A new value for Johnson Cook damage limit criterion in machining with large negative rake angle as basis for understanding of grinding
Introduction
Grinding is defined as the machining with geometrically undefined cutting edges and mainly applied to precision machining (DIN, 2003) and finishing. It can achieve high dimensional and geometrical accuracy as well as high material removal rates while also being able to machine hard-to-cut and ultra-hard materials. Diamond grains are distinguished because of its low coefficient of friction, high thermal conductivity and high wear resistivity resulting in prolonged tool lifetimes. Diamond is also used to machine hard-to-cut materials. For instance, researchers like Minton et al. (2013) have proved the importance of using diamond coated tools when turning titanium, in which temperatures reach in upwards of 500 °C given a cutting velocity of 80 m/min, 1 mm depth of cut, feed rate of 0.2 mm/rev and without the use of coolant. The abrasive grains in grinding tools are held within either a monolayer or a consumable layer and normally exhibit a negative rake angle. Understanding the physics of the grinding process is difficult because of its stochastic nature, high cutting speed, high temperature gradients and depth of cuts in the order of micrometers. High performance grinding as well as long service life of the grinding tool can be accomplished by studying the grinding characteristics such as grain-material interaction and grinding forces. To lay the basis for the stochastic description of the grinding tool and to reduce the complexity of the physics of the process, one can set sights on a single grain. For example, Akbari et al. (2012) analyzed the residual stresses of diamonds induced after brazing for monolayer grinding tools. In the present paper, the interaction between single grains with a workpiece material is studied.
Owing to its excellent mechanical properties especially at elevated temperatures, high temperature alloys are often difficult to machine and optimal processing parameters have yet to be defined. Thermal residual stresses due to temperature gradients between the machined surface and bulk material arise during the grinding process. When the plastically deformed surface layer cools, Cotell et al. (1994) explained that the shrinkage of the surface is hindered by the bulk material generating tensile residual stresses. Reducing the thermal residual stress in the processed subsurface, which adds to the mechanical residual stress, is of great concern in industrial applications. The high temperature that is generated due to frictional heating and plastic deformation during grinding is the primary source of defects on the processed surface. As mentioned by Brinksmeier et al. (1982); Jackson and Hitchiner (2013), transient temperature gradients contributes to residual stresses and micro cracking on ground surfaces. Sauvage et al. (2003); Skorupski et al. (2013) also showed that the localized temperature in the case of thin workpiece features can cause warping or even induce material phase transformations.
Excessive heat accumulation at the boundary between the grain and workpiece accelerates the wear of cutting edges and consequently leads to inefficient machining. This in turn leads to further input of heat to the grinding zone and causes greater damage to the tool and workpiece. Moreover, high temperatures increase the risk of grain pullout due to fracture, wear or chipping. Thus, by controlling the cutting temperature, the service life of the tool and productivity increases. Through the thermal analysis of the machining processes, the source of heat flux plays a key role. Most authors considered a uniform heat flux (Chang, 2007, Liu et al., 2009, Liu and Chou, 2007, Umbrello et al., 2007), while a select few considered a non-uniform heat flux in the rake face, e.g. (Haddag et al., 2013), to calculate the temperature distribution. Unlike previous numerical studies, the present model calculates the heat flux in a coupled thermomechanical analysis by considering both frictional heat and heat generated due to workpiece surface deformation. Since frictional heat is considered, flash temperature can also be studied. As mentioned in Blau (1992), Blok (1963), the flash temperature is localized at areas of contact where frictional heat dissipation occurs. The duration of the flash temperature is often in the order of microseconds, which is typically the interaction time of each single grain during the grinding process. Experimentally detecting the flash temperature is difficult. Furthermore, numerical modelling of the flash temperature, owing to extreme gradients and the unknown heat flux coupled between the workpiece and the grain, is not easy.
Finite element analysis (FEA) allows for a better understanding of grain-material interactions during single grain test. Subsequently, bond failure can be predicted and the causes thereof can be revealed. Also, the vectors of critical forces at the contact zone can be determined so that the orientation and shape of the grains can be optimized and accordingly, the grinding tool can then be appropriately engineered. In the following, common methods used to analyze machining processes are mentioned. As reported in Schermann et al. (2006), when using extensive mass scaling and an explicit time integration scheme to reduce the computation time, unrealistic cutting forces were calculated. Thermal modelling of surface grinding was carried out by Mamalis et al. (2003) using implicit time integration. Furthermore, implicit time integration was also used by Lohkamp et al. (2012) for micromachining of titanium with the consideration of crystal plasticity. According to Aurich et al. (2009), the simulation of burr formation can also be carried out by the implicit time integration scheme. In the present study, to simulate grain-material interactions in single grain machining experiments, the implicit time integration scheme is selected. This is to ensure a stable solution during chip formation and to avoid unrealistic results.
The kinematics of chip formation and deformation in the grinding process can be explained by Lagrangian, Eulerian, Arbitrary Lagrangian-Eulerian (ALE) adaptive meshing and a Coupled Eulerian-Lagrangian (CEL) formulation. The ALE is a general formulation in which the FE mesh is neither attached to the material nor fixed in the space. Instead, as (Movahhedy et al., 2002) have shown, it may have an independent and arbitrary motion which can be prescribed by the analyst. Therefore, ALE can model the large deformations by allowing the mesh to move independently of the material. Since ALE does not alter the topology of the elements and their connectivity, it implies some limitations of this method to maintain a high-quality mesh under severe deformation scenarios. Movahhedy et al. (2000) used ALE to simulate the machining of steel and was mainly used to study local effects at the cutting zone. It was shown that ALE has problems with 3D simulations and complex models. Another approach to prescribe mesh separation is to define a damage layer between the chip and workpiece. Then during the machining process, the damage layer or in other words the sacrificial layer with help of element deletion is removed and the chip and the workpiece separate from one another. For instance Hokka et al. (2012) simulated in 2D, serrated chip formation when machining a titanium alloy with this technique. This method, however, is unable to model the spring back of the workpiece after machining. Furthermore, since defining the exact location of the damage layer in 3D models and especially in single grain machining simulations is difficult, this approach is not implemented in the present study. Another appropriate method which is used in the present study is using remeshing; an early basic algorithm of which is explained in Tezuka (1992) and in more detail in Section 3.2. With help of a similar adaptive remeshing algorithm, and by implementing a user-defined subroutine, coupled thermomechanical chip formation in 2D is possible and has been demonstrated successfully using explicit time integration in Issa et al. (2011)
To validate the simulation results, some state variables or quantities that are important in the machining process are compared. In the following, reasons for selecting those state variables are discussed. In machining processes, large negative rake angles typically lead to higher cutting forces. As shown by Aurich and Dornfeld (2010), machining with large negative rake angles induces high compressive loads and subsequently generates high temperatures. In addition, Karpuschewski and Binh (2007) showed that, with larger chip thickness at constant cutting velocities higher cutting forces occur while for constant chip thickness the higher velocities reduces the cutting forces. Therefore, the state variables that are validated in the present study are cutting forces, normal force, passive force and temperature. Discontinuous chips which typical characterize a grinding process can be easily removed from the grain-surface interaction zone. This helps reduce tool wear and improves process performance by carrying heat away from the interaction zone. Therefore, it is important to understand the morphology of the chips and the ground surface during the grinding process. As proved by Karpuschewski et al. (2013); Wyen and Wegener (2010), the cutting edge radius greatly influences cutting forces. Therefore, in the present study, the influence of cutting edge radius on cutting forces is also investigated. In the present paper, a dynamic coupled thermomechanical finite element method with an implicit time integration scheme and updated Lagrangian description is used. It is intended to simulate 3D micromachining given large negative rake angles in 3D while considering a user-defined damage constitutive law at the workpiece.
Section snippets
Experimental setup
General purpose grinding tools have many abrasive grains which are distributed stochastically. In monolayer grinding tools, to improve the topography of the ground workpiece and optimize the grinding process, so called engineered grinding tools (EGTs) can be used which exhibit a defined grain pattern. Studying the interaction of single grains with the workpiece helps to understand the grinding process and the grinding tool design of EGTs. Some of these evaluations can be found in Anderson et
Coupled-thermomechanical finite element analysis
Three-dimensional simulations of the grinding process, interaction of several grains and their influence on surface roughness, temperature gradient and the distribution of the full residual stress tensor in the ground material can all be analyzed in a 3D model. Large temperature changes within the workpiece and high temperatures in the tool are expected during machining. The change of temperature, changes the material properties, which should be taken into account in mechanical analysis.
Comparison of simulation and experiment
In the simulation, a Ti-6Al-4 V workpiece with a length of greater than 3 mm is cut by a diamond exhibiting a 0.27 mm cutting edge length. The simulation time is derived from the length of the workpiece over the cutting speed. Cutting forces reach steady state after full penetration of the brazed diamond cutting tool into the workpiece and after a 0.5 mm length of cut, the results are plotted. The main objective of the optimization is the cutting force according to the design variables of the
Influence of cutting edge radius
It is proved experimentally by Wyen and Wegener (2010) that cutting forces reduce for sharper cutting edges. Therefore, the behavior of the code from a theoretically very sharp cutting edge radius of 0 μm to a very large cutting radius of 20 μm is investigated. In this analysis, the cutting speed, depth of cut and clearance angle, are set to 0.8 m/s, 30 μm and 0°, respectively. The sensitivity of the cutting forces for two different cutting edge radii is presented in Fig. 9. In addition, the
Conclusions
Grinding processes will only damage the surface integrity, if improper parameters are used i.e. dull tools, too high feed rates, large depth of cut, improper coolant, lubrication, or incorrect grinding tool hardness. To design a tool, optimize the process parameters or understand the physics of grinding, single grain machining tests can be used. When simulating the machining processing with large negative rake angles, the tool has the tendency to plough the workpiece material instead of forming
Acknowledgements
The authors would like to thank the Swiss National Science Foundation for the financial support under project number 200021–117847, the High Performance Computing Center of ETHZ, support from the Electron Microscopy Centre EMEZ of ETHZ, Jens Boos, Prof. Pavel Hora, Dr. Fredy Kuster and Dr. Josef Mayr.
References (59)
- et al.
Thermomechanical analysis of residual stresses in brazed diamond metal joints using Raman spectroscopy and finite element simulation
Mech. Mater.
(2012) - et al.
Experimental and numerical investigations of single abrasive-grain cutting
Int. J. Mach. Tools Manuf.
(2011) - et al.
3D finite element modelling of segmented chip formation
CIRP Ann.—Manuf. Technol.
(2006) - et al.
Burrs—analysis, control and removal
CIRP Ann.—Manuf. Technol.
(2009) The flash temperature concept
Wear
(1963)- et al.
Residual stresses—measurement and causes in machining processes
CIRP Ann.—Manuf. Technol.
(1982) - et al.
Chip formation mechanisms in grinding at low speeds
CIRP Ann.—Manuf. Technol.
(2003) Prediction of the cutting temperatures of stainless steel with chamfered main cutting edge tools
J. Mater. Process. Technol.
(2007)Effect of the elasticity formulation in finite strain on springback prediction
Comput. Struct.
(2010)- et al.
A family of single-step Houbolt time integration algorithms for structural dynamics
Comput. Methods Appl. Mech. Eng.
(1994)
On the measurement of temperature in material removal processes
CIRP Ann. —Manuf. Technol.
Characterization and numerical modeling of high strain rate mechanical behavior of Ti-15-3 alloy for machining simulations
Mater. Sci. Eng.
On the mechanics of the grinding process—Part I: stochastic nature of the grinding process
Int. J. Mach. Tools Manuf.
Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures
Eng. Fract. Mech.
Influence of tool edge preparation on performance of ceramic tool inserts when hard turning
J. Mater. Process. Technol.
Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys
Int. J. Plast.
Framework of grinding process modeling and simulation based on microscopic interaction analysis
Rob. Comput. Integr. Manuf.
Effect of grain shape on cutting force in superabrasive single-grit tests
CIRP Ann.—Manuf. Technol.
Temperature of internally-cooled diamond-coated tools for dry-cutting titanium
Int. J. Mach. Tools Manuf.
Adaptive mesh refinement in strain localization problems
Comput. Methods Appl. Mech. Eng.
Transfer operators for evolving meshes in small strain elasto-placticity
Comput. Methods Appl. Mech. Eng.
Phase transformations in surface layers of machined steels investigated by X-ray diffraction and Mössbauer spectrometry
Mater. Sci. Eng.: A
Adaptive remeshing process with quadrangular finite elements
Adv. Eng. Softw.
On the effectiveness of finite element simulation of orthogonal cutting with particular reference to temperature prediction
J. Mater. Process. Technol.
Hardness-based flow stress for numerical simulation of hard machining AISI H13 tool steel
J. Mater. Process. Technol.
Influence of cutting edge radius on cutting forces in machining titanium
CIRP Ann.—Manuf. Technol.
Comparison of transparent objects metrology through diamond cutting edge radii measurements
CIRP J. Manuf. Sci. Technol.
Burrs—Analysis, Control and Removal
Cited by (34)
Thermo-mechanical finite element analysis of the solid-state metal deposition via lateral friction surfacing
2024, CIRP Journal of Manufacturing Science and TechnologyDistribution estimation of Johnson-Cook parameters considering correlation in quasi-static state
2023, International Journal of Mechanical SciencesCitation Excerpt :Since the J-C model independently expresses the effects of strain rate and temperature, the coupling effect of the two variables cannot be considered in the high strain rate range where dislocation is the dominant mode of material deformation [26,27]. To overcome this drawback, researchers have proposed the modified J-C constitutive model that considers the coupling effect [28,29], the Zerilli-Armstrong (Z-A) constitutive model based on dislocation dynamics rather than a phenomenological approach [30], and the combined JC-ZA constitutive model that combines the J-C and Z-A models to complement the complex coupling effect between two variables [31,32]. Fortunately, in the quasi-static regime (0.1∼0.0001[/s]) that is the focus in this paper, the coupling effect between two variables and the inertia effect of the coupon could be ignored, and the J-C model parameters were determined by fitting the stress-strain response of the uniaxial tensile test with a conventional cross-head device to the J-C model [33–35].
Influence of contact force and rubber wheel hardness on material removal in abrasive belt grinding investigated by physical simulator
2022, Precision EngineeringCitation Excerpt :Doman et al. [21] reviewed the initial finite element grinding model and pointed out that the refinement of the abrasive grain-workpiece contact and the experimental verification of the model should be the direction of efforts. Akbari et al. [22] guided the selection of grinding parameters and grain shape using a single grain finite element model. Wang et al. [23] used a single grain finite element model to study the stress field in grinding process.
Study on shear fracture performance of subsea test tree under emergency conditions in the deepwater oil and gas completion testing
2022, Journal of Petroleum Science and EngineeringCitation Excerpt :The selected ball valve model outer diameter D1 is 243 mm, the ball valve through-hole diameter d1 is 162 mm, and the coiled tubing outer diameter D2 is 50.8 mm. The Johnson-cook damage criterion and constitutive equation are used in the damage calculation model of coiled tubing, and the shear failure fracture criterion is used (Akbari et al., 2016). In the analysis of coiled tubing, the hexahedral mesh is used in the coiled tubing mesh (Kim and Kim, 2021).