CHAPTER 2
MICROMECHANICS METHODS TO PREDICT MICRO-STRESSES IN
LAMINATED COMPOSITES AT CRYOGENIC TEMPERATURES
A finite element analysis based micromechanics method is developed to investigate
development of micro-cracks in a graphite/epoxy composite liquid hydrogen tank at
cryogenic temperatures. The unit-cell of the composite is modeled using finite elements.
Periodic boundary conditions are applied to the boundaries of the unit-cell. The
temperature dependent properties including the coefficient of thermal expansion of the
matrix material is taken into account in the analysis. The thermo-elastic constants of the
composite were calculated as a function of temperature. The stresses in the fiber and
matrix phases and along the fiber-matrix interface were calculated. When the laminated
composite structure is subjected to combined thermal and mechanical loads, the macro-
strains are computed from the global analysis. Then, the macro-strains and temperatures
are applied to the unit cell model to evaluate micro-stresses, which are used to predict the
formation of micro-cracks in the matrix. The method is applied to a composite liquid
hydrogen storage system. It is found that the stresses in the matrix phase could be large
enough to cause micro-cracks in the composite.
Micromechanics Model
The microscopic image of a uniaxial fiber reinforced laminate (Figures 2-1 and
2.2) shows that the fiber arrangement is quite random in reality. However, for
analytical/numerical modeling, it is convenient to assume some repetitive pattern of fiber
arrangement. The square unit cell is not a suitable model for glass, carbon, and graphite