Elastic crack problems, fracture mechanics, equations of elasticity and finite-part integrals

2013 ◽  
pp. 1-24 ◽  
Author(s):  
Whye-Teong Ang
Keyword(s):  
Fracture Mechanics ◽  
Finite Part ◽  
Crack Problems ◽  
Elastic Crack

scholarly journals A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

2012 ◽  
Vol 468 (2146) ◽  
pp. 2939-2961 ◽  
Author(s):  
Licheng Guo ◽  
Zhihai Wang ◽  
Naotake Noda
Keyword(s):  
Mechanical Properties ◽  
Fracture Mechanics ◽  
Functionally Graded Materials ◽  
Small Sample ◽  
Functionally Graded ◽  
Phase Volume ◽  
Graded Materials ◽  
Volume Fractions ◽  
Mechanics Model ◽  
Crack Problems

This study aimed to develop a method to build a ‘bridge’ between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the crack problems of FGMs with stochastic properties.

Evaluation of flexural fracture toughness for quasi-brittle structural materials using a simple test method

2002 ◽  
Vol 29 (4) ◽  
pp. 567-575 ◽  
Author(s):  
M.M Reda Taha ◽  
X Xiao ◽  
J Yi ◽  
N G Shrive
Keyword(s):  
Fracture Toughness ◽  
Fracture Mechanics ◽  
Brittle Fracture ◽  
High Performance ◽  
High Performance Concrete ◽  
Fibre Reinforced Concrete ◽  
Simple Test ◽  
Elastic Crack ◽  
Fracture Performance ◽  
Brittle Fracture Mechanics

As new structural concepts such as partial prestressing and steel-free bridge decks are more widely accepted and used, there is an increasing need for a reliable and reproducible fracture performance criterion that can describe resistance to crack growth. The required criterion should also be easy to determine experimentally so that it can be incorporated in structural specifications. The nonlinear behaviour of concrete and masonry materials suggested that quasi-brittle fracture mechanics approaches may be the most suitable for determining their fracture performance. The effective elastic crack model originally developed by Karihaloo and Nallathambi (1989) was modified to evaluate the critical crack depth under pure flexural stresses. A computer program was developed to calculate this depth iteratively from the experimental results. An experimental programme examining the fracture performance of four different structural materials (high performance concrete, mortar, fibre reinforced concrete, and masonry units) was carried out to examine the applicability of the model. As no post-peak data are required for the analysis, the model allows the use of a simple test setup to evaluate the fracture performance of quasi-brittle materials experimentally.Key words: fracture toughness, linear elastic fracture mechanics (LEFM), elastoplastic fracture mechanics (EPFM), quasi-brittle fracture mechanics, effective elastic crack, high performance concrete, masonry, fibre reinforced concrete.

Finite-part integral and boundary element method to solve embedded planar crack problems

1993 ◽  
Vol 60 (4) ◽  
pp. 373-381 ◽  
Author(s):  
T. Y. Qin ◽  
R. J. Tang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Finite Part ◽  
Crack Problems ◽  
Planar Crack ◽  
Element Method

Assessment of Power Plant Components With Flaws and Defects Operating in the Long-Term Creep Range

2019 ◽  
Author(s):  
Magdalena Speicher ◽  
Thorben Bender ◽  
Andreas Klenk ◽  
Falk Mueller ◽  
Christian Kontermann ◽  
...  
Keyword(s):  
High Temperature ◽  
Fracture Mechanics ◽  
Crack Initiation ◽  
Crack Growth ◽  
Creep Crack Growth ◽  
Material Behavior ◽  
Critical Crack Length ◽  
Creep Crack ◽  
Combining Data ◽  
Crack Problems

Abstract Originating from defects and flaws in high temperature components crack initiation and crack propagation under service conditions can occur. Fracture mechanics data and procedures are needed to study crack problems and to support an advanced remnant life evaluation. During subsequent research in the past 35 years, data were determined for different high temperature materials. Methodologies and concepts taking into account the specific material behavior were developed in order to be able to describe crack initiation and crack growth and have appropriate assessment methods available. For creep crack initiation two criteria principles were used and for creep crack growth assessment based on the integral C* parameter were applied. Furthermore, a method for determination of critical crack length was developed allowing decisions whether modified stress analysis methods are sufficient or more complicated fracture mechanics methods are needed. To provide data and methodologies in a user-friendly way, a program system combining data and methods was implemented. The paper describes developed features and shows comparisons to other methods. The methods can be applied for design purposes as well as remnant life assessments.

scholarly journals Approximation to Hadamard Derivative via the Finite Part Integral

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 983 ◽  
Author(s):  
Chuntao Yin ◽  
Changpin Li ◽  
Qinsheng Bi
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Numerical Methods ◽  
Three Dimensional ◽  
Cylindrical Wave ◽  
Physical Models ◽  
Finite Part ◽  
Numerical Examples ◽  
Crack Problems ◽  
Hadamard Derivative

In 1923, Hadamard encountered a class of integrals with strong singularities when using a particular Green’s function to solve the cylindrical wave equation. He ignored the infinite parts of such integrals after integrating by parts. Such an idea is very practical and useful in many physical models, e.g., the crack problems of both planar and three-dimensional elasticities. In this paper, we present the rectangular and trapezoidal formulas to approximate the Hadamard derivative by the idea of the finite part integral. Then, we apply the proposed numerical methods to the differential equation with the Hadamard derivative. Finally, several numerical examples are displayed to show the effectiveness of the basic idea and technique.

scholarly journals A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
S. D. Daxini ◽  
J. M. Prajapati
Keyword(s):  
Fracture Mechanics ◽  
Free Vibration Analysis ◽  
Meshfree Methods ◽  
Computational Techniques ◽  
Complex Nature ◽  
Dynamic Crack ◽  
Recent Contribution ◽  
Crack Problems ◽  
Cracked Structures ◽  
Impact Problems

Meshfree methods are viewed as next generation computational techniques. With evident limitations of conventional grid based methods, like FEM, in dealing with problems of fracture mechanics, large deformation, and simulation of manufacturing processes, meshfree methods have gained much attention by researchers. A number of meshfree methods have been proposed till now for analyzing complex problems in various fields of engineering. Present work attempts to review recent developments and some earlier applications of well-known meshfree methods like EFG and MLPG to various types of structure mechanics and fracture mechanics applications like bending, buckling, free vibration analysis, sensitivity analysis and topology optimization, single and mixed mode crack problems, fatigue crack growth, and dynamic crack analysis and some typical applications like vibration of cracked structures, thermoelastic crack problems, and failure transition in impact problems. Due to complex nature of meshfree shape functions and evaluation of integrals in domain, meshless methods are computationally expensive as compared to conventional mesh based methods. Some improved versions of original meshfree methods and other techniques suggested by researchers to improve computational efficiency of meshfree methods are also reviewed here.

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