Composite Materials Research Progress

154
Yuanxin Zhou, Hassan Mahfuz, Vijaya Rangari et al.
σ fiber element unbroken (21b)
i,
j ≤ S i,
j
The failure criterion of interface is
τ ≥ τ
i,
j m
interface broken (22a)
τ ≤ τ
i,
j m
interface unbroken (22b)
where, τm is the ultimate shear stress of matrix.
The failure criterion of matrix is
ε ≥ ε
i,
j m
matrix element broken (23a)
ε ≤ ε
i,
j m
matrix element unbroken (23b)
where, εm is the failure strain of the matrix
Simulation Procedure
Based on the above numerical constitutive model, a computational program is compiled to
simulate the microscopic dynamic failure process of unidirectional composites. The
simulation procedure is illustrated as following:
(A) Randomly assign a statistical strength Si,j (i=2,4,...2n, J=1,2,…m) to the fiber
element, definitely assign the tensile strength to the matrix and the shear strength to
the interface.
(B) Solve Equation (14) by iteration formula (15) using Ui,j k−1 , Ui,j k−2 and the boundary
conditon at time t=kΔt, obtain the displacement field Ui,j k (i=1,2,...2n+1,j=1,2,...m).
(C) Determine whether the element or the interface breakage (or the matrix element
unloading) has happened, if new breakage occurs, take the breakage into account and
repeat steps (B) and (C) until no new breakage occurs, else calculate the apparent
stress σc and strain εc using Equation (17) and (18).
(D) Increase a time step and repeat step (B) and (C) till the composites failure happens.
Here the "composites failure" is defined as the state when the stress σc drops from
σmax to about 50% of σmax.
Experimental Results of Fiber, Matrix and Composite
The statistical parameters of fiber were obtained from tension tests of T700 fiber bundles. The
tensile stress-strain curve of fiber bundle in Figure 22 shows considerable amount of nonlinearity.
The specimen failed gradually after reaching the maximum stress due to the tensile
strength distribution of fibers. Three parameters were determined from each stress-strain