PSI - Issue 2_A

Takuhiro Hemmi et al. / Procedia Structural Integrity 2 (2016) 2230–2237 Author nam / Structural Integrity P o edi 00 (2016) 000–000

2232

3

Stress tensor � ��

Thickness (30 ～ 100mm)

1mm

Propagation direction

(i) Finite element analysis � Local arrest toughness in macroscopic model � �� � Normal vector (ii) Microscopic model analysis 1mm

(iii) Macroscopic model analysis Fracture condition: � � � � ��

Width (300~2,400mm)

Step1

Step140

Initial crack (60mm)

Step70

Step120

Prediction results of fast crack propagation/arrest behavior

Crack arrest (158mm)

Fig.1.Outline of multiscale model

2. Evaluation of effective surface energy in the conventional model Effective surface energy is energy absorption upon a unit area of fracture surface which is formed with the crack propagation. This energy is outputted from microscopic model and inputted into macroscopic model. Thus, the value is much important parameter for connecting two models. The energy absorbing mechanism during brittle crack propagation has not been sufficiently clarified. In the present study, we assumed that the plastic work to form tear-ridge is dominant in the total absorbed energy to form the macroscopic fracture surface. The tear-ridge is formed as a result of the ductile fracture of uncracked ligament along grain boundary as shown in Fig2. The effective surface energy as the plastic work to form tear-ridge per unit area can be calculated by a line integral along grain boundaries � . Assuming the Tresca yielding condition without strain hardening, the plastic work to form tear-ridge per unit volume is expressed as the product of shear strength � � ( � ���� � ) and critical shear strain � �� . The width of uncracked ligament, where the plastic deformation is produced, is assumed to be 10% of the height of uncracked ligament based on the preliminary microscope observation. A schematic of the above assumed energy absorbing mechanism is shown in Fig.2. As a summary of the above assumptions, the surface energy � is approximately evaluated as � � 2 1 � ��� � � � � �� �� � (1) where � is an area of the entire domain, � is a ratio of width and height of uncracked ligament, i.e., � � ��1 as described above.