Reconstruction of a 2D stress field around the tip of a sharp material inclusion

0465823 - ÚFM 2017 RIV NL eng C - Conference Paper (international conference)
Krepl, Ondřej - Klusák, Jan
Reconstruction of a 2D stress field around the tip of a sharp material inclusion.
21st European Conference on Fracture. Amsterdam: Elsevier, 2016, s. 1920-1927. Procedia Structural Integrity, 2. ISSN 2452-3216.
[ECF21 - European Conference on Fracture /21./. Catania (IT), 20.06.2016-24.06.2016]
R&D Projects: GA ČR(CZ) GA16-18702S
Institutional support: RVO:68081723
Keywords : Generalized Fracture Mechanics * General Singular Stress Concentrator * Sharp Material Inclusion * Muskhelishvili plane elasticity
Subject RIV: JL - Materials Fatigue, Friction Mechanics
http://www.sciencedirect.com/science/article/pii/S2452321616302529

The stress distribution in the vicinity of a sharp material inclusion (SMI) tip exhibits a singular stress behavior. The strength of the stress singularity depends on material properties and geometry. The SMI is a special case of a general singular stress concentrator (GSSC). The stress field near a GSSC can be analytically described by means of Muskhelishvili plane elasticity based on complex variable function methods. Parameters necessary for the description are the exponents of singularity and generalized stress intensity factors (GSIFs). The stress field in the closest vicinity of an SMI tip is thus characterized by 1 or 2 singular exponents, and corresponding GSIFs. In order to describe a stress field further away from an SMI tip, the non-singular exponents, and factors corresponding to these non-singular exponents have to be taken into account. For given boundary conditions of the SMI, the exponents are calculated as an eigenvalue problem. Then, by formation of corresponding eigenvectors, the stress or displacement angular functions for each stress or displacement series term are constructed. The contribution of each stress or displacement series term function to the total stress and displacement field is given by the corresponding GSIF. The GSIFs are calculated by the over deterministic method. In the numerical example, the stress field for particular bi-material configurations and geometries is reconstructed using i) singular terms only ii) singular and non-singular terms. The reconstructed stress field polar plots are compared with FEA results.
Permanent Link: http://hdl.handle.net/11104/0264352