Fracture in plates of finite thickness

Abstract

Application of the plane theory of elasticity to planar crack or angular corner geometries leads to the concept of stress singularity and stress intensity factor, which are the cornerstone of contemporary fracture mechanics. However, the stress state near an actual crack tip or corner vertex is always three-dimensional, and the meaning of the results obtained within the plane theory of elasticity and their relation to the actual 3D problems is still not fully understood. In particular, it is not clear whether the same stress field as found from the well-known 2D solutions of the theory of elasticity do describe the corresponding stress components in a plate made of a sufficiently brittle material and subjected to in-plane loading, and what effect the plate thickness has. In the present study we adopt, so called, first order plate theory to attempt to answer these questions. New features of the elastic solutions obtained within this theory are discussed and compared with 2D analytical results and experimental studies as well as with 3D numerical simulations.

Comportamento a fatica dei giunti saldati in funzione della densità di energia di deformazione locale: influenza dei campi di tensione singolari e non singolari

“…l problema delle singolarità di tipo 'out-of-plane' per effetti tridimensionali legati al rapporto di Poisson è stato sollevato recentemente da Kotousov [27,28]. Tali singolarità potrebbero avere pratiche conseguenze sulle proprietà di resistenza a fatica di alcune geometrie di giunti saldati [29].…”

“…, e adottato il metodo proposto da Williams per i problemi piani, l'equazione caratteristica in λ ha la seguente forma [28] …”

“…Figura 9: Rappresentazione schematica dell'effetto 'out-of-plane'; sistema di coordinate utilizzato nella trattazione analitica (simbologia in accordo con le referenze [27][28][29]). …”

Evaluation of Fatigue Crack Front Shape for a Specimen with Finite Thickness

“…In other words, the crack front is assumed to be straight and the variation of the stresses along the thickness direction to be negligible. These common assumptions essentially reduce the dimensionality of the problem, significantly simplify the modelling approaches, and in many cases provide a satisfactory solution useful for analysis of practical problems [1]. Despite a large number of three-dimensional analytical, numerical and experimental studies carried out over the past decade [2], it is still unclear how adequate these common assumptions and simplifications are, and what influence the account for the crack front shapes has on fatigue life predictions.…”

Modelling of in-plane wave propagation in a plate using spectral element method and Kane–Mindlin theory with application to damage detection

“…One of refined plate theories is the Kane-Mindlin extensional theory [11] and it is equivalent to the Mindlin-Herrmann rod theory [19], for which a spectral element formulation was recently developed by Rucka [22,23]. The Kane-Mindlin theory includes the out-of-plane stress component and retains the simplicity of the 2D model [14]. In earlier papers, the Kane-Mindlin theory was used in analytical studies of static and dynamic fracture problems of cracked plates [9,10,13,14].…”