Fracture propagation in a cracked semicircular bend specimen under mixed mode loading using extended finite element meth
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ORIGINAL PAPER
Fracture propagation in a cracked semicircular bend specimen under mixed mode loading using extended finite element method M. Eftekhari 1 & A. Baghbanan 1 & H. Hashemolhosseini 1
Received: 29 September 2014 / Accepted: 1 April 2015 # Saudi Society for Geosciences 2015
Abstract The semicircular specimen under three-point bending (SCB) has been widely used to investigate mode I, mode II, and mixed mode I/II fracture behavior in brittle rocks. Compared to the other numerical methods, the extended finite element method (X-FEM) models a crack independently of the finite element mesh without any remeshing step in fracture propagation. In this regard, a numerical code called MEX-FEM, based on X-FEM, has been developed for modeling crack propagation in rock material. Since dimensionless stress intensity factors (i.e., YI and YII) in crack modeling of SCB specimen depend on crack length, crack angle, and span ratio, these factors and crack propagation trajectory are determined for different combinations of crack angle, crack length ratio, and span ratio. A very good agreement exists between the calculated factors YI and YII in this research work and those reported in the literature. The results show that the values of YI and YII increase by increasing the span ratio. The angle in which the pure mode II occurs decreases with increasing of the crack length ratio and it increases when the span ratio increases. The crack growth is along the initial crack when the specimen is subjected to pure mode I (i.e., the crack angle is 0), whereas in mixed mode, the crack is deviated toward the upper loading point. The results of this study demonstrate the utility and robustness of the X-FEM to simulate the crack growth in rock materials.
* M. Eftekhari [email protected]; [email protected] 1
Department of Mining Engineering, Isfahan University of Technology (IUT), Isfahan 8415683111, Iran
Keywords Semicircular bend (SCB) . Extended finite element method (X-FEM) . Crack . Stress intensity factor . Crack propagation
Nomenclature A Crack length Aω Nodal support area Aabove Nodal support area above the crack ω Abelow Nodal support area below the crack ω aj Additional degrees of nodal freedom associated with the Heaviside function blk Additional degrees of nodal associated with the elastic asymptotic crack tip functions CB Chevron edge-notched round bar in bending CCBD Central cracked Brazilian disk under diametric compression D Diameter of specimen H Modified Heaviside step function I Set of all nodes in the mesh I(1,2) Interaction integral J Set of nodes enriched with discontinuous enrichment K Set of nodes enriched with asymptotic enrichment KI Stress intensity factor mode I KII Stress intensity factor mode II N(x) Shape function P Compressive applied load R Radius of specimen r, θ Crack tip coordinates S Half span length SCB Semicircular bend SIF Stress intensity factor SR Chevron-notched short rod
Arab J Geosci
t ui Ux W(1,2) X-FEM YI YII α θc Δa
Thickness of specimen Nodal displacement Horiz
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