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.     

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.     

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.     

Numerical investigation of creep crack growth in cross‐weld CT specimens. Part II: influence of specimen size

A numerical investigation of the influence of specimen size on creep crack growth in cross‐weld CT specimens with material properties of 2.25Cr1Mo at 550 °C is performed. A three‐dimensional large strain and large displacement finite element study is carried out, where the material properties and specimen size are varied under constant load for a total of eight different configurations. The load level is chosen such that the stress intensity factor becomes 20 MPa √m regardless of specimen size. The creep crack growth rate is calculated using a creep ductility‐based damage model, in which the creep strain rate ahead of the crack tip perpendicular to the crack plane is integrated taking the degree of constraint into account. Although the constraint ahead of the crack tip is higher for the larger specimens, the results show that the creep crack growth (CCG) rate is higher for the smaller specimens than for the larger ones. This is due to much higher creep strain rates ahead of the crack tip for the smaller specimens. If, on the other hand, the CCG rate is evaluated under a constant C * condition, the creep crack growth rate is found to be higher for the larger specimens, except when the crack is located in a HAZ embedded in a material with a lower minimum creep strain rate; then, the creep crack growth rate is predicted to be higher for the smaller specimen. In view of these results, it is obvious that the size effect needs to be considered in assessments of defected welded components using results from CCG testing of cross‐weld CT specimens.     

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.     

Numerical investigation of creep crack growth in cross-weld CT specimens. Part I: influence of mismatch in creep deformation properties and notch tip location

Creep crack growth (CCG) in cross-weld CT specimens is investigated using two-dimensional finite element simulations. A creep ductility-based damage model describes the accumulation of creep damage ahead of the crack tip where a constraint parameter and the creep strain rate perpendicular to the crack plane are used as characterizing parameters.
The numerical results reveal that, not only the material properties of the region in which the crack is propagating, but also the deformation properties of the surrounding material influence the CCG behaviour. For the specimen configurations investigated, the location of the starter notch in the HAZ of the cross-weld CT specimen has, however, a minor influence on the CCG rate and the value of C *. This applies as long as the crack is propagating within a sufficiently narrow region that has material properties which can be regarded as homogeneous.     

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.     

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.     

In-plane and out-of-plane constraint effects on creep crack growth rate in Cr–Mo–V steel for wide range of C*

Abstract

In this work, the stress dependent creep ductility and strain rate model have been implemented in a ductility exhaustion based damage model and the creep crack growth (CCG) rates of a Cr–Mo–V steel in compact tension (C(T)) and middle tension (M(T)) specimens with different thicknesses and crack depths have been simulated over a wide range of C*. The effects of in-plane and out-of-plane constraints on CCG rates are examined. The results show that the in-plane and out-of-plane constraint effects on CCG rate are more pronounced for the high constraint specimen geometry (C(T)), while such effects are less significant for low constraint specimen geometry (M(T)). The constraint effects on CCG rates mainly occur in low and transition C* regions and the CCG rate increases with increasing in-plane and out-of-plane constraints. There exists interaction between in-plane and out-of-plane constraint in terms of their effects on CCG rate. The higher in-plane constraint strengthens the out-of-plane constraint effect on CCG rate and higher out-of-plane constraint also strengthens the in-plane constraint effect on CCG rate. The constraint effects on creep crack growth behaviour for a wide range of C* mainly arise from the interaction of crack-tip stress states and stress dependent creep ductility of the steel in different C* levels.     

Estimation of creep crack growth rate in IN-100 based on the Q* parameter concept

Since the high-strength Ni-based superalloy, cast IN-100, is considered to be brittle at high temperatures, the stable creep crack growth region is limited. Therefore, technically, it is very difficult to perform creep tests and there are few experimental results on the creep crack growth behaviour of this material. We performed creep crack growth tests using Ni-based superalloy, cast IN-100, and derived the Q* parameter for this material, which characterizes the creep crack growth rate. Using this Q* parameter, we derived a law for the creep rupture life of this material.     

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.     

The effect of constraint on creep fracture assessments

This paper describes a preliminary examination of the effect of in-plane constraint on creep crack growth under widespread creep conditions using the Q stress. Plane strain is assumed. Damage models for fracture of the process zone based on both ductility exhaustion and stress rupture are shown to predict a variation of the crack growth rate with Q. Lower levels of constraint lead to lower crack growth rates for a given C*. The results are used to outline a high temperature failure assessment diagram approach to constraint-dependent creep crack growth. 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.     

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.     

Creep fracture parameter C* solutions for semi-elliptical surface cracks in plates under tensile and bending loads

In order to predict and assess creep life for plate structures with semi-elliptic surface cracks under high temperature condition, the accurate calculation of the creep fracture mechanics parameter C* is a critical step. In this paper, the effects of crack sizes, plate geometries, and material creep properties on the parameter C* have been investigated under tensile and bending loads by extensive finite element analyses. Based on the results, the creep influence functions Hc for calculating C* values were obtained and fitted into equations for surface cracks in plates under both loads. The equations have been verified by finite element calculations. The C* solutions were obtained through these equations which are suitable for wide ranges of crack sizes, plate geometries, and materials.     

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.     

An experimental investigation of mixed-mode creep crack growth in Jethete M152 at 550°C

Creep crack growth tests have been made on Jethete M152 at 550°C under initially mixed-mode (i.e. K_I/K_II ≈ 1.6) and mode-II crack tip conditions using compact mixed-mode (CMM) specimens. The results of these tests have been compared with mode-I data obtained from compact tension (CT) tests, using a C* approach. The correlation between the mode-I, mode-II and mixed-mode data is reasonably good. However, the scatter band is greater than that obtained from the mode-I results only. The results indicate that the C* approach, which has been used successfully in mode-I situations, may also be useful for predicting creep crack growth in more general situations.     

Creep failure simulations of 316H at 550 °C: Part I – A method and validation

This paper proposes a method to simulate creep failure using finite element damage analysis. The creep damage model is based on the creep ductility exhaustion concept, and incremental damage is defined by the ratio of incremental creep strain and multi-axial creep ductility. A simple linear damage summation rule is applied and, when accumulated damage becomes unity, element stresses are reduced to zero to simulate progressive crack growth. For validation, simulated results are compared with experimental data for a compact tension specimen of 316H at 550 °C. Effects of the mesh size and scatter in uniaxial ductility are also investigated.     

Review of the fracture mechanics approach to creep crack growth in structural alloys

The application of the fracture mechanics approach to time-dependent high temperature crack growth has been reviewed. Available data on several structural alloys indicate that depending on the environmental sensitivity and creep ductility of the material, creep crack growth can be characterized by either linear elastic parameter, K, non-linear elastic-plastic parameter, J^*-integral, or reference stress, σ_ref. In particular for materials that are significantly sensitive to environment, K can adequately characterize the growth rate, and for materials that are significantly creep ductile, σ_ref can be used to predict creep life of a cracked body. Finally, for materials that are relatively ductile and wherein crack growth occurs predominantly by a deformation process, J^* integral appears to be the characterizing parameter for the growth rate. Data for several materials indicate that under steady state crack growth conditions, there may be a unique growth rate-J^* relation independent of temperature and material. This would have a profound impact in terms of the utility of fracture mechanics approach to predict creep crack growth rate and needs to be examined further. Conditions under which K, J^* or σ_ref is applicable are discussed in detail.