PSI - Issue 39

Andrea Pranno et al. / Procedia Structural Integrity 39 (2022) 688–699 Author name / Structural Integrity Procedia 00 (2019) 000–000

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(given by the aggregate interlocking) and also the toughening effect (given by the embedded discrete fibers) which is associated with an enlargement of the size of the fracture process zone.

Fig. 2. Trilinear taction–separation law for nano-enhanced UHPFRC structures.

Six fracture parameters are required to calibrate the trilinear traction-separation law. Specifically, the following four parameters are referred to the plain nano reinforced ultra-high performance concrete: t f (tensile strength), f UHPC G (initial fracture energy), F UHPC G (total fracture energy) of the plain nano reinforced UHPC, CTOD c (critical crack tip opening displacement), while the latter two parameters are referred to the nano reinforced UHPFRC: F UHPFRC G (total fracture energy of nano reinforced UHPFRC), and w f (final crack opening width). The parameters defining the first and the second branch of the softening curve are defined by the following relations:

2

F

G

CTOD



UHPC

L

c

2

f

G

f

(4)

f

,

,

,

w

w

w







UHPC

t

CTOD

f

1

2

f

4

f

1



c t

t

2

f

G

UHPC

where CTOD c is the critical crack tip opening displacement and L f denotes the fiber length. The parameter w 2 is defined by assuming the displacement related to the kink point between the two descending branches equal to CTOD c . Definitively, the constitutive behavior of the cohesive interfaces, also considering the damage irreversibility and the frictionless unilateral contact conditions, is defined by the following relations:

   

K w w 0

0



  max

n

n

t w

  max

,

,

t

t

w





(5)

t w

n

s

s

0

w w



w

n

n

max

w

max