Experimental characterization and finite element modeling of the residual stresses in laser-assisted mechanical micromachining of Inconel 625

Abstract

Laser-assisted mechanical micromachining offers the ability to machine difficult-to-cut materials, like superalloys and ceramics, more efficiently and economically by laser-induced localized thermal softening prior to cutting. Laser-assisted mechanical micromachining is a micromachining process with localized laser heating which could affect the cutting forces and the machined surface integrity. The residual stresses obtained in the laser-assisted mechanical micromachining process depend on both mechanical loading and the laser heating. This article focuses on the experimental process characterization and prediction of the cutting forces and the residual stresses in a laser-assisted mechanical micromachining–based orthogonal machining of Inconel 625. The results show that the laser assistance reduces the mean cutting forces by ∼25% and enhances the normal compressive residual stress at the surface by ∼50%. Since microscale residual stress measurement is very time-intensive, a coupled-field thermo-mechanical finite element model of laser-assisted mechanical micromachining has been developed to predict the temperature, cutting forces and the residual stresses. The cutting forces and residual stresses’ predictions are in good agreement with the measured values during machining. In addition, parametric simulations have been carried out for laser power, cutting speed, cutting edge radius, rake angle, laser location and laser beam diameter to study their effect on cutting forces and surface residual stresses.

Introduction

Many researchers have reported that laser-assisted machining (LAM) has an edge over conventional machining methods due to various advantages, which include lower cutting force at higher cutting speed, low specific cutting energy, smooth surface finish, less tool wear and increased compressive surface residual stress. Figure 1 shows a schematic of LAM. The laser source moving at a specified scan rate over a workpiece is followed by a conventional cutting tool. This moving laser heat source heats the surface layer of the workpiece prior to cutting thereby reducing material flow stresses and in turn the cutting forces. ¹

Figure 1.

Schematic presentation of laser-assisted machining.

LAM at the macroscale has been investigated for processing hard-to-machine ceramics and composites. Lei et al.^2,3 studied the mechanisms of material removal, chip morphology, shear zone stress distribution and tool wear during LAM of silicon nitride (Si₃N₄). Rozzi et al. ⁴ experimentally investigated surface quality, chip morphology and tool wear in laser-assisted turning of Si₃N₄ ceramics. Rebro et al. ⁵ experimentally found the optimum machining condition for LAM of reaction sintered mullite ceramics. Pfefferkorn et al. ⁶ investigated the LAM process on partially stabilized zirconia and observed improved tool life, lower specific cutting energy and higher material removal rate with laser assistance. Dandekar et al. ⁷ found that tool life improved by 1.7 times and the overall machining cost reduced by 40% during LAM of titanium alloy (Ti–6Al–4V). LAM has been reported for tool steels with 100% improvement of tool life and less machining chatter by Dumitrescu et al. ⁸ Skvarenina and Shin ⁹ show 5% and 60% improvement in surface roughness and tool life in laser-assisted turning of compacted graphite iron, respectively. Ding and Shin ¹⁰ found that the residual stress becomes more compressive in both the hoop and axial directions in laser-assisted turning of hardened steel. Wang et al. ¹¹ found that laser-assisted hot machining is an effective technique to machine Al₂O₃p/Al composites as it reduces machining forces by 50% and increases compressive residual stresses of the machined surface along with improved tool life.

As compared with LAM at macroscale, relatively fewer studies have been reported on LAM at the microscale. Laser-assisted mechanical micromachining (LAMM) has been reported by Singh and Melkote ¹² and Singh et al. ¹³ They developed a finite element (FE) model to characterize and predict the heat-affected zone (HAZ) in LAMM. Melkote et al. ¹⁴ reported that laser-assisted micro-milling resulted in reduced tool wear and better dimensional accuracy of the machined feature.

Surface integrity, especially, residual stress in orthogonal machining, has been extensively studied via FE models. Outeiro et al. ¹⁵ experimentally and numerically analyze the residual stresses during machining. Umbrello et al. ¹⁶ numerically modeled the residual stresses in conventional hard turning process incorporating the microstructure alteration. However, limited FE modeling studies have been reported in the literature on LAM/LAMM process. Tian and Shin ¹⁷ developed a multiscale FE model to simulate the chip formation and crack propagation in LAM of multiphase Si₃N₄. Shi et al. ¹⁸ and Singh et al. ¹⁹ developed a three-dimensional (3D) FE model for LAM for Inconel-718 and D2 tool steel, respectively.

Although high-power CO₂ and Nd:YAG lasers have been successfully used for laser-assisted turning by Tian and Shin ¹⁷ and Shi et al., ¹⁸ but limited work has been reported with fiber lasers. Excellent beam quality (M² < 1.1), longer maintenance-free service life, excellent wall plug efficiency and portability have made fiber laser an ideal competitor for Nd:YAG systems. Due to excellent M², smaller spot size is achievable and it requires less power for same result in comparison with Nd:YAG system. The wall plug efficiency of fiber laser is 35% as opposed to 5%–10% in case of Nd:YAG. These qualities have made fiber laser a suitable candidate for material processing application. The residual stresses have been studied experimentally at the macroscale LAM, but the residual stresses in LAMM have yet to be characterized. On the modeling front, most of the work reported on FE modeling of LAM/LAMM has been limited to the thermal softening effect and chip geometry,^13,17–19 and little to no work has been reported on the modeling of residual stresses. The residual stresses induced in the LAMM originate from the complex thermo-mechanical loading which needs to be better understood.

Inconel 625 has high corrosion-fatigue strength; good resistance to chloride-ion stress-corrosion cracking; high tensile, creep and rupture strengths; high allowable design strength at elevated temperatures (649 °C–760 °C); outstanding fatigue and thermal-fatigue strengths; very good oxidation resistance and excellent weldability. These properties make it a good candidate for sea-water applications, in aerospace and chemical processing industries and in nuclear water reactors. But the presence of nickel and chromium in its composition makes it very difficult to machine. This article presents a detailed experimental characterization of LAMM of Inconel 625. The cutting forces, surface roughness, temperature rise and the surface residual stress were studied. Note that the residual stress determination for small spot sizes is resource intensive and can take few hours for each measurement. Consequently, an experimental design with fewer runs is used to study the process and validate a coupled thermo-mechanical FE model of LAMM process which has been developed for predicting the cutting forces, temperatures and residual stresses. This model has been used to study the residual stresses obtained for different process conditions.

Experimental work

The experiments were conducted to characterize the residual stresses, surface roughness and the cutting forces in LAMM of Inconel 625. The nominal chemical composition of Inconel 625 is shown in Table 1.

Table 1.

Percentage chemical composition of Inconel 625.

Ni	Cr	Fe	Mo	Nb	Mn	Al	Others
57	21.9	7.9	4.6	1.2	0.001	2.7	4.7

Experimental setup

Schematic diagram of the LAMM setup is shown in Figure 2(a) and a picture of actual setup is shown in Figure 2(b). A 100-W continuous wave fiber laser has been used to investigate LAMM of Inconel 625. Specially designed optics has been used to control the laser beam. The experimental setup contains a tooling system and laser optics consisting of laser collimator, beam shaper, focusing lens and finally a magnifying lens on a translation stage in a cage system for proper alignment. The beam shaper is a diffractive optical element which converts the Gaussian beam to uniform beam at the focal plane. The magnifying lens can be translated on the cage to obtain the desired beam size which, in turn, varies the power density. This special optics is capable to generate 200–900 µm laser beam with Gaussian or uniform beam using a combination of beam shaper and magnifying lens.

Figure 2.

(a) Schematic of LAMM setup and (b) LAMM setup in operation.

An external power and pulse modulator unit has been interfaced with the laser to modulate the output power of laser, ranging from 10 to 100 W. The SPI-Fiber laser (model no. SP-100C-0020) with 1064 nm wavelength has been used in this experiment. The complete setup is mounted on a three-axis computer numerical control (CNC) micro-milling machine (MikroTools^®) (see Figure 2(b)) by replacing its spindle by a workpiece holder. The tool is mounted on a tool holder in front of the laser optics. The positioning resolution of the micro-milling machine is 0.1 µm and the accuracy is ±1 µm. TiAlN-coated tungsten carbide (WC) THINBIT^® grooving tool was used in this study.

Design of experiments

Selection of the proper conditions and the levels for each condition is important to understand the significance of each cutting condition and its impact on the residual stress distribution, cutting forces and surface roughness. The smaller spot size used for X-ray diffraction takes inordinately long time which restricts the number of physical experiments that can be carried out. Hence, a two-level three-factor full-factorial design of experiments with two replications for each run was used. Three parameters with two levels, namely, speed, uncut chip thickness, and laser power used in the experiments are mentioned in Table 2. The width of cut was kept fixed at 600 µm and the length of cut was 10 mm. The tool cutting edge–laser beam distance and laser beam diameter were both kept constant at 400 µm.

Table 2.

Experimental conditions.

Parameters	Level 1	Level 2
Uncut chip thickness (µm)	15	25
Speed (mm/min)	30	60
Laser power (W)	0	12

Experimental procedure

The distance between the tool and the laser beam was determined by putting on the target laser beam and measuring the location of the burnt spot relative to the tool cutting edge using a digital microscope (ProScope). If the spot was not at the required position, the laser optics assembly was translated by X–Z stage until the desired location was achieved. A miniature grooving tool (LGT027D2RE, 0.6858 mm wide and 0.005 mm nose radius) was mounted on a three-component dynamometer (Kistler Minidyne^® 9256C2). The uncut chip thickness was set by moving the tool towards the workpiece by Y stage while the cutting velocity was imparted by moving it along the X-axis. To ensure that the tool wear does not affect the results, a fresh tool was used in each experimental run. After all the experiments were conducted, surface roughness of the machined surface was measured by a white light interferometer (WYKO NT9100) and surface residual stress was measured by X-ray diffractometer (PANalytical X’pert PRO MRD). Multiple angle sin²ψ technique was used by varying ψ angle from −40° to 40° and diffraction peak was located for each ψ tilt angle. X-ray parameters used in this study are as follows: X-ray radiation—KAlpha, strain-free d-spacing—2.07286 Å and strain-free sin² (ψ)—0.400. A spot size of <500 µm has been used for measurement of the surface residual stresses.

Experimental results and discussions

Effect of process parameters on cutting forces

To predict the effect of the process parameters on the cutting forces, an analysis of variance (ANOVA) was carried out on the experimental force data. The ANOVA results showed that the effects of uncut chip thickness, cutting speed and laser power were statistically significant at a risk level (α) of 5% for both cutting and thrust forces. Furthermore, the second-order interaction effects of uncut chip thickness and cutting speed and cutting speed and laser power were also found to be statistically significant for the cutting and thrust forces.

The main effect plots obtained from the analysis of means (ANOMs) are shown in Figure 3. It can be seen from Figure 3(a) that the increase in the laser power from 0 to 12 W results in a reduction of 25% and 23% in the mean cutting and thrust forces, respectively. Consequently, it can be inferred that the laser heating is inducing thermal softening which results in lower cutting and thrust forces.

Figure 3.

Main effect plot for cutting force and thrust force: (a) laser power (W), (b) cutting speed (mm/min) and (c) uncut chip thickness (µm).

Figure 4(a) and (b) shows the average and the standard deviation of the cutting and thrust forces for both conventional machining and LAMM for all cutting conditions. The material removal at higher temperatures with laser results in lower cutting forces due to reduced material flow stresses. A reduction of 16%–48% in cutting forces is observed in LAMM as compared to conventional machining. The thrust forces exhibit a reduction of 8%–26% with laser assistance.

Figure 4.

Comparison of cutting forces in conventional and LAMM: (a) 15 µm and (b) 25 µm uncut chip thickness.

The ANOM further shows that there is a ∼33% increase in the mean cutting and thrust forces if the cutting speed increases from 30 to 60 mm/min as shown in Figure 3(b). Figure 4(a) shows a significant increase in the cutting and thrust forces for both conventional machining and LAMM with an increase in the cutting speed at 15 µm uncut chip thickness. The cutting forces increase by 42% and 74% in conventional and LAMM, respectively, if the cutting speed increases from 30 to 60 mm/min. At 25 µm uncut chip thickness, the increase in cutting forces for conventional machining and LAMM is limited to 10% and 20%, respectively, if the speed is increased from 30 to 60 mm/min. Note that the effect of cutting speed is more pronounced at the smaller uncut chip thickness. The phenomenon responsible for the increase in forces is different in conventional machining and LAMM. In conventional machining, the increase in forces is due to strain rate hardening which is more pronounced in plowing-dominated mechanism^10,20 experienced at smaller uncut chip thicknesses. On the other hand in the LAMM, the temperature rises in the workpiece during laser heating. The higher the cutting speed, the lower the temperature rise in the workpiece due to insufficient time for heat conduction. This could result in lower thermal softening at higher cutting speeds. The ANOM results further show a 58% increase in mean cutting force and a 49% increase in mean thrust force due to the change in uncut chip thickness from 15 to 25 µm (see Figure 3(c)).

Effect of process parameters on surface roughness

The ANOVA results on the surface roughness data show that laser power, cutting speed and uncut chip thickness are statistically significant factors at a risk level (α) of 5%. The two-way interaction effect of laser power and uncut chip thickness is found to be statistically significant.

LAMM was found to have slightly increased the surface roughness, R_a, in most cases. In general, an increase in R_a in LAMM could be the result of thermal softening of the workpiece which can result in burr formation and plastic deformation.^12,21 The main effect plots obtained from the ANOM are shown in Figure 5. The ANOM results show that with the increase in laser power from 0 to 12 W, the roughness increases by 23%. The surface roughness increases by 18% when the cutting speed is increased from 30 to 60 mm/min due to the increased tearing of the material. The surface roughness decreases by 8% if the uncut chip thickness is increased from 15 to 25 µm. The lower uncut chip thickness (15 µm) is just three times the edge radius (∼5 µm) which can induce plastic flow of the material due to increased plowing at smaller chip thickness. At higher uncut chip thickness, the cutting is shearing-dominated and plowing-induced plastic deformation is absent which could result in better surface finish. Figure 6 shows a typical profile of the machined surface acquired from the WYKO NT9100^® white light interferometer for both conventional and LAMM. The R_a value increases from 0.74 µm in conventional machining to 0.9 µm in LAMM (Figure 5).

Figure 5.

Main effect plot for average surface roughness (R_a): (a) laser power (W), (b) cutting speed (mm/min) and (c) uncut chip thickness (µm).

Figure 6.

Surface profile: (a) conventional and (b) LAMM (25 µm uncut chip thickness and 30 mm/min cutting speed).

Effect of process parameters on surface residual stresses

The main effect plots obtained from the ANOM are shown in Figure 7. It shows that an increase in the laser power from 0 to 12 W results in a reduction of 42% and 49% in the mean surface residual stress in the cutting and thrust directions, respectively. There is an increase of 62% and 12% in the mean surface residual stress in thrust and cutting directions, respectively, if the cutting speed increases from 30 to 60 mm/min. A decrease of 35% in the mean surface residual stress is observed in the cutting direction if the uncut chip thickness is increased from 15 to 25 µm.

Figure 7.

Main effect plot for surface residual stress in thrust and cutting directions: (a) laser power (W), (b) cutting speed (mm/min) and (c) uncut chip thickness (µm).

Figure 8 shows the average and standard deviation of the surface residual stress in LAMM compared to conventional machining in the thrust and cutting directions. Figure 8(a) shows that the compressive residual stresses exhibit an increase of 14%–34% in LAMM as compared to conventional machining. Figure 8(b) shows that the residual stresses in the cutting direction are tensile in nature. However, the laser heating reduces the tensile residual stress by 47%–73%. A steep thermal gradient exists through the thickness during the laser heating. ¹ The top layer gets heated while the substrate is still relatively cold which restrains the material flow in the surface layer. The higher temperature surface region experiences compressive plastic strain which does not recover on cooling. This phenomenon could explain the increased compressive residual stresses in the normal direction and reduced tensile stresses in the cutting direction with laser assistance.

Figure 8.

Residual stress condition in conventional machining and LAMM: (a) thrust direction and (b) cutting direction.

At smaller uncut chip thicknesses, the plastic stresses may be higher than the larger uncut chip thicknesses, even though the cutting forces are lower because their undeformed chip area is much smaller. The higher plastic stresses can explain the higher residual stress at smaller uncut chip thicknesses.

FE model of LAMM process

DEFORM 3D^®-V 6.1 has been used in simulation of the orthogonal machining of Inconel 625. The thermal model for determining the temperature distribution in the workpiece due to laser heating is based on a 3D transient heat conduction analysis of a moving uniform heat source applied to the workpiece surface.

Governing equation

The 3D transient heat conduction equation for the thermal problem is given by

$$\begin{array}{c}\frac{\partial }{\partial \mathrm{x}}\left(\mathrm{k}\frac{\partial \mathrm{T}}{\partial \mathrm{x}}\right)+\frac{\partial }{\partial \mathrm{y}}\left(\mathrm{k}\frac{\partial \mathrm{T}}{\partial \mathrm{y}}\right)+\frac{\partial }{\partial \mathrm{z}}\left(\mathrm{k}\frac{\partial \mathrm{T}}{\partial \mathrm{z}}\right)+\stackrel{·}{\mathrm{Q}}\hfill \\ =\mathrm{\rho }{\mathrm{c}}_{\mathrm{p}}\frac{\partial \mathrm{T}}{\partial \mathrm{t}}+\mathrm{\rho }{\mathrm{c}}_{\mathrm{p}}{\mathrm{V}}_{\mathrm{x}}\frac{\partial \mathrm{T}}{\partial \mathrm{x}}\hfill \end{array}$$

(1)

where ρ, c_p, k, $\stackrel{·}{\mathrm{Q}}$ and V_x are the density, specific heat, thermal conductivity, rate of volumetric heat generation and laser scan speed, respectively. Note that all the thermo-physical properties are considered to be temperature dependent as shown in Table 3. ²²

Table 3.

Temperature-dependent thermo-physical properties of Inconel 625 as used in Deform^® simulations. ²²

Temperature (°C)	Volume-specific heat (ρcp) (N/mm2/°C)	Thermal conductivity (k) (N/s/°C)	Thermal expansion coefficient (α) (/°C) × 10−6
20	3.46	9.8	12.8
93	3.60	10.8	12.8
204	3.85	12.5	13.1
316	4.06	14.1	13.3
427	4.31	15.7	13.7
538	4.52	17.5	14.0
649	4.77	19	14.8
760	4.98	20.8	15.3
871	5.23	22.8	15.8
927	−	−	16.2
982	5.44	25.2	−
1093	5.65	−	−

Material model

Johnson–Cook constitutive material model has been used to depict the flow stress of Inconel 625 as a function of strain, strain rate and temperature in this article which is given by

$$\begin{array}{c}\multicolumn{1}{c}{\overline{\sigma }=[\mathrm{A}+\mathrm{B}(\mathrm{\epsilon }{)}^{\mathrm{n}}][1+\mathrm{C\; ln}\left(\frac{\stackrel{·}{\overline{\epsilon }}}{{\stackrel{·}{\epsilon }}_0}\right)]}\\ [1-{\left(\frac{\mathrm{T}-{\mathrm{T}}_{\mathrm{room}}}{{\mathrm{T}}_{\mathrm{melt}}-{\mathrm{T}}_{\mathrm{room}}}\right)}^{\mathrm{m}}]\hfill \end{array}$$

(2)

The values of Johnson–Cook constants for Inconel 625 given by Flis and Scott are as follows: ²³ A = 400 MPa, B = 1798 MPa, C = 0.031, n = 0.91, m = 1 and T_m = 1300 °C.

Friction modeling at tool–chip interface

The friction at the workpiece–tool interface is considered to be hybrid in nature, that is, a combination of sliding and sticking friction. The sticking friction occurs in the area near the tool tip where the pressure is very high. The frictional shearing stress, τ_int, is equal to the average shear flow stress at tool–chip interface in the chip, k_chip

$${\tau }_{\mathrm{int}}(\mathrm{x})={\mathrm{k}}_{\mathrm{chip}},0<\mathrm{x}⩽{\mathrm{l}}_{\mathrm{p}}$$

(3)

where ${\mathrm{l}}_{\mathrm{p}}$ is the distance from the tool tip where ${\mu }_{\mathrm{e}}{\sigma }_{\mathrm{N}}(\mathrm{x})={\mathrm{k}}_{\mathrm{chip}}$ and ${\sigma }_{\mathrm{N}}(\mathrm{x})$ is the normal stress at given distance, x, from the tool tip.

The sliding friction acts in the remaining contact area where the frictional stresses are proportion to the normal stresses

$${\tau }_{\mathrm{int}}(\mathrm{x})={\mathrm{\mu }}_{\mathrm{e}}{\sigma }_{\mathrm{N}}(\mathrm{x}),{\mathrm{l}}_{\mathrm{p}}<\mathrm{x}⩽{\mathrm{l}}_{\mathrm{c}}$$

(4)

where ${\mathrm{\mu }}_{\mathrm{e}}$ is the coefficient of friction = 0.7 and l_c is the tool–chip contact length. The convective heat transfer coefficient at chip–tool interface is considered to be very high (100 kW/m² °C) as used in previous studies.^15,18,19

Numerical formulation, loading and boundary conditions

The workpiece is considered as elasto-plastic and meshed with 89,762 tetrahedral elements, while the tool, modeled as rigid, is meshed with 8024 elements. A refined mesh is used near the tool–workpiece interaction and heat flux incidence regions. As DEFORM 3D has the property of automatic remeshing, the distortion of the chip is automatically taken into account by remeshing the highly distorted elements. This is required to capture the steep temperature gradients and internal stress conditions as accurately as possible. The orthogonal cutting is modeled as translational cutting performed over a 7 mm × 2 mm × 0.6 mm workpiece over a distance of 5 mm. A solid model of the cutting tool used in the experiments has been created in SolidWorks^® and imported in Deform^®.

The workpiece is kept stationary while the tool is moving with the cutting velocity. The velocity of the bottom nodes is kept constrained in Z-direction. Again the velocity of the front nodes as seen from the cutting direction is constrained in X-direction. The initial condition at time t = 0 is given as

$$\mathrm{T}(\mathrm{x},\mathrm{y},\mathrm{z},0)={\mathrm{T}}_0$$

(5)

The ambient temperature T₀ = 25 °C and the convection coefficient from all the surfaces of the workpiece to environment is kept constant as 4.5 kW/m² °C. ¹⁸ To simulate the LAM process, the laser heat source needs to be modeled and calibrated. In DEFORM 3D, a heat exchange window is available to define heat exchange in a local area, as shown in Figure 9. The diameter of the cylindrical window is equal to that of laser beam. Through heat convection, the surface of the workpiece is heated to a temperature, T_wp. The heat flux in this heat exchange process can be expressed by

$$\mathrm{Q}=\mathrm{hA}({\mathrm{T}}_{\mathrm{wd}}-{\mathrm{T}}_{\mathrm{wp}})$$

(6)

where A is the area of the laser spot, h is the convection coefficient and T_wd is the temperature of the window.

Figure 9.

Laser heat source model and boundary conditions.

In the LAM tests, due to the reflection from the workpiece surface, the energy of the laser beam is only partly absorbed by the workpiece. The ratio of the energy absorption is defined by the material absorptivity. Therefore, the heat flux expressed by equation (6) can be related to the laser power (P) used in the LAM tests by

$$\mathrm{P}=\frac{\mathrm{Q}}{\mathrm{\eta }}=\frac{\mathrm{hA}}{\mathrm{\eta }}({\mathrm{T}}_{\mathrm{wd}}-{\mathrm{T}}_{\mathrm{wp}})$$

(7)

To keep a constant laser power during the simulation of the cutting process, a high temperature T_wd = 10,000 °C is assigned in the heat exchange window and the convection coefficient, h, is calculated as heat intensity of the heat window per degree Celsius temperature difference between the heat window and environment.

Calibration of heat source model

To ensure that the heat input window is correctly capturing the heat flux provided by the uniformly distributed moving laser beam, convection coefficient, h, used in the thermal model needs to be calibrated. The calibrations were carried using a K-type thermocouple (Omega 5TC-TT-K-40-36) of 75 µm diameter placed at a distance of 520 µm away from the laser scanning line. The convection coefficient, h, is selected such that the spatial and temporal predictions from the thermal model are in agreement with the experimental results. For 12 W laser, the convection coefficient, h, from the heat window to workpiece is found to be 9.5 kW/m²°C which has been used in all the other simulations.

Tool nose radius compensation

The tool geometry is imported from a solid model in SolidWorks. The imported tool model in DEFORM 3D does not have the resolution to capture the tool nose radius and it assumes the tool to be infinitely sharp. The tool nose radius is about 5–7 µm which cannot be ignored for uncut chip thicknesses of 15 and 25 µm. To incorporate the effect of tool nose radius, a chamfer of effective rake angle approximated by Manjunathaiah and Endres ²⁰ was used. The average rake angle (α_avg) is given by

$${\mathrm{\alpha }}_{\mathrm{avg}}=\mathrm{ta}{\mathrm{n}}^{-1}\left[\frac{(\frac{\mathrm{h}}{{\mathrm{r}}_{\mathrm{n}}}-1)\tan {\mathrm{\alpha }}_0-\sec {\mathrm{\alpha }}_0+\sin \mathrm{\theta }}{\frac{\mathrm{h}}{{\mathrm{r}}_{\mathrm{n}}}-1+\cos \mathrm{\theta }}\right]$$

(8)

where h is the undeformed chip thickness, r_n is the tool nose radius, α₀ is the nominal rake angle and θ is the chip separation angle. This work assumes the value of θ to be 15° as reported in the literature.^20,24

Modeling of residual stresses in DEFORM 3D

The residual stresses in LAMM have been modeled in DEFORM 3D. The material model has been considered elastic–viscoplastic. The residual stresses are generated in the surface/subsurface due to the recovery of elastic stresses post machining. Figure 10 shows how relaxation (unloading) induces residual stress under simple tension.

Figure 10.

How relaxation (unloading) induces residual stress under simple tension.

The machining simulation has to be executed for a total time step long enough to reach the steady-state condition as shown in Figure 11(a) and (b), following which the tool has to be released from the machined surface (unloading phase) for several time steps. During this phase, the workpiece is allowed to cool to an atmospheric temperature. The time step used in the simulation of unloading phase can be same as the one used in the loading phase. The residual stresses post relaxation can be obtained from the state variable option in the post processor as shown in Figure 12.

Figure 11.

(a) Stress and (b) temperature condition after terminating the cutting.

Figure 12.

Residual stresses state after relaxation phase.

Model predictions and validation

Thermal model validation

The heat source model was validated by measuring the surface temperature at different points away from the laser beam using a K-type thermocouple at the experimental conditions different than that used in the calibration. The bead size of the thermocouple is larger than the element size used in the model. But as the thermocouple bead is almost spherical in shape, the actual contact area is smaller ensuring temperature measurement over a smaller area. The thermocouple was kept fixed on the surface of the workpiece using conducting cement and was calibrated at different temperatures. The initial position of the thermocouple is measured using microscope camera. The distance between the thermocouple bead and the laser beam is controlled by moving the laser beam laterally. The laser was scanned close to the thermocouple at a constant speed and the temperature recorded using data acquisition system (NI PCIe-6363). The maximum temperature is observed when the laser beam center is closest to the thermocouple. Figure 13 shows the predicted and measured temperatures as a function of the distance from the laser beam center at 12 W laser power for two different scanning speeds. The temperature is measured at 10 different locations away from the laser scanning line and compared with the predicted temperature profile.

Figure 13.

Simulation and experimental temperature profile with distance for 12 W laser power.

The prediction error is 9%–11% at a distance of 200 µm from the laser beam center for a laser power of 12 W. The prediction error is less than 9%, when the thermocouple is located between 200 and 400 µm from the laser beam center. Above 400 µm, the prediction error range is 5%–13%. It is evident that there is a good agreement between the predicted and the measured temperature profiles. The prediction error may be due to approximation associated with the thermo-physical properties used in the model and/or the uncertainty associated with the exact location of the thermocouple with respect to the laser beam.

Validation of the cutting forces

The model is validated with the experimental results at two uncut chip thicknesses and two separate cutting speeds. The cutting speeds used in the validation experiments were 30 mm/in and 60 mm/min. The uncut chip thicknesses were 15 and 25 µm. There is good co-relation between the predicted and experimental force results. Figure 14(a) and (b) shows that the cutting force prediction errors are between 6% and 11% and the thrust force prediction errors are between 4% and 23%.

Figure 14.

Comparison of experimental and simulated cutting forces in conventional machining and LAMM for (a) 15 µm and (b) 25 µm uncut chip thicknesses.

Validation of the residual stresses

Figure 15(a) and (b) shows the predicted subsurface residual stress profile in the cutting and thrust directions for two different cutting speeds. For conventional machining, the magnitude of the tensile surface residual stresses in the cutting direction increases with an increase in the cutting speed. These results are in agreement with those obtained by Outeiro et al. ¹⁵ In the thrust direction, the surface residual stresses become more compressive at lower speed. Both the cutting and thrust direction residual stresses approach zero typically between 300 and 400 µm from the surface. The induced plastic strains due to the surface heating in LAMM either increase the compressive surface residual in the thrust direction or reduce the tensile surface residual stresses as compared with the conventional micromachining without the laser. However, the effect of speed on the residual stresses in LAMM is different for cutting and thrust directions. The compressive surface residual stresses with laser assistance in the thrust direction are strongly dependent on the cutting speed (laser scanning speed) as shown in Figures 15(b) and 16(b). A reduction in the cutting speed from 60 to 30 mm/min increases the temperature and the plastic strains induced are higher which results in higher compressive surface residual stresses in thrust direction. In the cutting direction, the effect of the cutting speed is not very pronounced and the tensile surface/subsurface residual stresses at 30 and 60 mm/min are similar in magnitude and nature as shown in Figures 15(a) and 16(a).

Figure 15.

Simulated in-depth residual stress distribution for both conventional machining and LAMM for 15 µm uncut chip thickness: (a) cutting direction and (b) thrust direction.

Figure 16.

Comparison of experimental and simulated surface residual stress in (a) cutting direction and (b) thrust direction.

The results obtained from the model have been validated with the experimental results. The predicted residual stresses at five different locations of the machined surface have been used to obtain the means and standard deviations for the surface residual stress predictions. Figure 16(a) and (b) shows that the predicted surface residual stresses in the cutting and thrust directions have good agreement with the experimental result. The prediction errors are between 10% and 19%. The residual stress condition on the machined surface is mostly dependent on the friction and heat transfer model between cutting tool–workpiece interface. The state of friction is greatly influenced by the tool nose radius and rake angle and uncut chip thickness which have been captured in this model.

Parametric study using FE model

The cutting forces and residual stresses are the two important aspects of LAMM. The effects of the following parameters on these two responses have been studied as a function of following parameters: cutting speed, cutting edge radius, rake angle, laser location and laser beam diameter.

The value of one parameter is changed at a time to study the effect of that particular parameter via FE simulations. The following parameters are used in the simulations: laser power = 12 W, uncut chip thickness = 40 µm, cutting speed = 100 m/min, cutting edge radius=5 µm, rake angle = 0°, laser beam diameter = 400 µm and laser location = 400 µm. Figure 17 shows the effect of process variables on the cutting forces.

Figure 17.

Cutting forces as a function of (a) laser power (W), (b) cutting speed (mm/min), (c) cutting edge radius (µm), (d) rake angle, (e) laser location (µm) and (f) laser beam diameter (µm).

Cutting forces

The forces arising from the laser-assisted orthogonal machining are the cutting force in the direction of the cutting speed and the thrust force in the direction normal to the cutting speed. Study of these forces would help us to choose optimal process parameters during machining.

Effect of laser power on cutting forces by FE model

Figure 17(a) shows the impact of laser power on cutting forces. As laser is focused on the work surface, the flow stress of the material at the primary shear zone reduces due to thermal softening. ¹² The cutting forces reduce as laser power is increased. A reduction of ∼30% compared to conventional machining is observed when 18 W laser is used.

Effect of cutting speed on cutting forces by FE model

Figure 17(b) shows the plots of the cutting and thrust forces as a function of cutting speeds. An increase in the cutting and thrust forces is observed with an increase in the cutting speed. There is lower thermal softening of the workpiece as less heat is conducted into the workpiece due to reduced laser–material interaction time available. In addition, the strain rate hardening effect also contributes to the increase in the forces. An increase of ∼21% and ∼24% in the cutting and thrust forces, respectively, are observed due to the increase in the cutting speed from 50 to 500 mm/min. The rate of increase from 50 to 200 mm/min is higher than the rate of increase from 200 to 500 mm/min which could be attributed to the fact that at higher speeds the thermal softening is inappreciable and only the strain hardening contributes to the increase in the cutting forces. ¹⁵

Effect of tool cutting edge radius on cutting forces by FE model

The impact on cutting and thrust force due to tool cutting edge radius is shown in Figure 17(c). When the tool cutting edge radius increases from 5 to 20 µm, the plowing force increases due to a decrease in the effective rake angle. As a result, the thrust force increase is significantly higher (∼38%) than the cutting force (∼10%).

Effect of rake angle on cutting forces by FE model

Figure 17(d) shows the cutting and thrust forces as a function of rake angle. Both the forces decrease as the rake angle becomes more positive. When the rake angle is negative, it requires more forces for chip formation ²⁵ due to increased plowing which affects the thrust forces. With the increase in rake angle, the flow of chip becomes easy and lower forces are required. The simulation results show a reduction of ∼20% in the cutting force and ∼33% in the thrust force as rake angle is increased from −10° to +10°.

Effect of laser location on cutting forces by FE model

The effect of laser location on the cutting and thrust forces is shown in Figure 17(e). Both the forces reduce significantly as the laser source is brought nearer to the tool cutting edge. The material removal temperature increases as the heat source comes near the tool. Consequently, the laser softening is more pronounced. The simulation results show a reduction of ∼19% and ∼33% in the cutting and thrust forces, respectively, as the laser beam–tool distance is reduced from 500 to 300 µm.

Effect of laser beam diameter on cutting forces by FE model

Figure 17(f) shows the plots of the cutting and thrust forces as a function of laser beam diameter for different laser powers. At low beam diameter, the laser heat intensity is high, but heat is absorbed in a small area. Consequently, it does not have too much effect on raising the temperature of primary shear zone. On the other hand, with high beam diameter, the area of local heat addition increases but due to low intensity it is not able to raise the temperature of primary shear zone to a significant level. As a result, there is no significant reduction in both the cutting and thrust forces.

Residual stress

For laser-assisted orthogonal micromachining, the cutting forces and laser heating play dominant role in plastic deformation and residual stress generation. The nature and the magnitude of the surface residual stresses in the cutting and thrust directions greatly affect crack initiation, crack propagation and the integrity of the machined surface. So the residual stress in the cutting and thrust directions is characterized as the function of process parameters in this parametric study.

Effect of laser power on residual stress by FE model

The effect of the laser power on the surface residual stresses in the cutting and thrust directions is shown in Figure 18(a). It shows that with increased laser power, both surface residual stresses tend to become more compressive as localized laser heating induces higher plastic strains ¹ in the surface layer as yield stress is lower at high temperature and the thermal gradient that exists through the surface. A reduction of ∼32% in the tensile surface residual stresses in the cutting direction and a ∼55% increase in the compressive surface residual stresses in the thrust direction are observed if an 18-W laser is used as opposed to conventional micromachining.

Figure 18.

Surface residual stress in cutting direction as a function of (a) laser power (W), (b) cutting speed (mm/min), (c) cutting edge radius (µm), (d) rake angle, (e) laser location (µm) and (f) laser beam diameter (µm).

Effect of cutting speed on residual stress by FE model

The influence of the cutting speed on the residual stresses is shown in Figure 18(b). With an increase in the cutting speed from 50 to 500 mm/min, the surface residual stresses increase (become more tensile in nature) by ∼63% and ∼24% in the cutting and thrust directions, respectively. This effect can be attributed to the lack of thermal softening in the workpiece at higher cutting speeds. The lower surface temperatures at higher speeds induce lower compressive plastic strains which results in surface residual stresses becoming more tensile in nature.^1,15

Effect of tool cutting edge radius on residual stress by FE model

The influence of the tool cutting edge radius on surface residual stress in the cutting direction is analyzed for three different edge radii: 5, 10 and 20 µm. As seen in Figure 18(c), the surface residual stresses increase by ∼44% and 32% when the cutting edge radius increases from 5 to 20 µm. An increase in tool cutting edge radius leads to a decrease in effective rake angle (α_avg) which increases plowing force on the machined surface. But the contact area of tool cutting edge and machined surface also increases. Simulated stress distribution during cutting operation shows that there is a decrease in induced plastic stresses in the thrust direction (σ₃₃) on the surfaces as edge radius increases as shown in Figure 19. As a result, the residual stresses post elastic recovery in the thrust direction become less compressive with an increase in the edge radius.

Figure 19.

Stress distribution in thrust direction (σ₃₃) for (a) 5 µm, (b) 10 µm and (c) 20 µm tool cutting edge radii.

Effect of rake angle on residual stress by FE model

The impact of tool rake angle on surface residual stresses is shown in Figure 18(d). The surface residual stresses decrease significantly as rake angle increases from −10° to 10°. The effect of rake angle is more pronounced in the thrust direction compared to the cutting direction. With positive rake angle, the magnitude of plowing force decreases and the chip formation becomes easier. In contrast, the negative rake angle increases the tool–workpiece surface contact area which reduces the stresses despite an increase in the magnitude of the thrust forces. As mentioned previously, the simulated stress distribution shows that there is a decrease in the induced plastic stresses on the machined surfaces as the rake angle becomes negative. Consequently, lower compressive residual stresses in the thrust direction are observed with an increase in the negative rake angle.

Effect of laser location on residual stress by FE model

Figure 18(e) shows the plots of the cutting and thrust forces as a function of laser location. As the laser heat source is brought nearer to the cutting edge, the temperature in the material removal plane increases and the expansion of the surface layer increases near the primary deformation zone. On the other hand, when the laser beam is focused away from the tool, the laser softening effect reduces and the cutting process tends towards a conventional machining process. Consequently, the compressive surface residual stresses in the thrust direction decrease by ∼37% and the tensile surface residual stresses in the cutting direction increase by ∼35% if the laser beam position is shifted from 300 to 500 µm from the cutting edge.

Effect of laser beam diameter on residual stress by FE model

The effect of laser beam diameter on surface residual stress is not significant in LAMM (see Figure 18(f)). Although decrease in beam diameter increases the heat intensity, it also reduces the heat input area; therefore, no appreciable effect of laser beam diameter is observed on the residual stresses for the range investigated in this study.

Conclusion

This article presents experimental characterization and modeling of orthogonal LAMM of Inconel 625. The LAMM process results in substantial improvement in the machinability due to reduced cutting forces. In addition, higher compressive subsurface residual stresses are obtained in the thrust direction in LAMM as compared to the conventional machining. The following conclusions can be drawn from this work presented in this article:

1. The main effect plots show that a reduction of 30% and 21% in the cutting force and the thrust force, respectively, is obtained in LAMM as compared to the conventional machining of Inconel 625.

2. LAMM resulted in ∼34% higher compressive surface residual stress in the thrust direction and ∼60% less tensile residual stress in the cutting direction as compared to the conventional machining.

3. The surface roughness increases by 28% during LAMM due to softening of the workpiece which results in increased surface tearing.

4. The heat source model predicts peak temperature within an error of 5%–13%.

5. The model predicts the cutting forces and thrust forces within 11% and the thrust forces within 23% of the measured values. The prediction errors are less than 10% in most of the cases.

6. The model prediction errors for surface residual stresses lie between 10% and 19%.

7. The cutting forces and surface residual stress in cutting direction are insensitive to the change in laser beam diameter for the parameters used in the simulations.