The classical Palmgren‐Miner (PM) rule, despite clearly approximation, is commonly applied for the case of variable amplitude loading, and to date, there is no simple alternative. In the literature, previous authors have commented that the PM hypothesis is based on an exponential fatigue crack growth law, ie, when da/dN is proportional to the crack size a, the case that includes also Paris law for m=2, in particular. This is because they applied it by updating the damage estimate during the crack growth. It is here shown that applying PM to the “initial” and nominal (Stress vs Number of cycles) curve of a cracked structure results exactly in the integration of the simple Paris power law equation and more in general to any crack law in the form da/dN=HΔσhan. This leads to an interesting new interpretation of PM rule. Indeed, the fact that PM rule is often considered to be quite inaccurate pertains more to the general case when propagation cannot be simplified to this form (like when there are distinct initiation and propagation phases), rather than in long crack propagation. Indeed, results from well‐known round‐robin experiments under spectrum loading confirm that even using modified Paris laws for crack propagation, the results of the “noninteraction” models, neglecting retardation and other crack closure or plasticity effects due to overloads, are quite satisfactory, and these correspond indeed very closely to applying PM, at least when geometrical factors can be neglected. The use of generalized exponential crack growth, even in the context of spectrum loading, seems to imply the PM rule applies. Therefore, this seems closely related to the so‐called lead crack fatigue lifing framework. The connection means however that the same sort of accuracy is expected from PM rule and from assuming exponential crack growth for the entire lifetime.

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A 3D peridynamic formulation of the thermo-mechanical problem allows to efficiently simulate the occurrence and propagation of cracks due to extreme thermal loading. The model is weakly coupled since no internal heat generation due to material deformation and damage is accounted for. As such, it is suitable to simulate low strain rate phenomena. Since the typical time scales of the mechanical and thermal systems may differ of several orders of magnitude, using a multirate explicit integration technique is suggested by the nature of the problem itself. Finally, the proposed formulation is used to model the thermal shock behavior of thin and thick slabs, in order to observe respectively a 2D ordered set of parallel cracks and a 3D honeycomb crack pattern addressed as columnar jointing