PSI - Issue 2_B

Tomoya Kawabata et al. / Procedia Structural Integrity 2 (2016) 2772–2779 Kawabata et al / Structural Integrity Procedia 00 (2016) 000–000

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incremental value of the whole strain component including elastic term is sufficient to be used for the determination of r p . An example of the comparison is shown in Fig.3. By using the whole strain increment one unique value of the coordination of the rotation center can be determined as the whole strain distribution is monotonically diminished from the tension side to the compression side. Thus r p is calculated from whole strain distribution in opening direction in all conditions which is the combinations of 14 a 0 / W conditions and 2 kinds of material shown in Table1. Fig.4 exemplified rotational center position of several a 0 / W conditions of YR=0.6. It cleary shows that the rotational center locates at smaller x ( W - a 0 ) position as a 0 / W is increasing.

Fig.4 Strain increment distribution and change of rotational center by a 0 / W

Fig.3 Contour map of equivalent plastic strain and strain increment distribution along crack line in ligament

Acoording to the summary about the change of r p of all conditions during the deformation up to the level of CTOD FEM =0.20mm, There seems to be relatively larger amout of the change of r p in the extreme cases of a 0 / W =0.05 or 0.7, however even in those cases, the amout of the change is limited to be less than 5% only. Fig.5 shows the summarized relationship between a 0 / W and the representative value of each conditions, ( r p ) av. which is computed by averaging the r p histories during CTOD FEM =0.05~0.2mm. This figure clearly indicate that by decreasing a 0 / W (in other words, shallower specimen), r p is increased and its dependency shows almost same between two materials and simillar tendency with the observation by [Wu et al(1988)]. This can be stated that r p is less affected by YR. As the summary of this method, the numerical function of r p can be drawn by the equation(3) which is regression curve by least square fitting without the effect of YR .

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

YR60 YR90 Regression[Eq.(3)]

δ =0.05-0.2mm

Averaged rp in CTOD range of

0

0.2

0.4

0.6

0.8

a 0 / W

Fig.5 Summary of rotational factor calculated from strain increment distribution along the ligament by 3D-FEM

= 2.51 � 0 � 4 − 4.71 � 0 � 3 + 2.88 � 0 � 2 − 0.79 � 0 � + 0.53 ･･･ (3)

� � = 6 0 2 ( ) ･･･ (4) ( ) = 1.45 − 2.18 + 13.71 2 − 5.96 3 − 36.9 4 + 70.7 5 ･･･ (5) ( ) = 0 � � ･･･ (6)

3.2 Extended line drawing method [method b] This method has been applied by many researchers especially in early time study for first establishment of calculation formula of CTOD as described in 2.2. In order to set up the r p of BS type equation which is divided

into elastic term and plastic one, extended line by which plastic component of CTOD has to be plastic deformation only without elastic component. However, in both of experimental methods and numerical analyses, sorting out plastic component is not so easy because the deformation proceeds in harmony with elastic and plastic component. It is noted that in previous researches shown in 2.2 extended lines were drawn by whole deformation so obtained rotational factors are not accurate for the current equation which is divided into two terms. Here, in order to sort out plastic component of extended line, the deformation information of cracked surface from the crack tip to the edge in