Creep Rupture Analysis Research Articles

Shakedown and creep rupture analysis of printed circuit heat exchangers based on the linear matching method framework

In the field of nuclear engineering, Printed Circuit Heat Exchangers (PCHEs) have become increasingly popular and the structural integrity assessment of these key power plant components is crucial. As part of the structural integrity assessment, creep rupture analysis considers the interaction of cyclic plasticity and creep behaviour, which is vital for components subjected to cyclic thermal-mechanical loads. The Linear Matching Method (LMM) framework has included a creep rupture module based on an extended shakedown algorithm, which has been adopted by several researchers. However, the current LMM framework mainly relies on linear extrapolation and requires users to provide a large amount of data points to estimate the rupture stress. This paper introduces a Unified Creep Rupture Equation (UCRE) for characterizing the creep rupture curves of diverse steel types. The UCRE is implemented in an extended shakedown algorithm and integrated into the LMM framework. The numerical method is validated through a comparative analysis, wherein the estimated rupture curves are compared with those provided in the ECCC data sheet, as well as against alternative numerical models. Shakedown and creep rupture analyses are then performed on a PCHE core. The proposed method facilitates the parametric study of changing materials and the process of material selection. Various geometric configurations are also considered and the proposed unitary cell model is verified by comparing the results with ones from full FE models. The UCRE has been proved to be an accurate engineering tool for the prediction of rupture strengths while the LMM framework has gained improved usability and versatility for engineering applications.

Application of soft constrained machine learning algorithms for creep rupture prediction of an austenitic heat resistant steel Sanicro 25

Creep rupture extrapolation is crucial for high-temperature materials served in power plants. Many analytical models can be used for creep rupture analysis, and fundamental models are also available. Machine learning is also an alternative. However, unphysical prediction curves occur readily in common machine learning algorithms, where one must manipulate the best results or ignore the less satisfactory ones. Using just high regression coefficients and low errors is not enough to obtain high accuracy of the methods. Nevertheless, five soft constrained machine learning algorithms (SCMLAs), where soft constraints, stability analysis by culling long-time or low-stress data, extrapolation from short to long times, and errors of solutions and algorithms are considered, are used for creep rupture prediction in this work. The models can generate reasonable results for fitting all data, extrapolating from short to long times, and stability analysis for Sanicro 25 after a number of tests. The errors of solutions for all the analyses are in a quite reasonable range, including extrapolation and stability analysis. The average relative standard deviation of the five SCMLAs is less than 2.5% at three times the maximum experimental creep rupture time. Creep rupture strength of the austenitic stainless steel Sanicro 25 can be predicted quantitatively by taking the average predicted stresses of the five SCMLAs. The method can also be used for other high-temperature alloys with similar creep degradation mechanisms.

Creep rupture limit analysis for engineering structures under high-temperature conditions

The efficient and accurate prediction of creep rupture limit poses a huge challenge for high-temperature engineering such as aerospace, nuclear and chemical industries. It is important to investigate the applicability of mainstream assessment approaches and related creep rupture failure mechanisms through theoretical and numerical views. In this study, major creep rupture assessment techniques are comparatively investigated for the first time, including the isochronous stress-strain (ISS) curve-based creep rupture limit analysis, the Omega creep damage model-based creep analysis and the direct method-based creep rupture assessment by an extended Linear Matching Method (LMM). New virtual creep test curves are generated from the Omega creep model and chosen as the unified creep source data to derive the key material parameters used for different methods. For proposing a reasonable strategy for evaluating high-temperature structures in terms of creep rupture, the balance between computational efficiency and accuracy is comprehensively analyzed. Through a practical engineering application of a high-temperature pressure vessel component, a profound insight into the techniques of creep rupture evaluation is delivered from different views. Moreover, several assessment curves are built based on a new understanding of creep rupture failure mechanism, with an effective numerical plan to validate the creep rupture boundary illustrated. It is demonstrated that the LMM direct creep rupture analysis is more suitable for calculating the structural creep rupture limit, with both monotonic and cyclic load conditions considered.

On Fatigue Design Curves for 2.25Cr-1Mo-V Steel Reactors at Elevated Temperature in Code Case 2605

Fatigue design method for 2.25Cr-1Mo-V steel reactors in code case 2605 (CC 2605) is reviewed. Main factors such as the accelerating function of fatigue action, the cyclic frequency, the strain damage factor (β) related to the fatigue design curves are addressed, and the applicable stress level for pure creep rupture analysis in CC 2605 is also discussed. Results indicate that, for the high loading levels, the accelerating function of fatigue action and strain damage factor contribute relatively remarkably to the fatigue design curve. The increase of cyclic frequency leads to a remarkable increase of the allowable fatigue cycle number and hence reduces the conservativeness of fatigue design curve. It should be stipulated in CC 2605 that the applicable stress level is higher than a value of around 200 MPa (slightly dependent on temperature) for the adjusted uniaxial Omega damage parameter and 16 MPa for the creep strain rate when the Omega creep-damage method is employed.

Creep rupture assessment by a robust creep data interpolation using the Linear Matching Method

The accurate assessment of creep rupture limit is an important issue for industrial components under combined action of cyclic thermal and mechanical loading. This paper proposes a new creep rupture assessment method under the Linear Matching Method framework, where the creep rupture limit is evaluated through an extended shakedown analysis using the revised yield stress, which is determined by the minimum of the yield stress of the material and the individual creep rupture stress at each integration point. Various numerical strategies have been investigated to calculate these creep rupture stresses associated with given temperatures and allowable creep rupture time. Three distinct methods: a) linear interpolation method, b) logarithm based polynomial relationship and c) the Larson–Miller parameter, are introduced to interpolate and extrapolate an accurate creep rupture stress, on the basis of discrete experimental creep rupture data. Comparisons between these methods are carried out to determine the most appropriate approach leading to the accurate solution to the creep rupture stresses for the creep rupture analysis. Two numerical examples including a classical holed plate problem and a two-pipe structure are provided to verify the applicability and efficiency of this new approach. Detailed step-by-step analyses are also performed to further confirm the accuracy of the obtained creep rupture limits, and to investigate the interaction between the different failure mechanisms. All the results demonstrate that the proposed approach is capable of providing accurate but conservative solutions.

Application of kinetic theory to the analysis of high-temperature creep rupture of metals under complex stress (review)

This paper gives an analytical review of the results obtained using the kinetic theory of creep and creep rupture to analyze the creep rupture of metals under complex stress. Special note is made of the outstanding contribution of Soviet scientists L. M. Kachanov and Yu. N. Rabotnov, who introduced the concept of material damage and developed the fundamentals of the kinetic theory. Different versions of this theory are used in studies of Russian and foreign scientists. The possibility of applying the kinetic theory to model the deformation and fracture of metals under creep conditions using scalar, vector, and tensor damage parameters and their combinations is considered.

Viscoelasticity, viscoplasticity, and creep failure of polypropylene/clay nanocomposites

Observations are reported on polypropylene/clay nanocomposites in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. New constitutive equations are derived in viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters are found by fitting the experimental data. The stress–strain relations are applied to the analysis of creep rupture. It is demonstrated that reinforcement of polypropylene with 1wt.% of nanoclay induces an increase in time to failure by an order of magnitude.

Creep rupture analysis and remaining life assessment of 2.25Cr–1Mo steel tubes from a thermal power plant

Superheater and reheater 2.25Cr–1Mo steel boiler tubes from a thermal power plant after 17 year of service at nominally 540 °C and 40 MPa were studied to predict their remnant life. The investigation included dimensional, hardness and tensile measurements in addition to accelerated stress rupture tests between 625 and 700 °C and microstructural examination. The microstructure of the service-exposed alloy was free from any signs of deterioration, and the hardness was within the expected ranges; however, tensile testing revealed an apparent loss of strength from room temperature to 600 °C. Accelerated rupture testing, on the other hand, did not reveal any degradation of rupture behaviour compared to that of the virgin alloy. Analysis of the stress rupture data predicted that the 17 years exposed superheater and reheater tubes could remain in continued service for at least 12 more years at the current stress–temperature conditions.

The linear matching method applied to the high temperature life integrity of structures. Part 1. Assessments involving constant residual stress fields

Design and life assessment procedures for high temperatures are based on ‘expert knowledge’ in structural mechanics and materials science, combined with simplified methods of structural analysis. Of these, R5 is one of the most widely used life assessment methods internationally with procedures based on reference stress techniques and shakedown calculations using linear elastic solutions. These have been augmented by full finite element analysis and, recently, the development of a new programming method, the linear matching method (LMM), that allows a range of direct solutions that include shakedown methods and simplified analysis in excess of shakedown. In this paper, LMM procedures are compared with calculations typical of those employed in R5 for cyclic loading problems when the assumption of a constant residual stress field is appropriate including shakedown and limit analyses, creep rupture analysis and the evaluation of accumulated creep deformation. A typical example of a 3D holed plate subjected to a cyclic thermal load and a constant mechanical load is assessed in detail. These comparisons demonstrate the significant advantages of linear matching methods for a typical case. For a range of cyclic problems when the residual stress field varies during the cycle, which include the evaluation of plastic strain amplitude, ratchet limit and accumulated creep strains during a high temperature dwell periods, the corresponding LMM and R5 procedures are discussed in an accompanying paper.

The linear matching method applied to the high temperature life integrity of structures. Part 2. Assessments beyond shakedown involving changing residual stress fields

In an accompanying paper, the application of the linear matching method to the high temperature life assessment of structures was discussed and compared with assessment procedures, typical of those used in R5, for a range of cyclic problems within shakedown. These included shakedown and limit analyses, creep rupture analysis and the evaluation of rapid cycle creep deformation. In this paper, procedures based on the linear matching method are presented for a range of cyclic problems at higher stress ranges beyond shakedown involving changing residual stress fields. These include the evaluation of the plastic strain amplitude, ratchet limit and accumulated creep strains during high temperature dwell periods. The results are compared with calculation methods typical of the R5 methodologies. As in the accompanying paper, a 3D holed plate subjected to cyclic thermal load and constant mechanical load is assessed in detail as a typical example. The results demonstrate the flexibility of the linear matching method compared with current typical applications of high temperature assessment procedures.

Kinetic theory of creep and creep-rupture strength analysis of structural components. Part 3. Upper and lower bounds for rupture onset time for non-uniformly heated structural components

Using Rabotnov’s kinetic theory of creep, an upper and lower bounds for a rupture onset time are derived for an arbitrary body (structural component) under stationary external thermomechanical loading. The bounds are then compared to those used in engineering practice. By way of illustration, the relevant results for a thick-walled non-uniformly heated pipe loaded by internal pressure are discussed.

Analysis of the influence of aggressive environment on creep and creep rupture of rod under pure bending

A method for modelling the influence of an aggressive environment on creep and creep rupture is suggested. This method is based on the introduction of a notion of structural elements and postulating elementary creep properties of these elements. The equations of behavior of a specimen as a whole are based on the behavior of the elements.A probabilistic approach is used for the analysis of creep and creep rupture of solids. Pure bending of a long thin rod in an aggressive environment is studied. It is supposed that the fracture of structural elements takes place only under tensional stresses. A system of integral-differential equations is derived; this system characterizes the process of damage accumulation and change of stress-strain state at times,which is caused by rod bending. It is demonstrated that rupture of any structural element in a tension area causes stress redistribution. This redistribution leads to a motion of the neutral lines at which stresses and strains equal zero. The numerical investigation of a derived system of equations is developed.

CDM Mechanisms-Based Modelling of Tertiary Creep: Ability to Predict the Life of Engineering Components

The paper demonstrates how computational CDM can be used to predict the behaviour of structural components, ranging from modest stress concentrators to the growth of cracks by creep. Size effects in CDM analysis are addressed, and it is shown how a non-local CDM approach can be used to predict the observed crack tip behaviour. The proviso being that the length scales, associated with the damage fields and gradients, be modelled to comply with continuum theory. It is shown how damage state variable theories may be used to provide traceability from the physics of micro-mechanisms to the macro-material behaviour described by constitutive equations. The paper presents a detailed analysis of creep rupture in ferritic steel weldments, and shows how multi-axial stress rupture criteria, weldment phase dimensions, and constitutive equations for each material phase of the weld, can be used in Finite Element CDM analyses to predict the results of experiments carried out on butt-welded pipes and cross-welded tension testpieces. Original results are presented which show how the above CDM techniques have been used to perform a three-dimensional CDM high-temperature creep rupture analysis of a welded cylinder-cylinder pressure vessel intersection; and, to predict damage initiation and crack growth. The paper also demonstrates how CDM conservatively predicts the vessel lifetime; and, how the experimentally observed weld failure mechanism is well predicted.

Stress relaxation in broken fibers in unidirectional composites: modeling and application to creep rupture analysis

This paper describes a model of stress relaxation in broken fibers in unidirectional metal matrix composites reinforced with long brittle fibers. A cylindrical cell with a broken fiber embedded in a power law creeping matrix is employed, and the broken fiber is assumed to have a bilinear distribution of axial stress. Then, on the basis of energy balance in the cell under constant overall strain, a relaxation equation of interfacial shear stress acting on stress recovery segments is derived in a simple form. The relaxation equation is approximated rationally and integrated to obtain an analytical solution, which is shown to agree fairly well with the numerical analysis of Du and McMeeking. (Du, Z.-Z., McMeeking, R.M., 1995. Creep models for metal matrix composites with long brittle fibres. J. Mech. Phys. Solids 43, 701–726.) Moreover, the relaxation equation is combined with Curtin's model (Curtin, W.A., 1991. Theory of mechanical properties of ceramic-matrix composites. J. Am. Ceram. Soc. 74, 2837–2845.), so that rupture time in long term creep is evaluated analytically and explicitly on the assumption of global load sharing. It is shown that the resulting relation represents well the dependence of creep rupture time on applied stress observed experimentally on a unidirectional metal matrix composite.

Recent Progress in Creep Rupture Analysis of Unidirectional Composites Reinforced with Long Brittle Fibers.

The present paper deals with state of the art in creep rupture analysis of unidirectional composites reinforced with long brittle fibers. Experiments, numerical simulations and analytical models related with the creep rupture analysis are treated mainly on metal matrix composites, which can be mathematically modeled more easily because of the assumption of global load sharing. It is described that matrix creep and statistical fiber fracture play important roles in understanding and predicting the creep rupture of such composites appropriately. It is emphasized from the mechanics point of view that two kinds of stress relaxation, i.e., relaxation of matrix normal stress and that of interfacial shear stress around fiber breaks, are the key to the creep rupture in short and long terms, respectively.

一方向連続繊維強化複合材の繊維破断部付近の界面せん断応力緩和モデルおよびクリープ破断解析

一方向連続繊維強化複合材の繊維破断部付近の界面せん断応力緩和モデルおよびクリープ破断解析

Strain-controlled creep rupture in an internally-notched pressurized tube by the finite element technique

A creep rupture analysis of an internally notched thick-walled tube, subjected to a constant internal pressure, is carried out in detail based on the local continuum damage mechanics approach using the finite element technique. A strain-controlled creep damage law, which is derived from a more complex strain-dependent creep damage law, is employed to evaluate the damage due to creep. Because of the presence of the notch and hence the associated extremely non-uniform damage field, a localized “crack”, which is defined as the region of ruptured zones, initiates at the notch tip and then propagates through the notched section. While the crack advances with a monotonically but slowly increasing rate during most of the rupture life, it propagates through more than half of the notched section in essentially zero time. This behavior of the crack propagation is a consequence of the creep ductility as well as the loss of load-carrying material at the notched section.

Bending creep rupture analysis using a non-linear energy criterion approach

Creep rupture analysis by simple bending induces a larger and therefore more accurately measured creep deflection. It also considers both tensile and compression behaviour simultaneously. However, the common assumption of a linear stress distribution across the cross-section of the beam leads to a nominal value for the calculated rupture stress. In this paper, the true bending rupture stresses for a wood polymer composite beam was determined using a Norton-Bailey or power creep deformation analysis. These values were then used to model the creep rupture behaviour of the material, using an energy criterion approach. The results indicated that a non-linear consideration consistently resulted in higher values for the elastic and anelastic modulus, as well as the upper and lower creep rupture stress limits.

Strain-controlled creep rupture analysis of a beam on Winkler foundation

Based on the previously proposed uniaxial strain-controlled creep damage law, a continuum mechanical creep rupture analysis is carried out for a beam resting on a high temperature elastic Winkler foundation. The analysis includes the determination of the non-dimensional time for initial rupture, the propagation of the rupture front with the associated thinning of the beam, and the influence of creep damage on the deflection of the beam.

Analysis of creep rupture in a notched tensile bar

For circumferentially notched, round tensile bars the creep rupture behaviour is analysed, based on constitutive relations that account for the nucleation and growth of grain boundary cavities in polycrystalline metals at high temperatures. Both diffusive cavity growth and growth by dislocation creep of the surrounding grains is incorporated in the model, and in some cases free grain boundary sliding is assumed. Failure by cavity coalescence is predicted at small overall strains in the range where cavity growth is constrained by the rate of dislocation creep of the grains, whereas outside this range large occur prior to failure. In the analyses for notched specimens, where the stress fields are strongly non-uniform, first failure occurs at the notch tip, and subsequently a macroscopic crack grows into the material. Various combinations of material parameters are considered, and in most cases the crack is found to grow in the plane of the notch. The results are related to earlier experimental and computational investigations of creep rupture in notched bars.