A new value for Johnson Cook damage limit criterion in machining with large negative rake angle as basis for understanding of grinding

Abstract

Grinding is one of the most complex manufacturing processes in industry and understanding its physics is still fairly limited due to the stochastic nature of the process. The physics behind the grinding process can be better understood through thermomechanical analysis of grain-material interactions, enabling the optimization of the process and grinding tool. When simulating the chip formation in machining processes, difficulties arise when the negative rake angle is large, when thermal effects on the tool and workpiece become prominent and when there is the necessity to consider damage within the constitutive equations of the workpiece material. These difficulties become further intensified given small depths of cut as in the case of grinding and the need for three-dimensional models.

A coupled thermomechanical dynamic analysis is performed to simulate linear machining experiments effectuated by single diamond grains. Damage is described within a Johnson-Cook model. The damage parameters when machining Ti-6Al-4 V are optimized in a three dimensional model and a new concept of applying a damage limit when machining with negative rake angle is suggested. Here, a Fortran subroutine is written to calculate the damage field variable. The simulated cutting forces and temperature in the tool as well as the workpiece are validated. Validation experiments are carried out by single grain machining experiments at a depth of cut of 30 $\mu m$ and at a linear cutting velocity of 0.8 m/s. Numerical challenges, such as chip separation criterion and settings of adaptive remeshing are addressed. Finally, it is shown that with an increase in the cutting edge radius, cutting forces and especially passive forces increase.

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.