A micromechanical constitutive model for dynamic damage and fracture of ductile materials (original) (raw)
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Modelling of Ductile Failure in Metals under High Velocity Impact Loading
The objective of the work presented in this paper was to generate the thermodynamically consistent coupled thermo-elastic-plastic damage model of solid media at a macroscopic level applicable to hypervelocity impacts. The model is based on the thermodynamics of irreversible processes and the assumption that damage within a continuum can be represented as a damage tensor ij ω [1], [4]. This allows for definition of two scalars that are 3 / kk ω ω = (the volume damage) [2], [3] and ij ij ω ω α ′ ′ = (a norm of the damage tensor deviator ij ij ij ωδ ω ω − = ′) [4]. The parameter ω describes the accumulation of micro-pore type damage (which may disappear under compression) and the parameter α describes the shear related damage. The parameter ω may be considered as a volume content of micro-pores in the material. In the damage-free material we have 0 = = α ω ; if damage is accumulated, ω and α increase in such a manner that they remain less than one. This damage evolution is then coupled...
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.
Modelling of dynamic behaviour of orthotropic metals including damage and failure
A physically based material model for metals, with elastic-plastic and damage/failure orthotropy is proposed in this paper. The model is defined within the frameworks of irreversible thermodynamics and configurational continuum mechanics and integrated in the isoclinic configuration. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Klepaczko (1990) was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model which was used to control evolution of flow stress during plastic deformation. In addition the constitutive model is coupled with a shock equation of state which allows for modelling of shock wave propagation in the material. The new model was implemented in DYNA3D and our in-house non-linear transient SPH code, MCM (Meshless Continuum Mechanics).
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.
International Journal of Fracture, 2006
Dynamic ductile fracture is a three stages process controlled by nucleation, growth and finally coalescence of voids. In the present work, a theoretical model, dedicated to nucleation and growth of voids during dynamic pressure loading, is developed. Initially, the material is free of voids but has potential sites for nucleation. A void nucleates from an existing site when the cavitation pressure p c is reached. A Weibull probability law is used to describe the distribution of the cavitation pressure among potential nucleation sites. During the initial growth, the effect of material properties is essentially appearing through the magnitude of p c . In the later stages, the matrix softening due to the increase of porosity has to be taken into account. In a first step, the response of a sphere made of dense matrix but containing a unique potential site, is investigated. When the applied loading is a pressure ramp, a closed form solution is derived for the evolution of the void that has nucleated from the existing site. The solution appears to be valid up to a porosity of 0.5. In a second part, the dynamic ductile fracture of a high-purity grade tantalum is simulated using the proposed model. Spall stresses for this tantalum are calculated and are in close agreement with experimental levels measured by Roy (2003, Ph.D. Thesis, Ecole Nationale Supérieure de Mécanique et d'Aéronautique, Université de Poitiers, France). Finally, a parametric study is performed to capture the influence of different parameters (mass density of the material, mean spacing between neighboring sites, distribution of nucleation sites. . .) on the evolution of damage.
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.
Fatigue & Fracture of Engineering Materials & Structures, 2020
Micromechanical modelling of void nucleation in ductile metals indicates that strain required for damage initiation reduces exponentially with increasing stress triaxiality. This feature has been incorporated in a continuum damage mechanics (CDM) model, providing a phenomenological relationship for the damage threshold strain dependence on the stress triaxiality. The main consequences of this model modification are that the failure locus is predicted to change as function of stress triaxiality sensitivity of the material damage threshold strain and that high triaxial fracture strain is expected to be even lower than the threshold strain at which the damage processes initiate at triaxiality as low as 1/3. The proposed damage model formulation has been used to predict ductile fracture in unnotched and notched bars in tension for two commercially pure α‐iron grades (Swedish and ARMCO iron). Finally, the model has been validated, predicting spall fracture in a plate‐impact experiment an...
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.
Numerical modelling of ductile damage mechanics coupled with an unconventional.PDF
Ductility in metals includes the material's capability to tolerate plastic deformations before partial or total degradation of its mechanical properties. Modelling this parameter is important in structure and component design because it can be used to estimate material failure under a generic multi-axial stress state. Previous work has attempted to provide accurate descriptions of the mechanical property degradation resulting from the formation, growth, and coalescence of microvoids in the medium. Experimentally, ductile damage is inherently linked with the accumulation of plastic strain; therefore, coupling damage and elastoplasticity is necessary for describing this phenomenon accurately. In this paper, we combine the approach proposed by Lemaitre with the features of an unconventional plasticity model, the extended subloading surface model, to predict material fatigue even for loading conditions below the yield stress.
Dynamic Failure of Ductile Materials
Procedia IUTAM, 2014
The failure of ductile materials subject to high loading rates is notably affected by material inertia. We analyze how strain localization and fracture are influenced by inertia through selected topics comprising dynamic necking, fragmentation, adiabatic shear banding and dynamic damage by micro-voiding. A multiscale modeling of the behavior of voided visco-plastic materials is proposed that extends classical models by including microscale inertia. Applications to spalling and dynamic fracture reveal that microscale inertia has first order effects on results.