modified 9Cr-1Mo steel can invoke a ratcheting instability when the applied cyclic loads exceed a certain level of the ratchet loading condition.     

A constitutive model for polyurethane foam with strain rate sensitivity

The present work investigates the strain rate dependent behavior of polyurethane foams and formulates a new constitutive model in order to improve the fit of the experimental data at various strain rates. The model has seven parameters that are decided by quasi-static compression tests at two strain rates. Two models for low and high density polyurethane foams are shown to give stress strain relation at various strain rates. Dynamic compression tests were carried out to give stress strain data at high strain rate and the results are compared with those of the constitutive model.