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.     

Applicability of C parameter in assessing Type IV creep cracking in Mod. 9Cr-1Mo steel welded joint

A welded joint of Mod. 9Cr-1Mo steel, whose Type IV cracking behavior is an important issue to be assessed, was subjected to a series of creep crack propagation experiments in order to clarify the applicability of existing standard ASTM E1457-98. Standard 1T-C(T) specimens made of base metal (BM) and welded joint (WJ), in which the heat affected zone (HAZ) was set to be the crack plane, were subjected to the experiments under 600, 650, and 700 °C, and with a few load level conditions. While the crack planes of BM specimens were fairly flat, those in WJ specimens showed bumpy surfaces following the shape of multi-path weld beads. The cracks in WJ specimens were of typical Type IV cracking, and their crack passed through nearby the interface of BM and weld metal. There are the fairly good relationships between the creep crack propagation rate (da/dt) and C^* parameter. All the BM and WJ data fallen in each one C^*-da/dt relationship for BM and WJ, respectively, regardless of the temperature and load level. The C^* parameter used here is defined for the homogeneous material and does not give a physically correct C^* for WJ, nevertheless all the WJ data still tends to gather each other on single C^*-da/dt relationship. This fact suggests that the geometrical limitations of E1457-98 standard also can act well as the limitation for the inhomogeneity of weld structure and may eliminate the effect of large scale inhomogeneity due to the combination of BM and weld metal. The da/dt of WJ were about 3-10 times faster than that of BM for the same C^* value. This difference can be attributed as the effect of difference in triaxiality, the relative constraint between the weld metal and the base metal, or the difference in resistance for creep crack propagation in HAZ material.     

The influence of material mismatch on the evaluation of time-dependent fracture mechanics parameters

The influence of material mismatch on the stress field of uniaxial specimens and the time-dependent fracture mechanics parameters is studied in the present work. The applicability of the conventional C^* equation based on the load line displacement is re-examined by using the finite element method. It is found that under the extensive creep condition the C^* value of hard weld/soft parent metal specimen can be significantly higher than that of a single weld metal specimen, and the material mismatch has little influence on C(t) in small scale creep in the studied cases. It is proposed that the C^* formula based on the load line displacement recommended by ASTM E1457 needs to be modified to interpret the CCG behaviour of welded specimens. Candidate modification factors have been proposed.     

Creep crack growth behavior of type 316L steel

The creep crack growth behavior of a 316L type stainless steel was studied at 600°C and 650°C using widely different specimen geometries. A strong emphasis was laid on crack initiation, early crack growth, and slow crack growth rates (a). The applicability of four load parameters, the stress intensity factor, the nominal stress, the reference stress, and the contour integral C^*, was investigated. Finite element calculations were made to compare the experimental load line displacement rates with the calculated values.It is shown that it is possible to correlate time to initiation (T_i) with C^*. The obtained experimental relation is not in full agreement with a theoretical expression derived from models for creeping solids. The reasons for this discrepancy are discussed. Furthermore, it is observed that there is no unique correlation between a and any of the four investigated load parameters, especially at low crack growth rates (a0^?3mm/h). At large crack growth rates (a?10^?2 mm/h) the apparent correlation between a and C^* is essentially due to the fact that the displacement rate is controlled by crack growth and not by the overall creep behavior of the specimens. A simple model based upon the data on crack initiation and the creep ductility exhaustion concept is shown to give results in reasonable agreement with the experiments.     

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.     

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.     

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.     

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.     

Surface effects on time-dependent fracture parameter of subsurface crack in plates under tension

Based on the comprehensive finite element (FE) creep analyses, the influence of free surface on the time dependent fracture mechanics parameter of a crack near the free surface in plates under tension has been investigated. It is found that the time dependent fracture parameter C* increases as the crack tip closes to the free surface. Such an increment is related not only to the crack configurations but also to the material properties, especially the creep exponent n of power creep law. In addition, more pronounced interaction is observed between the C* of subsurface crack and that of a single isolated crack compared to that denoted by SIF under the linear elastic fracture condition. Under the framework of reference stress method, we also developed a closed form solution for creep interaction factor. Overall good agreement is achieved between the proposed method for the C* of subsurface crack and the FE results which provides us 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.     

Creep crack growth behavior in 316 stainless steel at 594°C (1100°F)

The creep crack growth behavior of a type 316 stainless steel was characterized at 594°C (1100°F) using precracked single edge notch specimens loaded in displacement rate control. The steady-state crack growth rate, da/dt, correlated with J-integral and did not correlate with C ^*. The creep crack growth behavior in this material and temperature is compared with our previous creep crack growth rate data on a Cr-Mo-V steel at 538°C (1000°F) and on type 304 stainless steel at 594°C in which da/dt correlated with C ^*. A detailed discussion is included on why in some materials creep crack growth rate correlates with J integral and in others it correlates with C ^*.     

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.     

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.     

Creep crack growth in 316 stainless steel at 600°C

The creep crack growth behaviour of 316 stainless steel at 600°C has been investigated. Results have been obtained from seven compact tension (CT) specimens and five tensile specimens containing thumbnail surface cracks. The data were found to correlate on the basis of the C^* parameter. A reference stress approach, which can be used to estimate C^* values, is described.     

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.     

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.     

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.     

Fracture mechanics interpretation of multiple-creep cracking using damage-mechanics concepts

Abstract

Damage-mechanics concepts are incorporated into a fracture-mechanics interpretation of multiple grain-boundary cracking in uniaxial tensile creep specimens that undergo power–law creep deformation. Initially, methods of evaluating the fracture–mechanics creep parameter C^* for a structure containing a single macroscopic crack are extended to a uniform distribution of grain-boundary voids. Damage-mechanics models are then applied to describe damage accumulation. It is shown that, when the voids grow as disc-shaped cavities, the analysis yields predictions of growth rates which are consistent with characterizations of macroscopic crack growth behaviour involving the exhaustion of the available creep ductility in a process zone at the crack tip.

MST/195     

Effects of component size, geometry, microstructure and aging on the embrittling behavior of creep crack growth correlated by the Q parameter

The driving force for creep crack growth is dominated by local elastic-plastic stress in the creep damage zone around a crack tip, temperature and microstructure. In previous work, C^∗, C_t, load line displacement rate dδ/dt and Q^∗ parameters have been proposed as formulations of creep crack growth rate (CCGR). Furthermore, using parameters mentioned above, the construction of the algorithm of predictive law for creep crack growth life is necessary for life assessment procedures. The aim of this paper is to identify the effects of component size, geometry, microstructure, aging and weldment on the embrittling behavior of creep crack growth and incorporate these effects in a predictive law, using the Q^∗ parameter. It was found that for specimen size (width and thickness) and of material softening due to aging the values of the activation energy were the same whereas for grain size change and structural brittleness, which affected crack tip multi-axial stress state the values for the activation energy for CCGR differ.