The expanding role of the Anstis relationship in advanced materials research: A perspective

Abstract

Fracture toughness remains one of the most important parameters governing the structural reliability of brittle and quasi-brittle materials. Across a broad-spectrum of 2026 studies, the Anstis relationship continued to serve as one of the most widely adopted methods for evaluating indentation fracture toughness in ceramics, glass-ceramics, thermal barrier coatings, solid electrolytes, high-entropy systems, carbides, borides, composites, geological materials, and additively manufactured structures. The reviewed studies collectively demonstrate that the Anstis relationship remains valuable because it enables fracture toughness estimation from indentation-derived crack lengths while maintaining experimental simplicity and compatibility with heterogeneous or miniature materials systems. The collected publications further reveal a growing integration of fracture toughness evaluation with advanced microstructural engineering strategies including additive manufacturing, spark plasma sintering, eutectic architecture design, high-entropy alloying, defect engineering, phase transformation, residual stress tailoring, and interface-controlled reinforcement. Toughening mechanisms repeatedly observed across the literature include crack deflection, crack bridging, grain refinement, residual compressive stress development, transformation toughening, grain boundary pinning, and multiphase reinforcement. Applications span aerospace systems, thermal/environmental barrier coatings, dental restorations, hydrogen storage alloys, transparent ceramics, radiation shielding glasses, all-solid-state batteries, and ultra-high-temperature structural ceramics. The present perspective integrates fragmented findings from the 2026 excerpts provided into a coherent overview of the expanding role of the Anstis relationship in contemporary materials science research.