PSI - Issue 2_A

Shaowei Hu et al. / Procedia Structural Integrity 2 (2016) 2818–2832

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S. Hu et al./ Structural Integrity Procedia 00 (2016) 000–000

Fig.4 Semi-infinite plate subjected to a unit counter force across the crack

When the force P roles in the crack reaches maximum value P max , the crack tip opening displacement CTOD also reaches the critical value CTOD c , at this moment, the distribution of cohesive softened stress on fictitious crack is shown in Figure 5, thus the distribution of cohesive stress   x  on fictitious crack is:       0 0 s c t s c x a x CTOD f CTOD a a             (8) Above formula:   s c CTOD  is the cohesive stress on crack tip when crack tip opening displacement CTOD reaches critical value CTOD c , it can be calculated by the concrete nonlinear softening curve (Reinhardt et al. 1986):     3 3 1 2 1 2 0 0 0 1 exp 1 exp t w w w c c c c f w w w                                (9) Above formula: t f is concrete tensile strength, 1 c , 2 c is material constant, 0 w is the largest crack tip opening displacement. For the ordinary concrete, 1 2 c  , 2 6.93 c  , 0 160 w m   . When c w CTOD  , s  can be calculated by the formula (9). c CTOD can be calculated by the following formula (Reinhardt et al. 1986): 1 2 2 2 1 1.018 1.149 c c c c c c x a x x CTOD CMOD a H a a                                              (10) When the specimen is in a state of critical instability, 0 x a  . After the cohesive stress is calculated by formula (8), take the cohesive stress expression into formula (7), then integrate the length of crack extension on fictitious crack, the cohesive toughness c IC K caused by cohesive stress in the state of critical instability can be obtained:

F x a       

1

2 c a

  a x dx  

(11)

c IC a  

K



2 B a x 

2

0

With this, the unstable fracture toughness un

IC K can be calculated by formula (3), the cohesive toughness c IC K can

be calculated by formula (11), then take the unstable fracture toughness un

IC K and cohesive toughness

c IC K into

formula (6), the initial fracture toughness

ini IC K can be obtained. In this paper, when calculating the initial fracture

toughness ini IC K , the effect on fracture toughness by aggregate cohesive force is taken into account, and the fracture toughness calculation model for non-standard concrete wedge splitting tensile specimen with different initial seam height ratios is built. By this model, the initial fracture toughness ini IC K can be directly obtained by unstable fracture