539.375

anti-plane deformation, section-crack, elastic-plastic problem, plastic zone, plastic band.

The stress-strain state of an ideally elastic-plastic half-band of finite width with a central section-crack was analyzed. The state of anti-plane deformation is caused by tangential displacements of the strip faces. The elastic-plastic problem was solved and a continual zone of plastic deformations was found. The problem of the development of plastic deformations along the incision in its plane was solved. It is shown that at low loads, the continual plastic zone is shaped like a circle centered on the extension of the section, distant at a distance equal to the radius of the circle from the top of the section. The shape of the plastic zone and the length of the plastic strip are determined on the basis of a linear model of the plastic zone, according to which its characteristics are definite by the stress intensity factor. Load limits for which the linear model of the plastic zone provides sufficient investigation accuracy are established.

1. Bozhydarnyk V. V., Sulym G. T. Elementy teotii plastychnosti ta micnosti. T. 1. Lviv: Svit, 1999. 945 р. [Іn Ukrainian].
2. Panasyuk V. V., Savruk M. P., Dacyshyn A. P. Raspredelenie napryazhenii okolo treshchyn v plastinach i obolochkah. K.: Naukova dumka, 1976. 444 р. [Іn Russian].
3. Popov G. Ja. Koncentracia uprugih napriazhenii vozlie shtampov, razrezov, tonkich vkliuchenii i podkreplenii. K.: Naukova dumka, 1982. 344 р. [Іn Russian].
4. Stress intensity factors handbook. Yukitaka Murakami. The Society of Materials Science. Japan. Committee on Fracture Mechanics. 1987. Vol. 2. P. 641–1456.
5. Kryven’ V. A. Dvoperiodychna pruzhnoplastychna zadacha pozdovzhn’jgo zsuvu tila z zhorstkym rombichnym vrkiuchenniam. Matematychni metody і fiz mech polia. 2001. T. 44. No. 1. Р. 109–113.
6. Kryven' V. A. Antiplane problem for an elastic perfectly plastic body with biperiodic system of rhombic notches. Materials Science. 2001. Vol. 37. No. 6. Р. 866–872.
7. Kryven' V. A. Linear model of a plastic zone in the vicinity of a sharp notch under the conditions of longitudinal shear. Materials Science. 2004. Vol. 40. No. 7. P. 475–483.
8. Cherepanov G. P. Mechanika hrupkogo razrusheniia. М.: Nauka, 1974. 640 р. [Іn Russian].
9. Annin B. D., Cherepanov G. P. Uprugo plasticheskaja zadacha. Novosibirsk: Nauka, 1983. 238 р. [Іn Russian].
10. Kryven' V. A. Continuous and discontinuous solutions of an elastoplastic problem of antiplane deformation of a cracked body. Fiz. Khim. Mekh. Mater. 1985. Vol. 21. No. 6. P. 10–16.
11. Mushalishvili N. I. Singuliarnye integral’nye uravneniia. M.: Fizmatgiz, 1968. 512 р. [Іn Russian].

1. Bozhydarnyk V. V., Sulym G. T. Elementy teotii plastychnosti ta micnosti. T. 1. Lviv: Svit, 1999. 945 р. [Іn Ukrainian].
2. Panasyuk V. V., Savruk M. P., Dacyshyn A. P. Raspredelenie napryazhenii okolo treshchyn v plastinach i obolochkah. K.: Naukova dumka, 1976. 444 р. [Іn Russian].
3. Popov G. Ja. Koncentracia uprugih napriazhenii vozlie shtampov, razrezov, tonkich vkliuchenii i podkreplenii. K.: Naukova dumka, 1982. 344 р. [Іn Russian].
4. Stress intensity factors handbook. Yukitaka Murakami. The Society of Materials Science. Japan. Committee on Fracture Mechanics. 1987. Vol. 2. P. 641–1456.
5. Kryven’ V. A. Dvoperiodychna pruzhnoplastychna zadacha pozdovzhn’jgo zsuvu tila z zhorstkym rombichnym vrkiuchenniam. Matematychni metody і fiz mech polia. 2001. T. 44. No. 1. Р. 109–113.
6. Kryven' V. A. Antiplane problem for an elastic perfectly plastic body with biperiodic system of rhombic notches. Materials Science. 2001. Vol. 37. No. 6. Р. 866–872.
7. Kryven' V. A. Linear model of a plastic zone in the vicinity of a sharp notch under the conditions of longitudinal shear. Materials Science. 2004. Vol. 40. No. 7. P. 475–483.
8. Cherepanov G. P. Mechanika hrupkogo razrusheniia. М.: Nauka, 1974. 640 р. [Іn Russian].
9. Annin B. D., Cherepanov G. P. Uprugo plasticheskaja zadacha. Novosibirsk: Nauka, 1983. 238 р. [Іn Russian].
10. Kryven' V. A. Continuous and discontinuous solutions of an elastoplastic problem of antiplane deformation of a cracked body. Fiz. Khim. Mekh. Mater. 1985. Vol. 21. No. 6. P. 10–16.
11. Mushalishvili N. I. Singuliarnye integral’nye uravneniia. M.: Fizmatgiz, 1968. 512 р. [Іn Russian].