This paper is dedicated to the comparison of several numerical models for estimating the lifetime in a fatigue experiment. The models simulate the SPLASH experiment, which produces thermal fatigue by locally quenching stainless steel specimens. All models predict first a stabilized mechanical state (plastic shakedown) and then a lifetime prediction using several fatigue crack initiation criteria. The numerical methods are either completely nonlinear or combine approximate elastic solutions obtained from minimizing a potential energy or closed form solutions with a Neuber or Zarka technique to estimate directly the elastoplastic state. The fatigue criteria used are Manson, dissipated energy and dissipated energy combined with a hydrostatic pressure term. The latter had provided a best prediction over a series of anisothermal and isothermal LCF experiments in a classical fatigue analysis. The analysis shows that for fatigue criteria taking into account the triaxiality of the mechanical response we obtain a systematic and conservative error. As a consequence of this work, we show that simplified models can be used for lifetime prediction. Moreover the paper provides a general technique to asses from the point of view of the design engineer the combination between a numerical method and a fatigue criterion.

International audienceFor nuclear reactor components, uniaxial isothermal fatigue curves are used to estimate the crack initiation under thermal fatigue. However, such approach would be not sufficient in some cases where cracking was observed. To investigate differences between uniaxial and thermal fatigue damage, tests have been carried out using the thermal fatigue devices SPLASH and FAT3D: a bi-dimensional (2D) loading condition is obtained in SPLASH and crack initiation is defined as the first 150-μm surface cracks, whereas a tri-dimensional (3D) loading condition is obtained in FAT3D and crack initiation refers to the first 2-mm surface crack. All the analysed tests clearly show that for identical levels of strain, the number of cycles required to achieve crack initiation is significantly lower in thermal fatigue than in uniaxial isothermal fatigue. The enhanced damaging effect probably results from a pure mechanical origin: a nearly perfect biaxial state corresponds to an increased hydrostatic stress. In that frame, a Part II accompanying paper will be dedicated to investigate accurately on multiaxial effect, and to improve thus estimation of crack initiation under thermal fatigue

A B S T R A C TThe SPLASH experiment has been designed in 1985 by the CEA to simulate thermal fatigue due to short cooling shocks on steel specimens and is similar to the device reported by Marsh in Ref.[1]. The purpose of this paper is to discuss the mechanical and the fatigue analysis of the experiment using results from FEM computations. The lifetime predictions are obtained using a modified dissipated energy with a maximal pressure term and agree with the experimental observations. The numerical analysis of the mechanical state shows an important evolution of the triaxiality ratio during the loading cycle. Further comparisons and discussions of the fatigue criteria are provided in the second part of the paper (Part II) 2 .A = elastic 4th order tensor c, k = thermal capacity and conductivity E, ν = young's modulus and Poisson's coefficient J 2 = second invariant of the deviatoric stress tensor P = hydrostatic pressure p = cumulated plastic strain q = thermal flux r = heat source T = temperature field TF = triaxiality factor u = displacement field W p = dissipated energy density per cycle σ , = equivalent stress and strain ranges , e = strain tensor and its deviatoric part e , p = elastic and plastic strain tensors ρ = volumic mass σ Y = elastic limit σ, s = stress tensor and its deviatoric part I N T R O D U C T I O NA series of industrial structures like turbines, engines, nuclear or classical thermal plants are subject to thermomechanical cycling leading to fatigue. The actual design and

A B S T R A C TThe SPLASH experiment has been designed in 1985 by the CEA to simulate thermal fatigue due to cooling shocks on steel specimens and is similar to the device reported by Marsh in Ref.[1]. The purpose of this paper is to discuss the application of different fatigue criteria in this case. The fatigue criteria: dissipated energy, Manson Coffin, Park and Nelson, dissipated energy with a pressure term, are determined for the experiment using results from FEM computations presented in the first part of the paper (Part I) 2 and compared with results from uniaxial and multiaxial experiments from literature. The work emphasizes the evolution of the triaxiality ratio during the loading cycle.A = elastic 4th order tensor c, k = thermal capacity and conductivity E, ν = young's modulus and Poisson's coefficient J 2 = second invariant of the deviatoric stress tensor P = hydrostatic pressure p = cumulated plastic strain q = thermal flux r = heat source T = temperature field TF = triaxiality factor u = displacement field W p = dissipated energy density per cycle σ , = equivalent stress and strain ranges , e = strain tensor and its deviatoric part e , p = elastic and plastic strain tensors ρ = volumic mass σ Y = elastic limit σ, s = stress tensor and its deviatoric part I N T R O D U C T I O NIn Part I of this paper, we discussed the complete mechanical analysis of the SPLASH experiment and presented a first lifetime estimation with a modified dissipated energy with a pressure term fatigue criterion.We recall that the experiment is a thermal shock fatigue test. The sample is heated during the complete thermal cycle (7.75 s) by Joule effect and is cyclically cooled down during a very short period (0.25 s) by a water spray on a small area on two opposite faces. This leads to high gradients in the specimen and as a consequence a complete structural analysis is needed in order to estimate the values of the thermomechanical fields. The test is characterized by the temperature difference T between the

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