In this work, elastic-plastic fracture mechanics (EPFM) methods are extended to study the behavior of surface cracks. The material used is a tungsten inert gas (TIG) welded 2219-aluminum alloy, welded with 2319 weld wire. Calibration and a crack-growth test were performed. A multiple specimen R-curve technique was used. A group of specimens with the same initial crack geometry was tested to different deformation values. Several different groups were considered. Crack extension as a function of position along the crack front was determined and digitized into data files. A method to estimate values of the J integral as a function of position is presented. Local resistance curves were obtained. A parameter to characterize constraint is proposed. It is only based on the elastic solution for G. It is shown that the slopes of the resistance curves are uniquely related to the constraint parameter for all cases considered.