P. Livieri

Notch stress intensity factors and fatigue strength of aluminium and steel welded joints

According to a recent and appropriate definition, stress field parameters, namely notch stress intensity factors (N-SIFs), can be used to predict the fatigue behaviour of mechanical components weakened by V-shaped re-entrant corners, where the singularity in the stress distribution makes any failure criterion based on elastic peak stress no longer applicable. Commonly thought of as parameters able to control the fatigue crack initiation life, N-SIFs are, under certain circumstances, also useful for predicting the component total fatigue life. The fatigue strength of aluminium welded joints with different geometries and thicknesses are summarised in a single scatter band by using an N-SIF-based approach. The statistical analysis is carried out taking into account experimental data already reported in the literature, referring to welded joints with a thickness ranging from 3 to 24 mm. Results of steel and aluminium welded joints are then compared: at high number fatigue life, the relative fatigue strength is slightly greater than 2, in agreement with the value previously reported in the literature for butt spliced bolted joints. The value of the theoretical exponent quantifying the scale effect (0.326 against 0.25 suggested by Eurocodes) is discussed.

Autofrettaged cylindrical vessels and Bauschinger effect: An analytical frame for evaluating residual stress distributions

The paper reports analytical solutions valid for residual stresses in cylindrical pressure vessels subjected to autofrettage. The material behavior is thought of as obeying a generic monotonic σ-e curve and exhibiting the Bauschinger effect during the unloading phase. Under linear and power-hardening conditions, the solution is given in an explicit form. The circumstances under which it is possible to apply the superposition principle also in the presence of localized plasticity are clearly identified. When possible, the final stresses can be obtained by using in an appropriate manner the stress expressions related to the loading phase. Finally, the influence on residual stresses, both of the hardening law and of the shape of the unloading σ-e curve, is discussed.

Analytical Approach in Autofrettaged Spherical Pressure Vessels Considering the Bauschinger Effect

This paper presents an analytical study of spherical autofrettage-treated pressure vessels, considering the Bauschinger effect. A general analytical solution for stress and strain distributions is proposed for both loading and unloading phases. Different material models incorporating the Bauschinger effect depending on the loading phase are considered in the present study. Some practical analytical expressions in explicit form are proposed for a bilinear material model and the modified Ramberg-Osgood model.

A J-integral-based approach to predict the fatigue strength of components weakened by sharp V-shaped notches

In the present paper, Rices J-integral is applied to sharp V-shaped notches subjected to mixed mode loading. The material is thought of as obeying a linear elastic or a power hardening law. J, which is no longer an invariant, as it was in the crack-case, is analytically given as a function of the relevant Mode I-II Notch Stress Intensity Factors (N-SIFs). As soon as a convenient choice of the integration path is made, J is demonstrated to be able to summarise the fatigue properties of steel and aluminium welded joints of different geometry. By imposing the coincidence between elastic and plastic J-integral values, both the degree of singularity and the plastic N-SIF value are evaluated on the basis of the relevant linear elastic values. When N-SIFs are unknown, a general method suitable for determining J is reported. Finally, a new operator, JL, has been defined for sharp V-shaped notches. It is an invariant in the ambit of validity of the asymptotic stress distributions and in the presence of Mode I loading. In the linear elastic case, JL coincides with Rices J-integral when the notch opening angle is null (i.e. when the notch becomes a crack).

Plastic notch stress intensity factors for large V-shaped notches under mixed load conditions

The paper presents a two-terms asymptotic analysis of the near-tip stress fields of sharp V-shaped notches having the bisector inclined with respect to remotely applied tensile stress. Due to their geometry, mixed-load conditions are present at the notch tip. The governing of equations result in a leading order system and a second order system. As known, one of the most significant characteristics of singular stress fields in nonlinear materials is that the solution for mixed-mode loading cannot be expressed as a linear combination of mode I and mode II solutions. When the included angle is greater than 90° (as it generally happens in most welded joints, for example) a satisfactory description of the stresses at the notch tip can be obtained by imposing boundary conditions of the symmetric type in the leading-order system, and boundary conditions of antisymmetric type in the second order system. Finally, simple expressions of the plastic Notch Stress Intensity Factors are reported for a particular geometry, with the aim to explicitly describe the influence of scale effect, nominal stress and material properties on the intensities of the asymptotic stress distribution under nonlinear conditions.

On the second non-singular stress term of the V-notch solution: a new engineering solution

The non-singular stress terms are expressed by means complex eigenvalues and their corresponding complex coefficients for a number of sharp V-notches with varying notch opening angles. According to the literature the complex part of the solution introduces in the stress field equations an oscillatory function depending also on the logarithm of the radial distance from the notch tip. The intensity of the non-singular term depends on two parameters contrary to the conventional representation of the singular term the intensity of which is expressed by the notch stress intensity factor (NSIF). The aim of this paper is to investigate whether the stress field and the strain energy density can be described with sufficient accuracy by the real part of the Williams’ solution, neglecting the complex part of the eigenvalue and the corresponding complex coefficient. This engineering proposal strongly simplifies the problem allowing to define a real, unique, non-singular NSIF (

Predicting the fatigue strength of small thickness welded joints using the implicit gradient method

\text{ H }_\mathrm{ns}

On numerical integration for effective stress assessment at notches

) which governs the intensity of the non-singular part of the stress field.