A modeling study on residual stress-induced interfacial debonding
and stress–strain behavior of weakly bonded UD composites
, M. Tanaka, H. Tanaka, S. Kimura, M. Hojo
Mesoscopic Materials Research Center, Graduate School of Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
Residual stress-induced interfacial debonding and its inﬂuence on stress–strain behavior of unidirectional ﬁber-reinforced brittle matrix
composites with weak interface were studied using mini-composite model by means of the two-dimensional shear lag analysis combined
with a Monte Carlo method. Damages (fracture of ﬁber, matrix and interface) were accumulated intermittently, resulting in serrated stress –
strain curve. In this process, the residual stresses changed the strain, order and location of occurrence of damages, and consequently the shape
of stress–strain curve and strength of composite. Under the existence of compressive and tensile axial residual stresses in ﬁber and matrix,
respectively, the fracture of the matrix and the debonding from the fracture-ends of matrix were enhanced, while the fracture of ﬁber and the
debonding from the fracture-ends of ﬁber were suppressed. The residual stress-induced premature fracture of the matrix, followed by
debonding, reduced the strength of composite.
q 2002 Elsevier Science Ltd. All rights reserved.
Keywords: A. Ceramic–matrix composites (CMCs); B. Debonding; B. Residual/internal stress; C. Computational modelling
In brittle ﬁber/brittle matrix composites, crack arrest-
capacity is low when the interface is strong. To arrest
cracks, the interface is controlled to allow debonding [1,2].
In the fracture process of such weakly bonded composites,
damages (fracture of ﬁber, matrix and interface) arise at
many places. The spatially distributed damages interact
mechanically to each other and determine the species and
location of the next damage, one after another. As a result of
consecutive variation of the spatial distribution of damages
(damage map), mechanical properties such as stress–strain
curve, strength and fracture morphology of composites are
determined. Such a fracture process and the resultant
property of composites are strongly affected by residual
stresses. In the present study, the modiﬁed shear lag analysis
[3–6], in which residual stresses in ﬁber and matrix in the
ﬁber direction can be incorporated in contrast to ordinary
shear lag approach, was combined with the Monte Carlo
method and the inﬂuences of residual stresses on interfacial
debonding and stress –strain behavior of composite under
mechanical interactions among damages were studied by
using 2D model to a ﬁrst approximation. It has been
demonstrated that even 2D model can describe the behavior
of practical 3D composites fairly well [7–10].
As the shear lag analysis is constructed as to calculate the
axial stress distribution, the radial and circumferential
stresses cannot be incorporated. Due to such a simpliﬁed
nature, the calculated result is rough. It is a disadvantage of
this analysis. It is, however, emphasized that such a
simpliﬁcation makes it possible to solve interactions
among many damages (multi-body problem). It is an
advantage of this analysis.
For a description of the stress – strain behavior and the
strength, numerical calculation approaches using a statisti-
cal probability function have been proposed [11–15]. They
provide numerical solutions even for practical composites
of large size. On the other hand, the present simulation
approach provides concrete and visual solutions for the
elemental damage accumulation process but in a composite
of limited size.
2. Modeling and simulation method
Under the assumption that the composite has no residual
stress at fabrication temperature T
and it is cooled down to
test temperature T
, the residual axial stresses of ﬁber (
and matrix (
were, to a ﬁrst approximation,
1359-835X/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
PII: S 1 359 - 8 3 5 X ( 0 2 ) 0 0 1 4 3 - 4
Composites: Part A 33 (2002) 1337–1343
Corresponding author. Tel.: þ81-75-753-4834; fax: þ81-75-753-4841.
E-mail address: firstname.lastname@example.org (S. Ochiai).