To investigate how strain localization develops from a structural and stress heterogeneity, we introduced a V-shaped circumferential notch in cylindrical samples of Bentheim and Berea sandstones and conducted triaxial compression tests at confining pressure optimum for compactive failure. The critical stresses for initial yield map out a cap with a negative slope in the stress space, and the presence of the notch enhanced the local stress which induced damage to occur at remote stresses significantly lower than in the unnotched sample. Our mechanical and microstructural data demonstrate the spectrum of failure modes and depict the initiation and propagation of a localized structure. In the Bentheim sandstone we observed discrete compaction bands that propagated through the sample cross section with episodic force drops, and in the Berea sandstone, we observed diffuse bands accompanied by strain hardening. Compactive yield was marked by an upsurge in acoustic emissions, corresponding to the formation of a process zone at the notch tip. To probe the initial yield behavior and geometry of the process zone, we developed a micromechanical model using linear elastic fracture mechanics, which predicts a process zone extending 0.3--0.5 of the notch depth, in accord with the microstructural observations. Analysis of the stress path reveals the potential activation of multiple localization modes around the notch tip. The energy required to develop a compactive deformation band was inferred to range from 6 to 43 kJ m-2. In the Bentheim sandstone the energy was observed to be inversely dependent on the confining pressure.