An anisotropic model of damage mechanics based on endochronic theory of plasticity

In this paper, an endochronic plastic theory coupled with anisotropic damage is established from the irreversible thermodynamics where the history with plastic deformation and damage is incorporated in the constitutive equations. Experiments have been conducted to verify the proposed theory and a satisfactory correlation between the theoretical results and experimental data has been observed.     

A model of continuum damage mechanics for fatigue failure

This paper describes the development of a generalized model of continuum damage mechanics for fatigue fracture. With the introduction of a new damage effect tensor, the necessary constitutive equations of elasticity and plasticity coupled with damage are for the first instance derived. This is followed by the formulations of fatigue damage dissipative potential function and a fatigue damage criterion which are required for the development of a fatigue damage evolution equation. The fatigue evolution model is based on the hypothesis that the overall fatigue damage is induced by the summation of elastic and plastic damages.The validity of the damage model proposed is verified by comparing the predicted and measured number of cycles to failure for ten tensile specimens each applied with different load ranges and excellent agreement has been achieved.University of Science and Technology of China     

Concerning the fictitious continuum in damage mechanics

Consistent theories to describe damage processes are generally presented within the framework of effective stress and internal parameters. It is well known that damage is concerned with the progressive deterioration of elastic properties due to microscopic defects, such microvoids or microcracks. In the framework of Continuum Mechanics, damage is related to irreversible changes (on the microlevel) of small vicinities surrounding material points in the body. So a convenient definition of these small vicinities, named “representative material element”, will be recalled in Part 1, and application will be made to elastoplasticity in Part 2. In the subsequent parts, a fictitious suitable undamaged elastoplastic body accompanying the real damaged one is introduced in order to define the effective stress in the framework of large strains and its use in the construction of damaged elasticity law. Finally application is made to infinitesimal strains that concern most of the examples in literature. Due to limitation of place, plasticity coupled with damage is not considered in this paper.     

Reduction of mesh sensitivity in continuum damage mechanics

Summary Continuum damage theories can be applied to simulate the failure behaviour of engineering constructions. In the constitutive equations of the material a damage parameter is incorporated. A damage criterion and a damage evolution law are postulated and quantified based on experimental data. The elaboration of the mathematical formulation is performed by common finite element techniques. Without special precautions the numerical results appear to be unacceptably dependent on the measure of the spatial discretization. It is shown that a simple but effective procedure leads to the conservation of objectivity.     

A finite element analysis of continuum damage mechanics for ductile fracture

A finite element formulation of an anisotropic theory of continuum damage mechanics for ductile fracture is presented. The formulation is based on a generalized model of anisotropic continuum damage mechanics of elasticity and plasticity proposed earlier by the authors. The validity of the proposed anisotropic damage model and finite element formulation is verified by comparing the predicted fracture load of center-cracked tension specimen made of thin aluminium alloy 2024-T3 with those determined experimentally and excellent agreement is achieved. The proposed finite element analysis can thus provide an important design tool to solve practical problems of engineering significance which may have hitherto been found difficult using the conventional fracture mechanics concept.

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Résumé On présente une formulation par éléments finis d'une théorie anisotrope de la mécanique d'endommagement d'un continuum, applicable aux ruptures ductiles. Cette formulation est basées sur la généralisation d'un modèle de mécanique d'endommagement d'un continuum anisotrope pour l'élasticité et la plasticité, proposé précédemment par les auteurs. On vérifie la validité du modèle d'endommagement anisotrope proposé et de sa formulation par éléments finis, en comparant aux valeurs expérimentales la charge de rupture prévue pour une éprouvette mince de traction d'alliage d'aluminium 2024-T3 présentant une fissure centrale. On trouve un excellent accord. L'analyse par éléments finis proposée peut ainsi constituer un outil de conception important pour résoudre des problèmes pratiques de construction que l'on aurait trouvé difficiles à traiter par les concepts de la mécanique de rupture traditionnelle.

     

Finite element analysis of anisotropic damage mechanics problems

Elastic constitutive relationships for anisotropic damage mechanics have been developed in this paper. Implementation of these constitutive equations in the finite element analysis is explained. Validation of these relations is provided in the form of comparison of numerical results with the available experimental results. The application of these relationships to an anisotropic damaged foundation problem is discussed.     

Probabilistic analysis of continuum damage mechanics of brittle materials

Uncertainty of material properties in solution of engineering problems is often a fundamental question. Statistical methods give a powerful tool for analysis of uncertainty. Monte Carlo simulations together with Gumbel distribution are used as a possible way to study influence of data dispersion on assessment of damage of brittle materials.     

Non-singular antiplane fracture theory within nonlocal anisotropic elasticity

In the present paper, the distributed dislocation technique is applied for the analysis of anisotropic materials weakened by cracks. Eringen's theory of nonlocal elasticity of Helmholtz type is employed. The non-singular screw dislocation within anisotropic elasticity is distributed to model cracks of mode III. The corresponding dislocation density functions are evaluated using the proper crack-face boundary conditions. The nonlocal stress field within a plane weakened by cracks is determined. The crack opening displacement is also discussed within the framework of nonlocal elasticity. The stress singularity of the classical linear elasticity is removed by the introduction of the nonlocal theory of elasticity. The general anisotropic case and the special case of orthotropic material are studied. The effect of material orthotropy is presented for a crack which is not necessarily aligned with the principal orthotropy direction.     

Numerical prediction of slant fracture with continuum damage mechanics

Ductile specimens always exhibit an inclined fracture surface with an angle relative to the loading axis. This paper reports a numerical study on the cup-cone fracture mode in round bar tensile tests and the slant fracture in plane-strain specimens based on continuum damage mechanics. A combined implicit-explicit numerical scheme is first developed within ABAQUS through user defined material subroutines, in which the implicit solver: Standard, and the explicit solver: Explicit, are sequentially used to predict one single damage/fracture process. It is demonstrated that this numerical approach is able to significantly reduce computational cost for the simulation of fracture tests under quasi-static or low-rate loading. Comparison with various tensile tests on 2024-T351 aluminum alloy is made showing good correlations in terms of the load-displacement response and the fracture patterns. However, some differences exist in the prediction of the critical displacement to fracture.     

Structural mechanics of carbon nanotubes: From continuum elasticity to atomistic fracture

Summary Motivated by recent observations of bent, collapsed and twisted carbon nanotubes, we investigate their behavior at large deformations. These hollow molecules behave remarkably similar to their macroscopic homologs. They reversibly switch into different morphological patterns, and each shape change corresponds to an abrupt release of energy and a singularity in the stress-strain curve. These transformations, simulated using a realistic many-body potential, are accurately described by a continuum-shell model. In contrast, a response to axial tension proceeds smoothly up to a fracture threshold, beyond which a monoatomic carbon chain unravels between the tube fragments.     

A thermodynamic framework for a gradient theory of continuum damage

In this paper, we present a formulation of state variable based gradient theory to model damage evolution and alleviate numerical instability associated within the post-bifurcation regime. This proposed theory is developed using basic microforce balance laws and appropriate state variables within a consistent thermodynamic framework. The proposed theory provides a strong coupling and consistent framework to prescribe energy storage and dissipation associated with internal damage. Moreover, the temporal evolution equation derived here naturally shows the effect of damage—nucleation, growth and coalescence. In addition, the theoretical framework presented here is easily extendable to the addition of other defects (not shown here), and can be generalized to the development of consistent coupled transport equations for species, such as hydrogen (Bammann et al. in JMPS, 2009, submitted), as well as providing a consistent structure for modeling events at diverse length scales.     

A continuum damage mechanics model for void growth and micro crack initiation

A damage mechanics model is proposed to study the void growth and crack initiation. J₂ incremental flow theory along with a damage variable is used to model the material behaviour in elasto-plastic regime. Large deformation (large rotation and finite strain) finite element analysis is carried out for five different cases. In all the cases it is observed that the triaxiality and the plastic strain play an important role in void growth and crack initiation in ductile material. A failure curve is obtained for the material AISI-1090 spheroidised steel. Finally, it is concluded that the critical value of the damage variable can be taken as a crack initiation parameter.     

An alternative model for anisotropic elasticity based on fabric tensors

Motivated by the mechanical analysis of multiphase or damaged materials, a general approach relating fabric tensors characterizing microstructure to the fourth rank elasticity tensor is proposed. Using a Fourier expansion in spherical harmonics, the orientation distribution function of a positive, radially symmetric microstructural property is approximated by a scalar and a symmetric, traceless second rank tensor. Following this approximation, a general expression of the elastic free energy potential is derived from representation theorems for anisotropic scalar functions. Based on a homogeneity assumption for the elastic constitutive law with respect to the microstructural property, a particular elasticity model is developed that involves three independent constants beside the fabric tensors. Strict positive definiteness of the corresponding elasticity tensor is ensured under explicit conditions on the independent constants for arbitrary fabric tensors.     

An exponential ductile continuum damage model for metals

In the frame of continuum damage mechanics an isotropic ductile plastic damage model is derived. The model is based on void damage variable, defined using effective stress concept and thermodynamics. The damage evolution from this model is exponential with equivalent plastic strain as experienced in some low carbon steel like AISI 1015. The damage model is sensitive to stress triaxiality and emulates the damage evolution as recorded in experiments conducted on such metals. The model is validated by comparison with the Rice-Tracey model and other experimental results published in the literature. This model can be used to study the growth and coalescence of micro voids, influence of stress triaxiality on strain to rupture and crack initiation phenomena.     

A non-proportional loading finite element analysis of continuum damage mechanics for ductile fracture

This paper presents the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non-proportional loading. The condition of non-proportional loading is formulated by introducing a dynamic co-ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly. The finite element analysis developed under non-proportional loading is applied to predict the crack initiation load of a centre-cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre-cracked thin plates made of aluminium alloy 2024-T3. The analysis also reveals under non-proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.     

A composite ply failure model based on continuum damage mechanics

A material model including the failure behaviour is derived for a thin unidirectional (UD) composite ply. The model is derived within a thermodynamic framework and the failure behaviour is modelled using continuum damage mechanics. The following features describe the model: (i) The ply is assumed to be in a plane state of stress. (ii) Three damage variables associated with the stress in the fibre-, transverse and shear directions, respectively, are used. (iii) The plastic behaviour of the matrix material is modelled. (iv) The difference in the material response in tensile and compressive loading is modelled. (v) Rate dependent behavior of plasticity and damage (i.e. strength) is modelled.     

A continuum damage mechanics model for crack initiation in mixed mode ductile fracture

This paper presents the development of a fracture criterion based on the postulation that the threshold condition of crack initiation in mixed mode ductile fracture is satisfied when the overall damage w in an element at the prospective direction of crack path reaches its critical value w_c. The validity of the proposed criterion is checked by predicting the fracture loads of thin aluminium plates containing an isolated crack inclined at the angle of =30, 45, 60 and 75 degrees and the predicted loads are compared satisfactorily with those determined experimentally. The analysis is performed based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors, thus providing additional proof of the consistency, applicability and versatility of the model. When the fracture loads of the mixed mode plates calculated using conventional fracture mechanics are compared with those determined using the proposed damage model, a maximum close to 30 percent over-estimation of the loads from the conventional approach is observed as opposed to within 7 percent discrepancy between the computed and measured fracture loads using the damage approach. The observation reveals the importance of including damage consideration in any ductile fracture analysis.The effect of varying damage coefficients on the fracture loads is examined and it is found that the crack initiation load decreases with the increase of anisotropic damage coefficient.