Elastic-plastic Creep Analysis Research Articles

Thermomechanical Fatigue Life Prediction Method of the Trailing Edge Holes in the Turbine Blade for Turboshaft Engine

In this paper, a thermomechanical fatigue (TMF) life analysis method considering stress relaxation was established for turbine blade in a turboshaft engine. The nonlinear creep deformation of a superalloy is predicted by coupling creep damage in the framework of viscoplastic theory. The results revealed that the calculation error of the model for the elastic-plastic stress-strain curve was less than 5%, while the simulation accuracy for the creep curve is within the dispersion range of the inherent properties of material creep deformation. Based on the elastic-plastic creep analysis of a turbine blade, the creep damage and its evolution law of the leading edge and trailing edge of the blade are clarified, and a new method is provided for determining the local dangerous points on the blade. With the help of the linear damage cumulative life theory, the fatigue creep life of the trailing edge hole of a turbine blade considering the stress relaxation is obtained, which provides a more reasonable and better engineering application method for the blade life evaluation.

High-temperature bending fatigue properties of oxide dispersion-strengthened platinum–rhodium alloy under high axial stress

In this study, high-temperature bending fatigue tests were carried out using an oxide dispersion-strengthened platinum-rhodium alloy at 1400 °C with a relatively high axial stress. At a low stress amplitude, creep damage progressed throughout the cross-section of the sample due to axial stress. However, at a high stress amplitude, creep damage progressed only in the central part of the direction of thickness and fracturing originated from inside the sample. Elastic-plastic creep analysis also indicated that high tensile stress remained inside the sample due to the yielding near the surface. The fact that the life is determined by the creep due to the stress generated inside of the material is useful for life prediction.

Assessment of Residual Stress Due to Overlay-Welded Cladding and Structural Integrity of a Reactor Pressure Vessel

In this study, the residual stresses generated within the overlay-welded cladding and base material of reactor pressure vessel (RPV) steel were measured for as-welded and postwelded heat-treated conditions using the sectioning and deep-hole-drilling (DHD) techniques. In addition, thermo–elastic–plastic creep analyses considering the phase transformation in the heat-affected zone using the finite element method (FEM) were performed to evaluate the weld residual stress produced by overlay-welding and postweld heat treatment (PWHT). By comparing the analytical results with the experimentally determined values, we found a good agreement for the residual stress distribution within the cladding and the base material. The tensile residual stress in the cladding is largely due to the difference in the thermal expansion of the cladding and the base material. It was also shown that considering phase transformation during welding was important for improving the accuracy of the weld residual stress analysis. Using the calculated residual stress distribution, we performed fracture mechanics analyses for a vessel model with a postulated flaw during pressurized thermal shock (PTS) events. The effect of the weld residual stress on the structural integrity of RPVs was evaluated through some case studies. The results indicated that consideration of the weld residual stress produced by overlay-welding and PWHT is important for assessing the structural integrity of RPVs.

Simplified estimates of the creep crack growth parameter C(t) under primary/secondary stresses using the enhanced reference stress method

This paper describes simplified methods to estimate the fracture mechanics parameter, C(t), related to creep crack growth rates in non-steady state creep conditions produced by primary or secondary stresses. The methods proposed incorporate effects from initial plasticity and redistribution during a short period after a loading dwell starts, in addition to the estimate of the steady state creep crack growth parameter C∗ by the enhanced reference stress method. The methods have been validated by performing finite element elastic–plastic creep analyses of a circumferentially cracked cylinder subjected to load-controlled tension or thermal loads.

Long-Term Stability of Residual Stress Improvement by Water Jet Peening Considering Working Processes.

To prevent primary water stress corrosion cracking (PWSCC), water jet peening (WJP) has been used on the welds of Ni-based alloys in pressurized water reactors (PWRs). Before WJP, the welds are machined and buffed in order to conduct a penetrant test (PT) to verify the weld qualities to access, and microstructure evolution takes place in the target area due to the severe plastic deformation. The compressive residual stresses induced by WJP might be unstable under elevated temperatures because of the high dislocation density in the compressive stress layer. Therefore, the stability of the compressive residual stresses caused by WJP was investigated during long-term operation by considering the microstructure evolution due to the working processes. The following conclusions were made: The compressive residual stresses were slightly relaxed in the surface layers of the thermally aged specimens. There were no differences in the magnitude of the relaxation based on temperature or time. The compressive residual stresses induced by WJP were confirmed to remain stable under elevated temperatures. The stress relaxation at the surface followed the Johnson-Mehl equation, which states that stress relaxation can occur due to the recovery of severe plastic strain, since the estimated activation energy agrees very well with the self-diffusion energy for Ni. By utilizing the additivity rule, it was indicated that stress relaxation due to recovery is completed during the startup process. It was proposed that the long-term stability of WJP under elevated temperatures must be assessed based on compressive stresses with respect to the yield stress. Thermal elastic-plastic creep analysis was performed to predict the effect of creep strain. After 100 yr of simulated continuous operation at 80% capacity, there was little change in the WJP compressive stresses under an actual operating temperature of 623 K. Therefore, the long-term stability of WJP during actual operation was analytically predicted.

2506 低合金鋼平板の溶接残留応力解析結果に及ぼす各種影響因子の評価(一般セッション(2),OS・一般セッション講演)

Residual stress profiles of a low alloy steel JIS SQV2A were predicted by thermal elastic plastic analysis taking the phase transformation strain into consideration. Stress relaxation during post weld heat treatment (PWHT) was also predicted by thermal elastic plastic creep analysis. Effects of welding and PWHT conditions, such as heat input efficiency, preheating temperature, PWHT holding temperature, and holding time, on residual stress profiles were studied. The analysis results showed that the amount of longitudinal stress at the center of the weld decreased as the heat input efficiency or the preheating temperature rose, and that the amount of stress relaxation increased as the PWHT holding temperature rose. The effect of the PWHT holding time at 625℃ on stress relaxation was small.

Creep crack growth simulations in 316H stainless steel

Virtual methods of predicting creep crack growth (CCG), using finite element analysis (FE), are implemented in a compact tension specimen, C(T). The material examined is an austenitic type 316H stainless steel at 550 °C, which exhibits power-law creep–ductile behaviour. A local damage-based approach is used to predict crack propagation and the CCG rate data are correlated with the C ∗ parameter. Two-dimensional elastic–plastic–creep analyses are performed under plane stress and plane strain conditions. Finite element CCG rate predictions are compared to experimental data and to the NSW and modified NSW (NSW–MOD) CCG models’ solutions, which are based on ductility exhaustion arguments. An alternative version of the NSW–MOD model is presented for direct comparison with the FE implementation. The FE predictions are found to be in agreement with the appropriate analytical solutions, and follow the trends of the experimental data at high C ∗ values. Accelerated cracking behaviour is observed experimentally at low C ∗ values, which is consistent with the standard plane strain NSW–MOD prediction. The FE model may be developed to predict this accelerated cracking at low C ∗ values so that the trends between CCG rates at high and low C ∗ values may be determined.

Impact of the number of chips on the reliability of the solder balls for wire-bonded stacked-chip ball grid array packages

This investigation examines how the number of chips affects the reliability of solder balls for wire-bonded stacked-chip ball grid array packages under thermal cycling tests. The studied objects were packages with one, two, three and four stacked chips. Three-dimensional finite element analysis was utilized to simulate the stress/strain behavior of all studied packages. Two kinds of properties of 63Sn/37Pb eutectic solder were employed individually in the finite element analyses. One property of the solder was assumed to exhibit the elastic–plastic–creep behavior. Temperature-dependent stress/strain curves and Norton’s steady creep equation were used in the analysis. Another property of the solder governed by the Anand’s viscoplastic model was also employed to describe the behavior of solder balls. The simulation results in the elastic–plastic–creep analyses and viscoplastic analyses reveal that the von Mises stress, the non-linear strain, and the inelastic strain energy density of the critical solder balls increase with the number of stacked chips, but the increments become gradually stable as the number of chips increases. Three fatigue life prediction models—Darveaux’s model, the modified Coffin–Manson model and the creep-fatigue model—were applied to evaluate the fatigue life of the studied packages. Prediction results indicate that the fatigue life of the solder balls decreases as the number of stacked chips increases, and the decrease in predicted life shows stable behavior as the number of chips increases. The stable trend is consistent with experimental observation in the thermal cycling tests. By comparing with the experimental data, it is shown that the Darveaux’s model gives better prediction than the other two models.

多層溶接継手のクリープ変形挙動に及ぼす溶接金属部の不均一な高温強度特性の影響

Evaluation of creep properties of the welded joint through taking local fluctuation of the properties into consideration is experimentally or analytically seldom carried out. In this context, the purposes of the present study are to examine the surface strain distribution in the weld metal of a full thickness welded joint specimen and subsequently to investigate the local variation in the properties of the all-weld metal part of the joint using miniature specimens. A welded joint was prepared for 316FR steel plates by gas tungsten arc welding process using Mod. 316 filler wire. Creep tests were conducted at 823K in air using full thickness large welded joint specimens, HAZ and all-weld metal miniature specimens. By interrupting the creep test for the full thickness welded joint specimen, we observed the change in the uniaxial creep strain distribution in the weld metal in the thickness direction of the plate. The last layer of weld metal showed considerably larger creep strain than the central layers of the weld metal. The elastic-plastic creep analysis of the welded joint specimen by FEM was performed using these data. Finite element simulation performed for full-thickness welded joints provided creep strain distribution that is consistent with measured values. From the results above, it is concluded that the creep properties of weld metal in multi-pass, multi-layer welded joints strongly depend on the location of specimen sampling. It is necessary to take the fluctuation of material properties of a weld metal part into consideration when we perform simulation of creep deformation of a welded joint with sufficient accuracy.

Creep crack growth prediction using a damage based approach

This paper presents a numerical study of creep crack growth (CCG) in a fracture mechanics specimen. The material properties used are representative of a carbon–manganese steel at 360 °C and the constitutive behaviour of the steel is described by a power law creep model. A damage-based approach is used to predict the crack propagation rate in a compact tension specimen and the data are correlated against an independently determined C ∗ parameter. Elastic–creep and elastic–plastic–creep analyses are performed using two different crack growth criteria to predict crack extension under plane stress and plane strain conditions. The plane strain crack growth rate predicted from the numerical analysis is found to be less conservative than the plane strain upper bound of an existing ductility exhaustion model, for values of C ∗ within the limits of the present CCG testing standards. At low values of C ∗ the predicted plane stress and plane strain crack growth rates differ by a factor between 5 and 30 depending on the creep ductility of the material. However, at higher loads and C ∗ values, the plane strain crack growth rates, predicted using an elastic–plastic–creep material response, approach those for plane stress. These results are consistent with experimental data for the material and suggest that purely elastic–creep modelling is unrealistic for the carbon–manganese steel as plastic strains are significant at relevant loading levels.

Process capability study and thermal fatigue life prediction of ceramic BGA solder joints

The design and process capability of board-level assembly of ceramic ball grid array (CBGA) packages with respect to their reliabilities were investigated. Two types of FEM models were built for elastic and elastic–plastic–creep analyses, respectively. The effect of PCB material, PCB thickness, and the thickness of ceramic substrate on solder joint deformation was discussed. It was shown that the variation in assembly process would cause the highest stress in the joints change by 10% from the mean value. The failure location and fatigue life under the temperature cycling condition were also studied. It was concluded that the prediction was close to the first failure in the test and would be seen as a conservative estimation.

Study on inelastic analysis using the boundary element method. (2nd Report. Study on the boundary element 3-dimensional thermal elastic plastic creep analysis).

This study is concerned with an application of the boundary element method (BEM) to a 3-dimensional thermal elastic plastic creep analysis. The BEM has been applied to 2-dimensional or axisymmetric inelastic problems. Results of these analyses showed an applicability of BEM to inelastic problems, but did not provide a numerical example of 3-dimensional thermal elastic plastic creep analysis. We have already developed a 3-dimensional thermal elastic plastic analysis computer program using BEM, and also some numerical techniques which are valid for an accurate and efficient analysis. In this study, the function of our computer program was expanded to be applicable to 3-dimensional thermal elastic plastic creep analysis. The thermal elastic plastic creep analysis of a thick-walled cylinder was performed to confirm the applicability of BEM.

A Method for Simplified Elastic Plastic Creep Analysis of a Thin Circular Straight Pipe

薄肉円管が曲げモーメント,ねじりモーメント,軸力および内圧を受ける場合の弾塑性クリープ解析を簡易に行う方法を提案した.円管のはりとしての変形は,その弾性成分は弾性ばり理論によって,そのクリープおよび塑性成分はここで開発された各断面において定義される相当リファレンス応力によって計算される.ここで提案した簡易解析法は,配管系の非弾性解析のための有力な手段となる.

Modelling and accuracy of solutions in inelastic analysis through studies of benchmark problems

The accuracy of numerical solutions and the constitutive modelling are discussed in relation to the analysis of inelastic problems involving material nonlinearities. Regarding the solution techniques or computational strategies, attention is centered on the tangent stiffness method. The point to be emphasized in the discussion of the constitutive modelling is the importance of reexamination of classical approaches for the application to practical design with proper modifications, if required. A couple of benchmark problems have been solved and typical solution examples are given in the paper to show the level of elastic-plastic creep analysis capability that is being reached. Examples cover the combined tension and shear of an inelastic material element, international benchmark problems on pressure vessel and piping, and ones from the field of fracture mechanics. For elementary cases, exact solutions have been obtained and used as the basis for the comparison with the numerical solutions by the finite element method. At the end of paper, a brief introduction is made to the inelastic analysis programs being developed by the authors.

Finite element three-dimensional elastic-plastic creep analysis

This paper presents a continued development of computationally efficient finite element methods for accurately predicting the isothermal three-dimensional elastic-plastic creep responses of thick and thin shell structures subjected to mechanical and thermal loads. This work is applicable to a wide range of engineering structures and most recently has been used in the elastic-plastic creep analyses of high-temperature nuclear reactor components and rotating turbine blades. Previous work in this area for elastic-plastic analysis has been demonstrated by Levy et al. In that reference, use of a variable number of stress points within an element to describe elastic-plastic behaviour was demonstrated. These ideas have been extended for combined plasticity and creep behaviour. Thus, within an element, the order of the allowable total kinematic strain distribution is dependent on the number of element nodes (assumed displacement distribution), and the order of the allowable plastic strain distribution (and hence the elastic-plastic boundaries) and/or creep strain distribution is dependent on the number and location of the stress points used to numerically integrate the inelastic effects. This allows for an accurate representation of the elastic-plastic creep behaviour within an element. This higher inelastic representation results in the use of a minimum number of degrees of freedom for a given nonlinear analysis, which is particularly important for combined creep and plasticity behaviour and for cyclic loading, where computer times can be prohibitive. The basic numerical solution procedure for the elastic-plastic creep analysis is an incremental predictor-corrector iterative scheme combined with the ‘initial strain’ approach. Attention has been given to the time step increment strategy for combined plasticity and creep as this governs efficiency and accuracy. The methods have been implemented into the three-dimensional solid element module (HEX) of the Grumman PLANS finite element program. Sample problems are used to demonstrate and investigate the accuracy and efficiency of these methods. Sample problems include combined plasticity and creep analysis of a simple rod under time varying load, stress-relaxation of a simple rod, thermal stress-relaxation of a plate subjected to a temperature variation across the width, and creep analysis of an internally loaded thick-walled pressure vessel.

Elastic-plastic creep analysis of high temperature nuclear reactor components

In structures subjected to high temperatures and large thermal gradients, the total strain consisting of the sum of thermal, elastic, plastic, and viscous (creep) parts must be considered. Elastic and thermal strains are reversible and depend on the instantaneous stress and temperature levels; plastic and viscoelastic (creep) strains are irreversible, and their complete determination requires that loading and temperature histories be known. For many practical applications high mechanical or thermal loadings are of short duration; hence, viscoelastic (creep) strains are not significant. In such cases, the elastic and plastic strains represent the significant response of a structure to the applied loadings. An adequate description of the behavior of such structures can be obtained by the use of the theory of non-isothermal plastic deformation of elastic strain-hardening solids. For structures exposed to high temperature, long duration loadings, such as liquid metal fast breeder reactor components, the above theories do not provide adequate design evaluation and the knowledge of creep strain as a design allowable is necessary. Further, since the loading is transient with multiple complex cycles, creep and plasticity strain portions must be considered simultaneously. This paper presents a method for solving the problem of non-isothermal elastic-plastic creep structures. Finite element discretization is utilized, based on a number of flat and curved, thick and thin shell elements of triangular and quadrilateral form. Material nonlinearities are treated by the tangent stiffness method; geometric nonlinearities are considered by updating the geometry after each loading increment. Non-isothermal loading is considered by making a transition to the new temperature at the beginning of the load step and allowing the solution to settle at the position of overall equilibrium by iterative steps.