Numerical predictions of orthogonal cutting–induced residual stress of super alloy Inconel 718 considering dynamic recrystallization

Over the last few decades, a wide range of nickel alloys has been used in high-temperature industrial sectors to satisfy specific material performance goals for a few structurally and ecologically demanding applications [1]. Its corrosion-resistant capabilities make nickel alloys a welcome choice in high-endurance applications [2]. Corrosion resistance makes nickel-based alloys ideal for nuclear, marine, petrochemical, and other such industrial applications [3]. The heat resistance capabilities of nickel-based alloys also make them useful for other industrial purposes [4]. According to the aforementioned points, a hard turning can be considered as a practical machining process and offers many advantages, including direct machining of the workpiece in the hardened state, greater flexibility and cutting performance, and the elimination of the grinding process [5]. The existing residual stress state of the component may be changed due to mechanical, thermal, or chemical factors [6]. The mechanical factor is the material removal process, the thermal factor is the work done by friction, and the chemical factor is the possible reactions caused by cutting fluids [7]. Mechanical effects and plastic deformations of the machining processes change the surface finish and microstructure [8]. Thermal effects are created by the process, causing a change in the dislocation density and distribution and surface integrity [9]. Besides, pressure and the cooling temperature are essential effects that contribute to the formation of residual stresses [10]. The combination of these effects and other parameters of the machining like phase changing may form cracks on the surface of the component [11]. The cracks are the consequence of residual stresses, which are created because of plastic deformation and phase changes [12]. Phase changes are caused by local heating phenomena. Local heat increases due to friction and other abrasive effects of the machining. Tensile residual stresses are formed partially because of local heating [13]. Machining residual stress origins from thermal and mechanical factors affect the reliability and lifetime of the component [14, 15]. It has been well documented that the changes in cutting speed would change the residual stress depth profiles [16]. M´Saoubi et al. illustrated that the lowest cutting speed leads to the lowest residual stress, while the highest cutting speed can cause a great temperature gradient in the tool and workpiece that produces the highest residual stress on the workpiece [17]. Elsheikh et al. studied the induced residual stress imperfection during the machining operations and its consequence that can lead to lower fatigue life; hence, these phenomena should be analyzed and controlled. The affected layer is generated within the machined surface layer through the cutting process [14]. Hua and Liu illustrated that the cutting conditions such as the cutting edge radius, feed rate, and shape of cutting edge at the finishing operation affect residual stress, surface hardness, and surface roughness [18]. A previous research by Sasahara focused on the interaction of the cutting conditions with the machined surface property to some extent. Besides, the machining conditions’ effect on fatigue life is investigated through several fatigue tests using the specimen finished under various cutting conditions. It is shown that it is possible to get a longer fatigue life for machined parts than the virgin material or the carefully finished material without the affected layer, only by setting the proper cutting conditions. Such a situation was realized when the generated residual stress was small, and the induced surface hardness was high. A longer fatigue life for the machined components can be obtained by applying such cutting conditions as a low feed rate, a small corner radius, and a chamfered innovative tool [19]. Schijve studied the various sources of residual stress present as (i) inhomogeneous plastic deformation, in many cases at notches, (ii) production processes especially cutting process, and (iii) heat treatment [20].

In this research, according to ICME (Integrated Computational Materials Engineering), the development and supply of an innovative microstructure-based modeling approach are studied to predict the residual stresses induced in the machined surface during orthogonal cutting Inconel 718 with a geometrically determined cutting edge. Besides, grain size evolution is investigated by tracking temperature in the process taking advantage of the Johnson–Mehl–Avrami-Kolmogrov (JMAK) model relying on the capabilities of FORTRAN language in developing the user subroutine of VUHARD in the ABAQUS-explicit framework. The paper is organized as follows: Sect. 2 contains the aim and objective of the study. Section 3 includes the numerical approach, consisting of governing equations of the dynamic recrystallization (DRX) concept in material modeling. Section 4 focuses on the finite element (FE) modeling of the orthogonal cutting process using ABAQUS-explicit, which entails the implementation of formulation in the VUHARD user interface subroutine and utilized algorithm. Subsequently, in Sect. 5 the results from the proposed numerical method are presented and the effective input parameters vary to assess the efficiency of the model. In Sect. 6, conclusions are drawn and summarized.

The overall objective of the paper is the development of an innovative microstructure-based modeling approach to predict the residual stresses induced in the machined surface during orthogonal cutting Inconel 718 with a geometrically determined cutting edge. Another target of the current study is to forecast the grain size evolution based on dynamic recrystallization. At present, there is no ready constitutive material model in ABAQUS to explain the effect of DRX and grain size on the residual stress completely and track these features in an in situ process. The nuclear focus of this paper is to develop the constitutive material model that can truly explain the relation of the input variables, such as cutting velocity and depth of cut, to the output parameters such as residual stress, temperature distribution, and grains size evolution. Then the link between the fatigue life of the machined component with the residual stress induced by the cutting process is investigated by keeping track of heat flux and temperature. In line with monitoring, dynamic temperature-displacement analysis is selected to survey the temporal progression in parallel to other parameters related to the displacement, such as various kinds of stress and strain.

To define a suitable material model for Inconel 718, the grain size effect on the material flow stress behavior is included by adding grain size–dependent terms into the traditional JC model [21, 22]. The JMAK model calculates the recrystallized volume fraction and grain size as a function of strain, strain rate, and time. The average grain size is calculated with a rule of the mixture by volume. It is well documented that the traditional model assumes all JC parameters to be constants, which does not consider the recrystallization effect. However, at a higher temperature, the augmented grain size will reduce the flow stress. The Hall–Petch equation describes the relationship between \({A}_{hp}\), \({K}_{hp}\), and \(d\) in Eq. (1).where \(d\) is the average grain size and \({A}_{hp}\) and \({K}_{hp}\) are material constants. Then the modified JC flow stress model can be presented as shown in Eq. (2).where B, C, m, and \(n\) are material constants; \(\varepsilon\) is the plastic strain; \(\dot{\varepsilon }\) is the plastic strain rate; \({\varepsilon }_{0}\) is the reference strain rate, selected to be \(1 {(\mathrm{s}}^{-1})\); \({T}_{m}\) is the melting temperature of Inconel 718; \({T}_{0}\) is the environment temperature; and \(T\) is the temperature of the chip or shear plane. Table 1 represents the parameters for modified JC model parameters for Inconel 718 [23].

As reported by Johansson et al. [24], the machining process could significantly change the workpiece material microstructure. The initial workpiece material consists of equiaxed \(\gamma\) grains with an average grain size of \(5.9 \mathrm{\mu m}\) [25]. The temperature and large strain effect dominate the grain growth in the machining of Inconel 718. To decide on the grain size, the JMAK model [26] is used to describe the DRX process of crystalline material. Based on the assumption that nucleation and grain growth are randomly distributed, the average grain size \(d\) could then be expressed as Eq. (3).where \({d}_{0}\) is the initial average grain size, \({d}_{drex}\) is the dynamically recrystallized average grain size, and \({X}_{drex}\) is the recrystallized volume fraction. When \(\varepsilon\) is larger than a threshold value \({a}_{2}{\varepsilon }_{p}\), the DRX will occur. \({\varepsilon }_{p}\) is the peak strain as Eq. (4).where \(R\) is the gas constant, \({Q}_{act}\) is the activation energy, and \({a}_{1}\), \({h}_{1}\), \({m}_{1}\), and \({c}_{1}\) are material constants. The peak strain parameter for JMAK model is shown in Table 2.

The recrystallized volume fraction is defined with the Avrami equation as Eq. (5).where \({\beta }_{d}\), \({a}_{10}\), and \({k}_{d}\) are material constants (Table 3) and \({\varepsilon }_{0.5}\) is the strain that gives \({X}_{drex}=0.5\), which is calculated as Eq. (6).where \({a}_{5}\), \({h}_{5}\), \({n}_{5}\), \({m}_{5}\), and \({c}_{5}\) are material constants in Table 4.

The dynamically recrystallized average grain size \({d}_{drex}\) is given by Eq. (7).where \({a}_{8}\), \({h}_{8}\), \({n}_{8}\), \({m}_{8}\), and \({c}_{8}\) are material constants in Table 5; the results from \({X}_{drex}\) and \({d}_{drex}\) provide the average grain size in \(d\). Then the modified JC flow stress model in \(\sigma\) is computable. The modified JC flow stress model parameters are obtained from Jafarian et al. [27]. The JMAK model parameters are obtained from Huang et al. [23], Reyes et al. [28], and Loyda [29], as listed in the following tables. The initial grain size \({d}_{0}\) is assumed to be 5.9 \(\mathrm{\mu m}\) from microscopic observation.

In this research, a numerical technique for an orthogonal cutting model with respect to various forces at different cutting conditions is presented using FEM. In the modeling of orthogonal cutting, the VUHARD subroutine runs with 2 different conditions. In one of them, the cutting edge radius is around \(1 \mathrm{\mu m}\), and in the other one, it is around \(70 \mathrm{\mu m}\). The residual stress evolution in the feed direction (x-axis) and in the cutting velocity direction (y-axis) and Mises residual stress are measured at the points of interest \(P1\) to \(P9\) with the fixed location for each run. In Fig. 5, the position of the group of \(P\) points at workpiece is shown. \(P1\) is located at the machined surface, and \(P1\), \(P2\), … and \(P9\) are going into the depth of the workpiece until \(170 \mathrm{\mu m}\). \(P1\) has a \(50 \mathrm{\mu m}\) horizontally distance from the cutting edge of the tool.

This paper is concerned with the challenge of developing a proper material law, which is capable to consider the DRX effect that happens in a high-temperature process. Due to the specific range of temperature in the cutting process, a recrystallization effect may occur. To predict the induced residual stress and DRX, the FE commercial software ABAQUS-explicit is utilized and the VUHARD user subroutine is developed to illustrate the material model in the plastic zone of Inconel 718. To demonstrate the workpiece rim zone modifications, the CEL approach is implemented. Monitoring the residual stress as the main factor influencing fatigue life of machined components and grain size as a crucial parameter in the mechanics of material, it is possible to define a more realistic safety criterion. The grain size effect on the material flow stress behavior is included by adding the grain size–dependent term into the traditional JC model. The JMAK model calculates the recrystallized volume fraction and grain size as a function of strain, strain rate, and temperature. The average grain size is calculated with a rule of the mixture by volume. The proposed model is employed to investigate the effect of the key features of the orthogonal cutting process including cutting velocity, depth of cut, and cutting edge radius on the residual stress and grain evolution, as well as the affected domain. With cutting edge radius \(1 \mathrm{\mu m}\) and cutting velocity \(150 \mathrm{m}/\mathrm{min}\), by changing the chip thicknes values from 0.06 to 0.12 mm, the stress intensity firstly decreases, and then by increasing from \(0.12\) to \(0.2 \mathrm{mm}\), there is an increasing trend in stress intensity. The closer points to the cutting edge lead to an increase in the compressive stress, and the maximum value belongs to the primary shear zone where the stress value is maximum. On the other hand, the effect of changing the cutting edge radius on the residual stress in the feed direction is studied. The results illustrate that for the constant cutting velocity and depth of cut, increasing the cutting edge radius leads to an increase in the residual stress. The grain size varies by changing the cutting speed, so that increasing the cutting velocity induces more temperature evolution, consequently increasing residual stress.

The model provides significant improvement in the calculation of residual stress in machined surfaces to achieve the desired fatigue life and optimize the machining process parameters. Future directions in the scope of the present research can be outlined with a comparative study with JC material modeling to shed the light on the effect of the proposed execution efficiency of the results with the experiment-driven data.