Plastic deformation analysis in machining of Inconel-718 nickel-base superalloy using both experimental and numerical methods

Int. J. Mech. Sci. Vol.33, No. 10, pp. 829-842,1991

0020-7403/91 $3.00+ .00 © 1991PergamonPresspie

Printed in Great Britain.

PLASTIC DEFORMATION ANALYSIS IN MACHINING OF INCONEL-718 NICKEL-BASE SUPERALLOY USING BOTH EXPERIMENTAL AND NUMERICAL METHODS t ABDUL B. SADAT, MOHAN Y. REDDY ~; a n d B. P. WANG § Industrial and Manufacturing Engineering Department, California State Polytechnic University, Pomona, CA 91768, U.S.A.; ~Sanden International Inc., 601 South Sanden Blvd, Wylie, TX 75098, U.S.A.; and ~Department of Mechanical Engineering, University of Texas at Arlington, Box 19023, Arlington, TX 76019, U.S.A. (Received 25 September 1990; and in revised form 7 March 1991)

Abstract-- Surface region plastic deformation of Inconel-718 nickel-base superalloy workpieces was evaluated when machined under orthogonal cutting conditions at various cutting speeds. Plastic deformation analysis was accomplished by determining the residual stress and plastic strain distributions in the surface region. The residual stresses were tensile and maximum near the surface and decreased in magnitude with an increase in depth beneath the machined surface. Similarly, the plastic strains were maximum near the surface and decreased with an increase in depth beneath the machined surface. In addition, a finite element simulation of orthogonal machining was carried out for predicting the residual stress and plastic strain distribution. In general, the trend of the curves predicted by the finite element model was similar to those found experimentally.

1. I N T R O D U C T I O N

Machining is generally considered as a finishing process to produce specified dimensions, tolerances and surface finish. The type of surface generated and its characteristics are of great importance in estimating the service life of a machined component under dynamic loads. Machining can lead to a variety of surface damage such as residual stress generation and plastic deformation of the surface region, surface and subsurface crack and microcrack, surface cavity and void formation. The factors that have an influence on surface integrity in machining processes are: cutting conditions, tool geometry, tool and workpiece material and their condition, and whether or not a lubricant is used. Most of the research work carried out in the past was concerned with the effect of various parameters on the surface integrity of machined components using experimental approaches [1-9]. The evaluation of the quality of the surface region using experimental methods is a very tedious job, and because of the destructive nature of most testing techniques used, it can be an expensive approach. Because of the complex nature of the machining process, a theoretical approach is not suitable for this type of analysis. A complete theoretical analysis requires the establishment of quantitative relationships between various dependent and independent variables. In view of the aforementioned difficulties, attempts have been made in recent years to use the finite element numerical technique in analyzing metal cutting problems [10-17]. The most significant work of these late studies could be attributed to that of Strenkowski and Carroll [16]. Their work involved the finite element simulation of both incipient and steady-state cutting. Their work is based on a two-dimensional plane strain orthogonal cutting condition. A complete survey of finite element simulation in metal cutting is given in Ref. [18]. The objective of the present work is to use an experimental approach in evaluating the plastic deformation in the machined region of Inconel-718 nickel-base superalloy workpieces. In addition, an attempt will be made to use a finite element simulation to predict residual stress and plastic strain distribution in the surface region. Inconel-718 is known as a high-temperature alloy and it is used extensively in aircraft and gas turbine engines. tThe support for this work is provided by National Science Foundation, Grant No. DMC-8616575. 829

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PROCEDURE

The experimental work involved the orthogonal machining of test specimens for residual stress and plastic strain determination of the surface region using various cutting speeds. For residual stress analysis, ring specimens measuring 65 mm outside diameter, 54 mm inside diameter and 3.24 mm thickness were used. The ring specimens were machined from hot-rolled Inconel-718 nickel-base superalloy sheets using an abrasive water jet system (Flow System's water jet machine interfaced with a Nova robot and using 100 mesh silica garnet). The abrasive water jet machine was used for test specimen preparation to minimize surface region damage, which is significant if other machining methods are to be used. The chemical composition and significant mechanical properties of the work material are given in Tables 1 and 2, respectively. The ring specimen was then mounted on a specially made mandrel that was held in the chuck of a 3.7 kW, 43.18 cm Webb precision lathe. Silicon-nitride (sialon) based ceramic insert cutting tools (Kennametal, Kyon 2000) were used in orthogonal cutting with the application of a coolant. The cutting tool was moving in a radial direction, i.e. perpendicular to the axis of the ring. The tool holder was rigidly mounted on a three-component tool force dynamometer (Kistler Type, Model 9257A). The tool forces were recorded using a UV recorder (SOLTEC 5L40) after a steady-state cutting condition was established. The cutting action was suddenly stopped when the outside diameter of the ring was reduced to approximately 60.35 mm. A summary of the cutting condition is given in Table 3. The machined rings were then used for residual stress analysis. For this purpose, a modified deflection-etching technique was used. The machined ring specimen was slit between two inscribed marks and the change in the circumference of the ring due to partial relief of residual stresses was measured using an optical microscope. In order to relieve the residual stresses that may be present in the surface region, thin layers measuring 0.0127 mm were removed from the machined surface by chemical etching (while protecting the other

TABLE 1. CHEMICAL COMPOSITION OF INCONEL-718

NICKEL-BASE SUPERALLOY

(% Wt) C TI 0.03 0.99

MN CO 0.16 0.06

FE MO 18.09 3.0

S CB + TA 0.001 4.92

SI P

CU B

0.12 0.013

0.12 0.002

NI

CR

53.91

18.04

AL 0.54

TABLE 2. MECHANICAL PROPERTIES OF INCONEL-718 NICKEL BASE SUPERALLOY

As received Yield strength (MPa) Tensile strength (MPa) Hardness (Re)

Room temperature capability'

427 891 15

1223 1429 44

'Aged 1325°F, held for 8 hours, furnace cooled at 100°F per hour to 1150°F, held for 8 hours and air cooled.

TABLE 3. SUMMARY OF CUTTING CONDITIONS Cutting speed (m s- 1) Depth of cut (mm) Tool rake angle (degree)

0.2, 0.35, 0.63, 1.25, 1.61 0.028 5

Plastic deformationanalysisof Inconel-718nickel-basesuperalloy

831

surfaces of the ring from chemical action) and the change in the circumference of the ring was again measured. This process was continued until the change in the circumference of the ring was vanishingly small. The data were then used to compute the residual stress distribution in the machined surface. A more detailed description of this technique and the method used for residual stress calculation are given elsewhere [19]. For plastic strain analysis, circular blanks 65 mm in diameter were cut from hot-rolled Inconel-718 sheets measuring 1.62 mm in thickness using the abrasive water jet system. Three equispaced clamping holes each 5.00 mm in diameter were also machined using the water jet machine. The side surface of each blank was wet ground with successively finer grades of silicon carbide paper (400, 600, 800 and 1200 grits) and then carefully mirror polished using high-purity, 0.3 micron alumina powder. A cluster of rectangular grids, 20 #m, was photographically reproduced on a high-resolution glass emulsion plate through two stages of photographic (photolithograph) reduction technique. A number of repeat images were photographed during this process and the grids were then transferred to the annular area of Inconel blanks (Fig. lb) through a photo printing method. A brief summary of the process used is given in the Appendix. For more detailed description of this process the reader is referred to Ref. [20]. The geometries of the test specimens and the schematic of the machining process are shown in Fig. 1. A photomicrograph of the etched grids before machining is shown in Fig. 2. Cutting tests were carried out using an orthogonal cutting method similar to that used for machining the residual stress test specimens. However, in this case to prevent side spread and to ensure plane strain condition during the machining operation, two disks of the test specimens were placed together and then mounted on a specially-made mandrel. In this case, the grids were located in the middle (where the two disks face each other), rather on the free surface that will be in plane stress. Moreover, the flatness of the polished surfaces also ensured good contact for plane strain condition. Figure 3 shows a photomicrograph of the grid after machining. A Xerox microfiche machine was used to enlarge the grids ( x 1000)

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directly from the negative of the deformed grids. The plastic strain was then calculated from the displacement of the nodal points using Lagrangian strain tensor. 3. F I N I T E E L E M E N T M O D E L

Finite element procedures have been used for a wide range of problems in engineering. Their extensive applications to both linear and nonlinear problems have led to a rapid development of numerous codes in various fields of engineering. Among the many available finite element methods, the displacement-based finite method is considered one of the most important formulations. Because of its simplicity, generality and good numerical properties, the majority of general-purpose analysis programs have been written using this formulation [21]. Nearly all numerical metal cutting simulations are based on this method [18]. To simulate metal cutting, the finite element formulation must be able to handle nonlinear material properties, large deformation as well as nodal separation. The latter characteristics are required for chip formation. NIKE2D [22] is a general-purpose finite element code that can be applied to a wide range of material and geometrically-nonlinear problems. It allows for a multibody to be defined and joined at the interface using a slideline. It also allows for two contacting surfaces to be described as frictionless sliding surfaces or surfaces with traction. Hence this code is suitable f•r simulating metal forming and metal-cutting problems. It should be noted that in metal cutting in order to generate a surface, a layer of material is separated from the workpiece in the form of chip. NIKE2D allows for node separation by using an appropriate separation criterion [23]. In the present work, the program NIKE2D is used for cutting simulation. Figure 4 shows a mesh consisting of 656 elements including 16 elements for the cutting tool. In this model, an elastic material with a Young's modulus of 210 GPa is used for the cutting tool, while the elastic, linear strain-hardening behavior for the workpiece is used. For the workpiece used in this experimental study, the measured slopes for the stress-strain curve for the elastic behavior and linearly strain hardening response are 207 GPa and 433 MPa, respectively. An elastoplastic response occurs when the strain is more than 0.002. These data are used in the simulation. In Fig. 4, the boundary conditions used in the simulation are that the nodes along the bottom of the model are fixed in both the x- and y-directions while the nodes on the left edge are fixed in the x-direction only. With the workpiece fixed, the metal cutting process is simulated by prescribed x-motion of the right edge of the cutting tool (see Fig. 4). Thus, for a given cutting condition the calculated force to enforce the prescribed motion is the tool force required for this condition. In order to simulate chip formation, it is necessary to allow the node close to the cutting edge of the tool to separate. This separation is alllowed only when the effective strain at that point reaches a critical value. An attempt was made to use the procedure described by Strenkowski and Mitchum [23]. In their work they developed a chip separation criterion by studying the transition from indentation to incipient cutting. They studied the indentation of 70/30 brass using a 60 ° half-wedge indenter with depths of cut ranging from 12.25 to 24.5 mm. For the purpose of explanation, Figs 5 and 6 are reproduced here to show the contour of effective stress for indentation distances of 0.686 and 0.737 mm, respectively. In Fig. 5, the zone directly under the indenter surrounded by contour line g and a second zone along the outside edge of the workpiece is fully plastic. As the indenter advances into the workpiece the plastic zones expand and finally coalesce (Fig. 6). This was interpreted as the beginning of incipient cutting and also considered to be the beginning of a shear zone in metal cutting. The effective strain at the node nearest to the cutting edge of the tool for the indentation of 0.737 mm was calculated and then used as the chip separation criterion for subsequent chip formation. Using this procedure a plot of separation criterion for various depths of cut for the 70/30 brass workpiece was established [23]. The above procedure was first used in simulating chip formation when machining a workpiece of Inconel-718 nickel-base superalloy used in this investigation. The depth of cut was set to 0.028 mm. The effective strain from the chip separation criterion obtained this

Plastic deformation analysis of Inconel-718 nickel-base superalloy

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Plastic deformation analysis of Inconel-718 nickel-base superalloy

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way was very low and the cutting simulation resembled wood splitting, where a large crack developed ahead of the cutting edge of the tool. The explanation for this behavior is as follows. In Fig. 6, the beginning of incipient cutting which is also considered as the beginning of the shear zone is based on the initial yield strength of the material. This may be the case especially for materials with no work-hardening behavior. However, for materials such as Inconel-718 nickel-base superalloy which has a very high work hardenability, using the initial yield strength may be low, since the material work hardens to the limit along the shear zone. In the present work, the yield zone as described in Figs 5 and 6 is based on an average flow stress of yield strength of the material as obtained from room-temperature capability (1326 MPa, Table 2). This resulted in a critical strain of 0.54 that was used in subsequent simulation for chip separation. The coefficients of friction at the tool-chip interface obtained experimentally were: 0.64, 0.62, 0.60, 0.53, 0.46 which correspond to cutting speeds of 0.20, 0.35, 0.63, 1.25, 1.61 m s- 1, respectively. These measured values were used in the computer simulation. The effects of strain rate and temperature were not included in the cutting simulation for reasons discussed later in Section 5. Hence any variation of data with cutting speed observed from the computer simulation should be regarded as being due to the variation of friction coefficient at the tool-chip interface. 4. RESULTS 4.1. Experimental results

The variation of cutting force with cutting speed is given in Fig. 7. In general, the cutting forces decrease with an increase in cutting speed. Figure 8 shows the residual stress distribution in the machined surface region for various cutting speeds. The residual stresses are tensile for all cutting speeds. Except for the cutting speed of 0.20 m s-1 where the maximum stress occurs at a distance of about 0.02 mm from the machined surface, the residual stresses are generally maximum at the surface and decrease with an increase in depth beneath the surface. The shear strain distribution in the surface region was obtained from the grid analysis. A typical plot of shear strain vs depth beneath the machined surface for various cutting speeds is given in Fig. 9. Shear strains are maximum near the surface and decrease with an increase in depth beneath the machined surface. The shear strain for a cutting speed of 1.61 m s- i is the lowest at any given distance beneath the machined surface. From the figure, it can be seen that the depth to which plastic strain extends beneath the surface (depth of plastic deformation) decrease with an increase in cutting speed.

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Plastic deformation analysis of Inconel-718nickel-base superalloy

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4.2. Finite element simulations results Figure 10 is a screen dump of a cutting simulation for a depth of a cut of 0.028 mm, showing steady-state cutting. From the figure, it can be seen that the metal is deformed in a region ahead of the cutting tool as expected in orthogonal machining (the primary deformation zone). Plastic deformation of machined surface region can also be seen, which is similar to actual cutting as seen from the deformed grid of Fig. 3. The cutting force as predicted by the finite element model is shown in Fig. 7. The predicted cutting force decreases with an increase in cutting speed similar to that found experimentally. Figures 11 and 12 respectively show the contour of residual stress and shear strain for a depth of cut of 0.028 mm. The residual stresses are tensile and both the residual stress and shear strain are maximum near the surface and decrease with an increase in depth beneath the surface. The residual stresses and plastic strains in the machined surface region are greatly influenced by the presence of the frictional condition at the tool-workpiece interface, as discussed in detail in Section 5. Unfortunately, due to lack of knowledge of the friction coefficient and thermal effects at the tool-workpiece interface at various cutting speeds, the

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Plastic deformationanalysisof Inconel-718 nickel-basesuperalloy

839

computer simulation could not predict the changes in residual stresses and strains with cutting speeds to compare with those obtained experimentally (Figs 8 and 9). Research is currently underway to include these parameters in the program. 5. DISCUSSION OF THE RESULTS

Experimental data showed that tool forces decrease with an increase in cutting speed. This is to be expected because the shear angle as calculated using the cutting geometry also increased with an increase in cutting speed, therefore reducing the shear plane length (and also decreased the friction at the tool-chip interface) and, hence, reduced the tool forces. It is generally known that residual stresses may be produced due to inhomogeneous plastic deformation induced by mechanical and thermal events associated with the process of chip formation, and the interaction between the tool cutting edge and freshly-machined workpiece surface. Residual stresses due to the mechanical deformation consist of two parts, namely (1) due to the cutting action of the tool cutting edge, and (2) due to the rubbing or burnishing effect of the tool flank. During the cutting operation, the material ahead of the cutting point experiences compressive plastic deformation and the material behind experiences tensile plastic .deformation. If the tensile deformation is more than the compressive deformation, the resulting residual stress is compressive and vice versa. The rubbing or burnishing effect, which is similar to surface rolling or shot peening, produces compressive residual stresses. The heating of the surface produces compressive plastic deformation by thermal stresses, then tensile residual stresses upon cooling [24]. The final stress distribution in the surface region is the combined effect of the three components. A schematic sketch of the residual stress sources and residual stress distribution is given in Fig. 13 [24]. At the low cutting speed of 0.2 m s- 1 the effect of burnishing is more near the surface compared to other cutting speeds. This can lead to surface deterioration and cracks, and hence partial relief of residual stress in the surface region. This is believed to be the reason for the low stress at the surface for the 0.2 m s-1 cutting speed. The residual stresses near the surface increase with cutting speed, which may be due to the increase in temperature. Figure 9 showed that shear strains and the depth of plastic deformation decreased with an increase in cutting speed. This is expected because an increase in cutting speed led to an increase in shear plane angle and a decrease in tool force. Using the finite element method for metal cutting simulation required the chip separation criterion, to allow the nodes close to the tool cutting edge to separate and to form the chip.

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As discussed previously, the beginning of incipient cutting or the beginning of a shear zone was considered when the plastic zone close to the vicinity of the cutting edge joined the plastic zone along the outside edge of the workpiece (Figs 5 and 6). The plastic flow (1326 MPa) in this work was based on the room-temperature capability (Table 2) of Inconel-718 nickel-base superalloy. Based on this assumption, the shear strength of the material is 756 MPa. This is in good agreement with metal cutting data where the shear stress on the shear plane was found from a plot of shear force vs shear area (Fig. 14). The shear stress found this way was 754 MPa. From Fig. 14 it can be seen that the shear stress is independent of the depth of cut and cutting speed for the range selected here. In Figs 10-12, it is seen that in the finite element simulation, the tool nose region does not come into contact with the chip. This gap is due to modelling error. When a finer mesh and longer time for a prescribed tool movement are used in the simulation, this gap disappears. This requires much more computer time than the present situation requires and the results are generally similar to the present simulation. For more accurate simulation of metal cutting, in addition to an accurate estimate of the chip separation criterion, knowledge of the frictional condition at the chip-tool and tool-workpiece interfaces is also needed. Due to the lack of an accurate theoretical solution, the coefficient of friction at the chip-tool interface was found experimentally and then used in the cutting simulation. However, the coefficient of friction at the tool-workpiece interface was not known and it was assumed to be zero. This may be the reason for the lower value of the cutting force as predicted by the finite element model. The residual stresses predicted by the model are qualitatively in good agreement but quantitatively they seem to be higher. This again may be attributed to the tool-workpiece frictional condition which is responsible for rubbing or burnishing effects and thermal effects which are not considered in the simulation. The shear strains predicted by the model follow a similar trend to that obtained experimentally. However, the values predicted are lower than the experimental values, because the coefficient of friction at the tool-workpiece interface was assumed to be zero. A significant improven-tent can be made by applying a small value of the coefficient of friction at the tool-workpiece interface.

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Plastic deformation analysis of Inconel-718 nickel-base superalloy

841

In general, the finite element simulation of metal cutting requires a knowledge of material behavior, the value of the effective strain at the node closest to the tool cutting edge to allow chip formation, and a knowledge of the values of the coefficients of friction at the tool-chip and tool-workpiece interface. In this work, a linearly elastic, linearly strain hardening material model was assumed and the effect of strain rate and temperature was neglected for simplicity. Metal cutting normally involves both high strain rates and high temperatures on the shear plane. It is believed that the two effects tend to cancel each other, as suggested by Drucker [25]. This assumption seems to be in good agreement with the experimental observation as shown in Fig. 14. It appears that for the range of cutting conditions used, the shear stress on the shear plane is independent of the cutting speed and depth of cut. Tool forces are less affected by the variation in the value of the effective strain used for chip separation. However, surface region residual stresses and plastic strains are more affected by changes in the value of the plastic effective strain. It should be mentioned that in general, the application of the finite element method in metal cutting simulations shows a promising future. The prediction of tool forces using this technique is invaluable in the CAD/CAM area for designing a proper tool for a given work material. 6. C O N C L U S I O N

From the discussion of the results presented in the previous section, the following conclusions were made: (1) In general, the residual stresses and plastic strains were maximum near the surface and decreased with an increase in depth beneath the machined surface. (2) The residual stresses near the surface increase with an increase in cutting speed. (3) The trend of the curves for the residual stress and plastic strain distribution in the machined surface region as found experimentally, is also predicted by the finite element technique. (4) Knowledge of the frictional condition at the tool-chip and tool-workpiece interfaces, can lead to improvements in the prediction of the tool forces and residual stress and strain distributions. Acknowledgement--The support of the National Science Foundation (Grant No. DMC-86165765) for this work is greatly appreciated.

REFERENCES 1. M. FIELD and J. F. KAHLES,The surface integrity of machined and ground high-strength steel. DMIC Report 210, pp. 54-57 (1967). 2. W. P. KOSTER and L. J. FRITZ, Surface integrity in conventional machining. ASME Paper No. 70-GT-100 (1970). 3. W. S. Lou and C. RUBENSTEIN,The influence of flank wear, cutting speed, and cutting fluid on the surface and sub-surface workhardening produced in orthogonal planing operation. Int. J. Mach. Tool Des. Res. 12, 311 (1942). 4. J. A. BAILEY,S. JEELANI and S. E. BECKER. Surface integrity in machining AISI 4340 steel. Trans. ASME J. Engngfor Indus. 98, 999 (1976). 5. C. R. LIu and M. M. BARASH,The mechanical state of the sublayer of a surface generated by chip-removal process. Part 1: Cutting with a sharp tool. Trans. ASME J. Engngfor Indus. 98(4), 1202 (1976). 6. M. M. ELKHABEERYand J. A. BAILEY,Surface integrity in machining solution-treated and aged 2024-aluminum alloy, using natural and controlled contact length tools, Part I--Unlubricated. Trans. ASME J. Engn 0 for Indus. 106, 152 (1984). 7. Y. MATSUMOTO,M. M. BARASHand C. R. Lift, Effect of hardness on the surface integrity of AISI 4340 steel. Trans. ASME J. Engng for Indus. 108, 169 (1986). 8. A. B. SADATand J. A. BAILEY,Surface integrity in machining an annealed bearing bronze. Trans. ASME J. Engng for Mtls and Technol. 109, 78 (1987). 9. A. B. SADAT,Surface region damage of machined Inconel-718 nickel base superalloy using natural and controlled contact length tools. Wear 119, 225 (1987). 10. B. E. KLAMECKI,Incipient chip formation in metal cutting--a three dimension finite element analysis. Ph.D. dissertation, University of Urbana-Champaign (1973).

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APPENDIX (1) The specimen was first thoroughly cleaned with acetone and baked for about 30 min. A thin coating of Shipley's positive photoresist (AZ 1350 J) was then applied and the sample was subsequently baked for 30 min at 90°C. (2) After positioning the glass mask containing the grid pattern, the sample was exposed to high-intensity light for 75 s. (3) The sample was soaked in chlorobenzene for 20 min, dried, and then baked for 30 min. (4) The photoresist was developed in KTI positive developer (TMD-250, 100% dilution) until the grid lines were clearly visible and the sample was then baked again for 20 min. (5) The sample was then etched slowly through the photoresist for 15 min in an acid solution (1 HNO3, 1 HCI, 3 H20) and subsequently washed with acetone to remove the photoresist.