PSI - Issue 28

1282 Fatih Kocatürk et al. / Procedia Structural Integrity 28 (2020) 1276–1285 Author name / Structural Integrity Procedia 00 (2019) 000–000 7 � . �sin � � � ∗ � cos � . �. � ��� � � .����� ��.� ∗ �� � � � � ��� � � . �� � �� .���� � � .����� ��.� ∗ ��� ∗ ��� � � � . � The following equation is obtained after some simplifications: �cos � . � � sin � . ∗ � t� � �.� � .��� � �. ����� � �� ∗ � ��� � � .� �� � �� .���� � � .����� ��.� ∗ ��� ∗ � (12)

Fig. 4. (a) Schematic representation of fracture cone and (b) two-dimensional fracture cone surface area.

Here, if the dividend and denominator of the right-hand side of the Eq. (12) are simplified by taking parenthesis of �.�� � � � on the right hand side of the equation, Eq. (13) is obtained: �cos � . � � sin � . ∗ � t� � �.� � � ∗ .�.�� �� � � ∗ � � � ��.� �� � �� .���� � � .����� ��.� ∗ ��� ∗ � (13) tan � � � � �� � �� � � � � �� � ��� � � .���� � � ��.� ∗ ��� �� � �� .���� � � .����� ��.� ∗ ��� ∗ � ���� � .����� ��.� ∗ ��� �.��� �.��� ��� � � .� ∗ (14) tan defined in Eq. (14) is substituted in Eq. (13) and the mathematical formula Eq. (15) is obtained after the mathematical operations such as cross-multiplication and square root. ��� � �� � � .��� � � ��.� � ���.� � .� ����� � � � ∗ � .��� � � ���� � � �� ��.� � ��.�.�.������ � � .���.��� � � .����� � � .� �.��� � � .���� � (15) The resulting Eq. (15) also takes into account the radius of the head to shaft transition region to calculate the maximum socket depth. In order to test the model derived in Eq. (15), the sample specified in Section 2 was used with the following parameters: ��� � �.�� ��� � � �.�� ��� � �.�� ��� � ∗ � ����� � � ��.�� . Socket diameter, � , was selected as the minimum diameter corresponding to N10 socket form.