Plastic deformation matrix material

Electron Microscopic Results. Electron micrographs were obtained from deformation tests of toughened PP and PA. The micrographs of toughened PP shown in Figure 13 reveal ruptured particles and plastically deformed matrix material between these voids. The cavitation step inside the particles, with the subsequent deformation and fibrillation of the adjacent material, can also be clearly seen in Figure 14. 

Figure 15. Strained semithin sections of rubber-modified PA (HVEM images). The deformation direction is horizontal, (a) highly deformed particles with plastically deformed matrix material in between and (b) cavitation or microvoids inside particles.

The typical micromechanical behavior of this material at room temperature is shown in Figure 10. The lower magnification in Figure 10a shows a dense pattern of cavitated and elongated rubber particles and plastically deformed matrix material between the particles. The matrix deformation occurs mainly in the form of homogeneous shear deformation zones and a small number of short and relatively thin fibrillated crazes (40). 

The explanation of the effect of secondary component on the spreading of shear yielding (i.e., delocalization of shear banding) is based on a concept of local stress fields and stress concentrations in the matrix due to the presence of inclusions. This leads to a reduction of the external load needed to plastically deform the material. The original Goodier s solution (7) for an isolated particle in an isotropic matrix resulted in a maximum stress concentration of about 1.9 at the equator of the inclusion (8). It should be borne in mind that this solution... 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

Binders improve the strength of compacts through increased plastic deformation or chemical bonding. They may be classified as matrix type, film type, and chemical. Komarek [Chem. Eng., 74(25), 154 (1967)] provides a classification of binders and lubricants used in the tableting of various materials. 

Sandorf, 1980 Whitney, 1985 Whitney and Browning, 1985). According to the classical beam theory, the shear stress distribution along the thickness of the specimen is a parabolic function that is symmetrical about the neutral axis where it is at its maximum and decreases toward zero at the compressive and tensile faces. In reality, however, the stress field is dominated by the stress concentration near the loading nose, which completely destroys the parabolic shear distribution used to calculate the apparent ILSS, as illustrated in Fig 3.18. The stress concentration is even more pronounced with a smaller radius of the loading nose (Cui and Wisnom, 1992) and for non-linear materials displaying substantial plastic deformation, such as Kevlar fiber-epoxy matrix composites (Davidovitz et al., 1984 Fisher et al., 1986), which require an elasto-plastic analysis (Fisher and Marom, 1984) to interpret the experimental results properly. 

The descriptions presented in the foregoing sections are concerned mainly with composites containing brittle fibers and brittle matrices. If the composite contains ductile fibers or matrix material, the work of plastic deformation of the composite constituents must also be taken into account in the total fracture toughness equation. If a composite contains a brittle matrix reinforced with ductile libers, such as steel wire-cement matrix systems, the fracture toughness of the composite is derived significantly from the work done in plastically shearing the fiber as it is extracted from the cracked matrix. The work done due to the plastic flow of fiber over a distance on either side of the matrix fracture plane, which is of the order of the fiber diameter d, is given by (Tetelman, 1969)... 

Much attention has been focused on the microstructure of crazes in PC 102,105 -112) in order to understand basic craze mechanisms such as craze initiation, growth and break down. Crazes I in PC, which are frequently produced in the presence of crazing agents, consist of approximately 50% voids and 50% fibrils, with fibril diameters generally in the range of 20-50 nm. Since the plastic deformation of virtually undeformed matrix material into the fibrillar craze structure occurs at approximately constant volume, the extension ratio of craze I fibrils, Xf , is given by... 

There have been many efforts for combining the atomistic and continuum levels, as mentioned in Sect. 1. Recently, Santos et al. [11] proposed an atomistic-continuum model. In this model, the three-dimensional system is composed of a matrix, described as a continuum and an inclusion, embedded in the continuum, where the inclusion is described by an atomistic model. The model is validated for homogeneous materials (an fee argon crystal and an amorphous polymer). Yang et al. [96] have applied the atomistic-continuum model to the plastic deformation of Bisphenol-A polycarbonate where an inclusion deforms plastically in an elastic medium under uniaxial extension and pure shear. Here the atomistic-continuum model is validated for a heterogeneous material and elastic constant of semi crystalline poly( trimethylene terephthalate) (PTT) is predicted. 

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