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The virtual fields method for characterizing nonlinear behavior

The virtual fields method for characterizing nonlinear behavior. Dr. Stéphane AVRIL. Outline. General principle Damage of composites Elasto-visco-plasticity of metals. Outline. General principle Damage of composites Elasto-visco-plasticity of metals. Measurement of displacement fields.

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The virtual fields method for characterizing nonlinear behavior

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  1. The virtual fields method for characterizing nonlinear behavior Dr. Stéphane AVRIL

  2. Outline General principle Damage of composites Elasto-visco-plasticity of metals

  3. Outline General principle Damage of composites Elasto-visco-plasticity of metals

  4. Measurement of displacement fields

  5. Displacement fields available all along the test

  6. Reconstruction of strain fields all along the test

  7. Assume constitutive equations, you can get the stresses everywhere σ σ5 σ4 σ3 σ2 σ=g(ε,X) σ1 ε ε1 ε2 ε3 ε4 ε5

  8. Reconstruction of stresses fields all along the test

  9. Are the stresses at equilibrium? At each measurement step, the following equation should be satisfied:

  10. Principle of the identification Iterative approch for reconstructing the stress fields until cost function J is minimized:

  11. Choice of virtual fields in practice Shear: Tension: L εxx*= 0 εyy*= 0 εxy*= 1 εxx*= 0 εyy*= 1 εxy*= 0 L

  12. Graphical display: example in plasticity

  13. Outline General principle Damage of composites Elasto-visco-plasticity of metals

  14. In-plane shear non linearity 2D Sic/Sic composite (Camus, IJSS, 2000)

  15. Glass epoxy laminated plate

  16. Results of standard tests Tensile tests Shear tests non linear response Linear part Theshold

  17. Results of standard tests Shear response:

  18. Shortcomings of standard tests 3 different tests Large scattering

  19. Heterogeneous stress field Displacement field measured by full-field optical technique Virtual fields method New strategy 1 test Inverse problem

  20. Principle of the Virtual Fields Method Equilibrium equation Principle of virtual work :

  21. During the linear response Use of four independent virtual fields

  22. across S2 y Beyond the onset of nonlinearity Use of only one virtual field: uniform shear.

  23. Identification of parameters driving the nonlinear behaviour PTV : Damage induces material heterogeneities.

  24. Graphical interpretation K Threshold identified for the best alignment of data points

  25. Using real measurements « dissipated » virtual work Gxy

  26. 87,7 GPa 0,006 Reference Coeff. var (%) 12,8 33 83,6 GPa 0,0041 8,4 14,2 Results Identified Coeff. var (%) Chalal H., Avril S., Pierron F. and Meraghni F., Experimental identification of a damage model for composites using the grid technique coupled to the virtual fields method, Composites Part A: Applied Science and Manufacturing, vol. 37, n° 2, pp. 315-325, 2006.

  27. Summary Identification of a model with six parameters in one single test Decrease of result scattering thanks to the full-field measurements Prospects: handling more complex models taking into account coupling effects and plasticity.

  28. Outline General principle Damage of composites Elasto-visco-plasticity of metals

  29. Elastic properties identified during elastic regime with the virtual fields method Irreversible strains: need a model Implicit definition of constitutive equations Recursive algorithm: At the beginning, σ=0 Then, from one step to another:

  30. Implicit definition of constitutive equations Associated plasticity Von Mises criterion: N is the tensor of yield flow directions: if σeq < Y(p) Prandtl-Reuss rule with isotropic hardening: if σeq = Y(p)

  31. Introduction of constitutive parameters in the hardening law Bilinear model: Y(p) = Y0 + H p Power model (JohnsonCook): Y(p) = Y0 + αpn If the parameters are chosen, it is possible reconstruct the stress fields and to test their validity.  Iterative up to the minimization of the cost function.

  32. Application onto experimental data Standard with strain gage Statically undetermined

  33. Comparison and validation

  34. Complexity of loading path has been handled

  35. Application on a heterogeneous specimen (with Prof. M. Sutton, USC) Zone of FSW

  36. Measured strain fields subimages = different time steps

  37. Experimental results on a homogeneous specimen

  38. Summary Identification of model with up to 21 parameters in one single test. Possibility of handling complex specimen geometry and strain localization. Prospects: • Viscoplasticity with high-speed cameras (S53, p156) • Kinematic hardening, more complex loading paths • Software implementation with Camfit

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