BRITTLE-FRACTURE OF SOLIDS CAUSED BY INTENSE ELECTRON-BEAMS

In the mid 1960s, powerful pulse electron beam accelerators having a v oltage of some millions of volts were invented and later used to fract ure various materials. Experimental data analysis allowed discovery of a new mode of fracture in several ductile crystals caused by a specif ic energy supply to the crack tip. The mode differs from well known th ermomechanical modes of fracture caused by the ''heat-thermostress cra ck'' mechanism. This new mode is called the electron fracture mode (EF M). It is characterized by the following three special features. (i) I nitial macrocracks in a specimen do not affect the threshold of fractu re; that is, the value of the beam intensity at which the specimen bre aks. (ii) The fracture of different materials, which can be very ducti le at usual mechanical loads, occurs in a brittle manner; that is, the specimen usually splits by a crack without any residual deformation. (iii) The splitting cracks propagate with supersonic velocities. These data are controversial from the point of view of common fracture mech anics and, hence, they cannot be understood or explained from the trad itional position. The purpose of the present study is to create a simp le practical model of the EFM. The basic viewpoint can be briefly summ arized as follows: during irradiation of a solid by a high intensity e lectron beam, some solid plasma clots are formed and act as ''blades'' or ''wedges,'' cutting the crystalline specimen. In the Introduction, experimental data on the EFM are analyzed and discussed, while the pe culiarities of the EFM are specified. As a result, it is concluded tha t the processes caused by the EFM are unusual for the common concepts of fracture mechanics. In Section 2 the invariant GAMMA-integrals of a n electromagnetic deformable medium are modified for supersonic singul arities. The basic model and some problems serving to explain and desc ribe the EFM are formulated. In Section 3, the relativistic electron i nteractions in beams are considered. Using GAMMA-integrals, we derive the law of the interaction of two moving relativistic charges; that is , the generalized Coulomb's law for relativistic charges. In particula r, when two relativistic electrons, e, move with the same velocity, v, one behind the other along a rectilinear trajectory, the force, F, ac ting upon the rear electron is equal to: [GRAPHICS] where R is the dis tance between the electrons, c is the speed of light in the vacuum, an d a is the phase-speed of light in a medium having electromagnetic con stants, mu, epsilon, and epsilon'. It appears that two electrons movin g faster than the phase-speed of light attract one to the other, as di stinct from the common Coulomb law. Hence, the beams of such relativis tic electrons tend to self-pack and self-compress. The latter problem is studied using a periodic chain model of the electron beam. In Secti on 4, the dynamic elastic problem of supersonic cutting by a thin wedg e is formulated and solved, and the drag force is calculated. In Secti on 5, the problem of deceleration of the moving wedge is solved in qua si-steady approximation. The length of a resulting cut, that is, the f inal crack, is determined. Some applications of the analytical solutio ns are given. In Section 6, the theoretical results are analyzed and c ompared with experimental results. The role of relativistic electrons is estimated and some parameters of solid-state electron plasma clots are defined. In the Conclusion, the necessity of further study of this mysterious phenomenon is emphasized.