A new methodology is proposed to obtain the forming limit diagram (or FLD) of sheet materials by utilizing routinely obtained experimental load versus displacement traces and incorporating finite element (FE) analysis of strain history to extract the characteristic points of diffuse and localized necking and further the limit strains. The experimental data from hemispherical punch stretching test such as limit dome height, maximum load and location of inflection point are utilized to adjust the load curves in the FE simulations. An optimization procedure to obtain various parameters in material definition has been established to obtain a good agreement between the FE-based and experimental punch load versus displacement curves. An analysis of FE model based strain history is then carried out to determine the limit strains. This approach avoids using experimental strain measurement in the vicinity of the neck on the dome specimens. The materials tested with the new methodology include automotive sheets AA6111-T4, AA6181-T4 and DP600. The one utilized for optimization of FE inputs was AA6111-T4. The proposed method for FLD determination considers out-of-plane displacement, punch-sheet contact and friction, and avoids the use of a rather arbitrary inhomogeneity factor to trigger localization such as in the Marciniak-Kuczynski method. A new criterion to determine the localized necking is proposed by seeking an inflection point m the major strain rate curve, or, maximum point in the second order of derivative of major strain, (ε1)max. The proposed localized necking criterion is compared with other two methods to determine the onset of localized necking. These are (i) Bragard criterion for post-test of deformation, and (ii) critical major strain (ε1)cr based on comparison of strain of material inside the localized site and its vicinity in the un-necked site. The new criterion of (ε1)max exhibits a more definite physical meaning towards developing an understanding of flow localization, formability and fracture. This new approach for obtaining FLDs is rapid and accurate and could be implemented easily for routine FLO generation in a lab setting with little user input and subjectivity. / Thesis / Doctor of Philosophy (PhD)

Tube hydroforming process is a relatively new technology compared to conventional manufacturing via stamping and welding. However there is not much knowledge available for the product or process designers. The objective of this study will determine the flow stress and forming limit diagram of tubular materials to discuss the formability of tubes. Firstly, a mathematical model is proposed to examine the plastic deformation behavior of a thin-walled tube at different process parameters during the bulge hydroforming process without axial feeding. In the formulation of this mathematical model, an ellipsoidal surface and non-uniform thinning in the free bulged region and sticking friction between the tube and die are assumed. In the sticking friction mode, the elements after contact with the die do not move or slide. The effects of various forming parameters, such as the die entry radius, the bulge length, anisotropy, the initial thickness of the tube, etc., upon the forming pressures are discussed systematically. Secondly, an analytical model combined with hydraulic bulge tests is proposed to evaluate the properties of tubular materials considering anisotropy effect. Annealed AA6011 aluminum tubes and SUS409 stainless steel tubes are used for the bulge test. The tube thickness and radius at the pole and the internal forming pressure are measured simultaneously during the bulge test. The anisotropic values are obtained from tensile tests. From above experimental data, the effective stress - effective strain relations can be derived by this analytical model. The finite element method is used to conduct the simulations of hydraulic bulge forming with the flow stresses obtained by the above-mentioned model. The analytical forming pressures versus bulge heights are compared with the experimental results to validate the approach proposed in this study. Finally, this study also establishes the Forming Limit Diagram (FLD) of aluminum tubular material. An experimental system of tube hydroforming in which axial feed is applied to carry out the hydraulic bulge-forming test of the annealed aluminum alloy tubes. Furthermore, Hill¡¦s new yield criterion is also used to predict the Forming Limit Curves of sheets. The predicted forming limit diagrams are compared with the experimental data. The results of this study can provide useful knowledge for process design. In addition, the process parameters of flow stress and forming limit diagram obtained can improve the accuracy of the simulation results in industrial and academic fields.

ABSTRACT The objective of this study is to establish the Forming Limit Diagram (FLD) of tubes. An experimental system of tube hydroforming, the electrical chemical etching method and the image process system are used to carry out the sheet metal forming test and the hydraulic bulge-forming test of annealed aluminum alloy tubes. Furthermore, Hill¡¦s new yield criterion is also used to predict the Forming Limit Curves of sheets. The predicted forming limit diagrams are compared with experimental data. The forming limit diagrams of tubes are coincident with those of sheets. Also, the predicted forming limit curves by Hill¡¦s new yield criterion agree quite well with those by experiments. Therefore, Hill¡¦s new yield criterion can be used to establish the forming limit curves of sheets or tubes.

Com a grande demanda do mercado brasileiro, e mundial, por desenvolvimento de novas tecnologias, redução de custos e de complexidade, os processos industriais buscam cada vez mais alternativas inovadoras. Para que essa evolução seja possível, é fundamental que todos os componentes da cadeia industrial também se desenvolvam, tornando assim as matérias primas, como aços, polímeros, alumínio, e outros metais que estão na base da cadeia, um grande foco de estudos. A indústria siderúrgica, em específico, vem buscando este desenvolvimento nos últimos anos, trabalhando principalmente no desempenho que os materiais terão nos processos industriais, tais como estampagem, soldagem e muitos outros. O processo de estampagem requer o desenvolvimento destes materiais, já que este solicita matérias primas com um bom desempenho mecânico, capaz de absorver possíveis variações e dificuldades que existem em uma linha de produção industrial. Para que este objetivo seja atingido, deve-se dedicar tempo e recursos para encontrar a combinação ideal entre pesquisa e processo produtivo e, assim, otimizar as características mecânicas e químicas dos materiais para o desenvolvimento da cadeia industrial. No contexto da estampagem há um bom indicativo para prever qual será o desempenho de um material: a Curva Limite de Conformação (CLC). Neste presente trabalho os conceitos da CLC serão discutidos, e aplicados a dois aços inoxidáveis distintos, um da família ferrítica (DIN 1.4509) e outro da família austenítica (AISI 321). Além disso, também serão abordadas as principais características metalúrgicas e mecânicas, correlacionadas à estampagem, destes materiais e as principais formas de utilizar estas informações na prática industrial com o objetivo de aperfeiçoar o desempenho do material nos processos e principalmente, quando possível, promover a migração de uma liga austenítica, por uma liga ferrítica, com o objetivo de redução e estabilidade nos custos. / With the increase of the market demand, both in Brazilian, and in the world, for the development of new technologies, cost and complexity reduction, the industrial processes have been investigating for innovative solutions. In order to this evolution to take place all industrial chain players would have to develop. Therefore all raw materials, such as steels, polymers, aluminum and other metals are in evidence to become the focus of investigation. The steel industry, in particular, has been searching for this evolution over the last years, working in their processes with the goal to increase the performance of the grades on the industrial processes, such as deep drawing, welding, and many others. The deep drawing process is a great motivator to the development of the steels, since it requires a high mechanical performance from the material, to absorb possible variations and difficulties which may occur in an industrial production line. In order to achieve this goal, time and resources must be spent to find the perfect combination between research centers and production processes, optimizing the chemical and mechanical characteristics of the steels, so the development of the whole chain can also advance. Within the deep drawing field of study, a good indicative to predict the material\'s performance is the Forming Limit Diagram (FLD) and in this work the concepts of these FLD\'s will be discussed and applied to two stainless steel grades: a ferritic stainless steel (DIN 1.4509) and an austenitc stainless steel (AISI 321). In addition, the main metallurgical and mechanical properties of these materials, related to the deep drawing, will be approached along with the best ways to apply this kind of information to the industrial practices, in order to increase the material performance and, whenever possible change the austenitic stainless steel to the ferritic stainless steel, in order to reduce and keep the costs stable.

Magnesium, with a Hexagonal Close-Packed (HCP) structure, is the eighth most abundant element in the earth’s crust and the third most plentiful element dissolved in the seawater. Magnesium alloys exhibit the attractive characteristics of low densities and high strength-to-weight ratios along with good castability, recyclability, and machinability. Replacing the steel and/or aluminum sheet parts with magnesium sheet parts in vehicles is a great way of reducing the vehicles weight, which results in great savings on fuel consumption. The lack of magnesium sheet components in vehicle assemblies is due to magnesium’s poor room-temperature formability. In order to successfully form the sheets of magnesium at room temperature, it is necessary to understand the formability of magnesium at room temperature controlled by various plastic deformation mechanisms. The plastic deformation mechanisms in pure magnesium and some of its alloys at room temperature are crystallographic slip and deformation twinning. The slip systems in magnesium at room temperature are classified into primary (first generation), secondary (second generation), and tertiary (third generation) slip systems. The twinning systems in magnesium at room temperature are classified into primary (first generation) and secondary (second generation, or double) twinning systems. A new comprehensive rate-dependent elastic-viscoplastic Crystal Plasticity Constitutive Model (CPCM) that accounts for all these plastic deformation mechanisms in magnesium was proposed. The proposed model individually simulates slip-induced shear in the parent as well as in the primary and secondary twinned regions, and twinning-induced shear in the primary and secondary twinned regions. The model also tracks the texture evolution in the parent, primary and secondary twinned regions. Separate resistance evolution functions for the primary, secondary, and tertiary slip systems, as well as primary and secondary twinning systems were considered in the formulation. In the resistance evolution functions, the interactions between various slip and twinning systems were accounted for. The CPCM was calibrated using the experimental data reported in the literature for pure magnesium single crystals at room temperature, but needs further experimental data for full calibration. The partially calibrated model was used to assess the contributions of various plastic deformation mechanisms in the material stress-strain response. The results showed that neglecting secondary slip and secondary twinning while simulating plastic deformation of magnesium alloys by crystal plasticity approach can lead to erroneous results. This indicates that all the plastic deformation mechanisms have to be accounted for when modelling the plastic deformation in magnesium alloys. Also, the CPCM in conjunction with the Marciniak–Kuczynski (M–K) framework were used to assess the formability of a magnesium single crystal sheet at room temperature by predicting the Forming Limit Diagrams (FLDs). Sheet necking was initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field was assumed inside and outside the band, and conditions of compatibility and equilibrium were enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs were simulated under two conditions: a) the plastic deformation mechanisms are primary slip systems alone, and b) the plastic deformation mechanisms are primary slip and primary twinning systems. The FLDs were computed for two grain orientations. In the first orientation, primary extension twinning systems had favourable orientation for activation. In the second orientation, primary contraction twinning systems had favourable orientation for activation. The effects of shear strain outside the necking band, rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations were individually explored.

Magnesium, with a Hexagonal Close-Packed (HCP) structure, is the eighth most abundant element in the earth’s crust and the third most plentiful element dissolved in the seawater. Magnesium alloys exhibit the attractive characteristics of low densities and high strength-to-weight ratios along with good castability, recyclability, and machinability. Replacing the steel and/or aluminum sheet parts with magnesium sheet parts in vehicles is a great way of reducing the vehicles weight, which results in great savings on fuel consumption. The lack of magnesium sheet components in vehicle assemblies is due to magnesium’s poor room-temperature formability. In order to successfully form the sheets of magnesium at room temperature, it is necessary to understand the formability of magnesium at room temperature controlled by various plastic deformation mechanisms. The plastic deformation mechanisms in pure magnesium and some of its alloys at room temperature are crystallographic slip and deformation twinning. The slip systems in magnesium at room temperature are classified into primary (first generation), secondary (second generation), and tertiary (third generation) slip systems. The twinning systems in magnesium at room temperature are classified into primary (first generation) and secondary (second generation, or double) twinning systems. A new comprehensive rate-dependent elastic-viscoplastic Crystal Plasticity Constitutive Model (CPCM) that accounts for all these plastic deformation mechanisms in magnesium was proposed. The proposed model individually simulates slip-induced shear in the parent as well as in the primary and secondary twinned regions, and twinning-induced shear in the primary and secondary twinned regions. The model also tracks the texture evolution in the parent, primary and secondary twinned regions. Separate resistance evolution functions for the primary, secondary, and tertiary slip systems, as well as primary and secondary twinning systems were considered in the formulation. In the resistance evolution functions, the interactions between various slip and twinning systems were accounted for. The CPCM was calibrated using the experimental data reported in the literature for pure magnesium single crystals at room temperature, but needs further experimental data for full calibration. The partially calibrated model was used to assess the contributions of various plastic deformation mechanisms in the material stress-strain response. The results showed that neglecting secondary slip and secondary twinning while simulating plastic deformation of magnesium alloys by crystal plasticity approach can lead to erroneous results. This indicates that all the plastic deformation mechanisms have to be accounted for when modelling the plastic deformation in magnesium alloys. Also, the CPCM in conjunction with the Marciniak–Kuczynski (M–K) framework were used to assess the formability of a magnesium single crystal sheet at room temperature by predicting the Forming Limit Diagrams (FLDs). Sheet necking was initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field was assumed inside and outside the band, and conditions of compatibility and equilibrium were enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs were simulated under two conditions: a) the plastic deformation mechanisms are primary slip systems alone, and b) the plastic deformation mechanisms are primary slip and primary twinning systems. The FLDs were computed for two grain orientations. In the first orientation, primary extension twinning systems had favourable orientation for activation. In the second orientation, primary contraction twinning systems had favourable orientation for activation. The effects of shear strain outside the necking band, rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations were individually explored.

The increasing demand for powerful miniaturized products for all industrial applications has prompted the industry to develop new and innovative manufacturing processes to fabricate miniature parts. One of the major challenges facing the industry is the dynamic market which requires continuous improvements in design and fabrication techniques. This means providing products with complex features while sustaining high functionality. As a result, microfabrication has gained a wide interest as the technology of the future, where tabletop machine systems exist. Microforming processes have the capability of achieving mass production while minimizing material waste. Microforming techniques can produce net-shape products with intricacy in fewer steps than most conventional microfabrication processes. Despite the potential advantages, the industrial utilization of microforming technology is limited. The deformation and failure modes of materials during microforming is not yet well understood and varies significantly from the behavior of materials in conventional forming operations. In order to advance the microforming technology and enable the effective fabrication of microparts, more studies on the deformation and failure of materials during microforming are needed. In this research work, an effort to advance the current status of microforming processes for technologies of modern day essentials, is presented. The main contribution from this research is the development of a novel method for characterizing thin sheet formability by introducing a micro-mechanical bulge-forming setup. Various aspects of analyzing microscale formability, in the form of limiting strains and applied forces, along with addressing the well known size effects on miniaturization, were considered through the newly developed method. A high temperature testing method of microformed thin sheets was also developed. The aim of high temperature microforming is to study the material behavior of microformed thin sheets at elevated temperatures and to explore the capability of the known enhancement in formability at the macroscale level. The focus of this work was to develop a better understanding of tool-sheet metal interactions in microforming applications. This new knowledge would provide a predictive capability that will eliminate the current time-consuming and empirical techniques that, and this in turn would be expected to significantly lower the overall manufacturing cost and improve product quality.

The desire to reduce weight in automotive products is driven by a need to improve efficiency. As such, to allow further weight reduction, higher performance aluminium alloys are in demand for sheet metal body structures. Due to their high strength to weight ratio 7xxx alloys are seen as an ideal candidate for this, however their use to date has been limited by poor formability. Previous work indicated that by moving to high temperatures (>350°C) or by using a soft temper (W), good formability could be achieved but the samples required further heat treatment post-forming. This work explored the warm forming temperature range to improve formability whilst developing the required properties during processing. The performance of a 7xxx candidate alloy, 7021, has been assessed in stretching and drawing operations, both at room temperature and over the elevated temperature range of 150-250°C. The microstructure and other properties of the alloy were investigated in W, T4 and T6 tempers, before and after testing, through a range of techniques, including DSC, DMTA, SEM, EBSD and TEM.In the T4 temper, UTS and proof stress increased with temperature up to 190°C, due to dynamic precipitation. Increasing temperature only provided a modest increase in strain to failure for both the T4 and T6 temper. Cup height was not significantly improved in the warm forming temperature range during Erichsen cup testing. By deep drawing at 250°C it was possible to fully draw a cup (with an LDR of 2.2) in both the T4 and T6 temper of 7021, with both tempers having comparable post-forming hardness. This indicates that at 250°C the starting condition has no impact on drawability. Although full drawability is achieved at 250°C the final product would require further heat treatment if it were to replace 6016. However, by deep drawing 7021-T4 at 190°C, a fully formed cup was produced with a hardness between that of the T4 and T6 temper. The microstructure of the formed cup showed no grain boundary precipitation and a fine distribution of the strengthening phase η', suggesting there is a dynamic effect on the precipitation during deep drawing at this temperature. In conclusion, the work has shown that warm forming does not significantly improve stretching behaviour of 7021, but by using warm forming temperatures deep drawing is improved.

Com a grande demanda do mercado brasileiro, e mundial, por desenvolvimento de novas tecnologias, redução de custos e de complexidade, os processos industriais buscam cada vez mais alternativas inovadoras. Para que essa evolução seja possível, é fundamental que todos os componentes da cadeia industrial também se desenvolvam, tornando assim as matérias primas, como aços, polímeros, alumínio, e outros metais que estão na base da cadeia, um grande foco de estudos. A indústria siderúrgica, em específico, vem buscando este desenvolvimento nos últimos anos, trabalhando principalmente no desempenho que os materiais terão nos processos industriais, tais como estampagem, soldagem e muitos outros. O processo de estampagem requer o desenvolvimento destes materiais, já que este solicita matérias primas com um bom desempenho mecânico, capaz de absorver possíveis variações e dificuldades que existem em uma linha de produção industrial. Para que este objetivo seja atingido, deve-se dedicar tempo e recursos para encontrar a combinação ideal entre pesquisa e processo produtivo e, assim, otimizar as características mecânicas e químicas dos materiais para o desenvolvimento da cadeia industrial. No contexto da estampagem há um bom indicativo para prever qual será o desempenho de um material: a Curva Limite de Conformação (CLC). Neste presente trabalho os conceitos da CLC serão discutidos, e aplicados a dois aços inoxidáveis distintos, um da família ferrítica (DIN 1.4509) e outro da família austenítica (AISI 321). Além disso, também serão abordadas as principais características metalúrgicas e mecânicas, correlacionadas à estampagem, destes materiais e as principais formas de utilizar estas informações na prática industrial com o objetivo de aperfeiçoar o desempenho do material nos processos e principalmente, quando possível, promover a migração de uma liga austenítica, por uma liga ferrítica, com o objetivo de redução e estabilidade nos custos. / With the increase of the market demand, both in Brazilian, and in the world, for the development of new technologies, cost and complexity reduction, the industrial processes have been investigating for innovative solutions. In order to this evolution to take place all industrial chain players would have to develop. Therefore all raw materials, such as steels, polymers, aluminum and other metals are in evidence to become the focus of investigation. The steel industry, in particular, has been searching for this evolution over the last years, working in their processes with the goal to increase the performance of the grades on the industrial processes, such as deep drawing, welding, and many others. The deep drawing process is a great motivator to the development of the steels, since it requires a high mechanical performance from the material, to absorb possible variations and difficulties which may occur in an industrial production line. In order to achieve this goal, time and resources must be spent to find the perfect combination between research centers and production processes, optimizing the chemical and mechanical characteristics of the steels, so the development of the whole chain can also advance. Within the deep drawing field of study, a good indicative to predict the material\'s performance is the Forming Limit Diagram (FLD) and in this work the concepts of these FLD\'s will be discussed and applied to two stainless steel grades: a ferritic stainless steel (DIN 1.4509) and an austenitc stainless steel (AISI 321). In addition, the main metallurgical and mechanical properties of these materials, related to the deep drawing, will be approached along with the best ways to apply this kind of information to the industrial practices, in order to increase the material performance and, whenever possible change the austenitic stainless steel to the ferritic stainless steel, in order to reduce and keep the costs stable.

This thesis presents the development and implementation of a generalized optimization framework for use in sheet-stamping process simulation by finite element analysis. The generic framework consists of three main elements: a process simulation program, an optimization code, and a response filtering program. These elements can be filled by any combination of applicable software packages. Example sheet-stamping process simulations are presented to demonstrate the usage of the framework in various forming scenarios. Each of the example simulations is presented with a sensitivity analysis. These examples include analysis of a 2-dimensional single-stage forming, a 2-dimensional multi-stage forming, and two different 3-dimensional single-stage forming processes. A forming limit diagram is used to define failure in the 3-dimensional process simulations. Optimization results are presented using damage minimization, thinning minimization, and springback minimization with aluminum alloy 6061-T6 blanks.