Inverse Flow Stress Calculation for Machining Processes


Article Preview

Finite element modeling of the machining process has been quite successful in recent years. The model can be used to better understand the interactions between chip flow, heat generation, residual stress, tool stress, tool wear, tool chatter and dimensional accuracy. One of the key inputs to the model is the high strain rate (>104 1/sec) flow stress data. The split Hopkinson bar test has been commonly used to measure the flow stress at these high strain rates. The method is expensive and typically limited to the strain rate range from 102 to 104 1/sec. To overcome these limitations, an optimization based inverse methodology was developed. In this technique, the measured and predicted cutting forces were matched by iteratively adjusting the coefficients in the flow stress constitutive model. Since the method requires many FEM simulations to reach the final optimal condition, a computationally efficient FEM solver using ALE (Arbitrary Lagrangian Eulerian) method was adopted to make the method practical. The method was validated with experimental data with excellent agreement.



Edited by:

J.C. Outeiro




J. B. Yang et al., "Inverse Flow Stress Calculation for Machining Processes", Advanced Materials Research, Vol. 223, pp. 267-276, 2011

Online since:

April 2011




[1] P. Sartkulvanich, A. M. Lopez, C. Rodriguez, T. Altan, Inverse Analysis Methodology to Determine Flow Stress Data for FEM of Machining, Proceedings of the CIRP Conference on Modelling of Machining, Sept. 2008, Washington, DC.

[2] M.A. Kaiser, 1998, Advancement in the Split Hopkinson Bar test, Master thesis Virginia Polytechnic and State University, May 1, (1998).

[3] C. Fisher, DEFORM User's Group Presentation.

[4] Miguel Ávila, Joel Gardner, Corinne Reich-Weiser, Shantanu Tripathi, Athulan Vijayaraghavan, David Dornfeld, Strategies for Burr Minimization and Cleanability in Aerospace and Automotive Manufacturing,. UC Berkeley: Laboratory for Manufacturing and Sustainability. http: /www. escholarship. org/uc/item/9ks6b6dp.


[5] C. Hirt, A. Amsden, J. Cook, 1974, An arbitrary Lagrangian-Eulerian computing method for all flow speeds, Journal of Computational Physics, 14/3: 227-253.


[6] J. Donea, P. Fasoli-Stella, S. Giuliana, 1977, Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problem, Transactions of 4th International Conference on SMIR, 1-12.

[7] R. Haber, 1984, A mixed Eulerian-Lagrangian displacement model for large deformation analysis in solid mechanics, Computer Methods in Applied Mechanics and Engineering, 43: 277-292.


[8] A. Rodriguez-Feran, F.M. Casadei, A. Huerta, 1998, ALE stress update for transient and quasistatic processes, International Journal for Numerical Methods in Engineering, l. 41: 241-262.


[9] O.C. Zienkiewicz and J.Z. Zhu, 1992, The Superconvergent Patch Recovery (SPR) and adaptive finite element, Computer Methods in Applied Mechanics and Engineering, 101: 207-224.


[10] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, 1992, Numerical Recipes in Fortran 2nd Edition, Cambridge University Press.

[11] G.R. Johnson and Cook W.H., 1983, 7th International Symposium on Ballistics, La Hague, The Netherlands, 541–548.

[12] N. Tounsi, H. Attia, 2007, Identification of Constitutive Law for Stainless Steel AISI 304L In Machining, NRC (National Research Council Canada).