Local strain energy to assess the static failure of U-notches in plates under mixed mode loading

Abstract

The averaged value of the strain energy density over a well-defined volume is used to predict the static strength of U-notched specimens under mixedmode conditions due to combined bending and shear loads. The volume is centered in relation to the maximum principal stress present on the notch edge, by rigidly rotating the crescent-shaped volume already used in the literature to analyse U-and V-shaped notches subject to mode I loading. The volume size depends on the ultimate tensile strength σ u and the fracture toughness K IC of the material. In parallel, an experimental programme was performed. All specimens are made of polymethyl-metacrylate (PMMA), a material which exhibits quasi-brittle behaviour at −60 • C. Good agreement is found between experimental data for the critical loads to failure and theoretical predictions based on the constancy of the mean strain energy density over the control volume.

Fracture behaviour of notched round bars made of PMMA subjected to torsion at −60°C

“…In previous works by the authors [28,[37][38][39] tensile tests with PMMA specimens at low temperatures had shown an almost linear elastic mechanical behaviour up to failure (see Fig. 8a).…”

“…The problem becomes more involved if the loading symmetry is lost, i.e. when the notched structural component is subjected to mixed mode loading as widely discussed in previous works by other researchers [31][32][33][34][35][36] and also by the present authors [37][38][39][40][41][42].…”

“…The averaged value of the strain energy density (SED) over a well-defined control volume surrounding the notch tip has been used profitably to summarise the static strength data of notched specimens under static loads [19,[37][38][39][40][41][42] as well as notched components and welded joints under fatigue loading. Dealing with static loads, the SED approach has successfully been applied to assess the critical loads to failures of brittle or quasi-brittle materials weakened by U-and Vnotches.…”

“…While systematic experimental data on fracture of blunted notched specimens (with notches of different root radii) loaded under mode I and mixed mode loading (1+ II) have been recently provided [33,34,[37][38][39][40][41], the results from blunted notched specimens under torsion loading are relatively scarce since the research activity has mainly considered cracked bars under torsion [43][44][45][46][47][48].…”

“…The specimens have been tested at -60 °C to have a behaviour closer to the linear elastic one, as previously made under mode I and mode II loadings [37][38][39][40][41].…”