Probabilistic formulation of the multiaxial fatigue damage of Liu

Calvo, S.; Canales, M.; Gómez, Christian; Valdés, José R.; Núñez, José Luis Martín

doi:10.1016/j.ijfatigue.2010.10.003

Cited by 14 publications

(10 citation statements)

References 14 publications

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“…Calvo et al 89 presented a statistical method based on the Liu–Wang model. The model follows a statistical approach to numerically solve Equations (23) and (24).…”

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

“…Therefore, Equation (25) can be rewritten as in Equation (26).

ε_{n, italicmax} = a + f . ε_{n, italicmin} + g . σ_{n, italicmax} + h . σ_{n, italicmin} + j . τ_{\max} + k . τ_{\min} + l . γ_{\max} + m . γ_{\min} + n . N_{f} + p . σ_{f}^{'} + q . ε_{f}^{'} + r . b + s . c,

where the multipliers of each term are the derivatives of ε n , max with respect to each random variable and are defined as explained in Calvo et al 89 Calvo et al 89 reorganized Equation (26) based on N f , because the objective is finding the value of it. To this end, the approximate mean and variance of N f was obtained via the expectation and variance operators as in Equations (27) and (28), respectively.…”

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

“…To this end, the approximate mean and variance of N f was obtained via the expectation and variance operators as in Equations (27) and (28), respectively.

E ([], N_{f}) = \sum_{i = 1}^{n} b_{i} X_{i} = {N_{f}|}^{0}, b_{i} = \frac{1}{n}, \frac{f}{n}, \frac{g}{n}, \frac{h}{n} \dots

italicVar ([], N_{f}) = \sum_{i = 1}^{n} {b_{i}}^{2} italicvar ([], X_{i}) .

Calvo et al 89 analyzed a cylindrical dog‐bone specimen under 28.5 kN of axial force and 10 N m of a torsional load. A perturbation finite element method (PFEM) was used to solve the equation on the entire domain of the model.…”

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

“…A perturbation finite element method (PFEM) was used to solve the equation on the entire domain of the model. Through this analysis, Calvo et al 89 calculated the stress tensor for each node and thus the corresponding fatigue life along with the statistical moments through the Equations (26)–(28). Then, they carried a Monte Carlo simulation out with 1500 samples to verify the results.…”

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

See 3 more Smart Citations

General quantification of fatigue damage with provision for microstructure: A review

Jirandehi

Khonsari

2021

Fatigue Fract Eng Mat Struct

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Recent developments in microstructure‐sensitive computational modeling and experimental verification have provided significant insight on how one can estimate fatigue damage and predict useful life. As a myriad of methods and approaches are available, it is important to understand how to properly utilize them in a unified and efficient framework for the quantification of damage in safety‐critical components such as jet engine fan blades, gas turbine disks, and airframe structural connections. To this end, the microstructure‐sensitive studies considering crystal plasticity are reviewed, and methods for implementing the statistical representations of material microstructure are presented. Finally, a computational crystal plasticity approach utilizing the statistical representation of parameters and a new thermodynamically based framework is suggested.

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“…Calvo et al 89 presented a statistical method based on the Liu–Wang model. The model follows a statistical approach to numerically solve Equations (23) and (24).…”

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

“…Therefore, Equation (25) can be rewritten as in Equation (26).

ε_{n, italicmax} = a + f . ε_{n, italicmin} + g . σ_{n, italicmax} + h . σ_{n, italicmin} + j . τ_{\max} + k . τ_{\min} + l . γ_{\max} + m . γ_{\min} + n . N_{f} + p . σ_{f}^{'} + q . ε_{f}^{'} + r . b + s . c,

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

“…To this end, the approximate mean and variance of N f was obtained via the expectation and variance operators as in Equations (27) and (28), respectively.

E ([], N_{f}) = \sum_{i = 1}^{n} b_{i} X_{i} = {N_{f}|}^{0}, b_{i} = \frac{1}{n}, \frac{f}{n}, \frac{g}{n}, \frac{h}{n} \dots

italicVar ([], N_{f}) = \sum_{i = 1}^{n} {b_{i}}^{2} italicvar ([], X_{i}) .

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

Section: Microstructure‐sensitive Studies Using Statistical Representationmentioning

confidence: 99%

See 2 more Smart Citations

General quantification of fatigue damage with provision for microstructure: A review

Jirandehi

Khonsari

2021

Fatigue Fract Eng Mat Struct

View full text Add to dashboard Cite

show abstract

“…According to this, Ince et al [ 29 ] developed two different forms of multiaxial fatigue damage parameters based on generalized strain energy, which define the specific planes with the maximum amount of fatigue damage. Besides, probabilistic formulations of multiaxial fatigue damage have been investigated by [ 30 , 31 , 32 , 33 , 34 , 35 ], which open new perspectives for introducing the probabilistic approaches to a number of very general problems for estimating fatigue life of engineering components.…”

Section: Introductionmentioning

confidence: 99%

A New Energy-Critical Plane Damage Parameter for Multiaxial Fatigue Life Prediction of Turbine Blades

Zhu

Liu

et al. 2017

Materials

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As one of fracture critical components of an aircraft engine, accurate life prediction of a turbine blade to disk attachment is significant for ensuring the engine structural integrity and reliability. Fatigue failure of a turbine blade is often caused under multiaxial cyclic loadings at high temperatures. In this paper, considering different failure types, a new energy-critical plane damage parameter is proposed for multiaxial fatigue life prediction, and no extra fitted material constants will be needed for practical applications. Moreover, three multiaxial models with maximum damage parameters on the critical plane are evaluated under tension-compression and tension-torsion loadings. Experimental data of GH4169 under proportional and non-proportional fatigue loadings and a case study of a turbine disk-blade contact system are introduced for model validation. Results show that model predictions by Wang-Brown (WB) and Fatemi-Socie (FS) models with maximum damage parameters are conservative and acceptable. For the turbine disk-blade contact system, both of the proposed damage parameters and Smith-Watson-Topper (SWT) model show reasonably acceptable correlations with its field number of flight cycles. However, life estimations of the turbine blade reveal that the definition of the maximum damage parameter is not reasonable for the WB model but effective for both the FS and SWT models.

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Modeling Crack Initiation in Low Cycle Fatigue: A Review

Zahran

Zinovev

Terentyev

et al. 2022

Proceedings of the 10th International Conference on Fracture Fatigue and Wear

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The typical fatigue life of a component is mainly divided into two phases: crack initiation, and crack propagation. This study is concerned with the crack initiation life as some designers regard the crack initiation as the end of the design life of the component. Crack initiation is caused by the formation of persistent slip bands that interact with the matrix leading to embryonic crack formation. There are several studies defining the point of crack initiation, and this article addresses some of these definitions. The main aim of this study is to review the different modelling methodologies for crack initiation under low cycle fatigue. These models are divided into three main types: microscopic models, damage parameters, and probabilistic models. There is no preferred methodology among the ones discussed. The choice of which model to use depends on the type of loading, the material in use, and the required level of detail. This study is intended as a reference for using one of these models or introducing modifications to enhance them.

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Probabilistic formulation of the multiaxial fatigue damage of Liu

Cited by 14 publications

References 14 publications

General quantification of fatigue damage with provision for microstructure: A review

General quantification of fatigue damage with provision for microstructure: A review

A New Energy-Critical Plane Damage Parameter for Multiaxial Fatigue Life Prediction of Turbine Blades

Modeling Crack Initiation in Low Cycle Fatigue: A Review

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