M.S. Gadala

Simulation of the orthogonal metal cutting process using an arbitrary Lagrangian–Eulerian finite-element method

Abstract Two different finite-element formulations, the Lagrangian and the Eulerian, have been used extensively in the modeling of the orthogonal metal cutting process. Each of these formulations has some disadvantages that make it inefficient for modeling the cutting process. In this paper, it is shown that a more general formulation, the arbitrary Lagrangian–Eulerian (ALE) method may be used to combine the advantages and avoid the shortcomings of both of the previous methods. It is also shown that due to the characteristics of the cutting process, this formulation offers the most efficient modeling approach. Some preliminary results of this approach are presented to demonstrate its capabilities and potential in simulating the cutting process.

Numerical Analysis of Metal Cutting With Chamfered and Blunt Tools

In high speed machining of hard materials, tools with chamfered edge and materials resistant to diffusion wear are commonly used. In this paper, the influence of cutting edge geometry on the chip removal process is studied through numerical simulation of cutting with sharp, chamfered or blunt edges and with carbide and CBN tools. The analysis is based on the use of ALE finite element method for continuous chip formation process. Simulations include cutting with tools of different chamfer angles and cutting speeds. The study shows that a region of trapped material zone is formed under the chamfer and acts as the effective cutting edge of the tool, in accordance with experimental observations. While the chip formation process is not significantly affected by the presence of the chamfer, the cutting forces are increased. The effect of cutting speed on the process is also studied.

SIMULATION OF CHIP FORMATION IN ORTHOGONAL METAL CUTTING PROCESS: AN ALE FINITE ELEMENT APPROACH

Abstract Lagrangian and Eulerian finite element formulations have been traditionally used for modeling of the orthogonal metal cutting process. In this paper it is shown that a more general formulation, the arbitrary Lagrangian-Eulerian method (ALE), may be used to combine the advantages and avoid the drawbacks of both methods in a single analysis. Due to the characteristics of the cutting process, ALE formulation offers a very efficient modeling approach for the cutting process. A comprehensive ALE model along with strain rate and temperature dependent constitutive equations and a contact/friction algorithm is used to analyze the thermo-elasto-plastic process of plane strain orthogonal cutting. Simulation results for cutting of low carbon free cutting steel are presented and compared with available experimental data obtained under similar cutting conditions. Good agreement between the numerical and experimental results is observed.

Formulation and survey of ALE method in nonlinear solid mechanics

Abstract This paper investigates the applicability and accuracy of existing formulation methods in general purpose finite element programs to the finite strain deformation problems. The basic shortcomings in using such programs in these applications are then pointed out and the need for a different type of formulation is discussed. An arbitrary Lagrangian-Eulerian (ALE) method is proposed and a concise survey of ALE formulation is given. A consistent and complete ALE formulation is derived from the virtual work equation transformed to arbitrary computational reference configurations. Differences between the proposed formulations and similar ones in the literature are discussed. The proposed formulation presents a general approach to ALE method. It includes load correction terms and is suitable for rate-dependent and rate-independent material constitutive law. The proposed formulation reduces to both updated Lagrangian and Eulerian formulations as special cases.

On the mesh motion for ALE modeling of metal forming processes

Arbitrary Lagrangian-Eulerian finite element method is being increasingly used for simulation of metal-forming operations, due to its capability to combine the features of both Lagrangian and Eulerian approaches in a single analysis. An important consideration in applying this approach is an algorithm which decides upon the motion of all degrees of freedom of the finite element mesh in every step of the analysis, such that the resulted mesh retains an optimal shape and condition. Such an algorithm has to be effective, general, and computationally efficient.In this paper, an overview of the mesh motion problem is provided in which guidelines are given for designing mesh motion strategies for particular problems, and numerical schemes are proposed for moving the mesh on external boundaries and in the interior of the body consistent with the ALE principles. Some numerical examples are provided which demonstrate that with suitable mesh motion schemes, ALE formulation can be used effectively to solve problems which are otherwise difficult to solve in Lagrangian or Eulerian frameworks.

ALE formulation and its application in solid mechanics

In this paper an incremental approach is used to derive an arbitrarily-Lagrangian-Eulerian (ALE) finite element formulation including a complete expression of the external virtual work. The characteristics of this formulation and its differences from similar ones in literatures are discussed. A detailed discussion on the loading correction analysis is given based on the degenerated updated Lagrangian description from ALE, and a modified expression for the surface loading correction contribution to the system stiffness matrix is presented. Some of the numerical difficulties with the ALE formulation, namely the mesh motion and the stress integration scheme, are discussed and specific applications are given. A general 2D ALE program; ALEFE and its features are introduced. Sample numerical examples as well as a punch indentation, a sheet metal extrusion problem and a compression between wedge-shaped dies are given and compared to various other formulations and solutions in the literature.

SIMULATION OF METAL FORMING PROCESSES WITH FINITE ELEMENT METHODS

The traditional Lagrangian and Eulerian formulations in finite elements posses some inherent difficulties when used in simulation of metal-forming processes or general finite strain problems. A more general method of formulation, the Arbitrary Lagrangian–Eulerian (ALE), is developed to overcome such difficulties. A brief description of the ALE formulation is given with emphasis on the underlying differences between the developed formulation and existing ones in the literature. Some numerical algorithms for incorporating large deformation effect are presented. Typical metal-forming processes such as strip rolling, metal extrusion and punch forging are simulated using the ALE formulation and results are compared with available numerical and experimental ones. Special attention is given to numerical characteristics of the simulation, application of boundary condition and their effect on the results. Copyright

Guide roll simulation in FE analysis of ring rolling

Abstract A new method (thermal spokes) has been proposed to simulate the guide roll effect in FE analysis of the ring rolling process. The method is simple to use with existing FE formulations, does not introduce further nonlinearities, and results in more stable and faster solution to ring rolling simulations. The method has been successfully employed in a 2D FE simulation of rolling flat rings. A special feature of the method is its ability to take into account the stiffness of the adjustment mechanism of the guide rolls. On the other hand, a simple modification has been introduced on the lever arm principle, which might be used to estimate guide roll forces in elementary analysis. Incorporating the thermal spokes method in the ring rolling simulation showed important effects of the guide rolls on the ring–tool contact region, roll force and drive torque. Finite element results are in good agreement with experimental results and confirm the validity of the thermal spokes approach as well as the proposed modified lever arm principle.

A consistent eulerian formulation of large deformation problems in statics and dynamics

Abstract A concise survey of formulation methods of geometric and material non-linearity problems is given. The survey is concerned mainly with the differences between updated Lagrangian and Eulerian formulations, and with the specific nature and basic characteristics of each. The underlying mechanics and the spatial discretisation for an Eulerian formulation are discussed. An Eulerian formulation with the final equilibrium equations suitable for static and/or dynamic structural analysis is presented. Explicit forms for stiffness matrices and load vectors are given. Differences between the present formulation, the existing Lagrangian formulation, the updated Langrangian formulation and other attempted Eulerian formulations are discussed within the framework of a consistent classification of formulation methods.

Computational implementation of stress integration in FE analysis of elasto-plastic large deformation problems

Abstract In this paper, we compare different numerical implementation algorithms for the rate type constitutive equation and present an integration scheme based on the physical meaning of the stress. Numerical implementation of various schemes is investigated in conjunction with the return mapping algorithm and the conditions to maintain plastic consistency. Jaumann and Truesdell rates are taken as the objective stress rates in the constitutive equation. An alternative numerical treatment for rate of deformation tensor Dij is presented and is shown to maintain incremental objectivity. Numerical examples included a single element under rigid body rotation, a necking bifurcation of a bar in tension and a punch indentation process. It is shown that the use of Truesdell stress rate with specific numerical integration procedure gives more accurate results than other procedures presented.