Fiber matrix adhesion stress distribution

It was mentioned above that the simulation method of Termonia [67-72] can be used to calculate the stress-strain curves of many fiber-reinforced or particulate-filled composites up to fracture, including the effects of fiber-matrix adhesion. Such systems are morphologically far more complex than adhesive joints. Many matrix-filler interfaces are dispersed throughout a composite specimen, while an adhesive joint has only the two interfaces (between each of the bottom and top metal plates and the glue layer). If one considers also the fact that there will often he a distribution of filler-matrix interface strengths in a composite, it can be seen that the failure mechanism can become quite complex. It may even involve a complex superposition of adhesive failure at some filler-matrix interfaces and cohesive failure in the bulk of the matrix. 

The variation of die swell ratio De/D (where De and D are the diameters of the extrudates and die) of virgin PP, untreated and treated composites is represented in Table 9.5 [74]. It is evident that the swell ratio of the virgin matrix decreased with the incorporation of fibers. This is probably attributed to the distribution of fibers within the PP matrix which results in stress transfer from matrix to the fiber, thereby retarding the elastic recovery of the material [75]. Furthermore, the treated composites displayed a lesser die swell, thus confirming enhanced fiber-matrix adhesive strength. However, the swell ratio increased with the shear rate, which is probably due to the decrease of normal stress and elastic recovery at low shear rates. 

In order to relieve the stresses of compression at higher densities by thermoplastic processes instead of with wire or twine, several conditions must occur. A balance between the pressure, and retention time must be found so that the material is exposed to temperatures of 200° to 300°F (93-150°C), and pressures of 1000 psi to 1500 psi (6.9-10.3 MPa) at moisture levels of 12 to 25 (9, 10). Moisture and agglutinant substances such as soluble sugars, starches, extractives, phenolic acids and lignins which will plasticize at these conditions must be evenly distributed throughout the material. The geometry of the material must allow a uniform fiber matrix and intimate contact between adhesive surfaces during compression. 

The distribution of stress around discontinuous fibers in composites has been studied by a number of researchers. Theoretical analyses have been performed by Cox [82] and Rosen [83]. In these models only fiber axial stress distribution and the fiber-matrix interfacial shear stress distribution are determined. Amirbayat and Hearle [84] studied the effect of different levels of adhesion on the stress distribution, that is, no bond, no adhesion, perfect bond, and the intermediate case of limited friction. They also considered the inhibition of slippage by frictional forces resulting from interfacial pressure due to Poisson s lateral contractions of the matrix but did not consider the shrinkage of the matrix during curing. 

Another three-dimensional axisymmetric stress distribution for the stress around fiber breaks was obtained by Naim [93] using variational mechanics. In this study, breaks interaction was also included and it was assumed that both fiber and matrix were linearly elastic and a perfect adhesion at the fiber-matrix interface. To account for the stress singularity at the matrix crack tip of the fiber break, the matrix plastic-model was also included. Imperfect adhesion to mimic a failed fiber-matrix interface was added to this model to study the mechanism of interfacial failure, that is, the stress conditions that cause the extent of interfacial failure or its increase. It was suggested that due to the complexity of the multi-axial stress state, a simple maximum stress failure criterion was unrealistic and an energy release rate analysis was necessary to calculate the total energy release rate associated with the growth of interfacial damage. 

Supporting fibers in epoxy adhesive tapes are useful in that they provide for a positive stop under bonding pressure. This can be used to control bond line thickness and to help distribute stresses evenly during service. The supporting fibers that are used in these adhesives are primarily for the purposes of carrying the adhesive and convenient application to the substrate. Their reinforcing function within the epoxy matrix is generally considered to be of secondary importance. 

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