1,721,107 research outputs found
Fictitious notch rounding concept applied to sharp V-notches: Evaluation of the micro structural support factor for different failure hypotheses. Part I: Basic stress equations
No full textWith the aim to perform a comprehensive and accurate evaluation of the microstructural support factor of sharp V-notches (Neuber's notch rounding concept), in Part I of this contribution, the indispensable theoretical tools, especially the basic stress equations, are reconsidered and amended in respect of accuracy of results. First, the analytical solution derived by Neuber [Neuber H. Kerbsparmungslehre. 2nd ed. Berlin: Springer-Verlag; 19581 for sharp rounded V-notches with an arbitrary flank angle under tension loading is considered. The equation of the normal stress has been obtained with the restriction to the notch bisector. Using the Airy stress function suggested by Neuber, this solution is extended to the region outside the notch bisector, and the complete stress field is derived in this manner. A comparison between Neuber's solution, a more recent solution due to Filippi et al. [Filippi S, Lazzarin P, Tovo R. Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. Int J Solids Struct 2002;39:4543-65] and highly accurate FE results is performed. Filippi's equations which include Williams' solution [Williams ML. Stress singularities resulting from various boundary conditions in angular corners on plates in tension. J App] Mech 1952;19:526-8] for pointed V-notches, are shown to be superior
Significance of the Elastic Peak Stress evaluated by FE analyses at the point of singularity of sharp V-notched components
No full textThe paper presents an expression useful to estimate the notch stress intensity factor (NSIF)
from finite element analyses carried out by using a mesh pattern with a constant element
size. The evaluation of the NSIF from a numerical analysis of the local stress field usually
requires very refined meshes and then large computational effort. The usefulness of the
presented expression is that (i) only the elastic peak stress numerically evaluated at the
V-notch tip is needed and no longer the whole stress–distance set of data; (ii) the adopted
meshes are rather coarse if compared to those necessary for the evaluation of the whole
local stress field. The proposed expression needs the evaluation of a virtual V-notch tip
radius, i.e. the radius which would produce the same elastic peak stress than that calculated
by FEM at the sharp V-notch tip by means of a given mesh pattern. Once such a radius
has been theoretically determined for a given geometry, the expression can be applied in
a wide range of notch depths and opening angles
An approximate, analytical approach to the 'HRR' solution for sharp V notches
No full textThe well-known so-called 'HRR-solution' (Hutchinson, 1968 and Rice and Rosengren, 1968) considers the elasto-plastic stress field in a power-law strain hardening material near a sharp crack. It provides a closed form explicit expression for the stress singularity as a function of the power-law exponent 'n' of the material, but the stress angular variation functions are not found in closed form. More recently, similar formulations have appeared in the literature for sharp V-notches under mode I and II loading conditions. In such cases not only is the angular variation of the stress fields obtained numerically, but so is the singularity exponent of the stress field. In the present paper, approximate but accurate closed form solutions are first reported for sharp V-notches with an included angle greater than π/6 radians. Such solutions, limited here to Mode I loading conditions, allow a very satisfactory estimate of the angular stress components in the neighbourhood of the notch tip, in the entire range of notch angles and for the most significant values of n (i.e. from 1 to 15). When the notch opening angle tends towards zero, and the notch approaches the crack case, the solution becomes much more complex and a precise evaluation of the parameters involved requires a best-fitting procedure which, however, can be carried out in an automatic way. This solution is also reported in the paper and its degree of accuracy is discussed in detail
Fatigue strength assessment of welded joints: From the integration of Paris' law to a synthesis based on the notch stress intensity factors of the uncracked geometries
No full textIn the welded joints, the conventional welding procedures result in a small value of the weld toe and the weld root
radius. By assuming such a radius equal to zero, the paper demonstrates the effectiveness of the Notch-stress intensity factor
approach in summarising a number of experimental data from failures occurring at the weld toe. Then it is shown that
fatigue data from failures originated from both weld roots and weld toes can be summarised in a single scatter band by
using the mean value of the strain energy density in a well defined volume (area) surrounding the critical points. Finally,
a simplified application of the NSIF approach based on finite element analyses carried out with coarse meshes is presented
The effects of different boundary conditions on three-dimensional cracked discs under anti-plane loading
No full textAccordingly to the recent multi-scale model proposed by Sih and Tang, different orders of stress singularities are related to different material dependent boundary conditions associated with the interaction between the V-notch tip and the material under the remotely applied loading conditions. This induces complex three-dimensional stress and displacement fields in the proximity of the notch tip, which are worthy of investigation. Starting from Sih and Tang's model, in the present contribution the authors propose some analytical expressions for the calculation of the strain energy density (SED) averaged over a control volume embracing the V-notch tip. The expressions vary as a function of the different boundary conditions. Dealing with the specific crack case, the results from the analytical frame are compared with those determined numerically under linear-elastic hypotheses, by applying different constraints to the through-the-thickness crack edges in three dimensional discs subjected to Mode III loading. Free-free and free-clamped cases are considered. Due to three-dimensional effects, the application of a nominal Mode III loading condition automatically provokes coupled Modes (I and II). Not only the intensity of the induced modes but also their degree of singularity depend on the applied conditions on the crack flanks. The variability of local SED through the thickness of the disc is investigated by numerical analyses and compared with the theoretical trend. The capability of the SED to capture the combined three-dimensional effects is discussed in detail showing that this parameter is particularly useful when the definition of the Stress Intensity Factors (SIFs) is ambiguous or the direct comparison between SIFs with odd dimensionalities is not possible
Brittle fracture of sharp and blunt V-notches in isostatic graphite under pure compression loading
No full textBrittle failure of isostatic polycrystalline graphite under pure compression loading is investigated experimentally by using prismatic specimens weakened by sharp and rounded-tip V-notches. The notched samples are characterised by different geometry parameters, i.e. notch opening angle and notch root radius, with the aim to provide a complete set of static strength data. While there are a number of papers dealing with compression of unnotched specimens made of different materials, very few results are available from notched components under compression and, in particular, no data can be found for isostatic graphite. After the description of the experimental activity, a criterion based on the strain energy density (SED) is proposed for the fracture assessment of notched graphite components under compression. The criterion, which averages SED over a control volume surrounding the notch tip, is an extension of what the present authors have proposed in previous papers dealing with the cases of in-plane tension-shear loading and torsion loading in notched graphite specimens. Good agreement is shown to exist between the experimental results and the theoretical predictions obtained for the fracture loads. © 2013 Elsevier Ltd. All rights reserved
Fatigue properties of ductile cast iron containing chunky graphite
No full textThis work deals with experimental determination of high cycle fatigue properties of EN-GJS-400 ductile cast iron containing chunky graphite. Constant amplitude axial tests were performed at room temperature under a nominal load ratio R= 0. In order to evaluate the influence of chunky graphite morphology on fatigue life, fatigue tests were carried out also on a second set of specimens without this microstructural defect. All samples were taken from the core of a large casting component. Metallurgical analyses were performed on all the samples and some important microstructural parameters (nodule count and nodularity rating, among others) were measured and compared. It was found that a mean content of 40% of chunky graphite in the microstructure (with respect to total graphite content) does not influence significantly the fatigue strength properties of the analysed cast iron. Such result was attributed to the presence of microporosity detected on the surface fracture of the specimens by means of electron scanning microscope. © 2012 Elsevier B.V
Rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: Theoretical bases and applications
No full textIn the presence of sharp V-notches the stress distributions are singular and the intensity of the stress fields is given in terms of the notch stress intensity factors which are largely used in the literature for fatigue strength assessments of welded joints and other notched components. Very refined meshes are necessary to determine directly the NSIFs from the local stress distributions. Refined meshes are not necessary when the aim of the finite element analysis is to determine the mean value of the local strain energy density on a control volume surrounding the points of stress singularity. The SED in fact can be derived directly from nodal displacements, so that also coarse meshes are able to give sufficiently accurate values for it. The link between local SED and NSIFs is discussed with reference to some typical welded joints and to plates weakened by sharp V-notches. The SED-based procedure is found to be useful to determine theoretical stress concentration factors for holes and blunt U- and V-shaped notches. © 2010 Elsevier Ltd. All rights reserved
Brittle failure of inclined key-hole notches in isostatic graphite under in-plane mixed mode loading
No full textIn the present contribution, the fracture behaviour of specimens made of isostatic graphite and weakened by inclined key-hole notches is investigated. Different loading mixities are considered varying the inclination angle of the notch with respect to the direction of the applied load. The new data permit to enlarge the scarce number of results available in the literature for the same material under prevalent in-plane shear loading. A criterion based on local energy is used for the fracture assessment to summarise all the data in a single scatter band independent of the notch geometry and mode mixity. The local energy-based criterion allows to predict with sound accuracy the critical loads of the specimens independent of the mode mixity from pure mode I to prevalent mode II. A final synthesis is reported in the paper, summarising the new data together with previous results on the same material from U-notched specimens subjected to mode I + II loading. © 2013 Wiley Publishing Ltd
Practical expressions for the notch stress concentration factors of round bars under torsion
No full textStress concentration factors and generalised stress intensity factors of round bars weakened by different kind of notches are analysed under torsion loading. An exact, closed-form relationship correlating the generalised stress intensity factors of classic notches (parabolic, semi-elliptic and hyperbolic), characterized by an exact mathematical profile, and pointed V-notches is obtained by using in combination the analytical expressions already available in the literature and some new equations developed in the present contribution. Afterwards this link is discussed with reference to U- and blunt V-shaped notches. This allows us to provide a new analytical relationship between the generalised notch stress intensity factor (NSIF) and the maximum shear stress at the notch tip. By taking advantage of the new developed frame, simple but accurate expressions for the stress concentration factors, valid for a large bulk of different configurations changing the notch acuity, from shallow to deep, are developed. For some opening angles an explicit comparison between the new expressions and those proposed by Noda and Takase (Int J Fatigue, 2006;28:151-163) has been carried out, considering deep and shallow notches. © 2010 Elsevier Inc. All rights reserved
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