Comparison of different approaches for estimation of creep crack initiation

In large components such as rotors defects due to manufacturing processes have to be taken into account and crack assessments based on findings of non-destructive evaluation are necessary. Approaches are used in remaining life estimations, for example:

• Time Dependent Failure Assessment Diagram (TDFAD),

• Two Criteria Diagram (2CD) and

• Nikbin–Smith–Webster-Model (NSW-Model).

The TDFAD approach is currently being developed within the R5 procedures as an alternative to conventional methods for predicting incubation and the early stages of Creep Crack growth. A key requirement of TDFAD approaches is the evaluation of a time dependent creep toughness, denoted K_c mat. The 2CD approach has been developed independently in Germany to assess Creep crack incubation in ferritic steels. This approach uses crack tip and ligament damage parameters, R_K and R_σ, respectively. Furthermore the NSW-Model is employed for the estimation of creep crack initiation by using the creep fracture mechanics parameter C^*. Calculations and used parameters were compared for a ferritic 1CrMoV-steel.     

Specimen geometry effect on creep crack growth in 316L(N)

The ASTM E1457‐98 standard describes the procedure to determine the master curve da/dt versus C* parameter, for creeping solids. However, the methodology is only to be applied to compact tension (CT) specimens. The European collaborative program CRETE aims at extending the application of the ASTM E1457‐98 standard to other types of laboratory specimens. In this paper, an existing database of creep crack growth on 316L(N) stainless steel is utilized, concerning three types of specimens: circumferentially cracked round bars (CCRBs) and double edge notched tensile (DENT) specimens for tensile mechanical loading whereas the classical CT specimen combines tensile and bending loading modes. A modified procedure based on the ASTM E1457‐98 standard has been applied to the database, resulting in a unique master curve of da/dt versus C*. The geometry effect is then investigated by introducing the Q* parameter by analogy to the Q parameter in the elastic–plastic J‐Q approach.     

Creep crack initiation prediction considering constraint effect for pressurized pipelines with circumferential surface cracks

Theoretical 2‐parameter C*‐Q* approaches and numerical simulation were conducted to investigate the creep crack initiation (CCI) time and the effect of constraints induced by the geometrical sizes of pipelines with circumferential surface cracks. The theoretical enhancement model of the C*‐Q* approaches under the transient creep condition, which considered the load‐independent constraint parameter Q*, was proposed to predict the CCI time around the crack front. The results revealed that the distribution regulation of Q* along the crack front for circumferential internal surface cracks and external surface cracks was similar. The maximum constraint level occurred near the deepest crack front part for cracks with small a/c (a/c < 0.4), while it occurred near the free surface for cracks with large a/c (a/c > 0.4). The constraint values at the same position (2Φ/π) increased with the increasing of the crack depth when a/c kept constant. In addition, the circumferential internal surface cracks of pipelines were proved more dangerous than the external surface cracks with the same geometrical size. Furthermore, the CCI times were decided by the peak values of constraint, or the CCI firstly occurred at the position where the constraint level was maximum. Additionally, the variation of hydrostatic stresses, triaxiality, and multiaxial strain factor considering the constraint parameter Q* was discussed. The suitability of the analytical C*‐Q* approaches was verified to predict CCI. The comparison of CCI times between the analytical approach and the BS 7910 as well as the finite element results demonstrated that the solutions under stress intensity factor–Riedel‐Rice control (initially by stress intensity factor and then by transient creep stress or Riedel‐Rice conditions)—were more accurate when internal pressure P < 18 MPa, but the solutions under Hutchinson‐Rice‐Rosengren–Riedel‐Rice control (initially by plastic Hutchinson‐Rice‐Rosengren control and then by Riedel‐Rice conditions) were more appropriate when P > 18 MPa. Finally, the accuracy of C*‐Q* 2‐parameter approaches and the suitability of finite element simulation were validated.     

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.     

Probabilistic prediction models for crack initiation and progression of spray sealed pavements

Cracking is one of the primary distress modes in spray (chip)-sealed pavement surface performance and its prediction is a major concern for pavement engineers. In order to identify, manage and asses effectively and efficiently cracked pavement at a network level, a probabilistic modelling approach is utilised to develop cracking initiation and progression models. This study aims to predict the probability of pavement cracks occurring using a binary logistic model and cracks progression over time using an ordinal logistic regression model. These models have been developed to take into account the effect of variations among observations, among sections and among highways. Readily available historical time series data (from 2004 to 2011) from 40 highway segments have been collected and prepared for modelling. These time series include surface cracking as a performance parameter and traffic loading, expansion potential of subgrade soil, climate condition, condition of drainage system and pavement strength as predictor parameters. Cracking data include all types of cracking: transverse, longitudinal and crocodile cracking and is reported as a percent of the affected area. The study estimates the probability of crack initiation at a certain time and predicts the probability of a pavement maintaining its current level of cracking. It is found that with the 50% estimated probability, about 82% of the observations are correctly predicted by the crack initiation model and 65% of the observations are correctly predicted by the crack progression model. The study has concluded that the effect of time is stronger than the other variables on crack initiation and progression. Also, the effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any time is stronger than the effect of traffic loading in crack progression phase. The predicted probabilities have been successfully validated using another data-set from the same network and the results indicate that the developed probability models are well estimating the crack conditions and have the ability to predict future conditions accurately.     

Prediction of stable crack growth geometry in residually stressed glass

Processing procedures have been developed that produce stress distributions in glass with a maximum compressive stress below the surface. These glasses can exhibit rising apparent fracture toughness behavior and reduced strength variability associated with the stable growth of surface cracks under applied tensile stress. A weight function approach was used to determine stress intensity factors as a function of crack geometry for surface cracks under the effects of stress distributions similar to those found in these glasses. These calculations were then used to predict the growth behavior of surface cracks as a function of the applied and residual stress fields.     

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.     

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.     

Experimental investigation of specimen size effect on creep crack growth behavior in P92 steel welded joint

In order to clarify the effect of constraint induced by specimen size on creep crack growth behavior of P92 steel welded joint, creep crack tests were carried out on the compact tension specimens with thick thickness and thin thickness, the crack tip of which were located at different distinct zones of welded joint. Tested results revealed that even in thin thickness specimens, fine grained heat affected zone specimens exhibited a fast creep crack growth rate compared with other micro-zones specimens due to a low creep crack resistance and a high multistress state. The fractographies of these specimens exhibited an accelerated number of spherical particles that were caused by the coalescence of creep voids. Furthermore, the correlation of C^* with creep crack growth rate was dependent on specimen thickness. As the specimen thickness increased from 10 to 30 mm, the creep crack growth rate increased. This was due to the increase in constraint level ahead of crack tip during creep crack propagation.     

Prediction of creep crack growth in the presence of residual stress

Abstract

The mechanisms of creep crack growth are presented and the relationship between creep crack growth rate and uniaxial creep properties identified. Cracking under primary, secondary and combined primary and secondary loading is considered. The concepts described are applied to cracking in compact tension specimens of Type 316H austenitic stainless steel and Type 347 weld metal, each of which had previously been subjected to pre-compression to generate a tensile residual stress adjacent to the crack tip. Examples of the residual stress distributions produced before and after creep relaxation are presented and used to predict the crack growth anticipated. Comparisons are made between the behaviour of the two steels. Sensitivity studies are included to determine the extent to which the predictions are affected by the choice of material properties and analysis employed. For secondary loading only, it is shown that the amount of cracking predicted is relatively insensitive to the initial residual stress present.     

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.     

Characterization of incubation time on creep crack growth for weldments of P92

Most structures are mainly fabricated by welding which are likely to be regions of crack initiation and propagation. In such weldment, it is known that the multi-axial stress fields appear due to the plastic constraint induced by the differences in material micro-structure between the weld metal, heat affected zone (HAZ) and base metal. In the present study, the experiments of creep crack growth tests and the structural mechanical analyses of weldment were conducted to understand the effects of stress multi-axiality of weldment on the characteristics of creep crack growth, creep deformation and creep ductility. Additionally, to characterize the time of creep crack initiation up to the start of a brittle type creep crack growth, the distribution of stress multi-axiality (TF) through the base metal, fine-grain HAZ, coarse-grain HAZ to weld metal were investigated.     

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.     

Effects of side‐groove depth on creep crack‐tip constraint and creep crack growth rate in C(T) specimens

The effects of side‐groove depth on creep crack‐tip constraint and creep crack growth (CCG) rate in C(T) specimens have been quantitatively studied. The results indicate that with increasing side‐groove depth, the constraint level and CCG rate increase and constraint distribution along crack front (specimen thickness) becomes more uniform. The constraint and CCG rate of thinner specimen are more sensitive to side‐groove depth. Two new creep constraint parameters (namely R^* and A_c) both can quantify constraint levels of the specimens with and without side‐grooves, and the quantitative correlations of CCG rate with constraint have been established. The mechanism of the side‐groove depth effect on the CCG rate has also been analyzed.     

Effects of creep properties of materials on unified creep constraint parameter Ac for cracked pipes

Extensive finite element analyses of cracked pipes with different crack sizes and orientations have been conducted to investigate effects of creep properties of materials on the unified creep constraint parameter A_c. The results show that the constraint parameter A_c is independent on Norton’s coefficient A, and it is only affected by the creep exponent n of materials. For a given crack size, with increasing n, A_c decreases and constraint level increases. The A_c of lower constraint cracks is more sensitive to n. The unified correlation equations between A_c and n have been obtained for cracked pipes with a wide range of crack sizes and constraint levels. They may be used to estimate the constraint parameter A_c at different positions along the crack fronts in cracked pipes made of materials with different n values. The two-parameter C*-A_c approach for assessing creep life of cracked pipes has also been discussed.     

Influence of different load models on gear crack path shapes and fatigue lives

A computational model for determination of the service life of gears with regard to bending fatigue at gear tooth root is presented. In conventional fatigue models of the gear tooth root, it is usual to approximate actual gear load with a pulsating force acting at the highest point of the single tooth contact. However, in actual gear operation, the magnitude as well as the position of the force changes as the gear rotates. A study to determine the effect of moving gear tooth load on the gear service life is performed. The fatigue process leading to tooth breakage is divided into crack‐initiation and crack‐propagation period. The critical plane damage model has been used to determine the number of stress cycles required for the fatigue crack initiation. The finite‐element method and linear elastic fracture mechanics theories are then used for the further simulation of the fatigue crack growth.     

High temperature crack initiation and defect assessment of P22 steel weldments using time dependent failure assessment method

High temperature deformation and crack resistance of low alloy ferritic grade P22 steel weldments applied in power plants are reported. The creep crack initiation (CCI) and creep crack growth (CCG) data were determined using compact type (C(T)) and C-Shape (CS(T)) fracture mechanics specimens at 550 °C. The deformation and crack growth behaviour of similar weldment zones and significance of CCI and CCG in defect assessment of components were addressed. The weldments with industrially relevant properties were produced in butt welded pipe joint from which test specimens are sampled. The studied material covers a spectrum of microstructures and ductility over the weldment zones to give representative for a welded component. The emphasis is placed on the measurement and particularly analysis of crack initiation for failure assessment in P22 steel weldments. The particular importance of construction of isochronous curves for time dependent failure assessment diagram (TDFAD) method is reported. It is aimed to contribute to establishing guidelines for acceptable methodologies for testing, analysis and assessment of welded components using TDFAD for high temperature service.     

Effect of specimen geometry on fatigue crack growth rates for the railway axle material EA4T

This paper presents experimental results on fatigue crack growth propagation for the EA4T steel widely employed in the manufacturing of railway axles. Apart from standard M(T) and C(T) specimens, the investigations include bending tests on cylindrical bars and rectangular plates containing semi-elliptical surface cracks, geometries representative of surface flaws in components. The results give an evidence of the crack growth rate dependency upon the geometry and loading conditions of cracked specimens. The paper also concludes that fatigue crack growth rates correlate with crack tip plasticity, even within low and middle stress intensity factor ranges. Some remarks are provided with respect to the significance of the results for assessing residual lives of railway axles under in-service conditions.     

A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

Discussions of three-dimensional models for mixed-mode fatigue crack growth

This technical note discusses several three-dimensional models for mixed-mode fatigue crack growth that were developed recently by Bian and coauthors [1], [2], [3], [4] and [5]. However, these models are found being formulated from a generally incorrect three-dimensional crack-front stress field for embedded elastic elliptical cracks. The corresponding correct crack-front stress field for the elliptical cracks is thus presented, and then the three-dimensional fatigue crack growth models are corrected and expressed in much simpler functions.