ISSN 1068-3666, Journal of Friction and Wear, 2009, Vol. 30, No. 1, pp. 1–6. © Allerton Press, Inc., 2009. Original Russian Text © I.I. Argatov, Yu.A. Fadin, 2009, published in Trenie i Iznos, 2009, Vol. 30, No. 1, pp. 7–15. 1 + INTRODUCTION The problem of impacts of a spherical indenter against the elastic body surface is a definite practical challenge; its solution is used in particular in the math- ematical modeling of the erosion process [1, 2]. The solution of the dynamic contact problem of the theory of elasticity involves large mathematical difficulties; numerous publications deal with the exploration of its various aspects. The Hertzian impact theory is most often used in practical calculations [3] because it pro- vides expressions for all impact parameters as simple formulas. Papers [4, 5] disclose the obtained analytical solutions verifying the Hertz theory for the particular case when one of the interfaced bodies represents an elastic semispace. Numerical modeling of the process of impacts on an elastic semispace by a solid was per- formed in [6, 7]. The behavior of the contact pressure in the contact site center in the process of impacting was explored in articles [8, 9]. The studies in the domain of impacts are reviewed in [10, 11]. In order to apply the solutions of the dynamic con- tact problem to the development of methods of identifi- cation of the parameters of the abrasive particles impacting the 3D body surface and to the determination of the threshold at which erosion starts based on acous- tic emission data [12], it is necessary to know the dynamic response of the elastic semispace surface when it is impacted by a ball indenter. The above works concentrate mainly on the processes that occur in direct proximity to the contact zone, while no formulas are + Corresponding author, e-mail: argatov@home.ru derived that would determine the dynamic response of the elastic body’s surface to impacts. It is noteworthy that the problem of identification of particles from acoustic emission data was considered earlier in [13]. In this case, the target was an elastic plate and the method of identification [13] was based on the solving of the problem of impacts of particles against the elastic plate’s surface. The target from the surface of which the acoustic emission is registered is modeled by an elastic semispace in the present paper. The problem of the dynamic response of the elastic semispace also appears during the development of methods of identification of the modulus of elasticity of the base. Dynamic tests of materials are known [14] to be cheaper than quasistatic tests. One such method is proposed in [14], by which the assumption about the contact response nature of the elastic base is simplified a priori. The present work shows how to obtain an approximate analytical dependence of the contact response in the process of impacting; the obtained dependence allows for energy dissipation through transfer by elastic waves propagating over the contact spot (see works [4, 15], in particular). 1. APPROXIMATE CALCULATION OF THE DERIVATIVE OF THE ELASTIC CONTACT FORCE DURING IMPACTS BY THE BALL INDENTER Assume that a ball indenter with radius R, weight m, and made of material with density ρ 0 , Young modulus E 0 , and Poisson coefficient ν 0 , hits the surface of an elastic homogeneous isotropic body at a right angle Excitation of the Elastic Half-Space Surface by Normal Rebounding Impact of an Indenter I. I. Argatov + , Yu. A. Fadin Institute of Problems of Machine Studies, Russian Academy of Sciences, Bol’shoi Prospekt 61, St. Petersburg, 199178 Russia Received September 3, 2008 Abstract—A dynamic contact problem of the linear theory of elasticity regarding the response of the elastic half-space surface to the normal impact of an indenter is considered. If the indenter is spherical, the Hertzian theory serves to determine the impact parameters. The displacements of points on the surface remote from the contact spot are described by solving Lamb’s problem. In the case of impacts by a flexible plate indenter that transfers uniformly distributed load to the elastic half-space surface, a first order asymptotic model is applied, which takes into account the dissipative properties of the elastic base due to elastic energy transfer by waves to infinity. The main results of the work are obtained in closed form. Key words: impact, elastic semispace, identification of abrasive particles, identification of elastic modulus. DOI: 10.3103/S1068366609010012