Page 287 - Mechanics Analysis Composite Materials

272 Mechanics and analysb of composite materiab

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Fig. 6.1. An orthotropic layer or ply in a plane stressed state.

Fig. 6.2. Failure surface in the stress space.

“phenomenological” means that the actual physical mechanisms of failure at the
microscopic material level are not touched on and that we deal with stresses and
strains, Le., with conventional and not actually observed state variables introduced
in Mechanics of Solids. In the micro-approach, we evaluate the layer strength using
microstresses acting in the fibers and in the matrix and failure criteria proposed for
homogeneous materials. Being developed up to a certain extent (see, e.g., Skudra
et al., 1989), this approach requires the minimum number of experimental material
characteristics, i.e., only those determining the strength of fibers and matrices. As a
result, coordinates of all the points of the failure surface in Fig. 6.2 including points
A, B, and C corresponding to uniaxial and pure shear loading are found by
calculation. To do this, we should simulate the layer or the ply with a suitable
microstructural model (see, e.g., Section 3.3), apply a pre-assigned system of average
stresses 01, 02, 212 (e.g., corresponding to vector OD in Fig. 6.2), find the stresses
acting in material components, specify the failure mode that can be associated with
the fibers or with the matrix, and determine the ultimate combination of average
stresses corresponding, e.g., to point D in Fig. 6.2. Thus, the whole failure surface