The identification of optimal tire design parameters for satisfying different requirements, i.e. tire performance characteristics, plays an essential role in tire design. In order to improve tire performance characteristics, formulation and solving of multi-objective optimization problem must be performed. This paper presents a multi-objective optimization procedure for determination of optimal tire design parameters for simultaneous minimization of strain energy density at two distinctive zones inside the tire. It consists of four main stages: pre-analysis, design of experiment, mathematical modeling and multi-objective optimization. Advantage of the proposed procedure is reflected in the fact that multi-objective optimization is based on the Pareto concept, which enables design engineers to obtain a complete set of optimization solutions and choose a suitable tire design. Furthermore, modeling of the relationships between tire design parameters and objective functions based on multiple regression analysis minimizes computational and modeling effort. The adequacy of the proposed tire design multi-objective optimization procedure has been validated by performing experimental trials based on finite element method.

A review of some recent data from multiaxial fatigue data from different notched materials is carried out in the paper. The approach based on the strain energy density (SED) averaged over a control volume is first used to summarise uniaxial and multiaxial fatigue strength data of welded joints made of structural steel and aluminium alloys. In all welded joints, the weld toe and weld root regions are modelled like sharp, zero radius, V-notches with different opening angles. The control volume radius is 0.28 mm for structural steels, 0.12 mm for aluminium alloys. Afterwards the SED approach is applied to multi-axial fatigue data from plain and V-notched specimens made of AISI 416 stainless steel (hardened and tempered state), subjected to tension, torsion and combined tension and torsion, both in-phase and out-of-phase. Notched specimens are characterised by a very small root radius, ρ=0.1 mm, which results in high nonlinear effects ahead of the notch tips. All results are summarised in terms of Δ W-N (SED range versus cycles to failure) scatterbands. Together with the new results, a number of multi-axial fatigue data recently obtained from sharply notched specimens made of C40 steel (normalised state) and 39NiCrMo3 steel (hardened and tempered state) are represented with the aim to provide a global synthesis in terms of local SED. Finally a synthesis from Ti6Al4V alloy is carried out showing the capability of the SED approach to be applied also to light alloys.

The present work summarizes some recent experimental, theoretical and numerical results on brittle fracture of isostatic polycrystalline graphite. The analyses have been carried out on V-notched samples under mixed mode (I+II), torsion and compression loading, considering various combinations of the notch tip radius, opening angle and notch tilt angle. The static strength of the considered specimens is assessed through an approach based on the strain energy density averaged over a control volume. The center of the control volume is located on the notch edge, where the principal stress reaches its maximum value. The correct orientation is obtained by a rigid rotation of the crescent-shaped volume while the size depends on the fracture toughness and the ultimate strength of the material. This methodology has been already used in the literature to analyze U- and V-shaped notches subject to mode I loading with very good results and advantages with respect to classic approaches. The results reported in this new work show, also under mixed mode loading conditions, good agreement between experimental data and theoretical predictions.

Different criteria are available in the literature to assess the fracture behaviour of sharp V-notches. A typical and well-known criterion is based on the application of the notch stress intensity factors (NSIFs), which are able to quantify the intensity of the stress fields ahead of the notch tip. This work considers two recent energy-based criteria applied here to sharp V-notches. The first criterion is based on the averaged value of the strain energy density (SED), while the second one called Finite Fracture Mechanics (FFM) criterion is available under two different formulations: that by Leguillon et al. and that by Carpinteri et al. Considering the averaged SED criterion, a new expression for estimating the control radius Rc under pure Mode II loading is proposed and compared with the sound expression valid under pure Mode I loading. With reference to pure Mode II loading the critical NSIF at failure can be expressed as a function of the V-notch opening angle. By adopting the three criteria considered here the expressions for the NSIFs are derived and compared. After all, the approaches are employed considering sharp V-notched brittle components under in-plane shear loading, in order to investigate the capability of each approach for the fracture assessment. With this aim a bulk of experimental data taken from the literature is used for the comparison.

The present paper summarizes the results from uniaxial-tension stress-controlled fatigue tests performed at different temperatures up to 650°C on Cu-Be specimens. Two geometries are considered: hourglass shaped and plates weakened by a central hole (Cu-Be alloy). The motivation of the present work is that, at the best of authors’ knowledge, only a limited number of papers on these alloys under high-temperature fatigue are available in the literature and no results deal with notched components. The Cu-Be specimens fatigue data are re-analyzed in terms of the mean value of the Strain Energy Density (SED) averaged over a control volume. Thanks to the SED approach it is possible to summarize in a single scatter-band all the fatigue data, independently of the specimen geometry.