缝合式C/SiC复合材料非线性本构关系及断裂行为研究

C/SiC复合材料具有高比强度、高比模量和优良的热稳定性能等一系列优点, 广泛应用于航空航天领域中. 裂纹扩展进而引起的脆性断裂是其主要失效形式之一, 因而材料的断裂性能分析对材料的结构设计和应用有重要的指导意义. 本文开展了缝合式C/SiC复合材料简单力学试验和断裂试验, 研究了材料在不同载荷下的力学响应及断裂特征. 基于缝合式C/SiC复合材料简单力学试验, 建立了材料宏观非线性损伤本构方程, 并模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 本构方程采用简单函数描述了材料在复杂应力状态下的非线性应力-应变曲线, 并考虑了反向加载过程中造成的裂纹闭合. 基于商业有限元软件ABAQUS, 通过编写UMAT子程序实现非线性损伤本构方程, 采用单个单元验证了建立的本构方程的有效性. 在此基础上, 采用线弹性损伤本构和非线性损伤本构分别模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 采用非线性损伤本构方程模拟的力-位移曲线结果与试验结果更为吻合, 非线性损伤本构预测的失效载荷与试验失效载荷更为接近, 验证了所建立的非线性损伤本构方程的准确性, 为C/SiC复合材料断裂行为的研究提供了借鉴, 为缝合式C/SiC复合材料结构的设计和应用提供了理论基础.      

结构钢损伤本构关系的研究

回顾了结构钢损伤模型的发展史,提出了一种新的本构模型－结构钢弹塑性各向异性损伤本构模型,该模型采用混合强化准则,考虑Bauschinger效应,屈服平台、硬化（软化）效应及损伤和损伤演化影响。算例分析结果表明本文模型能够客观地反映结构钢在循环荷载作用下的工作性能、适用于进行钢结构及构件在循环荷载作用下弹塑性反应分析。     

有机玻璃在高应变率下的损伤型非线性粘弹性本构关系及破坏准则

对两种有机玻璃高应变率下的大变形和破坏行为进行了实验研究,通过改进文献[2]本构关系的非线性弹性项并引入损伤参量,建立了一个适用于更大变形范围、能描述应力平台及本构失稳的损伤型非线性粘弹性本构方程。相应地,从临界损伤量概念出发,提出以应变和应变率为控制变量的破坏准则。不论是本构关系还是破坏准则,理论计算均与试验结果吻合良好。     

沥青混合料一维非线性粘弹本构方程

本文根据Green-Rivlin提出的Frechet级数,提出了一个兼具长时粘流效应及短时粘弹效应的一维非线性本构方程,并对一种沥青混合料采用蠕变试验方式拟合了本构方程的参数向量。拟合结果表明:这一本构方程形式简洁,物理意义清晰,易于拟合,并对不同应力历史下的应变响应具有广泛的适用性。     

大变形下初始斜交异性本构方程

采用材料主轴法,建立了初始斜交异性材料在变形构形（Euler描述）下的斜交异性本构方程,以及在初始构形（Lagrange描述）下的形式。具体给出了斜交异性线弹性材料方程的显式,它在Lagrange描述下形式简洁,可方便地用于有限元计算。文中指出,在变形构形下是线弹性的材料,在Lagrange描述下其本构方程一般已成为非线性,我们称之为本构转换非线性。这种非线性在实际的有限元计算中还未引起重视。为理论简明,本构方程是对二维给出的。     

形状记忆合金的本构模型及其有限元实施

基于塑性力学中屈服面的概率以及Liang和Brinson提出的马氏体体积百分量和应力,温度间的关系,提出了适用于描述多信形状记忆合金的形状记忆效应和伪弹性效应的本构模型,并用T．T．法对该本构模型进行了非线性有限元实施,算例表明该本构模型与实验结果比较吻合,且只需对现有非线性有限元程度稍做修改就可得到实施,简单易行,有一定的实用价值。     

饱和和非饱和介质的弹塑性损伤模型

针对饱和和非饱和工程材料变形和强度特点,给出了一个具体的弹塑性损伤本构方程,该本构方程可以描述材料性质的劣化过程（即损伤和软化）以及饱和程度对材料变形强度特性的影响。此外,还讨论了该弹塑性损伤本构方程的有限元实施方法,编制了专用的有限元程序。对常规三轴试伯进行了有限元分析,得出了一些具体的结果。     

不同本构模型对橡胶制品有限元法适应性研究

为确定不同本构模型对橡胶制品进行非线性有限元分析的适应性,采用HyperMesh 和ABAQUS软件建立了橡胶标准试件和防尘罩制品的非线性有限元模型. 根据标准试件单轴拉伸试验数据,利用ABAQUS软件拟合了Mooney--Rivlin, Ogden 及Yeoh 3 种本构模型的特征参数,并给出了试件和制品轴向拉伸和压缩工况有限元分析结果. 实测试验与有限元分析结果对比发现:在应变不大于100% 时,两参数的Mooney--Rivlin本构模型计算误差较小;在应变大于100% 时, 用Yeoh 和Ogden 本构模型计算误差较小. 该结论对大变形橡胶元件的非线性特性理论分析具有实际意义.     

冲击载荷下混凝土材料的动态本构关系

利用改装的杆径为 74mm的直锥变截面式大尺寸Hopkinson压杆对混凝土材料进行冲击压缩实验 ,系统研究了混凝土的应变率硬化效应 ,采用一种新的方法损伤冻结法对混凝土材料在冲击载荷下的损伤软化效应进行了系统研究 ,给出了冲击载荷下混凝土的损伤演化方程 ;在对数据进行合理分析的基础上 ,结合粘弹性本构理论 ,得到混凝土材料的损伤型线性粘弹性本构关系。     

有机玻璃在高应变率下的损伤型非线性粘弹性本构关系及破坏准则

对两种有机玻璃高应变率下的大变形和破坏行为进行了实验研究,通过改进文献[2]本构关系的非线性弹性项并引入损伤参量,建立了一个适用于更大变形范围、能描述“应力平台”及“本构失稳”的损伤型非线性粘弹性本构方程。相应地,从临界损伤量概念出发,提出以应变和应变率为控制变量的破坏准则。不论是本构关系还是破坏准则,理论计算均与试验结果吻合良好。     

A modified damage model for advanced high strength steel sheets

More often than not, better formability in the simple tension test implies better formability performance in other stretching modes, especially in hole expansion performance since deformation in the hole expansion test is perceived to be in the same simple tension deformation mode. However, when the hole expansion formability is evaluated particularly for the twinning induced plasticity (TWIP) steel, its performance is so poor compared to other automotive steels, even though the TWIP steel has significantly superior formability in the simple tension test. Therefore, hole expansion formability was experimentally and numerically studied for advanced high-strength grade steel sheets, TWIP940 and a transformation induced plasticity (TRIP) 590 steel sheet, as well as a high-strength grade 340R steel sheet, particularly in conjunction with formability in the simple tension test and its surface condition sensitivity. In order to characterize mechanical properties, simple tension tests were performed to determine anisotropic properties and strain rate sensitivities. To account for macro-crack formation, an inverse calibration method based on a damage model utilizing a triaxiality-dependent fracture criterion and hardening behavior with stiffness deterioration was developed. In this approach, the damage model was inversely calibrated by performing numerical simulations and experiments for the simple tension test (with specimens prepared by milling and punching). Then, the damage model was applied to formability study in the hole expansion test. The damage model along with the anisotropic yield function Hill (1948) incorporated into the ABAQUS/Explicit FEM code performed well to predict hole expansion ratios (HER) and their surface condition sensitivity, elucidating the cause of the lukewarm hole expansion performance and strong surface condition sensitivity of the TWIP steel compared to the others.     

Computational modeling of inelastic large ratcheting strains

A framework for phenomenological hyperelasto-plasticity with initial anisotropy, kinematic hardening as well as anisotropic damage is presented in [Menzel et al., Int. J. Plasticity (2004), in press]. In this contribution, we exploit and extend this framework to include several back-stresses in order to capture the ratcheting response of polycrystalline metals subjected to cyclic stress with non-zero mid-value. The evolution equations for kinematic hardening resemble a linear combination of the multiple-Armstrong–Frederick and the Burlet–Cailletaud models, which are extended to the large strain setting. The capability of the model to capture various phenomenological characteristics, in particular multi-axial ratcheting, is illustrated by numerical examples. Comparisons with uni-axial and bi-axial experimental ratcheting results for carbon steel are given. Finally, the finite element analysis of a simplified railway turnout component subjected to cyclic loading is presented.     

Analysis of sheet metal formability through isotropic and kinematic hardening models

The present paper aims at analysing the sheet metal formability through several isotropic and kinematic hardening models. Specifically, a special attention is paid to the physically-based hardening model of Teodosiu and Hu (1995), which accounts for the anisotropic work-hardening induced by the microstructural evolution at large strains, as well as to some more conventional hardening models, including the isotropic Swift strain-hardening power law, and the Voce saturation strain-hardening law, combined with a non-linear kinematic hardening described by the Armstrong–Frederick law. The onset of localized necking is simulated by an advanced sheet metal forming limit model which connects, through the Marciniak–Kuczinsky analysis, the hardening models with the anisotropic yield criterion Yld2000-2d (Barlat et al., 2003). Both linear and complex strain paths are taken into account. The selected material is a DC06 steel sheet. The validity of each model is assessed by comparing the predicted forming limits with experimental results carefully obtained on this steel. The origin of discrepancy in the predicted results using different hardening models is thoroughly analyzed.     

Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior

This work gives the thermodynamically consistent theoretical formulations and the numerical implementation of a plasticity model fully coupled with damage. The formulation of the elasto-plastic-damage behavior of materials is introduced here within a framework that uses functional forms of hardening internal state variables in both damage and plasticity. The damage is introduced through a damage mechanics framework and utilizes an anisotropic damage measure to quantify the reduction of the material stiffness. In deriving the constitutive model, a local yield surface is used to determine the occurrence of plasticity and a local damage surface is used to determine the occurrence of damage. Isotropic hardening and kinematic hardening are incorporated as state variables to describe the change of the yield surface. Additionally, a damage isotropic hardening is incorporated as a state variable to describe the change of the damage surface. The hardening conjugate forces (stress-like terms) are general nonlinear functions of their corresponding hardening state variables (strain-like terms) and can be defined based on the desired material behavior. Various exponential and power law functional forms are studied in this formulation. The paper discusses the general concept of using such functional forms. however, it does not address the relevant appropriateness of certain forms to solve different problems. The proposed work introduces a strong coupling between damage and plasticity by utilizing damage and plasticity flow rules that are dependent on both the plastic and damage potentials. However, in addition to that the coupling is further enhanced through the use of the functional forms of the hardening variables introduced in this formulation.The use of this formulation in solving boundary value problems will be presented in future work. The fully implicit backward Euler scheme is developed for this model to be solved in a Newton–Raphson solution procedure.     

Anisotropic plasticity model coupled with Lode angle dependent strain-induced transformation kinetics law

A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations are embedded in the framework of finite strain isothermal rate-independent anisotropic plasticity. Experimental data for an anisotropic austenitic stainless steel 301LN is presented for uniaxial tension, uniaxial compression, transverse plane strain tension and pure shear. The model parameters are identified using a combined analytical–numerical approach. Numerical simulations are performed of all calibration experiments and excellent agreement is observed. Moreover, we make use of experimental data from ten combined tension and shear experiments to validate the proposed constitutive model. In addition, punch and notched tension tests are performed to evaluate the model performance in structural applications with heterogeneous stress and strain fields.     

A combined phenomenological model for the representation of anisotropic hardening behavior in high strength steel line pipes

Line pipes have anisotropic mechanical properties, such as tensile strength, ductility and toughness. These properties depend on both prestrain during the cold forming process and on the anisotropy of the mother plates. In this study, a phenomenological model combining isotropic and kinematic hardening is developed to represent anisotropic hardening behavior of high strength steel line pipes. The model is adjusted on experiments carried out on smooth and notched axisymmetric bars and plane strain specimens. The model is used to simulate bending tests carried out on large pipes containing a geometric imperfection. Numerical results suggest that prestraining in pipe forming process significantly affects the bending capacity of pipes.     

圆形中空夹层钢管超高性能钢纤维混凝土柱抗爆性能野外实验与数值模拟

通过6根圆形中空夹层钢管超高性能钢纤维混凝土(UHPSFRCFDST)柱爆炸破坏实验,研究了轴压、折合距离、空心率和迎爆面形状对其动态响应及损伤破坏的影响,并运用LS-DYNA软件建立了爆炸荷载作用下UHPSFRCFDST柱动态响应的有限元模型。在验证了模型有效性的基础上,运用参数化分析方法,研究了轴压比、空心率、含钢率、内层和外层钢管径厚比及其强度等关键参数对圆形UHPSFRCFDST柱抗爆性能的影响。结果表明:有限元模型能够有效地分析UHPSFRCFDST柱在爆炸荷载作用下的动态响应及损伤破坏;在小于临界轴压时,提高轴压比能够提升UHPSFRCFDST柱抗爆性能,但超过临界轴压后继续提高反而会加重其损伤破坏;减小空心率或内、外层钢管径厚比均可有效提升UHPSFRCFDST柱的抗爆性能,提高含钢率或外层钢管强度也能达到相同效果,但提高内层钢管强度对其抗爆性能的提升作用并不显著。     

Damage analysis and dynamic response of elasto-plastic laminated composite shallow spherical shell under low velocity impact

Based on the elasto-plastic mechanics, the damage analysis and dynamic response of an elasto-plastic laminated composite shallow spherical shell under low velocity impact are carried out in this paper. Firstly, a yielding criterion related to spherical tensor of stress is proposed to model the mixed hardening orthotropic material, and accordingly an incremental elasto-plastic damage constitutive relation for the laminated shallow spherical shell is founded when a strain-based Hashin failure criterion is applied to assess the damage initiation and propagation. Secondly, using the presented constitutive relations and the classical nonlinear shell theory, a series of incremental nonlinear motion equations of orthotropic moderately thick laminated shallow spherical shell are obtained. The questions are solved by using the orthogonal collocation point method, Newmark method and iterative method synthetically. Finally, a modified elasto-plastic contact law is developed to determine the normal contact force and the effect of damage, geometrical parameters, elasto-plastic contact and boundary conditions on the contact force and the dynamic response of the structure under low velocity impact are investigated.     

A numerical method for rapid estimation of drawbead restraining force based on non-linear,anisotropic constitutive equations

Numerical procedures to predict drawbead restraining forces (DBRF) were developed based on the semi-analytical (non-finite-element) hybrid membrane/bending method. The section forces were derived by equating the work to pull sheet material through the drawbead to the work required to bend and unbend the sheet along with frictional forces on drawbead radii. As a semi-analytical method, the new approach was especially useful to analyze the effects of various constitutive parameters with less computational cost. The present model could accommodate general non-quadratic anisotropic yield function and non-linear anisotropic hardening under the plane strain condition. Several numerical sensitivity analyses for examining the effects of process parameters and material properties including the Bauschinger effect and the shape of yield surface on DBRF were presented. Finally, the DBRFs of SPCC steel sheet passing a single circular drawbead were predicted and compared with the measurements.