FINITE ELEMENT ANALYSIS OF HASTELLOY C-22HS IN END MILLING

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1 Journal of Mechanical Engineering and Sciences (JMES) ISSN (Print): ; e-issn: ; Volume, , December 0 Universiti Malaysia Pahang, Pekan, Pahang, Malaysia DOI: htt://dx.doi.org/0.58/jmes FINITE ELEMENT ANALYSIS OF HASTELLOY C-HS IN END MILLING K. Kadirgama, M.M. Rahman, A.R. Ismail and R.A. Bakar Faculty of Mechanical Engineering Universiti Malaysia Pahang 6600 Pekan, Pahang, Malaysia Phone: ; Fax: kumaran@um.edu.my ABSTRACT This aer resents a finite element analysis of the stress distribution in the end milling oeration of nickel-based sueralloy HASTELLOY C-000. Commercially available finite element software was used to develo the model and analyze the distribution of stress comonents in the machined surface of HASTELLOY C-HS following end milling with coated carbide tools. The friction interaction along the tool-chi interface was modeled using the Coulomb friction law. It was found that the stress had lower values under the cut surface and that it increased gradually near the cutting edge. Keywords: Finite element analysis; stress; nickel based sueralloy; end milling. INTRODUCTION In many industries, nickel-based alloys reresent an imortant segment of structural materials. Critical comonents made of these alloys are often relied uon to function satisfactorily in corrosive environments. Highly corrosion-resistant alloy castings are often the subject of major concern because failures of cast comonents can lead to significant downtime costs and oerating roblems (Strenkowski & Carroll, 985). Over the years, nickel-chromium-molybdenum/tungsten alloys have roven to be among the most reliable and cost-effective materials for aggressive seawater alications with excellent resistance to localized corrosive attack (itting, crevice corrosion). Among these alloys, HASTELLOY C-tyes (C, C-4, C-76, and C-) are often used to serve the above-mentioned uroses. As these alloys are commonly subject to further machining after casting, it becomes vital to understand the changes in roerties imarted to the machined surfaces following cutting oerations such as end milling. For this reason, the finite element methodology is used in this study to determine the machined surface stress characteristics. In the ast decade, the finite element method, based on the udated-lagrangian formulation, has been develoed to analyze metal cutting rocesses (Strenkowski & Carroll, 985; Shih, Chandrasekar & Yang, 990). Several secial finite element techniques, such as element searation (Komvooulos & Erenbeek, 99; Shih & Yang, 993), the modeling of worn cutting tool geometry (Komvooulos & Erenbeek, 99; Shih & Yang, 993; Shih, 996), mesh rezoning (Komvooulos & Erenbeek, 99; Ueda & Manabe, 993), and friction modeling (Strenkowski & Carroll, 985; Komvooulos & Erenbeek, 99), etc., have been imlemented to imrove the accuracy and efficiency of finite element modeling. Detailed work-material modeling, which includes the couling of temerature, strain rate, and strain-hardening effects, has been alied to model material deformation (Shih et al., 990; Shih & Yang, 993; Shih, 996). An early analytical model for redicting residual stresses was roosed by Okushima and Kakino (97), in which residual 37

2 Finite Element Analysis of HASTELLOY C-HS in End Milling stresses were related to the cutting force and temerature distribution during machining. In another analytical model, a relation was derived between residual stresses and the hardness of the workiece (Wu & Matsumoto, 990). Shih and Yang (993) conducted a combined exerimental/comutational study of the distribution of residual stresses in a machined workiece. Liu & Guo (000) used the finite element method to evaluate residual stresses in a workiece. They also observed that the magnitude of residual stress is reduced when a second cut is made on the cut surface. Liu and Barash (98) measured the residual stress on the workiece subsurface with consideration of tool flank wear. Their findings indicated that under the condition of a lower cutting seed, the mechanical load had a greater imact on residual stress, whereas the thermal effect become the major factor affecting residual stress at higher cutting seed. Lee and Shaffer (95) roosed a shear-angle model based on the sli-line field theory, which assumes a rigid erfectly lastic material behavior and a straight shear lane. Kudo (965) modified the sli-line model by introducing a curved shear lane to account for the controlled contact between the curved chi and straight tool face. Henriksen (95) conducted a series of tests to understand residual stresses in the machined surface of steel and cast iron arts under various cutting conditions. Kono, Hara, Yazu, Uchida, and Mori (980), and Tonshoff, Wobker, and Brandt (995) revealed that residual stresses are deendent on the cutting seed. Matsumoto, Barash & Liu (986) and Wu and Matsumoto (990) observed that the hardness of the workiece material has a significant influence on the residual stress field. Konig, Berktold, and Koch (993) showed that friction in metal cutting also contributes to the formation of residual stresses. FINITE ELEMENT MODEL The finite element model (FEM) is comosed of a deformable workiece and a rigid tool. The tool enetrates through the workiece at a constant seed and constant feed rate. The model assumes lane-strain conditions because generally, the deth of cut is much greater than the feed rate. The FEM used in this study is based on commercially available finite element software called Thirdwave AdvantEdge. It uses six-noded quadratic triangular elements by default. AdvantEdge is an automated rogram and it is sufficient to inut rocess arameters in order to construct a two-dimensional simulation of an orthogonal cutting oeration. Thermal boundary conditions for Thirdwave AdvantEdge are given as:. The heat is generated because of the heavy lastic work done on the workiece. Its formula is given in Eq. (): P m f W R () where W P is the rate of lastic work, f is the fraction of lastic work converted into heat (assumed to be 0.9), m is the mechanical equivalent of heat (taken as ), and ρ is the density of the workiece material (8.6 g/cm 3 ). The heat is generated because of friction between the chi and the rake face of the tool according to Eq. (): 38

3 Kadirgama et al. / Journal of Mechanical Engineering and Sciences (0) q F V m () where F fr is the friction force, V r is the relative sliding velocity between the tool and chi, and m is the mechanical equivalent of heat (m = ) 3. The generated frictional heat is distributed to the chi and tool according to Eq. (3): fr r Q Q chi tool k k chi tool chi tool c c chi too l (3) where Q chi is the heat given to the chi, Q tool is the heat given to the tool, k is the conductivity, ρ is the density, and c is the heat caacity. Figure. Model for milling Certain assumtions are made in simulating the comlex rocedure of metal cutting with FEM. These assumtions are used to define the roblem to be solved, as well as to aly the boundary and loading conditions:. The cutting seed is constant.. The width of cut is larger than the feed (lane strain condition), and both are constant. 3. The cutting velocity vector is normal to the cutting edge. 4. The workiece material is a homogeneous olycrystalline, isotroic, and incomressible solid. 5. The workiece is set at a reference temerature of 0 C at the beginning of simulation. 6. The machine tool is erfectly rigid and there is no influence of machine tool dynamics on the machining. 7. There is constant friction between the tool-chi interaction and the toolworkiece interaction. 39

4 Finite Element Analysis of HASTELLOY C-HS in End Milling Figure shows the Thirdwave AdvantEdge model for a milling oeration and Figure shows an examle of a visual simulation of residual stresses induced after milling. Figure. Model of residual stress WORKPIECE AND TOOL MATERIAL MODELING The workiece material used for the simulation is HASTELLOY C-HS, the cutting tool is carbide coated with TiALN and with a 0 rake angle. After each ass (80 mm), the simulation was stoed. AdvantEdge uses an analytical formulation for material modeling. In a tyical machining event, in the rimary and secondary shear zones, very high strain rates are achieved, whereas the remainder of the workiece deforms at moderate or low strain rates. In order to account for this, Thirdwave AdvantEdge incororates a stewise variation of the rate sensitivity exonent: f o m, if (4) t where is the effective von Mises stress, f is the flow stress, is the accumulated lastic strain, o is a reference lastic strain rate, m is the strain rate sensitivity exonents, and is the threshold strain rate that searates the two regimes. In the t calculations, a local Newton-Rahson iteration is used to comute o according to the low rate equation, which switches to the high rate equation if the result lies above t. f, which is used in Eq. (5), is given as: f 0 T () 0 where T is the current temerature, 0 is the initial yield stress at the reference temerature T 0, is the reference lastic strain, n is the hardening exonent, and 0 n T 40

5 Kadirgama et al. / Journal of Mechanical Engineering and Sciences (0) is the thermal softening factor. In the resent study, it is assumed that the tool is not lastifying; hence, it is considered as an absolutely rigid body. Workiece Material The roerties of the workiece material (HASTELLOY C-HS) are shown in Tables and, and the cutting tool roerties and simulation are shown in Tables 3 and 4. Table. Chemical comosition for HASTELLOY C-HS. Ni Cr Mo Fe Co W Mn Al Si C B BAL (%) Table. Physical roerties of HASTELLOY C-HS at room temerature Proerties Value Density (g/cm 3 ) 8.6 Thermal Conductivity (W/m. C).8 Mean Coefficient of Thermal Exansion (μm/m. C).6 Thermal Diffusivity (cm /s) Secific Heat (J/kg. C) 4 Young Modulus (GPa) 3 Code name Table 3. Cutting tool roerties Comosition (%) %Co %WC %Cr3C %TaC %TiC %Nbc KC50M Table 4. Simulation conditions Coating PVD TiAlN Thickness (μm) 3.5 Simulation No. Cutting seed Feed rate Axial deth

6 Finite Element Analysis of HASTELLOY C-HS in End Milling RESULTS AND DISCUSSION The von Mises stress V, is used to estimate yield criteria for ductile materials. It is calculated by combining stresses in two or three dimensions with the result comared with the tensile strength of the material loaded in one dimension. The von Mises stress is also useful for calculating the fatigue strength (Schey, 000). The von Mises stress in three dimensions is exressed as (Schey, 000): 3 3 V (3) where,, 3 are the rincial stresses. Figure 3 shows the von Mises stress for simulation no.9 (Cutting seed 80 m/min, feed rate 0.5 mm, and axial deth.0 mm) after 80 mm. Most of the tensile stress V aears at the cutting tool edge. The von Mises criterion states that failure occurs when the energy of distortion reaches the same value as the energy for yield/failure in uniaxial tension. Mathematically, this is exressed as (Schey, 000): (4) The yield strength and ultimate tensile strength for the coated carbide cutting tool used in this simulation are 600 and 800 MPa, resectively. The von Mises stress at region 9 is 4488 MPa, which is higher than the yield strength and the ultimate tensile strength of the coated cutting tool. This stress can cause ermanent damage to the cutting tool because this stress is beyond the ultimate tensile strength and yield strength. Cutting seed, feed rate, and axial deth for this simulation are very high and this causes the high stress at the cutting edge, because high cutting seed, feed rate, and axial deth can cause high force in milling (Alauddin, Mazid, EL Baradi, & Hashmi, 998; Kadirgama & Abou-El-Hossein, 005). The radial deth for every simulation is 3.5 mm. This factor also contributes to higher stress. At region, at the cutting tool and chi contact, the von Mises stress is 50 MPa, whereas the yield strength and ultimate strength of the workiece are 359 and 759 MPa. The workiece starts to deform because the stress is above its yield strength. Figure 4 shows the von Mises stress for simulation no. 3 (Cutting seed 00 m/min, feed rate 0. mm/rev, axial deth.5 mm). The stress at the cutting tool edge (region 5) is 345 MPa. The von Mises stress is lower comared with that in simulation run no. 9. However, even though the stress is still higher than the yield strength and ultimate tensile strength, the damage should be less severe comared with simulation no.9. At region 3, the stress for the contact oint of the cutting tool and chi is 577 MPa. This value is almost the same as in simulation no. 9. From the von Mises stress distribution, shown in Figures 3 and 4, it can be seen that most of the tensile stress V is located at the edge of the cutting tool. The stress distribution also shows that the stress is lower under the cut surface and that it increases gradually near the cutting edge. High force is needed at the tool edge for workiece enetration, and this indirectly increases the stress at the tool edge. This distribution of the stress is the same for both cases. The 3 3 y 4

7 Kadirgama et al. / Journal of Mechanical Engineering and Sciences (0) velocity vectors around the tool ti for simulation no. 9, shown in Figure 5, clearly show the lastic flow of the material around the cutting edge. The same trend of flow was also observed by Movahhedy, Gadala, & Altintas (000). Figure 6 shows the 3D icture for von Misses stress distribution for simulation no. 9. Table 3 shows the average value of the von Mises stress at the cutting tool edge for every simulation. This value will be investigated through statistical methods to determine the relationshi between the variables (cutting seed, feed rate and axial deth) and the resonse (von Mises Stress). Figure 3. von Mises stress for simulation no. 9 Figure 4. von Mises stress for simulation no. 3 43

8 Finite Element Analysis of HASTELLOY C-HS in End Milling The deformation direction Figure 5. Velocity vectors for simulation no. 9 Cutting edge Figure 6. 3D icture for von Misses stress distribution for simulation no. 9 CONCLUSION In the milling oeration, cutting seed, feed rate, and axial deth lay the major role in roducing high stresses. The von Mises stress distribution also shows that the stress is lower under the cut surface and that it increases gradually towards the cutting edge. The highest comressive stress, xx aears at the cutting edge. Most of the tensile stress, V aears at the edge of the cutting tool. The stress distribution also shows that the stress is lower under the cut surface and that it increases gradually near the cutting edge. High force is needed at the tool edge for workiece enetration, and this indirectly increases the stress at the tool edge. This distribution of stress is the same for both cases. 44

9 Kadirgama et al. / Journal of Mechanical Engineering and Sciences (0) REFERENCES Alauddin, M., Mazid, M. A., EL Baradi, M. A., & Hashmi, M. S. J. (998). Cutting forces in the end milling of Inconel 78. Journal of Materials Processing Technology, 77, Henriksen, E. K. (95). Residual stresses in machined surfaces. Transactions ASME, Journal of Engineering for Industry, 73: Kadirgama, K., & Abou-El-Hossein, K. A. (005). Force rediction model for milling 68 tool steel using resonse surface methodology. American Journal of Alied Sciences, (8), -7. Komvooulos, K., & Erenbeek, S. A. (99). Finite element modelling of orthogonal cutting. Journal of Engineering for Industry-Transactions of the ASME, 6(3), Konig, W., Berktold, A., & Koch, K. F. (993). Turning versus grinding a comarison of surface integrity asects and attainable accuracy. Annals of the CIRP, 4(), Kono, Y., Hara, A., Yazu, S., Uchida, T., & Mori, Y. (980). Cutting erformance of sintered CBN tools, Cutting tool materials. Proceedings of the International Conference, American Society for Metals, Ft. Mitchell, KY, Kudo, H. (965). Some new sli-line solutions for two-dimensional steady state machining. International Journal of Mechanical Science, 7, Lee, E. H., & Shaffer, B. W. (95). The theory of lasticity alied to a roblem of machining. Journal of Alied Mechanics, 8, Liu, C. R., & Barash, M. M. (98). Variables governing atterns of mechanical residual stress in a machined surface. Journal of Engineering for Industry- Transactions of the ASME, 04, Liu, R., & Guo, Y. B. (000). Finite element analysis of the effect of sequential cuts and tool-chi friction on residual stresses in a machined layer. International Journal of Mechanical Sciences, 4, Matsumoto, Y., Barash, M. M., & Liu, C. R. (986). Effects of hardness on the surface integrity of AISI 4340 steel. Journal of Engineering for Industry-Transactions of the ASME, 08, Movahhedy, M., Gadala, M. S., & Altintas, Y. (000). Simulation of the orthogonal metal cutting rocess using an arbitrary Lagrangian-Eulerian finite element method. Journal of Materials Processing Technology, 03, Okushima, K., & Kakino, Y. (97). The residual stresses roduced by metal cutting, Annals of the CIRP, 0(), 3-4. Schey, J. A. (000). Introduction to manufacturing rocesses. New York: McGraw Hill. Shih, A. J. (996). Finite element analysis of orthogonal metal cutting mechanics. International Journal of machine Tools and Manufacturing, 36(), Shih, A. J., & Yang, H. T. Y. (993). Exerimental and finite element redictions of the residual stresses due to orthogonal metal cutting. International Journal for Numerical Methods in Engineering, 36(9), Shih, A. J., Chandrasekar, S., & Yang, H. T. Y. (990). Fundamental issues in machining. ASME PED, 43,. Strenkowski, J. S., & Carroll, J. T. (985). A Finite element model of orthogonal metal cutting. Journal of Engineering for Industry-Transactions of the ASME, 07(4),

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