Required Fatigue Strength (RFS) for evaluating of spectrum loaded components by the example of cast-aluminium passenger car wheels

Dedicated to Prof. Dr. V. Grubisic for introducing the RFS-method into durability design.
https://doi.org/10.1016/j.ijfatigue.2020.105975Get rights and content

Highlights

  • Multiaxial load assumptions and determination of load spectra for a required service life by the example of a safety component and determination of fatigue critical spots of a complex component.

  • Derivation of required local material quality (Required Fatigue Strength RFS) for each critical spot under consideration of required probability of failure of the component and probability of occurrence of the service load spectrum.

  • Numerical and experimental durability proof of a safety component.

Abstract

This paper displays, through the example of a cast aluminium wheel (G-AlSi7Mg0.3 T6, i. e. EN AC-42100 T6 or A 356 T6), the evaluation of critical areas through the method of Required Fatigue Strength (RFS). The RFS-values are derived from the local design spectra of the most critical areas of the component by searching the position of local particular Woehler-lines resulting in the prescribed allowable damage sum Dal within the cumulative damage calculation by the modified Palmgren-Miner hypothesis according to Haibach. The RFS-value is nothing more than the knee point of the calculated Woehler-line with defined slopes and cycle position of the knee point.

As long as the production process delivers a material quality, i.e. a component related fatigue strength exceeding the calculated RFS-values, the required service durability is fulfilled. The paper demonstrates, through the example of a cast aluminium passenger car wheel, the evaluation of critical areas through RFS-values derived from the local design spectra of the most critical areas of the component and the experimental verification of the required service durability for 300,000 km and load occurrence probability of Po,Load ≤ 1%.

Introduction

The usual method for the development and evaluation of components or structures submitted to variable amplitude (spectrum) loadings is the cumulative fatigue life calculation, according to a suitable modification of the Palmgren-Miner hypothesis, e.g. the modification according to Haibach [1], [2], [3], [4]. For this approach, knowledge of local stress spectra resulting from service loads, of the positions of material and component-related local Woehler-lines for fatigue critical areas and of the allowable damage sum Dal, is necessary, Fig. 1. The fatigue life estimation is carried out according to equations (1), (2), while, in most cases, the allowable damage sum is, on the basis of experience, smaller than the theoretical value Dth = 1.0 [3], [4]:Ncal=(Ls/Dspec)·DalDspec=ni/ Ni

However, there is also another means of evaluating components without knowledge of the real level of the local Woehler-line. This is performed by the damage equivalent method of Required Fatigue Strength (RFS) founded by V. Grubisic in the early 1970ies [5]. Using this method, the minimum required level of the Woehler-line is derived. This paper, which is an extended version of [6], will demonstrate the RFS-method using the example of a cast aluminium wheel, by evaluating critical areas through RFS-values derived from local spectra of the most critical areas of the component.

Section snippets

Brief description of the Required Fatigue Strength (RFS)-method

For the determination of the RFS-value, the following prerequisites are needed: the slope before the knee point, the position of the knee point with regard to the number of cycles only (not the strength level) and the modified course after the knee point [3] must be fixed. Once these prerequisites are met, the starting Woehler-line is placed at an arbitrary fatigue strength level. Then the position of the searched local Woehler-line is derived by shifting the starting Woehler-line upwards or

Determination of load and local stress spectra for a cast aluminium wheel

In service, wheels are subjected to multiaxial loads in the vertical, horizontal and longitudinal directions under different driving conditions, e.g. straight line driving including rough road excitation, cornering, acceleration or braking, Fig. 4 [15].

Based on extensive service load measurements, a vast and reliable data bank for the durability design of wheels is available, containing load-related spectra for different driving conditions, Table 1 and Fig. 5 [7], [8], [9], [10]. In the case of

Determination of local required fatigue strengths

As already explained in Section 2, for the determination of a RFS-value, the following features of a Woehler-line must be assumed. These are given here for the cast aluminium alloy G-AlSi7Mg0.3 T6 (EN AC-42100 T6, A 356 T6): slope k = 5.0 before the knee point at Nk = 5 · 106 cycles and modified slope after the knee point for castings k′ = 2 k-2 = 8.0, according to Haibach for the consideration of the damage contribution of small amplitudes of the spectrum. The cumulative damage calculation,

Evaluation of local required fatigue strengths

In order to decide whether the calculated RFS-values are acceptable, knowledge of the achievable fatigue strength is necessary. For the wheels discussed here, this depends on the applied low-pressure casting technology of the manufacturer and on the quality control, focused especially on the highly stressed areas of the part. There is a large amount of data available from experience gained with unnotched and notched specimens, which were removed from different parts of passenger and truck

Experimental durability proof

The established biaxial proof of aluminium passenger car wheels applies a standardised load file “LBF Standard/Eurocycle” representing a spectrum of 10,000 km length, which is equivalent in damage to the design spectrum of 300,000 km with Po,Load ≤ 1% [27], [28], [29], [30], Fig. 15. The test spectrum consists of repeated sequences (rounds), each of 30 km, in the biaxial test rig, Fig. 16 [31], until 10,000 km testing distance is reached; each run of 30 km in the test rig corresponding to

Summary

The investigation presented a methodology for the durability design of spectrum-loaded safety components, suggesting the required local material quality to be provided by the manufacturing process. This was demonstrated using the example of a cast aluminium wheel for passenger cars. The required material quality is defined by the so called Required Fatigue Strength RFS, which is nothing other than the knee point of the lowest achievable Woehler-line. For its determination, the knowledge of the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

Dr. G. Fischer, retired head of the LBF-department “Stress Analysis and Strength Evaluation”, is acknowledged for his kind support regarding detailed information about the application of the RFS-method for the numerical durability proof of different safety components.

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