EVALUATION OF DUCTILE FRACTURE CRITERIA IN A GENERAL THREE-DIMENSIONAL STRESS STATE CONSIDERING THE STRESS TRIAXIALITY AND THE LODE PARAMETER

This paper is concerned with evaluation of various ductile fracture criteria in a general three-dimensional stress state of stress triaxiality, the Lode parameter and the equiva- lent plastic strain to fracture. Evaluation is carried out by comparing fracture loci constructed by fracture criteria to experimental results of A12024-T351. Comparison demonstrates that the Modified Mohr-Coulomb criterion and a newly proposed criterion provide sufficient predictabil- ity of fracture strain. Moreover, evaluation is emphasized on the predicted cut-off value for stress triaxiality. The evaluation demonstrates that the Cockcroft-Latham, Brozzo, Oh, Ko-Huh and the new criteria coupled a reasonable cut-off value for ductile materials.     

一个新的普遍形式的局部损伤断裂准则

利用损伤函数概念，建立了一个普遍形式的局部断裂准则。该准则考虑了局掊应力，应变和损伤历史对断裂的影响，根据损伤力学理选取了一个新的连续损伤函数，从而导出一个新的连续损伤断裂准则。新的临界断裂参数ＷＤＣ，具有明显的物理意义，且易通过试验测得，是一个不依赖于应力状态的材料九。文中还从细观力学理论和有关的试验资料出发，选取了相应的损伤函数，再现了前人的细观力学准则和经验准则。     

准静态条件下金属材料的临界断裂准则研究

本文针对9种金属材料完成了具有不同约束程度的10类试样的延性断裂试验, 获得了发生拉、压、扭和裂尖断裂等破坏形式构型试样的载荷-位移试验关系; 基于圆棒漏斗试样拉伸试验所得直至破坏的载荷-位移曲线, 采用有限元辅助试验(finite-element-analysis aided testing, FAT)方法得到了9种材料直至破坏的全程等效应力-应变曲线, 以此作为材料本构关系通过有限元分析获得了各类试样直至临界破坏的载荷-位移关系模拟. 载荷-位移关系模拟结果与试验结果有较好的一致性, 表明用于解决试样颈缩问题的FAT方法所获得的全程材料本构关系针对各向同性材料具有真实性和普适性. 对应9种材料、10类试样的36 个载荷-位移临界断裂点, 通过有限元分析获得了对应的材料临界断裂应力、应变与临界应力三轴度, 研究表明, 第一主应力在延性变形过程中为主控断裂的主导参量; 通过研究光滑、缺口、裂纹等构型试样的断裂状态, 提出了$-1$至3范围的应力三轴度下由第一主应力主控的统一塑性临界断裂准则.      

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。     

Phenomenological nonlinear modelling of glassy polymers

Compared with the numerous works into the constitutive equations for the mechanical behaviour of metals, very little attention has been devoted to those of polymers. However, a model is required to describe both the complex shape of the stress–strain curves and strain rate sensitivity of glassy polymers. In this Note, a unified viscoelastic-viscoplastic model is presented in which the nonlinear pre-yield behaviour, the strain softening and the strain hardening are described by internal variables, in analogy with the models developed for metals. In order to check the predictive capability of the model, the numerical results are compared with the experimental data (monotone, creep and relaxation tests) of a typical amorphous glassy polymer. To cite this article: F. Zaïri et al., C. R. Mecanique 333 (2005).     

裂纹动态起始问题的研究进展

力图就前人提出的冲击载荷下裂纹的起始判据进行较全面的综述．这些较著名的判据有：（１）动态应力强度因子判据；（２）动态Ｊ积分判据；（３）最小作用量判据；（４）极小作用时间判据等．简要介绍了近年来有关裂纹在冲击载荷（特别是短脉冲）下动态起始的一些重要实验和实验中所发现的一些重要结论．实验公认，一般对于小范围屈服而言，材料的动态断裂韧性随加载（应变）率的提高而减小，此时材料的断裂形式为解理型；而对于大范围屈服则韧性随加载率的提高而增大，此时材料的断裂形式为纤维型．特别指出，Ｂｒｏｗｎ大学的平板撞击实验表明，裂纹在起始时，观察到一个不再满足二分之一阶奇异性的“尖峰”，按Ｃｌｉｆｔｏｎ和Ｆｒｅｕｎｄ等人所给出的模型，在裂纹起始断裂瞬间，在裂纹顶端会突然形成一个小洞，该洞的半径作为一个参数等于二相粒子的间距．     

Law of damage accumulation and fracture criteria in highly filled polymer materials

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2–3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account.     

Glass Fracture in the Region of Its Contact with Steel Balls

Results of experiments on indentation of steel balls of various diameters into glass specimens shaped as rectangular parallelepipeds are reported. The limiting load of formation of an annular crack near the contact area and the radius of this crack are experimentally determined. The field of the contact stress in the fracture region is found by using the Huber solution of the Hertz problem of ball indentation into an elastic half-space. Modeling fracture caused by contact interaction is based on using the local criterion of the maximum stress and several nonlocal criteria: average stress criterion, Nuismer criterion, and gradient criterion. For calculating the parameter that has the length dimension and is included into the nonlocal fracture criteria, the ultimate tensile stress and the critical stress intensity factor of glass are experimentally determined for beams without and with a notch. It is demonstrated that the experimental data on the annular crack radius are most adequately predicted by the gradient criterion among all criteria considered in the study. However, this criterion overpredicts the ultimate tensile stress in the course of beam bending, which is caused by the scale factor.     

汽车玻璃高温蠕变特性的实验与理论研究

通过对汽车用挡风玻璃进行不同温度、不同应力水平下的单轴拉伸蠕变实验,揭示了其非线性蠕变变形特性.实验发现,不同温度和载荷下的蠕变曲线形状类似,高温(550℃～590℃)下该材料的减速蠕变变形不很明显,主要表现为稳态和加速蠕变变形,且其断裂数据符合Monkman-Grant关系,应力和温度对其影响不显著.基于实验结果,本文建立了非线性高温蠕变本构方程.理论预测与实验数据进行了比较,结果表明所提出的本构方程能较好地描述汽车玻璃高温蠕变变形的全过程.     

On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part II. Numerical study

Non-linear finite element analyses of quasi-static and high-rate tensile tests with smooth and notched axisymmetric specimens of the structural steel Weldox 460 E have been carried out. The constitutive relation and fracture criterion of Johnson and Cook, which were adopted in the simulations, have previously been determined for Weldox 460 E steel. First, a validation study was completed to assess the accuracy of the constitutive relation and fracture criterion. The numerical results were compared with experimental data from tensile tests under quasi-static and dynamic loading conditions. Secondly, the use of Bridgman's analysis in the identification of the fracture criterion was evaluated, and the influence of adiabatic heating and inertia on the stress triaxiality in the tensile specimens was investigated. The results were finally used to discuss the identification of fracture criteria based on tensile tests with smooth and notched axisymmetric specimens.     

On the circumferential strain factor criterion of mixed mode brittle fracture

In this paper, the criteria of mixed mode brittle fracture are carefully examined. It has been shown that, the circumferential strain factor criterion is rational and safe.With the exception of opening mode, mixed mode plane strain fracture of comparatively ductile materials(metals), in general, does not follow the theory of linear elastic fracture mechanics.Like the stress intensity factor that which is concerned is playing an important role in pure opening mode crack problems. We believe that, in mixed mode crack problems, the circumferential strain factor will become a parameter to determine the rate of fatigue crack propagation per cycle, and of stress corrosion cracking per unit time.First published in Nanking Aeronautical Institute Report of Science and Technology, No. 680, Jan., 1980 (in Chinese).     

断裂力学判据的评述

从Inglis 和Griffith 的著名论文到Irwin 和Rice 等的奠基性贡献,对断裂力学中的线弹性断裂力学的K判据,界面断裂力学的G判据,和弹塑性断裂力学的J 判据作了扼要的综述. 介绍了在界面断裂力学G判据的基础上提出的界面断裂力学的K判据,以说明断裂力学的判据存在改进的可能性. 在综述中归纳出断裂力学判据中目前还没有较好解决的几个问题. 在总结以往断裂力学研究经验的基础上,指出裂纹端应力奇异性的源是对断裂力学判据存在的问题作进一步研究的切入点. 探讨了裂纹端应变间断的奇点是裂纹端应力奇异性的源的问题,从而对裂纹端应力强度因子的物理意义进行了讨论. 最后,阐述了进行可靠的裂纹端应力场的弹塑性分析是改进弹塑性断裂力学判据的关键,而进行可靠的裂纹端应力场的弹塑性分析的前提是要通过裂纹端应力奇异性的源的研究来获得作用在裂纹端的造成裂纹端应变间断的有限值应力.      

Creep,plasticity, and fatigue of single crystal superalloy

Single crystal components in gas turbine engines are subject to such extreme temperatures and stresses that life prediction becomes highly inaccurate resulting in components that can only be shown to meet their requirements through experience. Reliable life prediction methodologies are required both for design and life management. In order to address this issue we have developed a thermo-viscoplastic constitutive model for single crystal materials. Our incremental large strain formulation additively decomposes the inelastic strain rate into components along the octahedral and cubic slip planes. We have developed a crystallographic-based creep constitutive model able to predict sigmoidal creep behavior of Ni base superalloys. Inelastic shear rate along each slip system is expressed as a sum of a time dependent creep component and a rate independent plastic component. We develop a new robust, computationally efficient rate-independent crystal plasticity approach and combined it with creep flow rule calibrated for Ni-based superalloys. The transient variation of each of the inelastic components includes a back stress for kinematic hardening and latent hardening parameters to account for the stress evolution with inelastic strain as well as the evolution for dislocation densities. The complete formulation accurately predicts both monotonic and cyclic tests at different crystallographic orientations for constant and variable temperature conditions (low cycle fatigue (LCF) and thermo-mechanical fatigue (TMF) tests). Based on the test and modeling results we formulate a new life prediction criterion suitable for both LCF and TMF conditions.     

Experimental identification and mathematical modeling of viscoplastic material behavior

Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases.The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.     

Scale-dependent constitutive relations and the role of scale on nominal properties

Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a ‘background’ gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress–strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress–strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.     

A new approach to model strain change of gelled waxy crude oil under constant stress

Deformation of gelled waxy crude oil with loaded stress is worthy of research for the flow assurance of pipelining system. A dispersion parameter was introduced to characterize the disruption degree of wax crystal structure in crude oil with shear action. Based on fractional calculus theory, a rheological model incorporating dispersion parameter was proposed to describe creep of gelled waxy crude. A discrete and numerical algorithm was proposed to solve the model. Combining with the experimental results of five kinds of waxy crude oil, the model parameters were regressed and found to change monotonously with test temperature. Multiple creep curves of gelled waxy crude oil at a certain temperature can be described with this model.     

A new quasi-continuum constitutive model for crack growth in an isotropic solid

A new quasi-continuum constitutive model is established based on the randomized cohesive bonds model proposed by Gao and Klein (1998). This model bridges the microscopic discrete constitution characters and the macroscopic mechanical properties of material. In the presented constitutive model, both the bond stretch energy potential and the rotation energy potential are considered, which makes the presented constitutive model applicable to different Poisson-ratio and Young's modulus materials. By establishing a phenomenological bond stiffness function according to the complete stress–strain relationship of uniaxial tension test, the fracture criterion is directly incorporated into the constitutive model. The method requires no external fracture criterion when simulating fracture initiation and propagation, which brings convenience in the numerical simulation. At last, the presented constitutive model is applied to an example of crack growth in an isotropic solid.     

脆性断裂的非局部力学理论

本文提出一种脆性材料断裂的非局部力学理论,内容包括:Ⅰ、Ⅱ、Ⅲ型Griffith裂纹的非局部弹性应力场,裂纹尖端邻域非局部弹性应力场的渐近形式,脆性开裂的最大拉应力准则。文中给出了这种理论应用于三种基本型裂纹和Ⅰ-Ⅱ、Ⅰ-Ⅲ复合型裂纹临界开裂条件的计算结果,并把它们与一些试验资料和最小应变能密度因子理论进行了对比。