Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations

An estimation of the elastic-plastic stress state using elasticity-theoretical input data is an essential part of the service life estimation with the local strain approach in general and a German guideline based on it, in particular. This guideline uses two different notch root approximations (an e...

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Autores principales:	Ralf Burghardt, Lukas Masendorf, Michael Wächter, Alfons Esderts
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Neuber’s rule fatigue life calculation notch strains notch stresses fatigue of materials local strain approach Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/3db04c40d8134e90b6c17079626acaa3
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spelling	oai:doaj.org-article:3db04c40d8134e90b6c17079626acaa32021-11-11T15:21:49ZDetermination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations10.3390/app1121103392076-3417https://doaj.org/article/3db04c40d8134e90b6c17079626acaa32021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10339https://doaj.org/toc/2076-3417An estimation of the elastic-plastic stress state using elasticity-theoretical input data is an essential part of the service life estimation with the local strain approach in general and a German guideline based on it, in particular. This guideline uses two different notch root approximations (an extended version of Neuber’s rule and an approach according to Seeger and Beste) for this estimation. Both require the implementation of Newton’s method to be iteratively solved. However, many options are left open to the user concerning implementation in program code. This paper discusses ways in which notch root approximation methods can be implemented efficiently for use in software systems and elaborates an application recommendation. The following aspects and their influence on the computational accuracy and performance of Newton’s method are considered in detail: influence of the formulation of the root finding problem, determination of the derivative required for Newton’s method and influence of the termination criterion. The investigation shows that the advice given in the abovementioned guideline indeed leads to a conservative implementation. By carefully considering the investigated aspects, however, the computational performance can be increased by approximately a factor of 2–3 without influencing the accuracy of the service life estimation.Ralf BurghardtLukas MasendorfMichael WächterAlfons EsdertsMDPI AGarticleNeuber’s rulefatigue life calculationnotch strainsnotch stressesfatigue of materialslocal strain approachTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10339, p 10339 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Neuber’s rule fatigue life calculation notch strains notch stresses fatigue of materials local strain approach Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	Neuber’s rule fatigue life calculation notch strains notch stresses fatigue of materials local strain approach Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Ralf Burghardt Lukas Masendorf Michael Wächter Alfons Esderts Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations
description	An estimation of the elastic-plastic stress state using elasticity-theoretical input data is an essential part of the service life estimation with the local strain approach in general and a German guideline based on it, in particular. This guideline uses two different notch root approximations (an extended version of Neuber’s rule and an approach according to Seeger and Beste) for this estimation. Both require the implementation of Newton’s method to be iteratively solved. However, many options are left open to the user concerning implementation in program code. This paper discusses ways in which notch root approximation methods can be implemented efficiently for use in software systems and elaborates an application recommendation. The following aspects and their influence on the computational accuracy and performance of Newton’s method are considered in detail: influence of the formulation of the root finding problem, determination of the derivative required for Newton’s method and influence of the termination criterion. The investigation shows that the advice given in the abovementioned guideline indeed leads to a conservative implementation. By carefully considering the investigated aspects, however, the computational performance can be increased by approximately a factor of 2–3 without influencing the accuracy of the service life estimation.
format	article
author	Ralf Burghardt Lukas Masendorf Michael Wächter Alfons Esderts
author_facet	Ralf Burghardt Lukas Masendorf Michael Wächter Alfons Esderts
author_sort	Ralf Burghardt
title	Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations
title_short	Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations
title_full	Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations
title_fullStr	Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations
title_full_unstemmed	Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations
title_sort	determination of local stresses and strains within the notch strain approach: efficient implementation of notch root approximations
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3db04c40d8134e90b6c17079626acaa3
work_keys_str_mv	AT ralfburghardt determinationoflocalstressesandstrainswithinthenotchstrainapproachefficientimplementationofnotchrootapproximations AT lukasmasendorf determinationoflocalstressesandstrainswithinthenotchstrainapproachefficientimplementationofnotchrootapproximations AT michaelwachter determinationoflocalstressesandstrainswithinthenotchstrainapproachefficientimplementationofnotchrootapproximations AT alfonsesderts determinationoflocalstressesandstrainswithinthenotchstrainapproachefficientimplementationofnotchrootapproximations
_version_	1718435360992657408

Determination of Local Stresses and Strains within the Notch Strain Approach: Efficient Implementation of Notch Root Approximations

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