A technique to estimate the local multiaxial elastic–plastic behavior from a purely elastic solution

McDonald, Russell J.; Socie, D. F.

doi:10.1016/j.engfracmech.2010.12.001

Cited by 10 publications

(3 citation statements)

References 12 publications

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“…The still unknown proportionality factor f σ or f ε has to fulfil Equation or . An extension of this approach with respect to mixed stress and strain boundary conditions has been proposed in McDonald and Socie …”

Section: Crack Initiation Under Local Nonproportional Stresses and Stmentioning

confidence: 99%

“…An extension of this approach with respect to mixed stress and strain boundary conditions has been proposed in McDonald and Socie. 16,17 In their practical applicability for multiaxial nonproportional in-service loading, the mentioned incremental notch simulation approaches have the following disadvantages:…”

Section: Calculation Of Local Nonproportional Stresses and Strainsmentioning

confidence: 99%

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Fatigue of engineering structures under combined nonproportional loads: An overview

Vormwald

Hertel

Zerres

2018

Fatigue Fract Eng Mat Struct

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Nonproportionality in fatigue is a matter of loading sequences acting on structures. In such loading cases, a life assessment‐based search of the initiation site is required. This means that for a variety of potential sites, their stress‐strain sequences must be determined and the corresponding fatigue lives have to be calculated. For the determination of local stress‐strain sequences, a superposition of the action of loads at all times for all potential sites must be performed. The superposition has not only to be performed at a particular time of a load reversal but also for a sufficiently large number of intermediate points in time. For the assessment of crack initiation under local nonproportional stress‐strain sequences, a multiaxial fatigue damage hypothesis must be specified. Due to the superiority with respect to accuracy, critical plane approaches are the favourite ones when dealing with nonproportional fatigue of ductile metals. For describing fatigue crack growth, the time sequences for the stress intensity factors corresponding to the 3 opening modes must be obtained by superposition. A mixed‐mode hypothesis must be applied to predict both the direction and the increment of crack growth at each crack front point. A first prediction trial should be based on an appropriate extension of the maximum tangential stress hypothesis. An application of a variant of the maximum shear stress hypothesis might be an amendment. Especially in the case of crack turning, the consideration of crack face contact is mandatory.

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Section: Crack Initiation Under Local Nonproportional Stresses and Stmentioning

confidence: 99%

Section: Calculation Of Local Nonproportional Stresses and Strainsmentioning

confidence: 99%

Fatigue of engineering structures under combined nonproportional loads: An overview

Vormwald

Hertel

Zerres

2018

Fatigue Fract Eng Mat Struct

View full text Add to dashboard Cite

show abstract

“…Fatigue life prediction of notched components in complex service conditions requires the local stress-strain relationship of a material element at the notch-root to be known [1]. The notch stress-strain analysis and low-cycle fatigue concepts are often used in fatigue analysis to estimate crack initiation lives [2].…”

Section: Introductionmentioning

confidence: 99%

A Modified Method for Calculating Notch-Root Stresses and Strains under Multiaxial Loading

Liu

Wang

Jin

et al. 2014

Advances in Mechanical Engineering

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Based on the analysis of notch-root stresses and strains in bodies subjected to multiaxial loading, a quantitative relationship between Neuber rule and the equivalent strain energy density method is found. In the case of elastic range, both Neuber rule and the equivalent strain energy density method get the same estimation of the local stresses and strains. Whereas in the case of elasticplastic range, Neuber rule generally overestimates the notch-root stresses and strains and the equivalent strain energy density method tends to underestimate the notch-root stresses and strains. A modified method is presented considering the material constants of elastic-plastic Poisson's ratio, elastic modulus, shear elastic modulus, and yield stress. The essence of the modified model is to add a modified coefficient to Neuber rule, which makes the calculated results tend to be more precise and reveals its energy meaning. This approach considers the elastic-plastic properties of the material itself and avoids the blindness of selecting coefficient values. Finally the calculation results using the modified model are validated with the experimental data.

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A plastic correction algorithm for full-field elasto-plastic finite element simulations: critical assessment of predictive capabilities and improvement by machine learning

Palchoudhary,

Peter,

Maurel

et al. 2024

Comput Mech

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This paper introduces a new local plastic correction algorithm that is aimed at accelerating elasto-plastic finite element (FE) simulations for structural problems exhibiting localised plasticity (around e.g. notches, geometrical defects). The proposed method belongs to the category of generalised multi-axial Neuber-type methods, which process the results of an elastic prediction point-wise in order to calculate an approximation of the full elasto-plastic solution. The proposed algorithm relies on a rule of local proportionality, which, in the context of J2 plasticity, allows us to express the plastic correction problem in terms of the amplitude of the full mechanical tensors only. This lightweight correction problem can be solved for numerically using a fully implicit time integrator that shares similarities with the radial return algorithm. The numerical capabilities of the proposed algorithm are demonstrated for a notched structure and a specimen containing a distribution of spherical pores, subjected to monotonic and cyclic loading. As a second point of innovation, we show that the proposed local plastic correction algorithm can be further accelerated by employing a simple meta-modelling strategy, with virtually no added errors. At last, we develop and investigate the merits of a deep-learning-based corrective layer designed to reduce the approximation error of the plastic corrector. A convolutional architecture is used to analyse the neighbourhoods of material points and outputs a scalar correction to the point-wise Neuber-type predictions. This optional brick of the proposed plastic correction methodology relies on the availability of a set of full elasto-plastic finite element solutions to be used as a training data-set.

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A technique to estimate the local multiaxial elastic–plastic behavior from a purely elastic solution

Cited by 10 publications

References 12 publications

Fatigue of engineering structures under combined nonproportional loads: An overview

Fatigue of engineering structures under combined nonproportional loads: An overview

A Modified Method for Calculating Notch-Root Stresses and Strains under Multiaxial Loading

A plastic correction algorithm for full-field elasto-plastic finite element simulations: critical assessment of predictive capabilities and improvement by machine learning

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