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The conventional theoretical forming limit diagram (FLD) based on the plane stress state has defects due to the neglect of the stress in the thickness direction of the sheet. It is urgent to study the FLD which considers the stress in the thickness direction. Through the finite element simulation, it is further confirmed that the stress in the thickness direction will be induced in the deformation process. At the same time, the effect of the induced stress in the thickness direction on FLD is not the same as that always applied stress in the thickness direction during the deformation process. Based on the Modified Maximum Force Criterion (MMFC) instability theory, C-H instability theory, Mises and Hill48 yield criterion, the effects of the two stresses on FLD are compared. The induced stress in the thickness direction also affects the sensitivity of the coefficient of normal anisotropy r, but does not significantly change the effect of the stress-strain index n on Forming Limit Curves (FLC). The theoretical calculations of the three materials TRIP780, AA5182, and 5754O are compared with the experimental data, which proves that the FLD which considers induced stress in the thickness direction is more accurate than the FLD of the plane stress.

To meet the requirement of lighter weight and better performance in tube hydroforming, one of the most important tasks is to accurately predict the forming limit of thin-walled tubes under nonlinear loading paths. This work established the M-K+DF2012 model, a combination of the M-K model and the DF2012 ductile fracture criterion, for the forming limit prediction of thin-walled tubes under nonlinear loading paths. In this model, the failure of the groove is determined by the DF2012 criterion, and the corresponding strains in the uniform region are the limit strains. The limit strains of an AA6061 aluminum alloy tube under a set of linear loading paths and two typical nonlinear loading paths were tested. Parameter values of the M-K+DF2012 model for the tube were determined based on the experimental limit strains under linear loading paths, and the limit strains under the two nonlinear loading paths were predicted. Then the strain-based forming limit diagram (ε-FLD) and the polar effective plastic strain FLD (PEPS-FLD) of the tube under different pre-strains were predicted and discussed. The results show that the limit strains of the tube are obviously path-dependent, and the M-K+DF2012 model can reasonably capture the limit strains of the tube under both linear and nonlinear loading paths. The predicted ε-FLD shows a strong dependence on the pre-strain, while the predicted PEPS-FLD is weakly strain path-dependent and almost path-independent on the right-hand side for the AA6061 tube.

Sheet metal forming limit diagram (FLD) is a comprehensive index used to evaluate sheet metal formability. In this paper, the forming limit curves of GH605 sheet materials with 0.2 mm and 2.5 mm thickness under three different heat treatment conditions were obtained by numerical simulation of bulging. Then, the simulated forming limit results of the three materials with 0.2 mm thickness were compared with the experimental results. The results show that the simulated FLDs can be in good agreement with the experimental FLDs. The influences of work hardening index (n value) and anisotropy index (r value) on the forming limit are analysed from the view of material property difference. The comprehensive simulated and experimental results show that the formability of the sheets after the two kinds of solution treatment is significantly better than that of the annealed sheets. The forming limit curve increases with the increase of n value and r value, and the influence of n value on the forming limit curve is more significant than that of r value. The forming limit diagram established by numerical simulation can provide a theoretical basis for material development and process selection.

Forming limit of metal foil is an important index to evaluate its formability, and is of considerable significance to improve the quality of products. The ductile fracture (DF) behavior in microscale plastic deformation is remarkably affected by the geometry and grain size. To explore the size-dependent forming limit curve (FLC), the Holmberg and Marciniak tests of SUS304 foils with the thicknesses of less than 0.1 mm and diverse grain sizes were performed. In addition, the validity and feasibility of three types of existing failure models including Swift/Hill, Marciniak-Kuczynski (M-K) and DF criteria for predicting the micro-scaled FLCs were discussed. It is found that the Swift/Hill model possesses the worst accuracy with predicting deviation above 50%. Four classical DF criteria including Freudenthal, Ayada, Brozzo and Oh show great difference, and Oh model considering plastic anisotropy presents the best precision. The predicted deviation of M-K model is aggravated with increasing grain size and decreasing foil thickness, which is attributed to the intensified free surface roughening and transformation of fracture mechanism with miniaturization. This research thus provides a deeper understanding and valuable reference for the widespread application of FLC in microforming.

Advanced manufacture technologies, oriented to implants featured with high reliability, low cost and high biocompatibility, are key approaches to advance the rehabilitation efficacy and shorten the recovery period of patients. Considering the shortage of current fabrication processes, the incremental sheet forming (ISF) which is featured as a flexible forming technique is applied to manufacture implants. This review begins with the overview of ISF for different kinds of materials and implants. Then, the forming quality of implants formed by ISF was comprehensively reviewed and discussed in various aspects including the geometric accuracy, surface quality, and the forming limit. Moreover, various micro manufacturing processes and the size effect were summarized for the purpose of surface modification of medical implants. Based on the investigation of micro manufacture techniques, a novel macro-micro hybrid ISF technique was proposed to form the macro-profile and the micro-structures of implants synergistically through a single manufacturing process with different scales. Finally, future scope and potential research directions were addressed.

Roll forming can improve the material utilization rate and production efficiency of cups with a curved rotary profile, but there is no basis for the determination of forming limit. The DEFORM-3D software was used to simulate the roll forming of cups. The influence of the billet wall thickness and bottom thickness, coefficient of friction, radius of roller, and the fillet radius of the punch on the forming limit was studied, and the damage value and velocity vector were analyzed. The results showed that the forming limit of the billet’s wall thickness in roll forming for a cup is about 62%. With the increase of the ratio of the formed cup’s wall thickness to the billet’s bottom thickness, the forming limit of wall thickness will be slightly reduced. A larger radius of roller, fillet radius of punch, and friction coefficient between punch and billet and a smaller friction coefficient between roller and billet are good for decreasing the damage value and improving the roll-forming limit. According to the numerical simulation results, the roll-forming limit diagram of cups is established, and the accuracy of the forming limit diagram is verified by experiments.

This study investigates the effect of grain size and composition on the material properties and forming limits of commercially supplied stainless steel foil for bipolar plate manufacture via tensile, stretch forming and micro-stamping trials. It is shown that in commercially supplied stainless steel the grain size can vary significantly and that &lsquo, size effects&rsquo, can be influenced by prior steel processing and composition effects. While the forming limits in micro-stamping appear to be directly linked to the plane strain forming limits of the individual stainless steel alloys, there was a clear effect of the tensile anisotropy. In contrast to previous studies, forming severity and the likelihood of material failure did not increase with a decreasing channel profile radius. This was related to inaccuracies of the forming tool profile shape.

Phenomenological methods are more diagnostic tools than a predictor, so multi-crystalline material approaches based on their microstructures have been proposed during the last years. The purpose of this research is to review methods taking into account the effect of microstructures and texture deformation on predicting the behavior of sheet metals. These methods can be categorized into six general groups: Taylor-type models, crystal plasticity finite element methods, strain gradient methods, methods that consider dislocations, self-consistent methods, methods based on fast Fourier transform. This paper attempts to explain and compare these methods that have been used to forecasting forming limits or stress-strain curves.

We proposed a local one-sided rubber bulging method of metal tubes to evaluate various strain paths at an aimed portion and measured the forming limit strains of metal tubes at the place of the occurrence of necking under biaxial deformation. Using this method, since rubber is used to give pressure from the inner side of the tube, no sealing mechanisms were necessary unlike during hydraulic pressure bulging. An opening was prepared in front of the die to locally bulge a tube at only the evaluation portion. To change the restriction conditions of the bulged region for biaxial deformation at the opening, a round or square cutout, or a slit was introduced. The test was conducted using a universal compression test machine and simple dies rather than a dedicated machine. Considering the experimental results, it was confirmed that the strain path was varied by changing the position and size of slits and cutouts. Using either a cutout or a slit, the strain path in the side of the metal tubes can be either equi-biaxial tension or simple tension, respectively. Additionally, by changing the size of the cuts or slits, the strain path can be varied.

In this study, the experimental two-dimensional forming limit diagram (FLD) data for a ZIRLO&trade, sheet, which is used in nuclear fuel rod support grids, were converted and presented as a triaxiality failure diagram (TFD). Most previous studies assumed ZIRLO&trade, to be isotropic when calculating the effective stress and strain. However, for highly anisotropic materials, the anisotropy should be considered for calculations of effective stress and strain, hence, in this study, they were calculated by introducing the normal anisotropy coefficient. To obtain this parameter of the ZIRLO&trade, specimens, tensile tests were performed on specimens with 0&deg, 45&deg, and 90&deg, angles with respect to the rolling direction. It was observed that the average normal anisotropy coefficient measured during the tests was 4.94, which is very high. The von Mises isotropic and Hill 48 anisotropic yield criterion were applied to the FLD data that were experimentally determined using a limit dome height test and were converted into effective stress and effective strain. When the FLD is converted to TFD, the curve will increase in the top-right direction if the r-value is greater than 1, and this become more severe as the r-value increases. The TFD, which was converted considering the anisotropy, is almost the same to the TFD obtained using the digital image correlation method in the tensile tests of four specimens with different stress states. If anisotropy is not considered, then the formability is normally underestimated. However, a highly accurate TFD can be obtained with the method proposed in this study.

Ultrahigh strength steels are highly competitive materials for vehicles to concurrently meet the increasing demand of the weight reduction and passenger safety. Hot stamping is the key forming technology to manufacture automobile components with high strength. Hot stamping steel and its manufacturing technology experienced a fast development in the past decade. This paper reviewed the state of the art of the manufacturing and applications of hot stamping steels/components in the following aspects: (1) hot stamping steels (from traditional MnB steels to recently newly developed hot stamping steels); (2) forming technologies (from traditional hot stamping process to industry 4.0 intelligent production); (3) novel hot stamping + quenching & partitioning (Q&P) process and fundamentals of deformation assisted heat treatments; (4) simulation techniques for hot stamping process (modeling of the temperature-stress field, microstructure field and simulation of the manufacturing process); (5) the assessments of in-service performance of hot stamped components. Finally, the trends of the development of hot stamping steels and related forming technologies in the future will be discussed.

In this study, an investigation on the densification behavior and forming limit of powder metallurgy composites containing hard carbide particles were carried out. The selected composite materials are Al4TiC, Al4WC, Al4Fe3C and Al4Mo2C. The compacts of 0.82 and 0.86 relative density and 0.4 and 0.6 aspect ratio were prepared on a 1-MN capacity hydraulic press using suitable die-set assembly. Sintering was carried out at 594 ℃ for 60 minutes in an electrical muffle furnace. Hot upsetting was carried out at the sintering temperature immediately after the sintering process and the forming process was stopped once visible cracks were seen on the free surface. Flat dies on the upper and lower surface were employed under dry friction conditions during hot upsetting. Finally, the densification behavior and forming limit of sintered-forged aluminium composite preforms is presented in this research work. It was concretely noted that Al4TiC produced the best density amongst all the above mentioned aluminium composites. Further, it was seen that Al4Mo2C and Al4WC produced good final height and diameter strain at fracture.

Hot stamping is a method capable of manufacturing high-strength automotive body parts by inducing a martensitic phase transformation through forming and die quenching after heating a metal sheet into a high temperature austenite phase. However, it is not easy to solve various formability problems occurring in the hot stamping process due to the complexity of the process and material behavior during high temperature forming. In this study, fracture-related forming limits and martensite phase ratio were selected as criteria for evaluating hot stamping formability. First, a hot stamping test was performed on a T-type part that simplified the B-pillar, an automotive body part, and the fracture behavior according to the temperature and thickness of the sheet blank was investigated. Additionally, forming analysis was performed on the hot stamping process of mass-produced B-pillar parts by varying the temperature of the sheet blank, the thickness of the sheet blank, the die-blank friction coefficient, and the strain-rate sensitivity of material among various process and material variables. Based on the analysis results, the effect of each process and material variable on the hot stamping formability of B-pillar parts was quantitatively analyzed. By utilizing the results of this study, it will be possible to solve the formability problem that occurs in the mass-production hot stamping process for automotive body parts and improve the quality of parts in the future.

Formability is the limit to which a material can be deformed before failure and is upmost importance in powder metallurgy (PM) forming process. This is because the presence of porosity in the PM part after the sintering process. In this study two key strain hardening parameters are used to study the workability behavior or determining the failure zone. This can be used for design of PM parts and most importantly the die design as repressing needs to be employed before pores appear as cracks on the free surface. It is nearly impossible to produce defect free parts if this failure occurs. The hot formability behavior of aluminum metal matrix composites (MMC's) that is, Al-4TiC, Al-4WC, Al-4Fe3C and Al-4Mo2C (by weight percentage) are presented in this paper.

With the implementation of environmental protection, sustainable development and conservation-oriented policies, components and parts of thin-walled welded tubes have gained increasing application in the aircraft and automotive industries because of their advantages: easily achieving forming and manufacturing process at low cost and in a short time. The current research on welded tube plastic forming is mainly concentrated on tube internal high-pressure forming, tube bending forming, and tube spinning forming. The focuses are on the material properties and characterization of welded tubes, finite element modeling for welded tube forming, and inhomogeneous deformation behavior and the mechanism and rules of deformation coordination in welded tube plastic forming. This paper summarizes the research progress in welded tube plastic forming from these aspects. Finally, with a focus on the urgent demand of the aviation, aerospace and automotive industries for high-strength and light-weight tubes, this paper discusses the development trends and challenges in the theory and technology of welded tube plastic forming in the future. Among them, laser tailor-welded technology will find application in the manufacture of high-strength steel tubes. Tube-end forming technology, such as tube flaring and flanging technology, will expand its application in welded tubes. Therefore, future studies will focus on the FE modeling regarding how to consider effects of welding on residual stresses, welding distortions and microstructure, the inhomogeneous deformation and coordination mechanism of the plastic forming process of tailor-welded tubes, and some end-forming processes of welded tubes, and more comprehensive research on the forming mechanism and limit of welded tubes.

Ultrasonic vibration (UV) is widely used in the forming, joining, machining process, etc. for the acoustic softening effect. For parts with small dimensions, UV with limited output energy is very suitable for the microforming process and has been gaininf more and more attention. In this investigation, UV-assisted uniaxial tensile experiments were carried out utilizing GB 5052 thin sheets of different thicknesses and grain sizes, respectively. The coupling effects of UV and the specimen dimension on the properties of the material were analyzed from the viewpoint of acoustic energy in activating dislocations. A reduction of flow stress was found for the existing acoustic softening effects of UV. Additionally, the residual effects of UV were demonstrated when UV was turned off. The uniform deformation ability of thin sheet could be improved by increasing the hardening exponent with UV. The experimental results indicate that UV is very helpful in improving the forming limit in microsheet forming, e.g., microbulging and deep drawing processes.

In the present work, an efficient formulation for the prediction of forming-limit diagrams (FLDs) based on the well-known Marciniak and Kuczynski (MK) theory using a Visco- Plastic Self-Consistent (VPSC) crystal-plasticity model has been detailed. The present model extends the previous MK-VPSC implementation (Signorelli et al., Predictions of forming limit diagrams using a rate-dependent polycrystal self-consistent plasticity model, International Journal of Plasticity 25 (2009) 1e25) based on the NewtoneRaphson (N-R) method, which gives no guarantee of a robust iterative procedure. In order to avoid convergence problems and to reduce the computational cost of the coupled MK-VPSC scheme, a direct approach (DA) is proposed. The DA eliminates the need of the Jacobian evaluation associated with the N-R method as well as the iterative procedure tied to other possible minimization techniques. Moreover, the mechanical states outside and inside the groove are solved in the sample reference frame, avoiding the need to rotate the crystallographic orientations and the internal variables to the current band reference frame at each increment. In this way, only two calls to the material law are required per MK increment, obtaining a more robust numerical procedure with a significant computational cost reduction. Interestingly, the requirement of more complex boundary conditions does not substantially increase the number of internal VPSC iterations to achieve a given tolerance. Simulation results show that the direct MK-VPSC approach is consistent with that based on the N-R method. The generalized boundary conditions in the polycrystal model allowed us to calculate either strain-rate ratio or stress ratio based FLDs. The effect of using either strain-rate ratio or stress ratio paths on the FLDs has been investigated by imposing three types of pre-straining on the sheet metals. Formability predictions for a randomly-textured FCC material and for textured FCC, BCC and HCP polycrystals are presented and discussed. Finally, by considering dissimilar metals e extra deep-drawing quality steel (EDDQ), dual-phase steel (DP-780) and pure zinc (Zn20) e we evaluated the MK-VPSC model´s ability to predict forming-limit strains irrespective of microstructure and crystallography. The predicted results have been compared with experimental data and good agreement was found. Fil: Schwindt, Claudio Daniel. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Schlosser, Fernando. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); Argentina Fil: Bertinetti, María de Los Angeles. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); Argentina Fil: Stout, M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); Argentina Fil: Signorelli, Javier Walter. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); Argentina

This research focuses on the prediction of the forming limit of certain Advanced High Strength Steel grades under stretch-bending conditions. For these types of steels it is experimentally observed and shown that when there is a bending component added to the main membrane deformation the formability predicted by the regular FLCs underestimate the material behavior. Due to the added effects of thickness stress due to contact and small radius bending as well as bending stresses, a through-thickness stress gradient forms which gives additional stability to the material beyond the forming limits determined by tests that generate mostly uniform membrane deformation. It is observed experimentally and by the detailed simulations that the cross-sectional stability is not lost instantaneously but gradually. A surface dent forms first on the outer surface and progresses in a stable manner towards the contact side since on the contact side the material has still potential to harden. This process delays the localization of the strains and stabilizes the formation of the local neck. For the prediction of this phenomenon theoretically and using shell elements, a modified incremental form of the maximum tension stability criterion is proposed to be applied at integration points through thickness. It is shown that with this criterion the phenomenon of gradual loss of stability can be captured during stretch-bending with shell elements.

Single point incremental forming is used for rapid prototyping of sheet metal parts. This forming technology was applied to the fabrication of thin shell micropyramids of aluminum, stainless steel, and titanium foils. A single point tool used had a tip radius of 0.1 mm or 0.01 mm. An ultrasonic spindle with axial vibration was implemented for improving the shape accuracy of micropyramids formed on 5–12 micrometers-thick aluminum, stainless steel, and titanium foils. The formability was also investigated by comparing the forming limits of micropyramids of aluminum foil formed with and without ultrasonic vibration. The shapes of pyramids incrementally formed were truncated pyramids, twisted pyramids, stepwise pyramids, and star pyramids about 1 mm in size. A much smaller truncated pyramid was formed only for titanium foil for qualitative investigation of the size reduction on forming accuracy. It was found that the ultrasonic vibration improved the shape accuracy of the formed pyramids. In addition, laser heating increased the forming limit of aluminum foil and it is more effective when both the ultrasonic vibration and laser heating are applied.

In the household appliance industry piecework coating of body components has been successively substituted by usage of coil-coated sheets. For components with low strains or components not visible for the customer and therefore with no requirements concerning the visual impression these organic-coated materials bear a proper possibility for cost savings. But besides that, for high quality household appliances there are high visual requirements on the front panels. Already the gloss reduction of the coating layer due to higher strains restricts the application for front panels in most cases. From an economic point of view the application of coil-coated sheets even for these components is highly demanded. For an acceptable substitution the resulting paintwork properties after the forming process should be able to forecast within numerical simulations. Therefore the forming-induced gloss reduction of the respective coated material has to be determined in a proper manner. This paper deals with analyses concerning the forming-induced and strain-state-depending gloss reduction of a coil-coated material commercially used for white goods components. The investigations include measurements of strains and gloss by using an in situ approach. For that purpose, material specimens are formed using a modified experimental setup referring to the Marciniak-Test (ISO 12004-2). A fundamental advantage of the in situ measurements is a minor demand of experiments together with a high resolution of the measured variables. In conclusion, based on the experimental results a conceivable forming limit criterion is defined and integrated in an exemplarily simulation model. The front panel of a front-loading washing machine is used as a practice-oriented application example. Using of the pursued approach improper gloss reductions on the formed panel can be predicted within forming simulation. European Research Association for Sheet Metal Working (EFB) German Federation of Industrial Research Associations (AiF) Federal Ministry of Economic Affairs and Energy (BMWi)

An effect of tool rotation direction on forming limit in friction stir incremental forming was studied. A 3-axes NC milling machine and a hemispherical tool which with a diameter of 6 mm made of high speed steel was used for forming. The thickness of commercial A5052-H34 aluminum sheet was 0.5 mm. The forming tool was moved from the outside to inside in a pitch of 0.5 mm spirally, and the sheets were formed into frustum of pyramid shape. Formability evaluated by minimum wall angle of the pyramid was investigated by changing a tool rotation rate, tool feed rate and tool path direction. When the tool paths were clockwise and counter clockwise, they were defined to “advancing direction” and “retreating direction” as well as in friction stir welding, respectively. From the experimental results, forming limits by both rotation directions of advancing and retreating were almost the same, however, the range of formable working conditions in advancing direction was slightly wider than that in retreating direction. Evaluating the forming limits in relative velocity between the tool surface and the sheet, no difference of forming limit was obtained between forming in advancing direction and retreating directions.

Under stretch-bending conditions where the curvature is relatively large, the plane stress assumption leads to a significant inaccuracy in forming limit prediction. In processes where a contact pressure acts on the material combined with a small punch radius it is observed by FE simulations that a significant thickness stress gradient develops. This gradient influences the materials plastic flow behavior through thickness and hence affects the cross-sectional stability of the sheet. Based on this observation a theoretical study has been performed in order to quantify the effects of different process and material parameters on the formability of the sheet. Furthermore, it is observed numerically and experimentally that during stretch-bending the cross-sectional stability is not lost instantaneously but gradually over time. Therefore, the concept of FLC proves to be insufficient as to judge acceptability of the deformed product. Another approach is proposed where an instability criterion is developed that also accounts for the partial loss of stability of the cross-section. The criterion is implemented in FE environment to be used in Shell type elements. The results are compared with stretch-bending experiments on selected HSS and AHSS.

Microforming is an emerging technology to manufacture products in the light of miniaturization in several domains of industry. Plastic anisotropy is one of the material characteristics significantly affecting the micro forming process. The crystal orientation influences tensile strength, yield strength and ductility, depending on different grain sizes and principle sliding planes. The present work elaborates on the influence of the plastic anisotropic in microforming for a plane stress state condition. Yield function and constitutive equations for the anisotropic material with consideration of the crystal lattice constants and parameters of crystallography texture are proposed. The crystal orientation is considered in a subroutine VUMAT algorithm, as an internal variable based on the developed mathematical model which is implemented in Abaqus as an user material subroutine. Micro limiting dome height experimental tests for different strain paths are conducted with brass foils. The results are compared with that predicted with numerical analysis, considering critical damage and element deletions. The numerical and experimental results show a good agreement for the Alpha brass ultra-thin foils, using a set of failure criterion.

Zdolność do przyjmowania odkształceń plastycznych podczas kształtowania blach zależy od ich właściwości mechanicz- nych Odkształcalność blach zależy od rodzaju materiału - a ponadto, materiał który wykazuje dobrą odkształcalność podczas kształtowania wytłoczki o określonej geometrii, może sprawiać trudności podczas kształtowania wytłoczki o innej konfiguracji. Z tego powodu prowadzone są liczne prace badawcze mające na celu określenie relacji pomiędzy odkształcalnością blach a wartością parametrów mechanicznych materiału. Przy ocenie odkształcalności blach najczęściej korzysta się z wyznacza- nia wartości wykładnika krzywej umocnienia odkształceniowego oraz współczynnika anizotropii właściwości plastycznych. Znajomość charakterystyk odkształcenie-naprężenie oraz wskaźników umocnienia odkształceniowego jest bardzo ważna przy określaniu odporności na lokalizację odkształcenia. Badania eksperymentalne blach z różnych materiałów wykazały zasadnicze różnice ich odkształcalności. określane jako "typu mosiądz” oraz "typu stal”, przejawiające się brakiem lub wyraźną zależnością poziomu odkształceń granicznych od stanu odkształcenia. W pracy zawarte są wyniki badania właściwości mechanicznych w próbie jednoosiowego rozciągania oraz KOG w teście wg Marciniaka z płaskim stemplem, dla blachy ze stopu AMS 5599. Przeprowadzono obliczenia przebiegu krzywej odkształcalności granicznej przy pomocy różnych metod - wyniki obliczeń porównano z wynikami eksperymentu.

This paper deals with a new experimental technique for applying impulse tension loads. Briefly, the technique is based on the use of pulsed-magnetic-driven tension loading. Electromagnetic forming (EMF) can be quite effective in increasing the forming limits of metal sheets, such as aluminium and magnesium alloys. Yet, why the forming limit is increased is still an open question. One reason for this is the difficulty to let forming proceed on a certain influence monotonically: the main phenomena causing this increase in formability are considered to due to “body force” effect, inertia effect, changes in strain rate sensitivity. In this study, an impulse tension loading setup is presented. “Body force” effect and strain rate, which are known to be the two key factors leading to higher formability, can now be separated freely by our designed device. Reproducible and adjustable loading rate (80s-1~3267s-1) can be achieved by adjusting the discharge voltage and capacitance. The relation between the discharge voltage and strain rate was obtained with the help of finite element calculations and high-camera measurement results. The results of an exploratory experiment carried out on the designed device are presented for aluminum alloy AA5052 sheet. It shows that this technique could be used to study the dynamic response of sheets.

The formability of aluminum alloy sheet in electromagnetic impaction deformation has attracted the attention of numerous researchers for the past decades. However, the influences of die geometry and high-speed impaction electromagnetic deformation on formability have not been well established, thereby resulting in the formability of the sheet not being developed fully. In this study, the influence of die geometry on the formability of 5052 aluminum alloy in electromagnetic deformation was investigated by comparing the formability of 5052 aluminum alloys formed using a hemispherical die and a cylindrical die. The intriguing finding is that the formability of the 5052 aluminum alloy formed using a cylindrical die is considerably higher than that formed using a hemispherical die. Therefore, die geometry significantly influences the formability of 5052 aluminum alloy. The influence of die geometry on the formability of 5052 aluminum alloy in high-speed impaction electromagnetic deformation was explained in terms of strain rate, pressure stress, and stress state. This investigation enhances insight into the interaction between sheets and dies, and provides a reference for the studying influence of dies on the forming limit of sheets in high-speed impaction deformation.

This research focuses on the prediction of the forming limit of certain Advanced High Strength Steel grades under stretch-bending conditions. For these types of steels it is experimentally observed and shown that when there is a bending component added to the main membrane deformation the formability predicted by the regular FLCs underestimate the material behavior. Due to the added effects of thickness stress due to contact and small radius bending as well as bending stresses, a through-thickness stress gradient forms which gives additional stability to the material beyond the forming limits determined by tests that generate mostly uniform membrane deformation. It is observed experimentally and by the detailed simulations that the cross-sectional stability is not lost instantaneously but gradually. A surface dent forms first on the outer surface and progresses in a stable manner towards the contact side since on the contact side the material has still potential to harden. This process delays the localization of the strains and stabilizes the formation of the local neck. For the prediction of this phenomenon theoretically and using shell elements, a modified incremental form of the maximum tension stability criterion is proposed to be applied at integration points through thickness. It is shown that with this criterion the phenomenon of gradual loss of stability can be captured during stretch-bending with shell elements. © (2015) Trans Tech Publications, Switzerland.

This research focuses on the prediction of the forming limit of certain Advanced High Strength Steel grades under stretch-bending conditions. For these types of steels it is experimentally observed and shown that when there is a bending component added to the main membrane deformation the formability predicted by the regular FLCs underestimate the material behavior. Due to the added effects of thickness stress due to contact and small radius bending as well as bending stresses, a through-thickness stress gradient forms which gives additional stability to the material beyond the forming limits determined by tests that generate mostly uniform membrane deformation. It is observed experimentally and by the detailed simulations that the cross-sectional stability is not lost instantaneously but gradually. A surface dent forms first on the outer surface and progresses in a stable manner towards the contact side since on the contact side the material has still potential to harden. This process delays the localization of the strains and stabilizes the formation of the local neck. For the prediction of this phenomenon theoretically and using shell elements, a modified incremental form of the maximum tension stability criterion is proposed to be applied at integration points through thickness. It is shown that with this criterion the phenomenon of gradual loss of stability can be captured during stretch-bending with shell elements. © (2015) Trans Tech Publications, Switzerland.

Failure in ductile sheet metal structures is usually caused by one, or a combination of, ductile tensile fractures, ductile shear fractures or localised instability. In this paper the failure characteristics of the high strength steel Docol 600DP are explored. The study includes both experimental and numerical sections. In the experimental sections, the fracture surface of the sheet subjected to Nakajima tests is studied under the microscope with the aim of finding which failure mechanism causes the fracture. In the numerical sections, finite element (FE) simulations have been conducted using solid elements. From these simulations, local stresses and strains have been extracted and analysed with the aim of identifying the fracture dependency of the stress triaxiality and Lode parameter.

Taking Al–Li–S4–T8 Al–Li alloy as the study object, based on the stretching and deforming characteristics of sheet metals, this paper proposes a new approach of critical orange peel state characterizations on the basis of the precise measurement of stretch-forming surface roughness and establishes the critical criterion for the occurrence of orange peel surface defects in the stretch-forming process of Al–Li alloy sheet metals. Stretching experiments of different strain paths are conducted on the specimens with different notches so as to establish the Al–Li–S4–T8 Al–Li alloy, forming limit diagram and forming limit curve equation, with the surface roughness of characteristic critical orange peel structure as the stretch-forming failure criterion.

Subject of this work is the incorporation of forming limits in the numerical optimization of technological forming processes for sheet metal. Forming processes with non-linear load paths and strongly varying strain-rate, such as, e.g., combinations of deep drawing and electromagnetic forming are of particular interest. While in the latter impulse forming process inertial forces play a significant role, the first one is of quasi-static nature such that inertial forces may be neglected. Although classical forming limit diagrams provide an easily accessible method for the prediction of forming limits, they cannot be applied in situations involving pulsed loading along non-linear strain paths. Hence, they are extended to forming limit surfaces here. The target function to be minimized is computed via finite-element simulation. To avoid a large number of simulations, an interior point method is employed as optimization method. In this algorithm, forming limits appear via a logarithmic barrier function, which has to be computed sufficiently fast. The optimization algorithm is exemplarily applied to an identification problem for a twostage forming process.

Het vernieuwende Incrementeel Plaatvormgevingsproces (IPV) laat toe comp lexe driedimensionele vormen te produceren zonder specifieke gereedschap pen, wat een antwoord biedt op de industriële vraag naar snelle producti etechnieken voor kleine hoeveelheden en prototypes van schaalvormige str ucturen. Het is gebleken dat de vervormbaarheid van metaalplaat in dit p roces veel hoger is dan in traditionele plaatvormgevingsprocessen zoals strekken en dieptrekken. Deze thesis formuleert een verklaring voor deze hoge vervormbaarheid op basis van de plastische afschuiving over de pla atdikte die optreedt tijdens IPV. Eindige elementen modellering van de kleine plastische zone in een IPV p roces toegepast op aluminiumplaat toont duidelijk een significante afsch uiving over de plaatdikte aan. Dit vervormingsmechanisme is experimentee l geverifieerd door metingen van de totale afschuifhoek in laagkoolstofs taalplaat. Bovendien is het effect van deze afschuiving te zien in de op gemeten kristallografische vervormingstextuur. Het Marciniak-Kuczynski vervormingslimietmodel voor de voorspelling van gelokaliseerde insnoering is uitgebreid naar vervormingen met afschuivin g over de plaatdikte. Plastische anisotropie ten gevolge van de kristall ografische textuur is hierbij in rekening gebracht. Dit theoretische kad er voorspelt dat afschuiving over de plaatdikte het begin van gelokalise erde insnoering kan uitstellen, wat interessante toekomstperspectieven m et zich meebrengt betreffende afschuiving over de plaatdikte in andere v ormgevingsprocessen van metaalplaat. VOORWOORD i ABSTRACT iii CONTENTS v LIST OF TABLES viii LIST OF FIGURES ix LIST OF SYMBOLS AND ABBREVIATIONS xv 1. General introduction 1 1.1 Incremental Sheet Forming 1 1.2 The remarkable formability of ISF 4 1.3 Scope of this thesis 5 1.4 Outline of this thesis 6 2. Literature review 7 2.1 Introduction 7 2.2 The Single Point Incremental Forming Process 8 2.2.1 The final strain state in SPIF 8 2.2.2 FE modelling of SPIF 10 2.3 The limits of sheet formability 11 2.3.1 Stages of plastic instability in conventional forming processes 12 2.3.2 Stages of plastic instability in SPIF 14 2.3.3 Conventional formability tests 15 2.3.4 Influence of sheet curvature and/or sheet thickness 17 2.4 Forming Limit Models 19 2.4.1 A classification of analytical models for localized necking under monotonic loading 20 2.4.2 A conventional MK model revisited 22 2.4.3 Localized necking models beyond the classical FLC concept 28 2.5 Conclusion 35 3. Through-thickness shear in single point incremental forming 37 3.1 Introduction 37 3.2 Finite element analysis 38 3.2.1 Process description 38 3.2.2 FE modeling strategy 41 3.2.3 Mesh dependency 44 3.2.4 Validation of the material model 51 3.2.5 Validation of the FE contact model 53 3.2.6 Prediction of through-thickness shear 55 3.3 Direct measurement of through-thickness shear 56 3.3.1 Experimental set-up 56 3.3.2 Through-thickness shear measurement 57 3.3.3 Results and discussion 59 3.4 Texture analysis 62 3.4.1 Experimental set-up 62 3.4.2 Qualitative texture analysis 64 3.4.3 Quantitative texture analysis 69 3.4.4 Deformation texture and deformation mechanism 71 3.5 Conclusions 72 4. Generalization of the Marciniak-Kuczynski model 73 4.1 Introduction 73 4.2 Model zones and reference frames 75 4.3 Description of the rate of deformation in the matrix 78 4.4 Description of the rate of deformation in the groove 83 4.5 The strain definition in matrix and groove 83 4.6 Geometric compatibility 84 4.7 Force equilibrium 86 4.8 Solution procedure of an increment 88 4.9 Necking Criteria 89 4.10 Forming limit strain 90 4.11 Constitutive laws 91 4.11.1 The definition of the local frame 92 4.11.2 Facet method to describe anisotropy 93 4.11.3 Strain hardening 95 4.11.4 Simplifications for an isotropic von Mises material 96 4.12 Implementation 97 4.13 Comparison to a different MK model with TTS 99 4.14 Conclusion 101 5. Formability predictions 103 5.1 Introduction 103 5.2 Monotonic FLCs of the isotropic von Mises material 104 5.2.1 Forming Limit Curves 104 5.2.2 Critical groove orientations under monotonic loading 106 5.2.3 Detailed analysis of selected deformation modes 109 5.3 Monotonic FLCs of anisotropic materials 118 5.3.1 Material selection 118 5.3.2 Texture 119 5.3.3 Facet description based on the Taylor model 122 5.3.4 Formability predictions of anisotropic sheet 126 5.4 Formability in the Single Point Incremental Forming process 136 5.5 Conclusion 141 6. General conclusions and outlook 143 6.1 General conclusions 143 6.2 Outlook for future work 146 REFERENCES 147 LIST OF PUBLICATIONS 157 CURRICULUM VITAE 159 The novel Incremental Sheet Forming (ISF) process allows producing complex three-dimensional shapes from Computer Aided Design (CAD) models without specially designed forming tools. This process thus meets a demand for small batch production and rapid prototyping of industrial shell-like structures. The formability of a metal sheet subjected to this process is generally found to be much higher compared to traditional forming processes such as stamping and deep drawing. This thesis formulates an explanation for the remarkable formability on the basis of through-thickness shearing that occurs during ISF. While in the study of many conventional sheet forming processes through-thickness shear (TTS) can be neglected, several numerical and experimental investigations presented in this work have shown that this assumption does not hold for ISF. The finite element method, a numerical tool for solving non-linear field problems, is adopted for the simulation of ISF processes. Models of different spatial refinement, determined by the mesh density, have been investigated, using various models for the material constitutive behavior. A non-negligible TTS is indeed predicted by models with a sufficiently large mesh density. Such fine meshes also allow proper modelling of the small contact zone in ISF, as well as an accurate prediction of the forming force. On the experimental side, a direct measurement method of the overall TTS is proposed, and statistically non-zero through-thickness shear angles are observed for a low carbon steel sheet. The accuracy of these measurements is however limited, and the method itself is questionable as a defect needs to be introduced. Another experimental verification of TTS is performed from christallographic texture measurements by X-ray diffraction. The deformation texture contains evidence of TTS during the ISF process, although only in a qualitative sense. The Marciniak-Kuczynski (MK) model framework, which assumes an imperfection (groove) in an otherwise perfectly homogeneous sheet (matrix), is a commonly used analytical tool to predict the limit of sheet formability due to the onset of localized necking. An original extension to the MK model framework is presented in this thesis in order to explicitly account for TTS, which is usually disregarded in MK analyses. This is achieved by the introduction of additional force equilibrium and geometric compatibility equations that govern the connection between matrix and groove in the MK model framework. Furthermore, in order to integrate plastic anisotropy in the extended model featuring TTS, a material reference frame available in recent literature is incorporated, as well as a particular model for anisotropic yielding that relies on virtual testing of anisotropy (Facet plastic potential), since out-of-plane anisotropy related to TTS cannot be measured experimentally. The extended MK model shows that TTS delays the onset of localized necking in case the TTS is applied to the sheet in the same direction as the incipient necking direction. The underlying mechanism is a stress mode change within the groove towards the plane strain yield point, which brings about additional hardening that stabilizes necking. From the comparison of formability predictions between an aluminum and a low carbon steel sheet, it is also clearly seen that anisotropy influences the amount of delay in necking that is due to TTS. The occurrence of TTS in the ISF process postpones the onset of localized necking and thus contributes to the high formability that is observed. nrpages: 159 status: published

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In order to improve the mold filling in molding of aluminum foams, a molding process by using a rotating mold is proposed. Aluminum powder mixed with a foaming agent is formed to a precursor by hot powder extrusion and extruded into the mold through the die heated to a temperature higher than the melting point, and then the mold is filled with the aluminum foam. When the diameter of a cylindrical mold is large, the influence of gravity is significant and the mold is not filled successfully. In the proposed process, the aluminum foam is extruded into the rotating mold of large diameter and the shape of foam is improved. However, the effect of the mold rotation on the mold filling is limited.

Synchronous multi pass spinning is a metal spinning method that can form asymmetric shapes with a noncircular bottom and vertical walls from a metal sheet. In this method, the tool trajectory is calculated by linear interpolation between the mandrel shape and the blank disk shape along a pass set. Here, the pass set corresponds to the tool trajectory in conventional spinning. The aim of this study is to examine the effect of a pass set on the formability of a circular cup shape and a rectangular box shape. We have experimentally examined the formability using various pass sets made by simple rule. The angle growth of the rotational pass set, the incremental movement of the translational pass set, and the nominal product height are varied for comparison in the experiments.

An incremental sheet forming system with dynamic local heating by laser irradiation was developed to form magnesium alloy sheet which is typical lightweight hard-to-form sheet metal. In this process, tool contact area of a blank sheet is locally heated by a moving laser beam spot to increase the material ductility and decrease the material strength dynamically and partially. Incremental forming experiments of AZ31 magnesium alloy sheet was carried out under several laser irradiation conditions and forming speeds using the developed forming system. The experimental results show that the formability of AZ31 sheets increased remarkably with increasing laser power. Defocusing distance of laser beam and forming speed also affected the formability. The results also indicate that residual stress of the formed product was markedly reduced to almost zero by local heating.

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.

International audience; 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.