An Hybrid Approach Based on Machining and Dynamic Tests Data for the Identification of Material Constitutive Equations Walid Jomaa, Victor Songmene, and Philippe Bocher (Submitted February 11, 2015; in revised form January 17, 2016) In recent years, there has been growing interest for the identification of material constitutive equations using machining tests (inverse method). However, the inverse method has shown some drawbacks that could affect the accuracy of the identified material constants. On one hand, this approach requires the use of analytical model to estimate the cutting temperature. Nevertheless, the used temperature models lead to large discrepancies for the calculated temperatures even for the same work material and cutting conditions. On the other hand, some computation issues were observed when all material constants were determined, in the same time, using machining tests data. Therefore, this study attempts to provide a methodology for identifying the coefficients of the MarusichÕs constitutive equation (MCE) which demonstrated a good capability for the simulation of the material behavior in high speed machining. The proposed approach, which is based on an analytical inverse method together with dynamic tests, was applied to aluminum alloys AA6061-T6 and AA7075-T651, and induction hardened AISI 4340 steel (60 HRC). The response surface methodology was used in this approach. Two sets of material coefficients, for each tested work material, were determined using two different temperature models (Oxley and Loewen-Shaw). The obtained con- stitutive equations were validated using dynamic tests and finite element simulation of high speed machining. The predictions obtained are also compared to those performed with the corresponding Johnson and Cook constitutive equations (JCE) from the literature. The sensitivity analysis revealed that the selected temperature models used in the analytical inverse method can affect significantly the identified material constants and thereafter predicted dynamic response and machining data. Moreover, the MCE obtained using the hybrid method performed better than the JCE obtained by only dynamic tests. Keywords aluminums, finite elements modeling, hard steels, inverse method, machining, material constitutive equation 1. Introduction Over the few last decades, analytical and finite element modeling (FEM) of machining processes have received increasing attention. These techniques require accurate material constitutive equations in order to simulate the actual material behavior during the process. Umbrello et al. (Ref 1) showed that the material constants affect significantly the predicted cutting forces, chip formation, temperature, and residual stress distributions in finite element modeling of machining AISI 316L stainless steel. Thus, to succeed, two critical issues should be solved: first, the selection of the adequate constitutive equations for the material in use and, second, find the suitable constants. Many techniques had been used for the identification of constitutive equations applied to FEM. These techniques include split-Hopkinson pressure bar (SHPB) test Walid Jomaa, Victor Songmene, and Philippe Bocher, Mechanical Engineering Department, E ´ cole de technologie supe ´rieure, 1100 rue Notre-Dame Ouest, Montreal, QC H3C 1K3, Canada. Contact e-mails: walid.jomaa.1@etsmtl.net, Victor.Songmene@etsmtl.ca, and Philippe.Bocher@etsmtl.ca. Nomenclature A Yield strength coefficient in JCE in (MPa) B Hardening modulus in JCE C Strain rate sensitivity coefficient in JCE C w Specific heat of the workpiece material (J/kg °C) C 0 Strain rate constant on the primary shear zone f Cutting feed (mm/rev) F c Tangential force (N) F f Feed force (N) k prim Shear flow stress along AB (MPa) K w Thermal conductivity of the work material (W/m.°C) m Thermal softening coefficient in JCE m 1 , m 2 Low and high strain rate Sensitivity exponents n Strain hardening exponent in JCE n NL Strain hardening exponent r n Tool edge radius (mm) t c Chip thickness (mm) t u Undeformed chip thickness (mm) T Temperature (°C) T prim Average temperature on the primary shear zone (°C) T 0 Room temperature (°C) V Cutting speed (m/min) w Cutting thickness (mm) a Normal rake angle (°) a NL Thermal softening coefficient (MPa/°C) c prim Average shear strain at AB _ c prim Average shear strain rate at AB (s 1 ) c int Average strain rate along the tool/chip interface (s 1 ) JMEPEG ÓASM International DOI: 10.1007/s11665-016-1950-6 1059-9495/$19.00 Journal of Materials Engineering and Performance