Ductile Plastic Damage Research Articles

A three-dimensional multi-scale polycrystalline plasticity model coupled with damage for pure Ti with harmonic structure design

In this paper, we developed, on the basis of the crystalline plasticity and homogenization method, a three-dimensional multi-scale numerical model to simulate the non-linear and damage behaviors of pure titanium with harmonic structure (HS). The theoretical approach couples a kinematic hardening law for slip systems in the Ti hexagonal crystals; the consideration of the grain size effect modulated by the Hall-Petch law; a special localization-homogenization procedure to allow transforming the microscopic hardening law into the macroscopic constitutive law and avoiding the microstructure meshing of the grains in a bimodal grain distribution; and finally, the Lemaître-Chaboche macroscopic ductile plastic damage model in order to describe the granular damage. This model was implemented into a finite element code by means of the User Defined Material files. The results of the numerical simulation show that the proposed model can predict the crystalline plasticity behavior efficiently for bimodal HS Ti. Moreover, the computing time is optimized and reduced to a very low level.

Numerical modelling of ductile plastic damage in bulk metal forming

This work addresses the computational aspects of a model for rigid–plastic damage. The model is a modification of a previous established model formulated by Perzyna (Recent Advances in Applied Mechanics, Academic Press: New York, 1966, p. 243–377 (Chapter 9)) which is here extended to include isotropic damage. Such an extension is obtained by incorporating the constitutive equations introduced by Lemaitre (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31; A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) for ductile plastic damage into the original model. In its original version (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31) this model does not distinguish tension and compression in the damage evolution law, so it was necessary to introduce a refinement proposed by Ladevèze (in: J.P. Boehler, (Ed.), Proceedings of CNRS International Colloquium 351 Villars-de-Lans, France (Failure Criteria of Structured Media, 1983, p. 355) and Lemaitre (A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) which takes into account the partial crack closure effect with isotropic damage. The accuracy of the computational model, developed for the analysis of the material degradation in bulk metal forming processes, is shown through the discussion of the results of two examples, allowing to compare the simulation results with experimental and numerical results obtained by other authors.

Numerical shakedown analysis of damaged structures

A numerical method is proposed to predict the failure of mechanical structures. It is based on the generalization of the classical static shakedown theorem to damaged inelastic structures. Ductile plastic damage is taken into account by using the models of Lemaitre and Shichun-Hua. The obtained results are compared in the special case of limit analysis to those obtained by incremental methods.

A new free energy for plastic damage analysis

This work presents a new free energy for the ductile plastic damage analysis. The derivation here is based on the ductile plastic damage model proposed by Lemaitre and the examination of the plastic strain of a damaged material. The result given here can be used for the damage evolution law derived from the potential of dissipation.

An isotropic damage model for ductile material

A continuum isotropic ductile plastic damage model has been derived in the framework of internal variable theory of thermodynamics. The damage model is based on the concept of effective stress and the principle of strain equivalence. The damage model shows non-linear variation with respect to plastic strain, and is sensitive to stress triaxiality. The predictions using the model compare well with experimental results of certain aluminium alloys. This damage model can be used for such metals to study the effect of stress triaxiality on the strain to rupture.

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 Computational Model for Fe Ductile Plastic Damage Analysis of Plate Bending

This paper presents a computational model for the finite element plastic damage analysis of ductile flexural plates. The phenomenological damage model proposed by Lemaitre is adopted here. The damage effect parameters of a cross-section are defined and employed to account for the damage effect across the thickness of a bending plate. Similar to the effective stresses used in many damage models, the effective stress couples are introduced in this work and used in the yield function. The damage criterion is defined in terms of damage strain energy release rates. Based on the damage node model proposed here, the elastoplastic-damage stiffness matrix of element is derived. When the corresponding elastic stiffness matrix is given explicitly, the resulting elastoplastic-damage stiffness matrix can be evaluated without use of numerical integration. The feature of the expicit form of element stiffness matrix makes the computational model proposed here very efficient. Several numerical examples of ductile plastic damage analysis of plates are also given in this work to demonstrate the validity of the computational model.

A continuum damage model for ductile fracture of weld heat affected zone

In this paper, the ductile plastic damage behaviour of weld heat affected zone (HAZ) is studied by use of continuum damage mechanics (CDM). Based on a continuum damage variable, D, the effective stress concept and the thermodynamics, a general continuum damage model for Isotropie ductile fracture is derived from a new dissipation potential chosen by the author herein. A comparison between the damage model and experimental results is presented and a good agreement is found. The model is also used to analyse the ductile plastic damage evolution in thermally simulated welding coarse-grained HAZ of a low alloy steel. The effects of stress triaxiality on plastic damage evolution and on ductile fracture of the coarse-grained HAZ are discussed.

Determination of the ductile plastic damage variable for the annealed 30CrMnSi

Determination of the ductile plastic damage variable for the annealed 30CrMnSi

A kinetic equation for ductile damage at large plastic strain

In accordance with the viewpoint of continuous damage mechanics, a kinetic equation for the isotropic ductile plastic damage variable, based on the feature of void-type plastic damage and on thermodynamics, is derived. The damage variable is linear with equivalent strain and it is shown that it is affected remarkably by the triaxiality stress ratio. The kinetic equation of the damage variable in this paper may reflect not only the influence of a positive triaxiality ratio but also the influence of a negative triaxiality ratio. A comparison with the results of some experiments is presented on the influence of the triaxiality stress ratio on the strain to rupture: good correlation is found between the theoretical and experimental results.

A Continuous Damage Mechanics Model for Ductile Fracture

A model of isotropic ductile plastic damage based on a continuum damage variable, on the effective stress concept and on thermodynamics is derived. The damage is linear with equivalent strain and shows a large influence of triaxiality by means of a damage equivalent stress. Identification for several metals is made by means of elasticity modulus change induced by damage. A comparison with the McClintock and Rice-Tracey models and with some experiments is presented for the influence of triaxiality on the strain to rupture.