Distinguishing the different contributions to fatigue damage of short cracks having different sizes and locations on the specimen surface, three new concepts, referred to as effective short fatigue cracks (ESFCs), dominant effective short fatigue cracks (DESFC), and density of ESFCs, respectively, are introduced to facilitate an understanding of the mechanism of interaction and evolution of short cracks. These concepts are interrelated and in conjunction produce an 'effective short fatigue crack criterion'. Replica observations of 19 smooth axial specimens of 1Cr19Ni9Ti stainless steel weld metal during low-cycle fatigue tests reveal that the short cracks contribute to the fatigue damage of specimens due to the formation of a critical density of ESFCs. The density reflects the local microstructural growth conditions ahead of the DESFC tips. The DESFC behaviour is a result of interactive short cracks, and this behaviour is deemed suitable to describe the collective behaviour of short cracks. In the microstructural short-crack stage, the DESFC are located in the weakest zone. Due to an irregular microstructural barrier effect, the crack density is higher in this zone and increases with fatigue cycling to reach a maximum value at the transition point into the physical short-crack stage. Then, due to the effects of accelerating coalescence and the DESFC size shielding the formation of new cracks, the density decreases rapidly and tends gradually to a saturation value. This is why the short-crack growth rate is high initially and tends gradually to that of long-crack behaviour. The difference and change in local microstructural growth conditions ahead of DESFC tips are the intrinsic cause of the statistical behaviour of short cracks and the scatter of fatigue lives.

An experimental stndy into microstructural effects on short fatigue crack behaviour of 19 stainless steel weld metal smooth specimens during low-cycle fatigue is performed by a so-called ‘effective short fatigue crack criterion’. This material has a mixed microstructure in which it is difficult to distinguish the grains and measure the grain diameter. The columnar grain structure is made up of matrix-rich δ ferrite bands, and the distance between the neighbouring rich δ ferrite bands is an appropriate measure- ment for characterizing this structure. Particularly, the effective short fatigue cracks (ESFCs) always initiate from the bands of δ ferrite in the matrix in the weakest zone on one of the specimen surface zones which is orientated in accordance with the inner or outer surface of welded pipe from which the specimens were machined. These cracks exhibit characteristics of the microstructural short crack (MSC) and the physically small crack (PSC) stages. The average length of the ESFCs at the transition between MSC and PSC behaviour is ≈40μm, while the corresponding fatigue life fraction is ≈0.3 at this transition. Different from previous test observations, the growth rate of the dominant effective short fatigue crack in the MSC stage still shows a decrease with fatigue cycling under the present low-cycle fatigue loading levels. A statistical evolution analysis of the growth rates reveals that the short fatigue crack growth is a damage process that gradually evolves from a non-ordered (chaotic) to a perfectly independent stochastic process, and then to an ordered (history-dependent) stochastic state. Correspondingly, the microstructural effects gradually evolve from a weak effect to a strong one in the MSC stage, which maximizes at the transition point. In the PSC stage, the effects gradually evolve from a strong to weak state. This improves our understanding that the short crack behaviour in the PSC stage is mainly related to the loading levels rather than microstructural effects.

Modeling of random cyclic strain-life (CSL) relations of engineering material should be a basis of strain-based fatigue reliability analysis. A statistical model for the relations of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal under temperature of 240℃, is presented. In the model, a verified distribution, i.e. lognormal distribution, is used as an appropriate assumed distribution of the material fatigue life data. Based on the Coffin-Manson law, the relations are modeled by mean value-and standard deviation-cyclic curves of the logarithm of fatigue life. Then, fatigue analysis at an arbitrarily given probability can be made conveniently according to the normal distribution function. An approach for estimating the curves and their confidence bounds is developed by a linear regression technique. Different from the existent reliability analysis methods that considered the material constants in the law as independently random variables, present work treats them as dependently random variables from the fit of test data. Availability of the model has been indicated by an analysis of the material test data.

The size evolution of surface short cracks in 1Cr18Ni9Ti pipe-weld metal is investigated in this paper. A local viewpoint is used to explain the observed evolution of cracking phenomena. The so-called'effectively short fatigue crack criterion' is used to characterize distributed populations of cracks. Special attention is paid to the initiation zone of dominant effectively short fatigue cracks (DESFCs) and then the zones ahead of the DESFC tips. The results reveal that the evolutionary size exhibits significant characteristics of microstructurally short crack (MSC) and physically short crack (PSC) stages. Fatigue damage is contributed largely to the initiation, and irregular growth, of effectively short fatigue cracks (ESFCs) in the MSC stage. In the PSC stage, the damage is due mainly to the DESFC growth, and partially to the growth of ESFCs and the coalescence of ESFCs themselves and with the DESFC. The damage processes involve gradual transitions from a non-ordered/chaotic status in the fatigue initiation regime, to an independently random status at the boundary between the MSC and PSC stages. Finally, a subsequent transition occurs to a history-dependent random status.

This paper pays special attention to an issue that there is a significant scatter of the stress-strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Efforts are made to reveal the random fatigue damage character by fracture surface observations and to model the random responses by introducing probability-based stress-strain curves of Ramberg-Osgood relation and its modified form. Results reveal that the fatigue damage is subjected to, 3-D interacting and involved microcracks. The three stages, namely microstructural short cracks (MSC), physical short cracks (PSC) and long cracks (LC) subdivided by Miller and de los Rios, can give a good characterization of the damage process. Both micro-and macro-behaviour of the material have the character of three stages. The 3-D effects are strong in the MSC stage, tend to a gradual decrease in the PSC stage, and then show saturation after going to the LC stage. Intrinsic causes of the random behaviour are the difference and evolution of the microstructural conditions ahead of the dominant crack tips. The'effectively short fatigue crack criterion' introduced by Zhao et al. in observing the material surface short crack behaviour could facilitate an understanding of the mechanism of interaction and evolution. Based on the previous obtained appropriate assumed distribution, normal model, for the cyclic stress amplitude, the probability-based curves are approximated by the mean value and standard deviation cyclic stress-strain curves. Then, fatigue analysis at arbitrarily given reliability can be conveniently made according to the normal distribution function. To estimate these curves, a maximum likelihood method is developed. The analysis reveals that the curves could give a good modeling of the random responses of material.

This paper pays a special attention to the issue that there is a significant scatter of the stress-strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Statistical investigation is made to the cyclic stress amplitudes of this material. Three considerations are given. They consist of the total fit, the consistency with fatigue physics and the safety in practice of the seven commonly used statistical distributions, namely Weibull (twoand three-parameter), normal, lognormal, extreme minimum value, extreme maximum value and exponential. Results reveal that the data follow meanwhile the seven distributions but the local effects of the distributions yield a significant difference. Any of the normal, lognormal, extreme minimum value and extreme maximum value distributions might be an appropriate assumed distribution for characterizing the data. The normal and extreme minimum models are excellent. Other distributions do not fit the data as they violate two or three of the mentioned considerations.

Conventional preventive maintenance (PM) policies generally hold same time interval for PM actions and are often applied with known failure modes. The same time interval will give unavoidably decreasing reliabilities at the PM actions for degradation system with imperfect PM effect and the known failure modes may be inaccurate in practice. Therefore, field managers would prefer policy with an acceptable reliability level to keep system often at a good state. A PM policy with the critical reliability level is presented to address the preference of field managers. Through assuming that system after a PM action starts a new failure process, a parameter so-called degradation ratio is introduced to represent the imperfect effect. The policy holds a law that there is same number of failures in the time intervals of various PM cycles, and same degradation ratio for the system reliability or benefit parameters such as the optimal time intervals and the hazard rates between the neighboring PM cycles. This law is valid to any of the failure modes that could be appropriately referred as a'general isodegrading model', and the degradation ratio as a'general isodegrading ratio'. In addition, life cycle availability and cost functions are derived for system with the policy. An analysis of the field data of a loading and unloading machine indicates that the reliability, availability and cost in life cycle might be well modeled by the present theory and approach.

The case of limited data implies that some unknown uncertainties may be involved in fatigue reliability analysis. For the sake of statistical convenience, for consistency with the relevant physical arguments and, most importantly, to ensure the safety in design evaluation, an approach is developed to determine an appropriate distribution, from four possible assumed distributions—three-parameter Weibull, twoparameter Weibull, lognormal and extreme maximum-value distributions. The approach makes allowance for consistency with the fatigue physics and checking tail fit effects. An application to nine groups of fatigue life data of 16Mn steel (Chinese steel) welded plate specimens shows that the lognormal distribution and the extreme maximum-value distribution may be the appropriate distributions of the fatigue life under limited data.

probabilistic assessment is made of the design S-N curves for 1Cr18Ni9Ti pipe-welded joint. The material exhibits a character of random cyclic stress-strain and fatigue life responses. Then, both the S and N in the virtual stress amplitude-fatigue crack initiation life (S-N) data are random variables. A general maximum likelihood method, which considers the randomness of the test S-N data, is developed to model the probabilistic S-N relations of material. The design S-N curves with reduction factors of 20 on cycles, 2 on stress and 2.5 on stress applied to the best-fit S-N curve of test data as used in the ASME code and general practice, are assessed in a probabilistic sense. The results reveal that in the lower S regime the 20 and 2.5 reduction factor curves may be appropriate, while the reduction factor of 2 is slightly nonconservative. But in the higher S regime these curves are all much more conservative. The intrinsic cause is that the standard deviation of logN exhibits an increase with the S decreasing, while the constant reduction factors do not consider this increase. It is shown that from the general statistical scatter of S-N data the design S-N curves should be appropriately determined by a probabilistic approach.

A significant scatter of the cyclic stress