A probabilistic interpretation of the Miner number for fatigue life prediction

The Miner number M, used as a tool for lifetime prediction of mechanical and structural components in most of the standards related to fatigue design, is generally accepted as representing a damage stage resulting from a linear progression of damage accumulation. Nonetheless, the fatigue and damage approach proposed by Castillo and Fernández-Canteli, permits us to reject this conventional cliché by relating M to the normalized variable V, which represents percentile curves in the S-N field unequivocally associated to probability of failure. This approach, allowing a probabilistic interpretation of the Miner rule, can be applied to fatigue design of mechanical and structural components subjected to variable amplitude loading. The results of an extensive test program on concrete specimens under compressive constant and load spectra, carried out elsewhere, are used. A parallel calculation of the normalized variable V and the Miner number M is performed throughout the damage progression due to loading allowing probabilities of failure to be assigned to any value of the current Miner number. It is found that significant probabilities of failure, say P=0.05, are attained for even low values of M, thus evidencing the necessity of a new definition of the safety coefficient of structural or machine components when the Miner rule is considered. The experimental and analytical probability distributions of the resulting Miner numbers are compared and discussed, the latter still providing a nonconservative prediction in spite of the enhancement. A possible correction is analyzed

A probabilistic approach for multiaxial fatigue criteria

Models proposed to study the multiaxial fatigue damage phenomenon generally lack probabilistic interpretation due to their deterministic form. This implies failure compulsory happening at the plane exhibiting the maximum damage value, whereas the remaining planes are disregarded. Nevertheless, the random orientation of the predominant defect evidences the possibility of failure being initiated as a function of the predominant defect presence without requiring, necessarily, maximum values of the damage parameter, which emphasizes the need of introducing probabilistic concepts into the failure prediction analysis. In this paper, a probabilistic model is presented that enables the failure probability to be found for any selected plane orientation by considering the damage gradient as a parameter for both proportional and non-proportional loading. The applicability of the model is elucidated by means of an example. Assuming the cdf for the local failure of the material to be known, the probability of failure is calculated for a cross shaped specimen in which shift between the principal stresses sigma xx and sigma yy ranges from 0º to 180º

Evaluación de resultados de fatiga con alto y ultra alto número de ciclos mediante un modelo de regresión de Weibull

El modelo de fatiga de regresión de Weibull, propuesto por Castillo-Canteli, representa una alternativa posible y adecuada para la evaluación y predicción de vidas de fatiga ultra altas (VHCF). Este modelo proporciona una definición probabilística del campo S-N para los posibles mecanismos de rotura determinantes, basada en distribuciones de Weibull de mínimos, así como la existencia de un límite de fatiga asintótico y la propiedad de reducir todo el campo SN a una única función de distribución mediante la variable normalizada V=(log N-B)(log Δσ-C). De este modo, el doble mecanismo de rotura, interno y superficial, que caracteriza las vidas altas (HCF) y ultra altas (VHCF) en fatiga puede ser satisfactoriamente tratado como distribuciones independientes en este particular y complejo caso de muestras con resultados concurrentes, conocido como problema de datos confundidos. Una vez estimados los parámetros de ambas funciones de distribución se procede a la combinación y reconversión de ambas como campo S-N conjunto. El modelo permite establecer una estrategia para optimizar la programación de los ensayos. Por último se presentan dos ejemplos de aplicación, uno de un programa externo experimental y otro de resultados simulados, ambos con ultra alto número de ciclos y dos posible mecanismos de rotura.The fatigue Weibull regression model proposed by Castillo-Canteli represents a possible and adequate alternative for the assessment and prediction of very high cycle fatigue (VHCF) lifetimes. This model provides a probabilistic definition of the S-N field for the two determining failure mechanisms based Weibull distributions for minima, as well as the existence of an asymptotic fatigue limit and the capability to reduce the S-N field to a single cumulative distribution function by considering the normalized variable V=(log N-B) (log Δσ). In this way, both dual fracture mechanisms, i.e. the internal and the surface ones, characterizing the HCF and VHCF data can be adequately interpreted and handled as independent distributions in such a particular and complex case of concurrent populations, known as a confounded data problem. Once the model parameters of both normalized cumulative distribution functions are independently estimated for both failure mechanisms and subsequently combined and reconverted to a joint S-N field whereby. The model allows a test strategy to be established for optimizing the the fatigue program planning. Finally, two examples of application are presented, the first related to an external experimental program, and the second to simulated data both for VCCF with twofold failure mechanisms

Generalización del modelo probabilístico de Weibull mediante un parámetro energético basado en el gradiente de deformación

En este trabajo se analiza la aplicabilidad del parámetro generalizado de referencia GP = E(σmax (dε/dσ)max - σmin (dε/dσ)min), como sustitutivo al rango de tensiones convencional, Δσ = σmax - σmin , en un intento de superar las limitaciones evidenciadas en el modelo básico probabilístico de Weibull propuesto por Castillo y Fernández Canteli, en particular en lo referente a la superación de la tensión última, ahora evitada, y a la ambigua interpretación del parámetro B, que define la vida mínima garantizada. Los gradientes de deformación se calcularían a partir del diagrama cíclico tensión-deformación del material, definido, en principio, analíticamente. Con esta aproximación, se trata de representar el fenómeno de fatiga más adecuadamente que mediante el parámetro convencional Δσ , pero sobre todo de extender la aplicabilidad del modelo al dominio de fatiga de bajo número de ciclos. El resultado final como campo GPN puede reconvertirse, opcionalmente, a la forma tradicional del campo Δσ ? N que debería adoptar ahora una forma sigmoidal típica del campo experimental S-N, permitiendo el ajuste en la zona de bajo número de ciclos. Se discute la adecuación física del parámetro generalizado propuesto y se presenta un ejemplo de aplicación del nuevo modelo en la evaluación de resultados experimentales. El resultado no satisfactorio permite, sin embargo, algunas conclusiones de interés práctico.In this work, the applicability of the energetic reference parameter GP= E(σmax (dε/dσ)max - σmin (dε/dσ)min) is analyzed as an alternative to the conventional stress range Δσ = σmax - σmin , aiming at overcoming the limitations evidenced by the basic version of the Weibull probabilistic model of Castillo and Fernández Canteli. In this way, overpassing of the ultimate stress and the necessity of considering the dubious interpretation of the B parameter representing the minimum possible lifetime, is eluded. The strain gradients are calculated from the cyclic stress-strain curve of the material. With this approach a more reliable description of the fatigue progress, as that using the conventional Δσ parameter, is pursued but foremost an extension of the applicability of the probabilistic model to the low cycle fatigue domain. The final result as a GP-N field can be optionally reconverted to the conventional of the Δσ ? N field, which should speculatively adopt the typical sigmoidal shape fitting the experimental S-N field in the LCF region. The physical adequacy of the generalized parameter proposed is discussed and an example of application of the new model is introduced for the assessment of experimental data. The non-satisfactory result allows some conclusions of practical interest to be drawn.Los autores agradecen el apoyo obtenido prestado a través de Proyecto de investigación BIA2013- 48352-P del Ministerio Español de Economía y Competitividad, así como del Proyecto SV-PA-11- 012 y el apoyo obtenido por las Ayudas Predoctorales del Programa Severo Ochoa recibidas por el Gobierno Regional del Principado de Asturias

Evaluation of fatigue properties of S355 J0 steel using ProFatigue and ProPagation software

European Conference on Fracture - ECF22 - Loading and Environmental effects on Structural Integrity (22nd, 2018, Belgrade, Serbia

Generalization of the Weibull probabilistic compatible model to assess fatigue data into three domains: LCF, HCF and VHCF

In this work, three classes of fatigue models are reviewed according to the fatigue regimes commonly considered in the current components design. Particular attention is devoted to the so-called Class III fatigue models, covering the three fatigue regimes, namely, LCF, HCF and VHCF. The applicability and limitations of the proposed analytical sigmoidal solutions are discussed from the viewpoint of practical design. The compatible Weibull S-N model by Castillo and Canteli is revisited and improved by considering a new reference parameter GP = E·σM ·(dε/dσ)|M as the driving force alternative to the conventional stress range. In this way, the requirement, σM ≤ σu, according to the real experimental conditions, is fulfilled and the parametric limit number of cycles, N0, recovers its meaning. The probabilistic definition of the model on the HCF and VHCF regimes is maintained and extended to the LCF regime. The strain gradients may be calculated from the monotonic or cyclic stress–strain curve of the material although a direct derivation from the hysteresis loop is recommended. Some Class III fatigue models from the literature and another one improved by the authors are applied to the assessment of one experimental campaign under different stress ratios conditions and the results compared accordingly. Finally, the new probabilistic GP-N field is evaluated. The results confirm the practical confluence of the stress- and the strain-based approaches into a single and advantageous unified methodology.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Steel & Composite Structure

Finite life and propagating crack considerations for an extended interpretation of the Kitagawa-Takahashi diagram

Considerations resulting from S-N field analyses on the existence or non-existence of fatigue limit [1,2], besides being an everlasting topic of discussion in the fracture mechanics community, give rise to promote a more profound comprehension of some issues related to the Kitagawa-Takahashi (K-T) diagram, thus continuing former works of the authors [3,4]. To do this, arguments are provided to illustrate the necessity of revising some of the influencing concepts in the current conventional interpretation of the K-T diagram, such as the transcendence of considering probabilistic S-N field approaches avoiding arbitrary, deterministic bi- and trilinear S-N models (Fig. 1), which necessarily imply the K-T diagram to be referred to a defined finite lifetime, see [5], the contradictory definition of non-propagating cracks [6] and the necessary identification of the K-T with a particular fatigue mechanism. In this way, a probabilistic extension of the K-T diagram for finite life predictions is ensured even in the VHCF region with multiplicity of mechanisms (Fig. 2). It is hoped that this approach will enhance understanding, effectiveness and reliability of the K-T applications in practical component design