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A new approach for the modelling of residual stresses induced by turning of 316L
Journal of Materials Processing Technology 191 (2007) 270–273
A new approach for the modelling of residual stresses induced by turning of 316L F. Valiorgue a,∗ , J. Rech a , H. Hamdi a , P. Gilles b , J.M. Bergheau a ´ LTDS-ENISE, 42023 Saint-Etienne, France FRAMATOME ANP, Tour AREVA, 92084 Paris La D´efense, France a
b
Abstract Residual stresses induced by machining processes like turning play an important role on the lifetime of pieces. Several phenomena are responsible of these distributions: mechanical effects, thermal effects, microstructure modifications and/or a combination of the previous mechanisms. During the last 20 years, a large number of experimental investigations have shown the influence of machining parameters on the distribution of residual stresses, whereas only few works have tried to model the fundamental phenomena. Past works try to model the chip removal process by means of finite element software allowing large strains. Such models are very limited to predict accurately the residual stresses profiles in very narrow affected layers (some micrometers) and are very much CPU time consuming. The key idea presented in this paper consists in disconnecting the chip formation process on one hand and the modelling of the mechanisms leading to the residual stresses on the other hand. Indeed, this approach necessitates quantifying the thermo-mechanical load induced by the cutting tool onto the machined surface. Secondly, a finite-element model simulates the application and the movement of this thermo-mechanical load on to the machined surface so as to predict the residual stresses induced. © 2007 Elsevier B.V. All rights reserved. Keywords: Austenitic stainless steel; Numerical modelling; Residual stresses; Metal cutting
1. Introduction Various researchers have made investigations in the field of residual stresses induced by machining operations [1]. Nevertheless few of them were concerned by austenitic stainless steels [2]. These investigations were mainly experimental and have observed the residual stresses induced by X-ray diffraction. In the area of modelling, very few investigations have been made. Must of these studies propose to model the material removal mechanism by finite element analysis [3,4]. Those methods present numerous numerical problems and hardly respect the physical laws. For examples, the control of the contact and the chip-workpiece separation around the cutting edge are really hard to model. Moreover, the machining modelling leads to large strain, which necessitates the use of remeshing or adaptive mesh. However, the application of such a method to get quantitative results is questionable [5]. The aim of this paper is to introduce an original approach for the prediction of residual stresses. Especially the main objective is to get reliable results within an acceptable computational duration for an industrial application, i.e. lower than 8 h in order to optimise the manufacturing process. The first key idea of this ∗
Corresponding author.
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.03.021
new method is to disconnect the chip formation mechanism on the one hand, and the modelling of residual stresses on the other hand. Indeed, the modelling of the material removal mechanism is a very computational time consuming operation. Such models provides numerous informations related to the chip, the cutting tools and the machined surface, whereas the apparition of residual stresses in machined surfaces are only influenced by the thermo-mechanical loading supported in the primary shear zone and at the tool-workpiece interface. As a consequence, the key idea of this new approach consists in quantifying the thermomechanical loadings supported by the machined surface on the one hand and on the other hand, to program their application in a finite element model. This paper presents this new method. Section 2 will describe the model from its analytical aspect to the FEM developed with the SYSWELD® code. Section 3 will compare experimental and calculated results. Section 4 will present the sensitivity of each input data on the stability of the model. 2. Problematic modeling 2.1. Context of the study In the context of finish turning (Fig. 1a) the generation of residual stresses in the machined surface is determined by the
F. Valiorgue et al. / Journal of Materials Processing Technology 191 (2007) 270–273
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• Fc1 : Normal force generated by the material removal. • Ff1 : Force generated by the friction of the chip on the rake face. • Ff2: Normal force generated by the tool penetration in the machined surface (contact area l × f). • Fc2 : Force generated by the friction on the flank face. The cutting forces supported by the cutting tool in the Y direction correspond to the combination of Fc1 + Fc2 . Fc = Fc1 + Fc2 Fig. 1. Context of the study.
thermo-mechanical phenomena close to the tool tip radius Rε (Fig. 1b). When observing the removal mechanisms in the plane X–Y (Fig. 1c), it appears that the machined surface is submitted to a heat flux coming from the primary shear zone (PSZ) and a heat flux coming from the rubbing of the tool flank face. Additionally, the flank face induces a mechanical load in the direction X (Fig. 1b). As a consequence, by looking in the plane Y–Z (Fig. 1d), it is possible to model the loading by: • two heat flux sources (1) and (2): one corresponding to the effect of the primary shear zone and one corresponding to the rubbing effect. • one mechanical loading below the cutting flank face (2). N.B.: The cutting edge radius rβ has not been considered in this model. For a first approach, the mechanical action induced by the PSZ on the machined surface could be neglected. This parameters will of course be introduced in a future update of the model. The challenge of this approach is to quantify the geometry and the density of each sources. 2.2. Detailed description of the model As presented before, the model is loaded with two thermal and one mechanical loading. These three sources need to be quantified. 2.2.1. Mechanical sources description Fig. 2 illustrates the various mechanical loads applied by the chip and the machined surface to the insert.
(1)
The feed forces supported by the cutting tool in the X direction correspond to the combination of Ff1 + Ff2 . Ff = Ff1 + Ff2
(2)
The friction at each interface can be modelled as: Ff1 = μrf × Fc1
(3)
Fc2 = μff × Ff2
(4)
μrf1 is the friction coefficient on the rake face; μff is the friction coefficient on the flank face. 2.2.2. First thermal source description (PSZ) In orthogonal cutting, the power consumed for material removing is estimated by the following equation: P1 = Fc1 × Vc
(5)
A fraction of this power is consumed for the strain hardening of the stainless steel while the rest is dissipated into heat. Shet, Deng and Shi [6] proposed the following repartition: 15% for strain hardening and 85% for thermal dissipation in the context of steel machining. Additionally Schmidt and Roubik [7] assumed that 90% of the heat is dissipated through the chip and 10% through the workpiece (Φ1 in Fig. 1c). These data have been estimated in a different context but they have been assumed as acceptable in a first approach. As a consequence, the investigation on the sensitivity of this parameter on the stability of the model is necessary. Φ1 = Λ1 × Fc1 × Vc = 0.85 × 0.1 × Fc1 × Vc
(6)
N.B.: Λ1 can be considered as similar to a heat partition coefficient. The heat exchange surface of the first thermal source, generated in the primary shear zone, depends on the chip thickness. It has been assumed that the surface exchange is equal to the chip thickness multiplied by its width as shown in Fig. 1c. 2.2.3. Second thermal source description The heat flow generated at the insert-machined surface interface is due to the friction of the flank face on the machined surface. The energy dissipated at this interface is: P2 = Fc2 × Vc
Fig. 2. Mechanical loading.
(7)
It is supposed that 5% of this heat flux is transmitted to the machined surface (Λ2 : heat partition coefficient). As a conse-
272
F. Valiorgue et al. / Journal of Materials Processing Technology 191 (2007) 270–273
Fig. 3. Cutting forces measurement configuration.
Fig. 4. Workpiece-insert contact length.
quence, the heat flux transmitted to the machined surface, Φ2 , can be estimated by: Φ2 = Λ2 × Fc2 × Vc = 0.05 × Fc2 × Vc
(8)
2.3. Quantification of the model 2.3.1. Mechanical sources quantification Experimental tests have been carried out on a CNC lathe equipped with a dynamometer. The cutting tool used is a TiN coated carbide tool having a leading angle κr of 90◦ , a rake angle γ n of 0◦ and an inclination angle λs of 0◦ . The workpieces are made from an AISI 316L austenitic stainless steel having a geometry of a tube (external diameter, 80 mm; thickness, 3 mm). The cutting speed Vc is 60 m/min, the feed is 0.1 mm/rev, the depth of cut is equal to the tube thickness: ap = 3 mm. Each test has been replicated five times. Fig. 3 presents the configuration of the cutting force measurement.The measured cutting forces values are:
Additionally, the scientific literature provides an order of magnitude of the friction coefficients in the context of steel machining: μrf = 0.4, μff = 0.2 [8]. These data are assumed as acceptable for a first approach. Based on Eqs. (1)–(4) it is possible to determine: Fc2 = 60 N,
Ff1 = 422 N,
2.4. Description of the numerical model The flow stress model of the 316L stainless steel has been determined, based on the work of [2]: σ y = 967.4 × ε0.397 . pl
Fc = 1117 N ± 2%, Ff = 726 N ± 2%
Fc1 = 1056 N,
speed is equal to 1 m s−1 and the force Fc1 = 1056 N. Based on Eq. (6): Φ1 = 90 W. The model necessitates determining the heat flux density. By measuring the chip thickness, it is possible to determine it (Fig. 1c). The measurements of the average chip thickness provide a value of 0.35 mm with a deviation of 6%. Then the heat flow density is 90 W mm−2 . The power generated at the Third Shear Zone (P2 ) is calculated using the cutting speed and the force Fc2 . The cutting speed is equal to 1 m s−1 and the force Fc2 reaches 60 N. Based on Eq. (8): Φ2 = 3 W. The measurement of contact length between the insert and the machined surface equals provides a value of 0.059 mm ± 20% (Fig. 4). Then the heat flow density is 17 W mm−2 .
Ff2 = 303 N
To estimate the workpiece-insert contact length on the flank face, a binocular microscope has been used. The average value is 58 m with a deviation of 18% (Fig. 4). 2.3.2. Heat sources quantification The power generated at the primary shear zone (P1 ) is calculated using the cutting speed and the force Fc1. The cutting
(7)
The plasticity criteria is a von Mises one and an isotropic hardening is used. The sources are time space functions. The elements near the surface of the piece are smaller to take into account the high residual stress gradient. The elements used are quadrangle and linear (0.045 mm × 0.045 mm). The left and bottom sides of the piece are built-in (Fig. 5) and the thermal conductivity between the model and the air or the rest of the workpiece is taken into account. The material characteristics are: E = 176,500 MPa; ν = 0.3, since [2]. 3. Results Fig. 6 shows the residual stress profile (σ yy ) calculated with the model and the residual stress profile determined experimentally on a piece turned with the same cutting conditions.
Fig. 5. Numerical model.
F. Valiorgue et al. / Journal of Materials Processing Technology 191 (2007) 270–273
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Table 1 Sensitivity of the model to some strategic input parameters Original simulation
μrf = 0.4
μff = 0.2
Λ1 = 0.085
Λ2 = 0.05
S1 = 270 MPa
Sensitivity to μrf
μrf = 0.52 μrf = 0.28 μrf = 0.4 μrf = 0.4
μff = 0.2 μff = 0.2 μff = 0.26 μff = 0.14
Λ1 = 0.085 Λ1 = 0.085 Λ1 = 0.085 Λ1 = 0.085
Λ2 = 0.05 Λ2 = 0.05 Λ2 = 0.05 Λ2 = 0.05
S1 = 50 MPa (−80%) S1 = 280 MPa (4%) S1 = 330 MPa (22%) S1 = 230 MPa (−15%)
Sensitivity to Λ1
μrf = 0.4 μrf = 0.4
μff = 0.2 μff = 0.2
Λ1 = 0.11 Λ1 = 0.06
Λ2 = 0.05 Λ2 = 0.05
S1 = 310 MPa (15%) S1 = 245 MPa (−10%)
Sensitivity to Λ2
μrf = 0.4 μrf = 0.4
μff = 0.2 μff = 0.2
Λ1 = 0.085 Λ1 = 0.085
Λ2 = 0.065 Λ2 = 0.035
S1 = 310 MPa (15%) S1 = 245 MPa (10%)
Bold values are modified ones in order to test the sensitivity of the model.
is changed in a range of ±30%. Before presenting the results, it is necessary to say that the shape of the residual stress profiles remains unchanged. The most influenced parameter is the residual stress on the skin (S1 ). Most critical parameter are the friction coefficients. They control the tangential force applied on the machined surface (mechanical load) and the heat flux transmitted to the machined surface (heat flux load). 5. Conclusion
Fig. 6. Residual stress curves.
Concerning the results, both curves have a coherent shape, showing the efficiency of the model. They reveal a tensile stress at the top surface of the workpiece. The residual stress profile decreases rapidly with depth down to a minimum compressive stress value and then increases until it reaches the initial stress state of the material. The affected layer is lower than 100 m. The shape of both curves is in good agreement with previous works in the literature [2]. In a first approach, it seems to be reasonable to compare only the shape of the curves due to the numerous hypothesis of the model. The X-ray diffraction technique has been used to quantify the residual stresses by means of a machine ‘PROTO’ associated with ‘XRDWin’ software. The cubic centred face has been taken into account for this measurement. The X-ray source was a K␣ ray of manganesium (18 kV, 4 mA, λ = 0.21 nm, plane [3 1 1], 2θ = 152◦ ). The deviation of the measurements was: ±30 MPa. 4. Discussion To improve the numerical model it is important to determine the sensitivity of each hypothesis on the computed result. Table 1 shows the influence of some strategic input data when their value
In conclusion, this paper has shown that it is possible to predict the shape of the residual stress profile. This method does not model the chip removal mechanisms, but only the thermomechanical load on the machined surface. The application of this method in the context of 316L stainless steel turning has shown its velocity to provide a coherent result with experimental values. The stability of the model has also been investigated, showing that the friction parameters at the tool-chip-workpiece interfaces on the one hand and the heat partition coefficient at the flank face on the other hand, are the key parameters controlling the efficiency of the model. References [1] E.M. Trent, Met. Cutting (1991), ISBN 0408108568. [2] R. M’Saoubi, Residual stress analysis in orthogonal machining of standard and resulfurized AISI 316L steels, J. Mater. Process. Technol. 96 (1998) 225–233. [3] K.C. Ee, Finite element modelling of residual stresses in machining induced by cutting using a tool with finite edge radius, J. Mater. Process. Technol. 47 (2005) 1611–1628. [4] X.X. Yu, A Finite Element Analysis of Residual Stresses in Stretch Turning, vol. 37, Elsevier Science, 1997, pp. 1525–1537. [5] M. Barge, H. Hamdi, J. Rech, J.M. Bergheau, Numerical modelling of orthogonal cutting: influence of numerical parameters, J. Mater. Process. Technol. 164–165 (2005) 1148–1153. [6] C. Shet, X. Deng, G. Shi, A Finite Element Study of the Effect of Friction in Orthogonal Metal Cutting, vol. 43, Elsevier Science, 2002, pp. 573–587. [7] A.O. Schmidt, R.J. Roubik, Distribution of heat generated in drilling, ASME 71 (1949) 245–252. [8] L. Puigsegur, Caract´erisation thermique d’un proc´ed´e d’usinage par tournage. Approche analytique et par identification de syst`emes non entiers, 2002.
A new approach for the modelling of residual stresses induced by turning of 316L F. Valiorgue a,∗ , J. Rech a , H. Hamdi a , P. Gilles b , J.M. Bergheau a ´ LTDS-ENISE, 42023 Saint-Etienne, France FRAMATOME ANP, Tour AREVA, 92084 Paris La D´efense, France a
b
Abstract Residual stresses induced by machining processes like turning play an important role on the lifetime of pieces. Several phenomena are responsible of these distributions: mechanical effects, thermal effects, microstructure modifications and/or a combination of the previous mechanisms. During the last 20 years, a large number of experimental investigations have shown the influence of machining parameters on the distribution of residual stresses, whereas only few works have tried to model the fundamental phenomena. Past works try to model the chip removal process by means of finite element software allowing large strains. Such models are very limited to predict accurately the residual stresses profiles in very narrow affected layers (some micrometers) and are very much CPU time consuming. The key idea presented in this paper consists in disconnecting the chip formation process on one hand and the modelling of the mechanisms leading to the residual stresses on the other hand. Indeed, this approach necessitates quantifying the thermo-mechanical load induced by the cutting tool onto the machined surface. Secondly, a finite-element model simulates the application and the movement of this thermo-mechanical load on to the machined surface so as to predict the residual stresses induced. © 2007 Elsevier B.V. All rights reserved. Keywords: Austenitic stainless steel; Numerical modelling; Residual stresses; Metal cutting
1. Introduction Various researchers have made investigations in the field of residual stresses induced by machining operations [1]. Nevertheless few of them were concerned by austenitic stainless steels [2]. These investigations were mainly experimental and have observed the residual stresses induced by X-ray diffraction. In the area of modelling, very few investigations have been made. Must of these studies propose to model the material removal mechanism by finite element analysis [3,4]. Those methods present numerous numerical problems and hardly respect the physical laws. For examples, the control of the contact and the chip-workpiece separation around the cutting edge are really hard to model. Moreover, the machining modelling leads to large strain, which necessitates the use of remeshing or adaptive mesh. However, the application of such a method to get quantitative results is questionable [5]. The aim of this paper is to introduce an original approach for the prediction of residual stresses. Especially the main objective is to get reliable results within an acceptable computational duration for an industrial application, i.e. lower than 8 h in order to optimise the manufacturing process. The first key idea of this ∗
Corresponding author.
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.03.021
new method is to disconnect the chip formation mechanism on the one hand, and the modelling of residual stresses on the other hand. Indeed, the modelling of the material removal mechanism is a very computational time consuming operation. Such models provides numerous informations related to the chip, the cutting tools and the machined surface, whereas the apparition of residual stresses in machined surfaces are only influenced by the thermo-mechanical loading supported in the primary shear zone and at the tool-workpiece interface. As a consequence, the key idea of this new approach consists in quantifying the thermomechanical loadings supported by the machined surface on the one hand and on the other hand, to program their application in a finite element model. This paper presents this new method. Section 2 will describe the model from its analytical aspect to the FEM developed with the SYSWELD® code. Section 3 will compare experimental and calculated results. Section 4 will present the sensitivity of each input data on the stability of the model. 2. Problematic modeling 2.1. Context of the study In the context of finish turning (Fig. 1a) the generation of residual stresses in the machined surface is determined by the
F. Valiorgue et al. / Journal of Materials Processing Technology 191 (2007) 270–273
271
• Fc1 : Normal force generated by the material removal. • Ff1 : Force generated by the friction of the chip on the rake face. • Ff2: Normal force generated by the tool penetration in the machined surface (contact area l × f). • Fc2 : Force generated by the friction on the flank face. The cutting forces supported by the cutting tool in the Y direction correspond to the combination of Fc1 + Fc2 . Fc = Fc1 + Fc2 Fig. 1. Context of the study.
thermo-mechanical phenomena close to the tool tip radius Rε (Fig. 1b). When observing the removal mechanisms in the plane X–Y (Fig. 1c), it appears that the machined surface is submitted to a heat flux coming from the primary shear zone (PSZ) and a heat flux coming from the rubbing of the tool flank face. Additionally, the flank face induces a mechanical load in the direction X (Fig. 1b). As a consequence, by looking in the plane Y–Z (Fig. 1d), it is possible to model the loading by: • two heat flux sources (1) and (2): one corresponding to the effect of the primary shear zone and one corresponding to the rubbing effect. • one mechanical loading below the cutting flank face (2). N.B.: The cutting edge radius rβ has not been considered in this model. For a first approach, the mechanical action induced by the PSZ on the machined surface could be neglected. This parameters will of course be introduced in a future update of the model. The challenge of this approach is to quantify the geometry and the density of each sources. 2.2. Detailed description of the model As presented before, the model is loaded with two thermal and one mechanical loading. These three sources need to be quantified. 2.2.1. Mechanical sources description Fig. 2 illustrates the various mechanical loads applied by the chip and the machined surface to the insert.
(1)
The feed forces supported by the cutting tool in the X direction correspond to the combination of Ff1 + Ff2 . Ff = Ff1 + Ff2
(2)
The friction at each interface can be modelled as: Ff1 = μrf × Fc1
(3)
Fc2 = μff × Ff2
(4)
μrf1 is the friction coefficient on the rake face; μff is the friction coefficient on the flank face. 2.2.2. First thermal source description (PSZ) In orthogonal cutting, the power consumed for material removing is estimated by the following equation: P1 = Fc1 × Vc
(5)
A fraction of this power is consumed for the strain hardening of the stainless steel while the rest is dissipated into heat. Shet, Deng and Shi [6] proposed the following repartition: 15% for strain hardening and 85% for thermal dissipation in the context of steel machining. Additionally Schmidt and Roubik [7] assumed that 90% of the heat is dissipated through the chip and 10% through the workpiece (Φ1 in Fig. 1c). These data have been estimated in a different context but they have been assumed as acceptable in a first approach. As a consequence, the investigation on the sensitivity of this parameter on the stability of the model is necessary. Φ1 = Λ1 × Fc1 × Vc = 0.85 × 0.1 × Fc1 × Vc
(6)
N.B.: Λ1 can be considered as similar to a heat partition coefficient. The heat exchange surface of the first thermal source, generated in the primary shear zone, depends on the chip thickness. It has been assumed that the surface exchange is equal to the chip thickness multiplied by its width as shown in Fig. 1c. 2.2.3. Second thermal source description The heat flow generated at the insert-machined surface interface is due to the friction of the flank face on the machined surface. The energy dissipated at this interface is: P2 = Fc2 × Vc
Fig. 2. Mechanical loading.
(7)
It is supposed that 5% of this heat flux is transmitted to the machined surface (Λ2 : heat partition coefficient). As a conse-
272
F. Valiorgue et al. / Journal of Materials Processing Technology 191 (2007) 270–273
Fig. 3. Cutting forces measurement configuration.
Fig. 4. Workpiece-insert contact length.
quence, the heat flux transmitted to the machined surface, Φ2 , can be estimated by: Φ2 = Λ2 × Fc2 × Vc = 0.05 × Fc2 × Vc
(8)
2.3. Quantification of the model 2.3.1. Mechanical sources quantification Experimental tests have been carried out on a CNC lathe equipped with a dynamometer. The cutting tool used is a TiN coated carbide tool having a leading angle κr of 90◦ , a rake angle γ n of 0◦ and an inclination angle λs of 0◦ . The workpieces are made from an AISI 316L austenitic stainless steel having a geometry of a tube (external diameter, 80 mm; thickness, 3 mm). The cutting speed Vc is 60 m/min, the feed is 0.1 mm/rev, the depth of cut is equal to the tube thickness: ap = 3 mm. Each test has been replicated five times. Fig. 3 presents the configuration of the cutting force measurement.The measured cutting forces values are:
Additionally, the scientific literature provides an order of magnitude of the friction coefficients in the context of steel machining: μrf = 0.4, μff = 0.2 [8]. These data are assumed as acceptable for a first approach. Based on Eqs. (1)–(4) it is possible to determine: Fc2 = 60 N,
Ff1 = 422 N,
2.4. Description of the numerical model The flow stress model of the 316L stainless steel has been determined, based on the work of [2]: σ y = 967.4 × ε0.397 . pl
Fc = 1117 N ± 2%, Ff = 726 N ± 2%
Fc1 = 1056 N,
speed is equal to 1 m s−1 and the force Fc1 = 1056 N. Based on Eq. (6): Φ1 = 90 W. The model necessitates determining the heat flux density. By measuring the chip thickness, it is possible to determine it (Fig. 1c). The measurements of the average chip thickness provide a value of 0.35 mm with a deviation of 6%. Then the heat flow density is 90 W mm−2 . The power generated at the Third Shear Zone (P2 ) is calculated using the cutting speed and the force Fc2 . The cutting speed is equal to 1 m s−1 and the force Fc2 reaches 60 N. Based on Eq. (8): Φ2 = 3 W. The measurement of contact length between the insert and the machined surface equals provides a value of 0.059 mm ± 20% (Fig. 4). Then the heat flow density is 17 W mm−2 .
Ff2 = 303 N
To estimate the workpiece-insert contact length on the flank face, a binocular microscope has been used. The average value is 58 m with a deviation of 18% (Fig. 4). 2.3.2. Heat sources quantification The power generated at the primary shear zone (P1 ) is calculated using the cutting speed and the force Fc1. The cutting
(7)
The plasticity criteria is a von Mises one and an isotropic hardening is used. The sources are time space functions. The elements near the surface of the piece are smaller to take into account the high residual stress gradient. The elements used are quadrangle and linear (0.045 mm × 0.045 mm). The left and bottom sides of the piece are built-in (Fig. 5) and the thermal conductivity between the model and the air or the rest of the workpiece is taken into account. The material characteristics are: E = 176,500 MPa; ν = 0.3, since [2]. 3. Results Fig. 6 shows the residual stress profile (σ yy ) calculated with the model and the residual stress profile determined experimentally on a piece turned with the same cutting conditions.
Fig. 5. Numerical model.
F. Valiorgue et al. / Journal of Materials Processing Technology 191 (2007) 270–273
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Table 1 Sensitivity of the model to some strategic input parameters Original simulation
μrf = 0.4
μff = 0.2
Λ1 = 0.085
Λ2 = 0.05
S1 = 270 MPa
Sensitivity to μrf
μrf = 0.52 μrf = 0.28 μrf = 0.4 μrf = 0.4
μff = 0.2 μff = 0.2 μff = 0.26 μff = 0.14
Λ1 = 0.085 Λ1 = 0.085 Λ1 = 0.085 Λ1 = 0.085
Λ2 = 0.05 Λ2 = 0.05 Λ2 = 0.05 Λ2 = 0.05
S1 = 50 MPa (−80%) S1 = 280 MPa (4%) S1 = 330 MPa (22%) S1 = 230 MPa (−15%)
Sensitivity to Λ1
μrf = 0.4 μrf = 0.4
μff = 0.2 μff = 0.2
Λ1 = 0.11 Λ1 = 0.06
Λ2 = 0.05 Λ2 = 0.05
S1 = 310 MPa (15%) S1 = 245 MPa (−10%)
Sensitivity to Λ2
μrf = 0.4 μrf = 0.4
μff = 0.2 μff = 0.2
Λ1 = 0.085 Λ1 = 0.085
Λ2 = 0.065 Λ2 = 0.035
S1 = 310 MPa (15%) S1 = 245 MPa (10%)
Bold values are modified ones in order to test the sensitivity of the model.
is changed in a range of ±30%. Before presenting the results, it is necessary to say that the shape of the residual stress profiles remains unchanged. The most influenced parameter is the residual stress on the skin (S1 ). Most critical parameter are the friction coefficients. They control the tangential force applied on the machined surface (mechanical load) and the heat flux transmitted to the machined surface (heat flux load). 5. Conclusion
Fig. 6. Residual stress curves.
Concerning the results, both curves have a coherent shape, showing the efficiency of the model. They reveal a tensile stress at the top surface of the workpiece. The residual stress profile decreases rapidly with depth down to a minimum compressive stress value and then increases until it reaches the initial stress state of the material. The affected layer is lower than 100 m. The shape of both curves is in good agreement with previous works in the literature [2]. In a first approach, it seems to be reasonable to compare only the shape of the curves due to the numerous hypothesis of the model. The X-ray diffraction technique has been used to quantify the residual stresses by means of a machine ‘PROTO’ associated with ‘XRDWin’ software. The cubic centred face has been taken into account for this measurement. The X-ray source was a K␣ ray of manganesium (18 kV, 4 mA, λ = 0.21 nm, plane [3 1 1], 2θ = 152◦ ). The deviation of the measurements was: ±30 MPa. 4. Discussion To improve the numerical model it is important to determine the sensitivity of each hypothesis on the computed result. Table 1 shows the influence of some strategic input data when their value
In conclusion, this paper has shown that it is possible to predict the shape of the residual stress profile. This method does not model the chip removal mechanisms, but only the thermomechanical load on the machined surface. The application of this method in the context of 316L stainless steel turning has shown its velocity to provide a coherent result with experimental values. The stability of the model has also been investigated, showing that the friction parameters at the tool-chip-workpiece interfaces on the one hand and the heat partition coefficient at the flank face on the other hand, are the key parameters controlling the efficiency of the model. References [1] E.M. Trent, Met. Cutting (1991), ISBN 0408108568. [2] R. M’Saoubi, Residual stress analysis in orthogonal machining of standard and resulfurized AISI 316L steels, J. Mater. Process. Technol. 96 (1998) 225–233. [3] K.C. Ee, Finite element modelling of residual stresses in machining induced by cutting using a tool with finite edge radius, J. Mater. Process. Technol. 47 (2005) 1611–1628. [4] X.X. Yu, A Finite Element Analysis of Residual Stresses in Stretch Turning, vol. 37, Elsevier Science, 1997, pp. 1525–1537. [5] M. Barge, H. Hamdi, J. Rech, J.M. Bergheau, Numerical modelling of orthogonal cutting: influence of numerical parameters, J. Mater. Process. Technol. 164–165 (2005) 1148–1153. [6] C. Shet, X. Deng, G. Shi, A Finite Element Study of the Effect of Friction in Orthogonal Metal Cutting, vol. 43, Elsevier Science, 2002, pp. 573–587. [7] A.O. Schmidt, R.J. Roubik, Distribution of heat generated in drilling, ASME 71 (1949) 245–252. [8] L. Puigsegur, Caract´erisation thermique d’un proc´ed´e d’usinage par tournage. Approche analytique et par identification de syst`emes non entiers, 2002.