Coupled Eulerian-Lagrangian Formulation Research Articles

Evaluation of constitutive models used in orthogonal cutting simulation based on coupled Eulerian–Lagrangian formulation

Evaluation of constitutive models used in orthogonal cutting simulation based on coupled Eulerian–Lagrangian formulation

Comparison of the CEL and ALE approaches for the simulation of orthogonal cutting of 15-5PH and 42CrMo4 materials

The modeling of cutting processes by the finite element method represents a great challenge for scientific researchers. Indeed, the plastic strain and strain rate in cutting induce a high risk of mesh distortion, especially for models based on a Lagrangian formulation which were the first to be developed. To overcome this problem other formulations, such as the Arbitrary Eulerian-Lagrangian (ALE), which is a combination of the classical formulations (Eulerian and Lagrangian), have been developed. Despite very interesting results in the simulation of orthogonal cutting, the implementation of this type of model remains delicate, and in particular the choice of initial geometrical conditions which can lead to a sudden stop of the calculation induced by a mesh distortion. To overcome these limitations, the Coupled Eulerian-Lagrangian (CEL) approach has been developed to simulate the orthogonal cutting process. In this paper, the CEL and ALE approaches were compared to simulate the orthogonal cutting process. The first objective was to compare the quality of the predicted physical quantities (forces, chips) over a wide range of cutting speeds and cutting thicknesses for two different materials. The second objective was to evaluate the time required for a complete simulation, integrating the time to set up the initial conditions (chip geometry) and finally the computation time of the machining operation. This work has shown that ALE and CEL formulations lead to very similar quantitative results that are pretty close to the experimental results. The ALE formulation has the advantage of having a reduced computation time compared to the CEL formulation. However, the preparation of the simulation is easy and robust for the CEL, whereas the selection of initial geometrical conditions for the ALE calculation requires several trials and errors before finding stable conditions. The CEL formulation is therefore a solution to be favored when launching several simulations in an automated way thanks to its reliability.

Installation of groups of stone columns in clay: 3D Coupled Eulerian Lagrangian analyses

This paper describes the results of three-dimensional (3D) finite element analyses investigating the installation effects of groups of stone columns in purely cohesive soils. Installation of stone columns is simplified to the insertion of rigid cylindrical elements with conical tips in a single homogeneous soil layer (Tresca plasticity and a quasi-incompressible elastic law). Installation of a single column is simulated as the reference case and the installations of two columns and a group of nine columns are considered to study the interaction between the installation of several columns and the influence of the installation sequence. The process is simulated using a Coupled Eulerian Lagrangian formulation. Stone column installation alters the surrounding soil and the numerical results show the increase in horizontal stresses and pore pressures. The installation effects of several columns at common spacings overlap between each other and accumulate, producing higher horizontal stresses and pore pressures in a larger area. The installation sequence is mainly visible around the last column installed, where the radial stresses are lower.

Numerical modeling of defect formation in friction stir welding

This study presents an investigation of welding defect formation in joining AZ61 magnesium alloy with friction stir welding by means of a 3D finite element model. The numerical model was created and analyzed in the ABAQUS software. This numerical model uses coupled Eulerian Lagrangian formulation, modified Coulomb's friction law, Johnson-Cook material law, mass scaling technique, and temperature dependent friction coefficient values. The numerical model was validated with experimental results in terms of heat input, temperature distribution, plastic deformation type-amount, and weld defect formation in the weld zone. In friction stir welding, the heat input with a certain tool simply changes directly proportional to the ratio of tool rotation speed to tool feed rate for constant tool compressive force. In the numerical model, as in the experimental study, when the ratio of tool rotational speed to tool feed rate is 2, low heat input results in insufficient plastic deformation, leading to the formation of weld defects in the form of void. When the ratio of tool rotational speed to tool feed rate is 3, however, it was observed that sufficient heat input is provided, and no welding defects occur. The generated numerical model enables the determination of the welding defects that occur in the form of voids in the friction stir welding in a very short processing time. Besides, weld seam geometry can be predicted quite accurately with this model.

Thermo-mechanical modelling of the Friction Stir Spot Welding process: Effect of the friction models on the heat generation mechanisms

Friction Stir Spot Welding involves complex physical phenomena, which are very difficult to probe experimentally. In this regard, the numerical simulation may play a key role to gain insight into this complex thermo-mechanical process. It is often used to mimic specific experimental conditions to forecast outputs that may be substantial to analyse and elucidate the mechanisms behind the Friction Stir Spot Welding process. This welding technique uses frictional heat generated by a rotating tool to join materials. The heat generation mechanisms are governed by a combination of sliding and sticking contact conditions. In the numerical simulation, these contact conditions are thoroughly dependent on the used friction model. Hence, a successful prediction of the process relies on the appropriate selection of the contact model and parameters. This work aims to identify the pros and cons of different friction models in modelling combined sliding-sticking conditions. A three-dimensional coupled thermo-mechanical FE model, based on a Coupled Eulerian-Lagrangian formulation, was developed. Different friction models are adopted to simulate the Friction Stir Spot Welding of the AA6082-T6 aluminium alloy. For these friction models, the temperature evolution, the heat generation, and the plastic deformation were analysed and compared with experimental results. It was realized that numerical analysis of Friction Stir Spot Welding can be effective and reliable as long as the interfacial friction characteristics are properly modelled. This approach may be used to guide the contact modelling strategy for the simulation of the Friction Stir Spot Welding process and its derivatives.

A Analysis the influence of threaded pin profiles in friction stir welding by numerical simulation

Currently, the welding industry has made significant contributions in most production fields to meet the needs of people's lives. However, traditional welding methods have disadvantages such as: a large amount of energy consumption, production of many toxic gases that are harmful to the environment and the health of workers. Therefore, the friction stir welding method was introduced from the research of scientists to overcome the above disadvantages. Besides that, it is suitable for welding aluminum alloys and non-ferrous metals with low melting point. This green welding technology has been continuously researched to improve weld quality through two main research models: experiment models and numerical simulation models. Experimental results provide provides the basic mechanical properties of the materials at the weld and the process optimization parameters. It will be the basis to establish a numerical simulation model closest to reality, based on mathematical models and working principles, thereby helping to predict weld quality through prediction of formation defects, temperature distribution with changes in welding process parameters such as time, velocity, material or welding pin profile. In this study, the influence of threaded pin profiles on weld quality of alloy aluminum 7075 -T6 during friction stir welding was investigated by numerical simulation model through ABAQUS software to recommend a new pin profile bringing an efficient welding process. To increase the reliability of this research approach, the numerical simulation results of the temperature distribution are compared with the experimental results obtained from a foreign scientific paper with an average error of 14%. Threaded pin profiles are designed in combination with three cross-sections having different opening angles named TF0, TF30, TF60 and TF90. Coupled Eulerian-Lagrangian formulation is applied for this model where the welding tool is Lagrangian domain and workpiece is Eulerian domain. Because material deformation in friction stir welding process is large and related to temperature, the elastic-plastic Johnson-Cook model is used for workpiece. Results of this research shows a new pin profile named TF60 which it gives the best weld quality of the four configurations of the pin tool examined in this study through evaluating temperature distribution and predicting weld defect formation.

Behavioral studies of process parameters and transient numerical analysis on friction stir welded dissimilar alloys

Friction stir welding is a solid state technique in which welded joints are performed using non-consumable tool to heat the metal to plasticized state. The tool exerts high friction and sustained stirring over the metal substrate resulting in a sound weld. In the present work, influence of various process parameters on dissimilar welding of AA 6061 T6 and AA7075 T651aluminium alloys is investigated to enhance the strength properties. Cylindrical and Conical tool pin geometries are chosen to prepare butt welded joints. The tool geometry, rotational spindle speed and feed rate are the various process variables considered for the study. The ultimate tensile strength (UTS) and elongation for six welded joints are determined with rotational spindle speed of about 600, 800, 1000 RPM and feed rate of about 30, 45, 60 mm/min respectively. Irrespective of the process parameters, it is observed that, cylindrical tool rendered the better tensile and elongation property compared to the conical tool. Transient Finite Element Analysis is employed for non-linear problem in the Coupled Eulerian-Lagrangian Formulation. The parametric model with base weld plates and the tool is performed using ABAQUS software. Experimental strength results were validated with Finite Element Analysis. The corresponding strain, deformation and nodal temperature values were determined.

Combination of an Improved 3D Geometry and Coupled Eulerian-Lagrangian Formulation for Turning Simulation

This paper examines whether the Coupled Eulerian-Lagrangian formulation, combined with a thought-out 3D geometry, used recently in turning processes, can provide accurate simulation results. Oblique cutting cases were analyzed with the aid of commercial software for Finite Element analysis. An evaluation of the simulation results was performed by comparing the cutting forces and temperatures of the simulation with experimental turning results. Overall, simulation results with good correlation with experimental data were observed for cutting forces, including axial force distribution and temperature prediction, showing that this approach can be used in turning simulations, regardless of cutting conditions involved.

Simulation of Brain Response to Noncontact Impacts Using Coupled Eulerian-Lagrangian Method.

Finite element (FE) method has been widely used for gaining insights into the mechanical response of brain tissue during impacts. In this study, a coupled Eulerian-Lagrangian (CEL) formulation is implemented in impact simulations of a head system to overcome the mesh distortion difficulties due to large deformation in the cerebrospinal fluid (CSF) region and provide a biofidelic model of the interaction between the brain and skull. The head system used in our FE model is constructed from the transverse section of the human brain, with CSF modeled by Eulerian elements. Spring connectors are applied to represent the pia-arachnoid connection between the brain and skull. Validations of the CEL formulation and the FE model are performed using the experimental results. The dynamic response of brain tissue under noncontact impacts and the brain regions susceptible to injury are evaluated based on the intracranial pressure (ICP), maximum principal strain (MPS), and von Mises stress. While tracking the critical MPS location on the brain, higher likelihood of contrecoup injury than coup injury is found when sudden brain-skull motion takes place. The accumulation effect of CSF in the ventricle system, under large relative brain-skull motion, is also identified. The FE results show that adding relative angular velocities, to the translational impact model, not only causes a diffuse high strain area, but also cause the temporal lobes to be susceptible to cerebral contusions since the protecting CSF is prone to be squeezed away at the temporal sites due to the head rotations.

Numerical simulation of friction stir welding of pure copper plates

Friction Stir Welding (FSW) is a joining process which is performed at low temperatures, lower than the melting temperature of the base material, thus it is considered a solid state welding process. This feature makes it suitable for copper welding, material whose thermal diffusivity is higher than that of most steel alloys. Large heat losses identified at copper welding by fusion welding processes are thus reduced using FSW process. Because of the shown efficiency and the innovative character of this process, many actions have been initiated in order to optimize it. The aim of this paper is to develop a three-dimensional coupled thermo-mechanical finite element (FE) model of FSW process for pure copper plates using the Coupled Eulerian-Lagrangian (CEL) formulation given in the FE code ABAQUS V6.13. The CEL formulation is one of the few formulations that are capable of handling with such large deformations. The developed numerical model was validated by comparing its results related to the temperatures calculated in the process time with those measured in performed experiments using the same process parameters. This model was capable of simulating the FSW of copper plates and of anticipating the temperature distribution and burrs formation in the weld bead.

Development of a simulation model to study tool loads in pcBN when machining AISI 316L

This paper presents the development of a FE-simulation model to predict the mechanical stresses and thermal loads that a cutting tool of polycrystalline cubic boron nitride (pcBN) is subjected to, when machining AISI 316L. The serrated chip formation of AISI 316L has a major impact on the periodic loads acting on the cutting tool. Therefore, it is vital to correctly model this serrated chip formation. One of the major difficulties with FE-simulations of metal cutting is that the extreme deformations in the workpiece material, often leads to a highly distorted mesh. This paper uses the Coupled Eulerian-Lagrangian (CEL) formulation in Abaqus/Explicit, where the workpiece is modelled with the Eulerian formulation and the cutting tool by the Lagrangian one. This CEL formulation enables to completely avoid mesh distortion. To capture the chip serration process, the workpiece material is described with the Johnson-Cook damage model. The FE-simulation results are validated via comparison of the modelled cutting forces, chip serration frequency, and contact length against experimental ones.

Using coupled Eulerian Lagrangian formulation for accurate modeling of the friction stir welding process

Abstract Accurate modeling of Friction-Stir Welding (FSW) would allow a better understanding of the material flow and temperature distribution during the process. This is important for the optimization of the process parameters to avoid the conditions that generate defects in FSW. However, the numerical simulation of the process is challenging due to the numerous complexities involved in FSW. It is a fully coupled thermo-mechanical problem that includes large plastic deformation, heat flow, nonlinear contact and friction. In this study a finite element simulation with a coupled Eulerian Lagrangian formulation was used to predict the temperature distribution during the FSW process of two similar plates of AA2024. The plates were defined as Eulerian parts and the tool was defined as a Lagrangian one. The behavior of the plates’ material during the simulation process was modeled using the Johnson-Cook model. In order to verify the accuracy of the results obtained from the simulation, FSW experiments were conducted with the same welding parameters. Results show good accord between the predicted and the measured temperature distributions. Furthermore, it was shown that the temperature distribution along the welding line is asymmetric with the maximum temperature in the advancing side being higher than that in the retreating side.

On material flow in Friction Stir Welded Al alloys

AA6082-T6 joints were produced using a trigonal shape pin. The influence of Friction Stir Welding (FSW) process parameters on the formation of banded structures was predicted using numerical modeling and then experimentally validated by optical and electron microscopy. Special attention was paid to the formation and evolution of banded structures observed in the plane of the welded sheets. A finite element (FE) analysis based on the Coupled Eulerian–Lagrangian formulation was developed to predict and quantify the influence of FSW process parameters on the formation and extent of the banded structures. The combination of the experimental and numerical analyses showed that the formation of the banded structures is mainly related to the geometry of the pin whereas the friction conditions have a much smaller effect.

Time Efficient Simulations of Plunge and Dwell Phase of FSW and its Significance in FSSW

Friction Stir Spot Welding (FSSW) is gathering attention of automotive and aerospace sectors. It is an alternative for rivets, electric resistance welding and offers substantial advantages with regard to energy consumption, environmental protection and mechanical properties of weld. At present, research efforts are being made to gain a better understanding of the process, to explore different tool configurations, to optimize the set of process parameters and to widen the applicability of FSSW. In this regard, having reliable finite element model that is capable of simulating FSSW with minimal possible simulation time can turn out handy to reduce the number of physical experiments required in such studies and applications. The current work investigates the plunge and dwell phase of Friction Stir Welding (FSW) using three-dimensional (3-D) finite element (FE) modelling. A 3-D FE model is developed in the commercial code ABAQUS/Explicit using the Coupled Eulerian-Lagrangian Formulation, the Johnson-Cook material law, and Coulomb's Law of friction. A successful weld depends on proper material flow and temperature existing during the process. This is dictated by selected processing parameters. If the appropriate conditions are not present, cold or hot defects occur, leading to a faulty weld. Since FSSW comprises of plunge and dwell phase, the simulation results are explained in the context of modeling of FSSW. The simulation results include effect of process parameters (tool rotation speed, plunge velocity, plunge depth) and tool geometry (pin profile) on estimating temperature and morphology of weld region. Tools with square and triangular pin profile aided in increasing the process temperature and widening the weld nugget with less power consumption compared to their counterpart. Simulation time reduced to a greater extent in CEL when compared to Lagrangian, Eulerian and ALE.

Coupled Eulerian-Lagrangian (CEL) 방법을 이용한 Dynamically Penetrating Anchor의 동적 거동 분석

대수심 부유 구조물의 하부기초 기술 중 하나인 dynamically penetration anchor (DPA 또는 흔히 torpedo anchor로 칭함)의 거동특성을 시험결과 및 수치 해석적 접근을 통해 분석하였다. 기존의 유한요소 해석기법으로는 이러한 대수심 anchor 구조물의 거동 특성을 적절히 모사하기 어렵기 때문에 본 연구에서는 이러한 부분을 해결하기 위해 Coupled Eulerian-Lagrangian (CEL) 법을 통해 지반-구조물 사이에서 발생하는 메쉬(mesh)의 distortion 현상 및 경계조건 등의 문제점을 대변형의 관점에서 해결하고자 하였다. 실측치와의 비교를 통해, CEL 기법의 타당성을 검증하였고, 그 결과 본 연구에서 적용한 CEL 기법이 기존 유한요소 기술로는 구현이 불가능한 대수심 anchoring system의 자유낙하에 의한 전반적인 거동 및 지반의 변형특성을 적절히 예측함을 알 수 있었다. 또한 검증된 기법을 바탕으로 dynamic anchor의 거동에 영향을 주는 여러 요소들에 대한 매개변수 연구를 추가로 수행하였다. A fundamental study of the dynamically penetrating anchor (DPA - colloquially known as torpedo anchor) embedded into deep seabed was conducted using measurement data and numerical approaches. Numerical simulation of such a structure penetration was often suffered by severe mesh distortion arising from very large soil deformation, complex contact condition and nonlinear soil behavior. In recent years, a Coupled Eulerian-Lagrangian method (CEL) has been used to solve geomechanical boundary value problems involving large deformations. In this study, 3D finite element analyses using the CEL formulation are carried out to simulate the construction process of dynamic anchors. Through comparisons with results of field measurements, the CEL method in the present study is in good agreement with the general trend observed by in-situ measurements and thus, predicts a realistic large deformation movement for the dynamic anchors by free-fall dropping, which the conventional FE method cannot. Additionally, the appropriate parametric studies needed for verifying the characteristic of dynamic anchor are also discussed.