useful to develop a new composite material system for the liquid hydrogen composite

tank by changing the combination of constituent properties.

 Before finite element methods were widely available micromechanics analysis of

fiber-reinforced composites was performed using analytical methods (e.g., Chen and

Cheng [3]). They analyzed the unit cell of a composite by solving the governing elasticity

equations using an infinite series and employing a combination of Fourier series and least

square methods. The periodic boundary conditions for stresses and displacements were

satisfied on symmetric boundaries. Micromechanics analysis methods for elastic-plastic

composites were investigated using the bounding technique by Teply and Dvorak [4].

The problem of elastic-viscoplastic composites was solved by Paley and Aboudi [5]

imposing continuity of traction and displacement rate at the interfaces between the

constituents of a square unit cell. A square unit cell model was used by Nedele and

Wisnom [6] to investigate the behavior of fiber-reinforced composites subjected to shear

loading. Marrey and Sankar [7-9] developed micromechanics methods for textile

structural composites using the finite element method. Their method considered the

effects of stress gradients on the strength and stiffness properties of the composite. The

periodic boundary condition of various shapes of unit cells was described by Li [10]

using the symmetries of the fiber-matrix system to satisfy displacements and stresses in

the boundary.

 In the present study the micromechanics method is combined with a global

laminate analysis to predict the stresses in the fiber and matrix phases accurately. The

method is useful to predict development of micro-cracks in a composite laminate at

cryogenic temperatures. In order to predict the development of microcracks in fiber