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• The inverse isogeometric methodology with a new friction model is developed to estimate the initial blank. • The geometric modeling and deformation analysis are integrated and applied simultaneously to analyze the forming process. • The three-dimensional state of problem is converted to two-dimensional state by using the isogeometric transfer technique. • The governing equations are solved without concerning about pre-estimation results. • The presented model estimates the design parameters quickly in the initial stages of design. This paper proposes an inverse isogeometric analysis to estimate the blank and predict the strain distribution in sheet metal forming processes. In this study, the same NURBS basis functions are used for drawing a final part and analysis of the forming process. In other words, this approach requires only one modeling and analysis representation, in contrast to inverse FEM. This model deals with minimization of potential energy, deformation theory of plasticity, and infinitesimal deformation relations with considering a new non-uniform friction model. One advantage of the presented methodology is that the governing equations are solved in two-dimensional space without concerning about pre-estimation results. As a result, the convergence is guaranteed and the computation time decreases significantly which is important at the initial stages of design. Furthermore, by employing this model at the forming design stage, the effects of changing the final part geometry and material property can be simultaneously observed on the formability of the part. Moreover, the effects of isogeometric element size can be automatically studied on the solution accuracy. The capability of this method is demonstrated by presenting three examples including blank estimation of cylindrical cup, square box, and weld line movement in forming of tailor welded blanks. The results obtained by the presented model and those obtained by the forward FEM reveal reasonable accuracy with decreased computational costs. [ABSTRACT FROM AUTHOR]

In this paper, a less studied factor in the asymmetrical rolling process of sheets, namely the rolls horizontal displacement, is investigated using an analytical approach based on the slab method analysis. The presented method is capable of computing the force and torque of the process under different asymmetrical factors such as the rolls horizontal displacement, the interface friction inequality, and the rolls speed mismatch. A formula is presented to predict the outgoing sheet curvature induced by the rolls horizontal displacement. The results can be potentially used in producing curved sheets of various shapes by the asymmetrical rolling process. The analytical model is compared with a verified finite element code and good agreement has been observed. [ABSTRACT FROM AUTHOR]

Abstract: The major problem in determining the forming limit diagram (FLD) with the Marciniak–Kuczynski (M–K) model is the necessity of an experimental point in order to find the initial inhomogeneity coefficient and calibrate the diagram. The purpose of the present work is to eliminate this requirement. To do this, the usual assumption of geometrical inhomogeneity has been replaced with material inhomogeneity and it has been shown that the sensitivity of the diagram to variations of the inhomogeneity factor is reduced greatly with the new assumption. Using this advantage and collecting enough experimental data for different materials, an empirical law in terms of sheet thickness has been proposed which estimates the initial material inhomogeneity. Thus it is possible to determine the FLD in the absence of experimental data. The results show good agreement with experiments and this method has some advantages over other calibration methods. [Copyright &y& Elsevier]

Abstract: Normal stress has some role in the deformation analysis of hydroforming processes. In this study, analytical modeling is pursued to evaluate the effect of normal stress on the hydro-mechanical deep drawing (HDD) process. Analyses are carried out for axisymmetric elements of the formed cup-shaped part for increments of the punch travel. The formulations are obtained using mechanical and geometrical relations and the finite difference method, thereby being solved by proper numerical algorithms. Furthermore, in the present work, part thickness is variable, the loading and straining are non-proportional, and bending/unbending effects over the part curvature are considered. The results show that there are some differences between thickness values, radial and circumferential strains and stresses, and punch force under plane stress and three-dimensional stress conditions. Thus, the normal stress should be considered in the design of HDD processes in order to improve accuracy. [Copyright &y& Elsevier]

Abstract: The goal of this study is to evaluate the effects of proportional loading, plane stress, and constant thickness assumptions on hydro-mechanical deep drawing (HDD) by developing analytical models. The main model includes no simplifying assumption, and then each of the mentioned assumptions is considered in a specific model. The interrelationships between geometrical and mechanical variables are obtained in the finite difference form based on the incremental strain theory, thereby being solved by Broyden algorithm. Published experimental and FE results are used for evaluation of the results obtained in the present work. The results of models under proportional loading, plane stress, and constant thickness conditions show more differences with the experimental data in strain distributions than the results of the main model. Thus, the analyses will be more accurate and the results more reliable without considering such assumptions. [Copyright &y& Elsevier]

Abstract: The purpose of this work is to obtain a theoretical forming limit stress diagram (FLSD) and a suitable load path in tube hydroforming. The methodology for prediction of hydroforming stress limit diagram is based on Marciniak and Kuczynski (M–K) model. The numerical approach is based on the modified Newton–Raphson method. The comparison between the experimental and theoretical results for hydroforming stress limit diagrams as predicted by different methods indicates that the present approach is suitable for prediction of necking in tube hydroforming. Then the forming limit stress diagram determined by the proposed methodology is implemented to obtain the suitable load path in tube hydroforming. As a case study, the finite element (FE) model for bulge forming of straight tube has been constructed and verified with published experimental data. Ultimately, the suitable load path has been obtained by applying Adaptive Simulation Method in ANSYS Parametric Design Language (APDL). [Copyright &y& Elsevier]

Abstract: In this study, a methodology is presented for minimization of the exit profile curvature of the die in the extrusion process. By using the equations from Chitkara works, a set of non-uniform velocity equations were obtained. Some improvements in these velocity equations concerning the friction effects have been done. The objective functions for definition of the curvature were established according to the material flow distribution in the exit section. By variation of the Bezier coefficients and off-centricity values, the optimum die which yields the minimum exit curvature was designed. To verify the suggested objective functions (deviation criterion), three dies were manufactured by means of CAD/CAM package. Then, the direct extrusion process was simulated physically by plasticine. Comparisons of the exit curvatures showed good results concerning the objective functions in minimization of the profile curvature. [Copyright &y& Elsevier]

Abstract: A linear inverse finite element method has been developed and investigated to predict the optimum blank. To reduce the computation time, the part is unfolded properly on the flat sheet and treated as a 2D problem. This approach is employed primarily to design the optimum blank shape from the desired final shape with the linear formulations. The procedure is based on the minimization of energy for the unfolded elements. Two solution methods, Direct and Newton–Raphson methods have been examined for the solution of nodal displacements in the equilibrium equations. The convergence show high sensitivity to the initial guess for the strain path when assumed to be linear at the first step. Two applied examples are implemented to show the efficiency of this method. In S rail example, the thickness distributions have been compared with experimental analysis after obtaining the optimum blank with Linear IFEM. In circular cup example, the results have been compared with conventional forward incremental method. New calculation of the external forces vector has been displayed. In this calculation, both blank holder force (BHF) vector and in-plane force vector have been shown. Finally, in this approach good agreement was found between the forward incremental and Linear IFEM results. [Copyright &y& Elsevier]

• An integrated approach overlays high-resolution DIC strain fields to CP simulations. • One-to-one comparison by careful alignment and filtering of EBSD, SEM, DIC, and CP data. • Good agreement at the scale of grains, while the discrepancy is due to model limitations. • The strain evolution reveals new insights in ferrite-cementite strain partitioning. • Studying the effects of ferrite constitutive model and cementite morphology. This paper attempts to study the microstructural stress-strain evolution and strain localization in the ferrite-pearlite steel by high-resolution experimental-numerical integrated testing. Ferrite crystal orientations measured by electron backscatter diffraction (EBSD) were mapped onto precise scanning electron microscopy (SEM) micrographs of ferrite and cementite lamellar morphologies. Furthermore, in-situ SEM tensile testing was employed to map strains during the deformation using digital image correlation (DIC) at high spatial resolutions. Finally, spectral solver-based crystal plasticity (CP) simulations loaded by the local SEM-DIC boundary conditions were performed and compared to the experimental data. Crucially, all microstructure data was carefully aligned, and strains were filtered to the same spatial resolution, measured to be as small as ~75 nm. This integrated methodology yields new insights in the high degree of plastic strain partitioning between ferrite grains and pearlite colonies, and ferrite and cementite lamellae inside pearlite. One-to-one experimental-numerical comparison augmented with the numerical variation of the ferrite constitutive model, pearlite interlamellar spacing, and lamellar orientation reveals how the ferrite-cementite strain partitioning and the onset of strain localization depend on the morphology and distribution of ferrite grains and pearlite colonies. Importantly, this comparison showcases the limitations of state-of-the-art simulations in their capability to predict specific mechanisms and correct degrees of strain heterogeneity. [Display omitted] [ABSTRACT FROM AUTHOR]

• A multi-step inverse isogeometric analysis is presented to analyze sheet metal stamping processes. • The geometric modeling and deformation analysis are integrated and applied simultaneously at the initial stages of design. • A new NURBS-based mapping is developed to create the middle part. • In the presented model, the linear system of governing equations is solved without concerning about the convergence. • The presented model's performance is evaluated in forming a rectangular box and a two-stage drawing of a circular workpiece. Recently, isogeometric methodology has been successfully implemented in one-step inverse analysis of sheet metal stamping processes. However, these models are not capable of analyzing forming processes which require severe deformation and/or several forming stages. This paper presents a multi-step inverse isogeometric methodology to enhance the precision of one-step models in predictions of the initial blank, strain distributions, and drawability of the formed parts. This methodology deals with the minimization of potential energy, deformation theory of plasticity, and considering membrane elements. The presented methodology utilizes the NURBS basis functions to create the final, middle, and blank geometries, and also to analyze sheet metal deformation. The characteristics of the applied formulations make it possible to simultaneously observe the effects of changing part parameters on its formability. One advantage of this approach is that the linear system of governing equations is solved without concerning about the convergence. In addition, the presented methodology is able to successfully generate the middle geometry and to restrict the movements of physical nodes along the middle surface, by presenting a new NURBS-based mapping and sliding constraint technique. The performance of the presented model is evaluated under two classical problems including forming of a rectangular box and a two-step drawing of a circular cup. In forming of the rectangular box, the results of the presented model are compared with those of experiment and forward FEM simulation. Also, in the second problem, the presented approach is only compared with forward FEM simulation. Results comparisons indicate the credibility of the presented model in prediction of forming parameters at a low computation time. [ABSTRACT FROM AUTHOR]

• Single-parameter fracture mechanics was not valid for evaluating solder joint fracture behavior in DCB specimens. • The ability of two-parameter (J-Q) fracture mechanics was assessed. • The two curves overlap extracted from two sets of experimental data indicated the J-Q locus uniqueness and capability to predict fracture load. Two-parameter fracture mechanics theory is a novel approach to investigate the fracture behavior of solder joints. The present study showed that the single-parameter fracture mechanics was not valid for evaluating the fracture behavior of these joints. Therefore, the ability of the two-parameter (J - Q) fracture mechanics method was assessed. J (critical strain energy release rate) and Q (The constraint parameter) parameters were calculated for the double cantilever beam (DCB) specimens. The two-parameter fracture mechanics theory was observed to be valid for the DCB specimens examined in this research. The J - Q loci extracted from two distinct experimental data sets (adherend thickness and loading arm variation) were coincident. The overlap of two J - Q locus curves indicates the uniqueness of the J - Q locus and capability to predict fracture load. [ABSTRACT FROM AUTHOR]

A continuum implementation of stress gradient plasticity is established to analyze passivated thin films under tension. It is verified and evaluated by investigation of the tensile response of passivated Cu films with different thicknesses and grain sizes. The material parameters are fitted to the stress–strain experimental data, while the length scale parameter is directly characterized from the corresponding available discrete dislocation predictions. The numerical solutions give rise to boundary layers near the interface between film and passivation. This prediction is consistent with the formation of dislocation pileups at the film-passivation interface and also is responsible for the thickness-dependent hardening observed in passivated thin films. The numerical results are in good agreement with the experimental data and discrete dislocation predictions. [ABSTRACT FROM AUTHOR]

Abstract: In tube hydroforming, the inverse finite element method (IFEM) has been used for estimating the initial length of tube, axial feeding and fluid pressure. The already developed IFEM algorithm used in this work is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, in this paper a modeling technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no trial and error process. In addition, the solution provides all the components of strain. Using the forming limit diagram (FLD), the components of strain can lead us to measure the potentials for failures or wrinkles during the deformation. The results of analysis for free bulging and square bulging have been compared with some published experimental data and the results obtained by conventional commercial software. [Copyright &y& Elsevier]

Abstract: In this study, the sheet metal forming limits are presented both in strain and stress spaces. The computations are based on strain gradient theory of plasticity in conjunction with Marciniak and Kuczynski model. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. The nonlinear differential equation of the thickness variation is the second order ordinary type. The shooting method has been used with different solvers such as Backward Differentiation Formula (BDFs or Gear method), explicit Runge–Kutta (the Dormand–Prince pair), explicit Runge–Kutta (the Bogacki–Shampine pair), Adams–Bashforth–Moulton and Rosenbrock formula and Trapezoidal rule. The numerical results of these techniques are almost the same. However, major differences can be observed in the speed of calculations. It was found that the explicit Runge–Kutta (the Dormand–Prince pair) initial value problem solver has the best speed of calculation. The forming limit results obtained in this work have been compared with some published experimental data. [Copyright &y& Elsevier]

[Display omitted] • Prediction of strain localization and forming limit diagrams of ferrite-pearlite steels. • Developing a microstructure-based micromechanical approach using crystal plasticity model. • Observing intense stress/strain partitioning in the form of localized deformation bands. • Studying effects of pearlite volume fraction on formability and strain localization. • High dependency of local deformation pattern on microstructural morphology and loading direction. The main objective of this study is to predict the deformation behavior, strain localization, and forming limits of ferrite-pearlite steels by incorporating the contributions of the microstructural characteristics and mechanical properties of the underlying microstructure. A realistic microstructure-based micromechanical approach in the framework of the crystal plasticity (CP) model was carried out using the periodic representative volume element (RVE) generated from the scanning electron microscopy (SEM) image. The homogenized stress–strain curve of the realistic RVE was validated with the experimental data with an error of less than 6.71% at large strains. Afterward, the initial microstructural inhomogeneity criterion was applied to the realistic RVE under various loading paths to predict the forming limit diagram (FLD), which compared with the experimental results of the Nakazima-stretch forming test. Consequently, the contributions of the pearlite volume fraction and the microstructural morphology were studied by extending this approach to the synthetic microstructures with various pearlite volume fractions. In conclusion, the microstructure-level inhomogeneity at the microscopic level results in intense stress/strain partitioning and strain localization, emerging in the form of micro-localized deformation bands. Moreover, it has been found that the local deformation pattern at the micron-scale significantly depends on the microstructural morphology and loading direction. [ABSTRACT FROM AUTHOR]

Novel 1,4-benzoxazine derivatives were synthesized by an efficient and simple method in high yields. Readily available starting materials, operational simplicity, mild reaction conditions and novelty are the key advantages of this method. The synthetically attractive feature of the procedure is reflected by its applicability to a wide range of isatin and aniline derivatives. Besides their novel structures, these compounds may have important biological activities and industrial applications. Furthermore, we demonstrated that in Baeyer-Villiger oxidation reaction, the phenyl group migrate better than amidine groups but not as good as amide group. The migratory ability for these groups in Baeyer-Villiger oxidation reaction is ranked amide > phenyl > amidine. [ABSTRACT FROM AUTHOR]