Issue34

F. Berto, Frattura ed Integrità Strutturale, 34 (2015) 11-26; DOI: 10.3221/IGF-ESIS.34.02 22 temperature [45, 54-55]. The final synthesis has been carried out by normalising the local SED to the critical SED values (as determined from unnotched, plain specimens) and plotting this non-dimensional parameter as a function of the R / R 0 ratio. A scatterband is obtained whose mean value does not depend on R / R 0 , whereas the ratio between the upper and the lower limits are found to be about equal to 1.3/0.8=1.6 (Figure 6). The strong variability of the non-dimensional radius R / R 0 (notch root radius to control volume radius ratio, ranging here from about zero to about 500) makes stringent the check of the approach based on the local SED. The scatterband presented contains failure data from 20 different ceramics, 4 PVC foams and some metallic materials. Figure 6 : Synthesis of data taken from the literature. C ONCLUSIONS or many years the Strain Energy Density (SED) has been used to formulate failure criteria for materials exhibiting both ductile and brittle behaviour. SED is the most fundamental quantity in Mechanics being all physical quantities expressible in terms of it. From pico to macroscopic scale the energy absorption and dissipation can explain the most complex phenomena tied to fracture initiation and propagation. Keeping in mind that the design rules valid for large bodies (i.e high volume to surface ratio) can not be directly translated and applied to small bodies where local inhomogeneities play a fundamental role for the material damage initiation and propagation and being also aware of the recent contributions and efforts to develop a multiscaling and segmentation scheme able to capture the complex phenomena that happen at every level from pico to macro, the main purpose of the paper is to present a review of the approach based on the mean value of the local strain energy density. Dealing with static loading the approach is applied here to different materials and geometries both, under mode I and mixed mode (I+II) loading. About one thousand experimental data, taken from the recent literature, are involved in the synthesis. They were from U- and V-notched specimens made of very different materials. A scatter band is proposed by using as a synthesis parameter the value of the local energy averaged over control volume (of radius R 0 ), normalised by the critical energy of the material. Such a normalised energy is plotted as a function of the notch radius to critical radius ratio, R / R 0 . The strain energy density (SED) in a circular sector of radius R 0 located at the crack initiation sites has successfully been used to summarise also about nine hundred data from fatigue failures of welded joints. Under the hypothesis that all material inhomogeneities can be averaged, that ceases to be valid at pico- and micro-levels but at the same time is the basis of the volume-based theories applied to structural components , the Strain Energy Density Approach is shown to be a powerful tool both for static and fatigue strength assessment of notched and welded structures. F 0 0.4 0.8 1.2 1.6 0.1 1 10 100 1000 ceramic materials PMMA data metallic materials and other materials R/R 0 About 1000 data from static tests 0.4  m  R 0  500  m 2.5   t  1200 MPa 0.15   IC  55 MPa m 0.5 0.1   0.4 0  R/R 0  1000 0  2   150° Mode 1 and mixed mode (1+2) R  0 R 0 r 0 R R 0 +r 0 R 0 r 0 Steel AISI O1 Duralluminium PVC c W W Acrylic resin