Fractal Finite-Element Based Continuum Shape Sensitivity Analysis of Cracks

2007 ◽  
Author(s):  
B. N. Rao ◽  
R. M. Reddy
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Fracture Initiation ◽  
Actual Behavior ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Element Analysis ◽  
Probabilistic Fracture Mechanics ◽  
Fracture Parameters

Probabilistic fracture mechanics (PFM) that blends the theory of fracture mechanics and the probability theory provides a more rational means to describe the actual behavior and reliability of structures. However in PFM, the fracture parameters and their derivatives are often required to predict the probability of fracture initiation and/or instability in cracked structures. The calculation of the derivatives of fracture parameters with respect to load and material parameters, which constitutes size-sensitivity analysis, is not unduly difficult. However, the evaluation of response derivatives with respect to crack size is a challenging task, since it requires shape sensitivity analysis. Using a brute-force type finite-difference method to calculate the shape sensitivities is often computationally expensive, in that numerous repetitions of deterministic finite element analysis may be required for a complete reliability analysis. Therefore, an essential need of probabilistic fracture-mechanics is to evaluate the sensitivity of fracture parameters accurately and efficiently.

Adaptivity in linear elastic fracture mechanics based on shape sensitivity analysis

2005 ◽  
Vol 194 (34-35) ◽  
pp. 3582-3606 ◽  
Author(s):  
Roberto Saliba ◽  
Claudio Padra ◽  
Marcelo J. Vénere ◽  
Edgardo Taroco ◽  
Raúl A. Feijóo
Keyword(s):  
Sensitivity Analysis ◽  
Fracture Mechanics ◽  
Linear Elastic Fracture Mechanics ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Linear Elastic ◽  
Elastic Fracture

Parametric Study on Pressure-Temperature Limit Curve

2016 ◽  
Author(s):  
Shin-Beom Choi ◽  
Han-Bum Surh ◽  
Jong-Wook Kim
Keyword(s):  
Sensitivity Analysis ◽  
Fracture Mechanics ◽  
Crack Depth ◽  
Temperature Limit ◽  
Round Robin ◽  
Robin Problem ◽  
Limit Curve ◽  
Element Analysis ◽  
Probabilistic Fracture Mechanics ◽  
Key Parameter

The final goal of this study is to solve the round-robin problem for the safety of a reactor pressure vessel by adopting a finite element analysis and probabilistic fracture mechanics. To do so, a sensitivity analysis and a deterministic analysis should be conducted. This paper contains the results of the sensitivity analysis as intermediate results of a round-robin problem. Key parameters such as the initial Reference Temperature for Nil Ductility Transition, Ni contents, Cu contents, fluence, and input transient were chosen to conduct the sensitivity analysis. In addition, different values of crack depth to the thickness ratio are considered to develop FE models. Moreover, a series of FE analyses are carried out. As a result, each key parameter has an influence on RTNDT and KIc. This means that the P-T limit curve is shifted. If the value of each key parameter is increased, the P-T limit curve is moved to the right side. Therefore, the operating area of the P-T limit curve should be reduced. The results of this paper will be very helpful in enhancing our understanding of the P-T limit curve. In addition, it will be used to adjust the probabilistic fracture mechanics and solve the round-robin problem.

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.

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