Damage mechanics based predictions of creep crack growth in 316 stainless steel

This paper describes a novel modelling process for creep crack growth prediction of a 316 stainless steel using continuum damage mechanics, in conjunction with finite element (FE) analysis. A damage material behaviour model, proposed by Liu and Murakami [1], was used which is believed to have advantages in modelling components with cracks. The methods used to obtain the material properties in the multiaxial form of the creep damage and creep strain equations are described, based on uniaxial creep and creep crack growth test data obtained at 600 °C. Most of the material constants were obtained from uniaxial creep test data. However, a novel procedure was developed to determine the tri-axial stress state parameter in the damage model by use of creep crack growth data obtained from testing of compact tension (CT) specimens. The full set of material properties derived were then used to model the creep crack growth for a set of thumbnail crack specimen creep tests which were also tested at 600 °C. Excellent predictions have been achieved when comparing the predicted surface profiles to those obtained from experiments. The results obtained clearly show the validity and capability of the continuum damage modelling approach, which has been established, in modelling the creep crack growth for components with complex initial crack shapes.     

Issues relating to numerical modelling of creep crack growth

In this paper creep crack growth behaviour of P92 welds at 923 K are presented. Creep crack growth behaviour for P92 welds are discussed with C^* parameter. Creep crack growth behaviour of P92 welds has been compared with that of P91 welds with C^* parameter. NSW and NSW-MOD model were compared with the experimental creep crack growth data. Plane strain NSW model significantly overestimates the crack growth rate, and plane stress NSW model underestimates it. Whilst, NSW-MOD model for plane stress and plane strain conditions gives lower and upper bound of the experimental data, respectively.FE analysis of creep crack growth has been conducted. Constrain effect for welded joints has been examined with C^* line integrals of C(T) specimens. As a result, constant C^* value using the material data of welded joint gives 10 times lower than that of only HAZ property. Whilst, the predicted CCG rates for welded joint are 10 times higher than those for only HAZ properties. Compared with predicted CCG rate from FE analysis and the experimental CCG rate, it can be suggested that creep crack growth tests for lower load level or for large specimen should be conducted, otherwise the experimental data should give unconservative estimation for components operated in long years.     

Engineering C*‐integral and COD estimates for nonidealized circumferential through‐wall cracked pipes at elevated temperature

In this study, creep fracture mechanics parameters, C^*‐integral and crack opening displacement (COD) rate, are estimated for a nonidealized circumferential through‐wall crack (TWC) in pipes. The GE/EPRI and enhanced reference stress (ERS) methods are employed. As for creep condition, the Norton and RCC‐MRx creep models are considered for secondary and primary‐secondary creep strain, respectively. The bending moment, axial tension, and internal pressure are applied to a pipe with a nonidealized circumferential TWC, as individual loads. Three‐dimensional elastic‐creep finite element (FE) analyses are performed, and the predictions from the GE/EPRI and ERS methods are compared with FE results. For the Norton creep model, both methods show good agreement with the FE results. For the RCC‐MRx creep model, only the ERS method can be used, and it provides accurate predictions comparing with FE results. Based on the comparison results, the use of the present engineering C^*‐integral and COD estimation methods for nonidealized circumferential TWC is validated.     

An assessment of the crack tip opening displacement criterion for predicting creep crack growth

From a set of finite element (FE) simulations of creep crack growth in compact tension specimens, the critical value of the crack tip opening displacement, CTOD, for creep crack growth has been generated for a Ni-base superalloy (Waspaloy) at 700°C. It was found that the critical value is independent of the initial crack length, amount of previous creep crack growth and the load level. Hence, the CTOD seems likely to be a viable criterion for use in creep crack growth rate analysis. Good agreement was also obtained between the experimental test results and FE predictions of the creep crack growth with time and between the crack growth rate, da/dt, versus the C ^* parameter based on load-line displacement rate.     

Modelling of damage development and failure in notched-bar multiaxial creep tests

Finite‐element predictions of creep rupture in notched specimens are presented in this work. A damage model linked to the creep strain rate and stress triaxiality has been used to predict creep life under multiaxial stress conditions and the predictions have been compared with experimental data for a C–Mn steel. Finite‐element analyses have been conducted using primary–secondary (PS) and primary–secondary–tertiary (PST) creep laws. As expected a PST analysis gives a shorter predicted rupture life than a PS analysis. An additional term was included in the model to allow for an increase in hydrostatic strain due to creep damage. The incorporation of this term improved the agreement between the experimental data and the finite‐element predictions. A further enhancement to the model was to model the initiation and growth of a sharp crack in the vicinity of the notch, through the use of a nodal release technique linked to the damage evolution. It was found that the predictions obtained using the nodal release technique were very similar to those from the PST creep model incorporating the hydrostatic damage term. The effect of mesh size has also been examined and the finite‐element predictions were seen to be quite mesh sensitive with a finer mesh generally giving a shorter predicted life.     

Load history effects on creep crack growth

In this paper the effects of load history on the high-temperature creep crack growth process are studied through a combined experimental and computational approach. The general features of constitutive response during cyclic creep are reviewed. Next, fracture parameters for creep crack growth are reviewed, with special emphasis on integral parameters. Finally, examples comparing computational predictions of experiments which experience history dependent load histories are presented. This includes displacement time comparisons and fracture parameter comparisons.     

Numerical investigation of fatigue characteristics of concrete pavement

In concrete pavements, fatigue is one of the major causes of distress. Repeated loads result in the formation of cracks. The propagation of these cracks cause internal progressive damage within the structure, which ultimately leads to failure of the pavement due to fatigue. This paper presents a theoretical investigation of crack propagation within concrete pavement and its fatigue characteristics under cyclic loading. A numerical fatigue performance model has been developed for this purpose. The model is based on fictitious crack approach for the propagation of cracks and stress degradation approach for estimating the bridging stress under cyclic loading. Using the numerical model, a parametric study has been performed for a typical concrete pavement to evaluate its fatigue characteristics for different foundation strengths. The method can be used for prediction of crack propagation in concrete pavement under cyclic loading and gives an estimate of the incremental damage or the entire crack history of the pavement.     

Mixed-mode crack surface interference under cyclic shear loads

A previous modelling analysis predicted that crack surface interference under cyclic shear loads is a combination of cyclic shear attenuation and cyclic wedge-opening. In the present study, experimental evidence is provided on notched thin-walled tubular specimens to evaluate the modelling predictions. Tests were carried out with varied static tensions superimposed on fully reversed ( R _τ = −1) or pulsating ( R _τ = 0) cyclic shear loads. The crack surface interference was measured by near-tip strain gauge methods. Based on the single and dual strain gauge readings, the strains induced by the mode I and II interference are separately identified so that the cyclic wedge-opening behaviour was noted as a companion of the cyclic shear attenuation. The crack surface interference under cyclic shear loads is compared with the influence from varied static tensions and shear stress ratios. A comparison of the mode I crack surface interference is also made between the conditions with cyclic shear loads and cyclic tensile loads. Finally, the characteristics of crack surface displacements are discussed, and the experimental results of effective mode I and II stress intensity ranges are compared with the modelling predictions.     

INTERACTIONS BETWEEN TIME AND CYCLIC DEFORMATION PROCESSES IN A NIMONIC ALLOY

Interactive creep–fatigue behaviour of a nickel-base superalloy (IN 597) has been examined at 850 °C under various strain-limited, cyclic torsional loading conditions. In one test, forward creep deformation was reversed by creep under equal magnitude stress levels and strain limits. In other tests, forward creep strain was reversed by fast monotonic plasticity with and without a subsequent period of relaxation. These cycles were repeated within each test until fracture. This paper examines empirically the influence of a number of test variables upon cyclic creep curves, and demonstrates the usefulness of predictions based upon continuous low cycle fatigue and simple creep data when used in conjunction with a mechanical equation of state. A cyclic equilibrium condition was not achieved from these tests. Instead, a progressive softening occurred giving reductions to the amount of creep strain, creep time interval and reversed peak stress with each new cycle. Such reductions are expressed from derived formulae that embrace the range of inelastic strain, cycle number, creep dwell stress, reversed peak stress, and times expended in creep and relaxation.
Observations made on accumulated creep strain reveal the contribution to a creep–fatigue fracture from cyclic creep. This has led to a modified form of the linear damage rule which can provide conservative life predictions for components operating in service under similar cyclic conditions.     

Room-temperature creep behavior on crack tip of commercially pure titanium

The room-temperature creep behavior on crack tip of compact tensile (CT) specimen for commercially pure titanium (CP-Ti) was studied by experiment and finite element (FE) simulation in this paper. The experimental results indicated that the time-dependent deformation was observed on the crack tip of CP-Ti CT specimen at room temperature, which agreed with the primary creep, and crack propagation was not observed. In order to consider the creep behavior on crack tip, time-dependent J-integral was used to characterize the stress fields near crack tip. The room-temperature creep behavior on crack tip was analyzed by FE simulation, which was verified by experimental results. Then, the strain fields under different stress states were analyzed by FE simulation. The influences of the locations to crack tip and load on the room-temperature creep were analyzed, which shows that the creep significance on crack tip is enhanced with increasing of load and decreasing of distance to crack tip. The estimation formula of creep strain value along ligament direction of CP-Ti CT specimen was established and verified by FE simulation results.     

Some issues on creep damage modelling of welds with heterogeneous structures

Welded components are used widely in power plants. Many of these components operate at high temperatures and under high pressures. Defects or micro cracks may be found in the vicinity of the welds. These micro cracks or voids can grow under creep cracking conditions. These cracks are often found in a narrow zone close to the interface between the parent material and the heat-affected zones (HAZ), known as the type IV region, or in some cases, in the weld metal. Welds are metallurgically complex, with heterogeneous structures within the weld metal and the HAZ. It is important to have knowledge of the initial metallurgical features and the associated material property variations so that it may be possible to accurately model the possible failure modes of welds using, for example, finite element (FE) numerical modeling techniques. This paper describes a procedure related to the determination of the high temperature creep properties for each sub-region of welds from experimental results, and it also describes the subsequent failure modeling of welds, using a creep damage mechanics approach in FE analyses. Typical examples, for P91 welds in power plant, are used to illustrate the applications.     

Development of numerical model for the determination of crack opening and closure loads,for long cracks

A two‐dimensional finite element (FE) model has been developed for determining crack opening and closure stresses, with the eventual aim of investigating plasticity induced closure effects on crack growth under variable amplitude loading. An issue with model verification is obtaining accurate experimental values of crack opening and closure loads. Validation was therefore carried out using experimental data from constant amplitude loading tests, recently obtained by the authors 1 , 2 where there was good confidence in the accuracy of the opening and closing loads. Elastic–perfect plastic and work hardening material properties were investigated to determine the effect they had on crack growth. The modelling considered long cracks by dividing the crack into consecutive small lengths. For this purpose, the restart capability included in the ABAQUS code was employed. In addition, a mesh refinement strategy was optimised to reduce the memory requirements for the thousands of cycles analysed. This enabled both long crack lengths and small element sizes to be studied which has not been done in the literature before. The FE results were in good agreement with most of the experimental results, and possible reasons are given for some of the minor discrepancies observed.     

Numerical prediction of creep crack growth in different geometries using simplified multiaxial void growth model

Abstract

This paper considers the prediction of creep crack growth (CCG) in different fracture mechanics geometries using finite element (FE) analysis based on a material independent simplified multiaxial failure strain model at the crack tip. The comparison is first made by modelling C(T) specimen tests under plane stress and plane strain conditions using creep properties of a C–Mn steel at 360°C. In addition, in order to examine CCG due to different geometries, a single edge notch specimen (SENT), centre cracked tension specimen (CCT) and three-point bending (3PB) specimen have been modelled and analysed. In all cases, it is found, depending on the geometry, that for this steel at low creep temperatures the applied load develops a high reference stress/yield stress (σ_ref/σ_y) ratio, which helps reduce constraint at the crack tip. The predictions are analysed under plane stress/plane strain loading conditions identifying the effects of geometry on cracking rates and the implications for predicting long term test or component failure times exceeding where the applied σ_ref/σ_y<<1.     

Tensile cracks in polycrystalline ice under transient creep: Part I — Numerical modeling

The interaction between creep deformations and a stationary or growing crack is a fundamental problem in ice mechanics. Knowledge concerning the physical mechanisms governing this interaction is necessary: (1) to establish the conditions under which linear elastic fracture mechanics can be applied in problems ranging from ice-structure interaction to fracture toughness testing; and (2) to predict the ductile-to-brittle transition in the mechanical behavior of ice and, especially, the stability and growth of cracks subjected to crack-tip blunting by creep deformations. This requires a quantitative estimate of the creep zone surrounding a crack-tip, i.e., the zone within which creep strains are greater than the elastic strains.

The prediction of the creep zone in previous ice mechanics studies is based on the theory developed by Riedel and Rice (1980) for tensile cracks in creeping solids. This theory is valid for a stationary crack embedded in an isotropic material obeying an elastic, power-law creep model of deformation and for a suddenly applied uniform far-field tension load that is held constant with time. The deformation of ice at strain-rates ahead of a crack (i.e., 10⁻⁶ to 10⁻² s⁻¹) is dominated, however, by transient (not steady power-law) creep and the loading, in general, is not instantaneous and constant.

A numerical model is developed in this paper to investigate the role of transient creep and related physical mechanisms in predicting the size, shape and time evolution of the creep zone surrounding the tip of a static crack in polycrystalline ice. The model is based on the fully consistent tangent formulation derived in closed form (Shyam Sunder et al., 1993) and used in the solution of the physically-based constitutive theory developed by Shyam Sunder and Wu (1989a, b) for the multiaxial behavior of ice undergoing transient creep. The boundary value problem involving incompressible deformations ahead of a stationary, traction-free mode I crack in a semi-infinite medium is modeled and solved by a finite element analysis using the boundary layer approach of Rice (1968). This model is verified by comparing its predictions with (i) the known theoretical solutions for the elastic and HRR asymptotic stress and strain fields in an elastic-plastic material of the Ramberg-Osgood type, and (ii) the creep zone size for an isotropic material obeying the elastic power-law creep model of deformation.     

An approach to modeling time-dependent creep and residual stress relaxation around cold worked holes in aluminium alloys at room temperature

Creep behaviour of aluminium alloys is also observed at room temperature. As a result, a relaxation occurs of deliberately introduced beneficial residual stresses around fastener holes, before the relevant structural component is subjected to exploitation. Therefore, to adequately asses the life-time of the component with cold worked holes, it is necessary to quantify this relaxation. In this paper a combined iterative approach for building a time-dependent creep constitutive model of aluminium alloys at room temperature has been developed in order to be used in finite element (FE) simulations of the cold hole working process. The approach is based on an experimental study of the change in diameters of cold worked holes through mandrel cold working method and a subsequent series of FE simulations of the cold working process and of the following creep behaviour to determine the necessary equivalent stresses in the constitutive model. The obtained creep constitutive model has been founded on the power-law model. The model parameters A, n and m have been determined on the basis of a developed by the authors algorithm. The approach has been illustrated on D16T aluminium alloy widely used in the airspace industry. The material behaviour in the plastic field has been described by the nonlinear kinematic hardening model, obtained through a uniaxial tensile test. Both constitutive models have been used in FE simulations of the cold working processes and of subsequent residual stress relaxation around the cold worked open holes due to creep at room temperature. On the base of the FE results, mathematical models describing the residual stress relaxation have been obtained. Thus, the residual stresses are adequately evaluated immediately before introducing the structural component in operation.     

Near-tip behavior of deflected creep cracks

Near-tip displacement fields of a creep crack which exhibited moderate deflection from its initially mode I condition have been measured using the stereoimaging technique. From the measured displacement fields, near-tip strains and crack opening displacements (CODs) are obtained and compared with existing asymptotic solutions for stationary, deflected cracks. The comparison reveals that the near-tip strain field and CODs of a stationary deflected creep crack in stainless steel (creep exponent of 8) are of the Riedel-Rice type. The degree of mode mixity is also adequately predicted for the deflected crack. The results for stainless steel are compared with previous results for a glass-ceramic (creep exponent of 1.5), to assess the range of applicability of the RR field. Discrepancies between theory and experiment are discussed in terms of the dominant creep mechanism, which is dislocation creep for the stainless steel and grain boundary sliding for the glass-ceramic.     

Creep crack growth rate predictions in 316H steel using stress dependent creep ductility

Abstract

Short and long term trends in creep crack growth (CCG) rate data over test times of 500–30?000 h are available for Austenitic Type 316H stainless steel at 550°C using compact tension, C(T), specimens. The relationship between CCG rate and its dependence on creep ductility, strain rate and plastic strain levels has been examined. Uniaxial creep data from a number of batches of 316H stainless steel, over the temperature range 550–750°C, have been collected and analysed. Power-law correlations have been determined between the creep ductility, creep rupture times and average creep strain rate data with stress σ normalised by flow stress σ_0·2 over the range 0·2<σ/σ_0·2<3 for uniaxial creep tests times between 100 and 100?000 h. Creep ductility exhibits upper shelf and lower shelf values which are joined by a stress dependent transition region. The creep strain rate and creep rupture exponents have been correlated with stress using a two-stage power-law fit over the stress range 0·2<σ/σ_0·2<3 for temperatures between 550 and 750°C, where it is known that power-law creep dominates. For temperature and stress ranges where no data are currently available, the data trend lines have been extrapolated to provide predictions over the full stress range. A stress dependent creep ductility and strain rate model has been implemented in a ductility exhaustion constraint based damage model using finite element (FE) analysis to predict CCG rates in 316H stainless steel at 550°C. The predicted CCG results are compared to analytical constant creep ductility CCG models (termed NSW models), assuming both plane stress and plane strain conditions, and validated against long and short term CCG test data at 550°C. Good agreement has been found between the FE predicted CCG trends and the available experimental data over a wide stress range although it has been shown that upper-bound NSW plane strain predictions for long term tests are overly conservative.     

Finite element plastic loads for circumferential cracked pipe bends under in-plane bending

This paper proposes plastic loads (limit load and twice-elastic-slope (TES) plastic load) for pipe bends with circumferential through-wall and part-through surface cracks under in-plane bending, based on three-dimensional FE limit analyses. The material is assumed to be elastic-perfectly plastic, and both the geometrically linear (small strain) and nonlinear (large geometry change) effects are considered. Regarding a crack location, both extrados and intrados cracks are considered. Based on the FE results, closed-form approximations of limit and TES plastic loads are proposed for practical applications, and compared with corresponding solutions for straight pipes.     

Approximation of curved cracks under mixed-mode loading

The calculation of stress intensity factors or mechanical energy release rate for non-straight cracks can be complicated. Approximation to equivalent crack shapes can simplify calculations considerably, but this requires an understanding of the influence of key shape parameters on crack-tip stresses. A simple analytical model has been developed, based on the concept of a relaxed volume, to predict mechanical energy release rate and deflection angle for a range of crack shapes under mixed-mode loading. Results from this model compared well with those obtained from finite element (FE) simulations, and with predictions from previous analytical models. It was found that the crack length and orientation of the crack-tip with respect to loading direction are the key influences on fracture parameters, whilst curvature near the crack-tip can also affect results.     

A two-stage model for predicting crack growth due to repeated thermal shock

The growth of cracks in equipment that is exposed to repeated thermal down shocks presents a complex problem of analysis. The transient, highly non-linear nature of the stress profiles that are developed during the shock in addition to localized plasticity and environmental interactions makes difficult any accurate analytical predictions. The use of current analysis techniques based on linear stress approximations can result in overly conservative results that may lead to unnecessary and costly component replacements.This paper outlines results from an experimental investigation into crack growth in notched, flat plate specimens exposed to repeated one-dimensional thermal shocks. Analysis of the results shows that a simple two-stage growth model may be applicable for describing the crack growth. The model is comprised of a high strain fatigue region where crack growth is in the plastic range and a region where growth is described by linear elastic fracture mechanics. Allowances for the effects of mean loads and environment on the crack growth are also included in the model. The model is currently limited to the consideration of carbon steel components, operating at temperatures below the creep range.