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420                V AUBIN, P QUAEGEBEUR AND S. DEGALLAIX

            cyclic  hardeningkoflening  and  an  extra-hardening  occurs  under  cyclic  non-proportional
            loadings.
              a  As  austenitic stainless steels, the duplex  stainless steel is  sensitive to  loading path,
            although the extra-hardening observed is lower for the duplex stainless steel. Three goups of
            loading  paths  are  distinguished  with  increasing  stabilized  stress  responses:  (1)  tension-
            compression,  torsion  and  proportional  45"  paths,  (2)  clover  path,  (3)  square,  circle  and
            hourglass path.
                 Four sets of constitutive equations were selected (NLK, NPI, NP2 and TANA) and their
            material dependent parameters were identified on the data base,
                 The comparison of the test results and the simulations clearly shows that two models
            (NP2 and TANA) are able to accurately predict the experimental observations.

              The both  models selected are based on two opposite assumptions about the strengthening
            components. The macroscopic tests carried  out  do not  allow to  identify the most realistic
            assumption and to connect the macroscopic behaviour to a physical meaning. Supplementary
            tests are needed to bring out strengthening components involved in the extra-hardening and the
            way  they  affect  it.  These  necessary  pieces  of  information  can  notably  go  through  the
            measurement of the evolutions of variables X and R during non-proportional cyclic tests.


            ACKNOWLEDGEMENTS

            The  authors are grateful to FEDER and  the Nord-Pas-de-Calais Region for  their  financial
            support in the purchase of the biaxial equipment.


            REFERENCES

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