Creep Crack Growth Model Research Articles

Phase-field finite element modelling of creep crack growth in martensitic steels

Creep fracture presents a major concern for structural materials and critical components operating at elevated temperatures, thus requiring effective computational models. This study presents a phase-field framework for modelling creep crack growth and fracture behaviour of modern high-temperature materials such as Creep Strength Enhanced Ferritic (CSEF) martensitic steels. The model was formulated using the thermodynamic principles of the variational phase field theory of fracture and considering some physical aspects of creep fracture. Within the modelling framework, a dissipation potential dependent on creep damage is introduced to capture the effect of creep cavitation on the fracture energy and the creep crack growth resistance of the solid in a phenomenological manner. An elastoplastic power-law creep model is coupled to the phase-field formulations to account for the non-linear deformation processes ahead of the crack tip due to inelastic deformations, as well as their contribution to fracture at high temperatures. The capability of the proposed model is assessed against experimental data from compact tension (CT) creep tests conducted on P91 and P92 steels. Good agreement was obtained between the FE-predicted creep crack growth behaviour and the experimental measurements, showcasing the model’s feasibility. Further, numerical experiments were conducted using the proposed model to elucidate some key aspects influencing the fracture behaviour of martensitic steels. The proposed computational framework not only demonstrated good capability but was also able to offer improved mechanistic insights into the influence of material tendency to develop creep cavities on crack growth behaviour. This work contributes valuable insights into understanding the fracture process of CSEF steels at elevated temperatures and further demystifies the role of creep ductility.

Analysis of creep crack growth in bonded joints based on a Paris' law-like approach

Creep crack growth is one of the factors that could affect the durability of a bonded joint and compromise the safety of structures over long periods of time. However, numerical tools and test methods relating to creep crack growth in bonded joints are not widely available yet. In this work, a Creep Crack Growth Model (CCGM) is proposed for adhesively bonded joints. The model describes the relation between the crack growth rate and the energy release rate. The CCGM is fitted with results from Roller Wedge Driven creep crack growth (RWDC) tests and validated against the results obtained from tapered double cantilever beam (TDCB) tests with a constant load applied. Additionally, it is demonstrated that the proposed model can be introduced in a fatigue tool commercially available from the finite element method (FEM) code Abaqus to predict creep crack growth. The FEM results show that the phenomenological expression fitted from experimental tests results, which is used as input for the FEM tool, is reproduced with accuracy. Moreover, it is shown that the CCGM is capable of predicting creep crack growth rates when a different specimen geometry is used, thus demonstrating that the model correctly captures the physics of the problem.

Multiscale-constraint based model to predict uniaxial/multiaxial creep damage and crack growth in 316-H steels

A new failure ductility/multiscale constraint strain-based model to predict creep damage, rupture and crack growth under uniaxial and multiaxial conditions is developed for 316H Type stainless steels by linking globally uniform failure strains with a multiaxial constraint factor. The model identifies a geometric constraint and a time-dependent local constraint at the sub-grain level. Uniaxial and notched 316H steel as-received and pre-compressed data at various load levels and temperatures with substantial scatter were used to derive the appropriate constitutive equations by using the proposed empirical/mechanistic approach. Constrained hydrostatic development of creep damage at the sub-grain level is assumed to directly relate to the uniform lower-bound creep steady state region of damage development measured at the global level. Uniaxial and notched bar rupture at long terms is predicted based on the initial short-term creep or a representative tensile strength and a multiaxial constraint factor. The model is consistent with the well-known NSW remaining multiaxial ductility creep crack growth model which predicts crack growth bounds over the plane strain/stress states. This model, therefore, unifies the creep process response over the whole range of uniaxial, notched and crack growth processes which is extremely consequential to simple long term failure predictions of components at elevated temperatures.

Modeling the creep damage effect on the creep crack growth behavior of rotor steel

AbstractTo evaluate the fracture life of steam turbine HP-IP rotors more accurately, an understanding of the creep damage effect on creep cracking performance of service-exposed rotor steel, and a proper creep crack growth (CCG) model considering the creep damage effect, is essential. In the present work comparative CCG tests were carried out on virgin and rotor steel that had been in service for 16 years, to examine the differences in creep crack microstructure and CCG rate between these two specimen types. Test results showed that the CCG rate of service-exposed steel is accelerated by creep damage due to metallurgical deterioration. Based on the CCG model derived by Webster, an improved CCG model is proposed by replacing the constant exponent with a creep-damage-related variable. To validate the improved model, a comparison of da/dt vs. C* between experiment data and the CCG models was conducted. The predictive result of the improved model is in better agreement with the experiment results than the classical CCG and Webster models for the service-exposed rotor steel. With decrement of C* value within the improved CCG model, the remaining life of HP-IP rotors may be predicted more accurately.

Testing and assessment of cracking in P91 steels under creep-fatigue loading conditions

Abstract Future green energy options dictate that renewable energy source must be utilized when available. This poses a challenge to conventional power plant, which has generally been designed for base-load conditions, as they now need to operate in a ‘flexible’ manner. This flexible operation, in high temperature power plant components, could lead to a combination of creep and fatigue crack growth failure. Thus a better characterization of interactive creep-fatigue crack growth behaviour is required especially for assessing long term failure in plant. The industrial codes, such as R5 or BS7910, treat this interaction using linear accumulation of damage. However, this does not consider the degradation of properties and reduction in creep ductility in long term operations and their effect on the subsequent creep/fatigue behaviour. In this work creep-fatigue crack growth (CFCG) tests were performed on compact tension specimen of P91 steel in the as received and ex-service conditions at temperatures ranging between 600 °C to 625 °C, with the hold-times ranging from static to 600 s. The experimental results in addition to appropriate data from the literature have been analysed using stress intensity factor range, Δ K appropriate under fatigue control and the creep fracture mechanics parameter C* relevant under creep control. Scanning electron macroscopy (SEM) analysis confirms the influence of frequency on the mode of cracking. Within the scatter of experimental data for the present short term accelerated tests a linear cumulative damage rule can still predict the creep/fatigue interaction. However the effects due to low frequency cyclic loading as well as degraded the steel under ex-service conditions tending to reductions in creep ductility show factors of two or more faster cracking rates compared to as received static testing. Unavailability of long term tests at low stresses may pose additional problems under creep since creep is stress state controlled but fatigue in not. However using plane strain predictions of crack initiation and growth data using the NSW multiaxial ductility creep crack growth model suggest that conservative predictions of long term cracking can still be made under creep/fatigue and when there is a marked reduction creep failure ductility.

Grade 91 강의 고온 균열진전 실험 결과와 설계 물성치의 비교

The material properties of crack growth models at an elevated temperature were derived from the results of numerous crack growth tests for Mod.9Cr-1Mo (ASME Grade 91) steel specimens under fatigue loading and creep loading at an elevated temperature. These crack growth models were needed for defect assessment under creep-fatigue loading. The mathematical crack growth rate models for fatigue crack growth (FCG) and creep crack growth (CCG) were determined based on the test results, and the models were compared with those of the French design code RCC-MRx to investigate the conservatism of the code. The French design code RCC-MRx provides an FCG model and a CCG model for Grade 91 steel in Section III Tome 6. It was shown that the FCG model of RCC-MRx is conservative, while the CCG model is non-conservative compared with the present test data. Thus, it was shown that further validation of the property was required. Mechanical strength tests and creep tests were also conducted, and the test results were compared with those of RCC-MRx.

Behavior of Grade 91 material specimens with and without defect at elevated temperature

In a defect assessment and leak before break analysis under creep-fatigue loading, crack growth models are necessary. The French elevated temperature design code of RCC-MRx provides a fatigue crack growth (FCG) rate model and creep crack growth (CCG) rate model for Mod.9Cr-1Mo steel in Section III Tome 6. In this study, the crack growth models were derived from a number of crack growth tests for Grade 91 steel specimens under fatigue loading and creep loading at elevated temperature. The test data from the experiments of FCG and CCG were obtained, and the test data were compared with those of the RCC-MRx to investigate conservatism of the crack growth models in RCC-MRx. It was shown that the FCG rate model of RCC-MRx was conservative while the CCG model was non-conservative for Grade 91 steel when compared with present test data. In addition mechanical strength tests and creep tests were conducted and the test results were compared with those of the RCC-MRx.

A multiaxial creep-damage model for creep crack growth considering cavity growth and microcrack interaction

This article presents a concise multiaxial creep-damage model for creep crack growth considering the cavity growth and microcrack interaction. Special emphasis is put on developing and validating the multiaxial creep ductility factor (MCDF) based on power-law creep controlled cavity growth theory. Good agreements with the theoretical and experimental data prove the effectiveness of the proposed MCDF. The application of the proposed creep-damage model through finite element simulation of the creep deformation and crack growth in C-Shaped Tension and Compact Tension specimens of 316H tested at 550°C confirms the predictive capability of the proposed model.

Evaluation of the Testing and Analysis Methods in ASTM E2760-10 Creep-Fatigue Crack Growth Testing Standard for a Range of Steels

Abstract The development of the ASTM E2760-10, “Creep/Fatigue Crack Growth Testing” standard has initiated a phase of testing, analysis, and round robin initiatives associated with high temperature cyclic loading crack growth tests. Creep and fatigue are two complex independent mechanisms which may assist each other to drive the crack. A simplification of the macro creep/fatigue crack growth response of structures is therefore required. Using a linear cumulative damage method, as proposed in ASTM E2760, and other codes of practice, data for a range of steels are analysed. Limited crack growth data, using test methods similar to ASTM E2760, from previous collaborative projects for a range of steels are presented and analysed to identify the difficulties in the process. Creep-fatigue crack growth tests at frequencies ranging from 10 to 0.001 Hz are examined to consider the testing methodologies and in order to assess the effect of data scatter, dwell times, and the interaction region between creep crack growth (CCG) and fatigue crack growth mechanisms. Given the limited data available and the level of scatter, it can still be shown that the linear cumulative summation of static and high frequency data may be sufficient to predict creep/fatigue interaction both in terms of C* and ΔK, and the level of creep ductility will dictate appropriateness of the correlating parameter employed. Finally, in order to show that the level of data scatter can be dealt with in a predictive manner, the crack initiation and growth rates are also analysed using the NSW CCG model.

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

ABSTRACTDue 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.

Issues relating to numerical modelling of creep crack growth

Abstract 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.

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

Abstract 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.

Modelling Crack Growth in the Life Assessment of Elevated Temperature Components

Modelling of Creep Crack Growth (CCG) using analytical and numerical methods is relevant to life assessment procedures of components operating at elevated temperatures. This paper compares an analytical crack prediction and a numerical based virtual CCG technique used in fracture mechanics components with sample experimental results. Two approaches are presented. First the well developed strain exhaustion model called the NSW and the modified NSW-MOD models which predict plane stress/strain bound crack initiation and growth rates for engineering alloys and the second a damage-based approach used to numerically predict the crack propagation rate in Finite Element models of fracture mechanics specimens. The results from both methods are correlated against an independently determined C* parameter. As an example the NSW and the extended NSW-MOD strain exhaustion models are applied to compare to the experimental data and FE predictions for two steels at Carbon-Manganese steel tested at 360 oC and a weld 316H stainless steel at 550 oC. For values of C* within the limits of the present creep crack growth data presented the plane strain crack growth rate predicted from the numerical analysis is found to be less conservative than the plane strain NSW model but more conservative than plane strain NSW-MOD 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.

Creep crack growth in the absence of grain boundary precipitates in UDIMET 520

The effects of grain size and environment on creep crack growth (CCG) in Ni-base superalloy, UDIMET 520, were studied through experiments at 540 °C. Specially designed solution and aging treatments were used to produce γ′ strengthened microstructures with different grain sizes but without any M23C6 grain boundary precipitates. Five grain sizes, which fall into three groups (i.e., small, medium, and large), were employed. The creep crack growth rates (CCGRs) in specimens with small grain sizes were approximately 2.5 times lower than those with medium and large grain sizes, as a result of crack branching and the presence of some undissolved primary MC carbides at the grain boundaries. Otherwise, the CCGRs were insensitive to the grain size. Fractographic observations on the fracture surfaces and metallographic examinations on the cross sections of the interrupted CCG specimen revealed intergranular microcracks and a faceted intergranular mode of fracture in both air and argon environments. The test results suggest that the formation and propagation of intergranular cracks by grain boundary sliding (GBS) is the main micromechanism responsible for CCG in both air and argon environments at the relatively low test temperature employed. Grain boundary oxidation attack in the air environment simply accelerates the crack growth process. The present results are in agreement with the theoretical predictions of the GBS-controlled CCG model previously developed by the authors.

An intergranular creep crack growth model based on grain boundary sliding

An intergranular crack growth model is developed to describe the effect of microstructural features such as grain size, grain boundary precipitates, and serrated grain boundaries on creep crack growth under grain boundary sliding (GBS) conditions. The model considers quantitatively that several deformation mechanisms contribute to the stress redistribution ahead of the crack tip through a stress relaxation process. The crack tip region is divided into three zones: (a) the intragranular-deformation-controlled stress relaxation zone, (b) the GBS-controlled stress relaxation zone, and (c) the elastic region. Intergranular creep crack growth is considered to occur as a result of the GBS-controlled process in all cases. The derived creep crack growth model shows a complex dependence of the creep crack growth rate (CCGR) on fracture mechanics quantities, such as C(t) (the path-independent energy integral with its steady-state value as C*) and K (the stress intensity factor). For creep-brittle materials, the model predicts that the CCGR depends on K to the power of 2 and this is verified experimentally; however, when environmental effects contribute to the crack growth process, the power exponent will increase. A semiempirical factor is introduced to account for the effects of oxidation on CCGR.

Characteristics of interface cracks in creep regime

In this study, the growth behavior of interface cracks in bimaterials and in graded/layered materials at creep regime was studied. In the first part of the study, the evolution of the time-dependent stress states ahead of the stationary interface cracks was elucidated using a finite element model. In the second part, the observed stress states were incorporated into a creep crack growth model resulting from the growth of creep cavities ahead of the interface cracks. The growth model includes the effects of material deposition resulting from the growth of creep cavities on the crack tip stress fields. The results indicate that in graded/layered materials under identical applied loading, both the location of the interface crack and the extent of the transitional layer strongly influence the amplitude of the stress field ( C*) at steady state. Also, the time required to achieve the steady state varies considerably with these parameters. The growth rates of the interface cracks are much faster than the growth rate of a homogeneous crack in the fastest creeping sector of that interface. Due to large variation in the distribution of the stresses ahead of the interface cracks at creep regime, depending upon the location, the creep crack growth rates will be significantly different from each other under identical loading for a given graded/layered material.

Microstructural modelling of creep crack growth from a blunted crack

The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the underlying physical mechanisms such as the nucleation, growth and coalescence of grain boundary cavities accompanied by grain boundary sliding. Results are presented for \(C^* \)-controlled mode I crack growth under small-scale damage conditions. Particular attention is focused on creep constrained vs. unconstrained growth. Also the effect of grain boundary shear stresses on linking-up is investigated through shear-modified nucleation and growth models. The computations show a general trend that while an initially sharp crack tends to propagate away from the original crack plane, crack tip blunting reduces the crack growth direction. Under unconstrained conditions this can be partly rationalized by the strain rate and facet stress distribution corresponding to steady-state creep.

A probabilistic model for the growth of creep cracks

We present here a model for creep crack growth in which the primary mechanism for crack extension is the coalescence of the crack with adjacent voids. The model incorporates several key probabilistic features, notably random placement of the voids along the grain boundary, and random values for the grain boundary and self-diffusivities. The predictions of the model are in good agreement with C ∗- controlled crack growth data for type 304 stainless steel at lower C ∗ values. However, the agreement with K-controlled crack growth data for Inconel-718 is poor, possibly because crack growth in this material occurs by a different mechanism than that postulated here.

Meso-fracture of creep crack initiation and growth of engineering materials

High temperature engineering applications with fracture problems require practical answers from modelling developed from fundamental principles. The modelling at the atomistic level will invariably be unable to describe the problem at the macro level. However the use of meso-fracture mechanics modelling techniques, where assumptions and certain generalisations can be made, could provide an answer to macro engineering problems. In this paper a model for creep crack growth which links the micro to macro description for creep crack growth is presented to show the practical applicability of the use of mesofracture mechanics. It has been shown that creep crack growth can be separated into two regimes of failure consisting of initiation/incubation and a steady cracking behaviour. A creep process zone, described at a grain size level, modelling concept using the parameter C * is used to predict these two stages of crack growth. The model is used to describe crack initiation and growth behaviour in a range of engineering alloys showing its practical application.