Brittle failures from U‐ and V‐notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite‐size volumes

Abstract

A B S T R A C T A large bulk of static test results carried out on notched specimens are presented in a unified way by using the mean value of the strain energy density (SED) over a given finite-size volume surrounding the highly stressed regions. In plane problems, when cracks or pointed V-notches are considered, the volume becomes a circle or a circular sector, respectively, with R C being the radius. R C depends on the fracture toughness of the material, the ultimate tensile strength and the Poisson's ratio. When the notch is blunt, the control area assumes a crescent shape and R C is its width as measured along the notch bisector. About 900 experimental data, taken from recent literature, are involved in the local SED-based synthesis. They have been obtained from (a) U-and V-notched specimens made of different materials tested under mode I loading; (b) U-and V-notched specimens made of polymethyl-metacrylate (PMMA) and an acrylic resin, respectively, tested in mixed, I + II, mode; (c) U-notched specimens made of ceramics materials tested under mode I.The local SED values are normalized to the critical SED values (as determined from unnotched specimens) and plotted as a function of the R/R C ratio. A scatter band is obtained whose mean value does not depend on R/R C , whereas the ratio between the upper and the lower limits are found to be about equal to 1.6. The strong variability of the non-dimensional radius R/R C (ranging here from about zero to around 1000) makes stringent the check of the approach based on the mean value of the local SED on a material-dependent control volume.Keywords brittle fracture; critical radius; finite-size volume; notch; strain energy density. N O M E N C L A T U R Ea = notch depth E = Young's elastic modulus E 1 = strain energy on the control volume f ij , g ij = angular functions F(2α) = parameter to evaluate the strain energy density (blunt notches, R = 0) J = Rice's J integral l ch = characteristic length of the material K I , K U R,I , K V R,I = stress-intensity factor and notch stress-intensity factors for U-and V-shaped notches Correspondence: P. Lazzarin.

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

“…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].…”

“…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. About 1200 experimental data under mode I and mixed mode conditions (I + II) were summarised in Refs [40,42]. Recently the SED approach was also applied to summarise a number of fatigue data from V-notched specimens subjected to uniaxial and multiaxial loading [63,64].…”

“…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].…”