Failure Probability Analysis by Probabilistic Fracture Mechanics Based on FRI SCC Model

2010 ◽  
Author(s):  
Noriyoshi Maeda ◽  
Tetsuo Shoji
Keyword(s):  
Fracture Mechanics ◽  
Electric Current ◽  
Crack Growth ◽  
Failure Probability ◽  
Crack Depth ◽  
Threshold Value ◽  
Small Scale ◽  
Protective Film ◽  
Probabilistic Fracture Mechanics ◽  
Crack Growth Model

Failure Probability of a weld by stress corrosion cracking (SCC) in austenitic stainless steel piping was analyzed by probabilistic fracture mechanics (PFM) approach based on electro-chemical crack growth model (FRI model). In this model, crack growth rate da/dt where a is crack depth is anticipated as the rate of chemical corrosion process defined by electro-chemical Coulomb’s law. The process is also related to the strain rate at the crack tip, taking small scale yielding condition into consideration. Derived transcendental equation is solved numerically by iterative method. Compared to the mechanical crack growth equation like Paris’ law for SCC, FRI model can introduce many electro-chemical parameters such as electric current associated with corrosion of newly born SCC crack surface, the frequency of protective film break and mechanical parameters such as stress intensity factor change with time dK/dt. Stratified Monte-Carlo method was introduced which define the cell of sampling space by the ranges of a/c (c is crack length at surface) and the width of K of sampling space, Kw which has to be defined referring to KSCC below which no SCC is caused. Log-normal distributions were anticipated for a/c distribution and K distribution. Parameter survey performed shows that failure probability which is defined as the ratio of crack number whose depth reached 80% of wall thickness to the total crack number depends on many parameters introduced, especially on yielding stress, electric current decay parameter m, strain hardening index n in Ramberg-Osgood equation and dK/dt. From the requirements of FRI model, two types of threshold value of initial crack depth, cracks having smaller depth than this value can not grow, are proposed. Calculated failure probability does not reach 1 when cracks having smaller initial depth than the threshold value are included in the distribution of analyzing cracks.

Accounting for Constraint in Probabilistic Fracture Mechanics Analysis of Welds in Floating Production, Storage and Off-Loading (FPSO) Vessels

2003 ◽  
Author(s):  
Jens P. Tronskar
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Fracture Mechanics ◽  
Crack Growth ◽  
North Sea ◽  
Failure Probability ◽  
Crack Tip ◽  
Probabilistic Fracture Mechanics ◽  
Crack Tip Constraint

Revision 4 of the British Energy R6 document: “Assessment of the integrity of structures containing defects” provides methods to allow for loss of crack tip constraint for shallow weld flaws. The document also provides methods to estimate upper-bound values of the through thickness residual stress distribution for a range of common weld joint configurations. The present paper presents results of analyses where approaches to modify the R6 Option 1 or 2 failure assessment diagrams (FADs) for loss of crack tip constraint pertaining to primary and non-uniform residual stress have been applied. The modified FAD were formulated for probabilistic fracture mechanics analyses of semi-elliptical surface cracks located at transverse deck welds of Floating Production, Storage and Off-loading (FPSO) vessels designed to operate in the North Sea. The objective was to study the influence on the failure probability of modifying the FAD for constraint and allowing for non-uniform residual stress. Another objective was to study the influence of constraint correction on the combined fatigue and fracture failure probability for the vessels subjected to wave loading. Material and weld tensile properties and fracture toughness distributions for input to the probabilistic fracture mechanics analyses were obtained from testing of welded panels prepared using welding procedures for actual FPSO fabrication. The loading conditions were derived based on North Sea wave data pertaining to the offshore field where the FPSO is operating. The stresses were obtained from global FE analysis and fitted Weibull long-term and extreme value distributions. The results of the analyses demonstrate clearly the importance of correcting for crack tip constraint pertaining to both primary and secondary stress and to allow for non-uniform residual stress for shallow surface flaws of known crack heights. However, in combination with fatigue crack growth the effects become less prominent as the failure probability is governed by the uncertainty in the parameters of the crack growth relationship and the long-term stress distribution.

Probabilistic Fracture Mechanics Analysis of Nuclear Piping Considering an Embedded Crack

2002 ◽  
Author(s):  
Hideo Machida ◽  
Shinobu Yoshimura
Keyword(s):  
Fracture Mechanics ◽  
Aspect Ratio ◽  
Failure Probability ◽  
Surface Crack ◽  
Crack Depth ◽  
Crack Size ◽  
Crack Model ◽  
Pipe Surface ◽  
Probabilistic Fracture Mechanics ◽  
Embedded Crack

This paper presents probabilistic fracture mechanics analyses of nuclear piping with an embedded crack. If the same crack depth and the same aspect ratio are supposed to both the surface and the embedded cracks, break and leak probabilities of the embedded crack case are much smaller than those of the surface crack case. This is because both of length and area of the embedded crack are one half of those of the surface crack, and when the center position of the embedded crack is close to the pipe surface, the crack comes out to the outside of the pipe partially. Consequently, an effective crack size is smaller than that given by probabilistic density function. Even when both of the area and aspect ratio of the embedded crack are the same as those of the surface crack, this tendency does not change. Although the embedded crack grows in the two directions of an inner and an outer surface of the pipe and the crack growth rate is higher than that of the surface crack, this effect does not appear in the failure probability clearly. The surface crack is effective for conservative evaluation, but it is not proper for a rational evaluation. Employing the realistic embedded crack model can lead to rational failure probability.

Probabilistic Fracture Mechanics Assessment of Welded Joints of Offshore Structure Using a Bilinear Crack Growth Law

2008 ◽  
Author(s):  
Rizwan A. Khan ◽  
Suhail Ahmad
Keyword(s):  
Fatigue Crack ◽  
Fatigue Life ◽  
Fatigue Crack Growth ◽  
Fracture Mechanics ◽  
Crack Growth ◽  
Limit State ◽  
Published Data ◽  
Offshore Structure ◽  
Probabilistic Fracture Mechanics ◽  
Crack Growth Model

Design of welded structures for fatigue limit state is normally carried out by means of either linear or bilinear S-N curves approaches. To properly assess the effects of design, fabrication, inspection and repair strategy for structures degradation due to crack growth, Fracture mechanics (FM) models need to be applied. This paper deals with the application of a probabilistic fracture mechanics approach to predict the fatigue life of welded steel structure in the presence of cracks under random spectral loading. It is based on a BS7910 [1] proposed bi-linear relationship to model fatigue crack growth and incorporates a failure criterion to describe the interaction between fracture and plastic collapse. Uncertainty modeling, especially of fatigue crack growth parameters, is undertaken with the aid of recently published data in support of the bi-linear crack growth relationship. Results pertaining to fatigue reliability and fatigue crack size evolution are presented using the Monte Carlo Simulation technique, and emphasis is placed on a comparison between linear and bi-linear crack growth models. The bi-linear crack growth model is found to lead to higher fatigue life estimates and shows sensitivity to many other parameters in addition to the state of stress of the component. This leads to implications on inspection schemes for components of the marine structures and to ensure minimization of the surprises due to wide scatter of the fatigue phenomenon in marine environment. Variations in the system configuration, service life and coefficients of crack growth laws have been studied on the parametric basis.

The Influence of Flow Strength and Fracture Toughness on the Computed Reliability of Thermally Aged Grade CF-8M Cast Austenitic Stainless Steel Piping

2014 ◽  
Author(s):  
Timothy J. Griesbach ◽  
Dilip Dedhia ◽  
David O. Harris ◽  
Nathaniel G. Cofie ◽  
Kyle Amberge ◽  
...  
Keyword(s):  
Fracture Toughness ◽  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Fracture Mechanics ◽  
Failure Probability ◽  
Crack Depth ◽  
Random Variables ◽  
Low Flow ◽  
Flow Strength ◽  
Distribution Type

Thermal aging of cast austenitic stainless steel (CASS) piping is a concern for long-term operation of nuclear power plants. Traditional conservative deterministic fracture mechanics analyses lead to tolerable crack sizes well below the sizes that are readily detectable in these large-grained materials. This is largely due to the conservative treatment of the scatter in material properties and the imposition of multipliers (structural factors) on the applied loads. In order to account for the scatter in the tensile and fracture toughness properties that enter into the analysis, a probabilistic approach is taken. Application of the probabilistic fracture mechanics (PFM) model to representative problems has led to questions regarding the dominant random variables and the influence of the tails of their distributions on computed failure probability. The purpose of this paper is to report the results of a study to identify the important random variables in the PFM model and to investigate the influence of the distribution type on the computed failure probability. Application of the PFM model to a representative piping problem to compute the depth of a part-through part-circumferential crack that will fail with a defined probability (10−6 for example) revealed that the fracture toughness was not a dominant variable and the distribution of the toughness did not strongly affect the results. In contrast to this, the flow strength (which enters into the calculation of the applied crack driving force — J) was important in that low flow strength was controlling the low probability failures in the Monte Carlo simulation. Hence, the low-end tail of the flow strength distribution was influential. Various types of distribution of flow strength consistent with the available data were considered. It was found that the distribution type has a marked, but not overwhelming, effect on the crack depth that would fail with a given probability. From this it is concluded that the PFM model is quite robust, in that it is not highly sensitive to uncertainties in the dominant input distributions.

A Probabilistic Evaluation Model for Welding Residual Stress Distribution at Piping Joint in Probabilistic Fracture Mechanics Analysis

2008 ◽  
Author(s):  
Hiroto Itoh ◽  
Jinya Katsuyama ◽  
Kunio Onizawa
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Fracture Mechanics ◽  
Failure Probability ◽  
Evaluation Model ◽  
Residual Stress Distribution ◽  
Welding Residual Stress ◽  
Probabilistic Fracture Mechanics ◽  
Probabilistic Evaluation ◽  
Aging Knowledge

Stress corrosion cracking (SCC) has been observed at some piping joints made by Austenitic stainless steel in BWR plants. In JAEA, we have been developing probabilistic fracture mechanics (PFM) analysis methods for aged piping based on latest aging knowledge and an analytical code, PASCAL-SP. PASCAL-SP evaluates the failure probability of piping at aged welded joints under SCC by a Monte Carlo method. We proposes a simplified probabilistic model which can be applied to the failure probability analysis based on PFM for welded joint of piping considering the uncertainty of welding residual stress. And the probabilistic evaluation model is introduced to PASCAL-SP. A parametric PFM analysis concerning uncertainties of residual stress distribution using PASCAL-SP was performed. The PFM analysis showed that the uncertainties of residual stress distribution largely influenced break probability. The break probability increased with increasing the uncertainties of residual stress.

Fatigue Life Prediction Based on Probabilistic Fracture Mechanics: Case Study of Automotive Parts

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Mahboubeh Yazdanipour ◽  
Mohammad Pourgol-Mohammad ◽  
Naghd-Ali Choupani ◽  
Mojtaba Yazdani
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Fracture Mechanics ◽  
Crack Growth ◽  
Probabilistic Models ◽  
Fatigue Loading ◽  
Critical Fields ◽  
Propagation Of Uncertainty ◽  
Automotive Parts ◽  
Crack Growth Model

This paper studies the stochastic behavior of fatigue crack growth analytically and empirically by employing basic models in fracture mechanics. The research estimates the crack growth rate probabilistically, quantifies the uncertainty of probabilistic models under fatigue loading in automotive parts, and applies the simulations on W319 aluminum alloy, which has vast applications in automotive components’ products. Walker and Forman correlations are used in the paper. The deterministic simulations of these models are verified with afgrow code and validated experimentally with fatigue data of W319 aluminum. Then, the models are treated probabilistically by considering the models’ parameters stochastic. Monte Carlo (MC) simulation is employed to investigate the models under stochastic conditions. The paper is quantifies the propagation of uncertainty with calculating the standard deviations of crack lengths via cycles. The proposed procedure is useful for selecting a proper probabilistic fatigue crack growth model in specific applications and can be used in future fatigue studies not only in the automotive industry but also in other critical fields, to obtain more reliable conclusions.

Short Crack Growth Model in a Particulate Composite Using Nonlinear Elastic Fracture Mechanics

2003 ◽  
Author(s):  
Ying Zhang ◽  
Tsuchin Chu ◽  
Ajay Mahajan
Keyword(s):  
Fracture Mechanics ◽  
Crack Propagation ◽  
Crack Growth ◽  
Particulate Composite ◽  
Initial Crack ◽  
Short Crack ◽  
Video Tape ◽  
J Integral ◽  
Elastic Fracture ◽  
Crack Growth Model

The fracture mechanics model for a long crack does not work very well with short-crack propagation when the initial crack length is less than 5.1 mm (0.2 inch). In order to investigate the short crack effect, a series of tests of particulate composite specimens with long and short cracks were performed and the results recorded on a video tape. This test data was analyzed to determine the fracture parameters. Two initial crack lengths, 2.5 mm (0.1 inches) and 7.6 mm (0.3 inches) were used in the crack propagation tests. Based on the principle of linear elastic fracture mechanics (LEFM), the stress intensity factor KI was obtained. The instantaneous time-dependent J-integral for 0.1 and 0.3 inch crack specimens was determined by the NEFM analytical approach. The crack growth behavior was also investigated in the form of J-integral resistance curves. The calculated J-integral was reversed to derive a new KI. The new KI was compared with the measured value obtained from LEFM analysis results to determine the feasibility of applying the linear fracture approach to the non-linear behavior of the material. The results showed that the KI computed from the J-integral increased by 24.5%, and was at the time prior to the peak load for the 0.1 inch crack. For the 0.3 inch crack, the acceptable range was from the onset of propagation to the 9% strain stage (yield strain for the material), where the increase of the new KI was within 15.6%.

Failure Probability Analysis Based on FRI Model for Stress Corrosion Cracking Growth Introducing Residual Stress Distribution by Weld

2012 ◽  
Author(s):  
Noriyoshi Maeda ◽  
Tetsuo Shoji
Keyword(s):  
Residual Stress ◽  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Stress Distribution ◽  
Stress Corrosion ◽  
Crack Growth ◽  
Stress Corrosion Cracking ◽  
Failure Probability ◽  
Corrosion Cracking ◽  
Protective Film

Failure probability of welds by stress corrosion cracking (SCC) in austenitic stainless steel piping is analyzed by a probabilistic fracture mechanics (PFM) approach based on an electro-chemical crack growth model (FRI model, where FRI stands for “Fracture and Reliability Research Institute” of Tohoku University in Japan). In this model, crack growth rate da/dt, where a is crack depth, is anticipated as the rate of chemical corrosion process defined by electro-chemical Coulomb’s law. The process is also related to the strain rate at the crack tip, taking the small scale yielding into consideration. Compared to the mechanical crack growth equation like the power law for SCC, FRI model can introduce many parameters affecting the generation and break of protective film on the crack surface such as electric current associated with corrosion, the frequency of protective film break and mechanical parameters such as the stress intensity factor K and its change with time dK/dt. Derived transcendental equation is transformed into non-dimensional form, and then solved numerically by iterative method. The extension of surface crack by SCC under residual stress field is simulated by developing the stress distribution in polynomial form following ASME section XI appendix A. This simulation scheme is introduced into PFM framework to derive the failure probability of austenitic stainless steel piping in nuclear power plants to be used in developing a risk-informed inservice inspection (RI-ISI) program.

Failure Probability Analysis of Aged Piping Using Probabilistic Fracture Mechanics Methodology Considering Seismic Loads

2016 ◽  
Author(s):  
Yoshihito Yamaguchi ◽  
Jinya Katsuyama ◽  
Yinsheng Li
Keyword(s):  
Fracture Mechanics ◽  
Failure Probability ◽  
Power Plants ◽  
Fragility Curves ◽  
Safety Margin ◽  
Probability Analysis ◽  
Seismic Loads ◽  
Probabilistic Fracture Mechanics ◽  
Age Related ◽  
Piping Systems

Several nuclear power plants in Japan have been operating for more than 30 years and cracks due to age-related degradations have been detected in some piping systems during in-service inspections. Furthermore, several of them have experienced severe earthquakes in recent years. Therefore, failure probability analysis and fragility evaluation for piping systems, taking both age-related degradations and seismic loads into consideration, has become increasingly important for the structural integrity evaluation and the seismic probabilistic risk assessment. Probabilistic fracture mechanics (PFM) is recognized as a rational methodology for failure probability analysis and fragility evaluation of aged piping, because it can take the scatters and uncertainties of influence parameters into account. In our Japan Atomic Energy Agency (JAEA), a PFM analysis code PASCAL-SP was developed for aged piping considering age-related degradations. In this study, we improved PASCAL-SP for the fragility evaluation taking both age-related degradations and seismic loads into account. The details of the improvement of PASCAL-SP are explained and some example analysis results of failure probabilities, fragility curves and a preliminary investigation on seismic safety margin are presented in this paper.

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.

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