tesi A. Caggiano.pdf - EleA@UniSA - Università degli Studi di Salerno

Chapter 3. Zero-thickness interface model for FRCCwhere E s and E d are the steel fiber elastic modulus and the equivalent elastic one ofmatrix-fiber debonding, respectively. Two limiting situations can be recognized:• E d → 0, in which the serial structure response and, consequently, the uniaxialfiber strength vanish (debonding).• E d → ∞, representing the perfect bonding case between fiber and matrix.The bond-slip axial constitutive model can be completed by defining the followingmaterial parametersσ y,f = mi n[σ y,s ,σ y,d ] (3.36)H f ={H sH dif σ y,s < σ y,dotherwise(3.37)whereby σ y,s and σ y,d are the yield stress and the equivalent interface elastic limit,respectively.The parameters E d , σ y,d and H d required for the bond-slip model characterization,can be calibrated by analyzing a simple pull-out scheme as proposed in the followingsubsections and derived in detail in Chapter 4.3.4.1 Pull-out analysis of a single fiberFigure 3.11 shows an isolated fiber loaded by an axial force, P i . The fiber is embeddedin a cementitious matrix for a l emb length measure. The equilibrium scheme, proposedin in Figure 3.11, is used to simulate the complete slipping behavior.The following basic equations are used for analyzing the fiber-to-concrete debondingprocess:58• The equilibrium rule: dσ f [x]d x= − 4τ a[x]d f, being σ f the axial stress of the fiber, τ athe shear bond stress and d f the diameter of the fiber.d s[x]• The fiber constitutive law in axial direction: σ f [x] = E s d x, with E s the elasticsteel modulus and s[x] the slip between fiber and surrounding concrete mortarbased on the assumption of Figure 3.11.