Analyse the role of the non‐singular stress in brittle fracture by BEM coupled with eigen‐analysis

It is well known that in cracked plates under in-plane shear loading, an induced out-of-plane mode, due to the Poisson's effect, is automatically generated. Some recent studies have shown the importance of this coupled mode (called mode O) in plates weakened by sharp V-notches characterized by different notch opening angles. Particular attention has been paid to the scale effect focusing also on the implications of the coupled mode to different material scale levels. Also when the notch root radius is different from zero, the out-of-plane mode continues to exist, and its intensity with respect to the generating mode depends on the notch radius and the plate thickness. Aim of this paper is to discuss the main features of the out-of-plane mode dealing with three-dimensional plates weakened by blunt notches. In particular, some results from blunt V-notches, circular and elliptic holes are discussed in detail and presented here. The main key-point highlighted in the present contribution is that always three-dimensional effects exist in finite thickness plates, because mode I, II and III cannot exist in isolation. The importance of induced modes varies from case to case and depends on the geometry of the component and on the externally applied load. These effects cannot be neglected a priori even if, in some cases, they may be negligible

Section: Finite Thickness Plates Weakened By Circular and Elliptic Holesmentioning

confidence: 92%

Three‐dimensional effects in finite thickness plates weakened by rounded notches and holes under in‐plane shear

Berto

Marangon

2013

“…The fracture assessment and remaining strength calculation for V-notched plates are of great practical interest. [4][5][6][7] There are many cases in engineering designs where it is necessary to compute the stress fields inside notched elastic bodies. The advanced materials, such as surface modification materials, metal-ceramic bonded materials and composite materials will cause the interface problem, which is one kind of V-notch problems.…”

Section: Introductionmentioning

confidence: 99%

Singularity analysis near the vertex of the V‐notch in Reissner's plate by coupling the asymptotic expansion technique with the interpolating matrix method

Chen

Han

Wang

et al. 2014

Self Cite

A new numerical method for calculating the singularity orders of V‐notches in Reissner's plate is proposed in this paper. By introducing the asymptotic expansion of the generalised displacement field at the notch tip into the equilibrium equations of a plate, a set of characteristic ordinary differential equations with respect to the singularity order are established. In addition, by adopting the variable substitution technique, the obtained non‐linear characteristic equations are transformed into linear ones, which are solved by the interpolating matrix method. The singularity orders of moments and shear forces can be obtained simultaneously and can be distinguished from the corresponding characteristic angular functions conveniently. Four types of boundary conditions are proposed to investigate the influence of boundary conditions on the singularity order values. The effect of the Poisson's ratio on the singularity orders of the V‐notch in Reissner's plate is discussed. The present method is versatile for the singularity analysis of single material V‐notches and bi‐material V‐notches, and can be easily extended to multi‐material V‐notches.

“…Comparing with the analytical method, the numerical method has lower precision, but it is more suitable for the engineering application. The numerical methods, such as the finite element method, [29][30][31][32] the boundary element method [33][34][35][36][37][38][39] and the boundary finite element method, 40,41 are used to analyse the stress singularity in the vicinity at the vertex of the V-notch.…”

mentioning

confidence: 99%

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

Chen

Zhou

Niu

et al. 2015

Self Cite

A B S T R A C T The singularity for the V-notch under the generalised plane deformation is investigated by the combination of the asymptotic analysis with the interpolating matrix method developed by part of the authors before. The displacement asymptotic expansions at the vicinity of the V-notch vertex are introduced into the equilibrium equations, which are transformed into a set of characteristic ordinary differential equations with respect to the notch singularity orders. The boundary conditions and interfacial compatibility conditions are also represented by the combination of the singularity orders and characteristic angular functions. The determination of the singularity orders and characteristic angular functions are transformed into solving the ordinary differential equations with variable coefficients, which are solved by the interpolating matrix method. The present method is suitable for the singularity analysis for isotropic and orthotropic V-notches. It is versatile for analysing the stress singularity of single material V-notches, bimaterial V-notches, interface edges and cracks. The correctness of the results by the proposed method is ensured by the comparison with the published ones.Keywords asymptotic expansion; generalised plane strain state; orthotropic; stress singularity order; V-notch. N O M E N C L A T U R E(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.