Newton method for the optimization of a new constitutive equation for the plastic flow dependent on the strain. Application to magnesium alloys AZ80 and AZ61

Authors

  • V. Gutiérrez Dpto. de Matemáticas, Universidad de Castilla-La Mancha
  • I. Rieiro Dpto. de Matemáticas, Universidad de Castilla-La Mancha
  • M. Carsí Dpto. de Metalurgia Física, Centro Nacional de Investigaciones Metalúrgicas, CENIM, CSIC
  • O. A. Ruano Dpto. de Metalurgia Física, Centro Nacional de Investigaciones Metalúrgicas, CENIM, CSIC

DOI:

https://doi.org/10.3989/revmetalm.1323

Keywords:

Numerical methods, Garofalo equation, Constitutive equation, Modeling, Statistical analysis, Magnesium alloys, Creep

Abstract


A new numerical algorithm has been developed, based on Newton's method, for optimizing the parameters of a new strain dependent constitutive equation, based on the Garofalo equation. The adjustment is direct, with second order algorithms, for an equation derived from that of Garofalo with a nonlinear objective function. This new optimization algorithm has been applied to creep data of two magnesium alloys AZ80 and AZ61, having an unusual plastic behavior. A certain pseudo-stationary exists in the curves studied, in the sense that the usual deformation states are not manifested in an obvious way. The parameters of the new constitutive equation, dependent on strain, have been determined for these alloys. For analyzing the precision of the parameters and the accuracy of modeling of the stress-strain curves, a statistical treatment has been applied which allows assessing the quality of the constitutive equation proposed and the consistency of these parameters. Stress-strain curves have been compared with the modeling results, reaching a good agreement between the experimental data and the resulting modeling.

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References

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Published

2013-10-30

How to Cite

Gutiérrez, V., Rieiro, I., Carsí, M., & Ruano, O. A. (2013). Newton method for the optimization of a new constitutive equation for the plastic flow dependent on the strain. Application to magnesium alloys AZ80 and AZ61. Revista De Metalurgia, 49(5), 378–396. https://doi.org/10.3989/revmetalm.1323

Issue

Vol. 49 No. 5 (2013)

Section

Articles

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