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In this research, we investigate the effects of various microstructural features on the behavior of spherical steel sheets, using the crystal plasticity finite element method. The cementite phase ratio, the grain sizes of ferrite and cementite, and the percentage of residual pearlite in the steel structure due to incomplete annealing are the major microstructural parameters studied in this work. A grain generator software has been developed to generate hexagonal ferrite grains as well as circular cementite particles distributed in the ferrite matrix. We use a hard coating with special properties as an intermediate layer around the cementite grains to simulate the contact between ferrite grains and cementite particles. This software can also assist with the preprocessing including boundary condition and load producing and introducing constitutive modeling relations. We use representative volume elements (RVEs) to simulate the microstructure of the steel sheet. The hardening parameters in the simulations are calibrated according to the available experimental data in the literature. Several RVEs were prepared and solved to investigate the effect of the thickness of this layer on material behavior. We can replicate the experimental results by setting the ratio of this thickness to the cementite particles’ diameter to be 0.25. Moreover, by reducing the size of ferrite grains and cementite particles, the strength of steel increases. On the other hand, increasing the ratio of the cementite phase increases the strength of steel but the uniform plastic deformation of the material is reduced. We also model and discuss the remaining pearlite content and its effect on the flow behavior of the material. Finally, the effect of the cementite precipitation location and its bimodal size distribution were discussed in this study.

An efficient isogeometric-based framework is presented to integrate optimum design and formability analysis of sheet metal forming processes. To assess the quality of the formed parts, several objective functions such as fracture, wrinkling, thickness variation, and stretching are studied. In this framework, geometric parameters of addendum surfaces and middle tools are considered as design variables, the objective functions are calculated using the recently developed one-step and multi-step inverse isogeometric methods, and the optimum design variables are obtained using the genetic global optimization algorithm. The major advantage of employing the inverse methods is to analyze the formability of the parts with a low computation time. In this research, the effects of altering addendum surfaces and/or middle tools on the quality of the formed parts are simultaneously observed since modeling, formability analysis, and optimization stages of sheet metal forming simulation are integrated using the NURBS functions. To evaluate the performance of the inverse isogeometric models in calculation of the studied objective functions, the results obtained by these models are compared to those of experiment and forward FEM. Comparisons of the results indicate that these models predict the objective functions with acceptable accuracy at a low computation time. For instance, in sheet metal forming analysis of a rectangular box with three different addendum surfaces, the maximum error in prediction of minimum thickness using the one-step inverse model is approximately 4.65% more than forward FEM, while the solution time of forward FEM is around 40 times greater. Finally, the presented optimization procedure is applied to design addendum surfaces in forming of a rectangular box and the middle tools in a two-stage drawing of a square box. The results of these problems confirm the credibility of the present approach in rapid optimum design of addendum surfaces and intermediate tools with acceptable accuracy.

In the present study, damage initiation and growth in a polycrystalline aggregate are investigated. In this regard, an anisotropic continuum damage mechanics coupled with rate-dependent crystal plasticity theory is employed. Using a thermodynamically consistent procedure, a finite deformation formulation is derived. For this purpose, the damage tensor is incorporated in the crystal plasticity formulation for a cubic single crystal. The damage evolution is considered to be dependent on the history of damage, equivalent plastic strain, stress triaxiality, and Lode parameters. This material model is implemented in the commercial finite-element code Abaqus/Standard by developing a user material subroutine (UMAT). Using the available experimental tests of 316L single crystal in the literature, the crystal plasticity hardening and damage parameters are calibrated considering the stress–strain curve before and after necking, respectively. The damage sites in a single-phase polycrystalline aggregate are also considered using a polycrystalline model consisting of grains with random sizes and orientations. The results show that the damage arises at the grain boundaries and triple junctions. Moreover, growth of the damage mostly occurs in the grains with higher Schmid factor compared to the neighboring grains. The presented model manifests capacity for determination of damage initiation sites and damage evolution in polycrystalline models.

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.

The capability to standardize the fracture strength of solder joints is an effective tool to investigate the reliability of electronic devices. To achieve this purpose, in this research, the influences of joint arrangement (loading arm and load sharing) on the level of constraint imposed on joint deformation, fracture energy, and generally, fracture behavior of solder joints were investigated. Fracture behavior of solder joints using double-cantilever-beam (DCB) specimens as a function of loading arm and load sharing (i.e., the distance between two solder joints) was studied under mode I loading conditions at a strain rate of 0.03 s−1. By increasing the loading arm, the fracture force, Fci, decreased linearly, while the critical strain energy release rate for crack initiation, Jci, increased from a loading arm of 12.7 mm to 38.1 mm and then remained almost unchanged for loading arms of 38.1 mm to 71.1 mm. Plastic deformation in the solder layer and criteria such as opening stress (i.e., the predominant stress component in DCB specimen) and stress triaxiality factor were calculated. It was shown that for the larger loading arms (from 38.1 mm to 71.1 mm), the fracture behavior was as a normal DCB specimen (i.e., the normal stress caused by bending was predominant and normal stress caused by tensile loading could be ignored). For the loading arm of less than 38.1 mm, the fracture behavior was similar to that of tensile-type specimens (i.e., the normal stress caused by bending decreased significantly by decreasing the loading arm and normal stress caused by tensile loading became considerable). Variations in the distance between two solder joints did not affect the Jci value, while Fci was influenced by the joint arrangement. This behavior was attributed to stress distribution in the solder layer.

Recently, eliminating the gap between design and formability analysis of sheet metal parts has been studied to simulate sheet metal stamping processes. In this regard, a transfer-based inverse isogeometric formulation has been proposed. This method has various advantages such as solving the governing equations in two-dimensional networks without any concern about the convergence; however, it neglects the bending effect which is a major contributor in die/punch profile radii. The present work aims to consider the bending effects by introducing a bending-dependent inverse isogeometric formulation. The developed model deals with the minimization of potential energy, deformation theory of plasticity, classical plate theory, and considering a yield criterion in stress-resultant space. In addition to all advantages of the transfer-based inverse isogeometric formulation, one major benefit of this study is that the bending effects are included with a slight increase in the computation time. This methodology allows for accurately predicting the effects of changing die/punch profile radii and initial sheet thickness on the formability of the final part by presenting a new material updating process. To assess the credibility of this approach, an experimental setup and forward FEM software have been utilized to form a rectangular box. The results acquired by the developed method and those achieved by experiment and forward FEM reveal acceptable accuracy in the presented model. Also, strains and thicknesses predicted by the developed method, membrane inverse isogeometric model, and forward FEM for nine different values of punch radius to the sheet thickness ratio have been compared. Considering forward FEM as a reference method, the average of calculated error in the presented model for prediction of thickness at the middle of punch radius zone is around half of that in the membrane model. In solving the studied problems, the presented model requires only slightly more computation time (around 2%) than the membrane inverse isogeometric model and much less computation time than forward FEM. Therefore, the presented method is a valuable inverse forming solver especially when the bending effects are significant.

Effects of the grain size on the forming limits of stainless steel 316 L sheets are investigated using crystal plasticity finite element method (CPFEM) by modeling of all grains. For preparing simulation models with different grain morphology, a grain generator code is developed. Using data from metallographic images, texture, and material properties, the developed code can be used for preprocessing of CPFEM. In order to extract mechanical and metallurgical data required for CPFEM, some experiments are carried out on different samples. Moreover, for the purpose of implementing the crystal plasticity formulations, an Abaqus user material subroutine (UMAT) is developed. Concerning the computational costs, a series of simulations are conducted for determining the minimum size of the sheet in a way that the stress-strain curves reflect those curves in the macro scale. In the simulations, forming limit curves are determined by employing the in-plane bi-axial loading. Different orientations in the slip systems between neighboring grains work as the primary cause for deformation localization and occurrence of necking. Therefore, there is no need to impose other imperfections such as groove in M-K model. The predicted FLDs are in agreement with those obtained in the experiments. According to these results, the forming limits decrease with reduction of average grain size.