Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches

Abstract

The survey of research on the problems of fracture mechanics of solids with V-shaped notches is discussed. The methods of solution of plane problems of the elasticity theory for domains with angular points on boundary contours are considered. Special attention is paid to the results of the research which authors obtained applying the unified approach to the solution of stress concentration problems in the neighborhood of the vertices of sharp and rounded V-notches. The solutions of elastostatics problems for domains with rounded V-shaped notches were obtained by singular integral equation method. Based on the relation between stress intensity factor at the sharp notch vertex and the stress concentration factor at the vertex of rounded V-notch (notch with straight edges and vertex rounded with circular arc), the stress intensity factors for V-notches in various domains were obtained. The presented examples include notch stress intensity factors for periodically placed notches in the edge of halfplane, diamond and lens-like holes in infinite plane. Through limit transition from the system of periodically placed diamond-shaped ovals to infinite doublesided notch, the stress concentration factors for rounded deep V-notch and the notch stress intensity factors for sharp notch were obtained. The comparison between calculated data and known solutions for the hyperbolic notch documents strong influence of the notch shape in the neighborhood of the rounded vertex on the stress concentration values for small vertex radii. The numerical results are presented not only in graphical form but also the numerous approximation formulas are given. Based on the solution of the nonlinear problem of rounded V-notch with plastic strip at the vertex, the new deformation fracture criterion is proposed. This criterion contains only standard strength parameters and it is intended to determine fracture toughness of the elements with rounded notches made of quasibrittle materials.

Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

“…With reference to the mode I loading, an accurate review of the NSIF problem applied to blunt notches has been presented by Savruk and Kazberuk (2010). They revisited different expressions reported in the literature and used the method of singular integral equations to determine the relationships linking stress intensity factors of sharp V-shaped notches and stress concentration factors of the corresponding rounded notches as a function of the notch tip radius.…”

“…It was highlighted that this relationship is not unique, but, for the same curvature at the notch tip, depends on the shape used for the notch profile Kazberuk 2006, 2010). They also wrote that a comprehensive re-analysis of the mode II NSIFs at the tip of notches of different shapes is still missing in the literature (Savruk and Kazberuk 2010).…”

Effect of material properties on optimal radial strain gage locations in sharp V-notched configurations

“…Several researches had been attempted to recommend the brittle fracture criterion at the sharp Vnotches [4][5][6][7][8][9][10][11][12]. Because of widespread use of V K , significant efforts had been put in the development of several numerical [13][14][15][16] and experimental [17][18][19][20][21][22] methods for determination of NSIFs for different notched configurations.…”

“…These locations are optimal in the sense that they can be selected in a range as follows min max r r r   (11) where min 1.25 r   thickness of the plate (12) Thus, any radial strain gage location at distance r from the notch tip along the gage line if satisfies the criterion of Eq. (11) should be understood as a valid or optimal radial strain gage location.…”

An <i>In Situ</i> Three-Point Bending Study on Pre-Notch 7075 Aluminium Alloy with Acoustic Emission

“…In other words, the opening angles of notch specimen ranges from 0 degree to 180 degrees. In previous studies, most cases mainly concentrated on the crack initiation, 5,6) crack propagation rate and fracture toughness, 7,8) the shape of notch and the radius of notch tip, 9,10) the stress intensity factor and its distribution of notch tip 11,12) by the tension or three-point bending (TPB) or four-point bending (FPB).…”