Finite element analysis on the coined-bead mechanism during the V-bending process

The coined-bead technique is commonly applied to solve the spring-back problem in the V-bending process. However, the coined-bead mechanism on the spring-back/spring-go feature has not been clearly identified yet. In this study, the finite element method (FEM) and laboratory experiments were used to investigate the coined-bead mechanism and its effects on the spring-back/spring-go feature. The features were clearly identified using a stress distribution analysis. The results revealed that the mechanism of the coined-bead technique not only increases the compressive stress on the bending allowance zone, where the spring-back feature decreases, but also increases the reversed bending zone on the leg of the workpiece, where the spring-go feature increases. Therefore, after compensating for the increases in the compressive stress and the reversed bending feature, the amount of spring-back on the bent part was decreased. The FEM simulation bending force and bending angle results were agreed with those from the experimental results.     

Implementation of a constitutive model in finite element method for intense deformation

Since the constitutive information is one of the most important aspects of material deformation analysis, here a new constitutive model is proposed that can investigate the behavior of material during intense deformation better than existent models. The model that is completely based on physical mechanisms can predict all stages of flow stress evolution and also can elucidate the effects of strain and strain rate on flow stress evolution of material during intense plastic deformation. Here as an application, implementation of the constitutive model in finite element method (FEM) is used to compare two methods of sever plastic deformation (SPD) processes of copper sheet; repetitive corrugation and straightening (RCS) and constrained groove pressing (CGP). The modeling results are in good agreement with the experimental data and show that the hardness uniformity and its magnitude for RCSed sheet are higher than that for CGPed sheet. However, the prominence of these processes in strain uniformity depends on pass number.     

Comparison of workability strain and stress parameters of powder metallurgy steels AISI 9840 and AISI 9845 during cold upsetting

A complete experimental investigation on the workability behaviour of nickel–chromium–molybdenum steel grades namely AISI 9840 and AISI 9845 of powder metallurgy preforms was performed. Cold upsetting of aforesaid composites with different aspect ratios namely 0.42, 0.63 and 0.93 was carried out with graphite lubricant and the formability behaviour of the preforms under triaxial stress-state condition was determined. A new formability strain parameter was proposed, evaluated and compared with formability stress parameter for all the above said preforms. The characteristics of various stress and strain ratio parameters with respect to relative density were also analyzed and presented for comparison.     

Failure analysis of natural gas buried X65 steel pipeline under deflection load using finite element method

A 3D parametric finite element model of the pipeline and soil is established using finite element method to perform the failure analysis of natural gas buried X65 steel pipeline under deflection load. The pipeline is assumed to be loaded in a parabolic deflection displacement along the axial direction. Based on the true stress–strain constitutive relationship of X65 steel, the elastic–plastic finite element analysis employs the arc-length algorithm and non-linear stabilization algorithm respectively to simulate the strain softening properties of pipeline after plastic collapse. Besides, effects of the soil types and model sizes on the maximum deflection displacement of pipeline are investigated. The proposed finite element method serves as a base available for the safety design and evaluation as well as engineering acceptance criterion for the failure of pipeline due to deflection.     

Pseudo-elastic description of polymeric foams at finite deformation with stress softening and residual strain effects

Polymeric foams are typical materials for energy absorber in such areas as aircraft, car industry and in the field of electronic packaging. Besides the typical hyperelastic behaviour, non-linear stress–strain behaviour in large elastic deformation, polymeric foams may also exhibit some inelastic effects, like stress softening and residual strain. In this paper we first describe some experiment results that illustrate the stress softening in compressible expanded polypropylene (EPP) foams together with associated residual strain effects. Then, based on Ogden and Dorfmann’s results, a pseudo-elastic model is introduced to capture the stress softening and residual strain effects by including of two variables in the energy function. Numerical simulations of uniaxial-compression tests of two types of EPP foam are used to determine the material parameters of Ogden’s model, stress softening and residual strain effects. The numerical simulations indicate that the pseudo-elastic model provides reasonably accurate predictions of the inelastic behaviour of polymeric foam.     

Effect of carbon content on workability of powder metallurgy steels

Workability behaviour of steel powder metallurgy performs containing 0%, 0.4% and 0.8% of carbon were completely investigated experimentally. Cold upsetting of abovementioned powder metallurgy sintered steels preforms with two different aspect ratios namely 0.39 and 0.59 was carried out with graphite as lubricant and the formability behaviour of the preforms under triaxial stress state condition was determined. The formability stress parameter was evaluated for all the above said preforms and its variation with respect to axial strain was plotted, studied and discussed relative to their as sintered microstructures. Also the characteristics of various stress ratio parameters with respect to axial strain were analyzed and presented.     

Post processing of the hot torsion test results using a multi-dimensional modelling approach

A model selection scheme was extended to a multi-dimensional representation of the hot torsion test torque, twist and twist rate data to calculate partial derivatives of the torque data with respect to twist and twist rate. These enabled calculation of the instantaneous strain and strain rate hardening indices in the Fields and Backofen method. The concept of an iso-parametric shape function has been borrowed from the finite element method for adding twist rate as a dependant variable to the torque–twist models identified by the model selection scheme. Expressions to calculate the hardening indices, when employing a rational model of torsion data, were derived and presented. Subsequently, the models were used for post processing the data and determining hot strength behaviour, taking into account variations of strain and strain rate hardening indices during the deformation. To substantiate the technique, the hot flow behaviour of API-X70 micro-alloyed steel was determined using a range of hot torsion test data for the material. The flow stress obtained using the instantaneous hardening indices were compared with that obtained by the orthodox technique. For the investigated cases, the onset of dynamic recrystallization (DRX) predicted by the presented technique deviated considerably from those obtained when the average indices were used.     

Investigation of anisotropy problems in sheet metal forming using finite element method

This paper discusses the results of the numerical study of rectangular cup drawing of steel sheets using finite element methods. To be able to verify the results of the numerical solutions, an experimental study was done where the material behavior under deformation was analyzed. A 3D parametric finite element (FE) model was built using the commercial FE-package ABAQUS/Standard. ABAQUS allows analyzing physical models of real processes putting special emphasis on geometrical non-linearities caused by large deformations, material non-linearities and complex friction conditions. Friction properties of the deep drawing quality steel sheet were determined by using the pin-on-disc tribometer. The results show that the friction coefficient depends on the measured angle from the rolling direction and corresponds to the surface topography. A quadratic Hill anisotropic yield criterion was compared with von Mises yield criterion having isotropic hardening. The sensitivity of constitutive laws to the initial data characterizing material behavior is also presented. It is found out that plastic anisotropy of the matrix in ductile sheet metal has influence on deformation behavior of the material. When the material and friction anisotropy are taken into account in the finite element analysis, this approach gives better approximate numerical results for real processes.     

Investigation of finite element mesh independence in rate dependent materials

Crystal plasticity theory is commonly used in finite element analyses to predict large strain ductility in single crystal and polycrystal deformation. In the rate-dependent formulation of the theory it is possible, for cases of simple deformation, to achieve an analytical solution that is independent of any effects due to the finite element mesh spacing. In this study single crystal and polycrystal models were subjected to alternative loading conditions. The effect of the mesh density on the generation of strain localisations and shear bands was investigated with regard to consistency of results. It was found that, prior to the initiation of a narrow shear band, it was possible to achieve a numerical result independent of mesh spacing. In the larger polycrystal analyses, an element size was identified that enabled the generation of a mesh independent solution. This allowed the accurate prediction of the mechanical behaviour of the model up to, and including, the failure point. The implications of this for small-scale metallic device design are discussed.     

Evaluation the effect of aspect ratio for Young’s modulus of nanobelt using finite element method

The traditional nanoindentation method provides experimental data for the calibrating mechanical parameters of nanobelt through semi-empirical formulae. In this paper, a technique to identify Young’s modulus of nanobelts with different aspect ratios is introduced combining finite element method (FEM) and nanoindentation test. For the nanobelt on the substrate, the power function relationship is used to describe the loading curve of the nanobelt indentation behavior. The loading curve exponent of the power function which is the fitting parameter can reflect the influence of aspect ratio of nanobelt on Young’s modulus of nanobelts as well as the maximum indentation load. In the forward analysis, considering the substrate effect and the size effect, the numerical loading responses are simulated at the appropriate penetration depth, and then the dimensionless equations between the parameters characterizing the indentation loading curve and the properties of nanobelt/substrate system can be established via extensive FEM simulation. In the reverse analysis, the nanoindentation tests were performed on ZnO and ZnS nanobelts, and the experimental indentation loading curves can be fitted as power function. The maximum indentation loads and the loading curve exponents are extracted from two experimental loading curves, and then they are substituted into the dimensionless equations to solve the Young’s moduli of ZnO and ZnS nanobelts. The results show the Young’s moduli solved are close to previous values, indicating that the Young’s moduli are reasonable. This developed method is effective to identify the Young’s modulus of nanobelt and it can be applied to identify the Young’s modulus of other nanobelts in practice.     

Elastic behavior of glass-like functionally graded infinite hollow cylinder under hydrostatic loads using finite element method

A glass-like (viscoelastic) functionally graded cylinder is studied by using finite element method to investigate the mechanical responses. A subroutine is developed by using ANSYS parametric design language (APDL) to simulate two nonlinearities, which are the variation of material properties with respect to time and position. The cylinder is made of two different viscoelastic materials, namely, pure material one at inner and pure material two at outer surfaces. The material properties are assumed to be presented by simple power law distribution and moreover, bulk and shear moduli are varying with respect to time using the kernel functions depicted regarding Prony series. It is shown that the hoop stresses take the same values at the mean radius (middle of the thickness) for different values of time and grading index. It is found that the radial stress decreases to certain values for specific grading index and then by increasing the grading index it increases to maximum value that related to pure material cylinder. It is shown that unlike the zero axial stress in pure material cylinders, it varies along the thickness from minimum to maximum at inner and outer surfaces, respectively. It is concluded that the viscoelastic functionally graded (VFG) materials play an important role in steady and transient response of hollow cylinder under hydrostatic load.     

A heuristic model selection scheme for representing hot flow data using the hot torsion test results

The problem of “model selection” for expressing a wide range of constitutive behaviour adequately using hot torsion test data was considered here using a heuristic approach.     

A linear finite element model to predict processing-induced distortion in FRP laminates

Manufacturing processes for laminated composites often produce parts whose dimensions do not match the mold from which they were made. This distortion is commonly referred to as ‘spring-in’. The amount of spring-in can depend on many factors including the manufacturing process (cure temperature, resin bleed, and applied pressure), the part (geometry, material, thickness, cure shrinkage, thermal expansion and layup sequence), and the tool (surface, thickness and thermal expansion). Much of the current work devoted to spring-in relies on extensive resin characterization. While this approach has been reasonably successful, it does little to assist the designer using material systems that have not been fully characterized (which is not always possible or feasible). This study considers the ability of a linear elastic finite element model to describe and quantify many of the factors contributing to spring-in. The aim of this study is to show that spring-in can be accurately predicted without a complete resin characterization. Numerical predictions based on relatively simple mechanical tests were observed to compare favorably with experimental measurements. Spring-in was dominated by thickness shrinkage, which contributed approximately 3/4 of the measured distortion. The mold stretching contribution diminished with thickness and was negligible for parts thicker than 2.5 mm (0.1 in.). While the material system at hand did not exhibit a fiber volume fraction gradient, its effects were included in the formulation of the model. For materials that have reported a gradient, it was found to account for approximately 10% of the part spring-in.     

破片模拟弹侵彻钢板的有限元分析

根据破片模拟弹侵彻钢板的实验研究，采用MSC．Dytran对破片模拟弹侵彻钢板的侵彻过程、侵彻特性、钢板的破坏模式以及弹体的侵彻速度、靶板的侵彻阻力进行了有限元分析，并将分析结果与实验结果进行了比较．分析结果表明，破片模拟弹冲击钢装甲的侵彻过程可大致分为初始接触、弹体侵入、剪切冲塞和穿甲破坏4个阶段．有限元分析的破片模拟弹侵彻特性及靶板破坏模式与实验观测结果有较好的一致性，在靶板破口的正面，与弹体平面凸缘两端接触的部分，变形以剪切为主，而与切削面接触的部分，以挤压变形为主；靶板破口背面为剪切冲塞破坏；有限元模拟的弹体剩余速度与实验结果吻合较好，弹体侵彻过程中弹靶作用界面的速度和侵彻速度近似呈线性变化．有限元分析结果还表明，采用适当的模型，有限元法能较好地模拟破片模拟弹侵彻钢板的侵彻过程、侵彻特性以及钢板的破坏模式．     

Modelling of dendritic solidification using finite element method

Abstract

Computer based numerical modelling of solidification is being increasingly used in an effort to develop and improve casting processes, a long term goal of this work being the prediction of microstructural features such as grain shape, size, and dendrite arm spacings throughout a casting. In a numerical heat flow model this can be achieved only through the inclusion of the kinetics of nucleation and dendrite growth. In the present paper strategies for including columnar and equiaxed solidification kinetics into a finite element model are reviewed. A detailed model for columnar solidification is then presented together with results obtained from calculations on an Al–5 wt-%Cu alloy and a multicomponent nickel based superalloy. It is shown that the inclusion of a dendrite tip undercooling is important, particularly in systems having a low Stefan number. Furthermore, the thermal histories in the superalloy can only be accurately calculated if an experimentally determined solid fraction versus temperature relationship is employed. A model for equiaxed solidification is also discussed and results obtained for an Al–5 wt-%Cu alloy outlined. In particular, the effects of heat transfer coefficient, heterogeneous nucleation site density, and nucleation undercooling on the grain size variation along a one dimensional casting have been examined. Finally, it is shown that grain sizes predicted by the present finite element model agree reasonably well with those of a previous numerical model for an Al–7 wt-%Si alloy.

MST/1468     

Analysis of the interaction within a rectangular array of rectangular inclusions using a new hybrid finite element method

This paper deals with the interaction problem of a rectangular array of rectangular inclusions under longitudinal tension. A novel ad hoc hybrid finite element method is applied to a rectangular cell containing single or multiple inclusions. Generalized stress intensity factors at the corners of inclusions are systematically calculated with varying the material type, shape and arrangement of rectangular inclusions. Present numerical solutions are compared with existing results. The present method is found to be yield rapidly converging numerical solutions with high accuracy.     

Elastodynamic analysis of crack by finite element method using singular element

The finite element method using a singular element near the crack tip is extended to the elastodynamic problems of cracks where the displacement function of the singular element is taken from the solution of a propagating crack. The dynamic stress intensity factor for cracks of mode III or mode I deformations in a finite plate is determined.The results of computation for stationary cracks or propagating cracks under dynamic loadings are compared with the analytical solutions of other authors. It is shown that the present method satisfactorily describes the time variation of the stress intensity factor in dynamic crack problems.

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Résumé La méthode des éléments finis utilisant un élément singulier au voisinage de l'extrémité d'une fissure a été étendue aux problèmes élastodynamiques des fissures tels qu'ils se posent lorsque la fonction de déplacement d'un élément singulier est prise à partir de la solution d'une fissure en cours de propagation. Le facteur d'intensité des contraintes dynamiques correspondant à des fissures de mode III ou des déformations de mode I dans une plaque finie a été déterminé. Les résultats des calculs correspondant à des fissures stationnaires ou des fissures en cours de propagation sous des charges dynamiques sont comparées aux solutions analytiques obtenues par d'autres auteurs. On montre que la méthode présentée décrit de façon satisfaisante la variation en fonction du temps du facteur d'intensité des contraintes dans les problèmes de fissuration dynamique.

     

An unfitted finite element method using discontinuous Galerkin

In this paper we present a new approach to simulations on complex‐shaped domains. The method is based on a discontinuous Galerkin (DG) method, using trial and test functions defined on a structured grid. Essential boundary conditions are imposed weakly via the DG formulation. This method offers a discretization where the number of unknowns is independent of the complexity of the domain. We will show numerical computations for an elliptic scalar model problem in ?² and ?³. Convergence rates for different polynomial degrees are studied. Copyright © 2009 John Wiley & Sons, Ltd.     

Generalized finite element method using proper orthogonal decomposition

A methodology is presented for generating enrichment functions in generalized finite element methods (GFEM) using experimental and/or simulated data. The approach is based on the proper orthogonal decomposition (POD) technique, which is used to generate low‐order representations of data that contain general information about the solution of partial differential equations. One of the main challenges in such enriched finite element methods is knowing how to choose, a priori, enrichment functions that capture the nature of the solution of the governing equations. POD produces low‐order subspaces, that are optimal in some norm, for approximating a given data set. For most problems, since the solution error in Galerkin methods is bounded by the error in the best approximation, it is expected that the optimal approximation properties of POD can be exploited to construct efficient enrichment functions. We demonstrate the potential of this approach through three numerical examples. Best‐approximation studies are conducted that reveal the advantages of using POD modes as enrichment functions in GFEM over a conventional POD basis. Copyright © 2009 John Wiley & Sons, Ltd.     

Simulation of wheel impact test using finite element method

In order to achieve better quality, the wheel design and manufacturing use a number of wheel tests to ensure that the wheel meets the safety requirements. The impact performance of wheel is a major concern of new design wheel. The wheel impact test is intended to evaluate the impact performance of wheel, that the striker is dropped from a specified height above the tire–wheel assembly. In this study, nonlinear dynamic finite element is used to simulate the SAE wheel impact test. The wheel modeled as an elastic–plastic body is mounted at an incline of 13° to horizontal, and the striker is prescribed an initial velocity to simulate a drop height. The total plastic work concept of ductile fracture mechanics is used to predict the impact failure of wheel. Three-dimensional finite element method is employed to obtain the strain energy density of wheel at impact, and the critical strain energy density is based on the total plastic work of wheel material. Compared with actual tests, the finite element results show the total plastic work approach can be used to predict the wheel fracture during the impact test.