Mechanics of small damage in fiber-reinforced composite materials

In this work the new concept of small damage is examined within the framework of continuum damage mechanics. In particular, special emphasis is given to a new damage variable that is defined in terms of the elastic stiffness of the material. Only the scalar case is studied in this work. The scalar definition of the new damage variable was used recently by many researchers. The investigation of the new scalar damage variable and the new concept of small damage is carried out on fiber-reinforced composite materials.     

Theoretical modelling of ductile damage in duplex stainless steels – Comparison between two micro-mechanical elasto-plastic approaches

Ductile damage is a consequence of large strains more or less localized inside bands. Taking into account damage in constitutive behaviour of metallic materials is necessary to model various engineering problems involved in forming processes (stamping, punching, shearing…). Damage can be described at macroscopic level with continuum mechanics theories but introducing microstructural features can lead to more accurate predictions. In the present study, two polycrystalline plasticity models including damage effects in the framework of scale transition methods are investigated. These models are based on different approaches with direct application to duplex stainless steel. The first one is a variant of the Lipinski–Berveiller model in which ductile damage effects have been introduced. The second one is a generalized Cailletaud model taking into account ductile damage. Because of the microstructural complexity of the chosen materials, some particular developments of the micro-mechanical approaches are considered. Moreover, continuous damage mechanics is used at grains scale including its coupling with plastic or elastic–plastic flow. The modelling is justified from previous experimental results obtained by neutrons diffraction on duplex stainless steels. The developed models allow then deducing from the grains behaviour the macroscopic behaviour of the aggregate with damage effects.     

High-Temperature Physicochemical Mechanics of Materials

We propose to regard investigations in the field of high-temperature strength of structural metals and alloys interacting with corrosive media as high-temperature physicochemical mechanics of materials (HTPCMM). The most important feature of HTPCMM is the principle of correlation between deformation processes and physicochemical phenomena, which allows one to describe the features and regularities of changes in the properties of materials under service conditions most completely and correctly. We emphasize the most important role of diffusion as a controlling factor in a metal–medium system at high temperatures. Results of analytical investigations aimed at the development and investigation of physicomathematical models of elastic and elastoviscous multicomponent solid solutions with inherent degradation processes (accumulation of damage) are presented. The fact that, as a rule, these models are constructed within the framework of continuum mechanics on the basis of principles of nonequilibrium mechanics is noted Experimental data obtained, in particular, on refractory metals and titanium interacting actively with components of a vacuum or an inert atmosphere testify to the intensification of saturation of metals by interstitial impurities under conditions of long-term loading and to significant changes in the character of their creep, namely, under the influence of oxygen diffusion the creep rate decreases as stresses increase.     

Stress invariants in an orthotropic damage space

In the classical theory of plasticity, it is often convenient to express failure criteria and/or flow rules in terms of stress invariants (I₁,I₂,I₃) and deviatoric stress invariants (J_2D, J_3D). Within the framework of continuum damage mechanics, the microscopic degradation of materials is reflected through the damage variables that conceive the notion of net-stress (the term net-stress has been used here in place of the term effective-stress since the latter already has an established meaning in Geotechnical Engineering). Any operative yield or failure criterion in the continuum damage mechanics will then need to be expressed in terms of the net-stress. This motivates an attempt to find the equivalent stress invariants in terms of the net-stress. In this paper, the stress invariants in an orthotropic damage space have been successfully derived and presented.     

Modelling fabric reinforced composites under impact loads

The paper describes recent progress on the materials modelling and numerical simulation of the in-plane response of fibre reinforced composite structures. A continuum damage mechanics model for fabric reinforced composites under in-plane loads is presented. It is based on methods developed for UD ply materials (Compos. Sci. Technol., 43 (1992) 257), which are generalised here to fabric reinforcements. The model contains elastic damage in the fibre directions, with an elastic–plastic model for inelastic shear effects. Test data on a glass fabric/epoxy laminate show the importance of inelastic effects in shear. A strategy is described for determining model parameters from the test data. The fabric model is being implemented in an explicit FE code for use in crash and impact studies and preliminary results are presented on a plate impact simulation.     

A damage model based on Kelvin eigentensors and Curie principle

A general anisotropic damage model is developed that accounts for the thermodynamics of irreversible processes in the framework of generalized standard materials and Kelvin tensor decomposition. Damage is described by fourth-rank tensors, one per eigenspace of the initial stiffness tensor. Their number thus ranges from two for an initially isotropic material to six for an initially triclinic material. The yield criteria are expressed in terms of a limiting energy for each eigenspace. The second-rank eigentensors (at most six) of the fourth-rank damage tensors define the direction of influence of the damage, while the associated eigenvalues characterize its intensity. These eigentensors evolve during loading, inducing an evolution of the symmetry group of the elastic tensor subject to the constraints of the Curie principle.     

高应变率下岩石损伤模型研究综述与展望

系统阐述了岩石爆破损伤模型的国内外研究现状,阐明了各自的理论基础和基本思想,并且作了简要评述,指出了各种模型存在的不足,对岩石爆破损伤模型的发展趋势提出了建议。随着弹性力学、断裂力学和损伤力学等固体力学在岩石破碎领域的广泛应用,以此为理论基础的岩石损伤模型必将会进一步得到发展和完善。     

高应变率下岩石损伤模型研究综述与展望

系统阐述了岩石爆破损伤模型的国内外研究现状,阐明了各自的理论基础和基本思想,并且作了简要评述,指出了各种模型存在的不足,对岩石爆破损伤模型的发展趋势提出了建议。随着弹性力学、断裂力学和损伤力学等固体力学在岩石破碎领域的广泛应用,以此为理论基础的岩石损伤模型必将会进一步得到发展和完善。     

Creep and recovery of nonlinear viscoelastic materials of the differential type

In this work, the creep and recovery properties of rubberlike viscoelastic materials in simple shear are studied by two special constitutive equations for isotropic, nonlinear incompressible viscoelastic material of the differential type. The creep and recovery processes are of significant importance to both the mechanics analysis and engineering applications. The constitutive equations introduced in this work generalize the Voigt-Kelvin solid and the 3-parameter model of classical linear viscoelasticity. They describe the uncoupled non-Newtonian viscous and nonlinear elastic response of an isotropic, incompressible material. The creep and recovery processes are treated for simple shear deformation superimposed on a longitudinal static stretch. Closed form solutions are provided and both processes are described effectively by the exponential function.     

On analysis of the elasto-viscoplastic response of single crystals with anisotropic damage: constitutive modelling and computational aspects

Based on the concept of continuum damage mechanics, an anisotropic damage model for single crystals under the theory of crystal plasticity is presented. Damage and inelastic deformations are incorporated in the proposed model which is developed within the framework of thermodynamics with internal state variables. The dependence of the plastic anisotropy on the damage evolution has been considered. The anisotropic damage is characterized kinematically here through a second-order damage tensor which is physically based. The proposed model can successfully describe the interaction between the evolution of micro-structure of single crystals such as lattice orientation and the hardness development of each slip system and the process of material degradation. The Newton–Raphson iterative scheme is used to integrate the constitutive equations that work directly with the evolution equations for the elastic deformation gradient. The consistent algorithmic tangent stiffness for the present algorithm is formulated. The prescribed algorithm together with the consistent algorithmic tangent stiffness has been implemented into the ABAQUS finite element code by using user subroutine. Using the loading processes with homogeneous deformations and simulation of the classical tensile test of a notched bar illustrate the basic aspects of the model described. Numerical simulations show the validation and performance of the present model and algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

A description of micro- and macroscale damage of concrete structures

Some particularities of the microstructure of concrete are first presented: they lead us to conclude that damage by microcracking is the main phenomenon in the mechanical behavior of the material. An isotropic elastic damage model is then proposed by using the coupling of two damage variables, D_t (tensile effects) and D_c (compressive effects). The model is built according to the framework of thermodynamics, and then we show that it is possible to describe the birth and growth of cracks, using a combination linear elastic damage mechanics and linear elastic fracture mechanics. Some results attest the interest in that kind of approach.     

Determination and representation of the stress coefficient terms by path-independent integrals in anisotropic cracked solids

Because the elastic T-stress and other coefficients of the higher-order terms play an important role in fracture mechanics such as the stability of crack kinking, crack path, and two-parameter characterization of elastic-plastic crack tip fields, determination of all the coefficients in the crack tip field expansion in an anisotropic linear elastic solid is presented in this paper. Utilizing conservation laws of elasticity and Betti's reciprocal theorem, together with selected auxiliary fields, T-stress and third-order stress coefficients near the crack tip are evaluated first from path-independent line integrals. To determine the T-stress terms using the J-integral and Betti's reciprocal work theorem, auxiliary fields under a concentrated force and moment acting at the crack tip are used respectively. Through the use of Stroh formalism in anisotropic elasticity, analytical expressions for all the coefficients including the stress intensity factors are derived in a compact form that has surprisingly simple structure in terms of one of the Barnett-Lothe tensors, L. The solution forms for degenerated materials, monoclinic, orthotropic, and isotropic materials are also presented.     

Damage-dependent viscoelastic constitutive relations for glass-fiber woven/polyester composite plate

A damage-dependent viscoelastic constitutive model for a glass-fiber woven/polyester composite plate is presented in this paper. The constitutive relations were derived within the framework of thermodynamics and continuum damage mechanics from some results of the necessary material tests. The elastic moduli and the damage variable of the material are assumed to be anisotropic. In this theoretical model, both the damage- and the time-dependent properties are phenomenological reflections on the macroscopic deformation process.     

考虑材料组成特性的混凝土轴拉破坏过程细观数值模拟

为反映骨料、砂浆及其之间的界面过渡区的组合特点和材料性能,基于材料细观非均匀性和有限元方法的混凝土破坏过程细观数值模拟需进行复杂、细致的网格剖分,导致了繁重的前处理工作和可观的计算量。该文对混凝土材料细观单元材质组成的单一化假定进行改进,将内嵌界面过渡区材料的规则化单元视为一种广义复合材料单元,建立了复合型界面损伤模型。采用等效方法确定单元的复合弹性关系,通过有限元法计算单元的局部应力;用细观层次上弹性力学性能的弱化描述单元组成材料的损伤,混凝土材料的破坏过程通过单元各组分的损伤模拟。应用该复合型界面损伤模型研究了混凝土试件的单轴拉伸破坏过程,细观数值模拟结果符合混凝土试件的宏观破坏特征,表明该模型可作为分析混凝土材料破坏过程的一种有效途径。     

Application of the material force method to isotropic continuum damage

 The objective of this work is the exploitation of the notion of material forces in computational continuum damage mechanics. To this end we consider the framework of isotropic geometrically non–linear continuum damage and investigate the spatial and material settings that lead to either spatial or material forces, respectively. Thereby material forces essentially represent the tendency of material defects to move relative to the ambient material. In this work we combine an internal variable approach towards damage mechanics with the material force method. Thus the appearance of distributed material volume forces that are conjugated to the damage field necessitates the discretization of the damage variable as an independent field in addition to the deformation field. Consequently we propose a monolithic solution strategy for the corresponding coupled problem. The underlying kinematics, strong and weak forms of the coupled problem will be presented and implemented within a standard Galerkin finite element procedure. As a result in particular global discrete nodal quantities, the so–called material node point (surface) forces, are obtained and are studied for a number of computational examples. Received: 19 August 2002 / Accepted: 16 October 2002     

Correlation between fracture and damage for quasi-brittle bi-material interface cracks

Fracture at a bi-material interface is essentially mixed-mode, even when the geometry is symmetric with respect to the crack and loading is of pure Mode I, due to the differences in the elastic properties across an interface which disrupts the symmetry. The linear elastic solutions of the crack tip stress and displacement fields show an oscillatory type of singularity. This poses numerical difficulties while modeling discrete interface cracks. Alternatively, the discrete cracks may be modeled using a distributed band of micro-cracks or damage such that energy equivalence is maintained between the two systems. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in quasi-brittle bi-material interface beams. The study is aimed at large size structures made of quasi-brittle materials failing at concrete-concrete interfaces. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. It is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

A damage-mechanics-based approach for modelling decohesion in adhesively bonded assemblies

A cohesive interface model formulated within the framework of damage mechanics is presented for the simulation of decohesion in adhesively bonded assemblies. Characteristic features of the model are: the introduction of a single energy-based damage variable for describing the damage state of the interface; use of a decohesion propagation condition relying upon the linear elastic fracture mechanics (LEFM) energy balance; a treatment for the mixed-mode situation based on the definition of an equivalent energy release rate whose expression is consistently derived from the formulation. The comparisons between numerical and experimental responses obtained for typical test problems illustrate the capabilities of the proposed approach.     

A constitutive equation for non-linear electro-active solids

Summary Electro-active solids are solids that are either infused with electrorheological fluids or embedded with electrically conducting particles, the body as a whole however conducting negligible current. In this paper, we provide a mathematical framework, within the context of continuum mechanics, for the study of electro-active solids. The theory assumes that the body can be considered as a continuum, in the sense of homogenization, which is isotropic, incompressible, elastic and is capable of responding to an electric field. Appealing to standard techniques in continuum mechanics, we obtain a constitutive relation for the stresses in terms of the deformation and electric field. This is used in a study of triaxial extension, simple shear and anisotropy induced by the electric field.     

A discrete damage mechanics model for high cycle fatigue in polycrystalline materials subject to rolling contact

Fatigue behavior of polycrystalline materials is significantly influenced by their microstructural topology. The microstructural heterogeneity is one of the primary reasons for dispersion in high cycle fatigue lives of such materials. In this work, a damage mechanics based fatigue model that incorporates gradual material degradation under cyclic loading is presented in conjunction with a discrete material representation that takes the material microstructural topology into account. Microstructures are generated stochastically through the process of Voronoi tessellation. Micro-crack initiation, coalescence and propagation stages are modeled using damaged zones in a unified framework. The model is applied to study high cycle fatigue in rolling contacts. The effect of material topological disorder and inhomogeneity on fatigue life dispersion is studied. Fatigue damage is found to originate sub-surface and propagate towards the surface. Sub-surface damage patterns from the model are consistent with experimental observations. Propagation life is found to constitute a significant fraction of total life. Lives are found to follow a 3-parameter Weibull distribution. The relative proportion of lives spent in the initiation and propagation stages are in good quantitative agreement with experiments.