CRACK TIP FIELDS UNDER NON-STEADY CREEP CONDITIONS—I. ESTIMATES OF THE AMPLITUDE OF THE FIELDS

Abstract— Under non-steady creep conditions, the stress and strain rate fields near the tip of a stationary crack can be described by the singular fields of Hutchinson, Rice and Rosengren for power-law creeping materials. Estimation formulae are presented for describing the amplitude of these fields under load and displacement controlled boundary conditions. For constant loading, the formulae reduce to the result of Riedel and Rice for short times after load application and to the steady state line integral C * for long times. At intermediate times, the estimate is validated by detailed finite-element computation. For displacement-controlled loading, the amplitude of the near-tip fields is shown to fall rapidly, consistent with finite-element analysis. The implications of the results for data collection and defect assessments are discussed in a companion paper.     

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.     

CRACK GROWTH RATES DURING CREEP, FATIGUE AND CREEP-FATIGUE IN AN AUSTENITIC FEATURE WELD SPECIMEN

Abstract— Static creep crack growth tests and displacement controlled fatigue and creep-fatigue crack growth tests have been performed on austenitic feature weld specimens at 650°C. The creep-fatigue tests incorporated hold times of up to 96 h. During these tests, crack growth appeared to comprise cyclic and dwell components. Cyclic crack growth components were characterised by the fracture mechanics parameter K whilst creep crack growth contributions were correlated with C *. In order to determine K and C * for the non-standard feature weld specimen, elastic and elastic-plastic creep finite element analyses were conducted. Good correspondence is shown between the feature weld data and comparable data from compact tension specimen tests on similar materials. Equations obtained from the compact tension specimen results, which describe total crack growth rates as the sum of the cyclic and dwell contributions, are shown to adequately describe the features test results also. Furthermore, it is demonstrated that a reference stress approach can be used to estimate C * for the features specimens.     

RATE-DEPENDENT DEFORMATION AND FRACTURE OF α-TITANIUM

Aspects of combined rate-dependent deformation and crack growth in α-titanium at room temperature are examined. Results are presented for tests carried out on pre-cracked three point loaded single edge notch bend and compact tension specimens subjected to constant crack opening displacement rates and constant load. Curves of the ratio of the reference stress to the yield stress as a function of the ratio of the plastic displacement to specimen width are found to be different for different rates. The stress difference between continuously loaded curves and curves obtained from load relaxation tests (“relaxed” curves) is found to be similar to uniaxial results. Earlier uniaxial tests show that the “relaxed” curve represents a boundary below which no further creep takes place. The pre-cracked specimen constant load curves cross the “relaxed” curve, even though the contribution from crack growth to the overall deformation is found to be small. Sustained load crack growth is observed to take place under contained yielding conditions and the sustained load resistance curves are found to be different for different reference stresses.     

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.     

NUMERICAL ANALYSIS OF CRACK PROPAGATION IN PIEZOELECTRIC CERAMICS

The formulation of an isoparametric displacement – electric potential finite element method that accounts for the electro-mechanical coupling effect of piezoelectric materials is briefly presented in this paper. The crack propagation behaviour and the elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and mechanical – electrical mixed loads are investigated using this electro-mechanical finite element method. From the numerical results, it can be seen that crack propagation along the crack plane direction will be impeded and the crack will tend to propagate at an angle of about 84° to the crack plane under a negative electric field on the basis of the maximum stress criterion. The physical explanation of the phenomena is presented in this paper and it is shown that the mechanical strain energy release rate is not a good criterion for predicting crack propagation in the case where the ratio of the electric field to the mechanical load becomes large.     

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.     

TIME-DEPENDENT FATIGUE CRACK GROWTH IN TITANIUM METAL MATRIX COMPOSITES

Abstract The interaction of fatigue and creep in a titanium metal matrix composite was studied by employing loading frequencies of 10 Hz (in both air and vacuum environment) and 0.1 Hz with and without hold times (in air) at 500°C. It was shown that, for the same loading frequency, the crack growth rate is lower in vacuum than in air. In an air environment, however, where the influence of load-related creep and environmental effects exist, it was shown that a decrease in the loading frequency leads to a decrease in the crack growth rate. This behavior is interpreted in terms of the redistribution of fiber and matrix stresses occurring in response to the creep-related relaxation of matrix stresses. The result of this stress redistribution is the generation of a compressive axial residual stress in the matrix phase in the region of the composite ahead of the crack tip. As the crack bridges the fibers in this region, the release of the matrix residual compressive stress leads to the closure of the matrix fractured surfaces at the crack tip, thus leading to a decrease in the crack tip driving force. To support this concept, experimental measurements of the crack opening displacement at different loading frequencies are presented. In addition, a simple model is proposed to describe the nature of the residual stresses developed in the matrix phase during cyclic loading. Results of this model have been examined using finite element analysis. The influence of time-dependent effects during a fatigue cycle was, furthermore, investigated by carrying out high frequency fatigue tests on specimens which have been previously subjected to creep deformation. Results of these tests in terms of the crack growth rate and associated crack closure, support the conclusion that a predeformed matrix produces a decrease in the crack growth rate of the corresponding composite.     

STRESS STATE-RELATED FATIGUE CRACK GROWTH UNDER SPECTRUM LOADING

Abstract— The fatigue crack growth behaviour in aluminium alloy sheets of 2024-T3 and 7475-T761, subjected to standardized spectra (TWIST and FALSTAFF), was investigated using centre-cracked specimens. A strip crack closure model was used to interpret experimental data, and to make predictions for the crack growth.
The strip model is based on the Dugdale concept, but modified to keep plastically-stretched materials on the crack surface so that the crack opening load can be determined, and the fatigue crack growth can be analysed according to Elber's crack growth assumption. Differing from other models of the same kind, a variable constraint factor was introduced to account for the gradual transition of stress state at the crack tip resulting from the crack growth. It has been shown that the transition of stress state at the crack tip causes the unusual behaviour of the fatigue crack growth in sheets. Both experiments and predictions show that a crack may grow faster at a low load than at a higher one in a certain applied load range due to the crack tip stress state transition. The crack tip stress state also contributes to the thickness effect observed for the crack growth in sheets. In agreement with experimental results, it has been shown that a plane stress state will prevail at the crack tip in a thin sheet compared to that in a thick sheet. The plane stress state results in a higher crack opening level which leads to a longer fatigue life for thin sheets.     

EFFECT OF ELASTIC MISMATCH ON THE GROWTH OF A CRACK INITIALLY TERMINATED AT AN INTERFACE IN ELASTIC PLASTIC BIMATERIALS

Abstract A crack perpendicular to, and initially with the tip on, a bimaterial interface is studied. An asymptotic analysis is performed and crack growth proceeds straight ahead at constant remote load. Mode I conditions and plane strain are assumed. The materials on both sides of the interface are elastic perfectly-plastic with different elastic properties and the same yield stress. A finite element analysis is made and crack growth is simulated by an element relaxation technique. Because of the interface, the crack-tip driving force is not constant, which is reflected in the near-tip state. The development of the plastic zone and the crack opening displacements is presented for different elastic mismatches. Small scale yielding like results are obtained after a crack extension of about the plastic zone size from the interface, i.e. long before a square-root singular stress field may be expected to embed the plastic zone. An important observation is that the development of the crack opening displacement at the initial stage of growth is reversed when plasticity is introduced, as compared to the prediction by an elastic model. A region of stable crack growth is identified at the initial phase of growth into a stiffer material, solely due to elastic mismatch.     

Stress Intensity Controlled Kinetic Crack Growth and Stress History Dependent Life Prediction with Statistical Variability

Consistent with viscoelastic behavior, a power law form in terms of the stress intensity factor is used to specify crack kinetics (growth rate) in the central crack problem under Mode I conditions. The crack growth rate is integrated to obtain the crack size and thereby the stress intensity factor as a function of time. The crack is allowed to grow in a controlled, load dependent manner until it reaches the size at which it becomes unstable. The corresponding time at which this occurs is taken as the lifetime of the material under the specified load history. The special cases of constant load (creep rupture) and constant strain rate to failure are found to have a very simple relationship with each other. This lifetime relationship is verified through the comparison with corresponding data upon a polymeric composite. Finally the creep rupture case is generalized to a probabilistic formalism. The theoretically predicted lifetime distribution functions are verified with data, also upon a polymeric composite. Possible extension of the entire formalism to cyclic fatigue in metals is discussed. Dedicated to Professor Z.P. Bažant for his many contributions.     

A FRACTURE MECHANICS APPROACH TO HIGH-CYCLE FATIGUE CRACK GROWTH UNDER IN-PLANE BIAXIAL LOADS

Abstract Fatigue crack growth under biaxial tensile load conditions is reported for a structural sheet steel. The new test facility can operate at high frequency (0–40 Hz) thereby permitting real-time testing required for threshold investigations; specimens are of the cruciform type.
It is found that crack growth rate is affected by a cyclic tensile load applied in the direction of growth which decreases as the said load increases. The rate however increases if the biaxial loads are increasingly out of phase.
Within the test conditions reported LEFM can be applied to crack growth under biaxial load conditions. The threshold stress intensity range is shown to be a function of load biaxiality, phase difference and stress ratio.     

Small punch and uniaxial creep fracture behaviours of modified SUS304H steel at various temperatures

Commercial austenitic stainless steel SUS304H with small amount of vanadium addition was used in this study. Small punch (SP) creep and uniaxial tensile creep tests were conducted at 650, 700, and 750 °C to measure creep lives and the minimum displacement rates or the minimum creep strain rates. The measured parameters were compared between the two test methods, seeking empirical relationships among the parameters using Larson-Miller Parameter and Monkman-Grant relation. Magnitude of the applied stress (MPa) in the uniaxial tensile creep test was approximately equal to the applied load value (N) in the SP creep test at all test temperatures. It was shown that during the creep deformation of the SP creep specimen, crack initiation and accompanying crack growth occur simultaneously. Competing failure mechanisms of creep deformation and crack growth may affect the SP creep life and consequently determine the proportionality function, α, in the relation between the SP load and the tensile creep rupture stress in creep tests.     

Fatigue fracture of nylon polymers

The influence of glass fibres on the fatigue crack propagation rates of injection-moulded nylons has been determined. In contrast to previous results for unreinforced nylons, the cracking kinetics are independent of the oscillating load frequency. The fact that the crack growth rate per cycle is constant, when expressed in terms of the time under load, demonstrates that the contribution of creep crack extension is minimized by the glass fibres. Thus a true fatigue process is suggested for the fatigue fracture of the reinforced system, even when the glass fibres are preferentially aligned parallel to the crack growth direction. A complicating factor in characterizing the fatigue resistance of the glass-reinforced nylons is the tremendous influence of fibre orientation on crack growth rate. It is shown that the anisotropy problem can be handled by simply expressing the crack growth rate data in terms of the strain energy release rate rather than the usual stress intensity factor representation. Results for four different glass-filled nylons show that the diverse crack growth rates for cracking parallel versus perpendicular to the glass-fibre axes collapse on to individual strain energy release rate curves. Each single relationship therefore characterizes the fatigue fracture of the filled material and furthermore permits a prediction of the cracking rates for any glass-fibre orientation based upon the expected change in modulus. Finally it is demonstrated that the increased stress dependence of fatigue crack propagation (slope of the Paris plot) in filled nylons can be duplicated in unfilled samples under certain conditions. It is concluded that the fatigue fracture mechanism is matrix dominated in these chopped glass-fibre reinforced materials.     

CREEP, FATIGUE AND CREEP-FATIGUE CRACK GROWTH RATES IN PARENT AND SIMULATED HAZ TYPE 321 STAINLESS STEEL

Abstract— Crack growth rate data are presented from a range of fully reversed displacement-controlled fatigue and creep-Fatigue tests and from static load-controlled creep crack growth tests on aged 321 stainless steel (parent and simulated HAZ) at 650 ° C. In the creep fatigue tests, constant displacement tensile hold periods of 12–192 h were used. Crack growth rates comprised both cyclic and dwell period contributions. Cyclic growth contributions are described by a Paris-type law and give faster crack growth rates than those associated with pure fatigue tests. Dwell period contributions are described by the C* parameter. The total cyclic crack growth rates are given by summing the cyclic and dwell period contributions. Estimates of C* using a reference stress approach together with the appropriate stress relaxation creep data are shown to correlate well with experimentally measured C* values. Crack growth rates during static load-controlled tests correlate well with C* . Good agreement is obtained between crack growth rates during the static tests and those produced during the hold period of the creep-fatigue tests.     

Creep crack growth characteristics of polypropylene film at various temperatures

Creep crack growth rates were measured using centrally cracked tension specimens of thin polypropylene film at various temperatures and stress levels. The creep crack growth rates were correlated with the stress intensity factor. The experimental results showed that there is the region of the minimum constant crack growth rate which occupies more than 75% of the total creep failure life. This steady or constant creep crack growth rate depends on the test temperature and the initial stress intensity factor. The constant creep crack growth rate characteristics were analyzed on the basis of the Arrhenius type thermally activated process. It is found that creep crack growth behavior is closely related to the crack tip opening displacement and the creep zone size.     

A fatigue-to-creep correlation in air for application to environmental stress cracking of polyethylene

The present study was undertaken to determine whether the correlation between fatigue and creep established for polyethylene in air could be extended to environmental liquids. Fatigue and creep tests under various conditions of stress, R-ratio (defined as the ratio of minimum to maximum load in the fatigue loading cycle), and frequency were performed in air and in Igepal solutions. The load–displacement curves indicated that stepwise fatigue crack growth in air was preserved in Igepal solutions at 50 °C, the temperature specified for the ASTM standard. In air, systematically decreasing the dynamic component of fatigue loading by increasing the R-ratio to R = 1 (creep) steadily increased the lifetime. In contrast, the lifetime in Igepal was affected to a much smaller extent. The fatigue to creep correlation in air was previously established primarily for tests at 21 °C. Before testing the correlation in Igepal, it was necessary to establish the correlation in air at 50 °C. Microscopic methods were used to verify stepwise crack growth by the sequential formation and breakdown of a craze zone, and to confirm the fatigue to creep correlation. The crack growth rate under various loading conditions was related to the maximum stress and R-ratio by a power law relationship. Alternatively, a strain rate approach, which considered a creep contribution and a fatigue acceleration factor that depended only on strain rate, reliably correlated fatigue and creep in air at 50 °C under most loading conditions of stress, R-ratio and frequency. The exceptions were fatigue loading under conditions of R = 0.1 and frequency less than 1 Hz. It was speculated that compression and bending of highly extended craze fibrils were responsible for unexpectedly high crack speeds.     

DETERMINATION OF STRESS CORROSION CRACK INITIATION STRESS AND CRACK VELOCITIES USING SLOWLY STRAINED TAPERED SPECIMENS

Abstract— Previous work has shown that a single tapered cylindrical specimen subjected to slow strain rate testing can provide data for the crack initiation stress of 70/30 brass in 1N NaNO₂ solution. In order to test the wider applicability of that technique, crack initiation stresses of a further five systems were measured. These were 70/30 brass in an ammoniacal solution, copper in sodium nitrite and mild steel in carbonate–bicarbonate, hydroxide or nitrate solutions. The results are compared with those obtained from tests on plain cylindrical specimens subjected to interrupted slow strain rate tests or to constant load tests, and the agreement is reasonable. The method also is capable of providing data on the stress dependence of crack velocities.     

The cyclic creep behaviour of Type 316 stainless steel

The cyclic creep behaviour of a Type 316 stainless steel at 625° C has been examined as a function of the maximum applied stress and frequency using trapezoidal loading cycling between zero and a maximum stress. The so-called static-to-dynamic creep transition observed is interpreted in terms of recoverable anelastic strain behaviour without using an internal stress argument. Over the range of experimental conditions examined, failure occurs by static creep modes, namely wedge crack nucleation and growth. The loading strain increments appear to be damaging to about the same extent as the much slower strain occurring at constant load, such that it is the overall strain rate that determines the rate of damage. A cursory examination of square wave load cycling shows that the behaviour is very similar to that observed during trapezoidal loading and suggests that the rate of loading and unloading does not play an important part in determining the creep and rupture behaviour.