PSI - Issue 2_B

Kazuki Shibanuma et al. / Procedia Structural Integrity 2 (2016) 2598–2605 Author name / Structural Integrity Procedia 00 (2016) 000–000

2601

4

f

Fracture stress

Brittle crack propagation

Process zone

Plastic zone

Fig.4 Local stress criterion for brittle crack propagation in steel velocity. , the stress singularity in a linear strain hardening solid, is expressed by ( = t ⁄ ) and ( = s ⁄ ) as [ , ] = 0 � − ( 0.57 ⁄ ) 2 1 − ( 0.57 ⁄ ) 2 � (3) The derived from Eq.5 by Amazigo and Hutchinson (1977) are shown in Fig.5 made by Machida et al. (1995). 0,5

0.0 0.1 0.2 0.3 0.4 = / s

0,4

0,1 Stress singularity − 0,2 0,3

0,0

= ⁄

0,0

0,2

0,4

0,6

0,8

1,0

Fig. 5 Dependence of stress singularity on tangent modulus and crack velocity (Machida et al. (1995))

2.3. Strain hardening Assuming the power law hardening solid, tangent modulus, t , is written in below equation. t = d e d e = � e Y � −� 1 −1� Strain hardening exponent = 0.2 in this study. e can be written as e [ , ] = Y � 1 − 2 � d Y � 2 � − e [ , ] In case of = 0 , e [0, ] is constant and set to 1.Therefore, a next equation is established. t = �� 1 − 2 c � d Y � 2 � − [ , ] e [0, ] � −� 1 −1� 2.4. Yield point Yield point strongly depends on strain rate and temperature as widely known and can be written as Y = Y0 exp � (497.5 − 68.90 ln Y0 ) � 1 28.32 18.42 − ln ̇ e − 2 1 93 �� Eq.7 was reported by Gotoh et al. (1992) and Toyosada et al. (1994) Using Eq.4, Eq.5, and Eq.6, strain rate at the process zone can be obtained from ̇ e = ̇ e t = − Y t c � 1 − 2 c � d Y � 2 � − e [0, ]

(4)

(5)

(6)

(7)

(8)