Influence of Matrix and Cohesive Material Law Characteristics on the Tensile and Bond Behavior of FRCM Systems

Data Availability Statement

Notation

A

cross section area of a yarn;

a

major semiaxis of a yarn cross section, assumed with elliptical shape;

B(x_i)

bond force in the fiber at coordinate x_i of the discretized domain;

b

minor semiaxis of a yarn cross section assumed with an elliptical shape;

CP_i

phase of the cracking process;

c_i

crack formed;

E

yarn Young’s modulus;

F(x_i)

tensile force in the fiber at coordinate x_i of the discretized domain;

f_tf

tensile strength of the fiber;

f_tm

tensile strength of the matrix;

G(x_i)

gripping force at coordinate x_i of the discretized domain;

h

distance between nodes of the discretization;

k

secant modulus of the cohesive material law;

L

length of the domain;

M

matrix of coefficients;

m_i,j

coefficients appearing in matrix M;

N

number of nodes discretizing the domain;

n_y

number of embedded yarns;

p

step of the incremental procedure;

Q(x_i)

external load applied at coordinate x_i of the discretized domain;

q

vector of the known terms;

q_i

elements of the known terms vector Q(x_i);

s

vector of the unknowns;

s(x)

slip function;

$s(x_c^L)$

slip at the left edge of crack c_i;

$s(x_c^R)$

slip at the right edge of crack c_i;

s(x_i)

slip value at coordinate x_i of the discretized domain;

s*

known imposed slip;

w_i

width of crack c_i;

x_i

coordinate of nodes discretizing the domain;

δ₁

slip value reached at the end of the ascending branch of the trilinear CML;

δ₂

slip value reached at the end of the softening branch of the trilinear CML;

ρ_i

combination coefficient of the slip at the left and right edge of crack c_i;

τ(s(x))

shear bond stress function at the textile–matrix interface;

τ₁

maximum bond stress defining the CML;

τ₂

bond stress defining the frictional plateau of the trilinear CML; and

ψ

yarn perimeter.

References