Tensile Testing of FRCM Coupons for Material Characterization: Discussion of Critical Aspects

Data Availability Statement

Notation

A

parameter of the CML;

A_f

area of the cross section of the longitudinal fibers in a FRCM plane element;

A_m

area of the cross section of the matrix in a FRCM plane element;

b_f

width of the textile in a tensile specimen;

b_m

width of the matrix in a tensile specimen;

b₁

width of the matrix in a single-lap shear test;

d_min

distance between two consecutive cracks at the end of the cracking process of a tensile specimen;

E_FRCM

cracked elastic modulus of the FRCM computed according to AC434 (ICC 2013);

E_f

elastic modulus of the fibers;

E_m

elastic modulus of the matrix;

F

tensile force applied to a tensile test specimen;

f

function defining the distribution of the load transferred by the plates to the matrix at the ends of a tensile specimen;

F_J

tensile force corresponding to Point J of the load response, J ≡ A, C, E, or G;

F_max

tensile capacity of a tensile test specimen;

f_f

tensile strength of the fibers;

f_fe

effective stress of the FRCM, according to ACI 549 (ACI 2020);

f_fu

tensile strength of the FRCM, according to ACI 549 (ACI 2020);

f_t

tensile strength of the matrix;

g

global slip, that is, slip at the loaded end in a single-lap shear test;

G_f

fracture energy of the fiber–matrix interface;

$G_F^m$

fracture energy of the matrix;

j

natural number;

ℓ

bonded length in single-lap shear tests;

L_c

critical length, that is, twice the length needed to transfer the matrix-cracking force f_tA_m;

L_g

gripped length of a tensile specimen, that is, length of each portion of the plate glued to the specimen at its ends;

L_m

gauge length in the central portion of a tensile specimen;

L_t

free length of a tensile specimen, that is, length of the central part of the specimen between the plates;

m

generic value of L_m;

n

number of textile layers in a FRCM plane element;

P

tensile force applied to the textile in a single-lap or pullout test;

P_max

maximum load transferable at the fiber–matrix interface in a single-lap or pullout test;

p_f

width of the fiber–matrix interfacial surface, that is, contact perimeter;

q

tangential load per unit length transferred by the plates to the matrix at the two ends of a tensile specimen along the gripped length;

q₀

parameter defining the amplitude of the load transferred by the plates to the matrix at the ends of a tensile specimen;

s

slip;

s_E

modulus of the fiber–matrix slip at the ends of a tensile specimen;

s_F

slip at the free end in a single-lap shear test;

s_f

slip at the beginning of the friction branch in the CML, that is, τ = τ_f for s ≥ s_f;

s_max

maximum slip, that is, slip at the end of the plates, at the maximum load of a tensile specimen;

t_m

thickness of a tensile specimen;

t_f

equivalent thickness of the textile;

u_f

longitudinal displacement of the fibers;

u_m

longitudinal displacement of the matrix;

w

crack opening;

w_ch

characteristic crack opening defined as $w_{ch}=G_F^m/f_t$;

w_f

critical crack opening corresponding to zero stress transferred between the crack faces;

w_L

opening of the last formed crack during the cracking process of a tensile specimen;

y

reference axis placed in the center line of the midplane of a tensile specimen and longitudinal reference axis in single-lap shear tests;

α

parameter of the CML;

ΔL_m

elongation of the central portion of length L_m of a clevis-grip tensile specimen, evaluated on the matrix surface;

ΔL_t

elongation of a clevis-grip tensile specimen, evaluated as the relative displacement of the plates of a tensile specimen;

ɛ

strain;

ɛ₀₆

global strain ɛ_av or global strain of the central part ${\stackrel{⌢}{\epsilon }}_m$ corresponding to 0.6F_max;

ɛ₀₉

global strain ɛ_av or global strain of the central part ${\stackrel{⌢}{\epsilon }}_m$ corresponding to 0.9F_max;

ɛ_av

global strain of the tensile specimen, evaluated as ɛ_av = ΔL_t/L_t;

ɛ_av,max

deformation capacity of a tensile specimen in terms of ɛ_av, that is, strain ɛ_av corresponding to the tensile capacity F_max;

ɛ_f

local strain of the fibers in a tensile or single-lap specimen;

ɛ_fe

effective strain of the FRCM, according to ACI 549 (ACI 2020);

ɛ_ft

failure strain of the fibers;

ɛ_fu

ultimate strain of the FRCM, according to ACI 549 (ACI 2020);

ɛ_m

local strain of the matrix in a tensile or single-lap specimen;

${\stackrel{⌢}{\epsilon }}_m$

global strain of the central part of a tensile specimen, evaluated as ${\stackrel{⌢}{\epsilon }}_m=\mathrm{\Delta }{L}_m/L_m$;

${\stackrel{⌢}{\epsilon }}_{m,\max }$

deformation capacity of a tensile specimen in terms of ${\stackrel{⌢}{\epsilon }}_m$, that is, strain ${\stackrel{⌢}{\epsilon }}_m$ corresponding to the tensile capacity F_max;

ɛ_t

cracking strain of the matrix;

σ_f

axial stress in the fibers;

σ_intercept

fiber stress corresponding to the intercept of the secant line used to compute E_FRCM with the vertical axis of the F–ɛ_av response;

σ_m

axial stress in the matrix;

τ

shear stress at the fiber–matrix interface;

τ_f

friction shear stress at the fiber–matrix interface; and

τ_s

shear stress at the matrix-substrate interface in a single-lap shear test.

References