If by "compressive dwell in a multiaxial state of stress" you mean that all of the principal stresses are less than or equal to zero. Then it is easy the creep damage is zero. It is then a fatigue damage calculation only. However, for P91 you must take acount of the effect of environment on fatigue.

Article An improved method for calculation of creep damage during cr...

Article Advanced Ductility Exhaustion Methods for the Calculation of...

Chapter Creep-Fatigue-Oxidation Interactions

Thanks very much Michael, I always learn a lot from you and your good papers. I have a more question from your answer as below;

In my case, the concerning location of a FE model (in a structure level) has the maximum principal stress values in the compression, therefore I should consider it as a creep damage under the compressive dwell.

1. Some literature proved the creep damage of a P91 material under compressive dwell can be well predicted by SEDE method [1]. SMDE have an excellent prediction of creep damage for the stainless steel materials that have different micro-structures from the P91. Does the compressive dwell may result in significance in creep damage of P91?

[1] A generalized strain energy density exhaustion model allowing for compressive hold effect.

I have a very good SMDE model for Grade 91. However, so far I have not published the model for two reasons:

1. I have used a lot of confidential data in my work. This is just a minor excuse.

2. Nearly, all creep-fatigue tests on Grade 91 are largely fatigue dominated. Most of the tests lie in the LCF scatter band! Therefore, having a good prediction of the creep-fatigue tests on Grade 91 actually proves very little about creep damage. Indeed, all that is needed for a good prediction of Grade 91 is a fatigue damage model and any creep damage model that predicts between 0 and

Dear Cho,

For the compressive dwells, oxidation damage is necessary to be considered, as we discussed before. But one concept is that, oxidation damage is out of SEDE framework, but in the field of hysteresis energy. In the given reference [1], oxidation damage relies on two parameters, namely the correction-factor of oxidation as well as the fatigue damage per cycle. Fatigue damage per cycle relies on the damage function based on Ostergren's damage function.

Michael gives an excellent answer for your question. For your piping bend case, I agree that creep damage should set to be zero in the totally compressive loading waveforms. However, in my opinion, I insist on that SEDE for creep damage has its own advantages, at least when compared to DE. First of all, I think it is not a simply operation by multiplying or dividing by stress. Otherwise, it will show the same prediction results to DE model. Then, in some cases, values of rupture elongation obtained in creep tests are larger than those in short-time tensile tests conducted under strain controlled. Moreover, increase in rupture elongation at higher temperatures is often observed in many materials. No mechanism for explaining such a behavior of ductility seems to exist, rupture strain (DE) may not be an ideal index of the material ductility which means resistance agnist fracture in a broader sense and the strain energy density accumulated until failure would serve as a better alternative [2]. At last, SEDE model takes the energy dissipation concept into account, which shows physical meaning more or less.

As for SMDE, Michael has published a lot of valuable works for SMDE model. In our Pro.Tu's group, we have collected and carried out a lot of creep-fatigue experiments, and then we tried to use the results of different materials to validate different life prediction models. In our prediction results, SEDE model is not bad than SMDE. Thus in conclusion, we think that we should show respect to both SMDE and SEDE models. After all, in my viewpoint, both of them are qualified to predicting most creep-fatigue cases.

[1] A generalized strain energy density exhaustion model allowing for compressive hold effect.

[2] Systematic evaluation of creep-fatigue life prediction methods for various alloys

Thank you both for the valued comments on my question.

By the answers from both of you I have gained good understandings in the creep-fatigue life prediction of P91 steel as well as the extra view points on the both creep damage models.

For my problem I will consider the creep damage as zero but enhance the total damage with the oxidation effects.

Once again I appreciate your valuable answers and I will acknowledge the help from you guys in my research work.

I think till now in this very fruitful discussion, we have heard about the models those are modified versions of existing creep fatigue models for multiaxial state of stress or strain. If we look into the problem other way round, if available prediction models for multiaxial fatigue like critical plane model, Fatemi Socie model can be modified for time dependent creep fatigue interaction, we can have a new family of models. I think Mike and Wang, we can look into this problem from that side also. I am attaching one paper, where they have attempted to formulate creep fatigue model based on multiaxial fatigue lifing models. Please see.