Nonlinear Analysis of Fiber-Reinforced Composite Laminates Subjected to Uniaxial Tensile Load

Nonlinear Analysis of Fiber-Reinforced
Composite Laminates Subjected to
Uniaxial Tensile Load
WEN-PIN LIN*
Department of Civil Engineering
Chinese Military Academy
Fengshan, Taiwan 830, ROC

HSUAN-TEH HU
Department of Civil Engineering
National Cheng Kung University
Tainan, Taiwan, 701, ROC
(Received August 7, 2000)
(Revised July 6, 2001)

ABSTRACT: A nonlinear constitutive modeltogether with a mixed failure
criterion for a single lamina is developed to simulate the behavior of composite
laminates under uniaxial tension. In the model, fiber and matrix are assumed to
behave elastic–plastic and the in-plane shear to behave nonlinear with a variable
shear parameter. The damage onset for individual lamina is detected by a mixed
failure criterion, which is composed ofTsai–Wu criterion and maximum stress
criterion. After damage is taken place within the lamina, fiber and in-plane shear are
assumed to exhibit brittle behavior and matrix to exhibit degrading behavior. This
material model has been tested against experimental data and good agreement
has been obtained.
KEY WORDS: constitutive model, elastic–plastic, nonlinear, shear parameter,
mixed failurecriterion, post-damage mode.

INTRODUCTION
and high strength, the use of fiber-reinforced composite
laminate materials in aerospace industry or in applied engineering has increased
rapidly in recent years. In numerous cases involving the design of composite structures,
there is a need for more refined analysis that takes into account phenomena such as
progressive cracking and inelastic or nonlineardeformation of the composite materials.

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UE TO LIGHTWEIGHT

*Author to whom correspondence should be addressed.

Journal of COMPOSITE MATERIALS, Vol. 36, No. 12/2002
0021-9983/02/12 1429–22 $10.00/0
DOI: 10.1106/002199802021463
ß 2002 Sage Publications

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WEN-PIN LIN

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HSUAN-TEH HU

Such analysis is required not only to predict the deformational response,but also to
provide a method to evaluate the accurate stresses to be used in failure predictions.
Most of the advanced composite materials have organic matrices; therefore, there is a
significant nonlinear stress–strain behavior present in the transverse direction of lamina
and particularly in shear deformation [1]. A significant number of macro-mechanical
models have been proposed torepresent the constitutive relation of fiber-reinforced
composite materials such as nonlinear elasticity models [2,3], plasticity models [4–8], or
damage theory coupled with elasticity [9]. In addition, various failure criteria have also
been proposed to predict the onset of damage in single layer within the fiber-reinforced
composites. There are four types of failure criteria: (a) limit theories,(b) polynomial
theories, (c) strain energy theories, and (d) direct mode determining theories. The limit
theories compare the value of each stress or strain component to a corresponding
ultimate value, such as maximum stress theory and maximum strain theory [10]. The
polynomial theories use a polynomial in stress to describe a failure surface, such as Tsai–
Wu failure criterion [11] and Hoffmanfailure criterion [12]. The strain energy theories
attempt to use a nonlinear energy based criterion to define failure, such as Tsai–Hill
failure criterion [13]. Finally, the direct mode determining theories are usually with
polynomials in stress and use separate equations to describe each mode of failure, such
as Hashin failure criterion [14], Lee failure criterion [15] and Chang failurecriterion [16].
As for the post-damage process of individual lamina, there are two idealized types of
failure modes defined in the previous study [5]; namely, brittle and ductile. For the
brittle mode, the material is assumed to give up its entire stiffness and strength in
the dominant stress direction as the damage is reached, whereas for the ductile mode the
material remains its strength...