The edge crack problem is often observed in engineering applications. It is one of the most prominent factors causing damage and failure of engineering structures, and it is also one of the classical problems in fracture mechanics. Due to the structure heterigenety and the loading conditions complexity, multiple cracks often occur on the edge. The interaction between cracks will affect the crack propagation path and the failure mode of the structure. To study the mechanical properties of multiple edge cracks under different loading conditions is of great engineering significance. Engineers can rationally use the interaction between cracks to improve the life of structures under specific working conditions.
The research team of the State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences constructed the boundary value problems combining conformal mapping and plane elasticity theory. The complex function is solved by a semi-analytic method, and the corresponding mechanical parameters are calculated. The research team mainly studied double branched cracks (two cracks emanating at the same point at the edge) and Kalthoff-Winkler cracks (two spaced cracks) under far-field uniform tension or concentrated force loading at the boundary. The stress intensity factors, elastic stress fields, and crack opening displacement are calculated. The shielding effect between cracks is investigated. Compared with a single edge crack, the stress intensity factors of a double branched crack decrease due to the shielding effect. The SIFs decay exponentially with decreasing space between the two parallel cracks. KI=KI0-KI1-exp(-a/d)](Fig 1 and 2). The method is universal to study boundary crack problems, and the shielding effect of cracks plays a guiding role in engineering applications.
The above results have been published under the title “Elastic fields of double branched and Kalthoff-Winkler cracks in a half-plane” in the Journal of the Mechanics and Physics of Solids. The first author is doctoral student Yangjian Si. This work is supported by the NSFC Basic Science Center for ‘Multiscale Problems in Nonlinear Mechanics’ (No.11988102).
Fig 1: Normalized SIFs and stress fields of a symmetric double-branched edge crack (a1=a2,？θ1=θ2) subjected to far-field unform tension.
(a) Geometry and loading condition of the crack. (b) Von Mises stress field around the crack tip. (c) Normalized SIFs as a function of θ. Shielding effect between the two branches can be clearly observed.
Fig 2：Normalized SIFs of two parallel edge cracks (following Kalthoff-Winkler experiment) under far-field uniform tension.
(a) Geometry and loading condition of the crack. (b) Normalized SIFs as a function of a/θ. KI*=1.122-0.326[1-exp(-1.8a/d)] ，KII*=0.812[1-exp(-1.2a/d)]. The normalized SIFs converge to those of a single edge crack when d approaches to infinity.