PSI - Issue 28

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Author name / Structural Integrity Procedia 00 (2019) 000–000

242 Kris Hectors et al. / Procedia Structural Integrity 28 (2020) 239–252 damage can be correlated to the cycle ratio � � depending on the stress level that is applied. Based on the damage curve concept, Manson and Halford (Manson and Halford 1981) proposed the damage curve approach (DCA) that expresses the damage as a function of the cycle ratio and a postulated initial flaw size � (expressed in inches). The damage after a multi-level block load spectrum with sequences is expressed as: � � 0. 1 18 � � � �0.18 � � � � � � � �� � �.� � �5� with � � ���� � � � � �,� � � � � � �,� � � � � �� � �,� � �� ��� ����� � � ���,� � � � ��� ���,� � � ��� � � �.� �7� Here � and � are the applied number of cycles and the number of cycles to failure for a stress level � respectively. 1, 2, …, are the sequence numbers of the block loading. For constant amplitude loading this model reduces to Miner’s rule. A detailed derivation of this model can be found in the original work (Manson and Halford 1981). For the damage calculations in this paper � is assumed to be zero. 2.3. Modified damage curve approach In 2014, Gao et al. (Gao et al. 2014) proposed a non-linear damage accumulation model that is a modified version of the original damage curve approach. In order to include load interaction effects that are not considered by the original damage curve model, they suggested that the exponent ���,� (defined in equation 6) should be modified. An interaction factor defined as the ratio between the stress amplitude of the current load cycle and the previous load cycle was added. The new definition of ���,� is shown in equation 8. ���,� � � ��� � � �.� ����� � ��� � � , � � � ��� � �8� The idea of accounting for load interaction effects in this way was not novel, similar interaction factors with the same purpose can be found in the Freudenthal-Heller model (Freudenthal and Heller 1959) and the Corten-Dolan model (Corten and Dolan 1956). Except for the addition of a load interaction factor, there is another major difference between the model of Gao et al. and the original model of Manson and Halford. Although Gao et al. proposed the model as a modified version of the damage curve approach, both models are inherently different. Gao et al. define failure to occur when equation 6, where ���,� is determined using equation 8, equals to one. However, Manson and Halford define failure to occur when the damage as defined in equation 5 equals to one. Gao et al. omit the use of equation 5 and therefore, strictly speaking, their model is not a damage accumulation model but a lifetime prediction model. The important difference being that no physical parameter is linked to the occurrence of failure. 2.4. Damage stress model The damage stress model (DSM) was proposed by Mesmacque et al. (Mesmacque et al. 2005) with the intention of introducing a new damage indicator that is directly related to the S-N curve of the material. For an undamaged structure the lifetime can be assessed using the S-N curve. Mesmacque et al. introduced the idea that this concept can be extended to a damaged structure through the damage stress concept. Assume a structure was loaded with a stress � for � cycles. The residual lifetime can then be calculated as � � � . The residual lifetime,