# stress intensity factor

## A BRIEF OVERVIEW OF STATIONARY TWO-DIMENSIONAL THERMOELASTIC STATE MODELS IN HOMOGENEOUS AND PIECEWISE-HOMOGENEOUS BODIES WITH CRACKS

Purpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks.

## STUDY OF FINE-GRAINED FIBER CONCRETE CRACKING RESISTANCE FROM THE POINT OF VIEW OF DESTRUCTION MECHANICS

Fiber reinforced concrete began to appear in the market in the 60s of the last century, and since then the interest in this type of reinforcement has been steadily growing. The article presents the results of studies on the crack resistance of concrete reinforced with polypropylene fibers of various lengths and volume concentrations in fine-grained concrete. Waste from the wet magnetic separation of the Poltava mining and concentration plant was used as an aggregate in the concrete. Polypropylene fibers with the various lengths diameter of 0.2 mm were used for reinforcement.

## Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack

Purpose. A mathematical model to determine the two-dimensional thermoelastic state in a semi-infinite solid weakened by an internal crack under conditions of local heating is examined. Heat flux due to frictional heating on the local area of the body causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of practical interest.

## Mathematical modeling of stationary thermoelastic state in a half plane containing a periodic system of cracks due to periodic local heating by a heat flux

Purpose. To determine the two-dimensional thermoelastic state in a semi-infinite solid (half-plane), weakened by a system of periodic internal cracks under conditions of local heating on the edge of the half plane. Heat flux due to frictional heating on the local area of the body, causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of a practical interest.

## Mathematical modeling of stationary thermoelastic state in a half plane containing an inclusion and a crack due to local heating by a heat flux

The two-dimensional stationary problems of heat conduction and  thermoelasticity for a semi-infinite elastic body containing an inclusion and a crack  are  considered.  For this purpose, mathematical models of these  two-dimensional problems in the form of a system of singular integral equations (SIEs) of the first and the second kinds are constructed.  The numerical solution of the system of integral equations in the case of a half plane  containing an inclusion and thermally insulated crack due to local heating by a heat flux is obtained using the method of mechanical quadratures.  We pre

## Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source

Purpose. To determine the two-dimensional thermoelastic state in a circular plate, weakened by an edge or internal crack induced by a stationary heat sourse. This paper proposes using singular integral equation (SIE) to investigate thermostressed intensity in the vicinity of the crack tip, depending on the local heat source placement and identify typical mechanical effects.