Particle diameter plastic deformation

These differences were correlated with the size of the rubber particles in the systems the smaller the diameter of the dispersed phase (e.g. the lower the interparticular distance), the higher the benefits of a /3-nucleation (Fig. 25b). For the grades with the smallest particle sizes, it might be attributed to an easier plastic deformation of the matrix once the damage mechanisms initiated (by particle cavitation) as a result of the smaller matrix ligaments between the rubber phase. 

Expansion of the strip after pressure release is influenced by the physical characteristics of the material to be compacted (plasticity, brittleness, particle size and distribution, particle shape, etc.), the roll diameter, the speed of rotation, and the surface configuration of the rollers. With increasing roll diameter and/or decreasing speed the expansion of compacted material is reduced due to better deaeration during densification and a more complete conversion of elastic into permanent, plastic deformation. 

The deformation behavior of toughened PA is compared for larger and smaller particles in reference 26. In large particles with an average diameter, D, of about 1 xm and an average minimum interparticle distance, A, of about 0.5 xm, an intense plastic deformation appears in only a few bands. In the case... 

Figure 16. Modified PA with small particles of diameter D (D = 0.15 pm) and small interparticle distances A (A = 0.08 mm), showing beginning plastic deformation (HVEM image). The deformation direction is horizontal.

Figure 18. Effect of interparticle distance, A, on plastic deformation of matrix strands between particles (a) definitions of the size parameters D = particle diameter, vP = particle volume content, aQ = applied stress, and aK = stress concentration (b) with a small interparticle distance, a uniaxial stress state is dominant between the particles and microvoids after cracking of the particles, and plastic yielding can be obtained and (c) with a large interparticle distance, thick matrix strands favor a triaxial stress state between the particles and microvoids, and plastic yielding is hindered.

Particle Diameter Because plastic deformation depends on stress concentration in the whole volume between particles and not directly on the stress at the particles, D is not of primary importance. The only precondition is that for a given particle volume content, the particles must be small enough to ensure that A is less than the critical value according to equation 1. Therefore, the most important function of particles is to produce a dense pattern of microvoids. Recently, an increase of the toughness of modified PA with increasing tendency to form microvoids inside the particles (with decreasing stress to crack the particles or with decreasing cavitation strain) was found (6). The cavitation stress of an elastomer is dependent on its modulus (27). 

Addition of a small amount of core-shell toughening particles of 0.3 pm diameter to a polycarbonate/copolyester blend reduced the fatigue crack propagation rate by a factor >20 and gave rise to significantly more plastic deformation during fitacture [134]. 

Only small particles, less than 1 pm in diameter, would show this effect. Krupp explained this in terms of the equations for London-van der Waals attractive forces between rigid spheres, together with the Hertz equations of contacL Because the attraction is proportional to particle diameter, the force at the particle contact decreases with D. However, the elastic area of the contact spot decreases faster, from the Hertz Equation (9.1), with Thus, as the particle gets smaller, the contact pressure must rise to the point at which plastic deformation occurs. 

Scanning electron microscope studies were performed on polystyrene spheres sitting on polished silicon surfaces by Rimai, Demejo and Bowen. The bulk polymer had a Young s modulus of 2.55 GPa and a yield stress of 10.8 MPa when measured on a testing machine. With such a low yield point it was estimated that the particles should be plastically deformed under the adhesion forces. Therefore they applied the plastic deformation theory of Maugis and Pollock to fit the results, as shown in Fig. 9.28. This gave the expression for contact diameter d in terms of sphere diameter D... 

The selection of the dominant deformation mechanism in the matrix depends not only on the properties of this matrix material but also on the test temperature, strain rate, as well as the size, shape, and internal morphology of the rubber particles (BucknaU 1977, 1997, 2000 Michler 2005 Michler and Balta-Calleja 2012 Michler and Starke 1996). The properties of the matrix material, defined by its chemical structure and composition, determine not rally the type of the local yield zones and plastic deformation mechanisms active but also the critical parameters for toughening. In amorphous polymers which tend to form fibrillated crazes upon deformation, the particle diameter, D, is of primary importance. Several authors postulated that in some other amorphous and semiciystalline polymers with the dominant formation of dUatational shear bands or extensive shear yielding, the other critical parameter can be the interparticle distance (ID) (the thickness of the matrix ligaments between particles) rather than the particle diameter. 

When the particles touch, the force of attraction rises to such a large value that deformation of the particles occurs. This may be elastic deformation as demonstrated by Johnson et al. or it may be plastic indentation as noted by Krupp." In the elastic case, spherical particles form a small circle of intimate contact diameter d, which depends on the elastic modulus E, the Poisson ratio v of the material and the particle diameter D according to... 

The van der Waals forces become noticeable when particles can come sufficiently close together, that is, at separation distances of the order of the size of a molecule (i.e., 0.2-1 nm). Moreover, the magnitude of van der Waals forces becomes negligible compared with that of the gravitational force when the particle size exceeds a few microns. This is due to the fact that the gravitational force is proportional to the cube of the particle diameter, but the van der Waals force is proportional to the diameter. Once the particles are in contact, the overall van der Waals attraction is increased significantly due to the increase in the contact area. This situation is enhanced when plastic deformation takes place [6]. In Section 7.1.4, a number of well-established models for van der Waals forces due to dipole interactions between molecules are presented. 

Often, very small rubber particles or modifier particles are used to enhance the toughness, for instance, of PMMA or PP at lower temperatures. Figure 5.12 shows schematically one example with PBA core shell particles they consist of a hard core of PMMA (diameter about 180 nm) and a rubbery shell of poly(bu-tyl acrylate-co-styrene) (PBA) (approximately 40 nm thick). An outer PMMA shell increases compatibility between particles and matrix. The particles were preformed and possess spherical shapes with a narrow size distribution. Under load, the plastic deformation starts in the particles with cavitation and fibrillation of the rubbery shell. The second step is deformation in highly stressed zones between the particles in the form of crazes or homogeneous yielding. 

Note that variations of contact radius with particle diameter at equilibrium, which is in the absence of external force, for elastic and plastic deformation are different. That is,... 

For dispersion-strengthened composites, particles are normally much smaller, with diameters between 0.01 and 0.1 xm (10 and 100 nm). Particle-matrix interactions that lead to strengthening occur on the atomic or molecular level. The mechanism of strengthening is similar to that for precipitation hardening discussed in Section 11.9. Whereas the matrix bears the major portion of an applied load, the small dispersed particles hinder or impede the motion of dislocations. Thus, plastic deformation is restricted such that yield and tensile strengths, as well as hardness, improve. 

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