Damage accumulation

Regardless of the fatigue concept comes with the respective specific WÖHLER lines used, the fatigue analysis must be performed in conjunction with appropriate damage accumulation hypotheses. For this, the actual stress range is simplistic in a manageable set of n blocks, each with a constant stress range is classified (see figure at right). The lifetime is then predicted computationally by means of accumulation of damage components from the individual load cycles each voltage collective. A common hypothesis for the damage accumulation is the rule according to

This rule is based on the assumption that, in the case of a vibrating stress, each closed hysteresis loop causes partial damage to the material in the notch base considered. With the number of oscillation cycles ni on a stress horizon ∆σi the partial damage ni/Ni is determined, which is linearly included in the sum of the total damage D. In this case Ni is the number of cycles to failure assigned to the stress horizon ∆σi for the WÖHLER line of the construction detail in question. 

Classification of the load spectrum

By definition, failure due to fatigue stress occurs under the simplified assumption if the sum of the partial damages ni/Ni reaches the value D = 1.

This rule is based on the assumption that, in the case of a vibrating stress, each closed hysteresis loop causes partial damage to the material in the notch base considered. With the number of oscillation cycles ni on a stress horizon ∆σi the partial damage ni/Ni is determined, which is linearly included in the sum of the total damage D. In this case Ni is the number of cycles to failure assigned to the stress horizon ∆σi for the WÖHLER line of the construction detail in question. By definition, failure due to fatigue loading occurs under the simplified assumption if the sum of the partial damages ni/Ni reaches the value D = 1.

Should a failure be prevented before a certain useful life, the loss amount must be D<1. The partial safety factors on the resistance side and other influences (e.g. plate thickness effect) are to be considered. At non-periodic stress can swing widths that are smaller than the threshold value of the fatigue strength, cause damage. In this case the horizontal threshold value is omitted.

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