On kinematic, thermodynamic, and kinetic coupling of a damage theory for polycrystalline material (original) (raw)
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Engineering Structures, 2017
In this study, a generic formulation for constitutive modelling of engineering materials is developed, employing theories of plasticity and continuum damage mechanics. The development of the proposed formulation is carried out within the framework of thermodynamics with internal variables. In this regard, the complete constitutive relations are determined by explicitly defining a free energy potential and a dissipation potential. The focus is put on the rigour and consistency of the proposed formulation in accommodating the coupling between damage and plasticity, while keeping its structure sufficiently generic to be applicable to a wide range of engineering materials. In particular, by specifying the coupling between damage and plasticity in the dissipation function, a single generalised loading function that controls the simultaneous evolution of these dissipative mechanisms is obtained. The proposed formulation can be readily used for either enriching existing plasticity models with damage, or for the developments of new coupled damage-plasticity models. The promising features and the applications of the proposed formulation for describing the behaviour of different engineering materials are discussed in details.
A plasticity-damage theory for large deformation of solidsI. Theoretical formulation
International Journal of Engineering Science, 1992
A coupled theory of continuum damage mechanics and finite strain plasticity (with small elastic strains) is formulated in the Eulerian reference system. The yield function used is of the von Mises type and incorporates both isotropic and kinematic hardening. An explicit matrix representation is derived for the damage effect tensor for a general state of deformation and damage. Although the theory is applicable to anisotropic d.-unage, the matrix representation is restricted to isotropy.
A new thermodynamically consistent continuum model for hardening plasticity coupled with damage
International Journal of Solids and Structures, 2002
A phenomenological model for hardening-softening elasto-plasticity coupled with damage is presented. Specific kinematic internal variables are used to describe the mechanical state of the system. These, in the hypothesis of infinitesimal changes of configuration, are partitioned in the sum of a reversible and an irreversible part. The constitutive equations, developed in the framework of the Generalised Standard Material Model, are derived for reversible processes from an internal energy functional, postulated as the sum of the deformation energy and of the hardening energy both coupled with damage, while for irreversible phenomena from a dissipation functional.
Acta Mechanica, 2008
We formulate a macroscopic description of the mechanics of damaged materials. To represent the microstructure, the distribution of crack sizes is captured by way of the Minkowski functionals, or so-called quermass integrals, while a second-rank tensor is used to describe the average orientation of the cracks. A two phase-type approach is adopted to distinguish elastically strained material from unstrained regions in the wake of the cracks. Using nonequilibrium thermodynamic techniques, the driving force for the growth of the microcracks is naturally identified. In particular, Griffith's law is generalized to assemblies of polydisperse crack sizes. Due to the detailed characterization of the microstructure, we are also able to account for the plastic zones at the rims of the cracks that are known to hamper the crack growth, and to discuss possible forms of the damage parameter. The presented approach separates in a transparent fashion the incorporation of fundamental thermodynamic and mechanic principles on one hand, from the specification of the material and details of the crack formation and growth on the other hand.
International Journal of Engineering Science, 1990
coupled theory of elasticity and continuum damage mechanics is formulated here. It is assumed that the material undergoes damage with small elastic strains. The hypothesis of elastic energy equivalence is used in order to produce the proposed coupling. The damage variable used represents average material degradation which reflects the various types of damage at the microscale level like nucleation and growth of voids, cavities, micro-cracks and other microscopic defects.
International Journal of Engineering Science, 1990
coupled theory of elasticity and continuum damage mechanics is formulated here. It is assumed that the material undergoes damage with small elastic strains. The hypothesis of elastic energy equivalence is used in order to produce the proposed coupling. The damage variable used represents average material degradation which reflects the various types of damage at the microscale level like nucleation and growth of voids, cavities, micro-cracks and other microscopic defects.
Damage evolution under severe plastic deformation
International journal of fracture, 2002
The development and recovery of damage in continuously cast aluminium alloy 6061 due to plastic deformation is investigated for different stress histories. The processes of Equal Channel Angular Extrusion and Equal Channel Angular Drawing are used to introduce damage into the specimen for a specified stress history. The amount of plastic deformation is determined by the angle between the two intersecting channels, while the stress history is varied by applying different back-pressures. The damage is related to the density, measured using Archimedes' principle. The development of damage was observed to increase proportionally with the extent of accumulated plastic shear strain. The influence of stress history, characterised by a stress index, was found to be twofold. First, the stress index defines the intensity of the porosity development, which increases with the stress index as it changes from negative to positive values. Second, the stress index, when in the negative value region, governs the recovery process. A superimposition of high compressive stresses on the plastic shear deformation leads to a recovery of damage and an associated density increase. The kinematic equation for damage evolution is proposed and its coefficients are defined.
On the Modeling of Deformation-Diffusion-Damage Coupling in Elastic Solids
III European Conference on Computational Mechanics, 2006
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion-damage in elastic solids. The formulation is carried out within the framework of continuum mechanics, where, in addition to the standard fields, extra fields are introduced in order to describe diffusion and damage processes. The governing equations are then obtained after supplementing the basic balances with a thermodynamically consistent constitutive theory. The couplings are implemented via the free energy response and include both deformation and damage assisted diffusion. It is worth mentioning that a gradient damage theory is obtained, which allows the modeling of fracture problems. The numerical implementation is based on the finite element method and a Euler implicit scheme for spatial and temporal discretizations, respectively. A numerical algorithm is presented to solve the discrete system of equations. In order to illustrate the potentiality of the proposed model, applications in the context of hydrogen embrittlement are presented.
The mechanical anisotropic properties of aluminum alloy are studied using multi-level approaches for strain-rate and temperature-sensitive large plastic deformation of polycrystalline aggregates. Unlike previous researches, the thermal effect and the damage evolution process are considered simultaneously and integrated in the CPFEM method. In the microscopic constitutive equation of crystal plasticity, the shear strain rate on the slip system is described by an advanced exponential function based on thermal activated mechanism, instead of traditional phenomenological power-law function. To determine the rate-sensitive material parameters in this new model, the strain rate and temperature jump tests are performed. In addition, a simulation of one representative volume element is compared to the results of conventional tensile tests to obtain other thermal parameters. Coupled with the continuum damage evolution formula, this thermal affected crystal plasticity model is then implemented in a single crystal analysis for different orientation, temperature and strain rate conditions. Finally, this extended crystal plasticity model is applied in the finite element method to simulate the mechanical properties of 5052 aluminum alloy at absolute temperature 473 K. Taylor model is also used to compare these simulations as well as the experimental data. The results show that the damage model coupled in the crystal plasticity is able to predict the mechanical response of 5052 aluminum alloy; moreover, this model can simulate the explicit evolution of damage factor and local stress concentration in the deformation of standard tensile test specimen. In the simulation, the specimen is meshed by rectangular elements and each element is given an initial orientation at the first time increment step. This study argues that even in high temperature, the orientation mismatch between adjacent grains could lead to early cavity or crack initiation and the damage development is similar to the void evolution theory. An explanation of the possible fracture angle is given in the thermal tensile test due to polycrystalline anisotropy. At last, the analysis of stress heterogeneity and texture evolution is also shown in this study.
Survey of modern trends in analysis of continuum damage mechanics
A brief review of the damage mechanics literature is given. As this area of scientific research is very modern, the authors have restricted themselves to about 100 most important books and papers. Basic equations to introduce the isotropic model in the framework of thermodynamics are given in a form easily applicable in numerical symulations.