Issue 52

A.V. Tumanov et alii, Frattura ed Integrità Strutturale, 52 (2020) 299-309; DOI: 10.3221/IGF-ESIS.52.23 301 1 2 0 1 2 N a f T EU      (4) where E - Young's modulus. The fatigue damage accumulation rate can be obtained from the equation (3)   1 ln N f f f f f d dN N N N             (5) F ATIGUE CRACK GROWTH RATE or Ramberg-Osgood hardening law [26] the critical value of a strain energy density c W can be obtained from true stress-strain diagram: 0 p f n y c y W d E E                           (6) where  - is the strain hardening coefficient, p n - is the strain hardening exponent, y  - is the yield stress, f  - ultimate tensile stress. According to the classical Hutchinson-Rosengren-Rice model in the zone where fully plastic singularity is dominated the strain energy density W can be found from following expression [14]: 2 2 1 1 (1 ) 1 p p n n p y p e p n W K n E r           (7) where  - is Poisson's ratio, / r r a  - crack tip distance, a - crack length, e   - dimensionless equivalent Mises stresses which depend only on a polar coordinate  and normalized by   max 1 e     . The plastic stress intensity factor P K in small-scale and extensive yielding conditions in Eqn.(7) can be expressed directly using Rice’s J -integral [15]. That is 1 1 2 p n P p y p J E K I L             (8) where 2 2 2 1 1 1 2 cos 3 6 1 y n P e kk e r n J d E n                             cos sin r r y rr r y rr r u u u u r d d r r                                                   (9) In Eqns. (8-9) , i u are crack tip dimensionless displacement components, L is cracked body characteristic size, in our case is the crack length L a  , and p I is the numerical constant of the crack-tip stress–strain field, which should be F