Assessment of plastic collapse behavior for tubes with collinear cracks

The 40% of wall thickness criterion has been used as a plugging rule of steam generator tubes but it can be applicable just to a single-cracked tubes. In the previous studies preformed by the authors, a total of 10 local failure prediction models were introduced to estimate the coalescence load of two adjacent collinear through-wall cracks existing in thin plates, and the reaction force model and plastic zone contact model were selected as optimum models among them. The objective of this study is to verify the applicability of the proposed optimum local failure prediction models to the tubes with two collinear through-wall cracks. For this, a series of plastic collapse tests and finite element analyses were carried out using the tubes containing two collinear through-wall cracks. It has been shown that the proposed optimum failure models can predict the local failure behavior of two collinear through-wall cracks existing in tubes well. And a coalescence evaluation diagram was developed which can be used to determine whether the adjacent cracks detected by NDE coalesce or not.     

Determination of global failure pressure for tubes with two parallel cracks

The 40% of wall thickness criterion, which has been used as a plugging rule is applicable only to a single cracked steam generator tubes. In the previous studies performed by the authors, several failure prediction models were introduced to estimate the plastic collapse pressures of steam generator tubes containing two adjacent parallel axial through‐wall cracks. These models were applied preliminarily for thin plates with two parallel through‐wall cracks and the crack opening displacement (COD) base model was selected as the optimum one. The objective of this study is to verify the applicability of the proposed failure prediction model for real steam generator tubes with two parallel axial through‐wall cracks. For this purpose, a series of plastic collapse tests and finite element analyses have been carried out for the steam generator tubes with two machined parallel axial through‐wall cracks. Thereby, it was proven that the proposed failure prediction model can be used for estimating the global failure pressure quite well. Also, interaction effects between two adjacent cracks were assessed through additional finite element analyses to investigate the effect on the global failure behaviour.     

A method to predict failure pressures of steam generator tubes with multiple through-wall cracks

This paper proposes a simple numerical method to predict burst pressures of steam generator tubes with multiple through-wall cracks, based on the stress-modified fracture strain damage model with stress reduction technique. For validation, simulated results using the proposed method are compared with 31 published experimental data of Alloy 600 plates and tubes with single or two through-wall cracks, showing that predicted loads are within 10% of experimentally-measured ones for all cases considered. Furthermore, a parametric study is performed to investigate the interaction effect of two through-wall cracks in Alloy 600 steam generator tubes under internal pressure.     

Elastic-plastic fracture mechanics assessment for steam generator tubes with through-wall cracks

The present work provides an elastic‐plastic fracture mechanics (EPFM) assessment scheme for a steam generator tube with a through‐wall crack under internal pressure. Noting that the geometry and material are rather uniform for steam generator tubes, and furthermore the only loading to be considered is internal pressure, an engineering EPFM analysis method is proposed to assess through‐wall cracks in steam generator tubes. Important outcomes of the present work are closed‐form approximations for J and crack opening displacement (COD). Sufficient confidence in the proposed J and COD estimates is gained from good agreements with the finite element results over a wide range of the crack length and pressure magnitude. Another important element of the EPFM assessment is to determine relevant J‐resistance curve for steam generator tubes. To improve the accuracy of predicting tube failure, the present paper also proposes a new method to determine fracture toughness using an actual tubular specimen instead of using a standard specimen, from which J‐resistance curves of steam generator tubes are obtained. Using the proposed J and toughness estimates, maximum pressures of steam generator tubes with through‐wall crack are estimated based on EPFM analysis, which is compared with experimental results and predicted ones based on limit load approach.     

Strip yield analysis of two collinear unequal cracks in an infinite sheet

Plastic zone sizes and crack tip opening displacements (CTODs) are obtained for two collinear cracks in an infinite sheet subjected to known remote stress. Analysis is conducted by assuming the crack accompanying plastic zones as a fictitious crack and formulating integral equations based upon traction free and no stress singularity conditions. In addition, critical remote stress, plastic zone sizes, and CTODs when the adjacent plastic zones touched are obtained by assuming the coalesced fictitious cracks as a single fictitious crack and formulating integral equations based upon no stress singularity and zero coalesced point displacement conditions. Extensive numerical results are presented.     

Crack retardation equations for the propagation of branched fatigue cracks

The stress intensity factors (SIF) associated with branched fatigue cracks can be considerably smaller than that of a straight crack with the same projected length, causing crack growth retardation or even arrest. This crack branching mechanism can quantitatively explain retardation effects even when plasticity induced crack closure cannot be applied, e.g. in high R-ratio or in some plane strain controlled fatigue crack growth problems. Analytical solutions have been obtained for the SIF of branched cracks, however, numerical methods such as Finite Elements (FE) or Boundary Elements (BE) are the only means to predict the subsequent curved propagation behavior. In this work, a FE program is developed to calculate the path and associated SIF of branched cracks, validated through experiments on 4340 steel ESE(T) specimens. From these results, semi-empirical crack retardation equations are proposed to model the retardation factor along the crack path. The model also considers the possible interaction between crack branching and other retardation mechanisms.     

Modeling of coalescence of dispersed surface cracks. Part 2. Simulation model for multiple fracture

Abstarct A simulation model for multiple fracture has been developed that reproduces random processes of initiation, growth, and coalescence of dispersed surface cracks. The model is based on the method of statistical simulation (Monte Carlo method) and on the fracture regularities determined experimentally. The main factor responsible for fracture is found to be the coalescence of dispersed cracks, especially at the final stage, which accounts for about 30% of the total life. The ultimate state of a structure is defined by the condition according to which the length of the largest of the available damages is bigger than the calculated value of the maximum crack length.Translated from Problemy Prochnosti, No. 1, pp. 108–117, January–February, 2005.     

Reliability analysis for wind turbines with incomplete failure data collected from after the date of initial installation

Reliability has an impact on wind energy project costs and benefits. Both life test data and field failure data can be used for reliability analysis. In wind energy industry, wind farm operators have greater interest in recording wind turbine operating data. However, field failure data may be tainted or incomplete, and therefore it needs a more general mathematical model and algorithms to solve the model. The aim of this paper is to provide a solution to this problem. A three-parameter Weibull failure rate function is discussed for wind turbines and the parameters are estimated by maximum likelihood and least squares. Two populations of German and Danish wind turbines are analyzed. The traditional Weibull failure rate function is also employed for comparison. Analysis shows that the three-parameter Weibull function can obtain more accuracy on reliability growth of wind turbines. This work will be helpful in the understanding of the reliability growth of wind energy systems as wind energy technologies evolving. The proposed three-parameter Weibull function is also applicable to the life test of the components that have been used for a period of time, not only in wind energy but also in other industries.