Probabilistic Fracture Mechanics Using Fractal Finite Element Method

2008 ◽  
Author(s):  
R. M. Reddy ◽  
B. N. Rao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Mixed Mode ◽  
Fracture Parameter ◽  
Shape Sensitivity ◽  
Probabilistic Fracture Mechanics ◽  
Reliability Method ◽  
Cracked Structures ◽  
Element Method

This paper presents probabilistic fracture-mechanics analysis of linear-elastic cracked structures subjected to mixed-mode (modes I and II) loading conditions using fractal finite element method (FFEM). The method involves FFEM for calculating fracture response characteristics; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using continuum shape sensitivity analysis. Numerical examples based on mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that the predicted failure probability based on the proposed formulation of the sensitivity of fracture parameter is accurate in comparison with the Monte Carlo simulation results. Since all gradients are calculated analytically, reliability analysis of cracks can be performed efficiently using FFEM.

Fractal Finite-Element Method for Evaluating Sensitivities of Fracture Parameters for Multiple Cracked Systems

2008 ◽  
Author(s):  
R. M. Reddy ◽  
B. N. Rao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Material Derivative ◽  
Probabilistic Fracture Mechanics ◽  
Linear Elastic ◽  
Fracture Parameters ◽  
Mechanics Analysis ◽  
Cracked Structures ◽  
Element Method

The sensitivities of fracture parameters in cracked structures provide useful information for the prediction of stability and arrest of a single crack, the growth pattern analysis of a system of interacting cracks, configurational stability analysis of evolving cracks, probabilistic fracture mechanics analysis and universal size effect model. In the case of multiple crack systems, for example, sensitivities of fracture parameters at one crack tip due to the growth of any other crack must be calculated to determine the strength of the interaction. In probabilistic fracture mechanics analysis of linear-elastic cracked structures, the first and second order reliability methods require accurate estimates of fracture parameters, their sensitivities. This paper presents a new fractal finite element method based continuum shape sensitivity analysis for evaluating sensitivities of fracture parameters in a homogeneous, isotropic, and two dimensional linear-elastic multiple cracked system subject to mixed-mode loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of fracture parameters. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predict the first-order sensitivity of fracture parameters, more efficiently and accurately than the finite-difference method.

scholarly journals An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 507
Author(s):  
K. Yakoubi ◽  
S. Montassir ◽  
Hassane Moustabchir ◽  
A. Elkhalfi ◽  
Catalin Iulian Pruncu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Extended Finite Element Method ◽  
Research Study ◽  
Extended Finite Element ◽  
T Stress ◽  
Cracked Structures ◽  
Element Method

The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

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