PSI - Issue 38

Matthias Hecht et al. / Procedia Structural Integrity 38 (2022) 251–259 Matthias Hecht et al. / Structural Integrity Procedia 00 (2021) 000–000 7 In comparison between loading with constant and variable amplitudes, the endurable amplitude can be up to approximately 65 % higher at = 10 6 cycles, which leads to a lightweight design potential. Furthermore, under variable amplitudes, a smaller distance between the Gassner line of tension and multiaxial loading ( = 0°) is observed, than it is between the Woehler lines of tension and multiaxial loading without phase shift ( = 0°). 3.2. Damage accumulation and damage sums For the damage accumulation the shown load sequence is accessed and counted using ASTM E1049-85 Rainflow Counting [18]. Subsequently, the nominal stress amplitudes are transformed to an -ratio of = 0.1 for which the Woehler lines, see Figure 3, has been determined. The mean stress sensitivity of the adhesively butt-bonded double hollow cylinder specimens is currently being investigated in an ongoing research project. As not all results are available at the time of the submission of this paper, a preliminary mean stress sensitivity is used in the different loading situations, Table 1. The transformed stress amplitudes are then used to assign a partial damage to each cycle via the Palmgren-Miner linear damage accumulation and the experimentally determined Woehler lines of S = 50 %. As the Woehler lines of adhesively bonded joints do not have a knee point, Figure 3, and none has been identified in the literature, the damage accumulation hypothesis Palmgren-Miner modified according to Cortan and Dolan is applied, as the knee point is not required there. The damage for each load cycles has been accumulated until a theoretical damage sum of th = 1 was derived. The number of cycles passed until this point is the calculated fatigue life � cal . Since an equal slope between Woehler and Gassner line is assumed, there is here no significant influence which amplitude is assumed for the load sequence. The experimental fatigue life � experiment is then determined from the Gassner line of S = 50 % at the supposed amplitude. Subsequently, the real damage sum is calculated by using real = � experiment � cal ( th =1 ) . (9) Due to a constant stress ratio between normal and shear stress for the multiaxial test series, it is possible to use only one load channel for simplification purposes in the damage accumulation. The real damage sums determined are listed in Table 2: 257

Real damage sum real , mean

Table 2. Determined real damage sums Loading

Normal and shear stress amplitude

, = 15.3 MPa , = 14.2 MPa

Pure tension Pure torsion

0.04 0.09

Multiaxial, = 0° , = 13.3 MPa, , = 6.7 MPa 0.33 The real damage sums vary depending on the load condition in a range from 0.04 ≤ real , mean ≤ 0.33. A clear dependence of the real damage sum on the load condition is shown.