PSI - Issue 13

Hiroaki Ito et al. / Procedia Structural Integrity 13 (2018) 1105–1110 Author name / Structural Integrity Procedia 00 (2018) 000–000 5. Step 4 is repeated until the crack depth (i.e. the total of widths of grain lines and � ) reaches the thickness of the specimen. (Fig. 1 (4)) 2.2. K value calculation for three dimensional stress distribution Stress intensity factor at the crack tip, , is employed to calculate CTOD . And then, the weight function is employed in order to calculate for elliptical or semi-elliptical cracks with stress distributions, as shown in Fig. 2. is calculated by integrating weight function and the stress distribution, expressed as � � � � � � , , , � � � (2) where a is the crack depth from the surface in mm, � � is the stress distribution as the function of x in MPa, � , , � � , � � � is the weight function (Glinka et al., 1991), expressed as � , , , � � �2 � 2 � � �1 � � �1 � � � � � � �1 � � � � �1 � � � � � (3) where 1 , 2 and 3 are the functions of a/t and a/c . 1107 3

x

A

x

a

t

2c

y

Fig. 2 Notation for the semi-elliptical surface crack under one-dimensional stress field

2.3. Modeling of the fatigue crack closure Newman proposed a general equation for crack opening stress of a long crack (Newman, 1984), expressed as �� ��� � 0.�3� �o� ��� 2 � � 0.344 ��� � R σ � � � � � 2 (4) (5) where is the maximum normal stress in MPa, R is the stress ratio, is the yield strength in MPa and is the ultimate tensile strength in MPa. McEvily et al. proposed that the development of the crack closure is described by the following equation, σ ��,�� � �1 � � ������ � � � �� (6) where σ op,tr is the crack opening stress at a certain length of a crack in MPa, is the length of a crack in mm, � is the initial length of a crack in mm and is the material constant in mm -1 , commonly 6. (McEvily et al., 2003)