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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1. Introduction

Concrete is a multi-phase composite material consisting of fine and coarse aggregate bonded together with cement paste. Under external loading and environmental effects, the initial voids or defects at the matrix-aggregate interface grow over time, and inevitably cause the concrete rupture, even the global failure of concrete components or structures. From the perspective of fracture mechanics, herein the defects can be treated as cracks, therefore research on the crack propagation on the matrix-aggregate interface is of substantial significance in engineering practice (Cheng et al. 2018; Yang et al. 2018).

Fig. 1. (a) Schematic of concrete material; (b) Interfacial crack path of concrete

Crack onset and propagation at biomaterial interfaces is referred as interfacial problems which are increasingly applied to composite analysis (Pietropaoli and Riccio, 2011). Problems of delamination in composite materials are often analyzed in conjunction with finite element methods, and crack is prone to propagate along the interlaminar path. Interfacial crack propagation in concrete is fundamentally different. (Sogbossi et al. 2017). Since the micro cracks or defects are generated from the aggregate-matrix interface, some of the cracks tend to penetrate into the matrix, refer to Fig.1(a) and 1(b). Crack path 1, 2 or 3 are all possible case scenarios. These characteristics of concrete degradation has made modelling and simulation a frequently used analysis approach. Numerical methods such as the finite element method are preferred (Guzmán et al. 2017; Morales-Alonso et al. 2018), usually combined with the virtual crack closure technique. Considering the oscillatory singularity at the crack tip at a biomaterial interface, crack-tip singularity analysis and calculation of stress intensity factor are necessitated in numerical simulation on dynamic crack propagation (Shih and Asaro, 1988; Barnett and Asaro 1972; Gao et al, 1992; Suo, 1990). It shall be also emphasized that, when crack starts to propagate, the boundary varies accordingly. Thus, remeshing is needed for every step of propagation, which can be overcame by Meshless method (Belytschko et al. 1996), generalized finite element method and extended finite element method (Belytschko et al. 2009; Melenk and Babuška 1996 ). However, when it comes to simulation of interface crack through open commercial finite element software, these methods are still at preliminary stage. Method of maximum energy release rate is mostly adopted for determining the crack propagation direction (He and Hutchinson, 1989), since the interface crack is not restricted to grow on the interface. To conclude, although numerical simulation has been widely applied to concrete, researches on interface cracks generated from matrix and aggregate are still rare. The paper is organized as follows: an algorithm is formulated for dynamic crack propagation on matrix-aggregate interface in concrete materials. Subsequently a numerical case of concrete matrix with single aggregate is studied to validate the proposed algorithm. Influence of side-edge constraint, aggregate direction and fracture energy of the interface, was investigated, respectively. Discussion follows and the papers ends with some concluding remarks.

2. Algorithm for dynamic crack propagation on matrix-aggregate interface

The numerical simulation for dynamic crack propagation on concrete matrix-aggregate interface is implemented through commercial software Abaqus. User-written subroutines are integrated into the proposed algorithm. First, let fracture energy of matrix and interface denoted as C,m G and C , i G , respectively. Ratio of C,m G and C , i G is defined as

G

1



C,m

(1)

k



G

C,I