Modulus matrix

Equation (5.7) related the stress tensor to the strains throngh the modulus matrix, [Q, also known as the reduced stiffness matrix. Oftentimes, it is more convenient to relate the strains to the stresses through the inverse of the rednced stiffness matrix, [2] called the compliance matrix, [5]. Recall from Section 5.3.1.3 that we introduced a quantity called the compliance, which was proportional to the inverse of the modulus. The matrix is the more generalized version of that compliance. The following relationship then holds between the strain and stress tensors ... 

As noted previously, the modulus of a two-phase system is some kind of average of the moduli for the individual components. Thus when a rigid, high-modulus phase such as silica, glass, or steel is incorporated into a lower modulus matrix such as a polymer, the modulus of the composite is increased, in some proportion to the volume fraction of filler added. Other properties may be affected also for example, toughness, thermal expansion characteristics, and permeability (Sections 12.1.2 and 12.1.3). 

Clearly, the incorporation of a rigid particulate filler must invariably increase the modulus of a lower modulus matrix. However, in any optimization of properties, the effects of fillers on ultimate properties such as yielding. 

FIGURE 12.1 High-modulus fiber opposes strain around it in a low-modulus matrix, (a) Before deformation (b) after deformation. Arrows indicate force direction. (Adapted from Ref. I.)... 

High modulus matrix systems must produce a transverse ply strain capability of +0.003 to be of soious mig eming use. 

Another view is the inhibition layer theory, which holds that the structure of the stress relaxation transition layer between the matrix and the packing is not a flexible deformation layer, but an interfacial layer with a modulus between that of the matrix and the packing. The treatment agent is a part of the interfacial area, and this part is a substance with a medium modulus that is between that of the high-modulus reinforcing material and the low-modulus matrix. It has the effect of transferring stress uniformly and reducing interfacial stress, so that it can enhance the performance of the composite materials. The inhibition layer theory is not widely accepted because it lacks the necessary experimental basis. ... 

The fundamental issue in fibre reinforcement is the process of the transfer of stress from a low modulus matrix to a high-modulus reinforcing fibre. The strain in the fibre is usually the same as that in the matrix in the case of the axial deformation of composites with long aligned fibres with high aspect... 

Figure 3.28 Effect of fibre modulus on bridging load and fibre stresses in oriented fibre (45°) in a 30 GPa modulus matrix (after Katz and Li [61,62]).

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