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.     

Theoretical and numerical modelling of creep crack growth in a carbon-manganese steel

This paper presents an analytical and numerical study of time dependent crack growth at elevated temperatures. A triaxiality dependent damage model is used to represent the multiaxial creep ductility of the material and an analytical model to predict steady state crack growth in terms of the fracture parameter C^∗, designated the NSW-MOD model, is presented. This model is an enhancement of the earlier NSW model for creep crack growth as it accounts for the dependence of stress and strain on angular position around the crack tip. Elastic-creep and elastic-plastic-creep finite element analyses are performed for a cracked compact tension specimen and the crack propagation rate in the specimen is predicted. It is found that in general the NSW-MOD model gives an accurate estimate of the crack growth rate when compared to the finite element predictions and experimental data for a carbon-manganese steel. However, crack growth rates predicted from the finite element analysis at low values of C^∗ may be higher than those predicted by either the NSW or NSW-MOD model. This enhanced level of crack growth may be associated with the non-steady state conditions experienced at the crack tip.     

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.     

A modification of ASTM E 1457 C estimation equation for compact tension specimen with a mismatched cross-weld

For the compact tension (CT) specimen with a mismatched weld in creep properties, an equivalent homogeneity model is presented based on the limit load analysis. In use of the proposed equivalent material model and existing limit load solutions, the modified experimental C^∗ integral estimation equations for the CT specimens with weld centre crack, fusion line crack and asymmetric crack were derived. Finite element (FE) analysis for C^∗ integral of CT specimens with a mismatched weld was performed by using the ABAQUS software. Results show that, compared with the η_o factor for homogeneous CT specimens, a soft under-mismatched weld will increase the non-dimensional factor η_w while a hard over-mismatched weld will decrease the η_w value. It indicates that the current C^∗ estimation equation in ASTM E1457 may underestimate C^∗ for creep soft weld but overestimate it for creep-hard weld. The discrepancies between the C^∗ from ASTM E1457 and FE analysis are sensitive to the crack location in weld, to the mismatch ratio and to the weld width. Whether for under-mismatched weld (M < 1) or for over-mismatched weld considered herein, the predicted C^∗ parameters from the presented formulae are very close to FE results and thus can be used to interpret the creep crack growth behaviour of welded specimens.     

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.     

Interpretation of creep crack initiation and growth data for weldments

Creep crack growth testing of macroscopically homogeneous materials is well established and standardised test procedures are detailed in ASTM E1457. In ASTM E1457 the use of the compact tension C(T) specimen is specified and crack growth data are interpreted using the fracture mechanics parameter C^∗. The resulting benchmark crack growth data are used in assessment procedures, together with estimates of the value of C^∗ in the component, to predict creep crack growth behaviour. In this work, the results of a series of creep crack growth tests performed on a Type 316 stainless steel weldment at a temperature of 550 °C are presented. The initial crack is located within the heat affected zone (HAZ) of the weldment. Since there are currently no agreed methods for determining C^∗ in inhomogeneous laboratory specimens, this paper examines the application of procedures in ASTM E1457 for the characterisation of crack growth in weldments. In addition, the creep toughness parameter is evaluated for the material. It is shown that the creep crack growth rates in the weldment may be described by the C^∗ values obtained following ASTM E1457 in conjunction with parent material properties. Comparison of the results with similar data for Type 316H stainless steel parent material shows that the crack growth rates for the crack located within the HAZ are higher and the initiation times lower than the parent values, for the range of test conditions examined. Simple analytical models based on ductility exhaustion arguments have been shown to bound the crack initiation and growth data for the weldment.     

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.     

Sensitivity analysis of creep crack growth prediction using the statistical distribution of uniaxial data

Due to the variables and unknowns in both material properties and predictive models in creep crack growth (CCG) rates, it is difficult to predict failure of a component precisely. A failure strain constraint based transient and steady state CCG model (called NSW) modified using probabilistic techniques, has been employed to predict CCG using uniaxial data as basic material property. In this paper the influence of scatter in the creep uniaxial properties, the parameter C* and creep crack initiation and growth rate have been examined using probabilistic methods. Using uniaxial and CCG properties of C‐Mn steel at 360 °C, a method is developed which takes into account the scatter of the data and its sensitivity to the correlating parameters employed. It is shown that for an improved prediction method in components containing cracks the NSW crack growth model employed would benefit from a probabilistic analysis. This should be performed by considering the experimental scatter in failure strain, the creep stress index and in estimating the C* parameter.     

Fracture mechanics global approach concepts applied to creep slow crack growth in a medium density polyethylene (MDPE)

Creep fracture by slow crack growth is studied in a medium density polyethylene at 60 °C and 80 °C. Whereas elastic-plastic fracture mechanics load parameters fail to provide a unique temperature-independent correlation, that of the fracture mechanics for creeping solids C^∗ is proved to be relevant since this parameter correlates very well with the time to failure. Correlation established on both full notched creep tensile and double edge notched tensile tests was validated on cracked gas-pipe samples tested under hydrostatic pressure, extending the use of time to failure versus C^∗ diagram to predict lifetime of engineering components.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

A new method for assessing high-temperature crack growth

Experimental creep crack growth (CCG) test data are obtained by following standards that characterize CCG rates using the C* parameter. Such data are then used in high‐temperature failure assessment procedures. An alternative approach to defect assessment at high‐temperature failure is an extension of the R6 failure assessment diagram (FAD). At high temperature, creep toughness, K^c_mat, can be estimated from CCG tests and replaces low‐temperature toughness in R6. This approach has the advantage that it is not necessary to establish a creep fracture regime, such as small‐scale, primary or widespread creep. Also, a new strain‐based FAD has been developed, potentially allowing variations of stress and temperature to be accommodated. In this paper, the results of a series of crack growth tests performed on ex‐service 316H stainless steel at 550 °C are examined in the light of the limitations imposed by ASTM for CCG testing. The results are then explored in terms of toughness and presented in FADs.     

Effect of stress dependent creep ductility on creep crack growth behaviour of steels for wide range of C*

Abstract

In this work, the effect of stress dependent creep ductility on the creep crack growth (CCG) behaviour of steels has been investigated by finite element simulations based on ductility exhaustion damage model. The relationship between the transition region of creep ductility and the transition behaviour of CCG rate on da/dt-C* curves has been examined and the CCG life assessments of components and CCG resistance of materials for a wide range of C* were discussed. The results show that with increasing the transition region size of creep ductility, the transition C* region size on da/dt-C* curves increases. With moving transition region position of creep ductility to high stress region (increasing transition stress levels), the transition C* region on the da/dt-C* curves also moves to high C* region. Decreasing transition stress levels and transition region sizes of creep ductility and increasing the lower shelf and upper shelf creep ductility values can improve the CCG resistance of materials. If the extrapolation CCG rate data from the high C* region or from the transition C* region are used in life assessments of the components at low C* region, the non-conservative or excessive conservative results may be produced. Therefore, the CCG rate data should be obtained for a wide range of C* by long term laboratory tests or numerical predictions using the stress dependent creep ductility and model.     

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.     

Testing and modelling of creep crack growth in compact tension specimens from a P91 weld at 650 °C

Creep crack growth tests were performed, at 650 °C, on compact tension (CT) specimens machined from the parent material and from the weld region of a P91 weldment. Parent material tests were performed on a number of different CT specimen designs in order to investigate the effects of side grooves on the shape of the crack front. Tests of CT specimens machined from the weld region were performed with the initial cracks located within the heat-affected zone (HAZ) along the interface with the parent material (i.e. the type IV position). All of the specimens were prepared with initial cracks created by wire spark erosion. Good correlations between creep crack growth rates and C^∗ were obtained for both the parent and type IV test results. The results indicate that the crack growth rates in the weld specimens are about four times higher than those of the parent material specimens, at the same C^∗. Microstructural investigations of the fracture surfaces using SEM and hardness measurements have shown that the exact location of the initial crack within the weldment has a large effect on the crack growth rate, at various loading levels. The results of Finite Element (FE) analyses of the parent material specimen tests, using a creep continuum damage material model, compared favourably with those obtained from the experiments.