The accuracy of the approximate J-estimation procedure evaluated along rectangular contours in the elastic and the HRR crack tip fields was assessed. The path independency of the approximate J’s in the presence of LEFM and elastic-plastic stress fields was demonstrated experimentally in 7075-T6, 2024-0 and 5052–H32 SEN specimens with small stable crack growth of 1 to 2 mm. HRR field does not exist in a ductile material with relatively large strain-hardening exponent, i.e., N = 15. The approximate J and the COD resistance curves for 2024-0 and 5052-H32 specimens for small crack extension was established. These curves showed little sensitivity to the notch tip acuity due to large plastic yielding.