PSI - Issue 65

D.G. Solomonov et al. / Procedia Structural Integrity 65 (2024) 275–281 D.G. Solomonov and M.Sh. Nikhamkin / Structural Integrity Procedia 00 (2024) 000–000

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Fig. 3. Examples of temperature fields on the sample surface at the end of the loading block at different values of relative strain amplitude in the block ε a /ε st

Fig. 4. Increasing maximum θ max and average θ mid temperatures in region A in the block with cyclic operation in the loading block with ε a /ε st = 0.38

To determine the fatigue limit, we used the dependences θ ���� ��� (ε a ) and θ ���� � �� (ε a ), as well as the dependences θ max (ε a ) и θ mid (ε a ). Four options for processing the results using each of these functions were compared. Let us consider the example of the dependence θ ���� ��� (ε a ) (Fig. 5a, where the strain ε a is related to the limiting strain during static tension of the shell material, ε st ). Experimental points are approximated by two straight lines as follows: θ ���� ��� ���� =� � ε � ε �� +� � ⁄ (3) θ ���� ��� ����� =� � ε � ε �� +� � ⁄ , where k 1 and b 1 are the coefficients of the left branch of the approximation; k 2 and b 2 are the coefficients of the right one (Fig. 5 a). The linear approximation coefficients of each branch k 1 , k 2 , b 1 , and b 2 were determined by the least squares method, and the quality of the approximation was assessed by the coefficient of determination R 2 . The graph field in Fig. 5 a shows the values of these coefficients, as well as the values of R 2 . In accordance with [14], the abscissa of the point of intersection of these lines ε � is taken as the strain corresponding to the fatigue limit, � � � �� = � � � � � � � � � � . (4) In a similar way, ε � is determined using the dependencies θ ���� � �� (ε a ), θ max (ε a ), and θ mid (ε a ), Fig. 5 a–d. It may not be obvious to assign experimental points lying near the intersection to the right or left branch of the approximation when processing the experimental results. Depending on the choice made, the approximation of both branches, the point of their intersection, and the resulting value of the fatigue limit change. For example, this point is circled in Fig. 5 a. In order to formalize the solution to this problem, it is proposed to proceed from the choice in which the approximation proves to be more accurate, i.e. in which the total value of the determination coefficients for the right and left branches � �� =� �� +� �� proves to be the largest. The values of strain ε � determined by the IRT method, corresponding to the fatigue limit of the samples, are given in the table. The value of ε � obtained in previous standard fatigue tests for samples from the same batch under the same loading conditions is also given there.