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Crack initiation emerges due to a combination of elasticity, plasticity, and disorder, and it displays strong dependence on the material’s microstructural details. The characterization of the structural uncertainty in the original microstructure is typically empirical and systematic characterization protocols are lacking. In this paper, we propose an investigational tool in the form of the curvature an ellipsoidal notch: As the radius of curvature at the notch increases, there is a dynamic phase transition from notch-induced crack initiation to bulk-disorder crack nucleation. The notch length scale associated with this transition may provide an additional characteristic of the original material microstructure. We investigate brittle but elastoplastic metals with coarse-grained, microstructural disorder that could originate in a material’s manufacturing process, such as alloying. We perform extensive and realistic simulations using a phase-field approach coupled to crystal plasticity. The microstructural disorder and notch width are systematically varied. We identify this transition for various disorder strengths in terms of the damage evolution. We identify detectable precursors to crack initiation that we quantify in terms of the expected stress drops during mode I fracture loading. Finally, we discuss ways to observe and analyze this brittle to quasi-brittle transition in experiments.