122,147 research outputs found
A crack-like notch analogue for a safe-life fretting fatigue design methodology
No full textVarious analogies have recently been proposed for comparing the stress fields induced in fretting fatigue contact situations, with those of a crack and a sharp or a rounded notch, resulting in a degree of uncertainty over which model is most appropriate in a given situation. However, a simple recent approach of Atzori–Lazzarin for infinite-life fatigue design in the presence of a geometrical notch suggests a corresponding unified model also for fretting fatigue (called Crack-Like Notch Analogue model) considering only two possible behaviours: either 'crack-like' or 'large blunt notch.' In a general fretting fatigue situation, the former condition is treated with a single contact problem corresponding to a Crack Analogue model; the latter, with a simple peak stress condition (as in previous Notch Analogue models), simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical situation of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions can be readily stated. Not only is the model asymptotically correct if friction is infinitely high or the contact area is very small, but also remarkably accurate in realistic conditions, as shown by excellent agreement with Hertzian experimental results on Al and Ti alloys. The model is useful for preliminary design or planning of experiments reducing spurious dependences on an otherwise too large number of parameters. In fact, for not too large contact areas ('crack-like' contact) no dependence at all on geometry is predicted, but only on three load factors (bulk stress, tangential load and average pressure) and size of the contact. Only in the 'large blunt notch' region occurring typically only at very large sizes of contact, does the size-effect disappear, but the dependence is on all other factors including geometry
On the extraction of notch stress intensity factors by the post-processing of stress data on the free edges of the notch
No full textFollowing on the lines of a previous paper dedicated to cracked components by Ciavarella et al., here the case of a notch of semi-angle alpha is considered. Contrary to the crack case (alpha = 180 degrees), the free edges of the notch are easily accessible to experimental analysis; moreover they provide information about all the terms of the Williams series expansion of the stress field about the notch apex, including the most important, i.e. the symmetric and antisymmetric singular term notch stress intensity factors (N-SIFs), whereas for the crack case the mode I N-SIFs cannot be extracted from those stresses. Another important different feature is that symmetric and antisymmetric N-SIFs have different singularities, and in several cases they are so close that their contributions tend to overlap. Therefore, a simple procedure is here proposed to use radial stresses, to separate their symmetric and antisymmetric contributions alpha priori by computing the sum and difference of the stresses on the two edges, to post-process these quantities in the 'asymptotic region' with standard least-squares techniques and to extract the N-SIFs. The method is applied to a simple case known in the literature and solved by means of a boundary element code, and the results are almost coincident with previous results, even with quite coarse mesh discretizations
On the extraction of notch stress intensity factors by the post-processing of stress data on the free edges of the notch
No full textFollowing on the lines of a previous paper dedicated to cracked components by Ciavarella et al., here the case of a notch of semi-angle alpha is considered. Contrary to the crack case (alpha = 180°), the free edges of the notch are easily accessible to experimental analysis; moreover they provide information about all the terms of the Williams series expansion of the stress field about the notch apex, including the most important, i.e. the symmetric and antisymmetric singular term notch stress intensity factors (N-SIFs), whereas for the crack case the mode I N-SIFs cannot be extracted from those stresses. Another important different feature is that symmetric and antisymmetric N-SIFs have different singularities, and in several cases they are so close that their contributions tend to overlap. Therefore, a simple procedure is here proposed to use radial stresses, to separate their symmetric and antisymmetric contributions a priori by computing the sum and difference of the stresses on the two edges, to post-process these quantities in the 'asymptotic region' with standard least-squares techniques and to extract the N-SIFs. The method is applied to a simple case known in the literature and solved by means of a boundary element code, and the results are almost coincident with previous results, even with quite coarse mesh discretizations
The influence of the indenter tip-radius on indentation testing of brittle materials
No full textIndentation testing of a brittle material using a notionally ‘sharp’ indenter may reveal several important physical properties, including fracture toughness, surface finish information and the residual stress state. In the case of shallow cone indenters, the contact and fracture mechanics is well defined and closed-form solutions exist in elasticity theory. However, no real indenter is atomically sharp, and the scope of the present article is to quantify how a finite apex radius may modify the stress state induced by a conical indenter. In particular, implications for the load-displacement relation, occurrence of yielding and maximum contact pressure induced are found. A brief discussion of the influence of edge radius on the flat-ended indenter, once used to induce Hertzian type ring cracks, is also included, as this may be treated by a similar procedur
A Winkler solution for the axisymmetric Hertzian contact problem with wear and finite element method comparison
No full textContact problems with wear are often modelled according to the Reye-Archard law that applies locally to the wearing parts. In the transient regime, for geometries where the contact area cannot be assumed to be constant, a simple solution is possible when using the Winkler simplifying assumption. Here, we obtain such a solution in the axisymmetric contact problem, for an initially Hertzian geometry. Also, we explore the possibility to improve the solution by assuming that the Winkler constant adapts to the changing size of the contact. The correction is relevant in intermediate regimes before the solution tends to a 'rigid' asymptotic regime, independent of the elastic modulus. Comparison with a full finite element method simulation shows that the error in either contact area or peak pressure tends to be reduced from the initial error intrinsic in the Winkler assumption; however, the improvement remains small
A note on wear of elastic sliding parts with varying contact area
No full textWear of sliding parts in the transient regime depends on elastic behavior of the bulk of the materials, and in general the contact area cannot be assumed to be constant, so that the problem is nonlinear. Here we look at the simple example of the classical Hertzian geometry, obtaining a simple solution for transient to uniform pressure (which is also the "rigid" limit solution) assuming out-of-plane sliding, and the approximation of the "Winkler foundation" in plane strain. Wear is assumed to vary according to the Reye-Archard law, which applies locally and only to the wearing indenter. As a further improvement, we give a more refined solution using a Winkler constant which adapts to the changing size of the contact
Conditions of yield and cyclic plasticity around inclusions
No full textn this paper the stress field in the proximity of a circular (cylindrical) inclusion is considered. The conditions for in-plane plastic flow in the matrix are examined from a classical elasticity solution obtained by Goodier. Elementary cases are considered such as remote loading ranging from pure tensile and pure shear to equibiaxial tension. For proportional loading, it is argued that the upper bound to the shakedown limit is always twice the elastic limit; therefore, within the limits of our assumptions, if the elastic stress concentration for the equivalent stress is greater than two, there is a possibility of cyclic plasticity before bulk yielding, which means that possibly an arbitrarily large plastic strain can cumulate with increasingly high risk of exhaustion of ductility and void nucleation or detachment of the interface Consequently, conditions under which it is possible to reach twice the elastic limit before full-scale yielding are shown in the Dundurs plane representing all possible combinations of elastic parameters. Following these lines, it is shown that there is no possibility of cyclic plasticity under remote shear; there is a limited area of the Dundurs plane for tension, including the hole case; finally, in the equibiaxial limiting case, cyclic plasticity is always possible for any combination of elastic properties
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No full textA generalized Paris' law for fatigue crack growth
No full textAn extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wohler SN curve of the material, suggesting a more general "unified law". In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Delta a, the "fracture quantum". In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Delta a, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture "quantum" on the applied stress range level such that the correct convergence towards the Wohler-like regime is obtained. Hence, the final law includes both Wohler's and Paris' material constants, and can be seen as either a generalized Wohler's SN curve law in the presence of a crack or a generalized Paris' law for cracks of any size. (c) 2006 Elsevier Ltd. All rights reserved
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