S. Bhandari X. Feral Framatome, Tour Framatome, 92084 Paris La De ´fense Cedex, France J.-M. Bergheau 1 G. Mottet SYSTUS International, 69485 Lyon, Cedex 03, France P. Dupas EDF-DER, Les Renardie `res, Ecuelles, 77818 Moret sur Loing Cedex, France L. Nicolas CEA-DRN-DMT, CEN-Saclay, 91191 Gif sur Yvette, France Creep-Damage Analysis: Comparison Between Coupled and Uncoupled Models Numerical simulation of creep rupture of a reactor pressure vessel in a severe hypotheti- cal accident needs to perfectly take account of interactions between creep phenomena and damage. The continuous damage theory enables to formulate models strongly coupling elasto-visco-plasticity and damage. Such models have been implemented in various com- puter codes and, in particular, in ASTER at Electricite ´ de France, CASTEM 2000 at Commissariat a ` l’Energie Atomique and SYSTUS+® at SYSTUS International. The ob- jective of this paper is to present briefly a validation study of the three different numerical implementations and to compare the coupled approach to an uncoupled one on an ex- ample of a cylinder of the program ‘‘RUPTHER,’’ under internal pressure and heated to a temperature of 700°C. S0094-99300001004-0 1 Introduction Creep rupture of a reactor pressure vessel in a severe accident occurs after complex load and temperature histories leading to interactions between creep deformations, stress relaxation, mate- rial damaging, and plastic instability. The concepts of continuous damage introduced by Kachanov and Rabotnov allow to formulate models coupling elasto-visco-plasticity and damage. However, the integration of such models in a finite-element code creates some difficulties related to the strong nonlinearity of the constitutive equations. It was feared that different methods of implementation of such a model might lead to different results, which, conse- quently, might limit the application and usefulness of such a model. The Commissariat a ` l’Energie Atomique CEA, Electricite ´ de France EDF and SYSTUS International SYSTUS Int. have worked out numerical solutions to implement such a model in, respectively, CASTEM 2000 1, ASTER 2, and SYSTUS+® 3 codes. A ‘‘benchmark’’ was set up, chosen on the basis of a cylinder studied in the program RUPTHER 4. The objective of this paper is not to enter into the numerical details of the implementation of the model, but to present the results of the comparative study made using the three aforemen- tioned codes on a case of engineering interest. The results of the coupled model will be compared to an uncoupled model to evalu- ate differences one can obtain between a simple uncoupled model and a more sophisticated coupled model. 2 Description of Coupled Damage—Viscoplasticity Model As mentioned earlier, the failure of a reactor component under a severe accident transient involves several phenomena like plas- tic or viscoplastic straining, strain hardening, material damaging, metallurgical transformations, necking, etc. Therefore, an im- proved model of failure prediction should be able to: • cumulate properly the strains and damage undergone under various loading conditions; • account for the stress transfer from heavily damaged zones towards less damaged ones; • account for the instability as well as for the creep rupture. Among the various nonlinear models, those based on continuous damage mechanics, introduced by Kachanov 5 and Rabotnov 6, seem to have the desired characteristics. The model chosen by the three organizations CEA, EDF, and SYSTUS Int. is based on the work of Lemaitre and Chaboche 7 and describes the evolution of mechanical degradation from the perfect state of a structure to the time a macroscopic crack appears and propagates. Starting from • The definition of damage, as the ratio Dn= S D S where S is the area of a section of a volume of material, n ¯ its unit normal, D n the local damage relevant to the direction n ¯ , S D rep- resents the area of the cracks, such that if S ˜ is the effective resis- tant area, S D =S -S ˜ . • The notion of effective stress  ¯ =  1-D where  is the Cauchy stress tensor. • The isotropy assumption: D n =D n ¯ • The strain equivalence principle 7. A mathematical model is elaborated with the following equations:  ˙ = ˙ e + ˙ p (1) E= 1 -D  E 0 (2)  ˙ p = 3 2  ˙  '  eq (3) r ˙ = ˙  1 -D  =   eq  1 -D  Kr 1/M N (4) 1 Now with LTDS, UMR 5513 CNRS/ECL/ENISE, 42023 St. Etienne, Cedex 2, France. Contributed by the Pressure Vessels and Piping Division for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received by the PVP Division, May 31, 2000; revised manuscript received July 21, 2000. Technical Edi- tor: S. Y. Zamrik. 408 Õ Vol. 122, NOVEMBER 2000 Copyright © 2000 by ASME Transactions of the ASME Downloaded 10 Feb 2009 to 193.50.200.66. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm