纯铜—维动态损伤研究

在Johnson方法的基础上,本文采用细观方法提出了一个延性材料动态损伤模型.模型中考虑了材料的硬化、应变率效应和惯性效应.同时进行了纯铜一维层裂实验,对软回收试件进行了显微金相和定量金相分析,观察到了一些有意义的力学现象.利用一维Lagrange 有限差分动力学程序,采用本文提出的损伤模型对纯铜的层裂过程进行了数值模拟,得到了比较满意的结果.     

EXPERIMENTAL STUDY AND NUMERICAL ANALYSIS OF DYNAMIC FRACTURE IN DUCTILE SOLIDS

Spall tests in pure copper and LY12 aluminum alloy are performed. Themechanism of the nucleation, growth and coalescence of micro-voids is observed bymeans of microscopic observation of the recovered specimens. The model presented inRef. [4] is incorporated in a hydrodynamic one-dimensional finite-difference computercode to simulate the processes of spallation in pure copper and LY12 aluminum alloyspecimens. This model can satisfactorily describe the processes of spallation.     

延性材料动态断裂的实验研究和数值分析

本文对延性材料纯铜和ＬＹ１２铝合金进行了层裂实验，对软回收试件进行了仔细的定量和显微金相观测，观察到了两种材料中不同微损伤的形核、增长和聚合机制，为理论分析提供了真实的实验结果。将文〔４〕提出的延性动态损伤模型编入了一维Ｌａｇｒａｎｇｅ有限差分动力学程序，对两组层裂实验进行了数值模拟，计算结果与实验吻合较好。     

A first-order strain gradient damage model for simulating quasi-brittle failure in porous elastic solids

In order to simulate quasi-brittle failure in porous elastic solids, a continuum damage model has been developed within the framework of strain gradient elasticity. An essential ingredient of the continuum damage model is the local strain energy density for pure elastic response as a function of the void volume fraction, the local strains and the strain gradients, respectively. The model adopts Griffith’s approach, widely used in linear elastic fracture mechanics, for predicting the onset and the evolution of damage due to evolving micro-cracks. The effect of those micro-cracks on the local material stiffness is taken into account by defining an effective void volume fraction. Thermodynamic considerations are used to specify the evolution of the latter. The principal features of the model are demonstrated by means of a one-dimensional example. Key aspects are discussed using analytical results and numerical simulations. Contrary to other continuum damage models with similar objectives, the model proposed here includes the effect of the internal length parameter on the onset of damage evolution. Furthermore, it is able to account for boundary layer effects.     

Unusual plastic deformation and damage features in titanium: Experimental tests and constitutive modeling

In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure HCP Ti, as well as modeling of the observed behavior. Mechanical characterization data were conducted, which indicate that the material is orthotropic and displays tension-compression asymmetry. The ex-situ and in-situ X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All the parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined from very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen, and is diffuse; the level of damage close to failure being very low. On the other hand, for a notched specimen subject to the same loading the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.     

氮化物陶瓷颗粒增强铜基复合材料的干摩擦磨损性能研究

采用粉末冶金工艺制备了纯铜以及AlNp／Cu和TiNp／Cu系列铜基复合材料，研究了2种复合材料在不同颗粒含量、不同载荷及滑动速度等条件下与45^#钢对摩时的干摩擦磨损性能，用扫描电子显微镜观察其磨损表面形貌，用能谱仪分析了磨损表面的元素组成．结果表明：与纯铜相比，AlNpCu及TiNp／Cu复合材料的耐磨性能显著提高，随着氮化物颗粒含量增加，2种复合材料的磨损率先下降而后趋于稳定；载荷与滑动速度提高引起的热效应使得纯铜及其复合材料的磨损率增高；由于TiNp的硬度高于AlNp以及本身具有一定的自润滑性能，使得TiNp／Cu复合材料的耐磨减摩性能优于AlNp／Cu复合材料．     

受弯脱层层板后屈曲有限元分析

脱层是复合材料层板结构中主要的缺陷形式之一。当脱层层板受到压力载荷的作用会造成脱层的局部屈曲和扩展,从而使结构的强度和刚度大为降低。含脱层层板的弯曲问题包含了脱层的压缩问题,却比压缩问题更加复杂。本文对含穿透脱层层板在纯弯载荷作用下的后屈曲问题进行了基于一阶剪切层板理论的几何非线性有限元分析,运用虚裂纹闭合技术求解了纯弯载荷作用下的脱层尖端的能量释放率各型分量,并用脱层扩展判据求解了脱层起始扩展载荷。     

One-dimensional model of two-phase fluid displacement in a slot with permeable walls

A one-dimensional model is proposed for transportation of a two-phase fluid (sandcontaining fluid and pure fluid) in the Hele-Shaw cell with permeable walls through which the pure fluid can leak off, causing the growth of the sand concentration. The model describes the process of pure fluid displacement with the emergence of the Saffman–Taylor instability and extends Koval’s model to the case of sand concentration variation owing to pure fluid outflow through the cell walls. The Riemann problem is analyzed. New flow configurations, which are not predicted by Koval’s model, are discovered.     

复杂加载下混凝土的弹塑性本构模型

混凝土材料在不同应力路径下或复杂加载条件下会表现出差异性显著的应力应变关系,在小幅循环加载条件下,其应力应变关系会表现出类似于弹性变形的滞回曲线.在不同应力水平下,混凝土的应力应变关系以及破坏特性都具有静水压力相关特点,即随着静水压力增大,各向异性强度特性弱化.此外,混凝土受压及受拉破坏机理不同,因而对应于混凝土硬化损伤亦有不同,即可分为受压硬化损伤,受拉硬化损伤及两者的混合硬化损伤类型.基于Hsieh模型,对该模型进行了三点改进.（1）针对小幅循环加载下混凝土无塑性变形的试验规律,而模型中在应力水平较低的循环加载条件下始终存在塑性变形的预测问题,采用在边界面模型框架下,设置了应力空间的弹性域,初始屈服面与后续临界状态屈服面几何相似的假定.（2）基于广义非线性强度准则将原模型采用变换应力方法将其推广为三维弹塑性本构模型,采用变换后模型可合理的考虑不同应力路径对于子午面以及偏平面上静水压力效应形成的影响,并避免了边界面应力点奇异问题.（3）分别对拉压两种加载损伤模式建议了相应的硬化参数表达式,可分别用于描述上述加载中产生的应变软化及强度退化行为.基于多种加载路径模拟表明:所建立的三维弹塑性本构模型可合理地用于描述混凝土的一般应力应变关系特性.      

Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks

In the framework of rate-independent systems, a family of elastic-plastic-damage models is proposed through a variational formulation. Since the goal is to account for softening behaviors until the total failure, the dissipated energy contains a gradient damage term in order to limit localization effects. The resulting model owns a great flexibility in the possible coupled responses, depending on the constitutive parameters. Moreover, considering the one-dimensional quasi-static problem of a bar under simple traction and constructing solutions with localization of damage, it turns out that in general a cohesive crack appears at the center of the damage zone before the rupture. The associated cohesive law is obtained in a closed form in terms of the parameters of the model.     

纳米晶材料变形行为的微观力学模型

本文将纳米晶材料视为包括晶粒和晶界的两相复合材料。基于能量平衡概念推导出纳米晶材料的增量本构关系。最后将本文发展的模型用于纯铜的单轴拉伸实验,讨论了晶粒大小、形状和晶粒分布的影响,并将模型预测的结果和已有的实验结果进行比较。     

纯弯曲梁的应变损伤失效分析和预测

提出了纯弯曲梁的应变损伤失效分析方法,与Kachanov的材料受载横截面减少定义拉伸损伤变量类似,以梁的弯曲惯性矩阵减少定义弯曲损伤变量。推导了梁的弯曲应变损伤基本方程,其中的材料常数可由Kachanov拉伸损伤模型的材料常数确定。并且提出了便于工程应用的应变失效预测方程。     

混凝土分段曲线损伤模型

在对比分析国内外现有的混凝土受拉损伤模型基础上，结合素混凝土受拉应力应变曲线的试验结果，提出了一个新的混凝土分段曲线损伤模型，并利用应力连续条件确定了损伤模型中各系数的值。运用该模型到力学分析中，推导了矩形截面的混凝土梁在纯弯矩作用下，在损伤较小和损伤较大时的力学方程，算出了梁的最大承载能力，并与材料力学计算的梁承载能力进行了对比。详细分析了损伤区域及损伤应力在横截面上的变化过程，确定了极限状态下含损伤混凝土梁的应力分布和相应的承载能力，画出了损伤状态梁截面的应力分布图。     

一种基于空穴聚集的层裂模型

基于如下假设，给出了层裂过程中的应力松弛方程，并建立了一种基于空穴聚集的延性层裂模型:在层裂早期，微空穴的主要效应是减小应力作用面积；在层裂后期，应力按空穴聚集时的应力-空隙度依赖关系减小。把P.F.Thomason、D.L.Tonks等及S.Cochran等给出的依赖于应力（压力）的层裂空隙度方程分别耦合于守恒方程、计及损伤的状态方程及本构方程，建立了求解所有变量包括损伤的封闭方程组。这种基于空穴聚集的层裂模型已被应用于一维层裂试验的数值模拟。模型中的层裂强度及临界损伤度初始可以估计，最终的确定将使数值模拟结果与实测的速度（或应力）剖面以及观测的层裂面上的损伤基本一致。分别基于D.L.Tonk等及S.Cochran等给出的依赖于压力的层裂空隙度方程所作的一维层裂试验数值模拟结果基本一致，而与基于P.F.Thomason给出的依赖于应力的层裂空隙度方程所作的相应数值模拟结果有明显差异。     

Instability and failure of internally pressurized ductile metal cylinders

Forlong, ductile, thick-walled tubes under internal pressure instabilities and final failure modes are studied experimentally and theoretically. The test specimens are closed-end cylinders made of an aluminum alloy and of pure copper and the experiments have been carried out for a number of different initial external radius to internal radius ratios. The experiments show necking on one side of the tubes at a stage somewhat beyond the maximum internal pressure. All tubes, except for one aluminum alloy tube, failed by shear fracture under decreasing pressure. The aluminum alloy tubes exhibited localized shear deformations in the neck region prior to fracture and also occasionally surface wave instabilities. The numerical investigation is based on an elastic-plastic material model for a solid that develops a vertex on the yield surface, using representations of the uniaxial stress-strain curves found experimentally. In contrast to the simplest flow theory of plasticity this material model predicts shear band instabilities at a realistic level of strain. A rather sharp vertex is used in the material model for the aluminum alloy, while a more blunt vertex is used to characterize copper. The theoretically predicted bifurcation into a necking mode, the cross-sectional shape of the neck, and finally the initiation and growth of shear bands from the highly strained internal surface in the neck region are in good agreement with the experimental observations.     

Variational modelling of diffused and localized damage with applications to fiber-reinforced concretes

A variational model for the evolution of damage in elastic materials is proposed, which is based on incremental energy minimization. Analytical solutions are determined in the one-dimensional case of a tensile bar, and the issue of their stability is addressed. Analytical results have given insights into the properties that elastic and damage energies must have in order that specific evolution processes are captured, such as diffuse damaging, progressive damage localization or brutal failure. Accordingly, expressions of elastic and damage energies are proposed aimed at reproducing the evolution of damage observed in high-performance fiber-reinforced concretes, which typically exhibit initial micro-cracking and subsequent macro-crack opening. Tensile tests on bone-shaped samples and three-points bending tests are reproduced, by implementing the model in a finite element code, and numerical results are compared with experimental evidences.     

Homogenised constitutive model coupling damage and debonding for reinforced concrete structures under cyclic solicitations

A new stress resultant constitutive model for reinforced concrete plates under cyclic solicitations is presented. This model is built by the periodic homogenisation approach using the averaging method and couples damage of concrete and periodic debonding between concrete and steel rebar. In one-dimensional situations, we derive a closed-form solution of the local problem useful to verify and set up the plate problem. The one dimensional macroscopic constitutive model involves a limited number of parameters, the sensibility of which is studied. Comparison to experimental results underlines the pertinence of the model by considering internal debonding in order to properly represent the mechanical dissipation occurring during cyclic loadings on reinforced concrete panels.     

Constitutive model for flake graphite cast iron automotive brake discs: induced anisotropic damage model under complex loadings

The present paper details an elasto-viscoplastic constitutive model for automotive brake discs made of flake graphite cast iron. In a companion paper (Augustins et al. in Contin Mech Thermodyn, 2015), the authors proposed a one-dimensional setting appropriate for representing the complex behavior of the material (i.e., asymmetry between tensile and compressive loadings) under anisothermal conditions. The generalization of this 1D model to 3D cases on a volume element and the associated challenges are addressed. A direct transposition is not possible, and an alternative solution without unilateral conditions is first proposed. Induced anisotropic damage and associated constitutive laws are then introduced. The transition from the volume element to the real structure and the numerical implementation require a specific basis change. Brake disc simulations with this constitutive model show that unilateral conditions are needed for the friction bands. A damage deactivation procedure is therefore defined.     

A model of damage coupled to wear

The present paper presents a model of damage coupled to wear. The damage model is based on a continuum model including the gradient of the damage variable. Such a model is non-local in the sense that the evolution of damage is governed by a boundary-value problem instead of a local evolution law. Thereby, the well-known mesh-dependency observed for local damage models is removed. Another feature is that the boundary conditions can be used to introduce couplings between bulk damage and processes at the boundary. In this work such a coupling is suggested between bulk damage and wear at the contact interface. The model is regarded as a first attempt to formulate a continuum damage model for studying crack initiation in fretting fatigue.The model is given within a thermodynamic framework, where it is assured that the principles of thermodynamics are satisfied. Furthermore, two variational formulations of the full initial boundary value problem, serving as starting points for finite element discretization, are presented. Finally, preliminary numerical results for a simple one-dimensional example are presented and discussed. It is qualitatively shown how the evolution of damage may influence the wear behaviour and how damage may be initiated by the wear process.     

梁的蠕变开裂各向同性弯曲损伤分析

在梁的纯弯曲损伤基本假设条件下，导出了弯曲损伤的基本方程，与Ｋａｃｈａｎｏｖ的材料刚度劣化（受载横截面积减小）定义拉伸损伤变虽类似，以梁的弯曲刚度劣化（惯性矩减小）定义弯曲损伤变量，从而建立了与Ｋａｃｈａｎｏｖ拉伸损伤模型相类似的梁的各向同性弯曲损伤模型。最后，以受蠕变纯弯曲梁为实例进行了损伤分析，所得计算结果与Ｋａｃｈａｎｏｖ拉伸损伤模型所得结果比较吻合，表明该弯曲损伤模型是合理适用的。