A coupled theory of damage mechanics and finite strain elasto-plasticityI. Damage and elastic deformations (original) (raw)
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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.
A damage model for ductile crack initiation and propagation
Computational Mechanics, 2011
Damage-induced ductile crack initiation and propagation is modeled using a constitutive law with asymmetrical contraction of the yield surface, and tip remeshing combined with a nonlocal strain technique. In practice, this means that the void fraction depends on a nonlocal strain. Finite strain plasticity is used with smoothing of the complementarity conditions. The prototype constitutive laws take into account pressure sensitivity and the Lode angle effect in the fracture strain. Two plane idealizations are tested: plane stress and plane strain. Thickness variation in the former is included by imposing a null out-of-plane stress. In plane strain, pressure unknowns and bubble enrichment are adopted to avoid locking and ensure stability of the equilibrium equations. This approach allows the representation of some 3D effects, such as necking. The nonlocal approach is applied to the strains so that the void fraction value evolves up to one and this is verified numerically. Two verification examples are proposed and one validation example is shown, illustrating the excellent results of the proposed method.
International Journal of Fracture, 2012
In this paper we assess a crack propagation criterion based on the notion of configurational force in the spirit of Gurtin (Configurational forces as basic concepts of continuum physics. Applied mathematical sciences. Springer, Berlin, 2000). We extend the theory of Gurtin to finite strain elasto-plastic fracture and in addition take thermal effects into account. The global model is a system of nonlinear and non-smooth equations which are solved directly with a finite element discretization. Comparison with laboratory experiments is provided, thereby showing that the concept of configurational force can be successfully used for computational damage-based fracture tests on ductile materials.
Ductile fracture initiation and propagation modeling using damage plasticity theory
Engineering Fracture Mechanics, 2008
Ductile fracture is often considered as the consequences of the accumulation of plastic damage. This paper is concerned with the application of a recently developed damage plasticity theory incorporates the pressure sensitivity and the Lode angle dependence into a nonlinear damage rule and the material deterioration. The ductile damaging process is calculated through the so-called “cylindrical decomposition” method. The constitutive
This work outlines a rigorous variational-based framework for the phase field modeling of ductile fracture in elasticeplastic solids undergoing large strains. The phase field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with geometric features rooted in fracture mechanics. It has proven immensely successful with regard to the analysis of complex crack topologies without the need for fracture-specific computational structure such as finite element design of crack discontinuities or intricate crack-tracking algorithms. Following the recent work Miehe et al. (2015), the phase field model of fracture is linked to a formulation of gradient plasticity at finite strains. The formulation includes two independent length scales which regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones, and guarantees on the computational side a mesh objectivity in post-critical ranges. The novel aspect of this work is a precise representation of this framework in a canonical format governed by variational principles. The coupling of gradient plasticity to gradient damage is realized by a consti-tutive work density function that includes the stored elastic energy and the dissipated work due to plasticity and fracture. The latter represents a coupled resistance to plasticity and damage, depending on the gradient-extended internal variables which enter plastic yield functions and fracture threshold functions. With this viewpoint on the generalized internal variables at hand, the thermodynamic formulation is outlined for gradient-extended dissipative solids with generalized internal variables which are passive in nature. It is specified for a conceptual model of von Mises-type elasto-plasticity at finite strains coupled with fracture. The canonical theory proposed is shown to be governed by a rate-type minimization principle, which fully determines the coupled multi-field evolution problem. This is exploited on the numerical side by a fully symmetric monolithic finite element implementation. The performance of the formulation is demonstrated by means of some representative examples.
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.
Computers & Structures, 2002
The continuum damage model for ductile damage and ductile fracture is applied to metal forming and crack propagation by finite element method. The highly nonlinear equilibrium equation is formulated in order to include geometric, material nonlinearities and frictional contact condition. The effect of friction on the damage concentration is shown in the upsetting process. Then it is verified that the ductile fracture using this damage model is reasonable by the comparison with the experimental result in CCT specimen. The influence of the hole at the crack tip is shown through the numerical simulations of edge-cracked plates with different hole size. Finally, the strain energy release rate in this damage model is compared with J-integral using ABAQUS to relate the result of damage analysis to the concept of fracture mechanics.
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.
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...
Discrete crack modelling of ductile fracture driven by non-local softening plasticity
International Journal for Numerical Methods in Engineering, 2006
A combined approach towards ductile damage and fracture is presented, in the sense that a continuous material degradation is coupled with a discrete crack description for large deformations. Material degradation is modelled by a gradient enhanced damage-hyperelastoplasticity model. It is assumed that failure occurs solely due to plastic straining, which is particularly relevant for shear dominated problems, where the effect of the hydrostatic stress in triggering failure is less important. The gradient enhancement eliminates pathological localization effects which would normally result from the damage influence. Discrete cracks appear in the final stage of local material failure, when the damage has become critical. The rate and the direction of crack propagation depend on the evolution of the damage field variable, which in turn depends on the type of loading. In a large strain finite element framework, remeshing allows to incorporate the changing crack geometry and prevents severe element distortion. Attention is focused on the robustness of the computations, where the transfer of variables, which is needed after each remeshing, plays a crucial role. Numerical examples are shown and comparisons are made with published experimental results.