scholarly journals Anti-plane crack in human bone. I. Mathematical modelling

2018 ◽  
Vol 26 (1) ◽  
pp. 81-90
Author(s):  
Eduard Marius Crăciun ◽  
Marin Marin ◽  
Adrian Răbâea
Keyword(s):  
Composite Material ◽  
Crack Propagation ◽  
Mathematical Modelling ◽  
Hilbert Problem ◽  
Plane Crack ◽  
Propagation Angle ◽  
Linear Elastic ◽  
Elastic Composite ◽  
Crack Propagation Angle ◽  
Riemann Hilbert Problem

Abstract We consider an anti-plane crack in a bone, considered as an initially deformed orthotropic, linear elastic composite material. Elastic incremental fields in the composite material are obtained following theories of Guz’s representation and of Riemann-Hilbert problem. Critical values of crack propagation angle are determined using Sih’s generalized criterion.

Cracked Pre-Stressed Elastic Composite Subjected by Sliding Forces I. Mathematical Modelling

2014 ◽  
Vol 601 ◽  
pp. 96-99
Author(s):  
Eduard Marius Craciun ◽  
Ionel Nicolae ◽  
Viorel Bogdan Rădoiu ◽  
George Carlig ◽  
Liviu Mateescu
Keyword(s):  
Composite Material ◽  
Representation Theory ◽  
Crack Propagation ◽  
Mathematical Modelling ◽  
Riemann Problem ◽  
Collinear Cracks ◽  
Linear Elastic Material ◽  
Linear Elastic ◽  
Tangential Stresses ◽  
Elastic Composite

We consider one or two collinear cracks in a pre-stressed, orthotropic, linear elastic material representing a fiber reinforced elastic composite. Elastic incremental fields in the composite material, using Guzs representation theory, Cauchy-Riemann problem and critical values of incremental tangential stresses that producing crack propagation are obtained using Sihs generalized criterion.

Application of Multi-Parameter Fracture Mechanics to Study of Crack Propagation Angle in Selected Mixed-Mode Geometry

2013 ◽  
Vol 592-593 ◽  
pp. 209-212 ◽  
Author(s):  
Lucie Šestáková Malíková ◽  
Václav Veselý
Keyword(s):  
Fracture Mechanics ◽  
Crack Propagation ◽  
Mixed Mode ◽  
Initial Crack ◽  
Propagation Angle ◽  
Linear Elastic ◽  
Higher Order Terms ◽  
Elastic Fracture ◽  
Cracked Specimens ◽  
Crack Propagation Angle

The multi-parameter fracture mechanics becomes more and more significant, because it is shown that it can help to describe fracture processes occurring in cracked specimens more precisely than conventional linear elastic fracture mechanics. In this paper, the concept based on the Williams expansion derived for approximation of stress/displacement crack-tip fields is presented and applied on a mixed-mode configuration. Two fracture criteria for estimation of the initial crack propagation angle are introduced. A parametric study is performed in order to investigate the dependence of the crack propagation angle on the stress intensity factors ratio. Influence and importance of taking into account the so-called higher-order terms of the Williams expansion are discussed and some recommendations are stated.

scholarly journals Influence of Stress Intensity Factor on Rail Fatigue Crack Propagation by Finite Element Method

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5720
Author(s):  
Ruipeng Gao ◽  
Mengmeng Liu ◽  
Bing Wang ◽  
Yiran Wang ◽  
Wei Shao
Keyword(s):  
Stress Intensity Factor ◽  
Fatigue Crack ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Propagation ◽  
Crack Length ◽  
Rolling Contact ◽  
Mode I ◽  
Propagation Angle ◽  
Crack Propagation Angle

Wheel rail rolling contact fatigue is a very common form of damage, which can lead to uneven rail treads, railhead nuclear damage, etc. Therefore, ANSYS software was used to establish a three-dimensional wheel–rail contact model and analyze the effects of several main characteristics, such as the rail crack length and crack propagation angle, on the fatigue crack intensity factor during crack propagation. The main findings were as follows: (1) With the rail crack length increasing, the position where the crack propagated by mode I moved from the inner edge of the wheel–rail contact spot to the outer edge. When the crack propagated to 0.3–0.5 mm, it propagated to the rail surface, causing the rail material to peel or fall off and other damage. (2) When the crack propagation angle was less than 30°, the cracks were mainly mode II cracks. When the angle was between 30 and 70°, the cracks were mode I–II cracks. When the angle was more than 70°, the cracks were mainly mode I cracks. When the crack propagation angle was 60°, the equivalent stress intensity factor reached the maximum, and the rail cracks propagated the fastest.

scholarly journals Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann–Hilbert Problem

2021 ◽  
Author(s):  
Dmitrii Legatiuk ◽  
Daniel Weisz-Patrault
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Conformal Mapping ◽  
Crack Propagation ◽  
Function Theory ◽  
Hilbert Problem ◽  
Complex Function ◽  
Numerical Approach ◽  
Complex Function Theory ◽  
Riemann Hilbert Problem

AbstractIn this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.

scholarly journals Fatigue Crack Growth Analysis with Extended Finite Element for 3D Linear Elastic Material

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 397
Author(s):  
Yahya Ali Fageehi
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Fatigue Life ◽  
Crack Propagation ◽  
Crack Growth ◽  
Mixed Mode ◽  
Propagation Path ◽  
Loading Conditions ◽  
Extended Finite Element ◽  
Linear Elastic

This paper presents computational modeling of a crack growth path under mixed-mode loadings in linear elastic materials and investigates the influence of a hole on both fatigue crack propagation and fatigue life when subjected to constant amplitude loading conditions. Though the crack propagation is inevitable, the simulation specified the crack propagation path such that the critical structure domain was not exceeded. ANSYS Mechanical APDL 19.2 was introduced with the aid of a new feature in ANSYS: Smart Crack growth technology. It predicts the propagation direction and subsequent fatigue life for structural components using the extended finite element method (XFEM). The Paris law model was used to evaluate the mixed-mode fatigue life for both a modified four-point bending beam and a cracked plate with three holes under the linear elastic fracture mechanics (LEFM) assumption. Precise estimates of the stress intensity factors (SIFs), the trajectory of crack growth, and the fatigue life by an incremental crack propagation analysis were recorded. The findings of this analysis are confirmed in published works in terms of crack propagation trajectories under mixed-mode loading conditions.

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