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• Synchrotron radiation experiments were used to characterize the void evolution with strain. • Voids develop along the grain boundaries of Cu layer in the interface layer. • A newly developed damage model was constructed based on the GTN-Thomason and M-K models considering size effect individually. • The developed model takes into account the combined effects of interfacial void evolution and surface roughening affected by size effect. • The developed model can predict the variation of FLCs affected by size effect and was validated by experiments. Lack of systematic researches on mesoscaled deformation and damage criteria would obstruct the development of optimal microforming of clad foils. In this paper, a newly developed damage model, inspired by fracture mechanism, was developed to determine the forming limit of Cu/Ni clad foils via considering size effect and its influences on deformation and fracture behavior. The newly developed model integrates the interface separation model based on GTN-Thomason model and the Marciniak-Kuczynski (M-K) model to represent the two stages of ultimate strain before instability in the fracture process of Cu/Ni clad foils. In addition, the former model describes the first-stage strain of the interface separation dominated by void evolution; while the latter one models the second-stage strain of the localized instability of clad foils at interface separation locations via introducing the effects of surface roughness and interface separation on thickness. The results of the synchrotron radiation experiments indicate that void nucleation, growth and coalescence occurring in the interface layer are mainly located in the Cu layer grain boundary region. The localized high density of the nucleated voids is the direct cause of the localized instability. The results of surface roughness experiments demonstrate that surface roughness increases rapidly with strain and saturates at a low strain condition. The surface roughening becomes severe with the increase of grain size. The experimental results of the forming limit show that forming limit curves (FLCs) shift down and strain concentration occurs prematurely with the increasing grain size. The FLCs of Cu/Ni clad foils influenced by grain size are predicted by the newly developed model successfully. This study reveals the interfacial void evolution and surface roughening behavior and their influences on the forming limit of clad foils, in such a way to provide a theoretical basis for microforming of clad foils. [ABSTRACT FROM AUTHOR]

• The failure modes of fiber metal laminates(FMLs) are highly sensitive to the variation of fiber lay-up schemes, strain path and number of plies in CFRP core. • Compared with Unidirectional Cross lay-up FMLs and Quasi-isotropic lay-up FMLs, woven lay-up FMLs have higher forming limits. • Reasonable increase of stamping speed and intermediate CFRP layer can improve the forming limit of FMLs. • The research results provide a reliable data source for establishing the accurate forming limit criterion of FMLs and optimizing lay-up schemes. Due to the potential application need of the automotive and transportation industry for Fiber metal laminate parts made of steel sheets and carbon fiber reinforced polymer (i.e., Steel/CFRP based FML parts), the related combined forming process of FML parts has attracted extensive attention in the last decades. In order to design and fabricate the qualified Steel/CFRP based FML auto parts with various plane stress states, it is vital to thoroughly understand the formability and failure modes of Steel/CFRP based FMLs under various forming states and process conditions. Accordingly, in the present work, a series of deep drawing experiments were designed and conducted on Steel/CFRP based FML specimens with various width to embody their special forming features under different stress states. By considering the limit drawing height at fracture for the evaluation indicator of the forming limit of FMLs, authors studied systematically the influence of key process conditions such as lay-up scheme, stamping speed and the number of plies in the carbon fiber reinforced polymer prepreg (i.e.,CFRP prepreg) core on the formability and failure modes of FML specimens with various forming states. The research results are expected to provide a reliable data source for establishing the accurate forming limit criterion of FMLs and optimizing lay-up schemes. [ABSTRACT FROM AUTHOR]

Abstract: Electrohydraulic forming (EHF) is based upon the electro-hydraulic effect: a complex phenomenon related to the discharge of high voltage electrical current through a liquid. In EHF, electrical energy is stored in a bank of capacitors and is converted into the kinetic energy needed to form sheet metal by rapidly discharging that energy across a pair of electrodes submerged in a fluid. The objective of this paper is to report the results of formability testing of dual phase steels in EHF conditions and to provide an explanation of the observed formability improvement based on analysis of the experimental results and through the use of a modeling technique developed as part of this work for simulating the EHF process. Comparison of the maximum strains resulting from EHF into a conical die and a v-shape die to the maximum strains resulting from quasistatic LDH testing (limiting dome height) indicated that substantially higher strains can be accomplished in the EHF process. In order to obtain the maximum benefits of increased formability with EHF technology, it is necessary to get to the high strain rate regime and the accompanying high hydrostatic stresses in the sheet, which occurs mostly in the contact area between the blank and the die. If the blank decelerates and gets to quasistatic forming conditions before filling the die cavity completely, very limited improvement in formability can be anticipated. A numerical model of the EHF process has been developed, incorporating four distinct models that are integrated into one: (1) an electrical model of the discharge channel, (2) a model of the plasma channel, (3) a model for the liquid as a pressure-transmitting medium, and (4) a deformable sheet metal blank in contact with a rigid die. The relative improvement in plane strain formability in EHF conditions was between 63% and 190%, depending on the grade of dual phase steel. Numerical modeling showed that the peak strain rates occurring in EHF are approximately 20,000 units per second. [Copyright &y& Elsevier]

Abstract: A novel framework to predict the onset of plastic flow localization is presented. The proposed framework combines a classical strain localization analysis with a homogenization-based finite element method, and has high applicability to various types of material with a characteristic microstructure that may have significant heterogeneity as long as its representative volume element can be represented by a finite element discretization. According to the proposed method, a plastic flow localization analysis can be performed taking only one or two material points in macroscopic analysis. This means that localization analysis of materials involving very complex microstructures, which is hard to be satisfactorily treated in a fully micro-macro-coupled finite element analysis with the homogenization approach, can be carried out with a reasonable computational cost. As a practical application of the proposed general framework, a plane stress version, that is, a Marciniak–Kuczyński-type (M–K) approach, is considered, then the forming limit strains of FCC polycrystalline sheets are evaluated. Crystal plasticity theory is adopted as a constitutive model for each crystal grain, and the homogenization-based finite element method is used to evaluate the average material response to be used in M–K-type sheet necking analysis. A numerical convergence analysis is conducted to determine the appropriate size of the representative volume element in the homogenization, and the effect of the geometrical configuration of crystal grains is studied. Then, the forming limit strains of a textured material are evaluated. The computational results are compared with those obtained using the conventional Taylor-type polycrystalline model. [Copyright &y& Elsevier]

Abstract: The Forming Limit Diagram (FLD) of a textured zinc sheet has been identified via tensile and bulge tests. The strong anisotropy of the sheet is reflected in the tensile tests, and even more strikingly in the formability measured from the bulge tests. The dependence of the FLD on the orientation of the sheet is unusual, and is shown to be well captured by an anisotropic stress based criterion. The criterion is also able to predict the observed cracks orientations. [Copyright &y& Elsevier]

Abstract: In order to obtain reliable solutions for the initiation of localized instability in sheet metal forming, numerical procedures are developed for predicting forming limits using crystal plasticity. The Marciniak–Kuczynski (M–K) method is employed to calculate the initiation of the instability with rate-dependent elastic-crystal plasticity for cubic metals. The Nelder–Mead (N–M) direct search and Newton–Raphson (N–R) methods are used to solve the highly nonlinear equilibrium and associated compatibility equations under the M–K scheme. The N–M method eliminates the need of the first-order derivatives of the constitutive equations that may not be readily available for complex material models. The numerical results show that the calculation time using the N–M method is comparable to that using the N–R for the highly nonlinear M–K equations if the simplex size parameters are properly optimized. [Copyright &y& Elsevier]

Abstract: Tailored Heat Treated Blanks can considerably enhance the formability of fast-hardenable aluminum alloys, e.g. for car body parts. These blanks exhibit a properties distribution over the sheet plane, which is optimized for the forming operation. In this paper, the enhancement of the material strength of fast-hardenable aluminum alloys with a laser is in focus. Hereby, the working principle of the hardening is presented. Moreover, a process window for the hardening process is elaborated identifying the temperature and holding time as key parameters. Furthermore, heat treatment layouts are considered demonstrating the impact of hardening on the improvement of forming limit of fast-hardenable aluminum alloys. [Copyright &y& Elsevier]

Abstract: Plastic flow localization into a narrow band is investigated for a rate-independent polycrystalline sheet. Strain localization is considered to initiate at a point of bifurcation from the homogeneous deformation state or to result from the growth of a preexisting imperfection. Bifurcation analysis based on the rate-independent crystal plasticity model is found to give limit strains at a realistic strain level in the biaxial-stretching range. Limit strains predicted by the imperfection analysis are lower than those for bifurcation analysis and tend to approach those strain levels with decreasing amount of initial imperfection. Then, the bifurcation analysis is applied to the simulation of the forming limit for strongly textured sheets. The bifurcation analysis reveals the same trend of a texture dependence of limit strains as that for the imperfection analysis employing a rate-dependent model reported in the literature. [Copyright &y& Elsevier]

Abstract: Plastic deformation characteristics and limit strains are simulated for textured face-centered cubic polycrystalline sheets using a generalized Taylor-type crystal plasticity model. The r-values are predicted to be 1.04, 7.74, and 0.17 for the pseudo-random, {111}〈uvw〉, and {001}〈uvw〉 textures, respectively. The {111}〈uvw〉 texture gives limit strains as large as the random texture, whereas the {001}〈uvw〉 texture yields limit strains apparently higher than the other two, even though its r-value is extremely low. Thus, the r-value cannot act as an indicator of the stretchability of sheet metals. For the {001}〈uvw〉 texture, a superior strain-hardening ability under the plane-strain stretching mode is found to be responsible for the increase in the limit strains under plane strain and equi-biaxial stretching modes. It is concluded that the enhancement of the strain hardening ability for the plane-strain stretching mode is one of the key factors of high stretchability sheets. [Copyright &y& Elsevier]

A method of forming limit prediction for sheet metals at high temperatures and under nonproportional loading is presented. The method takes into account the strain-softening behaviors of the material at elevated temperatures. A localized necking criterion based on an isotropic damage-coupled acoustic tensor is developed and employed to determine the forming limits of strain-softening materials. The damage evolution equation is developed within the thermo-mechanical framework. A closed-form expression of the forming limit strains is derived by coupling the damage evolution equation into the localized necking criterion. A computer program, incorporating the incremental theory of plasticity, the damage evolution equation and the localized necking criterion, is developed to compute the forming limit strains under several nonproportional loading paths. A series of the uniaxial tensile tests is performed to measure the relevant mechanical properties of AA6061 at the elevated temperature of 450°C. The material damage variables are determined from the measured elastic modulii from a series of loading and unloading paths. The damage evolution equation of AA6061 at 450°C is formulated based on the test data. The computed limit strains are compared with the test results under various loading paths and a good agreement is observed. It is found that the critical damage value is independent on the stress states and loading paths. It may be concluded that the application of the material damage as a reliable criterion of localized necking including the nonproportional loading cases. [ABSTRACT FROM PUBLISHER]

Abstract: This paper explores the right-hand side of the forming limit diagram (FLD) for a BCC material in order to test the crystallographic slip assumptions. BCC crystals are considered with either 24 or 48 slip systems (BCC24 or BCC48). Identical uniaxial stress responses are assumed in order to compare the predicted FLDs. FLDs are performed using a rate-dependent polycrystal viscoplastic model together with the Marciniak–Kuczynski (M–K) approach. It is verified that the predictions of the limit strains carried out with the full-constraints (MK-FC) model are strongly affected by the selected deformation modes, showing unrealistically high limit strains in balanced-biaxial tension. Much more reliable values are found with the viscoplastic self-consistent (MK-VPSC) approach using either a BCC24 or BCC48 assumptions, enhancing the relevance of the selected transition scale model. Discrepancies between the numerical results, obtained using MK-FC and MK-VPSC, are interpreted in terms of the differences in the active slip systems selected by each model, and consequently, in the predicted lattice rotations and local curvature of the yield locus. Finally, it is found that the calculation of the FLD with MK-VPSC, using 48 slip systems, successfully predicts the right-hand side experimental tendency observed in a low carbon steel sheet metal obtained by bulge test. [ABSTRACT FROM AUTHOR]

n advanced sheet metal forming limit model is developed. Using the Marciniak-Kuczinsky analysis, this approach intends to join advantages of physics-based aspects of plasticity with advantages of phenomenological material description. It aims thus at connecting the most advanced physically-based hardening model accounting for the evolution of the anisotropic work hardening induced by the microstructural evolution at large strains of Teodosiu and Hu () with the advanced phenomenological anisotropic yield criterion Yld2000-2d (Barlat et al. Int J Plast 19:1297–1319, ). Two deep-drawing quality sheet metals are selected: a bake-hardening steel (BH) and AA6016-T4 aluminium alloy. Linear and complex strain paths are taken into account. By comparing the simulated and experimental results the model is validated. [ABSTRACT FROM AUTHOR]

In this research, the possibility of applying forming limit diagrams to the formability and fracture prediction of clad metal sheets is examined. The forming limits of clad metal sheets with different thickness combinations (e.g., A1050 1.0, 1.5, 2.0 mm/C1100 1.0 mm) are investigated via forming limits test (punch stretching tests). The true stress–strain curves of Al/Cu clad metal sheets are obtained through tensile tests. Using the experimental forming limit diagrams and the stress–strain curves, the fracture prediction of clad metal sheets are simulated by finite element analysis. Moreover, deep drawing tests are carried out to compare the experimental with the numerical results. These results can verify the accuracy of finite element model. Finally, significant differences in formability are found, and comparisons of the fracture prediction of clad metals with different initial thickness ratios are analyzed both numerically and experimentally. [ABSTRACT FROM AUTHOR]

The limiting value of strain describing necking/failure during a sheet stamping operation is quantified, predicted by the forming limit curve (FLC). The main aim of the present work is to analyse the applicability of the few existing necking criteria, namely the effective strain rate based criterion (ESRC - RC1), major strain rate based criterion (MSRC - RC2), thickness strain rate based criterion (TSRC - RC3), and thickness gradient based criterion (TGNC - RC4), in predicting the forming limit of unwelded and tailor-welded blanks. In the case of unwelded blanks, dry (μ  =  0.12) and low-friction (μ  =  0.02) conditions are simulated and forming limit results are predicted. In the case of tailor-welded blanks, the forming limits of laser-welded steel blanks and friction-stir-welded blanks made of aluminium alloy are predicted using the chosen necking criteria and then compared with results in the literature. The influence of friction on the whole forming limit curve and the non-linearity of strain paths in the stretching side of the forming limit diagram (FLD) are also predicted and discussed. It is found that the FLCs predicted by ESRC, MSRC, TSRC, and TGNC are comparable with experimental FLCs. The predictions are accurate in the low-friction condition, indicating that the necking criteria are also valid under changing friction conditions. Moreover, the overall FLC does not change much with changing friction conditions. The strain paths are non-linear in the dry friction condition, but they become linear in the low-friction condition. In the case of laser-welded blanks, the original strain rate based criteria defined for unwelded blanks underestimate limit strains on the stretching side of the FLD, where failure near the weld region is witnessed. Hence they are modified as RC1 ≥⃒ 25, RC2 ≥⃒ 32, and RC3 ≥⃒ 32, which show a better prediction level compared with the original criteria. The original and modified limit strain criteria show better correlation with results in the literature and the TGNC in the case of friction-stir-welded blanks modelled using the Hollomon and Swift strain-hardening laws. [ABSTRACT FROM AUTHOR]

With increasing diameters of aluminum alloy thin-walled tubes (AATTs), the tube forming limits, i.e. the minimum bending factors, and their predictions under multi-index constraints including wrinkling, thinning and flattening have been being a key problem to be urgently solved for improving tube forming potential in numerical control (NC) bending processes of AATTs with large diameters. Thus in this paper, a search algorithm of the forming limits is put forward based on a 3D elastic-plastic finite element (FE) model and a wrinkling energy prediction model for the bending processes under axial compression loading (ACL) or not. This algorithm enables to be considered the effects of process parameter combinations including die, friction parameters on the multi-indices. Based on this algorithm, the forming limits of the different size tubes are obtained, and the roles of the process parameter combinations in enabling the limit bending processes are also revealed. The followings are found: the first, within the appropriate ranges of friction and clearances between the different dies and the tubes enabling the bending processes with smaller bending factors, the ACL enables the tube limit bending processes after a decrease of the mandrel ball thickness and diameters; then, without considering the effects of the tube geometry sizes on the tube constitutive equations, the forming limits will be decided by the limit thinning values for the tubes with diameters smaller than 80 mm, while the wrinkling for the tubes with diameters no less than 80 mm. The forming limits obtained from this algorithm are smaller than the analytical results, and reduced by 57.39%; the last, the roles of the process parameter combinations in enabling the limit bending processes are verified by experimental results. [ABSTRACT FROM AUTHOR]

Abstract: For sheet metals, the endurance to fracture under different strain paths may be different. Based on plastic deformation energy, the sheet metal forming limit is calculated, and the relationship model between maximum allowable integral value of the general plastic work criterion and the strain path is built. In addition, the strain-hardening exponent, anisotropy coefficient and the initial thickness of the material are also taken into account to consider their effects on forming limit. In order to simplify the process of parameter determination, only uniaxial tension test is used to calculate the material property parameters and necessary limit strain, and the expression of the criterion is determined finally. Then the limit strains under other strain paths between uniaxial tension to equi-biaxial tension are predicted by the criterion combined with numerical simulation of the forming process. The criterion is also applied to limit strain prediction under bilinear strain path. [Copyright &y& Elsevier]

Abstract: Single-point incremental forming of thin aluminum foils, which did not require any die and any backing plate, was developed for fabricating customized parts of thin shell miniature objects. Thin aluminum foils were deformed incrementally using a round-tip single point tool on a desktop type of milling machine controlled with a personal computer. It was found that an aluminum foil 12μm thick was much smaller in forming limit than an aluminum foil 50μm thick when a single point tool with a tip radius of 0.5mm was not rotated, but its forming limit was improved greatly by rotating the tool up to 20,000rpm. Measured forming forces revealed that the tool rotation decreases the in-plane forces by approximately 50%. Hydrodynamic lubrication at the interface between a rotating tool and aluminum foil must have had a direct and favorable influence on the forming process, while increasing the forming limit of the thinner foil. It was also found that the optimum stepwise axial feed was found to be around the value of foil thickness. Then, incremental forming of arrays of dots 0.1mm in diameter, miniature pyramids, a miniature car and miniature letters was performed successfully under the optimized conditions at arbitrary positions of 12-μm-thick foils. [Copyright &y& Elsevier]

Deviation of raw material parameters, such as work hardening, anisotropy, yield stress, etc., leads to an uncertainty to the position of the forming limit curve (FLC). This paper presents a novel approach to statistically evaluate the forming limit in hydroforming processes when taking into account the variations in the material parameters. First, plastic instability based on the Hill’s quadratic plastic potential is employed to construct the deterministic FLC. Then, with using the assumption that all material parameters are normally distributed random variables, stochastic modeling of the FLC with a confidence level is carried out, and statistical evaluation of the FLC is performed. In this work, a first-order reliability method is adopted for the reliability assessment of the FLC, and this is verified with the Monte-Carlo simulation method. [ABSTRACT FROM AUTHOR]

Abstract: Individual grains in a polycrystal rotate during plastic deformation. This leads to a change in the crystallographic texture, and results in an increase or decrease of the macroscopic flow stress of the material. Such a change of strength as a result of grain rotations is called geometrical or texture hardening/softening. In the present study, for textured aluminum alloy sheets, the geometrical hardening/softening effect in the in-plane plane-strain stretching mode is numerically investigated using a generalized Taylor-type polycrystalline model. It is found that the cube texture () exhibits significant geometrical hardening when the major stretching direction is inclined at 45° relative to the orthotropic axes, and that a cube texture rotated about the normal direction (ND) shows a notable degree of geometrical hardening for any in-plane orientation of the sheet. Using the Marciniak-Kuczyński-type approach, forming limits for these textured sheets are analyzed. It is found that geometrical hardening definitely enhances the formability. It is, therefore, strongly suggested that texture control guided by the present results may be highly effective in producing aluminum alloy sheets with higher formability. [Copyright &y& Elsevier]

Abstract: To predict accurately the forming limit in sheet metal forming, the combination of FE simulation with tension tests is adopted in this paper to determine the material constants p and C in a ductile fracture criterion (DFC), which is advanced by the author. Forming limits of bore-expanding, hemispherical punch bulging and deep drawing (cylindrical, square-cup parts) are predicted by means of the DFC. Comparison of the results predicted by the DFC with experimental values shows that the precision of forming limit predicted by material constants obtained by the combination method is more accurate than that predicted by material constants obtained by the tension method, and that the critical punch stoke and the fracture initiation position in forming processes above mentioned are predicted accurately by the DFC. [Copyright &y& Elsevier]

The machining of a long trapezium spline is difficult due to its stiffness. In this paper, a special cold extrusion technique has been adopted on the basis of analyzing its three-dimensional velocity field and simulation using the software programme Deform-3D 5.0 to make a qualified trapezium spline ofΦ12× 840 with 16 teeth. [ABSTRACT FROM AUTHOR]

This article presents a review of the sheet metal formability analysis based on the theory of damage mechanics. Specifically, the damage anisotropy is considered. Forming limit analyses based on the anisotropic damage are summarized, including the accumulative critical damage method, the damage-coupled vertex theory and the damage-coupled acoustic tensor method. The accumulative critical damage method postulates that the critical damage at the localized necking is strain-path or loading history independent. It can be applied to predict the forming limit diagrams under either proportional or nonproportional loading. The vertex theory considers that localized necking is associated with the vertex developed on yield surface. The theory is applicable to engineering materials exhibiting the strain-hardening and/or strain-rate dependent behaviors. The acoustic tensor method, on the other hand, can only be applied to the strain-softening materials, which are often observed in warm/hot sheet metal forming or hydroforming. [ABSTRACT FROM AUTHOR]

The calculation method of forming limit of sheet metals based on M-K instability theory is proposed, and the method is applicable to different yield criterions and hardening models. The forming limit diagrams of AA5754-O, AA6111-T4 aluminum alloy sheet and DP steel sheet under combined loading paths are obtained based on mixed hardening model with YLD2000-2D yield criterion proposed by Barlat in 2003 and L-C nonlinear kinematic hardening model proposed by Lemaitre and Chaboche. The results show that the forming limit diagram made up of limit strain (FLD-strain) is evidently influenced by the loading path. The forming limit diagram made up of limit stress (FLD-stress) is also influenced by loading path and it is not an only curve, which differs from the conventional view. The degree of the influence of loading path on FLD-stress is related with pre-strain. The larger the pre-strain is, the greater the influence of loading path on FLD-stress will be. The change of FLD-stress is small only when pre-strain is small. In addition, the hardening behavior of the material will influence the path-dependence of FLD-stress: The larger the proportion of kinematic hardening in the whole hardening is, namely the more obvious Bauschinger effect of the material, the greater the influence of loading path on FLD-stress will be. [ABSTRACT FROM AUTHOR]

The paper overviews the methods of predicting the forming limit stress diagram in sheet metal forming, the maximum forming ratio, the forming limit diagram, the ductile fracture criteria (DFC), and so on. Making use of DFC, the forming limit can be predicted in the metal sheet with low ductility, and can be predicted when the forming path varies. In the finite element method, DFC can be applied to incremental approaches with a fully coupled elastoplastic-damage model, and can be applied to the one-step inverse approach. In order to predict the forming limit exactly, a criterion that indicates the material ability in essence is expected to be worked out, including the improvement of finite element method. [ABSTRACT FROM AUTHOR]

A new incremental sheet forming technology with local heating is proposed to form lightweight hard-to-form sheet metals such as aluminum-magnesium alloy (JIS A5083) sheet or magnesium alloy (JIS AZ31) sheet. The newly designed forming tool has a built-in heater to heat the sheet metal locally and increase the material ductility around the tool-contact point. Incremental forming experiments of A5083 and AZ31 sheets are carried out at several tool-heater temperatures ranging from room temperature to 873K using the new forming method. The experimental results show that the formability of A5083 and AZ31 sheets increases remarkably with increasing local-heating temperature. In addition, springback of formed products decreases with increasing local-heating temperature. The developed incremental sheet forming method with local heating has great advantages in not only formability but also shape fixability. It is an effective forming method for lightweight hard-to-form sheet metal for small scale productions. [ABSTRACT FROM AUTHOR]

Abstract: Powder metallurgy (P/M) manufacturing route has wide industrial applications due to a host of techno-economic advantages. However, the production of highly dense product for structural application with pore free at open surface is a challenging endeavour for the investigators. Thus, present investigation pertains to describe cold deformation behaviour and to develop forming limits for iron–0.8% carbon sintered P/M steel preforms. Experiments were conducted on 0.40 and 0.75 initial aspect ratio of 86±1% initial fractional theoretical densities under two different lubricant constraints namely, nil/no lubricant and graphite lubricant. The deformations were confined till the appearance of visible crack on the free surface of the deforming compacts. This aspect was quantized to evaluate the densification behaviour against compressive strain and to provide guidelines for introducing external constraints so as to produce components free from open surface pores. [Copyright &y& Elsevier]

Abstract: The warm formability of AZ31 sheet has affected with strain rate as well as temperature because elongations are changed by the temperature and strain rate at an elevated temperature. Therefore, the formability must be investigated with the effects of both strain rate and temperature. In this study, the effects of temperature and strain rate were investigated on square cup drawing by the experimental and FE analysis. And, the uni-axial tensile test and stretching test by the hemi-spherical punch were performed to analyze causes of forming limits for various forming conditions. AZ31 alloy sheet shows increased total elongation by increasing the deformation temperature from 200 to 400°C on uni-axial tensile test. The uniform elongation decreased by increasing the temperature and increased by the increasing the strain rate. On the other hand, the post-uniform elongation increased with higher temperature and lower strain rate. Forming limit by FLD test was worse on higher strain rate. Also, the failures were occurred frequently at high forming speed on square cup deep drawing. After all, the forming limit was dependent with the post-uniform elongation more than uniform elongation. Finally, the effect of strain rate must be considered on the FEM analysis. Therefore, the viscoplastic material model and strain rate-dependent FLD curve were used to simulate forming process and predict the failure. The simulated results show good agreement with the experimental results. [Copyright &y& Elsevier]

Abstract: In the present study, it was attempted to apply the incremental forming method to magnesium sheets at warm temperature in order to fully utilize the formability of the material. To assess the influence of temperature to the forming limit, plane-strain as well as axisymmetric stretching tests were performed at 20°C, 100°C, 150°C, 200°C and 250°C. Cones with different inclination angles were designed based on the forming limits at these temperatures, and formed incrementally. FEM analysis was used to understand the deformation characteristics observed in the experiment. A circular cup with an inclination angle that exceeds the forming limit was successfully formed by introducing the concept of the progressive forming to the incremental forming. [Copyright &y& Elsevier]

Abstract: This study investigated the forming characteristics of magnesium alloy (AZ31B) in bidirectional extrusion. Simultaneous forward–backward extrusion, which is frequently performed in industrial production, is conducted. The effect of process parameters such as forward extrusion ratio, backward extrusion ratio, and working temperatures were also examined. A high precision forging of the alloy was achieved under warm condition. A forming limit of the alloy in the combined process was found by parametric study. The deformation of the material appears to be localized, and the intrinsic limited formability of the alloy resulted in cracks on the extruded surface. We found that crack is initiated and developed easily under the low static pressure. [Copyright &y& Elsevier]

The sheet-metal-forming operations are principal processes in the automotive industry. Aluminium alloy 5052 sheet is a widely used material in the automotive industry. With the aim of finding the safe working strains for this metal under various forming processes, a set of wrinkling limit diagrams in terms of strain and strain increment ratios and a forming limit diagram with a wrinkling limit curve superimposed have been constructed for the same sheet metal with 2.0 mm thickness annealed at four different temperatures. It has been found that the onset of wrinkling takes place when the ratio (dεr/dεθ) of strain increments or the ratio (εr/εθ) of strain reaches a critical value during the drawing process. Further it was observed that, the higher the annealing temperature, the greater was the safe strain region, because of higher normal anisotropy and strain hardening index values. [ABSTRACT FROM AUTHOR]

Hole-flanging is a common sheet forming operation to produce structural sheet metal components. Flangers are used for appearance, rigidity, hidden joints, and strengthening of the edge of sheet metal parts. Trial-end-error is the most common approach for tooling and process design in flanging operations. This paper presents some experimental results of hole-flanging process performed on flat deep drawing steel sheets with circular hole drilled in the centre. Three punches of different geometry i.e. cylindrical, Hemispherical and conical were used in this experiment. The effect of both the punch geometry and material mechanical parameters (especially strain hardening and plastic anisotropy) on the limit expansion of the hole was determined. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this study is to determine the feasibility of cold recycling of sheet metal wastes. The authors focused on deformation behavior in incremental forming of nonuniform sheet metals flattened from sheet metal wastes. These flattened sheet metals were shaped into conical shells with various half-apex angles by incremental forming. The forming limit of the flattened sheet metals was compared with that of a sheet metal of uniform thickness. It was found that the forming limit of the flattened sheet metals is similar to that of the sheet metal of uniform thickness. Experimental results showed that strain localization can be approximately inhibited in the flattened sheet metals by incremental forming. These results suggest that the cold recycling of sheet metal wastes can be accomplished by incremental forming. [Copyright &y& Elsevier]

Abstract: One important issue when simulating tube hydroforming is to predict bursting, i.e. when the increase in cavity pressure cannot be compensated by hardening of the tube material. Traditionally, this is made by a forming limit diagram (FLD), where the limit strains determine whether a material point is experiencing necking or failure. However, the experimental FLD depends on the strain path, and the methods which are used to determine the FLD are adapted to conventional deep drawing which, depending on the process characteristics, could make it unsuitable for tube hydroforming applications. In this work, analytical and numerical forming limit predictions are studied from a hydroforming point of view. These predictions are then applied to free bulge cases, and a case with extensive feeding in a die where the results from the latter case is compared to experiments. Further, the influence from extrusion welds and a circumferential thickness distribution on the forming limit is also evaluated. [Copyright &y& Elsevier]

Abstract: Tearing and buckling failures concerning forming limit during the process will restrict the advantage exertion and successful realization of tube axial compressive forming process. So it is important to open out forming limit and realize process feasibility analysis. In this paper, the forming limit conception for tube axial compressive forming under both fillet and conical dies is proposed firstly by considering tearing and buckling failures. Through thorough study the failure models are established, then the failure mechanism are exploring and criteria for them are developed based on minimum energy principle for plastic forming. Combining with finite element simulation system developed the forming limit, process feasibility and effects of process parameters on them are investigated, then reasonable ranges for process parameters to realize stable forming are determined. The experiments for the forming process under fillet die with aluminum tube blanks with brand no. 5052, t 0/d 0 =0.024, 0.032 show that the method for forming limit and feasibility and the results obtained are reliable and practical. [Copyright &y& Elsevier]

Abstract: The strain-based forming limit diagram (FLD) is generally obtained on the linear (proportional) or near linear loading condition. So it often leads to erroneous assessments on the analysis of metal sheet formability under complex strain paths such as multi-step forming by the FLD criterion. In recent years, forming limit stress diagrams (FLSDs) have been intensively studied and have been considered being path-independent. In this study, it has been carried out that application of the FLSD to forming limit prediction for the multi-step forming of auto panels. Firstly, it was been performed that the forming limit tests of sheet metal for the SPECN steel sheet of thickness of 1.6mm under the loading conditions considered include both proportional and non-proportional loading. Secondary, the forming limit stress diagram (FLSD) of the sheet metal is gained by the transformation relations between the strain state and stress state in deformation of sheet metal. Afterwards, implementation of the forming limit stress diagrams into finite element numerical simulations of rear hanger of auto panels multi-step forming has been established by DANAFORM program code, the FLSD is applied to forming limit prediction in the stamping finite element analysis. The verification experiment of the simulation results were executed in motorcar manufacturing factory, the predicted results agree well with those determined experimentally. [Copyright &y& Elsevier]

Abstract: Since magnesium alloy sheet usually exhibits poor press formability, the sheet forming for complex shaped part has many difficult problems. Among these problems, the die design to prevent some defects is one of the important process variables. Therefore, the data for forming limit of AZ31 sheet is necessary to prevent the defect and get the good formed part. In this study, the forming limits on various forming process have been investigated using the experimental and FE analysis. Square cup drawing and stamping processes were used to investigate the formability of AZ31 sheet. Forming limit at elevated temperature could be predicted by FLD based on the diffuse necking. work-hardening exponent was one of the important properties to prevent the necking and improve the formability. [Copyright &y& Elsevier]

Abstract: Few previous attempts have been made to analyze numerically the strain path and the forming limit in complex lubricated sheet metal forming. Since usual approaches of solving the lubrication model are limited to axisymmetric and plane strain cases only, this paper developed a unified procedure for combining the finite element code of sheet metal forming, the current lubrication/friction model and forming limit theory, to predict the strain path and fracture strains for either a steady or an unsteady three-dimensional process including both axisymmetric and plane strain cases. The availability of the method must be proved by a published problem, and an axisymmetric stretch forming process was therefore adopted as a benchmark. Numerical results showed that the present analysis provides good agreement with the experimental data of the strain path and the fracture strain for various tribological parameters such as lubricant viscosity and composite roughness of tooling and workpiece, and the advantage of the developed model is that it can be applied to solve the complicated 3D geometric problems. [Copyright &y& Elsevier]

In this paper, the superplastic forming (SPF) potential of two fine-grained 5083 aluminum alloys were studied under various stress states with the use of both high temperature tensile testing and pneumatic bulge testing. Experiments with the pneumatic bulge test were performed at temperatures ranging from 475 to 525 °C under three different strain paths ranging from equi-biaxial to approaching plane strain. The effects of temperature on total elongation, m-value, final thickness distribution, dome height, and cavitation were investigated for the case of uniaxial and equi-biaxial stretching. Increased temperature in bulge forming was found to improve the thickness distribution in the formed parts, but did not have a significant effect on dome height. The shape of the forming limit diagram (FLD) was found to be significantly different than that of FLDs commonly used in room temperature stamping. Results indicate that determination of forming limits in SPF cannot be represented with a simple FLD and additional metrics such as external thinning and internal cavitation need to be considered to determine a material's SPF potential. [ABSTRACT FROM AUTHOR]

The effects of 2D and 3D prebending on the forming limit in the tube hydroforming process of an automotive rear subframe are evaluated and compared through finite element analyses and experimental tryouts. The influence of the strain path corresponding to each prebending method is discussed in terms of a forming limit diagram (FLD) and a forming limit stress diagram (FLSD). An incremental strain-to-stress transformation scheme to plot the FLSD from the FLD along an arbitrary strain path is proposed. A tube hydroformability testing system designed and manufactured to provide an arbitrary combination of internal pressure and axial feed is introduced. A forming limit diagram of the A6063 aluminum tube material is obtained from free bulging, T-shape forming and cross-shape forming tests using this system. [ABSTRACT FROM AUTHOR]

Abstract: Experimental results of copper X-joint hydroforming have been compared with the results of FEA simulations. An influence of loading history and properties of deformed tubular material on process feasibility has been presented. The method of forming limit curve (FLC) prediction was utilised in order to determine the onset of strain localization and bursting failure. Prediction of failure based on the FLC commonly used for sheet metal forming has given a considerable underestimation of hydroforming limit for X-joints. Hence, the modified FLCm has been suggested that could be used in hydroforming process planning. [Copyright &y& Elsevier]

Abstract: Continuous strip casting and direct rolling method are receiving attention as the integrated producing process to obtain wrought magnesium alloys. In this research, AZ61 strip was cast from molten metal by twin-roll strip caster and rolled by “Structure-Control rolling process”. The effects of casting conditions and rolling parameters on surface aspects and microstructure of the rolled sheet were investigated. The results obtained were as follows: (1) By casting 1.5mm strip, a better surface and finer microstructure were obtained compared to 3mm strip. (2) By using structure-control rolling with R.T. pass, a microstructure of mean grain size of 5μm was obtained. (3) By lowering the starting rolling temperature, mean grain size and duplex grain size degree decreased and hardness increased. In addition, the deformation resistance decreased and the fracture strain increased. [Copyright &y& Elsevier]

It has been observed that the forming limit curve at fracture (FLCF) of steel sheets, with a relatively higher ductility limit have linear shapes, similar to those of a bulk forming process. In contrast, the FLCF of sheets with a relatively lower ductility limit have rather complex shapes approaching the forming limit curve at neck (FLCN) towards the equi-biaxial strain paths. In this study, the FLCFs of steel sheets were measured and compared with the fracture strains predicted from specific ductile fracture criteria, including a criterion suggested by the authors, which can accurately describe FLCFs with both linear and complex shapes. To predict the forming limit for hydro-mechanical deep drawing of steel sheets, the ductile fracture criteria were integrated into a finite element simulation. The simulation, results based on the criterion suggested by authors accurately predicted the experimetal, fracture limits of steel sheets for the hydro-mechanical deep drawing process. [ABSTRACT FROM AUTHOR]

Abstract: Because of hexagonal close-packed (HCP) crystal structures, commercially pure titanium (CP Ti) shows low ductility at room temperature, and requires thermal activation to increase its ductility and formability. In the present study, the formability of CP Ti sheets at various temperatures was studied by the experimental approach. Tensile tests were first conducted to investigate the mechanical behavior of CP Ti sheets at various temperatures. Forming limit tests, V-bend tests, and cup drawing tests were also performed to examine the stamping formability of CP Ti sheets at various temperatures. The experimental results indicate that CP Ti sheets could be formed into shallow components at room temperature, although the formability is limited in cold forming. In addition, the results obtained from the V-bend tests reveal that springback can be reduced at elevated forming temperatures. The experimental results obtained in the present study can be of help to the die design of stamping CP Ti sheets. [Copyright &y& Elsevier]

Abstract: This research investigates the forging limit of sintered compacts by taking into particular consideration the effects of void evolution in the process. A new fracture criterion for a porous medium, which is based on the first principal strain energy density (FPSED), is developed as well. The experiment and the finite element analysis (FEA) have been conducted to examine the process. The material properties of porous compacts are measured by both the uni-axial tension and the compression tests. The finite element model is first verified with the upsetting experiment under different frictional conditions. By applying this new criterion, the fracture upsetting simulation demonstrates much better accuracy than the results derived from the equations proposed by other researchers. The fracture prediction in forging the gear blank is also presented as a practical application to reinforce the reliability of this model. Besides the degradation of the strength, this study specifically shows that voids in the sintered preform exponentially reduce the forging limit. [Copyright &y& Elsevier]

Abstract: The tube has high bending and torsional rigidity considering its weight. Thus, tubular products are effective industrial parts to reduce their weight and their employments volume is increasing. Spinning is a very effective and flexible manufacturing technology for short production runs in a variety of sizes and shapes. Spinning is widely applied to the tube forming corresponding to the increasing usage of the tubular parts. Magnesium and its alloys have many good properties as strength to weight ratio, vibration absorbability and excellent recyclability. It is very difficult to form the magnesium alloy to various shaped products. But, it is easy to form the alloys at high temperature. Therefore, authors have invented new Computer Numerical Control (CNC) spinning machine, which has roller tools with heaters. The heated tools heat and form the magnesium tubes into various shapes by the spinning. The forming possibility of magnesium tube and the properties of formed tube are made clear in this paper. [Copyright &y& Elsevier]

A strain forming limit criterion is widely used throughout the sheet metal forming industry to gauge the stability of the deformed material with respect to the development of a localized neck prior to fracture. This criterion is strictly valid only when the strain path is linear throughout the deformation process. There is significant data that shows a strong and complex dependence of the limit criterion on the strain path. But unfortunately, the strain path is never linear in secondary forming processes. Furthermore, the path is often to be nonlinear in localized critical areas in the first draw die. Therefore, the conventional practice of using a path independent strain forming diagram criterion often leads to erroneous assessments of forming severity process. In this study, the numerical results are based on MARC K7.1-3D finite element analysis (FEA) software using rigid-plastic flow method. This general purpose of FEA code is using both the implicit and explicit procedure. The model is employed to predict the stress–strain forming limit diagrams and thickness distribution of a deep drawing quality steel (DDQS) and aluminum alloy (AL) sheet. The predicted results agree well with those determined experimentally. [Copyright &y& Elsevier]

Thin-walled tube bending processes may produce a wrinkling phenomenon if the process parameters are inappropriate, especially for tubes with large diameter and thin wall thickness. How to predict this phenomenon rapidly and accurately is one of the urgent key problems to be solved for the development of this process at present. In this paper, a wrinkling wave function is proposed and a simplified wrinkling prediction model to predict the minimum bending radius for tubes is established based on thin-shell theory, forming theory, the energy principle and wave function. The minimum bending radius calculated according to the method established is in agreement with data reported in the literature. Furthermore, effects of parameters on the minimum bending radius are also analyzed: (1) the influence of bending angle on the minimum bending radius is negligibly small; (2) the effect of geometrical dimensions and material properties of tubes on the minimum bending radius is significantly large; (3) the minimum bending radius becomes larger with the original radius and strength coefficient of tubes increasing, whereas with the wall thickness and strain hardening exponent decreasing. The results are helpful to the design and optimization of the relevant processes in practice. [Copyright &y& Elsevier]

In this paper, recent developments in sheet hydroforming technology are summarized, several key technical problems to be solved for the development of sheet hydroforming technology are analyzed, and varied sheet hydroforming technologies are discussed. Compound deformation by drawing and bulging is the main direction for the development of sheet hydroforming technology, in which it is advantageous to increase the feeding of materials, and the ratio of drawing deformation (drawing in of the blank flange) to bulging, enabling the forming limit of a sheet blank to be increased. It is also advantageous to increase the local deformation capacity for sheet hydroforming, to increase the range of application of the process. Press capacity is one of the important factors restraining the range of applications. As one of the flexible forming technologies that is still under development, it has much potential for innovative applications. Its applications have been increasing remarkably, recently in automotive companies. A breakthrough in the technology will be obtained by the development of novel equipment. A new sheet hydroforming technology using a movable die is proposed in this paper, which has been developed recently by the authors. [Copyright &y& Elsevier]

The forming limit diagram (FLD) is used in sheet metal forming analysis to determine how close the sheet metal is to tearing when it is formed into a product shape in a stamping process. The strain-path dependent nature of the FLD causes the method to become ineffective in the analysis of complex forming process, especially restrikes, flanging operations, hydroforming, and even first draw dies with deep pockets or embossments. Experimental evidence for a path-independent stress-based FLD has been reported in the literature, suggesting that the path dependency of the strain-based approach arises from the path dependent constitutive laws governing the relationship between the stress and strain tensors. This paper reviews several theoretical models of sheet metal forming instability, including bifurcation analyses of diffuse and through-thickness neck formation, the M-K model and microscopic void damage models. The equations governing the deformation at the instant of the bifurcation is shown to be independent of path in all of these models, providing a solid theoretical bases for the stress-based approach. The stress-based FLD can now be used equally well for all forming processes, without concern for path effects. [Copyright &y& Elsevier]