MATERIALS PROCESSING AND DESIGN; Modeling, Simulation and Applications; NUMIFORM '07; Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes
908(2007); http://dx.doi.org/10.1063/1.2740786View Description Hide Description
This paper reviews aspects of the plastic behavior common in metals and alloys. Macroscopic and microscopic phenomena occurring during plastic deformation are described succinctly. Constitutive descriptions of plasticity at the microscopic and macroscopic scales, suitable for applications to forming, are discussed in a very broad fashion. Approaches to plastic anisotropy are reviewed in a more detailed manner.
908(2007); http://dx.doi.org/10.1063/1.2740787View Description Hide Description
The growth of internal voids in the process of friction stir welding of stainless steel was simulated using a damage model that considers both strain hardening and porosity evolution. In the void growth equations, the mean stress (hydrostatic stress) was scaled by the state variable for plastic flow resistance, i. e. strength. The damage model was coupled with the viscoplastic deformation and thermal processes using a steady‐state Eulerian formulation in a finite element scheme. The porosity and strength were calculated by integration of the evolution equations along streamlines of the flow field. The distributions of microvoids as well as the strength within the material were obtained. These distributions were used to model the effects of operational parameters such as the tool rotational and translational speeds as well as the pin threads on the growth of porosity.
908(2007); http://dx.doi.org/10.1063/1.2740788View Description Hide Description
Plastic packaging waste currently forms a significant part of municipal solid waste and as such is causing increasing environmental concerns. Such packaging is largely non‐biodegradable and is particularly difficult to recycle or to reuse due to its complex composition. Apart from limited recycling of some easily identifiable packaging wastes, such as bottles, most packaging waste ends up in landfill sites. In recent years, in an attempt to address this problem in the case of plastic packaging, the development of packaging materials from renewable plant resources has received increasing attention and a wide range of bioplastic materials based on starch are now available. Environmentally these bioplastic materials also reduce reliance on oil resources and have the advantage that they are biodegradable and can be composted upon disposal to reduce the environmental impact.
Many food packaging containers are produced by thermoforming processes in which thin sheets are inflated under pressure into moulds to produce the required thin wall structures. Hitherto these thin sheets have almost exclusively been made of oil‐based polymers and it is for these that computational models of thermoforming processes have been developed. Recently, in the context of bioplastics, commercial thermoplastic starch sheet materials have been developed. The behaviour of such materials is influenced both by temperature and, because of the inherent hydrophilic characteristics of the materials, by moisture content. Both of these aspects affect the behaviour of bioplastic sheets during the thermoforming process.
This paper describes experimental work and work on the computational modelling of thermoforming processes for thermoplastic starch sheets in an attempt to address the combined effects of temperature and moisture content. After a discussion of the background of packaging and biomaterials, a mathematical model for the deformation of a membrane into a mould is presented, together with its finite element discretisation. This model depends on material parameters of the thermoplastic and details of tests undertaken to determine these and the results produced are given. Finally the computational model is applied for a thin sheet of commercially available thermoplastic starch material which is thermoformed into a specific mould. Numerical results of thickness and shape for this problem are given.
908(2007); http://dx.doi.org/10.1063/1.2740789View Description Hide Description
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.
908(2007); http://dx.doi.org/10.1063/1.2740790View Description Hide Description
We propose to improve the Level Set method by introducing a convective derivative in the reinitialisation equation. Our approach allows to keep an unitary gradient for Level Set function at the interface. In this way, it is not necessary to regularize periodically the level set since the basic properties are preserved when it is convected. Moreover a local Level Set is introduced by using a sinus like function which enables to ensure a smooth transition. Examples are given in the context of finite element method for forming applications.
908(2007); http://dx.doi.org/10.1063/1.2740791View Description Hide Description
The paper discusses the utility and relevance of general purpose codes such as ABAQUS in forming simulations. The paper discusses some of the technologies embedded in ABAQUS and how they can be useful to simulating and solving industrial forming problems. The paper demonstrates this with three relevant examples pertaining to stamping, sheet‐stretching and forming of medical devices made out of super‐elastic materials.
908(2007); http://dx.doi.org/10.1063/1.2740792View Description Hide Description
Two analytical approaches are detailed for the determination of Forming Limit Diagrams (F.L.D.) and compared with experimental results. The first one is the “Enhanced Modified Maximum Force Criterion EMMFC” and the second one is the “Through‐Thickness Shear Instability Criterion TTSIC”. The criteria are both written in an intrinsic analytical form and are applicable to linear and non‐linear strain paths as it occurs in any FEM codes for sheet‐metal forming simulation. Finally, the two methods are complementary depending on the nature of failure and the predicted curves are in reasonable agreement with the trend of experimental results for a wide range of materials.
908(2007); http://dx.doi.org/10.1063/1.2740793View Description Hide Description
Prediction of the onset of necking is of large importance in reliability of forming simulation in present automotive industry. Advanced material models require accurate descriptions of the plastic material behaviour including the effect of strain rate. The usual approach for identifying the forming limits in industry is the comparison of a calculated strain map (major against minor strain) with a measured forming limit curve. This approach does not take into account the influence of strain path changes. Prediction of forming limit curves with classical material models can already demonstrate that the forming limits are influenced by this strain path change effect. Including the effect of strain rate on the plastic material behaviour has a strong influence in prediction of onset of instability. Neglecting this effect leads to underestimation of forming capacity of the material in stretch forming parts in particular. The shape of the yield locus will influence the predicted forming limit curves in the region from plane strain to bi‐axial. Damage controlled failure will become more important using (advanced) high strength steels. This will affect the stress strain curve at high deformation grades. The work hardening is not only controlled by dislocation interaction, but also by void growth and possible presence of micro‐cracks at the interface between the hard en soft phases.
908(2007); http://dx.doi.org/10.1063/1.2740794View Description Hide Description
The forming limits of austenitic stainless steel sheets were studied in this work. It was found that the observed limit of straining in stretch forming, when both of the principal stresses are positive, is not set by localized necking, but instead by inclined shearing fracture in the through thickness direction. It appears that the forming limits of austenitic stainless steels may be predicted fairly well by using the classical localized and diffuse necking criteria developed by Hill. The strain path‐dependence may be accounted for by integrating the effective strain along the strain path. The fracture criteria of Rice and Tracey and Cockcroft, Latham and Oh were also studied. The results were in qualitative agreement with the experimental observations. Recent experiments with high‐velocity electrohydraulic forming of austenitic stainless steels revealed localized necks in stretch formed parts, which are not commonly observed in conventionally formed sheet metal parts.
Possibilities And Influencing Parameters For The Early Detection Of Sheet Metal Failure In Press Shop Operations908(2007); http://dx.doi.org/10.1063/1.2740795View Description Hide Description
The concept of forming limit curves (FLC) is widely used in industrial practice. The required data should be delivered for typical material properties (measured on coils with properties in a range of +/− of the standard deviation from the mean production values) by the material suppliers. In particular it should be noted that its use for the validation of forming robustness providing forming limit curves for the variety of scattering in the mechanical properties is impossible. Therefore a forecast of the expected limit strains without expensive cost and time‐consuming experiments is necessary. In the paper the quality of a regression analysis for determining forming limit curves based on tensile test results is presented and discussed.
Owing to the specific definition of limit strains with FLCs following linear strain paths, the significance of this failure definition is limited. To consider nonlinear strain path effects, different methods are given in literature. One simple method is the concept of limit stresses. It should be noted that the determined value of the critical stress is dependent on the extrapolation of the tensile test curve. When the yield curve extrapolation is very similar to an exponential function, the definition of the critical stress value is very complicated due to the low slope of the hardening function at large strains.
A new method to determine general failure behavior in sheet metal forming is the common use and interpretation of three criteria: onset on material instability (comparable with FLC concept), value of critical shear fracture and the value of ductile fracture. This method seems to be particularly successful for newly developed high strength steel grades in connection with more complex strain paths for some specific material elements. Nevertheless the identification of the different failure material parameters or functions will increase and the user has to learn with the interpretation of the numerical results.
908(2007); http://dx.doi.org/10.1063/1.2740796View Description Hide Description
Ductile (or plastic) damage often occurs during sheet metal forming processes due to the large plastic flow localization. Accordingly, it is crucial for numerical tools, used in the simulation of that processes, to use fully coupled constitutive equations accounting for both hardening and damage. This can be used in both cases, namely to overcome the damage initiation during some sheet metal forming processes as deep drawing, … or to enhance the damage initiation and growth as in sheet metal cutting. In this paper, a fully coupled constitutive equations accounting for combined isotropic and kinematic hardening as well as the ductile damage is implemented into the general purpose Finite Element code for metal forming simulation. First, the fully coupled anisotropic constitutive equations in the framework of Continuum Damage Mechanics are presented. Attention is paid to the strong coupling between the main mechanical fields as elasto‐viscoplasticity, mixed hardening, ductile isotropic damage and contact with friction. The anisotropy of the plastic flow is taken into account using various kinds of quadratic or non quadratic yield criteria in the framework of non associative finite plasticity theory with two types of normality rules. The associated numerical aspects concerning both the local integration of the coupled constitutive equations as well as the (global) equilibrium integration schemes are presented. The local integration is outlined thanks to the Newton iterative scheme applied to a reduced system of 2 equations. For the global resolution of the initial and boundary value problem, the classical dynamic explicit (DE) scheme with an adaptive time step control is used. The numerical implementation of the damage is made in such a manner that calculations can be executed with or without damage effect, i.e. fully coupled or uncoupled calculations. For the 2D processes an advanced adaptive meshing procedure is used in order to enhance the numerical solution and to kill the fully damaged elements in order to describe the macroscopic crack propagation. Various 2D and 3D examples are given in order to show the capability of the methodology to predict the damage initiation and growth during various sheet metal forming processes.
908(2007); http://dx.doi.org/10.1063/1.2740797View Description Hide Description
Non‐linear Finite Element simulations are extensively used in forming and crashworthiness studies of automotive components and structures in which fracture need to be controlled. For thin‐walled ductile materials, the fracture‐related phenomena that must be properly represented are thinning instability, ductile fracture and through‐thickness shear instability. Proper representation of the fracture process relies on the accuracy of constitutive and fracture models and their parameters that need to be calibrated through well defined experiments. The present study focuses on local necking and fracture which is of high industrial importance, and uses a phenomenological criterion for modelling fracture in aluminium alloys. As an accurate description of plastic anisotropy is important, advanced phenomenological constitutive equations based on the yield criterion YLD2000/YLD2003 are used. Uniaxial tensile tests and disc compression tests are performed for identification of the constitutive model parameters. Ductile fracture is described by the Cockcroft‐Latham fracture criterion and an in‐plane shear tests is performed to identify the fracture parameter. The reason is that in a well designed in‐plane shear test no thinning instability should occur and it thus gives more direct information about the phenomenon of ductile fracture. Numerical simulations have been performed using a user‐defined material model implemented in the general‐purpose non‐linear FE code LS‐DYNA. The applicability of the model is demonstrated by correlating the predicted and experimental response in the in‐plane shear tests and additional plane strain tension tests.
908(2007); http://dx.doi.org/10.1063/1.2740798View Description Hide Description
In the following paper, a full mechanical characterization of the AA6016 T4 aluminum alloy car body sheet DR100 is presented. A comprehensive experimental program was performed to identify and model the orthotopic elasto‐plastic deformation behavior of the material and its fracture characteristics including criteria for localized necking, ductile fracture and shear fracture. The commercial software package MF GenYld + CrachFEM in combination with the explicit finite element code Ls‐Dyna is used to validate the quality of the material model with experiments, namely, prediction of the FLD, deep drawing with a cross‐shaped punch and finally, analysis of a simplified hemming process using a solid discretization of the problem. The focus is on the correct prediction of the limits of the material in such processes.
SEM‐EBSD based Realistic Modeling and Crystallographic Homogenization FE Analyses of LDH Formability Tests908(2007); http://dx.doi.org/10.1063/1.2740799View Description Hide Description
Homogenization algorithm is introduced to the elastic/crystalline viscoplastic finite element (FE) procedure to develop multi‐scale analysis code to predict the formability of sheet metal in macro scale, and simultaneously the crystal texture and hardening evolutions in micro scale. The isotropic and kinematical hardening lows are employed in the crystalline plasticity constitutive equation. For the multi‐scale structure, two scales are considered. One is a microscopic polycrystal structure and the other a macroscopic elastic plastic continuum. We measure crystal morphologies by using the scanning electron microscope (SEM) with electron back scattered diffraction (EBSD), and define a three dimensional representative volume element (RVE) of micro ploycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. Since nonlinear multi‐scale FE analysis requires large computation time, development of parallel computing technique is needed. To realize the parallel analysis on PC cluster system, the dynamic explicit FE formulations are employed. Applying the domain partitioning technique to FE mesh of macro continuum, homogenized stresses based on micro crystal structures are computed in parallel without solving simultaneous linear equation. The parallel FEM code is applied to simulate the limit dome height (LDH) test problem and hemispherical cup deep drawing problem of aluminum alloy AL6022, mild steel DQSK, high strength steel HSLA, and dual phase steel DP600 sheet metals. The localized distribution of thickness strain and the texture evolution are obtained.
908(2007); http://dx.doi.org/10.1063/1.2740800View Description Hide Description
The current report presents some results from a study on the prediction of necking failure in ductile metal sheets. In particular methods for creating Forming Limit Curves (FLCs) are discussed in the present report. Three groups of methods are treated: Experimental methods, Theoretical/analytical methods, and the Finite Element Method (FEM). The various methods are applied to two different materials: An aluminum alloy and a high strength steel. These materials do both exhibit a distinct necking behavior before fracture, and they do both exhibit only a small strain rate dependence. As can be expected, the resulting FLCs from the various experimental, theoretical, and numerical methods show a substantial scatter. The reasons for these deviating results are analyzed, and some conclusions are drawn regarding the applicability of the different methods.
908(2007); http://dx.doi.org/10.1063/1.2740801View Description Hide Description
A number of ductile failure criteria are nowadays being used to predict the formability of aluminium alloy sheets. Generally speaking, integral criteria (e.g. those proposed by Cockcroft and Latham, Brozzo et al., Oyane et al Chaouadi et al., etc.) have been probed to work well when the principal strains are of opposite sign, i.e. in the left side of the Forming Limit Diagram (FLD). However, when tensile biaxial strains are present, as occurs in stretch‐forming practice, their predictions are usually very poor and even non‐conservatives. As an alternative, local criteria, such as the classical Tresca’s and Bressan & Williams’ criteria, have demonstrated a good capability to predict the failure in some automotive aluminum alloys under stretching. The present work analyses experimentally and numerically the failure in AA2024‐T3 sheets subjected to biaxial stretching. A series of out‐of‐plane stretching tests have been simulated using ABAQUS. The experimental and the numerical FLD for different failure criteria are compared. The influence on the failure of the hydrostatic pressure and the normal stress to the fracture plane is also discussed.
908(2007); http://dx.doi.org/10.1063/1.2740802View Description Hide Description
The forming limits of sheets subjected to the Single Point Incremental Forming process (SPIF) is generally several times higher than those found in the Forming Limit Curve (FLC). In this paper it is shown that the non‐monotonic, serrated strain paths to which the material is subjected to during the SPIF process, play a role in the high formability, compared to the monotonic loading in the traditional FLC. The deformation history of an aluminium alloy truncated cone formed with the SPIF process is retrieved through a finite element (FE) model, and discussed. Subsequently, the strain paths at three different depths in the sheet are used as input into a Marciniak‐Kuczynski (MK) forming limit model. The usage of different constitutive models in this analysis shows that anisotropic hardening contributes to the delay of the onset of necking in the SPIF process. The large difference in the predicted forming limits that were obtained from the different layers indicates that an interaction between these layers should be taken into account for more accurate forming limit predictions of sheets subjected to the SPIF process.
908(2007); http://dx.doi.org/10.1063/1.2740803View Description Hide Description
Concerning the formability prediction of stamping, users now want to obtain totally accurate and reliable results. One way to improve the capability of dedicated software is to take into account the influence of stress or strain gradients as well as temperature gradients. Both of them play an important role in the way the material deforms and particularly how it will collapse. Through thickness gradients generally have a very positive effect relative to the possible surface extension on bends of small radii. This is not taken into account by software, sometimes leading to erroneous conclusions and limitative design. Temperature distribution is at the origin of strain localization. The tensile test example shows that the relatively good thermal conductivity of mild steels localizes strains in the centre of the specimen, allowing a reliable total elongation measurement. In the case of High Strength Steel, the lower conductivity suppresses this localization and allows fracture to appear in a larger domain, thus making elongation measurement more difficult. Finally, it is shown that, inversely, the absence of temperature localization in the hole expansion test allows the metal to strain at the same level that local necking in uniaxial tension, but all around the hole, thus delivering very high expansion ratios. It is suggested that gradients should be more carefully studied and their influence introduced in stamping simulation software.
908(2007); http://dx.doi.org/10.1063/1.2740804View Description Hide Description
The formability in sheet metal forming processes is mainly conditioned by ductile fracture resulting from geometric instabilities due to necking and strain localization. The macroscopic collapse associated with ductile failure is a result of internal degradation described throughout metallographic observations by the nucleation, growth and coalescence of voids and micro‐cracks. Damage influences and is influenced by plastic deformation and therefore these two dissipative phenomena should be coupled at the constitutive level. In this contribution, Lemaitre’s ductile damage model is coupled with Hill’s orthotropic plasticity criterion. The coupling between damaging and material behavior is accounted for within the framework of Continuum Damage Mechanics (CDM). The resulting constitutive equations are implemented in the Abaqus/Explicit code, for the prediction of fracture onset in sheet metal forming processes. The damage evolution law takes into account the important effect of micro‐crack closure, which dramatically decreases the rate of damage growth under compressive paths.