Academic literature on the topic 'Roll-Forming, Finite Element Method, Plane Strain, Strain Hardening'

Formability of AA5182-O aluminum alloy sheets in the warm working temperature range has been studied. Forming limit strains of sheets of two different thicknesses have been determined experimentally in different modes of deformation (biaxial tension, plane strain and tension–compression) by varying temperature and punch speed. A correlation has been established for plane strain intercept of the forming limit diagram (FLD0) with temperature, punch speed and thickness from the experimental results. This correlation has been used to plot the forming limit diagrams for failure prediction in the finite element analysis of warm deep drawing of cylindrical cups. The effect of strain and strain rate on material flow behavior has been incorporated using a strain rate–sensitive power hardening law in which the strain hardening exponent and strain rate sensitivity index have been experimentally determined. The predictions from simulations have been validated by warm deep drawing experiments. Large improvement in accuracy of failure prediction has been observed using the FLDs plotted based on the developed correlation when compared to the existing method of calculating FLD0 using only strain hardening coefficient and thickness. The results clearly indicate the importance of incorporating temperature and punch speed in failure prediction of Al alloys using FLDs in the warm working temperature range.

A semi-analytical method to predict springback in sheet metal forming processes has been developed for the case of plane strain. In the proposed hybrid method, for each deformation increment, bending, and unbending stretches are analytically superposed on membrane stretches which are numerically obtained in advance from a membrane finite element code. Springback is then obtained by the unloading of a force and a bending moment at the boundary of each element treated as a shell. Hill’s 1948 yield criterion with normal anisotropy is used in this theory along with kinematic and isotropic hardening laws during reverse loading. The method has been applied for the springback prediction of a 2008-T4 aluminum alloy in plane-strain draw-bending tests. The results indicate the necessity of including anisotropic hardening (especially Bauschinger effects) and elastoplastic unloading in order to achieve good agreement with experimental results.

In order to investigate the process of ISF through numerical and experimental approaches, finite element method (FEM) models for two truncated pyramids were developed to simulate the process and the simulated thickness distributions were compared with experimental results. The influences of process parameters on equivalent plastic strain, the maximum equivalent plastic stress and forming force were also discussed. The results show that ISF process is basically to be a plane strain deformation. Wall angle is a more significant influence factor of forming performance than tool diameter and depth increment. With increasing tool diameter, decreasing wall angle and step increment, uniform thickness distribution will be achieved. However, more wall angel, less tool diameter and depth increment contributes to decrease forming force. Additionally, process parameters have no connection with work hardening for a certain material during ISF.

The plasticity and formability of a commercially-pure aluminum sheet (AA1100-O) is assessed by experiments and analyses. Plastic anisotropy of this material is characterized by uniaxial and plane-strain tension along with disk compression experiments, and is found to be non-negligible (e.g., the r-values vary between 0.445 and 1.18). On the other hand, the strain-rate sensitivity of the material is negligible at quasistatic rates. These results are used to calibrate constitutive models, i.e., the Yld2000-2d anisotropic yield criterion as the plastic potential and the Voce isotropic hardening law. Marciniak-type experiments on a fully-instrumented hydraulic press are performed to determine the Forming Limit Curve of this material. Stereo-type Digital Image Correlation is used, which confirms the proportional strain paths induced during stretching. From these experiments, limit strains, i.e., the onset of necking, are determined by the method proposed by ISO, as well as two methods based on the second derivative. To identify the exact instant of necking, a criterion based on a statistical analysis of the noise that the strain signals have during uniform deformation versus the systematic deviations that necking induces is proposed. Finite element simulation for the Marciniak-type experiment is conducted and the results show good agreement with the experiment.

A fully implicit stress integration algorithm is developed for the distortional hardening model, namely the e−HAH model, capable of simulating cross−hardening/softening under orthogonal loading path changes. The implicit algorithm solves a complete set of residuals as nonlinear functions of stress, a microstructure deviator, and plastic state variables of the constitutive model, and provides a consistent tangent modulus. The number of residuals is set to be 20 or 14 for the continuum or shell elements, respectively. Comprehensive comparison programs are presented regarding the predictive accuracy and stability with different numerical algorithms, strain increments, material properties, and loading conditions. The flow stress and r−value evolutions under reverse/cross−loading conditions prove that the algorithm is robust and accurate, even with large strain increments. By contrast, the cutting−plane method and partially implicit Euler backward method, which are characterized by a reduced number of residuals, result in unstable responses under abrupt loading path changes. Finally, the algorithm is implemented into the finite element modeling of large−size, S−rail forming and the springback for two automotive steel sheets, which is often solved by a hybrid dynamic explicit–implicit scheme. The fully implicit algorithm performs well for the whole simulation with the solely static implicit scheme.

A pneumatic experimental design to evaluate strain rate sensitive biaxial stretching forming limits for 7075 aluminum alloy sheets was attempted with the finite element method. It was composed of apparatus geometric design with pressure optimization as the process design. The 7075 aluminum alloy material was characterized by conventional Voce-type hardening law with power law strain rate sensitivity relationship. For optimization of the die shape design, the ratio of minor to major die radius (k) and profile radius (R) were parametrically studied. The final shape of die was determined by how the history of targeted deformation mode was well maintained and whether the fracture was induced at the pole (specimen center), thereby preventing unexpected failure at other locations. As a result, a circular die with k = 1.0 and an elliptic die with k = 0.25 were selected for the balanced biaxial mode and near plane strain mode, respectively. Lastly, the pressure inducing fracture at the targeted strain rate was studied as the process design. An analytical solution that had been previously studied to maintain constant strain rate was properly modified for the designed model. The results of the integrated design were compared with real experimental results. The shape and thickness distribution of numerical simulation showed good agreement with those of the experiment.

Ideal plastic flows constitute a class of solutions in the classical theory of plasticity based on, especially for bulk forming cases, Tresca’s yield criterion without hardening and its associated flow rule. They are defined by the condition that all material elements follow the minimum plastic work path, a condition which is believed to be advantageous for forming processes. Thus, the ideal flow theory has been proposed as the basis of procedures for the direct preliminary design of forming processes, which mainly involve plastic deformation. The aim of the present review is to provide a summary of both the theory of ideal flows and its applications. The theory includes steady and nonsteady flows, which are divided into three sections, respectively: plane-strain flows, axisymmetric flows, and three-dimensional flows. The role of the method of characteristics, including the computational aspect, is emphasized. The theory of ideal membrane flows is also included but separately because of its advanced applications based on finite element numerical codes. For membrane flows, restrictions on the constitutive behavior of materials are significantly relaxed so that more sophisticated anisotropic constitutive laws with hardening are accounted for. In applications, the ideal plastic flow theory provides not only process design guidelines for current forming processes under realistic tool constraints, but also proposes new ultimate optimum process information for futuristic processes.

Since sheet-bulk metal forming processes inherit properties of both sheet and bulk metal forming processes, their analysis requires on one side following certain methods conventionally devised in these process classes analyses whereas on the other side leaving certain customs out. For instance, inherent anisotropy of the rolled sheet has to be taken into account whereas due to non-vanishing out of plane stress component, analysis with thin shells using the plane stress state assumption is no more applicable. Similarly, methods based on necking instabilities, i.e. forming limit diagrams, which are typically used in sheet metal formability assessment; fall short in sheet-bulk metal formability prediction. In the present study, we propose a local approach to fracture, more specifically a phenomenologically based Lemaitre variant CDM model, devised frequently in bulk metal forming analysis, as an alternative. For this purpose, a combined nonlinear isotropic-kinematic hardening plasticity with Hill48 type initial anisotropy is fully coupled with isotropic damage. Together with the concept of effective stress and equivalent strain principle, quasi-unilateral damage evolution is used, where the energetic contribution of the compressive stress state to the damage driving force is scaled with a so-called crack closure parameter, . For the quasi unilateral damage evolution is inactive whereas for it is fully active which completely suppresses the development of damage under compressive stress states. The framework devises state coupling between elasticity and damage and kinematic coupling between plasticity and damage which increases the relative effect of on the eventual damage development. To this end, a direct extension to the finite strains for metal forming analysis is realized using a corotational formulation and the developed framework is implemented as a VUMAT subroutine for ABAQUS Explicit. For evaluation of the predictive capability of the model, teeth forming process results for DC04 reported in Soyarslan et al. 2011, An Experimental and Numerical Assessment of Sheet-Bulk Formability of Mild Steel DC04, Journal of Manufacturing Science and Engineering, Vol. 133 6, (2011) S. (061008) 1-9, are used. Mechanical material characterization studies are realized using a hybrid experimental-numerical procedure. This methodology relies on minimizing the difference between the experimentally handled global clamp force demand diagrams and the diagrams from the simulations at the complete range of the experiments involving fracture. As known finite element solutions with softening material models are prone to pathological mesh dependence. For this fact, a crack band method is used where the minimum element size, as a controlling parameter of the localization size, is also fitted through the characterization studies and identically used in the process simulations. The simulations show that a correct prediction of the zone and time of fracture is possible for the selected process whereas since the teeth formation process is mainly a compressive process, once the quasi-unilateral damage development is not used, i.e. for , a premature crack prediction is recorded which is not compatible with the experimental findings.

This paper presents details of a quasi three-dimensional finite element formulation for shape rolling, TASKS. This formulation uses a mix of two-dimensional finite element and slab element techniques to solve a generalized plane strain problem. Consequently, quasi steady state metal forming problems such as rolling of shapes can be analyzed with minimal computational effort. To verify the capability of the formulation square-to-round single pass rolling is simulated by TASKS and results compared with a fully three-dimensional simulation reported in literature. The results indicate reasonable agreement in roll forces, torques, and effective strain distributions during rolling. However, due to the generalized plane strain assumptions, nonhomogenieties in the rolling direction cannot be simulated. The large computational economy realized via TASKS gives this formulation the power to analyze roll pass designs with reasonable computational resources.

Solid shell element models which possess only translational degrees of freedom and are applicable to thin structure analyses has drawn much attention in recent years and presented good prospect in sheet metal forming. In this study, a solid shell element model is introduced into the dynamic explicit elastic-plastic finite element method. The plane stress constitutive relation is assumed to relieve the thickness locking and the selected reduced integration method is used to overcome volumetric locking. The assumed natural strain method is adopted to resolve shear locking and trapezoidal locking problem. Two benchmark examples and a stage of roll forming process are calculated, and the calculating results are compared with those by solid element model, which demonstrates the effectiveness of the element.

Roll-forming is an efficient sheet forming process that is used in manufacturing long parts with constant cross-section. The theoretical, experimental and numerical analyses of the process are limited since the sheet takes a complex 3D shape during the process. In this study proper finite element method models to simulate the roll-forming process are examined both numerically and experimentally. In addition, the applicability of 2D plane strain models to the simulation of the process is investigated. To reveal the deformation of the sheet, important geometrical parameters of the sheet and the rollers are introduced. The effect of these parameters on the strain hardening and deformation of the sheet is analyzed at distinct parts of the sheet that undergoes different types of deformations. Having revealed the deformation mechanisms, the assumptions behind the theoretical knowledge is criticized. The mentioned studies are verified with a case study in which a roll-formed product is analyzed under service loads. The manufacturing of the product and service load application are simulated and the results are compared with the experiments. In addition, effects of cold forming on the behaviour of the product under service loads are examined. It is concluded that under some conditions, 2D plane strain simulations can be used to predict the strain hardening in the material that occurs during roll-forming and this hardening has a considerable effect on the response of the material under loading.

This chapter is concerned with the formulations and solutions for plane plastic flow. In plane plastic flow, velocities of all points occur in planes parallel to a certain plane, say the (x, y) plane, and are independent of the distance from that plane. The Cartesian components of the velocity vector u are ux(x, y), uy(x, y), and uz = 0. For analyzing the deformation of rigid-perfectly plastic and rate-insensitive materials, a mathematically sound slip-line field theory was established (see the books on metal forming listed in Chap. 1). The solution techniques have been well developed, and the collection of slip-line solutions now available is large. Although these slip-line solutions provide valuable insight into deformation modes and forming loads, slip-line field analysis becomes unwieldy for nonsteady-state problems where the field has to be updated as deformation proceeds to account for changes in material boundaries. Furthermore, the neglect of work-hardening, strain-rate, and temperature effects is inappropriate for certain types of problems. Many investigators, notably Oxley and his co-workers, have attempted to account for some of these effects in the construction of slip-line fields. However, by so doing, the problem becomes analytically difficult, and recourse is made to experimental determination of velocity fields, similarly to the visioplasticity method. Some of this work is summarized in Reference [2]. The applications of the finite-element method are particularly effective to the problems for which the slip-line solutions are difficult to obtain. The finite-element formulation specific to plane flow is recapitulated here.

One method to develop offshore gas reserves is to use a floating LNG plant (FLNG) on site and export the LNG via tankers. This alternative requires the use of a reliable LNG transfer system between the FLNG and the tanker under offshore conditions. One such system involves a flexible cryogenic hose whose main body is a pipe-in-pipe hose made of two concentric corrugated 316L stainless steel pipes (C-pipe) with flanged terminations. Thermal insulation is achieved by maintaining vacuum between the inner and outer corrugated stainless steel pipes. In addition, the hose assembly contains two outer layers of helical armor wires to sustain the axial load. Given the complexity and novelty of the transfer system, a finite element study was performed on the inner C-pipe — the critical fluid containment layer. The effects of strain hardening of corrugations due to cold forming and temperature were modeled. Finite element (FE) analyses of the C-pipe under axial, bending, and internal pressure loading were carried out to evaluate global load-deformation and local stress responses. Comparisons of full-scale tests at room and cryogenic temperatures to simulation predictions including the novel material model showed good agreement. However, fatigue life predictions for the C-pipe that were based on local stresses and sheet metal fatigue S-N curves did not agree with the full-scale fatigue test results. The results indicated that the spatial variation in strain hardening due to corrugation forming and biaxial local stresses during pipe deformation could play important roles in the fatigue response of the C-pipe.