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

725

4

3. Numerical case

Depicted in Fig. 4 is the simplified concrete model. One single aggregate is included in the matrix. Refer to Fig. 4 for the dimension of aggregate as well as concrete matrix. Tensile displacement is applied to one end, while the other end is fixed on the ground. To be determined is the side-edge constraint. The following material parameters are adopted as

L E

L

a

10mm, =5mm b

100mm,

200mm,







1

2

(5)

4 1 10 MPa, =0.2,   

-2

G

40J.m



a

C,m

Studied here are the influences of three factors including the ratio of matrix over interface fracture energy, aggregate direction and side-edge constraint. The numerical case is designed accordingly. First, the value of side edge constraint is a fixed number, values of the ratio of matrix and aggregate fracture energy vary from 1.5 to 2.5, while the values of aggregate direction range from 0, 30, 60 and 90 degrees. This leads to 8 cases. When it comes to the investigation of side-edge constraint influences, suppose o =2.0, =30 k  , the values of  vary from -0.5, 0, 0.5 to 1.0. This leads to 4 cases. 12 cases are inclusive. Notice  is defined as the ratio of macroscopic side deformation and normal deformation. h =    (6) Graphically displayed in Figs. 5 and 6 are the influences of three factors on dynamic crack propagation at concrete cement-aggregate interface. It is understood that increase of k also means the decrease of interface fracture energy, since the matrix fracture energy is stipulated to -2 C,m 40 J.m G  . Therebefore, the interface crack is prone to propagate on the interface surface, which is clearly demonstrated in Fig.5. Increase of aggregate angle from 0 to 90 degrees in a way reflects the transformation of mode I to mode II. When the value of aggregate angle is relatively small, change of aggregate angle seems put little effects on the path of interface crack propagation. Nevertheless, when the aggregate angle is set to be 90 degrees, interface crack sharply turns downward. In engineering practice, this rarely happens. In the numerical simulation, it turns out that the fracture strength for aggregate angle 90 degrees is much stronger that the rest of cases. This point will be further elaborated and emphasized in the extended version of this paper in the near future. 4. Discussions

Fig. 5. Influence of k and  on crack path