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.     

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.     

Effects of creep properties of materials on creep crack-tip constraint parameter R*

Extensive finite element analyses have been conducted to investigate the effect of creep properties of materials on the creep crack-tip constraint parameter R*. The results show that the parameter R* increases with increasing power law creep stress exponent n of materials, and it is sensitive to lower n values and lower in-plane and out-of-plane constraints. In the engineering estimations of the creep constraint parameter R*, only the creep exponent effect needs to be considered for cracked components with lower exponent n and lower constraint, and the Norton’s coefficient A of power law creep materials can be ignored due to its insensitivity to the R*. The R*-n relation formulae have been established for single-edge-notched tension specimen (it has similar constraint level to pressurised pipes) with different in-plane and out-of-plane constraints, and they may be used to estimate the creep crack-tip constraint levels for cracked pipes with lower exponent n and lower constraint.     

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.     

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.     

Predicting long-term creep failure of bimodal polyethylene pipe from short-term fatigue tests

Short-term fatigue testing was used to predict long-term creep failure of a bimodal polyethylene (BMPE) pipe with superior creep resistance. The stepwise crack propagation was studied by increasing the R-ratio (defined as the ratio of the minimum to the maximum stress intensity factor in the fatigue loading cycle) at 50 °C from 0.1 approaching creep (R = 1). Crack growth rate (da/dt) was related to the maximum stress intensity factor K _I,max and R-ratio by a power law relationship \frac\textda\textdt = B^￠ K_\textI,max⁴ (1 + R) ^{- 8.5} {\frac{{{\text{d}}a}}{{{\text{d}}t}}} = B^{\prime } K_{{{\text{I}},\max }}^{4} (1 + R)^{ - 8.5} . The correlation in crack growth kinetics allowed for extrapolation to creep fracture from short-term fatigue testing. The temperature dependence of crack growth rate was contained in the prefactor B′. A change in slope of the Arrhenius plot of B′ at 67 °C indicated that at least two mechanisms contributed to crack propagation, each dominating in a different temperature region. This implied that a simple extrapolation to ambient temperature creep fracture from elevated temperature tests might not be reliable.     

Effects of creep ductility and notch constraint on creep fracture behavior in notched bar specimens

The creep rupture life of U-type notched specimens and smooth specimens has been calculated based on the ductility exhaustion damage model using stress-dependent creep ductility. Effects of creep ductility and notch constraint on creep fracture behaviour in notched bar specimens have been investigated. The results show that the U-type notch exhibits notch strengthening effect under a wide range of stress level and notch constraint condition (notch acuity) for creep ductile materials. The lower equivalent stress in notched specimens plays main role for reducing creep damage and increasing rupture life. The rupture life of notched specimens of creep brittle materials (with lower creep ductility) decreases with the increase in stress level and notch constraint. With increasing creep ductility and decreasing notch constraint, the degree of the notch strengthening effect increases. In creep life designs and assessments of high-temperature components containing notches, the material creep ductility, notch constraint and stress levels need to be fully considered.     

Detailed three-dimensional analysis of side-grooved compact tension specimens under creep loading

Abstract

The three-dimensional (3D) effect on the stress field near the crack tip under creep loading has been investigated via detailed finite-element analyses on side-grooved compact tension (CT) specimens with various thicknesses. The mechanical properties used in the model are typical of those for a 9%Cr steel at 550°C and a Norton creep exponent of 10 was applied. Plane strain and 3D analyses for the CT specimens without side grooves were also performed and the differences in stress distributions in the three analysis conditions are discussed in relation to the creep J-integral C^*. The value of C^* was found to decrease with increasing thickness and to decrease significantly because of the enhanced constraint effect of the side grooves. With increasing thickness, the stress state in the central region is close to that under plane strain conditions, irrespective of the existence of the side groove. Stress triaxiality, however, is distributed more uniformly along thickness in the side-grooved specimen than in the specimen without side grooves. The C^* values of the side-grooved specimens are similar across the full range of thickness studied: no strong effect of thickness was observed.     

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.     

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.     

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.     

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.     

Correlation of fatigue and creep crack growth in poly(vinyl chloride)

Slow crack growth in PVC pipe was studied in order to develop a methodology for predicting long-term creep fracture from short-term tension-tension fatigue tests. In all cases, the crack propagated continuously through a crack-tip craze. In fatigue, the density of drawn craze fibrils gradually increased with decreased frequency and increased temperature. At the lowest frequency, 0.01 Hz, the fibril density in fatigue approached that in creep. The kinetics of fatigue and creep crack growth followed the conventional Paris law formulations with the same exponent 2.7, da/dt = A _f K _I ^2.7, da/dt = BK _I ^2.7, respectively. The effects of frequency, temperature and R-ratio (the ratio of minimum to maximum stress intensity factor in the fatigue loading cycle) on the Paris law prefactors were characterized. Comparison of frequency and R-ratio tests revealed that the fatigue contribution depended on strain rate. Therefore, at each temperature, crack growth rate was modeled as the product of a creep contribution that depended only on the maximum stress intensity factor and a fatigue contribution that depended on strain rate: (da/dt) = BK _I,max ^2.7 (1 + C), where B is the prefactor in the Paris law for creep and C is a coefficient defining the strain rate sensitivity. A linear correlation allowed extrapolation of the creep prefactor (B) from fatigue data. The extrapolated values were systematically higher than the values measured directly from creep and only converged at T _g . The difference was attributed to damage of the craze fibrils during crack closure upon unloading in the fatigue cycle.     

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.     

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.     

Mismatch effect in creep properties on creep crack growth behavior in welded joints

The finite element method based on ductility exhaustion model was used to systematically investigate the mismatch effect in creep properties on creep crack growth (CCG) behavior in welded joints. The crack-tip damage, stress states, CCG paths, CCG rate and rupture life were calculated for different configurations of creep properties between weldment constituents under the same load level, and the creep life assessment and design for welded joints were discussed. The results show that when the zone containing the crack is softer than at least one of the other two surrounding materials or both, the creep crack propagates straight along the initial crack plane. Otherwise, it will form a second crack in the soft material near interface. These simulation results were confirmed by the experimental observations in the literature, and the mechanism was analyzed. The harder surrounding materials can lead to higher CCG rate and shorter rupture life due to the higher constraint given from them. The early initiation and propagation of the second cracks increase CCG rate and reduce rupture life, and the incubation time of the second cracks in soft materials near interfaces should be accurately determined in the creep life assessment and design for the welded joints. A proper mismatch design with harder material containing crack and softer surrounding material can improve CCG properties of welded joints (decreasing CCG rate and prolong rupture life).     

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.     

Stress dependence of the creep behaviors and mechanisms of a third-generation Ni-based single crystal superalloy

Elevated temperature creep behaviors at 1100℃ over a wide stress regime of 120–174 MPa of a thirdgeneration Ni-based single crystal superalloy were studied. With a reduced stress from 174 to 120 MPa,the creep life increased by a factor of 10.5, from 87 h to 907 h, presenting a strong stress dependence.A splitting phenomenon of the close-(about 100 nm) and sparse-(above 120 nm) spaced dislocation networks became more obvious with increasing stress. Simultaneously, a_0010 superdislocations with low mobilities were frequently observed under a lower stress to pass through γ'precipitates by a combined slip and climb of two a_0110 superpartials or pure climb. However, a_0110 superdislocations with higher mobility were widely found under a higher stress, which directly sheared into γ'precipitates.Based on the calculated critical resolved shear stresses for various creep mechanisms, the favorable creep mechanism was systematically analyzed. Furthermore, combined with the microstructural evolutions during different creep stages, the dominant creep mechanism changed from the dislocation climbing to Orowan looping and precipitates shearing under a stress regime of 137–174 MPa, while the dislocation climbing mechanism was operative throughout the whole creep stage under a stress of 120 MPa, resulting a superior creep performance.     

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.     

Isothermal physical aging characterization of Polyether-ether-ketone (PEEK) and Polyphenylene sulfide (PPS) films by creep and stress relaxation

This paper considers the experimental characterization of isothermal physical aging of PEEK and PPS films using a dynamic mechanical analyzer. Using the short-term test method established by Struik, momentary creep and stress relaxation curves were measured at several temperatures within 15–35°C below the glass transition temperature (T _g ) at various aging times. Stress and strain levels were such that the materials remained in the linear viscoelastic regime. These curves were then shifted together to determine momentary master curves and shift rates using the PHYAGE program. In order to validate the obtained isothermal physical aging behavior, the results of creep and stress relaxation testing were compared and shown to be consistent with one another using appropriate interconversion of the viscoelastic material functions. Time–temperature superposition of the master curves was also performed. The temperature shift factors and aging shift rates for both PEEK and PPS were consistent for both creep and stress relaxation test results.