Effect of non-singular stress on the brittle fracture of V-notched structure

Abstract

The traditional brittle fracture criteria for V-notched structures are established on the base of the singular stress field at a V-notch tip where only two singular stress terms are adopted. The non-singular stress terms also play a significant role in determining the stress and strain fields around a V-notch tip, which in turn could affect the fracture character of V-notched structures predicted by the fracture mechanics criteria. In this paper, the effect of the non-singular stress on the brittle fracture properties for the V-notch problem is discussed. Firstly, the stress field around a V-notch tip is described by the Williams asymptotic expansions. At the same time, the stress field far from the V-notch tip is modeled by the conventional boundary element method since there is no stress singularity. By the combination of the Williams asymptotic expansions and the boundary integral equations, the complete stress field at a V-notch tip including several non-singular stress terms can be obtained. Then, three different brittle fracture criteria are introduced to predict the critical loading and initial crack propagation direction of V-notched structures under mixed-mode loading. Comparing with the existed experimental results, it can be found that the degree of accuracy of the predicted results when taking into account the non-singular stress terms is much higher than the predicted ones neglecting the non-singular stress.

Stress singularity analysis for orthotropic V‐notches in the generalised plane strain state

“…(x, y, z) = Cartesian coordinate system (ρ, θ, z) = cylindrical coordinate system (1, 2, 3) = principal axis of the orthotropic material E 1 , E 2 , E 3 = elastic modulus μ 12 , μ 13 , μ 21 , μ 23 , μ 31 , μ 32 = Poisson ratios G 12 , G 23 , G 13 = shear modulus σ 1 , σ 2 , σ 3 , τ 12 , τ 23 , τ 13 = stress components in Cartesian coordinate system ε 1 , ε 2 , ε 3 , γ 12 , γ 23 , γ 13 = strain components in Cartesian coordinate system S = compliance matrix e T = transformation matrix for strain components between (ρ, θ, z) and (x, y, z) T = transformation matrix for strain components between (1,2,3) and (x, y, z) D = stiffness matrix D ij (i, j = 1, …, 6) = elements of the stiffness matrix σ ρ , σ θ , σ z , τ ρθ , τ θz , τ ρz = stress components in cylindrical coordinate system ε ρ , ε θ , ε z , γ ρθ , γ θz , γ ρz = strain components in cylindrical coordinate system (l k , m k , n k ) = direction cosines between the kth principle axis and (x, y, z) u ρ , u θ , u z = displacement components in cylindrical coordinate system A k = amplitude coefficient in asymptotic expansions λ k = stress singularity order λ = abbreviation of λ k N = number of characteristic values truncated Correspondence: C. Z. Cheng.…”

“…The severity of the strong stress singularity may cause the crack initiation and propagation at the V‐notch apex, where failures are often started. The analysis of the stress singularity at the vicinity of the V‐notch tip is an important scientific topic …”

“…The analysis of the stress singularity at the vicinity of the V-notch tip is an important scientific topic. 3 The generalised plane strain state is a plane strain state plus the shear strain in the direction normal to the plane, as shown in Fig. 1, where the global coordinate Oxyz is defined such that x-y plane represents the geometrically symmetric surface, the body possesses rectilinear orthotropic and the applied tractions do not vary along the longitudinal z-direction.…”

The Research on Characterization of Crushability for Foundry Sand Particles

“…Crushing refers to the process that a bulk material which is crushed into small pieces or powders by exerting a mechanical external force to overcome intermolecular cohesion forces, and it depends on its mechanical property, including brittleness and strength. [1,2] In some certain fields, they may prefer more obvious crushing effect, while some prefer less. Foundry silica sand particles indicate a tendency to be crushed during the service [3,4].…”

On the stress state in rectilinear anisotropic thick plates with blunt cracks

“…The closed form solution for the elastic stress fields at the tip of a blunt crack in an isotropic material were derived by Creager and Paris 6 , and later extended to any notch opening angle by Lazzarin and Tovo, 7 for plane loadings, and by Zappalorto et al 8 and Zappalorto and Lazzarin 9 for the mode III problem. [11][12][13] The most recent advances on this topic are related to the study of the effect non-singular terms of the stress field close to a pointed V notch, 14,15 as well as materials with unconventional properties (such as angularly inhomogeneous elastic properties, 16 magneto-electro-elastic 17 and piezoelectric materials 18 ). 10 The problem of sharp and blunt V-shaped notches was also thoroughly investigated over the years by Savruk and co-workers.…”