Sigmoidal crack growth rate curve: statistical modelling and applications

Self Cite

111

The continuous increment of durability and reliability requirements for many machinery components is significantly enhancing the research activity in the Very‐High‐Cycle Fatigue (VHCF) characterization of metallic materials, in particular of high‐strength steels for critical structural applications. According to the area model, the VHCF strength of high‐strength steels can be estimated from the projected area of the ‘Optically Dark Area’ (ODA), which plays a key role in the VHCF response of high‐strength steels: more than 95% of the total VHCF life is consumed in the ODA formation, with crack growing even though the Stress Intensity Factor (SIF) is below the threshold for crack growth. Following the hydrogen embrittlement theory proposed by Murakami, hydrogen is supposed to assist crack growth within the ODA. The present paper proposes a general SIF formulation for the analytical model of the hydrogen assisted crack growth within the ODA. Starting from the general SIF formulation, a general expression for the material fatigue limit is obtained in the paper. The statistical method for the estimation of the parameters involved in the proposed model is finally illustrated in the paper and numerically applied to an experimental dataset.

“…If, according to the literature (e.g., Refs. ), log 10 [ K th ] is assumed to be Normal with mean

μ_{l K_{t h}}

and standard deviation

σ_{l K_{t h}}

, log 10 [ K th ] can be expressed in terms of the distribution parameters as follows:

\log_{10} ([], K_{t h}) = μ_{l K_{t h}} + σ_{l K_{t h}} Z,

where Z is a standardized Normal random variable (rv). The mean value of log 10 [ K th ] must be consistent with the deterministic model proposed in Eq.…”

Section: Methodsmentioning

confidence: 99%

S‐N curves in the very‐high‐cycle fatigue regime: statistical modeling based on the hydrogen embrittlement consideration

Paolino

Tridello

Chiandussi

et al. 2016

Self Cite

111

“…Figure a shows an example of a Paris plot reinterpreted by the present model. A similar model has been recently proposed by Paolino et al …”

Section: Generalisation: Other Possible Usesmentioning

confidence: 78%

Fitting fatigue data with a bi‐conditional model

Cova

Tovo

2016

The formulation of a probability‐stress‐life (P‐S‐N) curve is a necessary step beyond the basic S‐N relation when dealing with reliability. This paper presents a model, relevant to materials that exhibits a fatigue limit, which considers the number of cycles to failure and the occurrence of the failure itself as statistically independent events, described with different distributions and/or different degree of scatter. Combining these two as a parallel system leads to the proposed model. In the case where the S‐N relation is a Basquin's law, the formulations of the probability density function, cumulative distribution function, quantiles, parameter and quantile confidence interval are presented in a procedure that allows practically any testing strategy. The result is a flexible model combined with the tools that deliver a wide range of information needed in the design phase. Finally, an extension to include static strength and applicability to fatigue crack growth and defects‐based fatigue approach are presented.

“…Equation is obtained by assuming, according to the literature, a lognormal distribution for the global SIF threshold:

k_{italicth, g, α} = c_{italicth, g} ((), italicHV + 120) {\sqrt{a}}^{α_{th, g}} 10^{z_{α} σ_{italicth, g}},

where k th , g , α denotes the α ‐th quantile of the global SIF threshold.…”

Section: Methodsmentioning

confidence: 99%

Estimation of P‐S‐N curves in very‐high‐cycle fatigue: Statistical procedure based on a general crack growth rate model

Paolino

Tridello

Chiandussi

et al. 2017

Extensive experimental investigations show that internal defects play a key role in the very‐high‐cycle fatigue (VHCF) response of metallic materials and that crack growth from internal defects can take place even if the stress intensity factor associated to the initial defect is below the threshold for crack growth. By introducing a reduction term in the typical formulation of the threshold for crack growth, the authors recently proposed a general phenomenological model, which can effectively describe crack growth from internal defects in VHCF. The model is able to consider the different crack growth scenarios that may arise in VHCF and is enough general to embrace the various weakening mechanisms proposed in the literature for explaining why crack can grow below the threshold. In the present paper, the model is generalized in a statistical framework. The statistical distributions of the crack growth threshold and of the initial defect size are put into the model. The procedure for the estimation of the Probabilistic‐S‐N curves and of the fatigue limit distribution is illustrated and numerically applied to an experimental dataset.