PSI - Issue 13

Baijian Wu et al. / Procedia Structural Integrity 13 (2018) 722–727 Baijian Wu and Keke Tang/ Structural Integrity Procedia 00 (2018) 000 – 000

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In the proposed algorithm, the calculation of strain energy release rate is based on the virtual crack closure technique (VCCT). For a local coordinate system which originates at the crack tip, define 2 2       as depicted in Fig. 2. When the virtual crack closure length d v a along the angel of  , the energy release rate is given as: ( ) U V

B a       

(2)

G

 

B a



v

v

where U and V are elastic strain energy and external work,  is the mechanical energy of the system, refer to Fig.2.

Fig. 2. Calculation of energy release rate via VCCT

For each step, apply 0 F or 0 d corresponding to stress-controlled or displacement-controlled boundary conditions, and determine whether it is ordinary crack or interface crack. If it is ordinary crack, then calculate and get the crack propagation path. If it is interface crack, then the virtual crack length is given, interface energy release rate i G is achieved from Eq. (2). Subsequently the maximum energy release rate for crack penetrating into the matrix is determined. Every certain angle, m, G  is computed and find the maximum value of m,max G , let

G

k 

(3)

m,max

G

i

If k k  , the crack will propagate through the matrix, otherwise, it will continue to grow on the interface. Once the propagation direction is fixed, compute loading parameter  such that

C G G

 

(4)

where C G and G are the interface energy release rate and energy release rate of matrix. They are determined from the previously defined crack propagation direction. Figure 3 gives the computational flow chart of dynamic interface crack propagation. Keep in mind for each computational step, the numerical model needs to be re-meshed after the crack propagation, which is made possible by integrating the Python scripts.

Fig. 3. Flow chart of interface crack simulation

Fig. 4. Schematic of concrete matrix-aggregate