F.M. Andrade Pires

Numerical modelling of ductile plastic damage in bulk metal forming

Abstract 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 Ladeveze (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.

A Ductile Damage Nonlocal Model of Integral-type at Finite Strains: Formulation and Numerical Issues

This contribution is devoted to the formulation and numerical implementation of a ductile damage constitutive model enriched with a thermodynamically consistent nonlocal theory of integral type. In order to describe ductile deformation, the model takes finite strains into account. To model elasticity, a Hencky-like hyperelastic free energy potential coupled with nonlocal damage is adopted. The thermodynamic consistency of the model is ensured by applying the first and second thermodynamical principles in the global form and the dissipation inequality can be re-written in a local form by incorporating a nonlocal residual that accounts for energy exchanges between material points of the nonlocal medium. The thermodynamically consistent nonlocal model is compared with its associated classical formulation (in which nonlocality is merely incorporated by averaging the damage variable without resorting to thermodynamic potentials) where the thermodynamical admissibility of the classical formulation is demonstrated. Within the computational scheme, the nonlocal constitutive initial boundary value problem is discretized over pseudo-time where it is shown that well established numerical integration strategies can be straightforwardly extended to the nonlocal integral formulation. A modified Newton-Raphson solution strategy is adopted to solve the nonlinear complementarity problem and its numerical implementation, regarding the proposed nonlocal constitutive model, is presented in detail. The results of two-dimensional finite element analyses show that the model is able to eliminate the pathological mesh dependence inherently present under the softening regime if the local theory is considered.

A comparison of shear mechanisms for the prediction of ductile failure under low stress triaxiality

Purpose – The purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson‐Tveegard‐Needleman ductile damage constitutive model under low stress triaxiality.Design/methodology/approach – One of the most widely used ductile damage models is the so‐called Gurson‐Tveegard‐Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro‐voids. However, the GTN model does not include void distortion and inter‐void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi‐static finite element framework and their results critically appraised.Findings – Through the analysis of the evolution of internal variables, such a...

Assessment and Comparison of Non-local Integral Models for Ductile Damage

Over the past years, the non-local method has established itself as an effective remedy to the well-known pathological mesh dependency that inherently affects softening media. The non-local method incorporates an intrinsic length into the traditional continuum theory and therefore the size of the localising zone is resolved, attenuating the unwanted effects of spurious mesh dependency. However, despite many contributions that have successfully employed the non-local theory, it is still not clear how exactly should non-locality be formulated in the general sense. Aiming to answer the question of which non-local formulations effectively lead to mesh-insensitive results, we select in this article several constitutive variables to be non-local quantities by taking both Lemaitre and Gurson–Tvergaard–Needleman models as the base for the non-local enhancement. The resulting non-local constitutive models are employed in the numerical simulation of various specimens which are subjected to different values of stress triaxiality and third invariant at the fracture zone. The goal is to find which models present the best performance in the task of providing mesh-insensitive solutions for different stress states. The results show that strain-softening mesh dependency is stronger in plane strain than in the axisymmetric case. It is also found that the variables that regularise the solution in the axisymmetric case do not necessarily eliminate mesh sensitivity in the other cases. Furthermore, the results indicate that damage should be the preferred non-local variable in the case of implicit damage models. This result is in sharp contrast with the case of explicit damage models, for which it has already been shown in the literature that damage is a bad candidate for non-local variable.

Study of Tool Trajectory in Incremental Forming

Single point incremental forming (SPIF) is an innovative flexible sheet metal forming process which can be used to produce complex shapes from various materials. Due to its flexibility, it attracts a more and more attention in the recent decades. Several studies show that besides the major operating parameters, namely feed rate, tool radius, and forming speed etc., tool path is also an important processing parameter to affect the final forming component. In view of that, the present paper studies the influence of tool paths on the work piece quality by the finite element method coupled with the Continuum Damage Mechanics (CDM) model. The formability of incremental forming in different tool paths is also analyzed.

A radial point interpolation meshless method extended with an elastic rate-independent continuum damage model for concrete materials

ABSTRACT An advanced discretization meshless technique, the radial point interpolation method (RPIM), is applied to analyze concrete structures using an elastic continuum damage constitutive model. Here, the theoretical basis of the material model and the computational procedure are fully presented. The plane stress meshless formulation is extended to a rate-independent damage criterion, where both compressive and tensile damage evolutions are established based on a Helmholtz free energy function. Within the return-mapping damage algorithm, the required variable fields, such as the damage variables and the displacement field, are obtained. This study uses the Newton–Raphson nonlinear solution algorithm to achieve the nonlinear damage solution. The verification, where the performance is assessed, of the proposed model is demonstrated by relevant numerical examples available in the literature.

Impact of the geometry of inclusions at the micro-scale on the overall stochastic properties

ABSTRACT In this contribution, the establishment of relationships between the microstructure of the material and the macroscopic properties is numerically investigated. The material under study is composed by inclusions randomly distributed on a uniform matrix and its heterogeneous nature is characterized by the size, shape, spatial distribution, and properties of the inclusions. To conduct these analyses, a general framework that generates and simulates representative volume elements (RVEs) based on the commercial finite element (FEM) software ABAQUS and existing homogenization techniques is developed. Two- and three-dimensional RVEs are generated and the variation of the properties investigated using a statistical approach.

Computational Strategies for Polymer Coated Steel Sheet Forming Simulations

This contribution discusses current issues involved in the numerical simulation of large scale industrial forming processes that employ polymer coated steel sheet. The need for rigorous consideration of both theoretical and algorithmic issues is emphasized, particularly in relation to the computational treatment of finite strain deformation of polymer coated steel sheet in the presence of internal degradation. Other issues relevant to the effective treatment of the problem, including the modelling of frictional contact between the work piece and tools, low order element technology capable of dealing with plastic incompressibility and thermo mechanical coupling, are also addressed. The suitability of the overall approach is illustrated by the solution of an industrially relevant problem.

Numerical investigation of fracture onset in sheet metal forming

Sheet metal forming processes involve finite inelastic strains that are mainly restricted by the occurrence of strain localization and instability due to necking. Therefore the ability to predict the formability limit is of paramount importance in order to optimize the process, examine the influence of each parameter on the necking occurrence and consequently to improve the press performance. Forming limit diagrams, associated with finite element simulations are currently performed by powerful commercial codes. Nevertheless, when complex strain paths are involved these predictions may fail to give the right answer.

A Comparative Study of Failure with Incremental Forming

Incremental forming (ISF) is an innovative flexible sheet metal forming process which can be used to manufacture complex shapes from various materials. Due to its flexibility, it has attracted more and more attention over recent decades. Localized deformation and shear through the thickness are essential characteristics of ISF. These lead to specific failure modes and formability of ISF that are different from the conventional stamping process. In this contribution, three continuum damage models (Lemaitre, Gurson, extended GTN models) are formulated and fully coupled with the finite element simulation in a commercial software ABAQUS to predict failure in incremental forming. A comparative investigation of these three damage models has been carried out to analyze both the deformation behavior and failure mechanisms.