Dynamic Propagation of Mode Ⅲ Interfacial Crack Subjected to Variable Moving Concentrated Loads

2011 ◽  
Vol 197-198 ◽  
pp. 1712-1717
Author(s):  
Cheng Jin ◽  
Ying Ba ◽  
Min Lin ◽  
Bao Ke Guo
Keyword(s):  
Mechanical Model ◽  
Crack Surface ◽  
Interfacial Crack ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Moving Loads ◽  
Concentrated Loads ◽  
Dynamic Propagation ◽  
Complex Functions ◽  
Self Similar

Dynamic propagation of mode Ⅲ crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approaches of self-similar functions, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Px/t move along x-axial with velocity β. At last, analytical solutions of stress, displacement and stress intensity factor are attained, respectively.

Dynamic Propagation of Mode III: Crack Concerning Surfaces Subjected to Variable Moving Concentrated Loads

2010 ◽  
Vol 139-141 ◽  
pp. 2312-2315
Author(s):  
Cheng Jin ◽  
Ying Ba ◽  
Min Lin ◽  
Bao Ke Guo
Keyword(s):  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Moving Loads ◽  
Concentrated Loads ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Dynamic Propagation ◽  
Complex Functions ◽  
Self Similar ◽  
Superposition Theorem

Asymmetric dynamic propagation of mode III: crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approach of self-similar function, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Pt/x move along x-axial with velocity β. And then, analytical solutions of stress, displacement and stress intensity factors are attained, respectively. These solutions are utilizable to attain solutions of arbitrarily complex problems, using the superposition theorem

Dislocation Distribution Function of the Surfaces of Mode III Dynamic Crack Subjected to Unit-Step Loads and Moving Increasing Loads

2006 ◽  
Vol 324-325 ◽  
pp. 101-104
Author(s):  
Xin Gang Li ◽  
Nian Chun Lü ◽  
Guo Zhi Song ◽  
Cheng Jin
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Crack Propagation ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Dislocation Distribution ◽  
Unit Step ◽  
Complex Functions ◽  
Self Similar

By the theory of complex functions, dislocation distribution function concerning mode dynamic crack propagation problem under the conditions of unit-step loads and moving increasing loads was studied respectively. Analytical solution representations are attained by the methods of self-similar functions. The problems investigated can be transformed into Riemann-Hilbert problems and their closed solutions are obtained rather simple by this approach.

scholarly journals Dynamic Crack Propagation Problems of Fibre-Reinforced Concrete

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Y. H. Cheng ◽  
Lu Nian Chun ◽  
Li Xin-gang
Keyword(s):  
Analytical Solutions ◽  
Dynamic Stress ◽  
Dynamic Crack Propagation ◽  
Crack Model ◽  
Dynamic Crack ◽  
Dynamic Stress Intensity Factors ◽  
Fibre Concrete ◽  
Complex Functions ◽  
Self Similar ◽  
Superposition Theorem

Applying the built dynamic crack model of fibre concrete, bridging fiber segment is substituted by loads. When a crack propagates its fiber continues to break. By the approaches of the theory of complex functions, the problems dealt with can be translated into Riemann-Hilbert problems. Analytical solutions of the displacements, stresses, and dynamic stress intensity factors under the action of of moving variable loads and , respectively, are attained by the ways of self-similar measures. After those analytical solutions are utilized by superposition theorem, the solutions of arbitrary complex problems can be obtained.

scholarly journals Variable-order fracture mechanics and its application to dynamic fracture

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Sansit Patnaik ◽  
Fabio Semperlotti
Keyword(s):  
Dynamic Fracture ◽  
Crack Surface ◽  
A Priori ◽  
Computational Cost ◽  
Dynamic Crack Propagation ◽  
Benchmark Problems ◽  
Variable Order ◽  
Dynamic Crack ◽  
Brittle Solids ◽  
Complex Crack

AbstractThis study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More specifically, the reformulation of the elastodynamic problem via variable and fractional-order operators enables a unique and extremely powerful approach to model nucleation and propagation of cracks in solids under dynamic loading. The resulting dynamic fracture formulation is fully evolutionary, hence enabling the analysis of complex crack patterns without requiring any a priori assumption on the damage location and the growth path, and without using any algorithm to numerically track the evolving crack surface. The evolutionary nature of the variable-order formalism also prevents the need for additional partial differential equations to predict the evolution of the damage field, hence suggesting a conspicuous reduction in complexity and computational cost. Remarkably, the variable-order formulation is naturally capable of capturing extremely detailed features characteristic of dynamic crack propagation such as crack surface roughening as well as single and multiple branching. The accuracy and robustness of the proposed variable-order formulation are validated by comparing the results of direct numerical simulations with experimental data of typical benchmark problems available in the literature.

Self-Similar Interfacial Crack Growth in Anisotropic Material Under Anti-Plane Shear

1998 ◽  
Vol 14 (1) ◽  
pp. 17-22
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Release Rate ◽  
Anisotropic Material ◽  
Constant Velocity ◽  
Interfacial Crack ◽  
Plane Shear ◽  
Dynamic Propagation ◽  
Self Similar

ABSTRACTDynamic propagation of a crack along the interface in an anisotropic material subjected to remote uniform anti-plane shear is studied. The crack is assumed to nucleate from an infinitesimal microcrack and expands with a constant velocity. Explicit expressions for the stress intensity factor and the energy release rate are derived.

scholarly journals Influence of fracture incubation time on dynamic crack propagation in brittle solids

2019 ◽  
Vol 221 ◽  
pp. 01013
Author(s):  
Aleksandr Grigoriev ◽  
Evgeny Shilko
Keyword(s):  
Incubation Time ◽  
Shear Crack ◽  
Growth Dynamics ◽  
Longitudinal Shear ◽  
Dynamic Crack Propagation ◽  
Shear Mode ◽  
Dynamic Crack ◽  
Dynamic Propagation ◽  
Brittle Solids ◽  
Mode Ii Crack

The paper is devoted to theoretical study of the longitudinal shear (mode II) crack unstable growth dynamics in brittle materials. We considered two main regimes of the dynamic propagation of the crack (sub-Rayleigh and supershear) and their implementation conditions. The research was carried out by computer simulation with the Movable Cellular Automaton method, using the generalized kinetic fracture model, which takes into account the finite duration of local fracture (fracture incubation time). It is shown that the fracture incubation time is a key parameter, which determines the transition conditions of the shear crack growth process from the sub-Rayleigh regime to supershear.

Numerical Simulation for Dynamic Crack Propagation by MLPG

2006 ◽  
Vol 324-325 ◽  
pp. 495-498
Author(s):  
Ying Liu ◽  
Ling Tian Gao
Keyword(s):  
Crack Propagation ◽  
High Speed ◽  
Mass Matrix ◽  
Crack Edge ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Lumped Mass ◽  
Central Difference ◽  
Stress Criterion ◽  
Dynamic Propagation

In this paper, a new algorithm based on Meshless Local Petrov-Galerking (MLPG) method is presented for analyzing the crack dynamic propagation. A new modified Moving Least Squares approximation is proposed to simplify the treatment of essential boundary conditions. Explicit central difference with lumped mass matrix is adopted for the time integral. Visibility criterion with crack edge node adding technique and the maximum hoop stress criterion are used to describe the crack propagation and forecast the crack propagation direction. Based on this algorithm, three-point bend specimen for impact fracture test is investigated. Comparing the results with those obtained by the laser caustic method and high-speed photographs, the accuracy of the present algorithm is proved.

Analytical Solutions of Mode III Moving Crack under Concentrated Force Boundary Condition

2011 ◽  
Vol 214 ◽  
pp. 271-275
Author(s):  
Yun Tao Wang ◽  
Nian Chun Lü ◽  
Cheng Jin
Keyword(s):  
Analytical Solutions ◽  
Dynamic Stress ◽  
Hilbert Problem ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Moving Crack ◽  
Dynamic Stress Intensity Factors ◽  
Concentrated Force ◽  
Complex Functions ◽  
Self Similar

By application of the theory of complex functions, the problem for mode Ⅲ dynamic crack under concentrated force were researched. The Riemann-Hilbert problem is formulated according to relationships of self-similar functions. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation.

Symmetrical Dynamic Propagation Problems of Mode III Interface Crack

2013 ◽  
Vol 300-301 ◽  
pp. 806-809
Author(s):  
Nian Chun Lü ◽  
Yun Hong Cheng ◽  
Yun Tao Wang
Keyword(s):  
Interface Crack ◽  
Hilbert Problem ◽  
Mode Iii ◽  
Symmetrical Mode ◽  
Dynamic Propagation ◽  
Complex Functions ◽  
Arbitrary Complex ◽  
Self Similar ◽  
Superposition Theorem ◽  
Riemann Hilbert Problem

By the theory of complex functions, symmetrical dynamic propagation problems of mode Ⅲ interface crack were investigated. The problems considered can be very easily translated into Riemann-Hilbert problem by the methods of self-similar functions, and the universal expressions of analytical solutions for the surfaces of symmetrical mode Ⅲ interface crack subjected to moving alterable loadings Pt3/x3 and Px4/t3 were obtained, respectively. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be acquired.

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