Inelastic behaviour of steel under plasticity-creep interaction condition: An interim report of the Bench Mark project by the subcommittee on inelastic analysis and life prediction of high temperature materials, JSMS

Some of the interim results of the Bench Mark Project by the Subcommittee on the Inelastic Analysis and Life Prediction of High Temperature Materials, JSMS, is presented. The purpose of the present bench mark study is to review and evaluate the inelastic constitutive models relevant to material response under the plasticity-creep interaction.By specifying normalized and tempered steel at 600°C, sixteen bench mark problems of four categories are first established: (I) tensile stress-strain relations and creep curves, (II) material response under mixed modes of plastic and creep loading, (III) ratcheting and deformation under program loads, and (IV) cyclic deformation behaviour under the combination of different strain rates. Then, the outline of seventeen inelastic constitutive models of nine types discussed in this project is presented. Finally, the interim results of these bench mark tests are compared with the corresponding predictions of the constitutive models to evaluate their accuracy in simulating the actual behaviour of the material.     

Inelastic behaviour of 214Cr-1Mo steel under plasticity-creep interaction condition: An interim report of the Bench Mark project by the subcommittee on inelastic analysis and life prediction of high temperature materials,JSMS

Some of the interim results of the Bench Mark Project by the Subcommittee on the Inelastic Analysis and Life Prediction of High Temperature Materials, JSMS, is presented. The purpose of the present bench mark study is to review and evaluate the inelastic constitutive models relevant to material response under the plasticity-creep interaction.By specifying normalized and tempered $\text{2}\text{1}\text{4}\text{Cr-1Mo}$ steel at 600°C, sixteen bench mark problems of four categories are first established: (I) tensile stress-strain relations and creep curves, (II) material response under mixed modes of plastic and creep loading, (III) ratcheting and deformation under program loads, and (IV) cyclic deformation behaviour under the combination of different strain rates. Then, the outline of seventeen inelastic constitutive models of nine types discussed in this project is presented. Finally, the interim results of these bench mark tests are compared with the corresponding predictions of the constitutive models to evaluate their accuracy in simulating the actual behaviour of the material.     

A comparative study of anisotropic creep theories

Quantitative comparisons are drawn between the predictions of three kinds of multiaxial anisotropic creep constitutive equations (the author's model, the Murakami-Ohno model and the Mróz-Trampczynski-Hayhurst model) with special consideration of repeated stress changes. Numerical simulations of these anisotropic creep models are performed regarding the creep behavior observed for type 304 stainless steel at 650 °C under repeated multiaxial nonproportional loading conditions. From these results, it is shown that these creep models can reproduce fairly well the observed anisotropic creep behavior and that the predictive capabilities are almost comparable with each other. The similarities and differences between them are also discussed within the context of the structure of the theories and the procedure to determine the material constants involved.     

Description of creep-plasticity interaction with non-unified constitutive equations: application to an austenitic stainless steel

We present constitutive equations able to account for time independent plasticity together with creep and creep-plasticity interaction. A classical decomposition of the inelastic strain into a time independent plastic strain and a time dependent viscoplastic part is assumed. The coupling between both deformation modes (i.e. creep and plasticity) is obtained through an interaction between the plastic and viscoplastic state variables. In a first part, the capabilities of the model are described, and qualitative identifications are given in order to characterize the behaviour of the model. The practical applicability of the model is then tested, mainly using test results from the literature, but also specific data including creep, relaxation and tensile tests with various loading rates, as reported in the paper. The model is found able to discriminate between the increase of hardening produced by plasticity or creep. The effect of the loading rate on the subsequent amount of relaxation is correctly described and a good general agreement is observed between experiment and model predictions, even for complex loading paths (monotonic with temporary unloading periods, multiaxial loading paths in the stress space).     

The development of validation methodology of multi-axial creep damage constitutive equations and its application to 0.5Cr0.5Mo0.25V ferritic steel at 590 °C

Research progress on the development of validation methodology for multi-axial creep damage constitutive equations and its specific application to 0.5Cr0.5Mo0.25V ferritic steel at 590 °C is presented. A set of new phenomenological multi-axial creep damage constitutive equations was proposed aiming at overcoming the deficiency of inconsistency between predicted rupture strains and observed ones. Based on these explicit consistent requirements, an improved validation methodology is proposed and applied to 0.5Cr0.5Mo0.25V ferritic steel at 590 °C. It shows that the predictions of this new set of constitutive equations are consistent with experimental observations. It also reveals a significant difference in creep curves between different sets of constitutive equations and the need for experimental data so that the coupling of damage and creep deformation can be further examined.     

Finite element analysis for creep failure of coolant pipe in light water reactor due to local heating under severe accident condition

During severe accident of a light water reactor (LWR), the piping of the reactor cooling system would be damaged when the piping is subjected to high internal pressure and very high temperature, resulted from high temperature gas generated in a reactor core and decay heat released from the deposit of fission products. It is considered that, under such a condition, short-term creep at high temperatures would cause the piping failure. For the evaluation of piping integrity under a severe accident, a method to predict such high temperature short-term creep deformation should be developed, using a creep constitutive equation considering tertiary creep. In this paper, the creep constitutive equation including tertiary creep was applied to nuclear-grade cold-drawn pipe of 316 stainless steel (SUS316), based on the isotropic damage mechanics proposed by Kachanov and Ravotnov. Tensile creep test data for the material of a SUS316 cold-drawn pipe were used to determine the coefficients of the creep constitutive equation. Using the constitutive equation taking account of creep damage, finite element analyses were performed for the local creep deformation of the coolant piping under two types of conditions; uniform temperature (isothermal condition) and temperature gradient of circumferential direction (non-isothermal condition). The analytical results show that the damage variable integrated into the creep constitutive equation can predict the pipe failure in the test performed by Japan Atomic Energy Research Institute, in which failure occurred from the outside of the pipe wall.     

High temperature creep and cyclic deformation behaviour of AISI 316 L(N) austenitic steel and its modelling with unified constitutive equations

Creep tests at constant stress and low cycle fatigue (LCF) tests were performed with a view to investigating and modelling the deformation behaviour of AISI 316 L(N) austenitic stainless steel at 700 °C. All experiments were done on samples taken from two different sheets of the same batch of material.The creep stresses were selected from the high stress range. The results obtained from creep tests on samples from different sheets are compared with each other. The differences between them and the results of a creep test carried out at constant load are indicated.The LCF experiments were strain controlled. The effects of strain rate and strain amplitude on the cyclic hardening behaviour were investigated.The parameters of a set of constitutive equations are determined from these data. The quality of the parameter fit is discussed.     

High-temperature triaxial torsional creep tests of concrete at various hygral conditions

Results of an initial series of six-day creep tests under a program aimed at establishing fundamental deformation properties of concrete at high temperatures under triaxial loading with shear and various hygral conditions, both constant and transient, are reported. The tests are conducted in a novel large triaxial torsional testing machine with hygrothermal control. Tested are cylinders of six inch diameter, sealed or unsealed, loaded by compressive axial force, chamber pressure and torque. Some specimens are sealed wet, some are sealed after drying in an oven, and some are let to dry during the test. Significant differences in creep at various hygro-thermal conditions are observed. Particularly interesting is the fact that hygro-thermal changes affect not only normal creep strains but also shear creep strains. The results are of interest for the formulation of constitutive relations needed for the analysis of nuclear reactor accidents, radioactive waste disposal, and fire resistance.     

国产反应堆压力容器用16MND5钢的蠕变损伤本构模型研究

为了获得反应堆压力容器（RPV）材料在高温下的蠕变行为,保证RPV在严重事故工况下的完整性,本研究对国产RPV用16MND5钢的高温蠕变性能进行了测试,获得了600~900℃下材料的蠕变性能,并基于应变强化的基本蠕变本构模型与基于延性耗竭理论的蠕变损伤模型,建立了适用于16MND5钢的蠕变损伤本构模型,给出了材料的蠕变损伤模型参数。结果表明,本文提出的蠕变损伤本构模型的有限元模拟数据与试验数据符合性较好,验证了此蠕变损伤模型的正确性。该方法可用于严重事故情况下RPV的蠕变损伤分析,为RPV的完整性分析提供支持。      

Mechanics and mechanisms of creep deformation and damage

In recent years, several important advances in the understanding of the mechanics and mechanisms of creep deformation, damage and fracture in polycrystalline alloys have been achieved through the synergistic efforts of materials scientists and applied mechanicians. Current understanding, while far from complete, nonetheless provides a physically-based framework for developing computationally tractable continuum constitutive relations which capture major features of the intrinsic mechanisms of creep damage and deformation. Such models, when applied to the analysis of scientifically and technologically relevant boundary value problems, provide a basis for a local approach to high temperature fracture. The first section of the paper reviews certain aspects of the phenomenology, mechanisms, and mathematical models of creep fracture. It is concluded that an important internal damage parameter influencing macroscopic tertiary creep in conventional polycrystalline materials is the density of grain boundary facet cracks. The development of a “damage” constitutive model can conceptually be broken into two parts. One aspect is to quantify the effect of an (instantaneous) state of damage on the mechanical behavior. In the second part of the paper, this topic is explored for the case of a (generally non-dilute) distribution of aligned facet cracks in a power law creeping matrix. The remaining aspect of the model is to provide evolution equations for the damage variable(s). In the third section of the paper, we develop a simplified model for the evolution of facet crack density under conditions of creep-constrained cavitation. A central feature of the model is the variability in cavity nucleation potency over the grain boundary population.     

Long-term creep rupture behavior of smoothed and notched bar specimens of low-carbon nitrogen-controlled 316 stainless steel (316FR) and their evaluation

Low-carbon, nitrogen-controlled 316 stainless steel is regarded as a principal candidate for a main structural material of future fast breeder reactor plants in Japan. To grasp creep deformation and rupture behavior of this steel whose modeling is indispensable in the design of high-temperature components, a number of uniaxial tensile creep tests have been conducted for four products of this steel at 550 °C and higher temperatures. Long-term creep rupture data up to about 94,000 h were obtained and used to examine the applicability of rupture and deformation estimation methods developed earlier. In addition, two tests were conducted using round-bar specimens with circumferential notches to make investigation of the effect of stress multiaxiality on creep damage.     

The creep rupture properties of beta-phase Zircaloy-2 cladding in the region 1000–1500°C

Accurate creep parameters are essential for the prediction and assessment of fuel cladding behaviour under reactor accident conditions. To resolve uncertainties in the limited data available for beta-phase Zircaloy cladding, an extensive programme of isothermal stress rupture tests has been undertaken for Zircaloy-2 tubes in a non-oxidizing environment at temperatures from 1000 to 1500°C. The secondary creep parameters are calculated from an analysis of the strain histories obtained from each test using a novel photo-electronic technique for the continuous monitoring of tube deformation. The resulting creep equation is compared with recent rupture life data for Zircaloy tubes. The analysis also identifies an anomalous primary stage which significantly retards the early stage of deformation for low stress tests at 1200°C and above and which is found to be extremely sensitive to prior annealing. The influence of this primary component on predictions of cladding behaviour is assessed.     

A knowledge based system for creep–fatigue assessment

A knowledge based system was developed in the BRITE-EURAM C-FAT project to store the material property information necessary to perform complex creep–fatigue assessments and to thereby improve the effectiveness of data retrieval for such purposes. The C-FAT KBS incorporates a multi-level database which is structured to contain not only ‘reduced’ deformation and fracture test data, but also to enable ready access to the derived parameter constants for the constitutive and model equations used in a range of assessment procedures. The data management scheme is reviewed. The C-FAT KBS also has a dynamic worked example module which allows the sensitivity of predicted lifetimes to material property input data to be evaluated by a number of procedures. Complex cycle creep–fatigue endurance predictions are particularly sensitive to the creep property data used in assessment, and this is demonstrated with reference to the results of a number of large single edge notched bend specimen feature tests performed on a 1CrMoV turbine casting steel at 550°C.     

The interaction of rate and history-dependent effects and its significance for slow cyclic inelastic analysis at elevated temperature

Life prediction for creep and low-cycle fatigue interaction and the analysis of ratcheting phenomena are of great importance in the design of future high-temperature nuclear reactors. These problems involve slow cyclic load application, inelastic deformation, and are inherently nonlinear. Fortunately, finite element computer programs with their time following and nonlinear capabilities are now available for the efficient solution of these complicated problems. The task is now to ensure that a proper representation of the material deformation behavior, the constitutive equation, is used in these computer programs. A systematic study of structural metal deformation behavior in slow cyclic laboratory tests such as cyclic creep, cyclic relaxation, low-cycle fatigue with and without hold-time showed that rate and history dependence interact. A few examples of such interactions are given in this paper. It is further shown that constitutive equations based on the additive use of elastic, plastic, and creep strains are not capable of reproducing these interaction phenomena on principal grounds. New inelastic constitutive equations for metals must be developed and some presently pursued approaches are discussed briefly.     

A comparison between Japanese and French A16 defect assessment procedures for creep-fatigue crack growth

This paper presents the results of a benchmark on creep-fatigue crack growth evaluation for a plate subjected to cyclic bending loads with a 1 h dwell. The simplified creep-fatigue crack growth evaluation methods of JNC in Japan and A16 procedures proposed by CEA in France are presented. The methods, based on the reference stress approach, are compared each other. They are found to differ in the expression used for the reference stress solution used to estimate the creep strain. It is also pointed out that in contrast to the A16 procedures, the JNC method takes heterogeneous creep strain distribution into account for small scale yielding condition. The predictions obtained by the methods are also compared to the experimental data. It is found that the methods exhibit conservatisms which are significantly reduced when integrating the creep curve continuously without initialisation during the experiment [Proceeding of SMiRT 14(G13/2), Creep-Fatigue Crack Growth on CT25 Specimens in 316L(N) stainless steel at 650 °C].     

Comparison of crack initiation life estimation procedures under creep-fatigue conditions

This paper describes the application of “high temperature structural integrity assessment procedures” developed in the UK and Japan to creep-fatigue crack initiation in welded Type 316 features tests. The components were subjected to both fatigue and creep-fatigue loading at 630 °C. The loadings are representative of those on the upper seal gimbal joint in an advanced gas cooled reactor (AGR), except that the tests were isothermal and the imposed dwell times were reduced. It is demonstrated that application of the procedures gives accurate predictions of the observed crack initiation in the weldment, based on two different advanced inelastic constitutive models (BE and CRIEPI models) and best estimate materials data. Application of simplified assessment methods based on elastic analysis is shown to be conservative. Where appropriate, contrasts between the UK and the Japanese assessment procedures and inelastic modelling techniques have been highlighted.     

Fracture mechanics in creep situation interpretation of results on a test specimen

Fracture mechanics in creep situation is a difficult challenge for the 1990s. In France, CEA Saclay has conducted experimental tests on compact tension (CT) specimens at 650°C in order to investigate crack initiation under creep situations. The constitutive material is the 316SPH austenitic stainless steel used for most LMFR structures.Numerical simulations using SYSTUS code and simplified method analysis were performed on one of the tests (CT specimen at 650°C under constant load) to compare some parameters (notch opening, initiation time) with experimental values. The material constitutive law was represented by the complete elasto-viscoplastic CHABOCHE model for computation. Owing to geometrical characteristics such as thickness, the situation of the CT specimen was likely to be intermediate between plane stress and plane strain assumptions. From C^* parameter, incubation time obtained using the R5 rule was conservative in comparison with the test result.The continuum damage model developed at Ecole des Mines de Paris has also been used to assess creep damage in the notch tip area. The crack initiation time has been deduced from critical damage at characteristic distance (X_c = 0.05 mm). Considering critical damage specifically, for a CT specimen (D_c = 0.05), initiation time obtained was higher than the test result.The results of this study will contribute to the development of a methodology for nocivity analysis of cracks in creep situation.     

High temperature deformation and damage behavior of RAFM steels under low cycle fatigue loading: Experiments and modeling

Structural materials of fusion reactors are subjected to complex creep-fatigue loading and high irradiation doses. Correct modeling of their deterioration is a precondition of a sufficiently reliable lifetime prediction procedure. In the continuum mechanics approach selected for lifetime prediction of RAFM steels under creep-fatigue conditions, the inelastic strain rate modified (ISRM) damage model is coupled with a modified viscoplastic deformation model taking into account the complex non-saturating cyclic softening of RAFM steels. The resulting coupled model is a powerful prediction tool, which can be applied to arbitrary creep-fatigue loading provided that the material, temperature and possibly irradiation dose-dependent parameters of the model have been determined. Therefore, a fitting procedure has been developed for the parameters identification on the base of deformation and lifetime data from strain-controlled low cycle fatigue (LCF) tests without and with hold time as well as creep tests. The coupled deformation-damage model has been applied to F82H mod and EUROFER 97 in the reference (unirradiated) state under isothermal cyclic loading at 450, 550 and 650 °C. The comparisons between model and experiment show that the observed lifetimes in the LCF tests could be fairly well calculated even for the tests with hold time, which were not considered for the identification of the damage model parameters.