# Degradation of thermo-elastic properties in damaged composite laminates a theoretical study

Sammanfattning: Fiber composites are today widely used in different load carrying structures. The main reason is their high stiffness and strength to weight ratio. Due to these specific properties they are frequently used in car, marine and space industry. The damage that develops in such composites is generally much more complex in comparison with other conventional structural materials such as steel and aluminium. In those materials, one particular flaw might lead to failure. In laminated composites, many different kinds of defects can be obtained without leading to ultimate failure. If the composite laminates under life cycle undergo complex combinations of thermal and mechanical loading, it might lead to microdamage accumulation in plies. The first mode of damage is usually intralaminar cracking with the crack plane transverse to the laminate middle-plane, crossing the whole width of the specimen. The density of cracks in a ply depends on layer orientation with respect to mechanical loads, temperature change, number of cycles in fatigue, laminate lay-up, ply thickness and certainly material fracture toughness. Many papers have been written on this subject, covering a broad range from micromechanics based to continuum damage mechanics based models. Most of the research has, however, been focused on cross-ply laminates which are excellent for academic studies of phenomena but are seldom used in practical applications. Laminates with a general lay-up containing cracks in several layers of different orientation is, therefore, a challenge for any constitutive model. In paper A an attempt to derive the constitutive relationships for a damaged laminate is presented in the framework of the laminate theory. The most advantage is the transparency of derivations and simplicity of application. Stiffness, compliance matrices and thermal expansion coefficients of an arbitrary symmetric laminate with damage in certain layers are presented in an explicit form. Derivation of constitutive relationships is following the same routes as in classical laminate theory. As an input from homogenization theory the relationships between volume averaged and boundary surface averaged quantities is used. The differences between undamaged and damaged laminate case are indicated in each step of derivation. The damaged laminate stiffness and thermal expansion coefficient matrices are calculated from the undamaged laminate matrices multiplying it by a matrix which differs from the identity matrix by terms dependent on crack density in layers, stiffness matrix and orientation of these layers and includes a crack face displacement related matrix. The normalized COD (crack opening displacement) and crack face sliding are considered as dependent on the position of the cracked layer (outside or inside cracks) and on the constraint of the surrounding layers in terms of their stiffness and thickness. These dependences are analyzed using FEM calculated crack opening displacement profiles in generalized plane strain formulation and presenting the results in form of power laws. In a special case of balanced laminates with cracks in 90-layer only, expressions for thermo-elastic properties are presented in an explicit and compact form. In the paper B the sliding effect of a [Sm,90n]s laminate with transverse cracks in 90-layer is studied in order to determine the normalized average crack face sliding displacement. It is needed if a cross-ply laminate is subjected to shear loading or if a general laminate with cracks in other layer than 0- and 90-layer is subjected to any kind of loading. The normalized average crack face sliding displacement is approximated by a power law in the same way as the normalized average crack face opening displacement in paper A and used for in the constitutive equations in order to predict the in-plane shear modulus for the damaged laminate. A FE-model is constructed in order to calculate the shear modulus of the damaged laminate and to find the sliding displacement.

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