PSI - Issue 6

Tonsho Fumiaki et al. / Procedia Structural Integrity 6 (2017) 269–275 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

274

6

0.00E+00 1.00E+07 2.00E+07 3.00E+07 4.00E+07 5.00E+07 6.00E+07 7.00E+07 8.00E+07 9.00E+07 1.00E+08 Energy Flux density, Γ [J/ m∙s ]

specimen#2 specimen#3 specimen#5

0

0.05

0.1

0.15

0.2

0.25

0.3

crack length, a [m]

Fig. 8Overview of the model used in FEM analysis

0.6 0.8 1 1.2 1.4 1.6 1.8

0.6 0.8 1 1.2 1.4 1.6 1.8

0.6 0.8 1 1.2 1.4 1.6 1.8

a=60mm a=80mm a=100mm a=120mm a=140mm a=160mm

a=60mm a=80mm a=100mm a=120mm a=140mm a=160mm

Specimen#2

a=60mm a=80mm a=100mm a=120mm a=140mm a=160mm

Triaxiality

Specimen#3

Specimen#5

0.00E+00 5.00E+08 1.00E+09 1.50E+09 2.00E+09 2.50E+ 9 Max principal stress, σ 1 [Pa]

0.00E+00 5.00E+08 1.00E+09 1.50E+09 2.00E+09 2.50E+09 Max principal stress, σ 1 [Pa]

0.00E+00 5.00E+08 1.00E+09 1.50E+09 2.00E+09 2.50E+09 Max principal stress, σ 1 [Pa]

Fig. 8 shows the results of calculation of energy flux density, . No relation between the point where the crack branches and the transition of can be recognised. Further investigation is needed to validate the energy flux density theory in this study. 5-2 Stress triaxiality criterion Stress triaxiality is an index of the magnitude of multiaxiality caused by restriction from the material around.This value shows the magnitude of the stress which works in direction of crack curving, so this value can be the critical condition for crack bifurcation or surface roughening. Stress triaxiality is defined as = h (5) where h : hydrostatic stress, : Von Mises stress derived from h = 1 3 ( + + ) (6) = − 2 + − 2 + − 2 2 (7) where : maximum principal stress, : intermediate principal stress, : minimum principal stress Fig.9 shows the comparison of stress triaxiality. Triaxiality was calculated with stress extracted from crack tip in some step. Right-upper plot corresponds to crack tip. At near the crack tip, stress triaxiality tends to grow up bigger as the crack gets longer. From the point where the crack bifurcation started, critical conditions for crack branching are max principal stress, 1 > 1500MPa and triaxiality, > 1.1~1.3 . 5-3 Circumferential stress criterion Yoffe(1951) examined the near-tip stress distribution of a steadily propagating crack of constant length and noted that once the crack speed exceeds 60% of the shear wave speed, the angular direction which maximizes the hoop stress θθ changes from that of crack propagation at = 0 ° , to inclined orientations at = 60 ° .She suggested that Fig. 9Comparison of stress triaxiality