Identification of plasticity constants from orthogonal cutting and inverse analysis
Introduction
The reliability of numerical models such as FEM depends on various mechanical properties such as elastic constants, flow stress and fracture, these serve as material constants in constitutive models. In addition for a coupled thermo-mechanical simulation thermo-physical constants, such as thermal conductivity, heat capacity and plastic deformation energy also comes into account. For a simulation where contact between bodies is present, the contact conditions at interfaces both mechanical and thermal also need to be defined. All three of these aspects have to be taken into account when simulating a machining process. The Johnson–Cook plasticity model is widely used today to simulate materials subjected to high a temperature and strain rate gradients which are the case in a machining process. The Johnson–Cook plasticity model has been successfully used by many researchers to simulate various aspects of the machining process such as temperature distribution in the workpiece (Chen et al., 2004, Özel and Zeren, 2007), cutting forces (Hortig and Svendsen, 2007, Uhlmann et al., 2007), residual stresses in the machined surface (Mabrouki et al., 2008, Umbrello et al., 2007), strain in the deformation zones (Pujana et al., 2007, Zouhar and Piska, 2008) and chip formation characteristics (Akbar et al., 2010, Zhang et al., 2011). FEM simulation of manufacturing processes has been found to be a cost effective method of analyzing such processes, serving to keep the amount of experimental work and the resources needed at a minimum. This is in the line with use of a sustainable production approach.
A drawback when using FEM to simulate a cutting process however, is the lack of input data to the material models involved. There is thus a need of establishing a robust link between experimental data and the material constants of the constitutive models. Achieving this would considerably reduce the efforts needed to find input constants to FEM models. The development of these plasticity constants for the cutting process has been studied from different viewpoints. First, through the use and adjustment of laboratory testing experiments for the construction of material constitutive laws in conditions similar to those encountered in machining operations, such as Split-Hopkinson’s (Chandrasekaran and M’saoubi, 2005, Jaspers and Dautzenberg, 2002), second by the use of analytical cutting models (Tounsi et al., 2002) or numerical (Fallböhmer and Altan, 1997) in a combination with an inverse analysis.
Due to the severe deformation conditions present in the cutting process, it is possible to reach strains of the order of magnitude 1–2, strain rates higher than 104 s−1, temperatures up to 1000 °C and temperature rates up to the order of 106 °C s−1 (Arsecularatne and Zhang, 2004). These experimental tests methods, such as Split-Hopkinson’s, however are not able to produce as high strain rates or temperature rates that are present in the machining process deformation zones. Therefore it is desired to tune the constants in the constitutive models with experimental data from the actual cutting process.
How the Johnson–Cook constitutive model constants affect the cutting process parameters of the cutting process, such as chip compression ratio, cutting forces, temperatures and deformation zones was investigated in (Agmell et al., 2013). For simulation of the cutting process, even in a simplified orthogonal case, one can identify about 30 different cutting process parameters of interest related to tool development and analysis of the machinability of the workpiece material. The material that has been simulated is AISI 4140 where the FEM model used in (Agmell et al., 2011) has been employed and Johnson–Cook constitutive model constants being changed within the interval of ±30%. The present study was carried out to obtain a better understanding of how the Johnson–Cook constitutive model constants should vary within a material group according to the ISO standard having cutting process parameters that are similar. In the work reported on here, the variation of the cutting process parameters is studied for each of the Johnson–Cook constitutive model constants respectively, when they are changed by ±15% and ±30% for each constant. A polynomial function of the fourth order is interpolated between these data points. An inverse analysis using a Kalman filter is performed in order to determine the Johnson–Cook constitutive model constants. The Kalman filter has been successfully used for inverse identification of mechanical properties in Aoki et al., 1997, Bocciarelli et al., 2005, Delalleau et al., 2006, Nakamura and Gu, 2007 which suggest that it can be a feasible method. To validate the method and the estimated Johnson–Cook constitutive model constants, new FEM simulations of the cutting process was carried out; the cutting process parameters obtained are then compared with experimental values from the experiments performed.
Section snippets
Machining mechanics and theoretical aspects
The parameters that will be presented in this section are general cutting parameters used to describe an orthogonal cutting process. The uncut chip thickness is defined as the uncut thickness of the chip or the distance between the surface prior to machining and the newly formed surface. The cutting speed of a machining operation is defined as the relative speed of the workpiece to the cutting edge. The friction at interface between the tool and the workpiece decelerates the chip, which
Experimental investigation
The experimental tests were performed on a cylindrical tube with a thickness of 4 mm. The uncut chip thickness was set to 0.10 mm for all of the experimental tests. The cutting tests were performed in a lathe of the fabricate, Monforts RNC 700 Single Turn. The cutting forces was measured with a cutting force sensor of the fabricate Kistler Z15814. The chip compression ratio was determined with a micrometer: Mitutoyo No. 422-260. The experimental data for the cutting force was based on
Inverse analysis
The Kalman filter, is an inverse analysis technique used in several engineering applications. The algorithm is utilized here to estimate five unknown Johnson–Cook constitutive model constants on the basis of two experimentally measured cutting process parameters. In the formulation employed, the five unknown constants are represented in state vector form as = (At, Bt, Ct, nt, mt)T. At time t = 0 the initial estimates are assigned where = (A0, B0, C0, n0, m0)T and the equation that follows are
Material model
The tool was modeled as a cemented carbide material and the reference material of the workpiece was modeled as AISI 4140. The general thermal and mechanical properties are presented in details in Table 2. Since the specific heat of the workpiece material is highly temperature-dependent a temperature-dependent model was employed, see Fig. 5. The Johnson Cook constitutive model was employed to model the plasticity of the workpiece material, which was developed by Johnson and Cook (1983). This
Finite element model
The orthogonal cutting process was simulated by use of a two dimensional model in ABAQUS/Explicit v6.12-3, with a fully coupled thermo-mechanical analysis being performed. The ALE formulation with use of Lagrangian boundary conditions was employed in this model. The time integration of the model was an explicit scheme. The workpiece length was chosen to be 5 mm and its height to be 2 mm. The cutting tool had a clearance angle of 5°, a rake angle of 0°, an edge radius of = 50 μm, and a height
Results
There are a vast number of cutting process parameters that can be studied in a FEM simulation of orthogonal cutting. For example strain in the deformation zones, temperature distribution in the workpiece material, the angle of the shear plane, cutting forces, chip thickness ratio, stagnation zone and strain rate in the shear band. Some of these cutting process parameters dependence of Johnson–Cook constitutive model constants have been investigated in Agmell et al. (2012). In this study two of
Conclusions
This study shows that, through employing an inverse procedure based on use of a Kalman filter and metal cutting experiments, one can identify plasticity constants for FEM simulations in the form of Johnson–Cook constitutive model constants. The principle involved assumes, that there is a reference workpiece material with similar metal cutting behavior characteristics and well-known plasticity constants. The inverse procedure of finding the plasticity constants is a time effective method, an
Acknowledgments
This research is a part of the ShortCut research project financed by the Swedish Foundation for Strategic Research SSF. It is also a part of the strategic research program of the Sustainable Production Initiative SPI, involving cooperation between Lund University and Chalmers University of Technology. The authors would like to thank Seco Tools for providing the necessary tools. A special thanks to Rachid M’Saoubi, Christer Bäck and Tommy Lethola for assisting in the experimental work. The
References (32)
- et al.
The link between plasticity parameters and process parameters in orthogonal cutting
Procedia CIRP
(2013) - et al.
Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping
J. Mech. Mater.
(2005) - et al.
Modelling the effects of flank wear land and chip formation on residual stresses
CIRP Ann. – Manuf. Technol.
(2004) - et al.
On the measurement and prediction of temperature fields in machining AISI 1045 steel
CIRP Ann. – Manuf. Technol.
(2003) - et al.
Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test
J. Biomech.
(2006) - et al.
Simulation of chip formation during high-speed cutting
J. Mater. Process. Technol.
(2007) - et al.
Material behaviour in conditions similar to metal cutting: flow stress in the primary shear zone
J. Mater. Process. Technol.
(2002) - et al.
Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures
J. Eng. Fract. Mech.
(1985) - et al.
A contribution to a qualitative understanding of thermo-mechanical effects during chip formation in hard turning
J. Mater. Process. Technol.
(2006) - et al.
Numerical and experimental study of dry cutting for an aeronautic aluminium alloy (A2024-T351)
Int. J. Mach. Tools Manuf.
(2008)
Identification of elastic–plastic anisotropic parameters using instrumented indentation and inverse analysis
J. Mech. Mater.
Computational modelling of 3D turning: influence of edge micro-geometry on forces, stresses, friction and tool wear in PcBN tooling
J. Mater. Process. Technol.
2D and 3D numerical models of metal cutting with damage effects
Comput. Methods Appl. Mech. Eng.
Analysis of the inverse identification of constitutive equations applied in orthogonal cutting process
Int. J. Mach. Tools Manuf.
From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation
Int. J. Mach. Tools Manuf.
Finite element modeling and cutting simulation of Inconel 718
CIRP Ann. – Manuf. Technol.
Cited by (56)
A phenomenological model for plastic flow behavior of rotating band material with a large temperature range
2023, Defence TechnologyCitation Excerpt :The Steinberg-Cochran-Guinan-Lund (SCGL) model was developed for high strain-rate situations firstly [9] and then extended for low strain-rate situations [10]. The hardening/softening laws, revealed by the experimental data, are the main difference between various phenomenological models and determine the application range of these models [11–13]. On the other hand, physically-based models focus on micromechanical mechanisms, and their parameters are more difficult to determine.
Experimental and numerical investigations in the turning of 42CrMo alloy steel
2023, Materials Today: ProceedingsChallenges and issues in continuum modelling of tribology, wear, cutting and other processes involving high-strain rate plastic deformation of metals
2022, Journal of the Mechanical Behavior of Biomedical MaterialsCitation Excerpt :The material model parameters are generally obtained through quasi-static and high dynamic (Split Hopkinson Pressure Bar, Taylor's impact, etc.) tensile, compression, torsion and shear tests at different temperature and strain rates (Banerjee et al., 2014; Ozel and Karpat, 2007; BATRA and KIM, 1990; Batra and Jaber, 2001; Zhan et al., 2014; Wang et al., 2013). Other methodologies include slot milling experiments (Sartkulvanich et al., 2004), parametric optimization (Guo et al., 2006) and inverse modelling approach (Agmell et al., 2014; Amiri et al., 2013) have also been used to determine the material model parameters. The rate-independent plasticity models are based on quasi-static experimental testing methods viz. tension, compression and torsion tests.