Numerical modelling of ductile damage mechanics coupled with an unconventional.PDF (original) (raw)
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Journal de Physique IV (Proceedings), 2006
It is well established that spall fracture and other rapid failures in ductile materials are often dominated by nucleation and growth of micro-voids. In the present work, a mechanistic model for failure by cumulative nucleation and growth of voids is fully coupled with the thermoelastoplastic constitutive equations of the Mechanical Threshold Stress (MTS) which is used to model the evolution of the flow stress. The damage modeling includes both ductile and brittle mechanisms. It accounts for the effects of inertia, rate sensitivity, fracture surface energy, and nucleation frequency. The MTS model used for plasticity includes the superposition of different thermal activation barriers for dislocation motion. Results obtained in the case of uncoupled and coupled model of plasticity and damage from the simulations of the planar impact with cylindrical target, are presented and compared with the experimental results for OFHC copper. This comparison shows the model capabilities in predicting the experimentally measured free surface velocity profile as well as the observed spall and other damage patterns in the material under impact loading. These results are obtained using the finite element code Abaqus/Explicit.
A damage model for ductile metals
Nuclear Engineering and Design, 1989
A physically-based theory of damage for ductile metals is outlined. It rests upon a direct extension of the authors recently proposed viscoplastic model for finite deformations to include the effects of dislocation-void interactions as they manifest themselves in void nucleation, growth, and coalescence. Emphasis is put on illustrating the general structure of the present framework within which coupling effects of texture development, void formation, and adiabatic heating can be considered and their role to the localization of deformation and failure can be evaluated. No special attention is placed on justifying the various growth laws and simplifying assumptions pertaining to the detailed structure of the model, for example the manner that spatial gradients of the damage variable enter into the theory. Such simplifications, however, facilitate the solution of the relevant equations for a case of homogeneous triaxial state of stress permitting a qualitative comparison with experimental data obtained for Bridgeman-notch specimens.
2012
In this work, a constitutive modeling that couples plasticity, grain size evolution (due to plastic deformation and dynamic recrystallization) and ductile damage has been developed. The effect of grain size on the material yield stress (Hall-Petch) and on the melting temperature has been considered. The model has been used to investigate computationally the behavior of high purity copper in dynamic tensile extrusion test (DTE). An extensive numerical simulation work, using implicit finite element code with direct integration, has been performed and the results have been compared with available experimental data. The major finding is that the proposed model is capable to predict most of the observed features such as the increase of material ductility with the decreasing average grain size, the overall number and size of fragments and the average grain size distribution in the fragment trapped into the dime.
A micromechanical constitutive model for dynamic damage and fracture of ductile materials
International Journal of Fracture, 2010
This paper proposes a detailed theoretical analysis of the development of dynamic damage in plate impact experiments for the case of high-purity tantalum. Our micro-mechanical model of damage is based on physical mechanisms (void nucleation and growth). The model is aimed to be general enough to be applied to a variety of ductile materials subjected to high tensile pressure loading. In this respect, the work of Czarnota et al. (J Mech Phys Solids 56:1624-1650, 2008) has been extended by introducing the concept of nucleation law and by entering a nonlinear formulation of the elastic response based on the Mie-Grüneisen N. Jacques (B) Laboratoire Brestois de Mécanique et des Systèmes, EA 4325, equation of state.
Ductile Damage Evolution Under Different Strain Rate Conditions
2000 ASME International Mechanical Engineering Congress and Exposition, 2000
Failure of ductile metals is always controlled at microstructural level by the formation and growth of microcavities that nucleate from inclusions embedded in the ductile matrix, also at high deformation rate. Many damage models have been proposed to describe both evolutions of these cavities under the action of increasing plastic deformation, and the associated effects on the material behavior. Basically, two classes of damage models are currently available: the Gurson’s type model and continuum damage mechanics (CDM). In the framework of CDM, Bonora (1997) proposed a non-linear damage model for ductile failure that overcome the main limitations presented by others formulations: the model is material independent and its validity under multiaxial state of stress conditions has been verified for a number of class of metals, (Bonora, 1998, Bonora and Newaz, 1997). In addition, this model has the main feature to require a limited number of physically based parameters that can be easily identified with ad hoc tensile tests. In this paper, for the first time, the effect of the strain rate on ductile damage evolution has been studied in a quantitative manner evaluating the material loss of stiffness under dynamic loading. Damage measurements on SA537 Cl 1 steel have been performed according to the multiple strain gauge technique on hourglass shaped rectangular tensile specimen. Dynamic effect was introduced performing the test at different imposed displacement rates. An extensive scanning electron microscopy analysis has been performed in order to correlate damage effects with the microstructure morphological modification as a function of the applied deformation rate.
Damage evolution in ductile materials: from micro- to macro-damage
Computational Mechanics, 1995
This research presents a new simulation concept of damage evolution for metallic materials under large displacements and deformations. The complete damage range is subdivided into both the micro-damage and the macro-damage range. The micro-damage phase is described by the Cocks/Ashby void-growth model for isotropic, ductile materials under isothermal conditions. After having reached a critical void-volume fraction, a macro-crack is introduced into the model. With such a concept the damage evolution from nucleation and growth of first micro-voids to initiation of macro-cracks and complete failure of the material can be simulated. Applying the Finite Element Method for the numerical formulation, at every incremental macro-crack step the Finite Element mesh is adapted such that the crack path remains independent of the initial mesh.
Modeling of the Degradation of Elastic Properties due to the Evolution of Ductile Damage
International Journal of Damage Mechanics, 2007
An elasto-plastic constitutive model for porous materials is formulated within the thermodynamic framework. The formulation facilitates a natural modeling of damage as well as growth and the shrinkage of voids. Metal plasticity is used for demonstrating the possibilities of the formulation. The yield function employed is assumed to depend upon the void-volume fraction, whereas the free energy is dependent on a scalar damage field. To show the capabilities of the model the algorithmic constitutive equations are derived and implemented into a finite element program. It is shown that an extremely simple system involving only two scalar equations needs to be solved in the constitutive driver. Two numerical examples are considered: the necking of an axi-symmetric bar and localization in a notched specimen.
On the coupling of anisotropic damage and plasticity models for ductile materials
International Journal of Solids and Structures, 2003
In this contribution various aspects of an anisotropic damage model coupled to plasticity are considered. The model is formulated within the thermodynamic framework and implements a strong coupling between plasticity and damage. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. The damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The model considers different interaction mechanisms between damage and plasticity defects in such a way that two-isotropic and twokinematic hardening evolution equations are derived, one of each for the plasticity and the other for the damage. An additive decomposition of the total strain into elastic and inelastic parts is adopted in this work. The elastic part is further decomposed into two portions, one is due to the elastic distortion of the material grains and the other is due to the crack closure and void contraction. The inelastic part is also decomposed into two portions, one is due to nucleation and propagation of dislocations and the other is due to the lack of crack closure and void contraction. Uniaxial tension tests with unloadings have been used to investigate the damage growth in high strength steel. A good agreement between the experimental results and the model is obtained.
Fatigue and Fracture Mechanics of High Risk Parts || The Fracture Mechanics of Ductile Metals Theory
1997
Almost all metallic materials manifest some plastic deformation in the region at the crack tip before catastrophic crack propagation. The general principle from which the Griffith theory [1] (see Section 3.1 of Chapter 3) is derived is not limited to materials that obey Hooke's law. The principle applies as well when dissipative mechanisms, such as plastic deformation, are present. Irwin and Orowan [2,3] showed that Griffith's principle can also be applied to materials that manifest ductile behavior, that is: (6.l) where U E is the stored energy, and Up is the energy consumed per unit thickness in plastic straining in the region at the crack tip. For ductile metals, where Up » Us' the expression for surface energy, Us' was omitted from Eq.
International Journal for Numerical Methods in Engineering, 1995
This paper deals with a class of rate-independent metal plasticity models which exhibit non-linear isotropic hardening, non-linear kinematic hardening (Chaboche-Marquis model) and ductile damage (Lemaitre-Chaboche model). The backward Euler scheme is used to integrate the rate constitutive relations. The non-linear equations obtained are solved by the Newton method. The consistent tangent operator is obtained by exact linearization of the algorithm. Despite the complexity of the constitutive equations, closed-form expressions are derived, without any approximations. Analytical, numerical and experimental results are presented and discussed.