Fracture Statistics Models and Crack Propagation in Random Media

1994 ◽  
Vol 47 (1S) ◽  
pp. S141-S150 ◽  
Author(s):  
D. Jeulin
Keyword(s):  
Crack Propagation ◽  
Fracture Energy ◽  
Random Media ◽  
Probabilistic Models ◽  
Heterogeneous Media ◽  
Crack Nucleation ◽  
Crack Arrest ◽  
Two Dimensions ◽  
Unstable Crack ◽  
Probability Of Fracture

Crack propagation in heterogeneous media is of primary interest for engineering purposes, in order to predict the overall toughness and the probability of fracture from data on the microstructure. Probabilistic models for mode I crack propagation in two dimensions are presented. They are developed for brittle elastic materials with a random distribution of fracture energy. These models enable us to calculate in a closed form the probability of fracture involving crack nucleation and propagation that differ from the usual fracture statistics models based on the weakest link model. The use of the Griffith’s crack arrest criterion is applied to random function models for the distribution of the fracture energy and for various loading conditions resulting in stable or unstable crack propagation. From the models are deduced some statistical size effects.

Steady-State Crack Propagation in Pressurized Pipelines

1977 ◽  
Vol 99 (1) ◽  
pp. 112-121 ◽  
Author(s):  
C. Popelar ◽  
A. R. Rosenfield ◽  
M. F. Kanninen
Keyword(s):  
Steady State ◽  
Crack Propagation ◽  
Driving Force ◽  
Crack Arrest ◽  
Operating Conditions ◽  
Unstable Crack ◽  
Crack Driving Force ◽  
Plastic Yield ◽  
Pressurized Pipelines ◽  
Full Scale Tests

Previous work at Battelle-Columbus on the development of a theoretical model for unstable crack propagation and crack arrest in a pressurized pipeline is extended in this paper by including the effect of backfill. The approach being developed involves four essential aspects of crack propagation in pipelines. These four components of the problem are: 1 – a shell theory characterization of the dynamic deformation of a pipe with a plastic yield-hinge behind an axially propagating crack, 2 – a fluid-mechanics treatment of the axial variations in the gas pressure acting on the pipe walls, 3 – an energy-based dynamic fracture mechanics formulation for the crack-driving force, and 4 – measured values of the dynamic energy absorption rate for pipeline steels. Comparisons given in the paper show that the steady-state crack speeds predicted by the model are in reasonably good agreement with the crack speeds measured in full-scale tests, both with and without backfill. The analysis further reveals the existence of a maximum steady-state crack-driving force as a function of the basic mechanical properties of the pipe steel and the pipeline goemetry and operating conditions. Quantitative estimates of this quantity provided by the model offer a basis for comparison with the empirical crack-arrest design criteria for pipelines developed by AISI, the American Gas Association, the British Gas Council, and British Steel. These are also shown to be in substantial agreement with the predictions of the model developed in this paper.

Mechanism of irregular crack-propagation in thermal controlled fracture of ceramics induced by microwave

2020 ◽  
Vol 21 (6) ◽  
pp. 610
Author(s):  
Xiaoliang Cheng ◽  
Chunyang Zhao ◽  
Hailong Wang ◽  
Yang Wang ◽  
Zhenlong Wang
Keyword(s):  
Crack Propagation ◽  
Industrial Application ◽  
Ceramic Materials ◽  
Advanced Technology ◽  
Analytical Models ◽  
Propagation Mechanism ◽  
Unstable Crack ◽  
Fracture Simulation ◽  
Initial Stage ◽  
Controlled Fracture

Microwave cutting glass and ceramics based on thermal controlled fracture method has gained much attention recently for its advantages in lower energy-consumption and higher efficiency than conventional processing method. However, the irregular crack-propagation is problematic in this procedure, which hinders the industrial application of this advanced technology. In this study, the irregular crack-propagation is summarized as the unstable propagation in the initial stage, the deviated propagation in the middle stage, and the non-penetrating propagation in the end segment based on experimental work. Method for predicting the unstable propagation in the initial stage has been developed by combining analytical models with thermal-fracture simulation. Experimental results show good agreement with the prediction results, and the relative deviation between them can be <5% in cutting of some ceramics. The mechanism of deviated propagation and the non-penetrating propagation have been revealed by simulation and theoretical analysis. Since this study provides effective methods to predict unstable crack-propagation in the initial stage and understand the irregular propagation mechanism in the whole crack-propagation stage in microwave cutting ceramics, it is of great significance to the industrial application of thermal controlled fracture method for cutting ceramic materials using microwave.

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Stress Intensity Factor Calculation Using a Weight Function Method

2007 ◽  
Author(s):  
Rui Sun ◽  
Zongwen An ◽  
Hong-Zhong Huang ◽  
Qiming Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Propagation ◽  
Weight Function ◽  
Function Method ◽  
Method Comparison ◽  
Finite Size ◽  
Unstable Crack ◽  
Weight Function Method

Propagation of a critical unstable crack under the action of static or varying stresses is determined by the intensity of strain field at tips of the crack. Stress intensity factor (SIF) is an important parameter in fracture mechanics, which is used as a criterion to judge the unstable propagation of a crack and plays an important role in calculating crack propagation life. SIF is related to both geometrical form and loading condition of a structure. In the paper, a weight function method is introduced to study crack propagation of center through cracks and edge cracks in a finite-size plate. In addition, finite element method, linear regression, and polynomial interpolating technique are used to simulate and verify the proposed method. Comparison studies among the proposed and current methods are performed as well. The results show that the weight function method can be used to calculate SIF easily.

Short Crack Propagation Model Applied to Shot Peened Aluminium Alloys

2009 ◽  
Vol 65 ◽  
pp. 53-61 ◽  
Author(s):  
J. Solis ◽  
J. Oseguera-Peña ◽  
I. Betancourt
Keyword(s):  
Surface Roughness ◽  
Residual Stresses ◽  
Crack Propagation ◽  
Aluminium Alloys ◽  
Micromechanical Model ◽  
High Strength ◽  
Crack Arrest ◽  
Propagation Model ◽  
Safe Load ◽  
Compressive Residual Stresses

The Navarro-Rios micromechanical model was used to assess the bounds of two different damage zones: crack arrest region and crack propagation region of controlled shot peening (CSP) of high strength aluminium alloys. Performance of CSP in terms of fatigue resistance was investigated. This comparison indicated that CSP in terms of fatigue depends on the competition between its beneficial and detrimental products, i.e. surface roughness and compressive residual stresses respectively. The gathered information can be used for safe load determinations in design.

scholarly journals Lattice reduction in two dimensions: analyses under realistic probabilistic models

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Brigitte Vallée ◽  
Antonio Vera
Keyword(s):  
Dynamical Systems ◽  
Probabilistic Models ◽  
Two Dimensions ◽  
Lattice Reduction ◽  
Lll Algorithm ◽  
Transfer Operators ◽  
International Audience ◽  
Dimension 2

International audience The Gaussian algorithm for lattice reduction in dimension 2 is precisely analysed under a class of realistic probabilistic models, which are of interest when applying the Gauss algorithm "inside'' the LLL algorithm. The proofs deal with the underlying dynamical systems and transfer operators. All the main parameters are studied: execution parameters which describe the behaviour of the algorithm itself as well as output parameters, which describe the geometry of reduced bases.

A Markov Chain Fracture Model for Intergranular Crack Propagation in Polycrystalline Materials

2010 ◽  
Vol 89-91 ◽  
pp. 29-34
Author(s):  
Muhammad A. Arafin ◽  
Jerzy A. Szpunar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Crack Propagation ◽  
Intergranular Crack ◽  
Crack Nucleation ◽  
External Stress ◽  
Polycrystalline Materials ◽  
Multiple Crack ◽  
Stress Direction ◽  
Nucleation Sites

A model for intergranular damage propagation in polycrystalline materials is proposed, based on Markov Chain theory, Monte Carlo simulation and percolation concept. The model takes into account crack branching and coalescence, multiple crack nucleation sites, crack-turning etc., as well as the effect of grain boundary plane orientations with respect to the external stress direction. Both honeycomb and voronoi microstructures were utilized as the input microstructures. The effect of multiple crack nucleation sites has been found to have great influence on the crack propagation length. It has been observed that percolation threshold reported in the literature based on hexagonal microstructure is not applicable when the effect of external stress direction on the susceptibilities of grain boundaries is considered. The successful integration of voronoi algorithm with the Markov Chain and Monte Carlo simulations has opened up the possibilities of evaluating the intergranular crack propagation behaviour in a realistic manner.

The Comparison of Self-Compacting Rock-Filled Concrete with Large-Size Natural and Recycled Aggregate

2014 ◽  
Vol 513-517 ◽  
pp. 20-23
Author(s):  
Hai Chao Wang ◽  
Xue Hua Wang ◽  
Xue Hui An
Keyword(s):  
Fracture Toughness ◽  
Crack Propagation ◽  
Fracture Energy ◽  
Fracture Mechanism ◽  
Recycled Aggregate ◽  
Propagation Process ◽  
Fracture Characteristics ◽  
Three Point Bending ◽  
Large Size ◽  
Crack Propagation Process

The different fracture characteristics of self-compacting rock-filled concrete with large-size natural and recycled aggregate are analyzed by three-point bending experiment. According to the analysis of the crack propagation process, the fracture mechanism differences of self-compacting rock-filled concrete with large-size natural and recycled aggregate are discussed. The further analysis of the differences of fracture toughness, fracture energy, and are gain

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