Finite Element Modeling of Stresses Induced by High Speed Machining with round Edge Cutting Tools

High speed machining (HSM) produces parts with substantially higher fatigue strength; increased subsurface micro-hardness and plastic deformation, mostly due to the ploughing of the cutting tool associated with residual stresses, and can have far more superior surface properties than surfaces generated by grinding and polishing. In this paper, a dynamics explicit Arbitrary Lagrangian Eulerian (ALE) based Finite Element Method (FEM) modeling is employed. FEM techniques such as adaptive meshing, explicit dynamics and fully coupled thermal-stress analysis are combined to realistically simulate high speed machining with an orthogonal cutting model. The Johnson-Cook model is used to describe the work material behavior. A detailed friction modeling at the tool-chip and tool-work interfaces is also carried. Work material flow around the round edge-cutting tool is successfully simulated without implementing a chip separation criterion and without the use of a remeshing scheme. Finite Element modeling of stresses and resultant surface properties induced by round edge cutting tools is performed as case studies for high speed machining of AISI 1045 and AISI 4340 steels, and Ti6Al4V titanium alloy. INTRODUCTION Finite Element Method (FEM) based modeling and simulation of machining processes is continuously attracting researchers for better understanding the chip formation mechanisms, heat generation in cutting zones, tool-chip interfacial frictional characteristics and integrity on the machined surfaces. Predicting the physical process parameters such as temperature and stress distributions accurately play a pivotal role for predictive process engineering of machining processes. Tool edge geometry is particularly important, because its influence on obtaining most desirable tool life and surface integrity is extremely high. Therefore, development of accurate and sound continuum-based FEM models are required in order to study the influence of the tool edge geometry, tool wear mechanisms and cutting conditions on the surface integrity especially on the machining induced stresses. This paper aims to review the FEM modeling studies conducted in the past and to develop a FEM model for most satisfying simulation of the physical cutting process and most reasonable predictions for cutting forces, temperatures and stresses on the machined surface. In continuum-based FEM modeling, there are two types of analysis in which a continuous medium can be described: Eulerian and Lagrangian. In a Lagrangian analysis, the computational grid deforms with the material where as in a Eulerian analysis it is fixed in space. The Lagrangian calculation embeds a computational mesh in the material domain and solves for the position of the mesh at discrete points in time. In those analyses, two distinct methods, the implicit and explicit time integration techniques can be utilized. The implicit technique is more applicable to solving linear static problems while explicit method is more suitable for nonlinear dynamic problems. A majority of earlier numerical models have relied on the Lagrangian formulation [1-6], where as some of the models utilized the Eulerian formulation [7]. However, it was evident that the Lagrangian formulation required a criterion for separation of the undeformed chip from the workpiece. For this purpose, several chip separation criteria such as strain energy density, effective strain criteria were implemented as exclusively reported in [8]. Updated Lagrangian implicit formulation with automatic remeshing without using chip separation criteria has also been used in simulation of continuous and segmented chip formation in machining processes [9-16]. Arbitrary Lagrangian Eulerian (ALE) technique combines the features of pure Lagrangian analysis and Eulerian analysis. ALE formulation is also utilized in Copyright © 2005 by ASME 1 simulating machining to avoid frequent remeshing for chip separation [17-22]. Explicit dynamic ALE formulation is very efficient for simulating highly non-linear problems involving large localized deformations and changing contact conditions as those experienced in machining. The explicit dynamic procedure performs a large number of small time increments efficiently. The adaptive meshing technique does not alter elements and connectivity of the mesh. This technique allows flow boundary conditions whereby only a small part of the workpiece in the vicinity of the tool tip needs to be modeled. The ALE formulation with pure Lagrangian boundaries was also applied to the simulation of orthogonal cutting using a round edge cutting tool by the authors [23]. On the other hand, the friction in metal cutting plays an important role in thermo-mechanical chip flow and integrity of the machined work surface. The most common approach in modeling the friction at the chip-tool interface is to use an average coefficient of friction. Late models consist of a sticking region for which the friction force is constant, and a sliding region for which the friction force varies linearly according to Coulomb’s law. FEM simulation of machining using rounded/blunt/worn edge tools is essential in order to predict accurate and realistic stress, temperature, strain and strain rate fields. Recent FEM studies reported in the literature include effects of edge geometries in the orthogonal cutting process [24-25], simulation of machining non-homogenous materials [26], predicting stresses on machined surfaces of hardened steels [27-29]. Recently, Guo and Wen [30] used FE simulations to investigate the effects of stagnation and the round edge geometry on the chip morphology, stress and temperature fields in the machined surface. Davies et al. [31] investigated the effects of work material models on the predictions of the FE simulations. Deshayes et al. [32] simulated the serrated chip formation in orthogonal machining and presented comparisons with experimental results. The round edge of the cutting tool and the highly deformed region underneath has dominant influence on the residual stresses of the machined surface. This also signifies the proposed work when compared the earlier FEM modeling studies that relied on chip-workpiece separation criteria. The use of a separation criterion undermines the effect of the cutting edge on the residual stress formation on the machined surface. In this study, the work material is allowed to flow around the round edge of the cutting tool and therefore, the physical process simulated more realistically. MATERIAL CONSTITUTIVE MODELING Accurate and reliable flow stress models are considered highly necessary to represent work material constitutive behavior under high-speed cutting conditions especially for a new material. The constitutive model proposed by Johnson and Cook [33] describes the flow stress of a material with the product of strain, strain rate and temperature effects that are individually determined as given in Equation (1). In the Johnson-Cook (J-C) model, the constant A is in fact the initial yield strength of the material at room temperature and a strain rate of 1/s and ε represents the plastic equivalent strain. The strain rate ε is normalized with a reference strain rate 0 ε . Temperature term in the J-C model reduces the flow stress to zero at the melting temperature of the work material, leaving the constitutive model with no temperature effect.