International Research Journal of Engineering and Technology (IRJET) Volume: 04 Issue: 02 | Feb -2017
www.irjet.net
e-ISSN: 2395 -0056 p-ISSN: 2395-0072
Unguided crack growth simulation in asymmetric specimens using bond-based peridynamics Asghar Sami1 and Umit Keskin2 1Graduate
Student, Islamic Azad University, Tabriz Branch, Tabriz, Iran Student, Okan University, Istanbul, Turkey ---------------------------------------------------------------------***--------------------------------------------------------------------2Graduate
Abstract – Peridynamics is a nonlocal continuum theory
which reformulates the classical mechanics by substituting the differential term with integral term. Therefore, the peridynamic formulation is valid everywhere regardless of presence of discontinuities such as cracks. This makes peridynamics a robust and promising technique in predicting failure in engineering materials and structures. This work aims to develop peridynamic simulations to model unguided crack growth in asymmetric specimens. The presence of asymmetric circular notches around a macro crack tip has been studied on damage pattern of a precracked specimen. The results indicates that peridynamics is successfully able to simulate complex failure modes in engineering structures. Key Words: Peridynamics, Bond-based theory, Crack growth, Brittle material, Failure.
1. INTRODUCTION Finite element method (FEM) is widely used in various applications in solid mechanics [1-7]. However, the FEM equations become singular in presence of discontinuities such as cracks. Therefore, additional efforts are required to make the FEM sufficient in fracture mechanics. Extended finite elements (XFEM) and cohesive zone model (CZM) are improvements on the classical FEM to avoid singularity around the crack tip. CZM [8, 9] is mesh dependent, where crack can only follow between the elements. Although XFEM [10, 11] can predict arbitrary crack growth, it is computationally costly. Furthermore, both methods require an extra criterion to obtain the crack growth path. Since most of the FE methods are costly, there is always a need to more efficient methods. Spectral finite element is a computationally very efficient alternative. The drawback of the spectral finite element is in modelling complex and realistic structures. Khalili et al. [12-14] formulated WSFE-based elements and implemented them in Abaqus through user defined element (UEL) subroutine. The WSFE-based UEL has the computational efficiency of the WSFE and also is capable of modelling realistic structures. The WSFE-based UEL is a huge step forward since the introduction of spectral finite element to the FEM. Later one they even proved the ability of the WSFEbased UEL in generating baseline data for structural health monitoring (SHM) purposes [15]. © 2017, IRJET
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Peridynamics is an alternative continuum mechanic formulation which reformulates the equation of motion by substituting differential terms with integral terms [16-23]. Therefore, the peridynamic equations are valid in discontinuities and consequently is a perfect technique in predicting material failure. Furthermore, the damage modeling is an inherent feature of the peridynamics and there is no need for extra criteria for crack initiations and propagation. Ha and Bobaru [24] studied dynamic crack branching in brittle materials using peridynamics. Yaghoobi and Chorzepa [25] used peridynamics to predict the response of fiber reinforced concrete (FRC) structures. Chorzepa and Yaghoobi [26] used peridynamics to investigate fracture in FRC beams under dynamic loading. A mesoscale modeling of cementitious composites are conducted by Yaghoobi et al. [27] to investigate damage mechanics using peridynamics. The main focus of this work is to study the ability of peridynamics to accurately predict the complex failure modes of a material. In doing so, a 2D peridynamic model is provided. In addition to a symmetric macro crack, asymmetric circular notches are provided in the plate. The number of the circular notches and their positions are varying in different simulations to study if peridynamics is able to predict unguided and complex crack growth. The original peridynamic form, so called “bond-based peridynamics”, is used in this study. Despite of some limitations such as a fixed Poisson’s ratio [17,21], BBPD has been proven very robust technique is fracture mechanics. The material is assumed to be linear elastic and fracture is occurred with no plastic deformation. Results indicate that the presented modeling method provides a promising technique in fracture analysis of asymmetric bodies.
2. THEORY The classical continuum theory is based on the assumption that material points interact only with their nearest neighboring points. In the peridynamic theory, a material point is influenced by any points within a finite distance as shown in Fig. 1. Peridynamic equation of motion of a material point at and time in the reference configuration is written as [17]
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