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.

Major ampullate (MA) dragline silk supports spider orb webs, combining strength and extensibility in the toughest biomaterial. MA silk evolved ~376 MYA and identifying how evolutionary changes in proteins influenced silk mechanics is crucial for biomimetics, but is hindered by high spinning plasticity. We use supercontraction to remove that variation and characterize MA silk across the spider phylogeny. We show that mechanical performance is conserved within, but divergent among, major lineages, evolving in correlation with discrete changes in proteins. Early MA silk tensile strength improved rapidly with the origin of GGX amino acid motifs and increased repetitiveness. Tensile strength then maximized in basal entelegyne spiders, ~230 MYA. Toughness subsequently improved through increased extensibility within orb spiders, coupled with the origin of a novel protein (MaSp2). Key changes in MA silk proteins therefore correlate with the sequential evolution high performance orb spider silk and could aid design of biomimetic fibers.

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.

Spider silk is considered as the basis of a new family of high performance fibers that would reproduce the excellent mechanical properties of the silk, in particular its extreme toughness. However, it has been observed that the mechanical properties of spider silk are severely influenced by humid environments that give rise to significant decreases in its length and elastic modulus. The change from stiff to compliant tensile properties is associated with the glass transition from a glassy to a rubbery state; here, we have found that it depends on both temperature and relative humidity. The glass transition was identified at different temperatures and relative humidities by monitoring the variation of the elastic modulus and observing the emergence of supercontraction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 994–999, 2006

Two fracture criteria are proposed and applied to blunt-notched components made of brittle materials loaded under mixed mode; the former is based on the averaged strain energy density over a given control volume, the latter on the cohesive crack zone model. In both instances use of the equivalent local mode I hypothesis is made. Only two material properties are needed: the ultimate tensile strength and the fracture toughness. Numerical predictions of rupture loads from the two criteria are compared with experimental measurements from more than 160 static tests with notched beams. The samples are made of PMMA and tested at −60 • C to assure a bulk behaviour almost linear elastic up to rupture. Notch root radii range from 0.2 to 4.0 mm and load mixicity varies from pure mode I to a prevailing mode II. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.