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.

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

Brittle failure of components weakened by cracks or sharp and blunt V-notches is a topic of active and continuous research. It is attractive for all researchers who face the problem of fracture of materials under different loading conditions and deals with a large number of applications in different engineering fields, not only with the mechanical one. This topic is significant in all the cases where intrinsic defects of the material or geometrical discontinuities give rise to localized stress concentration which, in brittle materials, may generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. Whereas cracks are viewed as unpleasant entities in most engineering materials, U- and V-notches of different acuities are sometimes deliberately introduced in design and manufacturing of structural components. Dealing with brittle failure of notched components and summarizing some recent experimental results reported in the literature, the main aim of the present contribution is to present a review of some local approaches applicable near stress raisers both sharp and blunt. The reviewed criteria allowed the present authors to develop a new approach based on the volume strain energy density (SED), which has been recently applied to assess the brittle failure of a large number of materials. The main features of the SED approach are outlined in the paper and its peculiarities and advantages accurately underlined. Some examples of applications are reported, as well. The present review is based on the authors’ experience over more than 15 years and the contents of their personal library. It is not a dispassionate literature survey.

Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches

Weld bead geometry cannot, by its nature, be precisely defined. Parameters such as bead shape and toe radius vary from joint to joint even in well-controlled manufacturing operations. In the present paper the weld toe region is modelled as a sharp, zero radius, V-shaped notch and the intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). When the constancy of the angle included between weld flanks and main plates is assured and the angle is large enough to make mode II contribution non-singular, mode I NSIF can be directly used to summarise the fatigue strength of welded joints having very different geometry. By using a large amount of experimental data taken from the literature and related to a V-notch angle of 135°, two NSIF-based bands are reported for steel and aluminium welded joints under a nominal load ratio about equal to zero. A third band is reported for steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch and units for NSIFs are the same as conventional SIF used in LEFM. Afterwards, in order to overcome the problem related to the variability of the V-notch opening angle, the synthesis is made by simply using a scalar quantity, i.e. the mean value of the strain energy averaged in the structural volume surrounding the notch tips. This energy is given in closed form on the basis of the relevant NSIFs for modes I and II and the radius RC of the averaging zone is carefully identified with reference to conventional arc welding processes. RC for welded joints made of steel and aluminium considered here is 0.28 mm and 0.12 mm, respectively. Different values of RC might characterise welded joints obtained from high-power processes, in particular from automated laser beam welding. The local-energy based criterion is applied to steel welded joints under prevailing mode I (with failures both at the weld root and toe) and to aluminium welded joints under mode I and mixed load modes (with mode II contribution prevailing on that ascribable to mode I). Surprising, the mean value of ΔW related to the two groups of welded materials was found practically coincident at 2 million cycles. More than 750 fatigue data have been considered in the analyses reported herein.

Fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values

Rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: Theoretical bases and applications

Fatigue analysis of welded joints: state of development

— An experimental study within the Canadian Offshore Corrosion Fatigue Research Programme was performed on the early development of fatigue cracking along the wavy toe of manual fillet welds between structural steel plates. Stress relieved and as-welded cruciform joints were tested under R =−1 and R= 0 loading at different stress amplitudes. The depth and the opening level of cracks as small as 10–20 μm were monitored using miniature strain gauges installed along the toe apex, in combination with beach marking. Most of the “initiation life” (25% to 50% of total life), conventionally defined by a crack depth of 0.5 mm, is consumed in short crack propagation. Three types of short crack development for different combinations of local mean stress and stress range are identified and analyzed. Growth rates in as-welded specimens are faster than in stress relieved specimens, which results in shorter “initiation lives”. This is associated with a higher effective stress range, particularly under R = - 1 loading where cracks are open over nearly the full stress range. The V-notch stress intensity factor is a promising parameter to rationalize the crack “initiation life”. It takes into account the thickness effect experimentally observed. Under R = - 1 loading of as-welded joints, using R = 0 data and taking the whole stress range gives a reasonably conservative approximation of the crack “initiation life”.

B. Nie

Papers

Early development of fatigue cracking at manual fillet welds