The paper by Dominique Leguillon investigates the distinction between strength and toughness as criteria for crack initiation at a notch. It argues that both energy and stress criteria are necessary but not sufficient for fracture. Experiments by Parvizi et al. on cross-ply laminates support this, showing that the energy criterion provides a lower bound for crack lengths, while the stress criterion gives an upper bound. Together, they form a complementary criterion for crack nucleation. The energy criterion aligns with the Griffith criterion for crack growth, while the stress criterion applies to uniform traction along a straight edge. Comparisons with experiments on notched materials and bimaterial structures show good agreement. The paper discusses the paradox that arises when applying these criteria to a crack at a notch. The Griffith criterion fails to predict such a mechanism because the energy release rate vanishes, while the stress criterion suggests a crack will always form. The paper resolves this by combining both criteria, leading to a criterion that incorporates both toughness and strength. This criterion defines a characteristic length for crack initiation and is consistent with experimental results. The paper also presents a detailed analysis of the singular stress field around a notch tip, showing that the stress field tends to infinity near the tip, making the stress criterion trivially satisfied. The crack initiation length is derived using the energy criterion, which provides a lower bound for crack lengths. The paper compares this with the stress criterion, which provides an upper bound. The two criteria are shown to be complementary, with the energy criterion governing the process when the stress criterion is trivially satisfied. The paper concludes that the correct criterion for crack initiation at a notch combines both strength and toughness. This criterion is derived using the singular stress field around the notch tip and is shown to be consistent with experimental results. The paper also compares its results with those of Seweryn and finds good agreement, although some discrepancies remain. The paper emphasizes the importance of considering both energy and stress criteria in fracture mechanics and highlights the role of the notch geometry in determining the crack initiation length.The paper by Dominique Leguillon investigates the distinction between strength and toughness as criteria for crack initiation at a notch. It argues that both energy and stress criteria are necessary but not sufficient for fracture. Experiments by Parvizi et al. on cross-ply laminates support this, showing that the energy criterion provides a lower bound for crack lengths, while the stress criterion gives an upper bound. Together, they form a complementary criterion for crack nucleation. The energy criterion aligns with the Griffith criterion for crack growth, while the stress criterion applies to uniform traction along a straight edge. Comparisons with experiments on notched materials and bimaterial structures show good agreement. The paper discusses the paradox that arises when applying these criteria to a crack at a notch. The Griffith criterion fails to predict such a mechanism because the energy release rate vanishes, while the stress criterion suggests a crack will always form. The paper resolves this by combining both criteria, leading to a criterion that incorporates both toughness and strength. This criterion defines a characteristic length for crack initiation and is consistent with experimental results. The paper also presents a detailed analysis of the singular stress field around a notch tip, showing that the stress field tends to infinity near the tip, making the stress criterion trivially satisfied. The crack initiation length is derived using the energy criterion, which provides a lower bound for crack lengths. The paper compares this with the stress criterion, which provides an upper bound. The two criteria are shown to be complementary, with the energy criterion governing the process when the stress criterion is trivially satisfied. The paper concludes that the correct criterion for crack initiation at a notch combines both strength and toughness. This criterion is derived using the singular stress field around the notch tip and is shown to be consistent with experimental results. The paper also compares its results with those of Seweryn and finds good agreement, although some discrepancies remain. The paper emphasizes the importance of considering both energy and stress criteria in fracture mechanics and highlights the role of the notch geometry in determining the crack initiation length.