Modeling for fracture in materials under long-term static creep loading and neutron irradiation. Part 2. Prediction of creep rupture strength for austenitic materials

We present some results of prediction of creep rupture strength and plasticity for austenitic materials prior to and after irradiation with variable neutron flux rates, based on physicomechanical model as outlined in Part 1. The calculated results are compared with the available experimental data. __________ Translated from Problemy Prochnosti, No. 5, pp. 5–15, September–October, 2006.     

Theoretical-experimental model for predicting crack growth rate in structural alloys under combined action of fatigue and creep

Holding periods of 300 and 3600 s in a trapezoidal load cycle are shown to increase the crack growth rate dozens of times for alloy éP962 and several-fold for alloy éP742 at a temperature of 973 K. It is demonstrated that in the presence of the first portion on the creep crack growth diagram, whereon the crack growth rate decreases, the crack growth kinetics for a trapezoidal load cycle can be predicted using the hypothesis of the linear summation of fatigue and creep crack growth rates provided that the peculiarities of the first portion of the creep crack growth diagram are taken into account. Empirical approaches are proposed for determining the mean crack velocity in the first portion of the creep crack growth diagram. __________ Translated from Problemy Prochnosti, No. 1, pp. 105–112, January–February, 2009.     

Theoretical-Experimental Model for Predicting Crack Growth Rate in Structural Alloys of Aircraft Gas Turbine Engine Disks with Regard to Fatigue and Creep

Hold times of 300 and 3600 s under trapezoidal cyclic loading are shown to result in an increase in crack growth rates by many factors of ten for EP962 alloy and several times for EP742 alloy at a temperature 973 K. It has been found that in case the creep crack growth diagram has a first segment where the crack growth rate decreases, the crack growth kinetics under trapezoidal cyclic loading can be predicted by means of the hypothesis of linear summation of fatigue and creep crack growth rates considering special features of the first segment of the creep crack growth diagram. The authors put forward empirical approaches to determining the mean rate on the first segment of the creep crack growth diagram. __________ Translated from Problemy Prochnosti, No. 6, pp. 15 – 25, November – December, 2005.     

Modeling for fracture in materials under long-term static creep loading and neutron irradiation. Part 1. A physico-mechanical model

The paper presents a physico-mechanical model for predicting creep rupture in neutron-irradiated materials. The model is based on the approach whereby damage is described as voids on grain boundaries. The equations for void nucleation and growth which were proposed by the authors earlier are augmented to include neutron irradiation of material. Constitutive equations are derived to describe viscoplastic deformation of material including void propagation. A criterion for plastic stability of a unit cell is employed as a fracture criterion. __________ Translated from Problemy Prochnosti, No. 3, pp. 5–22, May–June, 2006.     

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.     

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.     

Stochastic model for the size distribution of dispersed cracks. Part 2. Unsteady-state crack growth

The stochastic model for describing the statistical length distribution of dispersed cracks over a given time interval was developed. The parameters of crack length and rate distributions at the beginning of the time internal and the intensity of crack initiation per unit surface area were used as the initial data for the numerical representation of this stochastic model. The model was used to obtain time-predicted crack size distributions and the distributions of remnant life to the initiation of the crack of a maximum admissible length for the initial exponential flaw length and growth rate distributions. Experimental investigations confirmed that small surface crack growth rate distributions under low-cycle loading of and éI698VD nickel-based alloy corresponded to the exponential one. Kiev International University of Civil Aviation, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 59–67, July–August, 1999.     

Damage assessment in structural metallic materials for advanced nuclear plants

Future advanced nuclear plants are considered to operate as cogeneration plants for electricity and heat. Metals and alloys will be the main portion of structural materials employed (including fuel claddings). Due to the operating conditions these materials are exposed to damaging conditions like creep, fatigue, irradiation and its combinations. The paper uses the most important alloys: ferritic-martensitic steels, superalloys, oxide dispersion strengthened steels and to some extent titanium aluminides to discuss its responses to these exposure conditions. Extrapolation of stress rupture data, creep strain, swelling, irradiation creep and creep–fatigue interactions are considered. Although the stress rupture- and the creep behavior seem to meet expectations, the long design lives of 60 years are really challenging for extrapolations and particularly questions like negligible creep or occurrence of diffusion creep need special attention. Ferritic matrices (including oxide dispersion strengthened (ODS), steels) have better irradiation swelling behavior than austenites. Presence and size of dispersoids having a strong influence on high-temperature strength bring only insignificant improvements in irradiation creep. A strain-range-separation based approach for creep–fatigue interactions is presented which allows a real prediction of creep–fatigue lives. An assessment of capabilities and limitations of advanced materials modeling tools with respect to damage development is given.     

Estimation of dynamic fatigue strengths in brittle materials under a wide range of stress rates

This paper aims to statistically estimate the dynamic fatigue strength in brittle materials under a wide range of stress rates. First, two probabilistic models were derived on the basis of the slow crack growth (SCG) concept in conjunction with two-parameter Weibull distribution. The first model, Model I, is a conventional probabilistic delayed-fracture model based on a concept wherein the length of the critical crack growth due to SCG is enough larger than the initial crack length. For the second model, Model II, a new probabilistic model is derived on the basis of a concept wherein the critical cracks have widely ranging lengths. Next, a four-point bending test using a wide range of stress rates was performed for soda glass and alumina ceramics. We constructed fracture probability–strength–time diagrams (F–S–T diagrams) with the experimental results of both materials using both models. The F–S–T diagrams described using Model II were in good agreement with plots of the fracture strength and the fracture time of both materials more so than Model I.     

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

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

Creep induced rate effects on radial cracks in multilayered structures

This paper considers foundation and epoxy creep induced loading rate effects on radial cracks in multilayered structures. These include top layers of glass or silicon that are bonded to polycarbonate foundations with epoxy. The creep properties of the epoxy join and the polycarbonate foundation are determined using compression experiments and spring-dashpot models. The measured creep parameters are then incorporated into an analytical mechanics model, and finite element simulations are used to predict the effects of creep on the critical loads for radial cracking at different loading rates. The models suggest that the combined effects of creep and slow crack growth must be considered in the predictions of the critical loads required for radial cracking in the systems containing glass top layers. Since slow crack growth does not occur in silicon, the model considering the creep effect is used to predict the critical loads for radial cracking in the systems containing silicon top layers. In both of the structures, analytical solutions are obtained for bi-layer structures and finite element simulations are used for tri-layer structures. Our results show that the analytical solutions obtained by bi-layer structures provide good estimations for tri-layer structures when the epoxy thickness is less than 100 μm. The predictions obtained for both systems are shown to provide improved predictions by comparing with experimental results reported by Lee et al. [J. Am. Ceram. Soc., 2002, 85(8), 2019–2024]. In both systems, the modeling of join/substrate creep is shown to be important for the accurate prediction of loading rate effects on radial cracking.     

In-service creep of materials for steam lines of thermal power plants and extension of their life

An analysis of 200,000 h of laboratory creep data for chromium-nickel-molybdenum-niobium steel tested at service loads and temperatures demonstrated a multistage creep nature, a transient stage of long duration (up to 20,000–25,000 h), an extended accelerated creep stage as compared to the duration of the steady-state one, and the existence of an avalanche creep stage. The relationships and their alternating sequences common to laboratory tests and service of mateirals in the structural elements of thermal power plants show that the creep data can be used to predict the service life of these materials. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 56–61, May–June, 1998.     

A damage model for crack prediction in brittle and quasi-brittle materials solved by the FFT method

In this paper, we present a damage model and its numerical solution by means of Fast Fourier Transforms (FFT). The FFT-based formulation initially proposed for linear and non-linear composite homogenization (Moulinec and Suquet in CR Acad Sci Paris Ser II 318:1417–1423 1994; Comput Methods Appl Mech Eng 157:69–94 1998) was adapted to evaluate damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed for brittle materials. This non-local model was then connected to the Griffith criterion with the aim of predicting crack growth. By using the proposed model, we carried out several numerical simulations on different specimens in order to assess the fracture process in brittle materials. From these studies, we can conclude that the present FFT-based analysis is capable of dealing with crack initiation and crack growth in brittle materials with high accuracy and efficiency.     

The influence of porosity on the fatigue crack growth behavior of Ti–6Al–4V laser welds

The effect of porosity––a common welding defect––on the fatigue crack growth rate (FCGR) in Ti–6Al–4V laser welds was investigated. The experimental results reveal that porosity was present in partial penetration welds over a narrow fusion zone (FZ) with martensite structure. The FCGR of the FZ was lower than that of the base plate. The fracture surface morphology of weld metal was much rougher as compared to that of the base plate. Randomly oriented martensite in the FZ led to local cleavage fracture along a preferred plane, thus, altering the crack growth direction significantly out of the primary crack plane. The zigzag crack path in the FZ resulted in a reduced FCGR at a given ΔK compared to the base plate. Besides, the porous weld showed a serration on the crack growth curve, and behaved the similar crack growth characteristics as the defect free one. SEM fractography revealed that the deflection of crack path around porosity together with local notch blunting as the crack tip pierced into porosity, balanced the increased FCGR for the occurrence of instant crack advance as the crack front reached the porosity at a low stress ratio. In contrast, the serration and drop in FCGR occurred sparingly at a high stress ratio as the crack front met the porosity.     

Influence of the modes of operation and structural factors on the crack propagation in 12Cr–2Ni–Mo steel

We study the influence of temperature, specimen sizes, loading frequency, and the time of holding under long-term static loading on the crack growth rate in 12Cr–2Ni–Mo steel. It is shown that the influence of these factors on the crack growth rate is insignificant. A numerical-experimental model is proposed for the evaluation of the time of subcritical crack growth with regard for the duration and cyclic character of loading. Translated from Problemy Prochnosti, No. 3, pp. 66–77, May–June, 2009.     

Mechanical fatigue of Sn-rich Pb-free solder alloys

Recent fatigue studies of Sn-rich Pb-free solder alloys are reviewed to provide an overview of the current understanding of cyclic deformation, cyclic softening, fatigue crack initiation, fatigue crack growth, and fatigue life behavior in these alloys. Because of their low melting temperatures, these alloys demonstrated extensive cyclic creep deformation at room temperature. Limited amount of data have shown that the cyclic creep rate is strongly dependent on stress amplitude, peak stress, stress ratio and cyclic frequency. At constant cyclic strain amplitudes, most Sn-rich alloys exhibit cycle-dependent and cyclic softening. The softening is more pronounced at larger strain amplitudes and higher temperatures, and in fine grain structures. Characteristic of these alloys, fatigue cracks tend to initiate at grain and phase boundaries very early in the fatigue life, involving considerable amount of grain boundary cavitation and sliding. The growth of fatigue cracks in these alloys may follow both transgranular and intergranular paths, depending on the stress ratio and frequency of the cyclic loading. At low stress ratios and high frequencies, fatigue crack growth rate correlates well with the range of stress intensities or J-integrals but the time-dependent C* integral provides a better correlation with the crack velocity at high stress ratios and low frequencies. The fatigue life of the alloys is a strong function of the strain amplitude, cyclic frequency, temperature, and microstructure. While a few sets of fatigue life data are available, these data, when analyzed in terms of the Coffin–Mason equation, showed large variations, with the fatigue ductility exponent ranging from −0.43 to −1.14 and the fatigue ductility from 0.04 to 20.9. Several approaches have been suggested to explain the differences in the fatigue life behavior, including revision of the Coffin–Mason analysis and use of alternative fatigue life models.     

FEM simulation of viscous properties for granular materials considering the loading rate effect

The deformation and strength characteristics of sandy soils as a kind of granular materials are very complex. The experimental results show that when the strain rate suddenly changes in monotonic loading (ML) case, the stress–strain curve of sandy soils changes sharply and then gradually converges into the original inferred one that would be obtained by continuous ML at constant strain rate after having exhibited clear yielding. Similar behaviors are also observed when ML is restarted at a constant strain rate following a creep loading or stress relaxation stage. An elasto-viscoplastic constitutive model for granular materials is developed, which consists of three components. One of the most important features of the model is that it can take into account the effects of loading rate due to viscous properties on the stress–strain behavior. The stress ratio-axial strain–time relations from four drained plain strain compression (PSC) tests on the saturated Toyoura sand are successfully simulated by the finite element method (FEM) code incorporating the proposed constitutive model. It is shown that the FEM code can simulate the viscous behaviors of sand accurately under arbitrary loading history.     

The variation of beta phase morphology after creep and negative creep for duplex titanium alloys

The creep resistance of SP700 (Ti–4.5Al–3V–2Mo–2Fe) is superior to Ti–6–4 (Ti–6Al–4V) at 500 °C under a constant load corresponding to an initial stress of 100 MPa. The β phase grains in the SP700 alloy prefer to orient along the loading axis in contrast to the Ti–6–4 alloy. The grain growth occurs during the stress drop incubation period. The observation of different amounts of negative creep/anelasticity upon loading is closely associated with the difference in the amount of grain/subgrain coarsening.     

Proposal of a new concept on creep fracture remnant life for a precracked specimen

Abstract

The creep life time of a smooth specimen can be predicted using existing laws for creep deformation and steady state creep rate. When crack growth behaviour is involved, it is necessary to construct a law of creep crack growth rate to predict creep fracture life. Creep fracture life can be measured by integrating the law of creep crack growth rate. One example is the creep crack growth rate, represented by the parameter Q*. In this study, we investigated the applicability of this prediction method to creep fracture remnant life for a cracked specimen. The Ω criterion is proposed to predict creep fracture remnant life for a smooth specimen for creep ductile materials. In this study, the correlation between Q*_L derived from the paremeters Q* and Ω is investigated. The correlation between Q_L* and Ω provided a unified theoretical prediction law of creep fracture remnant life for high-temperature creep-ductile materials in the range from smooth to precracked specimens.