Quasi-elastic impact

At a quasi-elastic impact the film thinning velocity is much smaller than the particle velocity. Thus dh/dt is very much less than unity and can be neglected in deriving Eq. (11.5). It is easy to obtain the well-known formula of Evans (1954) for the film deformation time from Eq.(11.6),... 

Using (11.17), one can show that the second term in the root in Eq. (11.13) is much smaller than unity. Moreover, a quasi-elastic impact is obtained in the case A<0.01. Therefore Eq. (11.13), after some simplifications, takes the form... 

Using real values, it is easy to make sure that at a quasi-elastic impact (0.005bubble surface (a=4) the values of h. at 2ap = 100 pm they are approximately... 

The relation between / h and A at B=1 has been calculated (Fig. 11.5b). It shows that the relative thinning of film during an inelastic impact (A>0.01 with h - h /3) depends even less on A than in the case of a quasi-elastic impact (A<0.01 with h h /4). 

Collisions between particles with smooth surfaces may be reasonably approximated as elastic impact of frictionless spheres. Assume that the deformation process during a collision is quasi-static so that the Hertzian contact theory can be applied to establish the relations among impact velocities, material properties, impact duration, elastic deformation, and impact force. 

In this chapter, two simple cases of stereomechanical collision of spheres are analyzed. The fundamentals of contact mechanics of solids are introduced to illustrate the interrelationship between the collisional forces and deformations of solids. Specifically, the general theories of stresses and strains inside a solid medium under the application of an external force are described. The intrinsic relations between the contact force and the corresponding elastic deformations of contacting bodies are discussed. In this connection, it is assumed that the deformations are processed at an infinitely small impact velocity and for an infinitely long period of contact. The normal impact of elastic bodies is modeled by the Hertzian theory [Hertz, 1881], and the oblique impact is delineated by Mindlin s theory [Mindlin, 1949]. In order to link the contact theories to collisional mechanics, it is assumed that the process of a dynamic impact of two solids can be regarded as quasi-static. This quasi-static approach is valid when the impact velocity is small compared to the speed of the elastic... 

The basic theories of elastic deformations associated with various contact forces under static contact conditions have been introduced in the last section. Assuming that an impact process of two solids can be regarded as quasi-static, the theories given in 2.3 are used directly to link the dynamic deformations of the colliding solids with the impact forces. In this section, the collisions of elastic spheres are described. 

For many engineering applications, impact fracture behavior is of prime practical importance. While impact properties of plastics are usually characterized in terms of notched or un-notched impact fracture energies, there has been an increasing tendency to also apply fracture mechanics techniques over the last decade [1, 2 and 3]. For quasi-brittle fracture, a linear elastic fracture mechanics (LEFM) approach with a force based analysis (FBA) is frequently applied to determine fracture toughness values at moderate loading rates. 

High rate fracture parameters are important in the assessment of structural integrity, particularly in applications where there is a risk of rapid crack propagation. Linear elastic fracture mechanics provide a method for assessing fracture parameters under quasi-static conditions but under impact conditions various dynamic effects make both experimental measurement and analysis difficult. 

It should be noted that the composites damage and failure models discussed here are based on an assumption of rate-independent behaviour, and materials properties used for validation studies are based on quasi-static tests. This is currently standard practice in impact simulations of composite structures, which is an important assumption in the work. Reasons for this are the lack of international dynamic test standards for measuring rate-dependent composites properties, so established test procedures are missing. Dynamic failure models for composites are not well understood nor implemented in current commercial FE codes. In justification it should be pointed out that carbon fibres are highly elastic, thus fibre-dominated properties show no... 

Klepaczko J R, Hsu T R, Bassim M N. Elastic and pseudoviscous properties of coal under quasi-static and impact loadings. Canadian Geotechniacl Journal 1984 21 203-212. 

Material properties. In addition to the common knowledge that the materials must be stronger, tougher, and lighter [79], it is envisioned that the materials must be less stiff during impact so that the impact duration can be extended and the elastic wave will have sufficient time to reach and be reflected by the boundary many times for a quasi-static response, as discussed by Olsson [76]. However, this requirement is contradictory to the structural requirement that is, the material must be stiff to provide structural capacity. 

When an atmospheric spray specimen was subjected to a quasi-static test with an indenter of 1 mmcj), both the substrate and the bond coat were affected with marked plastic deformation, and in particular, the substrate underwent so drastically that the limit of elastic-plastic deformation was stepped over to present a porous zone with concentrated cracks. As the indenter size grew, the area of plastic deformation in the substrate and the bond coat was reduced, to present Hertz cone cracks in the cross-section. In addition to Hertz cone cracks, a number of cracks were seen in parallel to the substrate, which were thought to have occurred when the load was eliminated. With an indenter of 4 mmcj), the area of plastic deformation was reduced further, and lateral cracks were observed as the load was eliminated. Debonding between the bond coat and the substrate was observed only with the 4-mm indenter. Comparing to impact tests results(Fig. 7), qusi-static tests(Fig. 14) can reproduce similar fracture behavior. 

Figure 8.10 The relation between yield stress Oy and ratio of elasticity modulus to the Griinesen parameter E/y in quasi-static (1) and impact (2) tests for nanocomposites HDPE/EP [31]...

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