Characterization of micro- to macroscopic deformation behavior of amorphous polymer with heterogeneous distribution of microstructures

In the present study, we clarify the micro- to macroscopic deformation behavior of an amorphous polymer with a slightly heterogeneous distribution of molecular chains; in other words, the distribution of the initial shear strength of the polymer. The micro- to macroscopic deformation behaviors of polymer under macroscopically uniform tension and shearing, uniaxial extension of a plane strain block and surface deformation of the plane strain block under compression were investigated by means of computational simulation with the nonaffine molecular chain network model. The results revealed the onset of microscopic shear bands emanating from slightly weak points and their evolution, and the interaction and percolation of new shear bands. The effects of distribution patterns and standard deviation of initial shear strength on the deformation, the interaction of weak points, the transition from microscopic shear band formation to macroscopic neck propagation and the evolution of surface undulation under compression have been demonstrated.     

Numerical evaluation of micro- to macroscopic mechanical behavior of carbon-black-filled rubber

We investigate the characteristic deformation behavior of rubber with carbon black (CB) filler. The deformation behaviors of a plane strain rubber unit cell containing CB fillers under monotonic and cyclic strain are investigated by computational simulation with a nonaffine molecular-chain network model. The results reveal the substantial enhancement of the resistance of the rubber to macroscopic deformation, which is caused by the marked orientation hardening due to the highly localized deformation in the rubber. The disentanglement of the molecular chain during the deformation of rubber results in the magnification of the hysteresis loss, i.e., the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes. The increase in volume fraction and in aggregation of the distribution of CB substantially raises the resistance of the rubber to deformation and hysteresis loss. The effect of the heterogeneous distribution of the initial average number of segments of molecular chains on the hysteresis loss has been clarified.     

Effective mechanical behavior of hyperelastic honeycombs and two-dimensional model foams at finite strain

The aim of the present study is the analytical and numerical determination of the effective stress–strain behavior of solid foams made from hyperelastic materials in the finite strain regime. For the homogenization of the microstructure, a strain energy-based concept is proposed which assumes macroscopic mechanical equivalence of a representative volume element for the given microstructure with a similar homogeneous volume element if the strain energy of both volume elements is equivalent, provided that the volume average of the deformation gradient is equal for both volume elements. The concept is applied to an analysis of hyperelastic solid foams using a two-dimensional model. The effective stress–strain behavior is analyzed under uniaxial and biaxial loading conditions in the tensile and in the compressive range as well as under simple shear deformation. It is observed that the effective mechanical behavior of cellular solids at infinitesimal and finite deformation is essentially different on both, the quantitative and the qualitative level.     

Computational evaluation of strain-rate-dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining

The molecular chain network model for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior are used to derive a constitutive equation for rubber. The new eight-chain-like model contains eight standard models consisting of Langevin springs and dashpot to account for the interaction of chains with their surroundings. Monotonic and cyclic deformation behavior of rubber with relaxation under different strain rates have been examined. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes. The validity of the results is checked through comparison with experimental results. The deformation behaviors of a plane strain rubber unit cell containing carbon-black (CB) under monotonic and cyclic straining are investigated by computational simulation using the proposed constitutive equation and homogenization method. The results reveal the substantial enhancement of the resistance of CB-filled rubber to macroscopic deformation, which is caused by the marked orientation hardening due to the highly localized deformation of rubber. The role of strain rate sensitivity on such characteristic deformation behaviors as increases in the resistance to deformation, hysteresis loss, and the effects of the distribution morphology and the volume fraction of CB on the deformation behavior is clarified. The increases in the volume fraction and in the aggregation of the distribution of CB substantially raise the resistance to deformation and hysteresis loss.     

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.     

Computational characterization of micro- to mesoscopic deformation behavior of semicrystalline polymers

In the present study, we clarify the micro- to mesoscopic deformation behavior of semicrystalline polymers by the finite element homogenization method. The crystalline plasticity theory using a penalty method for the inextensibility constraint in the chain direction and the nonaffine molecular chain network theory were used to the representation of the deformation behavior of crystalline and amorphous phases, respectively, in the composite microstructure of a semicrystalline polymer. Various directional tensions are applied to the two-dimensional plane-strain unit cell model of a composite microstructure. The results reveal a highly anisotropic deformation behavior caused by the rotation of the chain direction and lamella interface, which depends on tensile direction and manifests as substantial hardening/softening in the early stage of deformation. The mesoscopic structure of a semicrystalline polymer was modeled using a voronoi polygon comprised of composite microstructures with different lamella interface directions. The initial isotropy of the response of the mesoscopic scale was verified. Due to their interaction with the surrounding grains, the individual grains of the mesoscopic scale show a conservative response as compared with that of the unit cell, and a very nonuniform response depending on the location of the respective grain is observed; these are typical of the mesoscopic response of semicrystalline polymers.     

射频器件超细引线键合工艺及性能研究

作为有源相控阵雷达的关键组成部分,T/R （Transmitter and receiver）组件的尺寸与性能决定着装备的重量和功能。引线键合是T/R组件中常用的互连技术之一,随着组件集成度的提高势必也要开发相应的高密度引线键合技术,这使得键合线的尺寸越来越小,而超细的引线会使焊点力学性能降低,造成可靠性下降等问题。采用超声热压楔形键合的方法实现了的超细金丝与金焊盘的连接,并对工艺进行优化。结果表明,随键合压力、键合时间和超声功率的增大,键合后引线形变量逐渐增大,而键合后金丝的拉力先增加后减小,且工艺参数对金带形变量的影响小于金丝;由于第二焊点作用力过大会导致引线形变量较大、最大拉力小于第一焊点,需增加题焊点数量;最后,通过正交试验方法获得了金线和金带的最佳键合工艺参数,实现了超细尺寸引线的键合,对T/R组件的小型化具有重要意义。     

大锻件控性锻造过程的计算机模拟技术

提出能够模拟大锻件空洞型缺陷演化和微观组织演变等控性指标的数值模拟方法。基于典型体元模型建立空洞体积变化与宏观应力应变场关系的数学模型,以图从多尺度角度揭示宏观的塑性变形及其应力状态对随机分布的微小空洞的体积变化影响规律。将该模型与有限元法集成,当锻件内任意一点有空洞型缺陷(给定缺陷体积百分比)时,能够模拟得到成形过程中空洞型缺陷的体积变化,从而可被用来评估含缩孔缩松缺陷材料的压实状态。采用元胞自动机方法建立一种转子钢的微观组织演变模拟方法,根据"应变—位错密度—动态再结晶—流动应力"之间的宏微观相互影响规律,模拟出动态再结晶晶粒尺寸和完成分数。将这些模型与热力耦合有限元法相结合,构造大锻件控性锻造过程的数值模拟技术。根据大锻件增量成形的变形特点开发基于刚性区自由度凝聚技术的快速有限元法,从而为大锻件成形的工艺优化提供有效的计算工具。     

An internal state variable plasticity-based approach to determine dynamic loading history effects on material property in manufacturing processes

Worked materials in large deformation processes such as forming and machining experience a broad range of strain, strain rate, and temperatures, which in turn affect the flow stress. However, the flow stress also highly depends on many other factors such as strain path, strain rate and temperature history. Only a model that includes all of these pertinent factors is capable of predicting complex stress state in material deformation. In this paper, the commonly used phenomenological plasticity models (Johnson–Cook, Usui, etc.) to characterize material behavior in forming and machining were critically reviewed. Although these models are easy to apply and can describe the general response of material deformation, these models lack the mechanisms to reflect static and dynamic recovery and the effects of load path and strain rate history in large deformation processes. These effects are essential to understand process mechanisms, especially surface integrity (residual stress, microhardness, and microstructure) of the manufactured products.As such a dislocation-based internal state variable (ISV) plasticity model was used, in which the evolution equations enable the prediction of strain rate history and temperature history effects. These effects can be quite large and cannot be modeled by the equation-of-state models that assume that stress is a unique function of the total strain, strain rate, and temperature, independent of the loading path. The temperature dependence of the hardening and recovery functions results in the prediction of thermal softening during adiabatic temperatures rises, which are common in metal forming and machining.The dynamic mechanical behaviors of three different benchmark work materials, titanium Ti-6Al-4V, AISI 52100 steel (62 HRc), and aluminum 6061-T6, were modeled using the ISV approach. The material constants were obtained by using a nonlinear regression-fitting algorithm in which the stress–strain curves from the model were correlated to the experiments at different (extreme) temperatures. Then the capabilities of the determined material constants were examined by comparing the predicted material flow stress with the test data at different temperatures, strains, and strain rate history. The comparison demonstrates that the internal state variable plasticity model can successfully recover dynamic material behavior at various deformation states including the loading path effect. In addition, thermal softening due to adiabatic deformation was also captured by this approach.     

双相不锈钢各组相循环变形行为的纳米压痕试验和有限元表征方法研究

对双相不锈钢的奥氏体相和铁素体相,分别开展了不同加载模式（接触载荷和压入位移）和不同加载波形下的单向、循环纳米压痕试验,对比分析了两相的基本力学性能和压痕循环变形行为的演化规律。基于压痕试验结果和修正ABDEL-KARIM-OHNO非线性随动硬化准则的弹塑性本构模型,提出一套双相不锈钢奥氏体相和铁素体相的塑性和循环塑性行为的本构模型参数表征方法。通过对微结构代表性体积单元整体拉伸和循环变形行为进行模拟,并与宏观试验结果对比,验证了参数表征方法的合理性。研究结果表明,铁素体相的强度、硬度和抗棘轮变形的能力均高于奥氏体相,两相之间通过晶界产生一定的交互作用;在接触载荷控制的循环加载条件下,奥氏体相与铁素体相均产生明显的压痕棘轮现象,且载荷水平越高压痕棘轮变形程度越大;所发展的本构模型参数表征方法可为研究多相材料各组相、小体积材料的循环变形行为提供借鉴和参考。     

A tensile test device for in situ atomic force microscope mechanical testing

The microstructure and mechanical behavior of polymeric-based materials can be controlled at the micro- and nanometer length scales through blending, copolymerization, and the incorporation of micro- and nanometer particles. To facilitate the study of morphology, deformation mechanisms, and mechanical properties of micro- and nanocomposite materials, a tensile testing machine with an integral commercial atomic force microscope (AFM) was designed and built. This testing machine determines the macroscopic stress–strain behavior of materials under different controlled loading conditions, and simultaneously allows the microscopic structure changes to be observed using the AFM.     

Modeling and estimation of deformation behavior of particle-reinforced metal–matrix composite

In order to estimate the characteristic feature of the deformation behavior of materials with a length scale, the strain gradient plasticity theories, corresponding variational principle and a finite element method are given. Then the finite element method is applied to the estimation of the mechanical characteristics of the particle reinforced metal–matrix composites modeled under plane strain conditions. The effects of the volume fraction, size and distribution pattern of the reinforcement particles on the macroscopic mechanical property of the composite are discussed. It has been clarified that the deformation resistance of the composite is substantially increased with decreasing particle size under a constant volume fraction of the reinforcement material. The main cause of the increase of the deformation resistance in the plastic range is the high strain gradient appearing in the matrix material, which increases with the reduction of the distance between particles.     

机械形体热变形非相似性特征的机理分析与实验验证

在微观层面建立铝材料正方体纳米原子模型,采用结合修正莫斯势能的分子静力学理论和算法,对其进行仿真求解,对形体热变形机理给予了科学的论证,并给出宏观热变形实验结果。微观分析与宏观实验从机理理论和实验两个层面论证了机械形体热变形非相似性特征的客观存在,弥补了机械形体热变形非相似性特征长期局限于实验验证的缺陷,完善了机械形体热变形理论基础。同时,将分子静力学理论引入对热膨胀机理的研究中,拓展了热变形理论研究思路。     

Discussion of cyclic plasticity and viscoplasticity of single crystal nickel-based superalloy in large strain analysis: comparison of anisotropic macroscopic model and crystallographic model

The inelastic behavior of nickel-based superalloy is investigated in detail by application of a macroscopic anisotropic plasticity model developed here, and the results are compared to predictions based on crystal plasticity, which incorporates the kinematic hardening. Uniaxial deformation processes and simple shear deformations at large strain are considered. The plastic spin concept coupled with an anisotropic Chaboche model is provided in the framework of macroscopic viscoplasticity. The plastic spin formulation used here is based on the concept of the noncoaxiality between the stress and plastic rate of deformation. The present model succeeds in reproducing the inelastic behavior during large deformation. It is shown that the plastic spin associated with the anisotropic flow rule plays a key role in the macroscopic model. Simulation results find these two different scale models provide similar predictions under uniaxial deformation for [0 0 1] and [1 1 1] orientation, while their predictions for simple shear deformation at large strain exhibit quantitative difference, but their trends are the same. The interpretations for simulation results are pursued in detail.     

Micro- to macroscopic responses of a glass particle-blended polymer in the presence of an interphase layer

A multi-scale model which can be used to evaluate the interaction between a microstructure and the heterogeneous deformation behavior of ternary composites on the micro- to macroscopic scale has been developed based on the large deformation finite element homogenization method. Using four different interphases consisting of a rubber, two different types of polymer and an elastic material with intermediate stiffness of particle and matrix, the elasto-plastic behaviors of the composites have been confirmed to be markedly influenced by the interphase properties and the interphase with a stiffness well below that of the matrix shows a suitable effect on the micro- to macroscopic deformation behaviors of the composites. Therefore, a computational simulation has been performed for the present interphase to clarify the effects of the macroscopic strain ratio, interphase properties and particle volume fraction on macroscopic characteristics such as deformation resistance, elasticity modulus and yield stress, and on microscopic characteristics such as shear band pattern, mean stress in the matrix and normal stress on the particle surface. The results provide guidelines for selecting interphase properties and processing parameters to achieve desired overall composite characteristics.     

小变形循环载荷下Q235材料特性的试验研究

为进一步挖掘材料的承载能力,以焊接结构常用材料Q235为研究对象,通过应变控制下的循环加载试验,得到了Q235在小变形量循环载荷作用下的应力应变曲线及特征,应力随循环周次的变化规律,并给出了相应的数学模型。试验结果表明,Q235在小应变对称循环载荷作用下表现出循环硬化特性和包申格效应,随循环周次的增加,循环硬化速率和包申格能量参数变化率最终均会达到一个稳定值;Q235在小应变非对称循环载荷作用下的变形特征,可以看作是其对应变初值和对称应变循环载荷叠加作用的响应,且随循环周次的增加,材料响应应力峰值与屈服应力逐渐回归于相同幅值对称应变作用下的相应数值。     

Influence of porosity on cavitation instability predictions for elastic–plastic solids

Cavitation instabilities have been found for a single void in a ductile metal stressed under high triaxiality conditions. Here, the possibility of unstable cavity growth is studied for a metal containing many voids. The central cavity is discretely represented, while the surrounding voids are represented by a porous ductile material model in terms of a field quantity that specifies the variation of the void volume fraction in the surrounding metal. As the central void grows, the surrounding void volume fractions increase in nonuniform fields, where the strains grow very large near the void surface, while the high stress levels are reached at some distance from the void, and the interaction of these stress and strain fields determines the porosity evolution. In some cases analysed, the porosity is present initially in the metal matrix, while in other cases voids nucleate gradually during the deformation process. It is found that interaction with the neighbouring voids reduces the critical stress for unstable cavity growth.     

A phenomenological constitutive model for the pseudoelastic behavior of shape memory alloys

Shape memory alloys (SMAs) possess the distinctive ability to recover large mechanically-induced inelastic strains upon unloading, which is known as the pseudoelastic behavior. This paper deals with an extension of the phenomenological viscoplasticity theory, which has been developed by the author to depict the negative strain rate sensitivity, to model the macroscopic behavior of the phase transformation. Unlike most phenomenological models for the pseudoelasticity, the proposed model does not employ a kinetic law describing the evolution of the martensitic volume fraction and the transformation loading and unloading conditions but introduces two internal state variables concerned with the evolution of the elastic modulus and the back stress. The applicability of the constitutive model to SMAs is validated by comparing simulation results with experimental data on uniaxial and torsional loading reported in the literature. And then it is demonstrated that the same constitutive equations can be applied to model the highly nonlinear unloading behavior of solid polymer.     

Material flow stress and failure in multiscale machining titanium alloy Ti-6Al-4V

Titanium Ti-6Al-4V alloy is a typical difficult-to-machine material due to its unique physical and mechanical properties. The material properties of Ti-6Al-4V play an important role in process design and optimization. However, the dynamic mechanical behavior is poorly understood and accurate predictive models have yet to be developed. This work focuses on the dynamic mechanical behavior of machining Ti-6Al-4V beyond the range of strains, strain rates, and temperatures in conventional materials testing. The flow stress characteristics of strain hardening and thermal softening can be predicted by the Johnson–Cook model coupled with the adiabatic condition. The predicted flow stresses at small strains agree very well with those from the split Hopkinson pressure bar (SHPB) tests, while the predicted flow stresses at large strains also agree with the calculated flow stresses based on the cutting tests with a suitable depth of cut. Heat fraction and temperature parameter control the range of thermal softening and the decrease rate of flow stress. The material may exhibit super plasticity at a small depth of cut with a large radius of the cutting edge in micromachining. Strain rate is one important factor for material fracture close to the cutting edge. The failure strain increases linearly with the increase of homologous temperature, while it only increases slightly with the strain rate.     

Micromechanical modeling of dual phase steels

Dual phase (DP) steels having a microstructure consisting of a Ferrite matrix, in which particles of Martensite are dispersed, have received a great deal of attention due to their useful combination of high strength, high work hardening rate and ductility, all of which are favorable properties for forming processes. Experimental investigation into the effect of the harder phase volume fraction, morphology and phase distribution on mechanical properties of the dual phase steels is well established and comprehensive in the literature. In the present work, a micromechanical model is developed to capture the mechanical behavior of such materials, adopting the constitutive behavior of the constituents from the literature. Analytical approaches have been used in the past to model the DP steel material behavior, but theoretical treatments are based on the assumption of uniform deformation throughout the constituents, neglecting the local strain gradients. This assumption contradicts experimental observations, reduces the understanding of the mechanics and mechanism of deformation of such materials. Based on the micromechanical modeling of cells, several idealizations are investigated out of which the axisymmetric model is shown to display intrinsic ability to capture the expected material behavior in terms of the trend of the stress–strain curves with increasing volume fraction of the second phase and in terms of the deformation fields of the constituents.