PSI - Issue 33

Davide Palumbo et al. / Procedia Structural Integrity 33 (2021) 528–543

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� � � � √��� cos � � �� � ��� � � � , � � � � √��� cos � � �� � ��� � � � ��2� Under a generic sinusoidal loading in which the load changes between its maximum and minimum values, P min and P max , the SIF ratio R can be defined as: � � ��� � ��� � � ���� � ���� , �� � �� � � � � � � � �� � ���� with K Imin and K Imax , the minimum and maximum value of SIF and K Im , K Ia the mean and the amplitude values of SIF, respectively. In this way, the instantaneous value of SIF can be expressed as: � � � � �� � �� s�� � �� � � � s�� � ���� and the principal stresses and their rate of change, become: � � � �� √��� cos � � �� � ��� � � � � � � s�� � , � � � �� √��� cos � � �� � ��� � � � � � � s�� � ���� � � � � �� √��� cos � � �� � ��� � � � cos , � � � � �� √��� cos � � �� � ��� � � � cos ���� ���� Substituting Equations (15), (16) and (17) in Eq. (9), neglecting the static components, we obtain an equation that can be expressed as the sum of two functions f 1 and f 2 multiplied for cos( ω t) and sin(2 ω t) : �� � � � cos � � s�� 2 ���� Where � � � � √ � � � �� � � � � � � �� cos � � � � 2 cos � � �� � ��� � �� � � � � � �� cos � � � � �� � s�� � � � �� (19) and � � � � � � � cos � � � � �� � ��� � �� � � � �� � �� cos � � � �� � s�� � � � �� (20) By integrating Eq. (18), considering Δ T<