PSI - Issue 38

Matthias Hecht et al. / Procedia Structural Integrity 38 (2022) 251–259

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Matthias Hecht et al. / Structural Integrity Procedia 00 (2021) 000–000

1. Introduction In the context of electromobility, aspects of lightweight designs are becoming increasingly relevant, for example to increase the vehicles range in distance. Steel-intensive lightweight design concepts are therefore being further developed, particularly for automotive body structures. Adhesive bonding is a particularly suitable joining technique, as it enables high material utilization due to the laminar load transfer. It also has positive properties in terms of crash behavior, damping and electrochemical separation. In most applications, the in-service loading of bonded joints is complex: A multiaxial stress state is present that is often non-proportional. In addition, variable amplitude loading must be considered. A generally valid and reliable assessment method does not yet exist. Therefore, in current practice, bonded joints are probably often over dimensioned, leading to a not fully exploited lightweight potential. In this paper, investigations on adhesively butt-bonded double hollow cylinder specimens with respect to the service life under multiaxial loading with variable amplitudes are presented. It is shown how a pure tensile or torsional load and a multiaxial load with and without phase shift affect the fatigue life. In addition, real damage sums for tensile, torsional und multiaxial loading without phase shift are derived. 1.1. Variable amplitude loading The first investigations on fatigue behavior under variable amplitudes were carried out by Ernst Gassner [1]. In contrast to Woehler tests commonly used at that time, the specimens were loaded by many blocks of different amplitudes instead of one block with constant amplitudes over the entire test. Since servo-hydraulic testing machines have been used for fatigue tests, more complex and realistic random load spectra can be applied. To characterize such tests, it is necessary to specify the load sequence, the maximum value of stress � max , the stress amplitude � a , the ratio � = � min � max (1) between the minimum � min and the maximum of stress � max , the sequence length s , and the sequence shape [2]. When selecting the load sequence, care must be taken that it is run through at least five to ten times during the test [3]. A partial damage is determined from the stress amplitudes of the Gassner test using the Woehler line and the total damage is determined from the partial damages [4]. For this purpose, the total damage sum of the spectrum (cumulative frequency distribution) [2] tot = ∑ i i n i=1 (2) is calculated from the sum of the quotients between the number of cycles at a load amplitude and the corresponding endurable load amplitudes from the Woehler line . Finally, the lifetime is calculated from the total damage sum under the assumption that failure occurs as soon as the damage sum reaches the value of one. cal = s real cal (3) al ≤ real ≤ th = 1 (4) To determine the partial damage, following variants of the Palmgren-Miner rule are mostly used [5]: In the first proceeded original form it is assumed that loads below the knee point of the Woehler line do not contribute to the damage [6]. In the modification by Cortan and Dolan, these loads are taken into account by a continuation with the same slope of the Woehler line after the knee point ′ = [7]. In Palmgren-Miner modified according to Haibach the slope after the knee point is defined by ′ = 2 − , depending on the material [8]. Theoretically, failure occurs at the theoretical damage sum of th = 1 [6]. In reality, the damage sum up to failure varies highly and the average is often below the theoretical value of th = 1. This has already been investigated many times for base materials and welded joints [9].