An Assessment of the C* and KI Parameters for Predicting Creep Crack Growth in a Ni-Base Superalloy (Waspaloy) at 700^C

The results of experimental creep crack growth tests, using compact tension specimens, made from a Ni-base superalloy (Waspaloy) at 700^{^}C are presented. The experimental results indicate that the creep crack growth rate data for the Ni-base superalloy Waspaloy, at 700^{^}C, can be correlated using the C^* parameter, calculated from load-line displacement rates. The mode-I stress intensity factor, K_I, does not appear to be capable of correlating the data except at high creep crack propagation rates. Analytical solutions indicate that creep crack growth was occurring under transient creep conditions in the experiments. Finite element (FE) simulations were performed in which the experimentally determined crack growth versus time results were imposed. The good agreement between the resulting FE solutions for load-line displacements and corresponding C^* values with the experimental results show that the FE simulation was successful. The FE simulation revealed that the creep zone increases as the crack growth and a transient state of creep occurs in the vicinity of the advancing crack tip. An apparent correlation between the crack growth rates and the C^* parameter has been shown. This information is helpful in assessing the likely usefulness of the C^* and K_I parameters for predicting creep crack growth in more general situations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Creep crack initiation and growth in AISI 316 (N) weld – FEM and experiments

Abstract

There are two aspects of the creep crack growth behaviour, namely, the crack initiation and the crack propagation. An incubation period is often observed prior to the onset of creep crack growth. In this study, creep crack initiation and propagation in pre-cracked compact tension (CT) specimens of a 316 (N) stainless steel weld at T = 550 and 625°C under static loading is investigated. Both the crack initiation time and the crack growth rate are measured as a function of fracture parameter C*. It is shown that it is possible to correlate the creep crack initiation time with the C* parameter. It is also shown that the creep crack growth rate can be correlated with the C* integral. Additionally, finite element analyses by using the ANSYS software have been performed at one test condition (T=625°C) in order to estimate numerically the crack mouth opening displacement rate history for a propagating crack using the node release technique. When the FEM results are compared with the experimental data, the results show a very satisfactory prediction capability.     

Comparison among estimation methods of C* parameter for axially oriented external surface crack in cylinders

Abstract

C^* is usually used to describe the creep crack growth. ASTM E1457 allows C^* to be calculated from creep load line displacement rate. However in components it is difficult or impossible to measure load line displacement rate. Therefore for the components C^* must be determined by finite element methods or reference stress concepts. Estimates of C^* obtained by reference stress methods will depend on the collapse mechanism adopted and therefore several estimations are proposed. This paper presents a numerical study of non-linear fracture mechanics parameter predictions under elevated temperature for axially oriented external surface crack in cylinder. Comparison of C^* calculated from FE analysis and different reference methods is conducted. The values of C^* obtained from the API579 net section solution are also found to be slightly conservative and give the closest agreement to the F.E. contour integral C^*. In addition, the comparison between C^* of homogeneous material and TYPE IV cracking is conducted. The difference between homogeneous material and TYPE IV cracking is almost negligible and therefore the reference stress solutions for homogenous material could be applied to estimate C^* for TYPE IV cracking.     

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.     

BEHAVIOUR OF A 1Cr-1Mo-0.25V STEEL AFTER LONG-TERM EXPOSURE-II. CREEP CRACK INITIATION AND CREEP CRACK GROWTH

Both the initiation and the propagation of creep cracks have been studied in a 1Cr-1Mo-0.25V steel at 550°C using CT type specimens. The material taken from a large turbine casing was investigated in two conditions: (i) unaged and (ii) after a long exposure in-service time of about 150,000 h at 540°C. In both cases the material was found to be creep ductile, which is justified in terms of fracture mechanics applied to creeping solids. It is shown that fracture mechanics is unable to provide unique correlations with global load-geometry parameters, either K or C* for all the stages of both crack initiation and crack growth. However there exists a unique correlation between C* and the time to initiation, t_i. This correlation does not depend on the initial conditions of the material. During crack growth two stages are defined. Stage I is a transient regime in which C* is almost constant, but the correspondence between the crack growth rate and C* is not unique since largely dependent on the initial loading applied to the specimens. It is shown that the apparent correlation between the crack propagation rate in stage II which corresponds to large crack growth rate is doubtful. A simplified method based on reference length and reference stress is used to calculate C* parameter and to simulate the load-line displacement rate. The results obtained from this method are compared to those derived from finite element calculations published in the literature.     

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.     

Evaluation of C* integral for interacting cracks in plates under tension

A closed form solution for C* integral of two interacting cracks in plates under tension is developed on the basis of reference stress method. Comprehensive finite element (FE) creep analyses are carried out to provide the benchmark of the interaction evaluation of multiple cracks. Results indicate that more pronounced interaction is observed between the C* of double cracks and that of a single crack compared to that denoted by stress intensity factor (SIF). Overall good agreement is achieved between the proposed method for C* of multiple crack interaction and the FE results which provides confidence in practical application.     

Prediction of creep crack initiation in Cr–Mo–V steel specimens with different geometries

By using stress dependent creep ductility and strain rate model in a ductility exhaustion based damage model, the creep crack initiation (CCI) behaviour in Cr–Mo–V steel specimens with different geometries and dimensions (different constraints) over a wide range of C^* has been predicted by finite element simulations. The predicted creep crack initiation time agree well with the existing experimental data. In low and transition C^* regions, the constraint induced by specimen geometries and dimensions has obvious influence on CCI time. With increasing constraint level of specimens, the CCI time decreases due to the increase of stress triaxiality ahead of crack tip. Different CCI trends and constraint effects on CCI behaviour in a wide range of C^* result from the interaction of crack-tip stress state and stress dependent creep ductility of the steel. It is suggested that in CCI life assessments of high temperature components, the long-term CCI time data at low C^* region should be obtained and used, and the constraint effects need to be considered by using constraint dependent CCI data.     

Inclusion of primary creep in the estimation of the C t parameter

The problem of time-dependent fracture under transient creep conditions is investigated via finite element analyses of fracture specimens with stationary cracks. The constitutive models consist of linear elasticity with combinations of power-law secondary creep and two primary creep laws. Two proposed parameters are studied. One is a contour integral, C(t), which characterizes the crack tip singularity strength. The other one, C _t, is evaluated based on the load line deflection rate and has been used successfully in correlating experimental creep crack growth data.It is evident that accurate constitutive modeling is essential to good agreement with experimental data. The inclusion of primary creep resolves earlier discrepancies between the experimental and analytical load line deflection rates which are used to calculate the respective values of C _t. The loading boundary condition is also an important factor that has been addressed. A more general formulation of C _twhich includes primary creep is presented. In small scale and transition creep, the C _tparameter does not characterize the crack tip stress singularity but rather is related to the crack tip creep zone growth rate. At times past transition time, C _tand C(t) both approach a path-independent integral, C ^*(t), which characterizes the stationary crack tip stress field. The relationship between C _tand C(t) is discussed. The interpretation and estimation of the C _tparameter are given based on the numerical results and analytical manipulations.     

Proposal of a new concept on creep fracture remnant life for a precracked specimen

Abstract

The creep life time of a smooth specimen can be predicted using existing laws for creep deformation and steady state creep rate. When crack growth behaviour is involved, it is necessary to construct a law of creep crack growth rate to predict creep fracture life. Creep fracture life can be measured by integrating the law of creep crack growth rate. One example is the creep crack growth rate, represented by the parameter Q*. In this study, we investigated the applicability of this prediction method to creep fracture remnant life for a cracked specimen. The Ω criterion is proposed to predict creep fracture remnant life for a smooth specimen for creep ductile materials. In this study, the correlation between Q*_L derived from the paremeters Q* and Ω is investigated. The correlation between Q_L* and Ω provided a unified theoretical prediction law of creep fracture remnant life for high-temperature creep-ductile materials in the range from smooth to precracked specimens.     

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.     

Estimations of creep fracture mechanics parameters for through-thickness cracked cylinders and finite element validation

This paper compares engineering estimation schemes of C* and creep crack opening displacement (COD) for cylinders with circumferential and axial through‐thickness cracks at elevated temperatures with detailed 3D elastic‐creep finite element results. Engineering estimation schemes include the GE/EPRI method; the reference stress (RS) method where the reference stress is defined based on the plastic limit load; and the enhanced reference stress (ERS) method where the reference stress is defined based on the optimised reference load, recently proposed by the authors. Systematic investigations are made not only on the effect of creep‐deformation behaviour on C* and creep COD, but also on effects of the crack location, the cylinder geometry, the crack length and the loading mode. Comparison of the finite element (FE) results with engineering estimations provides that for idealised power law creep, estimated C* and COD rate results from the GE/EPRI method agree best with FE results, suggesting that published plastic influence functions for plastic J and COD for through‐thickness cracked cylinders are reliable. For general creep‐deformation laws where either primary or tertiary creep is important and thus the GE/EPRI method is hard to apply, on the other hand, the ERS method provides more accurate and robust estimations for C* and COD rate than the reference stress method. As these two methods differ only in the definition of the reference stress, the ERS method maintains benefits of the reference stress method in terms of simplicity, but improves accuracy of the estimated J, C* and COD results.     

Non-linear fracture mechanics analyses of part circumferential surface cracked pipes

This paper provides engineering estimates of non-linear fracture mechanics parameters for pipes with part circumferential inner surface cracks, subject to internal pressure and global bending. Solutions are given in the form of two different approaches, the GE/EPRI approach and the reference stress approach. For the GE/EPRI approach, the plastic influence functions for fully plastic J solutions are tabulated based on extensive 3-D FE calculations using deformation plasticity, covering a wide range of pipe and crack geometries. The developed GE/EPRI-type fully plastic J estimation equations are then re-formulated using the concept of the reference stress approach for wider applications. The proposed reference stress based estimates are validated against detailed 3-D elastic-plastic and elastic-creep FE results. For a total of 26 cases considered in this paper, agreement between the proposed reference stress based J and C ^* estimates and the FE results is excellent. An important aspect of the proposed estimates is that they not only are simple and accurate but also can be used to estimate J and C ^* at an arbitrary point along the crack front.     

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.     

Modelling the effect of creep–fatigue interaction on crack growth

Time-dependent creep–fatigue crack growth (CFCG) is a major consideration in estimating the remaining life of elevated temperature components. Fracture mechanics approaches have proven useful in providing a framework for characterizing crack growth under service conditions, and in defining safe operating conditions and selecting inspection criteria and intervals. Experimental and analytical approaches have been developed to characterize crack growth under combined creep and fatigue loading conditions using (C_t )_avg as the crack tip parameter. The analytical approaches that have been proposed to characterize CFCG are limited in their application because they do not completely account for the effect of creep–fatigue interactions in modelling crack tip deformation, and thus, accurately estimating the (C_t )_avg value. A new creep-reversal parameter, C_R , is defined in this study to quantify the extent of creep–fatigue interaction at the crack tip, and is used in an analytical scheme, suitable for components, for calculating (C_t )_avg . This approach does not rely on any simplifying assumptions regarding the extent of reinstatement of C_t , which is dependent on the amount of creep reversal due to cyclic plasticity, during the unloading part of a trapezoidal loading waveform cycle. The (C_t )_avg values calculated by this approach compare well with the experimentally obtained values for compact type (CT) specimens, thus providing an experimental verification of the approach.     

C* estimation for cracks in mismatched welds and finite element validation

A C^* integral estimation method is proposed for a crack located in the weld with a mismatch in mechanical properties from the surrounding base material. The method involves the definition of an equivalent stress-creep strain rate (ESCSR) relationship based on the mechanical properties of both the weld and base materials and the geometrical dimension of welding seam. The value of creep fracture mechanics parameter C^*, for the mismatched weldment, is then estimated using the proposed ESCSR in conjunction with the reference stress (RS) method where the reference stress is defined based on the plastic limit load and the GE/EPRI estimation scheme. Referring to the equivalent stress-plastic strain (ESPS) curve in R6 and SINTAP procedures, an approximate solution for the ESCSR relationship has been obtained. Detailed formulae for the compact tension (CT) specimens have been derived on the basis of limit load solutions. Nonlinear finite element analysis of 48 cases with various degrees of mismatch in creep behaviour and different dimension of welding seam has been performed for CT specimens. Overall good agreement between the ESCSR method and the FE results provides confidence in the use of the proposed method in practice.     

Langzeitiges Kriechrißverhalten kennzeichnender Kraftwerksstähle

Long Term Creep Crack Behaviour of Typical Power Plant Steels The creep crack behaviour of the steels was investigated in a wide loading range up to a test duration of 40 000 h and down to a creep crack growth rate of 2 · 10^?5 mm/h with specimens of different shape and size. For steels of type l%Cr-l%Mo-0.6%Ni-0.3%V, 1%Cr-0.9%Mo-0.7%Ni-03.%V, 12%Cr-1%Mo-0.3%V-0.22%C and 12%Cr-l%Mo-0.3%V-0.20%C tested at 550°C, the creep crack growth rate could be described by the parameter C₂* with significantly smaller scatter bands than by the parameter C₁* or the stress intensity factor K_I. For steel 12%Cr-2%Ni-1%Mo tested at 450°C, parameter K_I leads to the smallest scatter band. The creep crack initiation can be described in a two-criteria diagram based on nominal stress and stress intensity factor. However the method is assumed to be over-conservative in case of increasing specimen size. As a result of several aperiodic creep fatigue crack tests, precracking under fatigue conditions gave a weak increase of the creep crack growth rate whereas by precracking under creep conditions the fatigue crack rate was strongly decreased.     

Estimation of high‐temperature fracture parameters for small punch specimen with a surface crack

An outline of a newly proposed methodology for evaluating creep crack growth (CCG) parameters using cracked small‐punch (SP) specimens is explained. Three‐dimensional finite element analyses were performed to calculate the stress intensity factor along the crack front for a surface crack formed at the centre of a SP specimen. Effects of crack ratio, (a/t); crack aspect ratio, (a/c); and thickness of the specimen, (t), on the fracture parameters were studied. It was observed that the minimum variation of K‐value along the crack front can be achieved when a/c was 0.50 except the location very near the intersection of the crack and free surface. This condition is similar to the case of constant K‐values along the crack front of the conventional compact tension specimen. Thus, it can be argued that the SP specimen with a surface crack is a suitable specimen geometry for CCG testing. The proposed CCG test method was found to be practically applicable for the crack geometry of 0.10 to 0.30 of a/t with constant aspect ratio of 0.50. An estimation of the K and C_t‐parameter under the small scale creep condition was derived. Future work for further development of the suggested CCG testing is discussed.     

Representation of the high-temperature crack tip fields using reference stress concepts

In a previous paper, it was shown that an estimation approach to crack tip properties under cyclic creep loading conditions was described, using a methodology based on the linear matching method (LMM). The calculations revealed the possibility of obtaining the crack tip parameters, C* (n), for cracked structures subjected to both mechanical loads and temperatures, using the HRR field criterion as the crack tip condition. In this paper, those calculated values of C* (n) are re‐interpreted and presented in terms of the reference stresses, insensitive to the constitutive models and creep exponent. These reference stress values are compared with those currently used for life assessment of high‐temperature plant, showing that current practice is significantly conservative for thermal loading.     

Quantitative characterization of creep constraint induced by crack depths in compact tension specimens

In this paper, the C(t) and C∗ integrals, stress redistribution time t_red and creep crack-tip stress distributions in the CT specimens with various crack depths have been calculated by the finite element method (FEM), and the creep constraint induced by crack depths are quantitatively investigated in detail. The results show that the creep constraint could be characterized by the new constraint parameter R. The constraint effect induced by crack depths at non-steady-state creep is more pronounced than that at steady-state creep. The effects of the crack depths, load levels (C∗) and distances from the crack tips on the creep constraint parameter R are analyzed.