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Modelling of damage initiation and propagation in metal forming
Abstract
Continuum damage mechanics is used to model crack initiation as well as crack propagation in metal forming simulations. For
this purpose, a gradient damage formulation is coupled to an existing largestrain elastoplasticity framework. The resulting
equations are solved by the finite element method. Crack initiation and crack growth are traced using remeshing. The numerical
framework has been successfully used to model metal forming operations in two dimensions. Aspects of the – far from trivial
– extension to three dimensions are discussed.
... Applications of remeshing techniques for crack growth modeling can be found in, e.g. [Saouma and Zatz, 1984], [Chiaruttini et al., 2013] for FCG using LEFM, and in [Mediavilla et al., 2006b], [Peerlings et al., 2008], [Feld-Payet, 2010], [El Khaoulani and Bouchard, 2012], [Javani et al., 2016] for cracking in ductile materials. Despite its computationally demanding cost and not easy implementation, such a method has nevertheless provided very promising results. ...
This PhD project aims at assessing the capabilities associated with the local approach to fracture to simulate the propagation of a long fatigue crack in
structural components. To this end, a three-step approach is considered. First, the cyclic non-linear behavior
of the Nickel-based superalloy AD730™ is studied using dedicated cyclic characterization tests at three
target temperatures (20, 550 and 700°C). Crack propagation tests on laboratory specimens are then performed in order to evidence the main crack driving mechanisms. Next, a set of constitutive equations for
the cyclic non-linear behavior of AD730™ is proposed and calibrated. A strong behavior-damage coupling is
settled leading to a time-incremental damage model for fatigue. The model is implemented in a finite element
code using a fully implicit resolution scheme. In order to solve for the mesh-dependency issue, a non-local
extension of the damage model is proposed using an implicit gradient formulation. Finally, an error-based
mesh adaption procedure is considered in order to refine the mesh in the fracture process zone, close to
the crack-tip where the non-linear phenomena occur. Once crack onset is achieved, a crack path tracking algorithm is used to evaluate the geometry and the direction of the crack increment. Then, a damage-to-crack transition consisting in remeshing steps, fields transfer
and equilibrium recovery is performed. This way, crack growth kinetics can be captured. The whole numerical
loop is assessed on calculations conducted on a SEN-T specimen subjected to complex fatigue and
creep-fatigue loading conditions. The capabilities of the proposed approach and its limitations are finally discussed.
... Boyer et al. [3] modified Rice and Tracey damage model by including the effect of shear stress to predict void formation in the ductile metals. General information on continuum damage mechanics on crack initiation in metal forming can be found in the study of Peerlings et al. [30]. Teng et al. [6] conducted split Hopkinson Bar tests on C-shaped specimens to investigate adiabatic shear band formation (ASB) and the effects of ASB on crack formation were determined both experimentally and numerically. ...
... This has the benefit that technologies developed in decades of FE research can rather straightforwardly be used in QC frameworks, e.g. adaptivity (Peerlings et al., 2008). ...
The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a single lattice defect) in macroscale simulations. Since the method works directly and only on the beam lattice, QC frameworks do not require the construction and calibration of an accompanying continuum model (e.g. a cosserat/micropolar description). Furthermore, no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized. Hence, the method is relatively straightforward to implement and calibrate. In this contribution, four variants of the QC method are investigated for their use for planar beam lattices which can also experience out-of-plane deformation. The different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice.
... It is also imperative to mention that the high stacking fault energy of IF steel results in the recovery during annealing leading to the paucity of mobile dislocations and, hence, limited hardening. Therefore, it is also conspicuous that the plasticity is predominantly governed by softening and=or damage growth [28, 29] or stable void growth mechanisms without perceptible hardening. Figures 6a–d present different features concerning fracture of the tensile samples. ...
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The identification of Johnson-Cook parameters and the effect of different temperature gradients on A1050 sheet metal formability were performed. Tensile tests and modified Erichsen were carried out at different temperatures and also combined with numerical simulation to identify Johnson-Cook model parameters and the failure criterion. The obtained parameters were validated using the steam bulge test. A good correlation between numerical and experimental results was obtained in terms of failure behavior during the hot forming process. It was observed that hot forming improves the Erichsen index, and the thermal gradient strongly affects the failure zone position in the deformed specimens.
The use of ultra-high strength steels through sheet metal forming process offers a practical solution to the lightweight design of vehicles. However, sheet metal forming process not only produces desirable changes in material properties but also causes material damage that may adversely influence the service performance of the material formed. Thus, an investigation is conducted to experimentally quantify such influence for a commonly used steel (the 22MnB5 steel) based on the hot and cold forming processes. For each process, a number of samples are used to conduct a uniaxial tensile test to simulate the forming process. After that, some of the samples are trimmed into a standard shape and then uniaxially extended until fracture to simulate the service stage. Finally, a microstructure test is conducted to analyze the microdefects of the remaining samples. Based on the results of the first two tests, the effect of material damage on the service performance of 22MnB5 steel is analyzed. It is found that the material damages of both the hot and cold forming processes cause reductions in the service performance, such as the failure strain, the ultimate stress, the capacity of energy absorption and the ratio of residual strain. The reductions are generally lower and non-linear in the former process but higher and linear in the latter process. Additionally, it is found from the microstructure analysis that the difference in the reductions of the service performance of 22MnB5 by the two forming processes is driven by the difference in the micro damage mechanisms of the two processes. The findings of this research provide a useful reference in terms of the selection of sheet metal forming processes and the determination of forming parameters for 22MnB5.
A proper modelling and understanding of ductile damage and fracture gives us the capability to predict the behavior of metals and alloys in extreme loading cases. Fracture is the final stage of this behavior and a three dimensional modelling provides us with a comprehensive tool to predict it in a realistic manner. Here we focus on three different aspects of numerical modelling: (ielement technology, (iiremeshing issues and (iii3D crack insertion. Each aspect is developed and evaluated independently and finally the combination of them is used for the modelling of large deformation three dimensional crack initiation and propagation.
This chapter describes the material failure by coalescence of microscopic voids. The voids nucleate mainly at second phase particles, by decohesion of the particle-matrix interface or by particle fracture, and subsequently the voids grow because of plastic straining of the surrounding material. The growth of voids to coalescence by plastic yielding of the surrounding material involves so large geometry changes that finite strain formulations of the field equations are a necessary tool. A convected coordinate formulation of the governing equations is used. Convected coordinates are introduced, which serve as particle labels. The convected coordinate net can be visualized as being inscribed on the body in the reference state and deforming with the material. It is found that after nucleation, cavities elongate along the major tensile axis and that two neighboring cavities coalesce when their length has grown to the order of magnitude of their spacing. This local failure occurs by the development of slip planes between the cavities or simply necking of the ligament. A detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and are also elaborated in this chapter.
This paper is devoted to two distinct extensions of Gurson’s (1977) famous model for plastic voided metals. Gurson’s work was based on an approximate limit analysis of a typical elementary volume in a porous material, namely a hollow sphere subjected to conditions of arbitrary homogeneous boundary strain rate. The first extension consists in considering a more general geometry, namely a spheroidal volume containing some spheroidal confocal cavity. The aim here is to incorporate void shape effects into Gurson’s model. The second extension again considers a hollow sphere, but now subjected to conditions of inhomogeneous boundary strain rate. The goal is to account for possible strong variations of the macroscopic mechanical fields at the scale of the representative cell (i.e. of the void spacing), as encountered near crack tips.
This paper presents a numerical–experimental analysis of damage engineering applied to a well-known industrial problem. Many food cans are manually opened by raising a tab on the lid, thus initiating a crack, which is propagated along a circumferential groove. The influence of the groove geometry and depth on the opening force and the resistance against premature opening is investigated for some packaging materials, by making use of dedicated experimental techniques and an operator-split damage-plasticity framework. Attention is focused on a small part of the groove at a location halfway the circular crack-path, 900 from the crack initiation point. First, the groove manufacturing is analyzed by pressing a punch into a thin sheet of the material. Grooved specimens are loaded in tension, simulating the internal pressure during sterilization, and in shear, simulating the opening. Experiments have been carried out using a miniaturized tensile/compression stage located in the objective field of an optical microscope. For the computational analysis, an operator-split damage-plasticity model is proposed, where ductile damage is easily operated in conjunction with standard plasticity models. Simulations are done within a geometrically non-linear context, using a hypo-elasto-plastic material model with non-linear hardening and a contact algorithm to simulate the contact bodies in the groove forming process. An arbitrary–Lagrange–Euler (ALE) technique and adaptive remeshing are used to assure mesh quality during the large deformation process. The operator-split procedure used for the solution of the governing equations, allows to make easy use of a non-local damage operator as an extra feature within a commercial FEM package. Experimental results reveal that a reduction up to 20% for the opening force with unchanged pre-opening resistance can be reached with the use of an asymmetric punch for the groove forming. Numerical and experimental results are in good agreement. Simulations show that the industrial process of can lid production can be optimized considerably by controlling damage evolution in the first stage of the process.
Continuum Damage Mechanics (C. D. M. ) has developed continuously since the early works of Kachanov and Rabotnov. It constitutes a practical tool to take into account the various damaging processes in materials and structures at a macroscopic continuum level. The main basic features of C. D. M. are considered together with its present capabilities, including damage definitions and measures, and its incorporation into a thermodynamic general framework. Practical damage growth equations will be reviewed in the second part of the paper.
Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
Continuum Damage Mechanics (CDM) allows the description of the influence of damage onthe stress-strain behavior of materials. In the paper, some practical damage growth equations are reviewed for creep, fatigue, creep-fatigue interaction, ductile damage, and brittle damage. The capabilities of CDM to improve both the crack initiation and crack propagation predictive tools are then discussed. Particular attention is given to the new developments of the 'local approaches to fracture. '
Building on the local approach to fracture, a framework for finite element simulations of damage development during metal forming is presented. Its application to the fabrication of a food-can lid demonstrates the capabilities, but also the limitations of the framework. One such limitation, the phenomenological basis on which the damage evolution laws are formulated, is subsequently addressed by studying the micromechanics of the underlying damage mechanism – micro-void-growth. Finite element studies illustrate the relevant phenomena and are subsequently used to calibrate evolution laws which are based on understanding of these phenomena. The paper closes with directions for future developments.
Continuum approaches to fracture regard crack initiation and growth as the ultimate consequences of a gradual, local loss of material integrity. The material models which are traditionally used to describe the degradation process, however, may predict premature crack initiation and instantaneous, perfectly brittle crack growth. This nonphysical response is caused by localisation instabilities due to loss of ellipticity of the governing equations and—more importantly—singularity of the damage rate at the crack tip. It is argued that this singularity results in instantaneous failure in a vanishing volume, even if ellipticity is not first lost. Adding strong nonlocality to the modelling is shown to preclude localisation instabilities and remove damage rate singularities. As a result, premature crack initiation is avoided and crack growth rates remain finite. Weak nonlocality, as provided by explicit gradient models, does not suffice for this purpose. In implementing the enhanced modelling, the crack must be excluded from the equilibrium problem and the nonlocal interactions in order to avoid unrealistic damage growth. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
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. Copyright © 2005 John Wiley & Sons, Ltd.
The basic equations to model the coupling between strain and damage behaviors are written within the framework of the thermodynamics of irreversible processes. The damage is represented by a scalar internal variable which expresses the loss of strength of materials during such processes as fatigue, ductile or creep strains. Applications are given in elasticity coupled with damage for brittle failure of concrete or high-cycle fatigue of metals, in plasticity coupled with damage for ductile fracture or low-cycle fatigue, and in visco-plasticity coupled with creep and fatigue damages.
This paper addresses the simulation of ductile damage and fracture in metal forming processes. A combined continuous–discontinuous approach has been used, which accounts for the interaction between macroscopic cracks and the surrounding softening material. Softening originates from the degradation processes taking place at a microscopic level, and is modelled using continuum damage mechanics concepts. To avoid pathological localisation and mesh dependence and to incorporate length scale effects due to microstructure evolution, the damage growth is driven by a non-local variable via a second order partial differential equation. The two governing equations, i.e. equilibrium and non-local averaging, are solved in an operator-split manner. This allows one to use a commercial finite element software to solve the equilibrium problem, including contact between the tools and work piece. The non-local averaging equation is solved on a fixed configuration, through a special purpose code which interacts with the commercial code. A remeshing strategy has been devised that allows: (i) to capture the localisation zone, (ii) prevent large element distortions and (iii) accommodate the crack propagation. To illustrate the capabilities of the modelling tool obtained by combining these continuum mechanics concepts and computational techniques, process simulations of blanking, fine-blanking and score forming are presented.
Together with error evaluation and mesh refinement, transfer operators represent the essential component of the adaptive procedure applied to history-dependent materials. Aspects of the transfer operation discussed in this work relate to: equilibrium conditions, consistency with the constitutive equation, geometric issues and diffusion of state variables between successive meshes. In this paper attention is restricted to small strain rate-independent elasto-plasticity. Numerical examples are presented to illustrate some practical features of the computational procedure.