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Significance
Fracture originating from sharp notches has stayed stubbornly difficult to treat within a single predictive framework, largely because such features sit uncomfortably between two classical limits. On one side lies the crack, governed by stress intensity factors and asymptotic singular fields. On the other lies the blunt notch, where peak stress concepts and net-section arguments still carry explanatory weight. Sharp V-notches occupy the grey zone between these descriptions, and that’s precisely where many engineering components actually operate. Bolts, grooves, machined joints, and cutouts don’t fail as ideal cracks, however, they don’t behave like smoothly rounded features either. Previously, local approaches have tried to bridge this gap by introducing material length scales into fracture assessment and the theory of critical distances and related strain-energy concepts succeeded in rationalizing certain trends, but they rely on assumptions that don’t always survive contact with geometry. Treating the critical distance as a fixed material constant, for instance, becomes questionable once notch angle and notch acuity vary independently. Experimental evidence keeps showing that geometry doesn’t just modulate stress amplitude; it reshapes how the local stress field decays away from the notch tip, and that decay controls failure. Linear elastic notch stress fields offer a more faithful description of what happens near a sharp V-notch. The Williams eigenfunction solution captures how stress scales with distance and notch opening angle, but on its own it doesn’t close the loop to failure. Something extra is needed to connect that local field to a material’s resistance to fracture. That connection becomes even more fragile when fracture toughness isn’t known a priori, which is often the case in engineering practice. A recent research paper published in Engineering Fracture Mechanics and led by Professor Xiangqiao Yan from the Center for Composite Materials and Structure at Harbin Institute of Technology, the researcher developed a local fracture assessment framework for sharp V-notches based on linear elastic notch stress fields. He introduced a stress concentration factor eigenvalue and associated geometric–material characteristic parameters that link notch geometry to failure.
Professor Yan grounded his approach in the linear elastic stress field ahead of sharp and rounded V-notches under Mode I loading and focused on the circumferential stress along the notch bisector, because that component dominates tensile fracture and carries the eigenvalue dependence on notch opening angle. He used established analytical forms for the notch stress field, to express failure through a local stress condition evaluated at a finite distance from the notch tip, which is consistent in spirit with point-based local criteria but no longer tied to a fixed distance. The author defined k* as the stress concentration factor associated with a specific notch radius （ 𝑃*） that acts as a geometric threshold for a given pointed V-notch. Below that radius further sharpening doesn’t change the fracture response in a meaningful way. To make k* operational, the author formulated a system linking fracture toughness, critical distance, notch radius, and stress concentration factor through the local stress field equations. Plus, he assumed that the product of stress concentration factor and critical distance remains invariant across notches sharing the same pointed geometry. The study then tested this framework against extensive experimental data drawn from the literature. Professor Xiangqiao Yan also examined U-notched and V-notched specimens made of PMMA at low temperature and at room temperature, as well as ceramic materials such as silicon nitride and yttria-stabilized zirconia. Across bending, tensile, and Brazilian-disc configurations, he extracted geometric–material characteristic parameters by fitting k*, the associated notch radius （𝑃*), and the critical distance（Lc* ). Once those parameters were fixed, the researcher predicted fracture toughness and failure stress for other notch radii without further calibration.
To summarize, the new method proposed by Professor Xiangqiao Yan successfully predicts fracture behavior across different notch radii using a single calibrated parameter set. We believe what stands out is how consistently the predictions tracked experimental measurements and errors typically stayed within a few percent, even when notch depth, loading configuration, or material behavior changed and this is excellent accuracy. The author also didn’t tune parameters specimen by specimen; he carried them across geometries tied to the same pointed notch and this transferability is the real test of a local approach, and here it held up across brittle polymers and ceramics. The study also addressed cases where fracture toughness wasn’t directly known, and proposed an empirical route to estimate it so the local framework remains usable under practical constraints. All of these results reinforce the idea that k* captures a physically meaningful transition in notch behavior rather than acting as a fitting convenience
We think the study of Professor Xiangqiao Yan is significant because it gives engineers a reliable way to predict fracture from sharp notches without pretending every notch is a crack. The work shows elegantly that sharp notches have their own governing behavior, controlled by the notch stress field and a geometry-dependent characteristic scale. Once that scale is identified through the stress-concentration eigenvalue, fracture predictions become consistent across different notch radii and loading setups. That’s why the approach works where mixed or ad-hoc methods usually don’t. The question, how the new method can help engineers? For instance, in mechanical design of fasteners, grooves, keyways, and threaded components, sharp V-notches are unavoidable and designers often oversize parts because fracture predictions are too conservative. The reported method lets engineers assess failure more accurately without redesigning the notch or assuming a pre-existing crack that isn’t there. In another field such as polymer and ceramic components, especially brittle or semi-brittle materials, fracture toughness is not always well characterized. The new framework allows toughness to be inferred from notched tests themselves, which makes it practical for materials qualification, quality control, and failure analysis when standard fracture specimens aren’t available. Also, in pressure vessels, plates with holes, and disk-type specimens used in testing and validation, the proposed method supports geometry transferability and results from one notch configuration can be applied to another, provided the pointed notch geometry is the same and this reduce the need for repeated, expensive test campaigns. Another application we can think of is in fatigue-critical and fracture-critical components operating near the crack–notch transition, the study clarifies when a notch should be treated as crack-like and when it shouldn’t and this boundary is often guessed in practice; but using the new method it can be a measurable geometric parameter rather than a guess. Indeed, the new method restores physical meaning to local fracture criteria and gives engineers a tool that’s both predictive and interpretable, which is exactly what’s needed when safety, weight, and cost are all in tension.
Reference
Xiangqiao Yan, A local approach for fracture analysis of sharp notches under Mode I loading, Engineering Fracture Mechanics, Volume 290, 2023, 109404,
Go to Journal of Engineering Fracture Mechanics .
