In order to clarify the transition of the coefficient in ASTM standard equation by the degree of work hardening, elastic-plastic finite element method analysis in which stress-strain curve was approximated by two straight line of Young's modulus E and tangential modulus E_twas carried out. By dividing stress by yield stress and strain by yield strain, various stress-strain curves could be expressed only by using the value of E_t/E. Based on the non-linear crack mechanics, the loading stress when equivalent plastic strain at node point of a crack tip became a constant value was obtained as an analysis solution. Imitating the normalized arrangement manner of numerical solution in Dugdale model in which similarity rule is effective under continuum mechanics, dimensionless quantities relevant to stress intensity factor and crack size were defined. Element size dependency in analytical solution was eliminated and transition in coefficient of small scale yielding condition equation against the value of E_t/E. was proposed. When normalized crack size a/l_0=200 and ratio of tangential modulus to Young's modulus (E_t/E) is 0.2, the coefficient of small scale yielding was 2.5 which is equal to ASTM standard condition equation.