A fundamental understanding and characterization of ductile crack growth, and a rigorous basis for predicting final fracture (as opposed to crack growth initiation), are only possible from incremental elastic-plastic solutions of crack growth. Previous analytical investigations have provided leading-order (in distance, r, from the crack tip) asymptotic solutions for the near-tip stress and deformation fields. Such solutions have a limited range of validity. Here we review our recent work which derives plane strain tensile elastic-ideally plastic stress and deformation solutions valid through second order in r. We explain how the higher-order solution structure is derived, and we show with specific examples how these second-order solutions can be used to estimate the radius of validity, as a function of angle about the crack tip, of previous leading-order solutions. Comparisons with full-field numerical solutions demonstrate that the new second-order solutions substantially extend the leading-order solutions' range of validity. Such quantitative estimates of solutions' regions of validity seem essential for determining when ductile crack growth characterization based on homogeneous-continuum-mechanical asymptotic solutions is applicable to actual polycrystalline or composite materials with their finite-sized microstructures.
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