Journal of Materials Engineering and Performance

, Volume 25, Issue 3, pp 1010–1027 | Cite as

An Hybrid Approach Based on Machining and Dynamic Tests Data for the Identification of Material Constitutive Equations

  • Walid Jomaa
  • Victor SongmeneEmail author
  • Philippe Bocher


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 Marusich’s 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 constitutive 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.


aluminums finite elements modeling hard steels inverse method machining material constitutive equation 



Yield strength coefficient in JCE in (MPa)


Hardening modulus in JCE


Strain rate sensitivity coefficient in JCE


Specific heat of the workpiece material (J/kg °C)


Strain rate constant on the primary shear zone


Cutting feed (mm/rev)


Tangential force (N)


Feed force (N)


Shear flow stress along AB (MPa)


Thermal conductivity of the work material (W/m.°C)


Thermal softening coefficient in JCE

m1, m2

Low and high strain rate Sensitivity exponents


Strain hardening exponent in JCE


Strain hardening exponent


Tool edge radius (mm)


Chip thickness (mm)


Undeformed chip thickness (mm)


Temperature (°C)


Average temperature on the primary shear zone (°C)


Room temperature (°C)


Cutting speed (m/min)


Cutting thickness (mm)


Normal rake angle (°)

\(\upalpha_{\rm NL}\)

Thermal softening coefficient (MPa/°C)


Average shear strain at AB

\(\dot{\upgamma }_{\text{prim}}\)

Average shear strain rate at AB (s−1)


Average strain rate along the tool/chip interface (s−1)


Strain rate constant on the secondary shear zone


Equivalent shear strain at AB


Equivalent plastic strain

\(\dot{\upvarepsilon }_{\text{p}}\)

Equivalent plastic strain rate (s−1)

\(\dot{\varvec{\upvarepsilon }}_{\varvec{t}}\)

Transition strain rate (s−1)

\(\upvarepsilon_{0}\), \(\dot{\upvarepsilon }_{0 }\)

Reference strain and strain rate (s−1)


Resultant cutting force direction (°)


Angle of friction (°)


Mass density of the work material (kg/m3)


Flow stress (MPa)


Yield stress (MPa)


Shear angle (°)



A part of the research presented in this paper was financed by the Fonds de recherche du Québec - Nature et technologies by the intermediary of the Aluminium Research Centre – REGAL.


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© ASM International 2016

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentÉcole de technologie supérieureMontrealCanada

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