Three-dimensional simulation of flat rolling through a combined finite element–boundary element approach

This paper presents an innovative approach for analysing three-dimensional flat rolling. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the rigid–plastic numerical modelling of the workpiece allowing the estimation of the roll separating force, rolling torque and contact pressure along the surface of the rolls. The boundary element method is applied for computing the elastic deformation of the rolls. The combination of the two numerical methods is made using the finite element solution of the contact pressure along the surface of the rolls to define the boundary conditions to be applied on the elastic analysis of the rolls. The validity of the proposed approach is discussed by comparing the theoretical predictions with experimental data found in the literature.     

Transient Finite Element Simulation of the Temperature Field during Cryogenic Turning of Metastable Austenitic Steel AISI 347

The process chain in manufacturing often consists of many steps. As part of current researches the possibility of combining two process steps, turning and hardening, is investigated to optimize the manufacturing time and to decrease the energy consumption of the process. For metastable austenitic steels, deformation induced hardening during turning can be used to achieve surface hardening [1] and thus to increase the wear resistance [2] as well as the fatigue strength [3], by applying high passive forces onto the workpiece. This enables an austenite-martensite phase transformation, for which it is necessary to maintain low process temperatures, typically below room temperature. Thus, cryogenic coolants are applied [4]. For a better understanding of the influence of cutting parameters on the process temperatures and thus martensite formation, knowledge of the exact temperature distribution in the workpiece and in the contact zone between workpiece and tool is essential. Since the experimental determination of the temperature field is hardly possible, an inverse determination of the process temperatures via transient finite element simulation is performed. The present finite element approach only takes thermal loads into account. The simulations are performed in the finite element program FEAP (Finite Element Analysis Program) with an Eulerian mesh, which requires special consideration of the rigid body rotation of the workpiece. In order to prevent unphysical oscillations in the solution, introduced by the convective time derivative, a streamline upwind / Petrov–Galerkin stabilization scheme is utilized. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Surface Deformation due to Shear and Ploughing in a Halfspace

Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Load share and finite element stress analysis for double circular-arc helical gears

The authors analyze the tooth surface contact and stresses for double circular-arc helical gear drives. The geometry of such gear drives has been represented by the authors in their previous paper [1]. The proposed approach is based on application of (i) computerized simulation of meshing and contact of loaded gear drives, and (ii) the finite element method. Load share between the neighboring pairs of teeth is based on the analysis of position errors caused by surface mismatch and elastic deformation of teeth. The authors have investigated the conditions of load share under a load and determined the real contact ratio for aligned and misaligned gear drives, respectively. Elastic deformation of teeth and the stress analysis of the double circular-arc helical gears are accomplished by using the finite element method. The finite element models for the pinion and gear are constructed, respectively. Contact pressure is spread over elliptical area. The stress analysis for aligned and misaligned gear drives, respectively, has been performed. The numerical results have been compared with those obtained by other approaches.     

Geometrically nonlinear shell finite element based on the geometry of a planar curve

An engineering approach for constructing a curved triangular finite element of a thin shell is considered. The approach is based on the assumption that the triangle sides are planar nearly circular curves before and after deformation. A geometrically nonlinear formulation of a triangular finite element of a thin Kirchhoff–Love shell is given. The predictive capabilities of the element are tested using benchmark problems of nonlinear deformation of elastic plates and shells.     

Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation

The large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The Von-Karman type nonlinear strain–displacement relationships are employed where the ends of the beam are constrained to move axially. The effects of the transverse shear deformation and rotary inertia are included based upon the Timoshenko beam theory. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A statically exact beam element which devoid the shear locking effect with displacement fields based on the first order shear deformation theory is used to study the geometric nonlinear effects on the vibrational characteristics of functionally graded beams. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law exponent, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible. Some new results for the nonlinear natural frequencies are presented in both tabular and graphical forms which can be used for future references.     

Microstructure analysis on IN 718 alloy round rod by FEM in the hot continuous rolling process

Based on physical metallurgy rules and experiential equations, models for microstructure analysis on IN 718 alloy in the round rod hot continuous rolling process has been developed using the finite element method (FEM) on the software ANSYS/LS-DYNA. The dynamic and metadynamic recrystallization models in and after deformation, the grain growth models in the compensated reheating process for IN 718 alloy are regressed, and corresponding processes are involved in these models. For a real rolling practice, the calculated central grain sizes were examined and are in good agreement with the measured ones. The element in the center of the workpiece is a typical one possessing the maximum of the effective strain, the temperature and the grain size in the rolling process. In the hot continuous rolling process, the relationship between the final grain size of the typical element and the inlet velocity of the first stand has been regressed by FE analysis, and the lower rolling speed is beneficial to the grain refinement.     

A finite element method for contact/impact

Ideas from the analysis of differential-algebraic equations are applied to the numerical solution of frictionless contact/impact problems in solid mechanics. Index-one and two formulations for dynamic contact–impact within the context of the finite element method are derived. The resulting equations are shown to stabilize the kinematic fields at the contact interface, at the expense of a small energy loss, which is shown to decrease consistently with mesh refinement. This energy dissipation is shown to be necessary for the establishment of persistent contact. A Newmark-type time integration scheme is derived from the proposed formulation, and shown to yield excellent results in modeling the transition to contact/impact.     

有曲率突变的轴对称壳(波纹壳)的有限元解

本文指出了在一般用直线单元的轴对称壳的有限元法中,由于忽视了曲率对斜度变形的影响,并不能用以处理曲率突变的轴对称壳问题.本文提出了考虑曲率影响的、以壳的斜度变形为连续参数的直线单元有限元法,并用以处理C型波纹壳的计算.和Turner-Ford的实验结果比较,以及和钱伟长教授的解析解比较,都证明这个理论是正确的.     

Accurate modeling of contact using cubic splines

In this paper, we develop and implement a new method for the accurate representation of contact surfaces. This approach overcomes the difficulties arising from the use of traditional node-to-linear surface contact algorithms. In our proposed method, contact surfaces were modeled accurately using C¹-continuous cubic splines, which interpolate the finite element nodes. In this case, the unit normal vectors are defined uniquely at any point on the contact surfaces. These splines preserve the local deformation of the nodes on each flexible contact surface. Consequently, a consistent linearization of the kinematic contact constraints, based on the spline interpolation, was derived. Moreover, the gap between two contact surfaces was modeled accurately using an efficient surface-to-surface contact search algorithm. Since the continuity of the splines is not affected by the number of nodes, accurate stress distribution can be obtained with less finite elements at the contact surface than that using the traditional linear discretization of the contact surface. Two numerical examples are used to illustrate the advantages of the proposed representation. They show a significant improvement in accuracy compared to traditional piecewise element-based surface interpolation. This approach overcomes the problem of mismatch in a finite element mesh. This is very useful, since most realistic engineering problems involve contact areas that are not known a priori.     

Investigations of the influence of geometrical irregularities and roughness on the normal contact stiffness of joints

Conducting experiments is necessary to determine the normal contact stiffness of rough surfaces. In compression tests the interface of specimen pairs is loaded in normal direction and the deflection is measured by extensometers with strain gages. The results can be used for example to describe the contact behaviour of joints in finite element analyses. It is shown that geometrical irregularities which are superposed by the surface roughness have a large influence on the elastic deformation of a joint and on the determination of the contact stiffness. They can be characterized by a skewed and a waved form of the surface with wavelengths which are larger than the surface roughness. In the experimental setup several different surfaces are compressed. In addition, the influence of the size of the contact area on the deformation of a joint is analysed. The results of the normal contact tests are compared with numerical simulations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Contact Homogenization Framework for Granular Interfaces

A computational contact homogenization framework is developed for contact interfaces with dry granular third bodies. The micro-to-macro transition procedure that forms the basis of this framework consists of projecting the macroscale contact pressure and slip velocity to the observable test surface of a representative contact element. The solution of the local microscale problem reveals a macroscale friction coefficient where inelastic effects are taken into account in a finite deformation setting. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite element model of localized deformation in frictional materials taking a strong discontinuity approach

A finite element model of localized deformation in frictional materials taking a strong discontinuity approach is presented. A rate-independent, non-associated, strain-softening Drucker–Prager plasticity model is formulated in the context of strong discontinuities and implemented along with an enhanced quadrilateral element within the framework of an assumed enhanced strain finite element method. For simple model problems such as uniform compression, the strong discontinuity approach has been shown to lead to mesh-independent finite element solutions when localized deformation is present. In this paper, a finite element analysis of localized deformation occurring in a more complex model problem of slope stability is conducted in a nearly mesh-independent manner. The effect of dilatancy on the orientation of slip lines is demonstrated for the slope stability problem.     

Configurational Forces in Crystal Plasticity

The surface morphology of micro machined surfaces depends on the heterogeneous microstructure. A crystal plasticity model is used to describe the plastic deformation in cp-titanium with its hcp crystal structure. Therefore the basal and prismatic slip systems are taken into account. Furthermore, self and latent hardening are considered. The rate dependency is motivated by a visco plastic evolution law. The cutting process of cp-titanium is modeled within the concept of configurational forces for a standard dissipative media. This framework is implemented into the finite element method. An example illustrates the effects of the microstructure on plastic deformation and configurational forces. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling frictional contact in shell structures using variational inequalities

A new variational inequality-based formulation is presented for the large deformation analysis of frictional contact in shell structures. This formulation is based on a seven-parameter continuum shell model which accounts for the normal stress and strain through the shell thickness and accommodates double-sided shell contact. The kinematic contact conditions are expressed accurately in terms of the physical contacting surfaces of the shell. Furthermore, Lagrange multipliers are used to ensure that the kinematic contact constraints are accurately satisfied and that the solution is free from user-defined parameters. Large deformations and rotations are accounted for by invoking the Piola–Kirchhoff stress and the Green–Lagrange strain measures. Three examples involving a strip friction test, ring contact and sheet compression tests are used to verify the developed formulations and algorithms, and test various aspects of the solution technique. Photoelastic analysis of the ring compression example is performed for experimental verification.     

Finite element modelling of anisotropic elastic–viscoplastic behaviour of metals

An implementation of the unified theory of visco-plasticity of Bodner in a three-dimensional finite element program for the analysis of anisotropic inelastic behaviour of selected metals is presented in this paper. A derivation of an effective hardening parameter for the anisotropic (directional) deformation state is also given in this paper using some basic assumptions introduced by Bodner. The effect of the imposed strain rate on the level of the stress–strain curve is also investigated. A comparison of the results of the present finite element model with some published theoretical and experimental results for pure titanium and 2024-T4 aluminium alloy is also made.     

基于FEMLIP的全风化边坡失稳破坏全过程的数值模拟研究

边坡坡角和强度是影响边坡稳定性的重要因素,而边坡失稳往往伴随着大变形的发生,其变形从数十米至数千米不等.目前,传统有限元法在处理大变形问题时常常因网格畸变而导致计算终止.因此,为了实现边坡失稳破坏全过程的模拟,并研究边坡坡角和强度对边坡稳定性的影响,基于Lagrange(拉格朗日)积分点有限元法（FEMLIP）,采用C语言编写了能够模拟边坡失稳滑塌全过程的Ellipsis程序,并通过一个典型案例对该方法的正确性和可行性进行了验证.采用该方法分析了边坡在不同坡角和强度条件下的稳定性和滑坡过程.研究结果表明,Lagrange积分点有限元法可以较准确地模拟边坡的潜在滑移面,并且可以模拟边坡失稳后的滑坡发展过程,为边坡滑坡大变形分析提供了一种新的数值计算方法.     

Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads

The finite element dynamic response of an unsymmetric composite laminated orthotropic beam, subjected to moving loads, has been studied. One-dimensional finite element based on classical lamination theory, first-order shear deformation theory, and higher-order shear deformation theory having 16, 20 and 24 degrees of freedom, respectively, are developed to study the effects of extension, bending, and transverse shear deformation. The theories also account for the Poisson effect, thus, the lateral strains and curvatures can be expressed in terms of the axial and transverse strains and curvatures and the characteristic couplings (bend–stretch, shear–stretch and bend–twist couplings) are not lost. The dynamic response of symmetric cross-ply and unsymmetric angle-ply laminated beams under the action of a moving load have been compared to the results of an isotropic simple beam. The formulation also has been applied to the static and free vibration analysis.     

Prediction of diameter errors in bar turning: a computationally effective model

Machining accuracy can be considerably affected by the deflections of the machine–workpiece–tool system as well as the thermal expansion of material during machining. An improved model for predicting dimensional errors in turning process is presented. This model uses a geometric analysis in the machine frame, in which the elastic deflections of the machine–workpiece–tool system due to the cutting force are studied. In this paper, our workpiece deflection model [A.-V. Phan, G. Cloutier, J.R.R. Mayer, International Journal of Production Research 37 (1999) 4039–4051; G. Cloutier, J.R.R. Mayer, A.-V. Phan, Computer Modeling and Simulation in Engineering 4 (1999) 133–137] earlier developed is employed. As described in Phan et al. (1999), this deflection model is general, accurate and computationally effective thanks to its closed-form solutions derived from the finite element technique. Also, due to the coupling between the cutting force and actual depth of cut, iterative computations are performed to obtain the coupling value of this force which provides further accuracy to the prediction. Finally, via numerical examples, the predicted diameter error on a workpiece, the ratio between the coupled cutting force and its nominal value along the part axis as well as the influence of the cutting force components on the error prediction are computed using the proposed model. The results provide additional insight into the error formation in the turning process.     

Combined unstructured and hanging-node-based remeshing with boundary control for metal forming simulations

During finite element simulation of metal forming process, the mesh which represents the workpiece undergoes extreme large deformation, which could result in highly distorted mesh and numerical failure in simulation. To overcome the problem and improve computation efficiency, advancing front quad meshing technique and non–conforming mesh refinement approach are combined to generate new mesh according to desired mesh size distribution. Application of the combined remeshing strategy to rolling simulation will be presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)