Abstract
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.
Highlights
Formulation of the Root Finding Problem for Use in Newton’s Method In Section 2, the formulation of the root finding problem was described in the form defined in [25]. The disadvantage of this formulation is that it optimizes the difference of the strain εel,pl,RO calculated with the material behavior according to Ramberg and Osgood and εel,pl,NRA calculated with the notch root approximation
In the case of the extended notch root approximation according to Neuber, no special considerations have to be made with regard to stability
The theoretical background of notch root approximations is reviewed as far as it is necessary for practical implementation in the FKM Guideline nonlinear [25]
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. These variants differ primarily in the procedures used to determine the local stresses and strains, e.g., the notch root approximations [6,7,8,9,10,11,12,13,14,15,16], and in the load parameters used to evaluate the damage of individual stress-strain hystereses, [17,18,19,20,21,22,23,24] Both can have a significant influence on the calculation result of the component lifetime. The FKM Guideline nonlinear allows two different calculation procedures for fatigue strength assessment, which differ in the estimation of the local stresses and strains and the load parameter used. Bothelastic-plastic notch root approximations are used the FKM Guideline nonlinear in such a This relationship between the linear-elastic stress and elastic-plastic stress is called the way that they establish the relationship between a linear-elastically determined stress and load-notch-strain curve of the component.
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