PSI - Issue 79

Daniel Hofferberth et al. / Procedia Structural Integrity 79 (2026) 313–321

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the yield strength. With this information, the endurable load amplitudes under alternating loading of each type of specimen were drawn on the ordinate of the Haigh-Diagram, and the endurable load amplitudes under pulsating tensile loading on the angle bisection (R = 0). By the definition of the means stress sensitivity M according to Schütz (Schütz65) equation (3) can be applied. �� � � � ������ � ����� � 1 (3)

Fig. 7: (a) Haigh-Diagram; (b) V 90% -Diagram

The resulting mean stress sensitivities M are listed in Table 3, resulting in values between M = 0.64 and M = 0.78 indicating a high influence of mean stresses on the fatigue behaviour of bonded specimens with PA12 matrix.

Table 3: Mean stress sensitivity according to Schütz

Specimen type

ISO 2740

ISO 3928 (R30)

ISO 3928 (R09)

Mean stress sensitivity M

0.64

0.78

0.65

The fatigue assessment approach based on the V 90% concept is commonly used for metallic materials including sintered components (Hofferberth10, Baumgartner2025) as well as glass fiber reinforced polyamide (Sonsino2008). Due to the consideration of the two size effects (statistical size effect and stress gradient effect), the results can be transferred for an assessment of various components. For the assessment, the knowledge of the results from fatigue tests for a probability of survival of P S = 50 % with constant or variable amplitude loading, the stress concentration factor for the calculation of local stresses and the highly stressed volume is required. The endurable local stress amplitude σ 1,max , calculated by using equation (1), is plotted over the highly stressed volume V 90% for each load ratio in a log-log diagram. The course of the resulting straight line for each stress ratio was calculated by a regression analysis and describes the correlation of statistical and stress gradient size influence [Schönborn15]. Equation (4) shows the known relationship between the endurable local stress amplitude and the V 90% . In case of materials with a statistically higher amount of weak spots, like fiber-reinforced PA materials, the highly stressed volume will be calculated for a larger material area, for a drop of the maximum stress of 20 %. The so called V 80% can be applied for an assessment of plastic components [Sonsino08]. The highly stressed volume diagram for bonded magnets, made of PA and NdFeB powder can be evaluated by for the investigated specimens. For this, the endurable local stress amplitudes ( � ⋅ � ) at �� 10 � cycles are evaluated and plotted versus the derived volume �� % , Fig. 7. The exponents of the power function were determined by a regression analysis to v = 0.065 for alternating loading and v = 0.066 for pulsating tensile loading for P S = 50 %. These values are slightly lower than the exponents of a sintered alloy (Distaloy AE + 0.6C) with density dependent exponents