Paolo Lazzarin

A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches

The problem of evaluating linear elastic stress fields in the neighborhood of cracks and notches is considered. An analytical solution valid for cracked and notched components is given in general terms, according to Muskhelishvilis method based on complex stress functions. The solution is particularly useful for V-shape notches in wide and finite plates under uniform tensile loading. It will be demonstrated that some remarkable solutions of fracture mechanics and notch analysis already reported in the literature can be considered special cases of this general solution, as soon as appropriate values of the free parameters are adopted.

Fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity

Abstract The paper summarizes the results of experimental work carried out in order to analyse the initiation and propagation of fatigue cracks on plates in a deep drawing steel and in a cast aluminium alloy. The plates were characterized by lateral V and U-shape symmetric notches, with a notch root radius ranging from 0.1 to 10 mm, the notch depth being 10 mm and the plate thickness 2 mm for the steel and 5 mm for the light alloy. In order to estimate the crack initiation life two new parameters are proposed; they are no longer based on the peak values of strain and stress, but on the averaged values of such quantities in the neighbourhood of the notch tip. The dimension of the process-zone is correlated to the intrinsic crack length of the material. The estimates need an elastoplastic approach and a numerical solution. Experimantal data and expected values are compared.

Relationships between local and structural stress in the evaluation of the weld toe stress distribution

Abstract This paper deals with the problem of determining, by proper stress analyses, the stress fields near arc-welded joint toes and the use of such distributions in fatigue strength predictions. In particular, the relationships between the local stress field and the structural (geometrical) stress field are investigated under the hypothesis that highly stressed zones remain under linear elastic conditions. The local stress distribution is given for different joints in terms of the relevant notch stress intensity factors (NSIFs), having modelled their weld beads like re-entrant sharp corners. The structural stress distribution is, in contrast, the stress field linearly distributed through the thickness of the welded plates (and sometimes on the plate surfaces), beyond the zone affected by local effects due to the beads. The aim of the proposed methodology is to provide an explicit link between NSIF values and structural stress at a well-defined distance from the weld toe. Such a distance is chosen equal to the main plate thickness. The expressions obtained allow a direct comparison with the well-known “hot-spot stress” approach; it is demonstrated that there are circumstances of practical interest in which the usual hot-spot stress (which is the simple linear extrapolation at the weld root of the structural field) is not able to predict accurately the fatigue behaviour of the joints, whereas the combination of structural field and NSIF-based field is more advantageous. The complete methodology can be simplified for rapid calculations involving weldments of different types. Some examples are also reported and discussed.

Different solutions for stress and strain fields in autofrettaged thick-walled cylinders

In the first part of the paper we will present an analytical solution to the plastic stress and strain distribution induced by a single over-pressure cycle in a cylindrical vessel. The solution is valid for materials which, during the loading phase, can be described by a linear hardening law as well as by the modified Ramberg-Osgood law. We will clarify the conditions for which the stress field expressions can be simplified, thus facilitating a parametric analysis of their increase with respect to the values one would obtain when considering an ideal elastic-perfectly plastic behaviour of the material. In the second part of the paper, residual stress fields will be numerically evaluated, taking into account, during the unloading phase, both the variability of the stress flow and the Bauschinger effect factor as a function of pre-strains.

Elastic stress distributions in finite size plates with edge notches

In fatigue crack growth analysis it is essential to know the stress distributions in the neighbourhood of stress raisers. If such distributions ahead of the uncracked notch are known, stress intensity factors may be obtained via the weight function or other methods. The procedure described in the present paper reconsiders the principal elastic stress expressions already reported by the authors for infinite plates with semi-infinite symmetric V-shaped notches and adapts them to some practical cases, in which the mutual influence of the notches as well as that of the plate finite size play an important role in stress distributions. The aim is therefore to give an approximate close-form solution for the longitudinal stress, valid for the entire ligament length, namely from notch tip to notch tip. Theoretical and numerical stress values are compared on this line, examining plates with semicircular, V and U-shaped notches subjected to remote uniaxial tension.

Scatter bands summarizing the fatigue strength of aluminium alloy bolted joints

Abstract A large number of geometrical, technological and environmental factors theoretically influence the fatigue behaviour and the failure modes of the bolted joints. In order to make clear the influence of some of such variables, in this work over one hundred aluminium symmetric double butt joints were tested, subdivided into eight series, with the purpose to compare their fatigue properties and display failure mechanisms. All tests have been carried out under load control, taking into account plates in 7020-T6 and 6061-T6 light alloys connected by means of A2-70 stainless bolts or 8.8 high strength bolts, in such a way that failure modes were different. The new results, together with those already presented by one of the authors in a recent contribution (Atzori et al. ‘Proceedings of the Sixth International Conference on Aluminium Weldments’, Cleveland, OH, 1995, pp. 243–254), in which 2024-T4 aluminium alloy and 10.9 high strength bolts had also been considered, allow both a comparison among the series and their synthesis in a very reduced number of scatter bands which seem to depend, for the three alloys taken into account, mainly on the nominal load ratio R, as soon as different definitions of the nominal stress amplitudes are chosen for friction or bearing-type joints.

A re-analysis on fatigue data of aluminium alloy bolted joints

A great deal of work has been done in the last years to improve the state of knowledge on fatigue behaviour of aluminium bolted joints, as well as the calculation methods and design standards. This paper summarizes the results of a statistical analysis performed on ca 750 fatigue data reported in the literature or, more recently, obtained by several laboratories. All data are pertinent to friction and bearing-type aluminium butt splice bolted joints. In spite of the fact that a large number of factors could theoretically influence the fatigue behaviour and the failure modes of the joints (yield stress of the plates, type of bolts, bolt pattern, bolts to member ratio, nominal load ratio, surface finishing, plate thickness and so on), it will be demonstrated that all data can be summarized in a very reduced number of scatter bands the reference values of which, being related to different probabilities of survival, can be used for establishing trends, planning future research and for design purposes.