Anisotropic material plane stress state

The macromechanical behavior of a lamina was quantitatively described in Chapter 2. The basic three-dimensional stress-strain relations for elastic anisotropic and orthotropic materials were examined. Subsequently, those relations were specialized for the plane-stress state normally found in a lamina. The plane-stress relations were then transformed in the plane of the lamina to enable treatment of composite laminates with different laminae at various angles. The various fundamental strengths of a lamina were identified, discussed, and subsequently used in biaxial strength criteria to predict the off-axis strength of a lamina. 

In order to describe completely the state of triaxial (as opposed to biaxial) stress in an anisotropic material, the compliance matrix will have 36 terms. The reader is referred to the more advanced composites texts listed in the Bibliography if these more complex states of stress are of interest. It is conventional to be consistent and use the terminology of the more general analysis even when one is considering the simpler plane stress situation. Hence, the compliance matrix [5] has the terms... 

The continuous chain model includes a description of the yielding phenomenon that occurs in the tensile curve of polymer fibres between a strain of 0.005 and 0.025 [ 1 ]. Up to the yield point the fibre extension is practically elastic. For larger strains, the extension is composed of an elastic, viscoelastic and plastic contribution. The yield of the tensile curve is explained by a simple yield mechanism based on Schmid s law for shear deformation of the domains. This law states that, for an anisotropic material, plastic deformation starts at a critical value of the resolved shear stress, ry =/g, along a slip plane. It has been... 

Wu s explanations for this fundamental observation were couched in field theory, such as overlapping of concentrated stress fields around particles or a transition in local stress state from plane strain to plane stress, and could not furnish a specific material dimension, which, as we present below, depends on the type of the polymer and its crystalline state. The required fully consistent explanation for the discovery was provided by the studies of Muratoglu et al. (1995a), who proposed that the material-specific level of A is a consequence of a preferred form of crystallization of polyamide lamellae near particle interfaces, extending to a certain distance I away from the interface. This results in an anisotropic plastic resistance in this layer, which upon percolation through the matrix and in an... 

A very simple yield criterion for anisotropic materials is the critical resolved shear stress of Schmid [14]. This is concerned with crystal slip. The law states that yield occurs when the resolved shear stress in the slip direction in the slip plane reaches a critical value. Although this law is extensively used in metal plasticity, it is of restricted application in polymers. 

If a diacid is mixed with the glycidyl terminated rigid rod monomer the reaction is much slower. The resulting cured material will exhibit a smectic phase with high values of isotropization enthalpy. If stressed above Tg, the smectic planes will orient, and macroscopically this implies a transition from an opaque state to a transparent state for the anisotropic film. The oriented polymer will relax back to the unoriented state if heated above Tg. No double peak exotherm can be observed by DSC analysis, since at the reaction temperature the forming thermoset is above its isotropization temperature. 

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