P. Lazzarin

A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches

The paper presents an energetic approach useful to predict of the static and fatigue behavior of components weakened by sharp re-entrant corners. Despite the fact that stresses and strain energy density tend toward infinity at the point of singularity, the energy in a small volume of material surrounding the notch tip has obviously a finite value and such a value is thought of as the entity that controls the failure. The energy, averaged in a volume of radius R (which depends on the material properties), is a precise function of the Notch Stress Intensity Factors and is given in closed form for plane stress and plane strain conditions, the material being thought of as isotropic and linear elastic. The method is validated taking into account experimental data already reported in the literature, concerning both static tests carried out on polymethyl metacrylate (PMMA)and Duraluminium specimens and fatigue tests on welded joints and notched components in structural steels. As a matter of fact, the method proposed here is the re-formulation, on one hand, of some recent area/volume criteria (in which averaged values of the maximum principal stress are used to predict component fatigue limits) and, on the other, of N-SIF-based criteria, where the Notch Stress Intensity Factors are thought of as the parameters that control static and fatigue failures.

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corners, where the singularity in the stress distribution makes any failure criterion based on elastic peak stress no longer applicable.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.

Notch Sensitivity and Defect Sensitivity under Fatigue Loading: Two Sides of the Same Medal

Notch sensitivity and defect sensitivity are two different aspects of the fatigue behavior of materials. The paper extends the Kitagawa diagram to blunt cracks (U-shaped notches) and presents the simple expression (a*/a0)0.5 = Kt. In such an expression a0 is the El-Haddads length parameter and a* is a particular blunt crack depth corresponding to the intersection between the ΔKth and δσ0/Kt curves. The new expression provides an explicit bridging between the notch sensitivity and the sensitivity to defects.

Stress field parameters to predict the fatigue strength of notched components

Abstract The stress field parameters, namely the notch stress intensity factors (N-SIFs) according to a more recent definition, 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 the elastic peak stress no longer applicable. When the notch root radius is small but different from zero, the N-SIF can still be used, since a comprehensive analytical approach is available for open sharp and blunt notches. The fatigue strength reduction factor can be given as a function both of the elastic peak stress (only if it has a finite value) and of the N-SIF (for every notch tip radius value), by assuming that the fatigue strength of notched elements depends on a mean stress value in the critical zone. The welded joints are an example of practical N-SIF use in fatigue strength prediction. In this case not only the fatigue crack initiation life but also the fatigue crack propagation phase are strictly correlated to the N-SIF value for the reason that the residual life is mainly dependent on crack propagation in the zone just governed by N-SIFs.

Cracks and notches: analogies and differences of the relevant stress distributions and practical consequences in fatigue limit predictions

The point and the area methods due to Taylor and valid both for cracks and for notches are discussed. The aim is to highlight that in some circumstances the analogies of the relevant stress fields are so strong as to make them indistinguishable; at the same time, there exist other circumstances of interest in which the correlation has to be found between notch and sharp re-entrant corner. This fact has practical consequences on the size effect when the notch tip radius is small.

High-temperature fatigue strength of a copper–cobalt–beryllium alloy

This article summarizes the results from uniaxial tension stress-controlled fatigue tests performed at 650°C on Cu-Be specimens. Two geometries are considered: hourglass-shaped specimens and plates weakened by a central hole. The motivation of this present study is that, at the best of the authors knowledge, only a limited number of studies on copper alloys under high-temperature fatigue are available in the literature, and no results from these alloys deal with notched components. In the present contribution, after a brief review of the recent literature, material properties and experimental procedure are described. The new data from un-notched and notched specimens are summarized in the corresponding fatigue curves. By analyzing the fatigue behavior of the plates weakened by central holes, a reduction of the fatigue strength about equal to 40% at 2 million cycles can be noted, whereas the inverse slope, k, is very close to that of un-notched specimens. All fatigue data from un-notched and notched specimens are reanalyzed here in terms of the mean value of the strain energy density. The approach, successfully used to summarize fatigue data from notched specimens tested at room temperature, is extended here for the first time to high-temperature fatigue. In the plates with central holes, the strain energy density is evaluated over a finite size control volume surrounding the highly stressed zone at the hole edge. A value of the radius equal to 0.6mm seems to be appropriate to summarize all fatigue data in a quite narrow scatter band.

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.

A two-term stress function approach to evaluate stress distributions in bonded joints of different geometries

The paper presents a method for the evaluation of the singular stress fields in bonded joints of different geometries. The stress distributions are represented by a two-term stress expansion, under the hypothesis that both the first and the second terms are in the variable separable form. The method is based on the stress function approach, where the formulation is completed analytically and the resulting set of ordinary differential equations is solved numerically. The capability of the formulation to account for the actual elastic properties of the substrates allows an accurate description of the singular stress field to be obtained even in the case of joints made of materials with comparable elastic properties. The influence of adhesive joint design parameters such as the type of joint, geometry and material properties on the generalized stress intensity factors will also be presented and discussed.

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.