2. Relationship between the bands of localized deformation and the state of deformed material Institute of Structural Macrokinetics and Materials Science, Russian Academy of Sciences, Chernogolovka, Moscow, 142432 Russia, e-mail: svburavova@yandex.ru A.F. Belikova, S.N. Buravova, Yu.A. Gordopolov

3. Photo of a site of an internal cavity of a thick-walled pipe after compression. Material damage of thick-walled pipes is preceded by formation of set of cracks in vicinity of inner surface. Cracks are localized between ledges of a relief. 1,2 - explosive 3 - a thick-walled pipe; 4 - an internal cavity of a pipe.

4. Regeneration of a radial crack in the shear band crossing a material with structure, not undergone deformation change. The arrow specifies a band of localization of deformation. Discovery of shear band motion over unstrained material cast new light on the relationship between localization of deformation and state of strained materials Thermoplastic model of deformation localization: loss of stability adiabatic plastic current which results from heat evolution that leads thermal softening of material. According to thermoplastic model of adiabatic shear band formation intensive material deformation is necessary for their formation

5. The scheme of moving the triple shock configuration on front of a shock wave consisting of oblique (1), longitudinal waves (2), front of a shock wave(3) and tangential rupture (4). Р1- a shock wave pressure, Р2 – a oblique shock wave pressure, Р3 – pressure in the collision field of longitudinal shock waves.. Loss of stability of the shock wave during a collapse of thick-walled pipe is shown the violation of its circumferential form. At the front shock waves appear the triple shock configuration. At the moment of a meeting of longitudinal waves there is a braking transversal velocity projection of a flow. Output of ledges ( oblique wave ) on a free internal surface is accompanied by unloading. The interference of rarefaction waves from two nearest ledges of a relief creates areas of tensile pressure between ledges, where the collision area of longitudinal waves is localized.

6. The collapse of a thick-walled pipe is rationalized in terms of spallation mechanism: formation bands of localized deformation is associated with the rarefaction wave interference resulting in negative (tensile) strain that did not exceed a material strength. Radial cracks and their extensions in the form of shear bands arise at the stage of unloading after the deformation condition of a material is already generated. The processes of damaging and cracking are independent and proceed consecutively.

7. Please forward your questions to: gordop@ism.ac.ru svburavova@yandex.ru

8. Thank you for your attention!