Issue 43

F. Berto et alii, Frattura ed Integrità Strutturale, 43 (2018) 1-32; DOI: 10.3221/IGF-ESIS.43.01 2 A powerful parameter able to fully include the scale effect is the local strain energy density as recently discussed by Sih and co-authors in Refs [1-6]. Taking into account recent advances regarding new materials as well as those developed for aggressive environments or obtained by additive manufacturing processes, the present paper is aimed to give a complete overview of the volume based strain energy density approach [7-16]. The concept of “elementary” volume was first used many years ago by Neuber [17-19] and it states that not the theoretical maximum notch stress is the static or fatigue strength-effective parameter in the case of pointed notches, but rather the notch stress averaged over a short distance normal to the notch edge. In high cycle fatigue regime, the integration path should coincide with the early fatigue crack propagation path. A further idea was to determine the fatigue-effective notch stress directly (i.e. without notch stress averaging) by performing the notch stress analysis with a fictitiously enlarged notch radius, ρ f , corresponding to the relevant support [20-26]. Fundamentals of Critical Distance Mechanics applied to static failure have been developed in [27, 28]. This “Point Criterion” becomes a “Line criterion” in Refs. [29-31] who dealt with components weakened by sharp V-shaped notches. Afterwards, this critical distance-based criterion was extended also to structural elements under multi-axial loading [32, 33] by introducing a non-local failure function combining normal and shear stress components. The pioneering work by Sheppard has to be mention at this point. In fact dealing with notched components the idea that a quantity averaged over a finite size volume controls the stress state in the volume by means of a single parameter, has been first introduced in [34]. For many years the Strain Energy Density (SED) has been used to formulate failure criteria for materials exhibiting both ductile and brittle behavior. Since Beltrami [35] to nowadays the SED has been found being a powerful tool to assess the static and fatigue behavior of notched and unnotched components in structural engineering. Different SED-based approaches were formulated by many researchers. Dealing here with the strain energy density concept, it is worthwhile contemplating some fundamental contributions by Sih [36-40]. The strain energy density factor S was defined as the product of the strain energy density by a critical distance from the point of singularity. Failure was thought of as controlled by a critical value S c , whereas the direction of crack propagation was determined by imposing a minimum condition on S . The deformation energy required for crack initiation in a unit volume of material is called Absorbed Specific Fracture Energy (ASFE) and its links with the critical value of J c and the critical factor S c were widely discussed. This topic was deeply considered in Refs. [41-44]. The concept of strain energy density has also been reported in the literature in order to predict the fatigue behavior of notches both under uniaxial and multi-axial stresses [45-46]. It should be remembered that in referring to small-scale yielding, a method based on the averaged of the stress and strain product within the elastic-plastic domain around the notch was extended to cyclic loading of notched components [47]. In particular in Ref. [48] it was proposed a fatigue master life curve based on the use of the plastic strain energy per cycle as evaluated from the cyclic hysteresis loop and the positive part of the elastic strain energy density. The averaged strain energy density criterion, proposed in Refs [7-16], states that brittle failure occurs when the mean value of the strain energy density over a control volume (which becomes an area in two dimensional cases) is equal to a critical energy W c . The SED approach is based both on a precise definition of the control volume and the fact that the critical energy does not depend on the notch sharpness. The control radius R 0 of the volume, over which the energy has to be averaged, depends on the ultimate tensile strength, the fracture toughness and Poisson’s ratio in the case of static loads, whereas it depends on the unnotched specimen’s fatigue limit, the threshold stress intensity factor range and the Poisson’s ratio under high cycle fatigue loads. Several criteria have been proposed to predict fracture loads of components with notches , subjected to mode I loading [49-65]. The problem of brittle failure from blunted notches loaded under mixed mode is more complex than in mode I loading and experimental data, particularly for notches with a non- negligible radius, has been faced by other criteria [66-69] and only recently with the SED approach [70-76]. In the recent years the SED has been applied to assess the fracture behavior of innovative materials subjected to aggressive environmental conditions as well as to micro-components and additive manufactured materials showing some sound advantages that will be discussed in more details in the present contribution. In particular after this short introduction the analytical background of the SED approach will be discussed in section 2. Master curves for static and fatigue loadings obtained reanalyzing more than 2000 data taken from the literature will be presented in section 3 while in section 4 the advantages of the approach will be discussed considering in particular the capacity of taking into account 3d effects and the capacity of the criterion to take into account in an unified way internal defects of the material and geometrical discontinuities. In section 5 some recent applications will be discussed considering materials subjected to multiaxial loadings and high temperature. Some advanced applications related to fracture at nano-scale, fatigue behavior of additive manufactured materials and new generations of welding techniques will be treated.