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The influence of Johnson–Cook material constants on finite element simulation of machining of AISI 316L steel
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International Journal of Machine Tools & Manufacture 47 (2007) 462–470 www.elsevier.com/locate/ijmactool
The influence of Johnson–Cook material constants on finite element simulation of machining of AISI 316L steel D. Umbrelloa,, R. M’Saoubib, J.C. Outeiroc a
Department of Mechanical Engineering, University of Calabria, 87036 Rende (CS), Italy b Corrosion and Metals Research Institute (KIMAB), SE-11428 Stockholm, Sweden c Portuguese Catholic University, 3080-024 Figueira da Foz, Portugal Received 22 April 2006; received in revised form 5 June 2006; accepted 14 June 2006 Available online 1 August 2006
Abstract In literature, five different sets of work material constants used in the Johnson–Cook’s (J–C) constitutive equation are implemented in a numerical model to describe the behaviour of AISI 316L steel. The aim of this research is to study the effects of five different sets of material constants of the J–C constitutive equation in finite-element modelling of orthogonal cutting of AISI 316L on the experimental and predicted cutting forces, chip morphology, temperature distributions and residual stresses. Several experimental equipments were used to estimate the experimental results, such as piezoelectric dynamometer for cutting forces measurements, thermal imaging system for temperature measurements and X-ray diffraction technique for residual stresses determination on the machined surfaces; while an elastic–viscoplastic FEM formulation was implemented to predict the local and global variables involved in this research. It has been observed that all the considered process output and, in particular the residual stresses are very sensitive to the J–C’s material constants. r 2006 Elsevier Ltd. All rights reserved. Keywords: Machining; FEM; Residual stresses; Work material model; Austenitic stainless steel
1. Introduction In the context of metal cutting, a large strain, large strain-rate and high temperature are usually reported in the literature. It is well known that the microscopic and macroscopic response of the material under high strain-rate loadings is affected by strain, strain rate, temperature, and microstructure of the material. So, to accurately analyse this process using numerical methods such as finite element analysis (FEA), the knowledge of material constitutive behaviour under these severe loading conditions is a prerequisite and hence correct work material flow stress data need to be used. In fact, the success and reliability of numerical models are mainly dependent upon mechanical (elastic constants, Corresponding author. Tel.: +39 984 494820; fax: +39 984 494673.
E-mail addresses: [email protected] (D. Umbrello), rachid.msaoubi@ kimab.com (R. M’Saoubi), [email protected] (J.C. Outeiro). URLs: http://www.unical.it, http://www.kimab.com, http://www.crb. ucp.pt. 0890-6955/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2006.06.006
flow stress, fracture stress/strain, etc.) and thermo-physical (density, thermal conductivity, heat capacity, etc.) properties of the work material, and contact conditions at tool–chip and tool–workpiece interfaces [1–5]. The correct selection of these parameters is often regarded as a critical step if one wants to predict with a reasonable accuracy forces, temperatures, chip morphology, tool wear and ultimately the surface integrity of the machined components (residual stresses, surface roughness, microstructure, etc.). Although many studies on finite element (FE) modelling of the orthogonal cutting process have been published until now, recent reviews on this topic [6,7] indicated that these were mainly focused on the prediction of strains, stress and cutting temperatures. Only a few studies on FE modelling involving the prediction of the machining residual stresses can be found in the literature, with special attention to the residual stresses in plain carbon steels and hardened steels [6–9]. Moreover, as far as the authors know, no sensitivity study is available about the influence of the constants used
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in the material constitutive equation on the residual stresses in the machined component, particularly those made in AISI 316L steel. The proposed paper presents a sensitivity study about the influence of the constants used in the Johnson–Cook’s (J–C) material constitutive equation on the forces, temperatures, chip morphology and residual stresses in the machined components of AISI 316L steel. For such study, five different sets of work material constants used in the J–C’s constitutive equation [10] (found by the application of several methods) are selected from literature [11–14]. Although such model is widely used in FE models to describe the constitutive behaviour of metals at high strain rates over a wide range of temperatures, its applicability over a wide range of strain is, however, limited due to the use of SHPB methods that permits to achieve only a limited range of strains. As suggested in Chandraserkaran et al. [11] the information from SHPB tests can be used only as a starting point while the identification of J–C parameters applicable for metal cutting requires additionally the combined use of machining tests and analytical chip formation models. It should also be mentioned that J–C model have been subjected to modifications by several authors to capture more accurately the behaviour of some metals and alloys at high strain rate [15–17]. However, such ambitious task was not undertaken in the present study which was aimed mainly at investigating the effect of various J–C constant obtained from literature on the modelling of RS during machining of AISI 316L and implemented in a FE model to simulate orthogonal cutting of AISI 316L by a comparison between the obtained predicted results (chip morphology, forces, temperatures and residual stresses) and those obtained from experimental studies.
2. Experimental and numerical procedures 2.1. Material properties, cutting tool and cutting regime parameters Round bars (150 mm in diameter) of austenitic stainlesssteel AISI 316L were selected for this study. Microstructure of the steel consisted of an equiaxed grain structure characterized by an approximate grain size of 50 mm and material hardness was close to 170HV. Orthogonal cutting tests were carried out on a lathe using radial feed motion (Fig. 1) using uncoated (ISO M10–M30) tungsten carbide tool. The thermo-physical properties both for workpiece and cutting tool are presented in Table 1. To model the elastic behaviour of AISI 316L steel a Poisson ratio (n) of 0.30 and a temperature (T)-dependent Young’s modulus given by experimental data [19], reported in Table 2, were used. To model the thermo-visco plastic behaviour of AISI 316L steel a J–C’s constitutive equation was employed,
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Fig. 1. Configuration of the orthogonal cutting tests and the directions of the measurements of the cutting forces and the residual stresses.
which can be represented by the following: T T room m _ seq ¼ ðA þ Bn Þ 1 þ C ln 1 , T m T room _0 (1) where is the plastic strain, _ is the strain rate (s1), _0 is the reference plastic strain rate (s1), T is the temperature of the work material (1C), Tm is the melting temperature of the work material (1399 1C) and Troom is the room temperature (20 1C). Coefficient A is the yield strength (MPa), B is the hardening modulus (MPa), C is the strain rate sensitivity coefficient, n is the hardening coefficient and m the thermal softening coefficient. Table 3 shows the five different sets of work material constants used in the J–C constitutive equation, found by several researchers [11–14]. These work material constants were found by the application of several methods. The M1 and M2 (Ref. [11]) sets of material constants were identified from high strain rate mechanical testing on hat-shaped specimens using the Split Hopkinson’s Pressure Bar method (SHPB) as well as instrumented orthogonal milling tests to generate information about material flow stress in machining based on different analytical chip formation models, namely continuous chip for M1 and serrated chip for M2. The M3 set of material constants (Ref. [12]) where obtained using SHPB tests that were carried on cylindrical compression specimens while M4 set of material constants (Ref. [13]) where based on SHPB experiments using hatshaped specimens. Finally, the M5 set of material constants (Ref. [14]) were determined using a methodology based on analytical modelling of the orthogonal cutting process along with metal cutting experiments. Finally, the range of the cutting tools geometry was as follows: the normal rake angle (gn) and the normal flank (an) angle were 01 and 111, respectively; the tool cutting edge angle (kr) was 901, the tool cutting edge inclination
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Table 1 Thermo-physical properties of AISI 316L steel [18] and WC-Co cutting tool Density (kg/m3): rw ðTÞ ¼ 7921 0:614 T þ 0:0002 T 2 Thermal conductivity (W/(mK)): kw ðTÞ ¼ 14:307 þ 0:0181 T 6 106 T 2 Specific heat (J/(kg K)): cp;w ðTÞ ¼ 440:79 þ 0:5807 T 0:001 T 2 þ 7 107 T 3 Density (kg/m3): 13000 Thermal conductivity (W/(mK)): 62.7 Heat capacity (J/(kg K)):234
AISI 316L steel
WC-Co cutting tool
Table 2 Young’s modulus of AISI 316L steel [19] T (1C) E (Gpa)
20 210.3
150 191.7
260 180.0
350 191.0
425 188.2
480 186.2
540 156.5
650 113.7
1200 68.0
Table 3 AISI 316L material constants for J–C constitutive model
Chandrasekaran et al. [11] Chandrasekaran et al. [11] M’Saoubi [12] Changeux et al. [13] Tounsi et al. [14]
M1 M2 M3 M4 M5
A
B
C
n
m
_0
305 305 301 280 514
1161 441 1472 1750 514
0.01 0.057 0.09 0.1 0.042
0.61 0.1 0.807 0.8 0.508
0.517 1.041 0.623 0.85 0.533
1 1 0.001 200 0.001
angle (ls) was 01, and the tool cutting edge radius (rn) of 0.030 mm. Concerning to the cutting regime parameters, the range for the cutting speed (nc) was 100–200 m/min, for the uncut chip thickness (b) was 0.1–0.2 and the width of cut (ap) was kept constant and equal to 6 mm. No cutting fluid was used in the tests.
2.2. Experimental set-up and parameters Orthogonal cutting tests were performed on a 15 HP numerically controlled lathe equipped with a specially designed experimental set-up. In measuring the cutting force components (tangential force and the thrust force) a Kistler-type 9255B three-component piezoelectric dynamometer was used. The tangential force component (Fc) was measured in the direction of the primary motion and the thrust force component (Ft) in the direction of feed motion. This experimental set-up also included thermal imaging equipment developed to assess the temperature distribution in the deformation zone. In particular, the temperature was measured on the lateral face of the cutting tool where tool chip interface temperature can be determined (under orthogonal cutting conditions) with good accuracy. A detailed description of this equipment and its calibration can be found in [20]. The residual stress state in the machined layers of the workpiece was analysed by the X-ray diffraction technique using the sin2 c method [21]. The parameters used in the Xray analysis are the same used in earlier investigation [9].
The residual stresses were determined for the stable cutting zone (where the cutting force components are stable) on the surface and in-depth, in the directions shown in Fig. 1. These directions are selected because the analysis of the residual stress tensors at the workpiece surface and subsurface allowed us to conclude that these directions are the directions of the principal stress components. To determine the in-depth residual stresses, successive layers of material were removed by electropolishing, to avoid the reintroduction of residual stress. Further corrections to the residual stress data were made due to the volume of material removed. Due to circularity of the workpieces, a circular mask with a diameter of 2.5 mm was applied to limit the region of analysis. The error associated with the method used was generally less than 50 MPa. 2.3. Numerical model and parameters The commercial FEA software DEFORM-2DTM, a Lagrangian implicit code, was used to simulate the orthogonal cutting process of AISI 316L. An FEM model of the orthogonal cutting process was developed and was composed of the workpiece and the tool. The workpiece was initially meshed with 3000 isoparametric quadrilateral elements, while the tool, modelled as rigid, was meshed and subdivided into 1000 elements. A plane-strain coupled thermo-mechanical analysis was performed using orthogonal assumption. The constitutive law used and implemented in the FEM model to take into account this complex material behaviour is given by Eq. (1). The thermo-physical
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properties of both workpiece and uncoated tool are in Table 1. Another consideration concerns the interface heat transfer coefficient, h, utilized in the preliminary thermomechanical numerical simulation. Usually a large h value is adopted, assuming perfect interface heat transfer conditions. However, the role of this parameter requires careful investigation, since it controls the effectiveness of the numerical simulation when a fully thermo-mechanical analysis is run, as reported in a recent study conducted by Filice et al. [22]. They found a value of h close to 1000 kW/m2 K, which permitted a satisfactory agreement between their numerical data and the experimental evidence in all the investigated cases. During the machining of AISI 316L steel, tensile stress plays an important role; therefore its effect should also be included in the material response such as the fracture criterion. In this research, Cockroft and Latham’s criterion is employed to predict the effect of tensile stress on chip segmentation during orthogonal cutting. Cockroft and Latham’s criterion is expressed as Z f s1 d ¼ D, (2) 0
where f is the effective strain, s1 is the principal stress, and D is a material constant. Cockroft and Latham’s criterion states that when the integral of the largest tensile principal stress component over the plastic strain path in Eq. (2) reaches the value of D, usually called damage value, fracture occurs or chip segmentation starts. As far as friction modelling is concerned, a simple model based on the constant shear hypothesis (t ¼ mt0 ) was implemented in the FE code. This assumption is based on recent investigation [23] where it is shown that both cutting forces and chip morphology can well predicted setting in
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the right way the friction coefficient independently of which friction law is taken into account. On the contrary, friction model became strategically important when other variables are considered, such as shear angle, normal pressure and thermal effects [24], even if either normal pressure and temperature were found with good accuracy using shear model too [25,26]. The determination of both D and m values were established by an iterative procedure based on chip geometry and cutting forces, respectively (Fig. 2). Finally, taking into account that, at moment using the DEFORM-2DTM FE code is not possible to obtain directly the numerical residual stresses, the authors have proposed the follow procedure: 1. An elastic-visco-plastic was implemented for the investigated cases and it was executed for a total time step long enough to reach the steady-state condition. 2. For several time steps the tool was released from the machined surface (unloading phase) and the workpiece is cooled down to the room temperature. 3. The numerical residual stress profiles were collected for few selected time steps and the average values were taken into account, using the procedure described in [27]. 3. Fe analysis and discussion of results To validate the orthogonal cutting model the predicted and experimentally measured chip morphology, cutting forces, temperatures and residual stresses on the machined affected layers were compared and their differences were discussed. The simulated cutting conditions are the same used in the experimental work, reported in Section 2.1.
Fig. 2. Flow chart for determining the friction factor, m, and the critical damage value, D.
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3.1. Cutting forces For each of the five sets of work material constants, both the experimental and the predicted averaged forces in the tangential direction (Fc) and in the thrust direction (Ft) are reported in Table 4. It is obvious that, except for the material constants set M4 [13], the predicted average tangential forces Fc agree well with the experimental one. In particular, the best prediction is given by for the material constants set M5 [14]. Similar observation could be made when comparing the thrust forces Ft. In fact, except again for the material constants set M4, the predicted thrust forces are almost close to the experiment, even if the error obtained by the material constants set M3 [12] underestimates the thrust value by 25.4%. The large discrepancy in cutting forces for the material constants set M4 can be attributed to its relatively lower flow stress. 3.2. Chip morphology The comparison between the experimental and the predicted chip morphology are shown in Fig. 3. The chip curl of the material constants set M2 and M5 have the largest radius, followed by the material constants set M4, M1 and M3, respectively. Comparing with the experimental chip curl it can be seen that only the material constants set M2 and M5 agree well. The average values of the chip geometry (valley, peak and pitch), including chip compression ratio (CCR) were also taken into account. As shown Table 5 and also in the above Fig. 3, the predicted and measured chip geometry parameters are very close when the material constants set M5 is still selected even if the material constants set M2 presents more regular chip geometry, but the average pitch is higher than the material constants set M5 and, especially, when compared to the experimental one. Concerning the average valley, it can be observed that the material constants set M1, M2 and M5 give the best predictions, even if only M2 and M5 present a more realistic chip curl and this result is due to the higher critical damage value (D) found by the iterative procedure (Fig. 2).
Table 4 Comparison between experimentally (EXP) and numerically (NUM) obtained forces (V c ¼ 100 m= min, b ¼ 0:2 mm, ap ¼ 6 mm)
EXP NUM_M1 NUM_M2 NUM_M3 NUM_M4 NUM_ M5
Fc (N)
Ft (N)
3494 3430 3598 3323 3195 3435
2838 3002 3171 2607 1954 2883
Fig. 3. Comparison between experimentally (EXP) and numerically (NUM) obtained chip geometry (vc ¼ 100 m= min, b ¼ 0:2 mm, ap ¼ 6 mm).
ARTICLE IN PRESS D. Umbrello et al. / International Journal of Machine Tools & Manufacture 47 (2007) 462–470 Table 5 Comparison between experimentally (EXP) and numerically (NUM) obtained chip geometry (vc ¼ 100 m= min, b ¼ 0:2 mm, ap ¼ 6 mm)
EXP NUM_M1 NUM_M2 NUM_M3 NUM_M4 NUM_M5
Valley (mm)
Peak (mm)
Pitch (mm)
CCR
255 219 215 160 190 235
407 423 423 310 417 412
167 239 315 240 310 225
2.0 2.1 2.1 1.6 2.1 2.1
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This effect is also noticeable in the other the material constants set M3 and M4 which use a lower D value. Similarly observations can be drawn when both the average peak and pitch are taken into account. It is important to denote that an irregular predicted chip shape was obtained for all the investigated material constants set. As suggested by Davies and Burns [28] when modelling shear localization in high-speed machining using a non-linear dynamic approach, the irregular chip shape may be due to an instability, which is the result of the competition between
Fig. 4. Predicted temperature distributions (vc ¼ 100 m= min, b ¼ 0:2 mm, ap ¼ 6 mm). The highest temperature region occurs at the tool—chip interface, for all the investigated cases.
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strain hardening and thermal softening. When strain hardening was not considered in their material flow stress model, the instability in the shear zone was interpreted as a ‘‘Hopf bifurcation’’ that led to periodic oscillations and formation of regular chip segments. On the contrary when strain hardening was considered (so is the case in the present study), the oscillations became irregular. They also found that this irregularity disappears gradually when increasing cutting speed leading to asymptotic periodic oscillations. 3.3. Temperature distributions
machined component [29]. As a result, an accurate prediction of residual stresses is needed in FE modelling of machining. The effects of the five different sets of work material constants used in this investigation on the prediction of residual stresses on machined surface and subsurface along the axial and circumferential directions are shown in Figs. 6 and 7, respectively. The measured residual stresses are higher at the surface, sometimes reaching a value of around 1000 MPa in the circumferential direction. The level of measured residual
Fig. 4 shows the predicted temperature fields generate during the FEA of the cutting process. It is not surprising that the material constants set M1, M2, M3 and M4 have a similar distribution pattern while M5 presents a highest temperature field. The reason could be that the material constants set in Tounsi et al.’s work [14] are identified through machining test (important in this case the role of the J–C term which include the effect of the temperature). The maximum temperature are 584, 591, 515, 453 and 841 1C for M1, M2, M3, M4 and M5 material constants set, respectively. Unfortunately, when comparing the predicted temperature distributions with those obtained experimentally (see Fig. 5), it can be observed that, even if the best prediction is considered, his maximum temperature is lower (about 200 1C less) than the experimental one. Possible reason for this difference could be due to the fact that the temperatures are obtained for a very short cutting process time (about 0.003 s), which is not sufficient to reach the steady-state temperature in the tool. Fig. 6. Comparison between measured and predicted residual stresses along axial direction (vc ¼ 200 m= min, b ¼ 0:1 mm, ap ¼ 6 mm).
3.4. Residual stresses The residual stresses are of critical importance since these can affect the functional behaviour of the whole
Fig. 5. Experimental temperature b ¼ 0:2 mm, ap ¼ 6 mm).
distribution
(vc ¼ 100 m= min,
Fig. 7. Comparison between measured and predicted residual stresses along circumferential direction (vc ¼ 200 m= min, b ¼ 0:1 mm, ap ¼ 6 mm).
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stresses in both directions decreases continuously with depth into the machined surface, stabilizing at a level corresponding to that found in the work material before machining (zero in axial direction and about 200 MPa in circumferential direction). As shown in Figs. 6 and 7, the predicted and measured in-depth residual stress profiles are very well correlated by the material constants set M5 while the other proposed models tend, in general, to overestimate (M1, M2 and M3) or underestimate (M4) the residual stresses. Furthermore, M4 gives compressive residual stresses both in axial and circumferential directions, while the other ones never present compressive residual stresses in accordance with the experimental evidences.
4. Conclusions The aim of the present work is to investigate the influence of the constants used in the Johnson–Cook’s (J–C) material constitutive equation on the forces, temperatures, chip morphology and residual stresses in the machined components of AISI 316L steel. The five sets of work material constants used in the J–C’s constitutive equation were implemented in a numerical machining model and the results were compared with experimental data. Results show that a reasonable prediction of cutting forces, chip morphology, temperature distributions and residual stresses is obtained when using material constants set M5 [14]. A possible reason could be that the constants for J–C model in Tounsi et al. work [14] are identified through machining tests where material shear flow stress is matched to the one obtained in the primary shear zone based on cutting forces results. This also partly the case in Chandrasekaran et al. [11] who identified the J–C constants using both results from split Hopkinson’s bar tests as well as those from orthogonal slot milling experiments. This is not the case for the other sets of work material constants, which are identified only through high-speed deformation tests where the range of strain, strain rate and temperature appears to be limited. The good agreement obtained between the experimental and numerical results indicate that the proposed FEM model appears to be suitable for studying the influence of cutting parameters on residual stress arising from machining.
Acknowledgments J.C. Outeiro gratefully acknowledges the financial support from FEDER through the Project POCI/EME/ 56406/2004, approved by the Fundac- a˜o para a Cieˆncia e a Tecnologia (FCT) and POCI 2010. Authors also thank the reviewers for their inputs and comments.
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International Journal of Machine Tools & Manufacture 47 (2007) 462–470 www.elsevier.com/locate/ijmactool
The influence of Johnson–Cook material constants on finite element simulation of machining of AISI 316L steel D. Umbrelloa,, R. M’Saoubib, J.C. Outeiroc a
Department of Mechanical Engineering, University of Calabria, 87036 Rende (CS), Italy b Corrosion and Metals Research Institute (KIMAB), SE-11428 Stockholm, Sweden c Portuguese Catholic University, 3080-024 Figueira da Foz, Portugal Received 22 April 2006; received in revised form 5 June 2006; accepted 14 June 2006 Available online 1 August 2006
Abstract In literature, five different sets of work material constants used in the Johnson–Cook’s (J–C) constitutive equation are implemented in a numerical model to describe the behaviour of AISI 316L steel. The aim of this research is to study the effects of five different sets of material constants of the J–C constitutive equation in finite-element modelling of orthogonal cutting of AISI 316L on the experimental and predicted cutting forces, chip morphology, temperature distributions and residual stresses. Several experimental equipments were used to estimate the experimental results, such as piezoelectric dynamometer for cutting forces measurements, thermal imaging system for temperature measurements and X-ray diffraction technique for residual stresses determination on the machined surfaces; while an elastic–viscoplastic FEM formulation was implemented to predict the local and global variables involved in this research. It has been observed that all the considered process output and, in particular the residual stresses are very sensitive to the J–C’s material constants. r 2006 Elsevier Ltd. All rights reserved. Keywords: Machining; FEM; Residual stresses; Work material model; Austenitic stainless steel
1. Introduction In the context of metal cutting, a large strain, large strain-rate and high temperature are usually reported in the literature. It is well known that the microscopic and macroscopic response of the material under high strain-rate loadings is affected by strain, strain rate, temperature, and microstructure of the material. So, to accurately analyse this process using numerical methods such as finite element analysis (FEA), the knowledge of material constitutive behaviour under these severe loading conditions is a prerequisite and hence correct work material flow stress data need to be used. In fact, the success and reliability of numerical models are mainly dependent upon mechanical (elastic constants, Corresponding author. Tel.: +39 984 494820; fax: +39 984 494673.
E-mail addresses: [email protected] (D. Umbrello), rachid.msaoubi@ kimab.com (R. M’Saoubi), [email protected] (J.C. Outeiro). URLs: http://www.unical.it, http://www.kimab.com, http://www.crb. ucp.pt. 0890-6955/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2006.06.006
flow stress, fracture stress/strain, etc.) and thermo-physical (density, thermal conductivity, heat capacity, etc.) properties of the work material, and contact conditions at tool–chip and tool–workpiece interfaces [1–5]. The correct selection of these parameters is often regarded as a critical step if one wants to predict with a reasonable accuracy forces, temperatures, chip morphology, tool wear and ultimately the surface integrity of the machined components (residual stresses, surface roughness, microstructure, etc.). Although many studies on finite element (FE) modelling of the orthogonal cutting process have been published until now, recent reviews on this topic [6,7] indicated that these were mainly focused on the prediction of strains, stress and cutting temperatures. Only a few studies on FE modelling involving the prediction of the machining residual stresses can be found in the literature, with special attention to the residual stresses in plain carbon steels and hardened steels [6–9]. Moreover, as far as the authors know, no sensitivity study is available about the influence of the constants used
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in the material constitutive equation on the residual stresses in the machined component, particularly those made in AISI 316L steel. The proposed paper presents a sensitivity study about the influence of the constants used in the Johnson–Cook’s (J–C) material constitutive equation on the forces, temperatures, chip morphology and residual stresses in the machined components of AISI 316L steel. For such study, five different sets of work material constants used in the J–C’s constitutive equation [10] (found by the application of several methods) are selected from literature [11–14]. Although such model is widely used in FE models to describe the constitutive behaviour of metals at high strain rates over a wide range of temperatures, its applicability over a wide range of strain is, however, limited due to the use of SHPB methods that permits to achieve only a limited range of strains. As suggested in Chandraserkaran et al. [11] the information from SHPB tests can be used only as a starting point while the identification of J–C parameters applicable for metal cutting requires additionally the combined use of machining tests and analytical chip formation models. It should also be mentioned that J–C model have been subjected to modifications by several authors to capture more accurately the behaviour of some metals and alloys at high strain rate [15–17]. However, such ambitious task was not undertaken in the present study which was aimed mainly at investigating the effect of various J–C constant obtained from literature on the modelling of RS during machining of AISI 316L and implemented in a FE model to simulate orthogonal cutting of AISI 316L by a comparison between the obtained predicted results (chip morphology, forces, temperatures and residual stresses) and those obtained from experimental studies.
2. Experimental and numerical procedures 2.1. Material properties, cutting tool and cutting regime parameters Round bars (150 mm in diameter) of austenitic stainlesssteel AISI 316L were selected for this study. Microstructure of the steel consisted of an equiaxed grain structure characterized by an approximate grain size of 50 mm and material hardness was close to 170HV. Orthogonal cutting tests were carried out on a lathe using radial feed motion (Fig. 1) using uncoated (ISO M10–M30) tungsten carbide tool. The thermo-physical properties both for workpiece and cutting tool are presented in Table 1. To model the elastic behaviour of AISI 316L steel a Poisson ratio (n) of 0.30 and a temperature (T)-dependent Young’s modulus given by experimental data [19], reported in Table 2, were used. To model the thermo-visco plastic behaviour of AISI 316L steel a J–C’s constitutive equation was employed,
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Fig. 1. Configuration of the orthogonal cutting tests and the directions of the measurements of the cutting forces and the residual stresses.
which can be represented by the following: T T room m _ seq ¼ ðA þ Bn Þ 1 þ C ln 1 , T m T room _0 (1) where is the plastic strain, _ is the strain rate (s1), _0 is the reference plastic strain rate (s1), T is the temperature of the work material (1C), Tm is the melting temperature of the work material (1399 1C) and Troom is the room temperature (20 1C). Coefficient A is the yield strength (MPa), B is the hardening modulus (MPa), C is the strain rate sensitivity coefficient, n is the hardening coefficient and m the thermal softening coefficient. Table 3 shows the five different sets of work material constants used in the J–C constitutive equation, found by several researchers [11–14]. These work material constants were found by the application of several methods. The M1 and M2 (Ref. [11]) sets of material constants were identified from high strain rate mechanical testing on hat-shaped specimens using the Split Hopkinson’s Pressure Bar method (SHPB) as well as instrumented orthogonal milling tests to generate information about material flow stress in machining based on different analytical chip formation models, namely continuous chip for M1 and serrated chip for M2. The M3 set of material constants (Ref. [12]) where obtained using SHPB tests that were carried on cylindrical compression specimens while M4 set of material constants (Ref. [13]) where based on SHPB experiments using hatshaped specimens. Finally, the M5 set of material constants (Ref. [14]) were determined using a methodology based on analytical modelling of the orthogonal cutting process along with metal cutting experiments. Finally, the range of the cutting tools geometry was as follows: the normal rake angle (gn) and the normal flank (an) angle were 01 and 111, respectively; the tool cutting edge angle (kr) was 901, the tool cutting edge inclination
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Table 1 Thermo-physical properties of AISI 316L steel [18] and WC-Co cutting tool Density (kg/m3): rw ðTÞ ¼ 7921 0:614 T þ 0:0002 T 2 Thermal conductivity (W/(mK)): kw ðTÞ ¼ 14:307 þ 0:0181 T 6 106 T 2 Specific heat (J/(kg K)): cp;w ðTÞ ¼ 440:79 þ 0:5807 T 0:001 T 2 þ 7 107 T 3 Density (kg/m3): 13000 Thermal conductivity (W/(mK)): 62.7 Heat capacity (J/(kg K)):234
AISI 316L steel
WC-Co cutting tool
Table 2 Young’s modulus of AISI 316L steel [19] T (1C) E (Gpa)
20 210.3
150 191.7
260 180.0
350 191.0
425 188.2
480 186.2
540 156.5
650 113.7
1200 68.0
Table 3 AISI 316L material constants for J–C constitutive model
Chandrasekaran et al. [11] Chandrasekaran et al. [11] M’Saoubi [12] Changeux et al. [13] Tounsi et al. [14]
M1 M2 M3 M4 M5
A
B
C
n
m
_0
305 305 301 280 514
1161 441 1472 1750 514
0.01 0.057 0.09 0.1 0.042
0.61 0.1 0.807 0.8 0.508
0.517 1.041 0.623 0.85 0.533
1 1 0.001 200 0.001
angle (ls) was 01, and the tool cutting edge radius (rn) of 0.030 mm. Concerning to the cutting regime parameters, the range for the cutting speed (nc) was 100–200 m/min, for the uncut chip thickness (b) was 0.1–0.2 and the width of cut (ap) was kept constant and equal to 6 mm. No cutting fluid was used in the tests.
2.2. Experimental set-up and parameters Orthogonal cutting tests were performed on a 15 HP numerically controlled lathe equipped with a specially designed experimental set-up. In measuring the cutting force components (tangential force and the thrust force) a Kistler-type 9255B three-component piezoelectric dynamometer was used. The tangential force component (Fc) was measured in the direction of the primary motion and the thrust force component (Ft) in the direction of feed motion. This experimental set-up also included thermal imaging equipment developed to assess the temperature distribution in the deformation zone. In particular, the temperature was measured on the lateral face of the cutting tool where tool chip interface temperature can be determined (under orthogonal cutting conditions) with good accuracy. A detailed description of this equipment and its calibration can be found in [20]. The residual stress state in the machined layers of the workpiece was analysed by the X-ray diffraction technique using the sin2 c method [21]. The parameters used in the Xray analysis are the same used in earlier investigation [9].
The residual stresses were determined for the stable cutting zone (where the cutting force components are stable) on the surface and in-depth, in the directions shown in Fig. 1. These directions are selected because the analysis of the residual stress tensors at the workpiece surface and subsurface allowed us to conclude that these directions are the directions of the principal stress components. To determine the in-depth residual stresses, successive layers of material were removed by electropolishing, to avoid the reintroduction of residual stress. Further corrections to the residual stress data were made due to the volume of material removed. Due to circularity of the workpieces, a circular mask with a diameter of 2.5 mm was applied to limit the region of analysis. The error associated with the method used was generally less than 50 MPa. 2.3. Numerical model and parameters The commercial FEA software DEFORM-2DTM, a Lagrangian implicit code, was used to simulate the orthogonal cutting process of AISI 316L. An FEM model of the orthogonal cutting process was developed and was composed of the workpiece and the tool. The workpiece was initially meshed with 3000 isoparametric quadrilateral elements, while the tool, modelled as rigid, was meshed and subdivided into 1000 elements. A plane-strain coupled thermo-mechanical analysis was performed using orthogonal assumption. The constitutive law used and implemented in the FEM model to take into account this complex material behaviour is given by Eq. (1). The thermo-physical
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properties of both workpiece and uncoated tool are in Table 1. Another consideration concerns the interface heat transfer coefficient, h, utilized in the preliminary thermomechanical numerical simulation. Usually a large h value is adopted, assuming perfect interface heat transfer conditions. However, the role of this parameter requires careful investigation, since it controls the effectiveness of the numerical simulation when a fully thermo-mechanical analysis is run, as reported in a recent study conducted by Filice et al. [22]. They found a value of h close to 1000 kW/m2 K, which permitted a satisfactory agreement between their numerical data and the experimental evidence in all the investigated cases. During the machining of AISI 316L steel, tensile stress plays an important role; therefore its effect should also be included in the material response such as the fracture criterion. In this research, Cockroft and Latham’s criterion is employed to predict the effect of tensile stress on chip segmentation during orthogonal cutting. Cockroft and Latham’s criterion is expressed as Z f s1 d ¼ D, (2) 0
where f is the effective strain, s1 is the principal stress, and D is a material constant. Cockroft and Latham’s criterion states that when the integral of the largest tensile principal stress component over the plastic strain path in Eq. (2) reaches the value of D, usually called damage value, fracture occurs or chip segmentation starts. As far as friction modelling is concerned, a simple model based on the constant shear hypothesis (t ¼ mt0 ) was implemented in the FE code. This assumption is based on recent investigation [23] where it is shown that both cutting forces and chip morphology can well predicted setting in
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the right way the friction coefficient independently of which friction law is taken into account. On the contrary, friction model became strategically important when other variables are considered, such as shear angle, normal pressure and thermal effects [24], even if either normal pressure and temperature were found with good accuracy using shear model too [25,26]. The determination of both D and m values were established by an iterative procedure based on chip geometry and cutting forces, respectively (Fig. 2). Finally, taking into account that, at moment using the DEFORM-2DTM FE code is not possible to obtain directly the numerical residual stresses, the authors have proposed the follow procedure: 1. An elastic-visco-plastic was implemented for the investigated cases and it was executed for a total time step long enough to reach the steady-state condition. 2. For several time steps the tool was released from the machined surface (unloading phase) and the workpiece is cooled down to the room temperature. 3. The numerical residual stress profiles were collected for few selected time steps and the average values were taken into account, using the procedure described in [27]. 3. Fe analysis and discussion of results To validate the orthogonal cutting model the predicted and experimentally measured chip morphology, cutting forces, temperatures and residual stresses on the machined affected layers were compared and their differences were discussed. The simulated cutting conditions are the same used in the experimental work, reported in Section 2.1.
Fig. 2. Flow chart for determining the friction factor, m, and the critical damage value, D.
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3.1. Cutting forces For each of the five sets of work material constants, both the experimental and the predicted averaged forces in the tangential direction (Fc) and in the thrust direction (Ft) are reported in Table 4. It is obvious that, except for the material constants set M4 [13], the predicted average tangential forces Fc agree well with the experimental one. In particular, the best prediction is given by for the material constants set M5 [14]. Similar observation could be made when comparing the thrust forces Ft. In fact, except again for the material constants set M4, the predicted thrust forces are almost close to the experiment, even if the error obtained by the material constants set M3 [12] underestimates the thrust value by 25.4%. The large discrepancy in cutting forces for the material constants set M4 can be attributed to its relatively lower flow stress. 3.2. Chip morphology The comparison between the experimental and the predicted chip morphology are shown in Fig. 3. The chip curl of the material constants set M2 and M5 have the largest radius, followed by the material constants set M4, M1 and M3, respectively. Comparing with the experimental chip curl it can be seen that only the material constants set M2 and M5 agree well. The average values of the chip geometry (valley, peak and pitch), including chip compression ratio (CCR) were also taken into account. As shown Table 5 and also in the above Fig. 3, the predicted and measured chip geometry parameters are very close when the material constants set M5 is still selected even if the material constants set M2 presents more regular chip geometry, but the average pitch is higher than the material constants set M5 and, especially, when compared to the experimental one. Concerning the average valley, it can be observed that the material constants set M1, M2 and M5 give the best predictions, even if only M2 and M5 present a more realistic chip curl and this result is due to the higher critical damage value (D) found by the iterative procedure (Fig. 2).
Table 4 Comparison between experimentally (EXP) and numerically (NUM) obtained forces (V c ¼ 100 m= min, b ¼ 0:2 mm, ap ¼ 6 mm)
EXP NUM_M1 NUM_M2 NUM_M3 NUM_M4 NUM_ M5
Fc (N)
Ft (N)
3494 3430 3598 3323 3195 3435
2838 3002 3171 2607 1954 2883
Fig. 3. Comparison between experimentally (EXP) and numerically (NUM) obtained chip geometry (vc ¼ 100 m= min, b ¼ 0:2 mm, ap ¼ 6 mm).
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EXP NUM_M1 NUM_M2 NUM_M3 NUM_M4 NUM_M5
Valley (mm)
Peak (mm)
Pitch (mm)
CCR
255 219 215 160 190 235
407 423 423 310 417 412
167 239 315 240 310 225
2.0 2.1 2.1 1.6 2.1 2.1
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This effect is also noticeable in the other the material constants set M3 and M4 which use a lower D value. Similarly observations can be drawn when both the average peak and pitch are taken into account. It is important to denote that an irregular predicted chip shape was obtained for all the investigated material constants set. As suggested by Davies and Burns [28] when modelling shear localization in high-speed machining using a non-linear dynamic approach, the irregular chip shape may be due to an instability, which is the result of the competition between
Fig. 4. Predicted temperature distributions (vc ¼ 100 m= min, b ¼ 0:2 mm, ap ¼ 6 mm). The highest temperature region occurs at the tool—chip interface, for all the investigated cases.
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strain hardening and thermal softening. When strain hardening was not considered in their material flow stress model, the instability in the shear zone was interpreted as a ‘‘Hopf bifurcation’’ that led to periodic oscillations and formation of regular chip segments. On the contrary when strain hardening was considered (so is the case in the present study), the oscillations became irregular. They also found that this irregularity disappears gradually when increasing cutting speed leading to asymptotic periodic oscillations. 3.3. Temperature distributions
machined component [29]. As a result, an accurate prediction of residual stresses is needed in FE modelling of machining. The effects of the five different sets of work material constants used in this investigation on the prediction of residual stresses on machined surface and subsurface along the axial and circumferential directions are shown in Figs. 6 and 7, respectively. The measured residual stresses are higher at the surface, sometimes reaching a value of around 1000 MPa in the circumferential direction. The level of measured residual
Fig. 4 shows the predicted temperature fields generate during the FEA of the cutting process. It is not surprising that the material constants set M1, M2, M3 and M4 have a similar distribution pattern while M5 presents a highest temperature field. The reason could be that the material constants set in Tounsi et al.’s work [14] are identified through machining test (important in this case the role of the J–C term which include the effect of the temperature). The maximum temperature are 584, 591, 515, 453 and 841 1C for M1, M2, M3, M4 and M5 material constants set, respectively. Unfortunately, when comparing the predicted temperature distributions with those obtained experimentally (see Fig. 5), it can be observed that, even if the best prediction is considered, his maximum temperature is lower (about 200 1C less) than the experimental one. Possible reason for this difference could be due to the fact that the temperatures are obtained for a very short cutting process time (about 0.003 s), which is not sufficient to reach the steady-state temperature in the tool. Fig. 6. Comparison between measured and predicted residual stresses along axial direction (vc ¼ 200 m= min, b ¼ 0:1 mm, ap ¼ 6 mm).
3.4. Residual stresses The residual stresses are of critical importance since these can affect the functional behaviour of the whole
Fig. 5. Experimental temperature b ¼ 0:2 mm, ap ¼ 6 mm).
distribution
(vc ¼ 100 m= min,
Fig. 7. Comparison between measured and predicted residual stresses along circumferential direction (vc ¼ 200 m= min, b ¼ 0:1 mm, ap ¼ 6 mm).
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stresses in both directions decreases continuously with depth into the machined surface, stabilizing at a level corresponding to that found in the work material before machining (zero in axial direction and about 200 MPa in circumferential direction). As shown in Figs. 6 and 7, the predicted and measured in-depth residual stress profiles are very well correlated by the material constants set M5 while the other proposed models tend, in general, to overestimate (M1, M2 and M3) or underestimate (M4) the residual stresses. Furthermore, M4 gives compressive residual stresses both in axial and circumferential directions, while the other ones never present compressive residual stresses in accordance with the experimental evidences.
4. Conclusions The aim of the present work is to investigate the influence of the constants used in the Johnson–Cook’s (J–C) material constitutive equation on the forces, temperatures, chip morphology and residual stresses in the machined components of AISI 316L steel. The five sets of work material constants used in the J–C’s constitutive equation were implemented in a numerical machining model and the results were compared with experimental data. Results show that a reasonable prediction of cutting forces, chip morphology, temperature distributions and residual stresses is obtained when using material constants set M5 [14]. A possible reason could be that the constants for J–C model in Tounsi et al. work [14] are identified through machining tests where material shear flow stress is matched to the one obtained in the primary shear zone based on cutting forces results. This also partly the case in Chandrasekaran et al. [11] who identified the J–C constants using both results from split Hopkinson’s bar tests as well as those from orthogonal slot milling experiments. This is not the case for the other sets of work material constants, which are identified only through high-speed deformation tests where the range of strain, strain rate and temperature appears to be limited. The good agreement obtained between the experimental and numerical results indicate that the proposed FEM model appears to be suitable for studying the influence of cutting parameters on residual stress arising from machining.
Acknowledgments J.C. Outeiro gratefully acknowledges the financial support from FEDER through the Project POCI/EME/ 56406/2004, approved by the Fundac- a˜o para a Cieˆncia e a Tecnologia (FCT) and POCI 2010. Authors also thank the reviewers for their inputs and comments.
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