Cracked Components Research Articles

破壊力学 高温下における欠陥評価のためのＪ積分簡易解析法 （第１報） 高温下における欠陥評価のためのＪ積分簡易解析法の体系化

J-integral is an effective inelastic fracture parameter for the flaw evaluation of cracked components at high temperature. The evaluation of J-integral for an arbitrary crack configuration and an arbitrary loading condition can be generally accomplished by detailed numerical analysis such as finite element analysis, however, it is time-consuming and requires a high degree of expertise for its implementation. Therefore, it is important to develop simplified J-integral estimation techniques from the viewpoint of industrial requirements. In this study, a simplified J-integral evaluation method is proposed to estimate two types of J-integral parameters. One is the fatigue J-integral range to describe fatigue crack propagation behavior, and the other is the creep J-integral to describe creep crack propagation behavior. This paper presents the systematization of the simplified J-integral evaluation method incorporated with the reference stress method and the concept of elastic follow-up, and proposes a comprehensive evaluation procedure. The verification of the proposed method is presented in Part II of this paper.

Three-dimensional boundary element analysis of fatigue crack growth in linear and non-linear fracture problems

This paper presents general boundary element procedures for the elastic and elastoplastic numerical modelling of three-dimensional fatigue crack growth. The elastic and elastoplastic boundary element formulations are briefly introduced, followed by the description of the crack propagation strategies. In both cases, fatigue crack growth is numerically modelled through an incremental crack extension procedure. For each crack extension the dual boundary element method is used to perform a single region analysis of the cracked component and the corresponding fracture parameter ( K or J depending on if the analysis is elastic or elastoplastic) is computed along the crack front. New positions of the crack front are determined using the Paris law. The capabilities of the proposed procedures are demonstrated by comparison of numerical predictions with experimental results.

Mode I stress intensity factors and weight functions for short plates under different boundary conditions

Stress intensity factors and weight functions are available in literature predominantly for cracked components under stress boundary conditions. In order to provide weight function solutions including displacement boundary conditions, rectangular plates with different length-to-width ratios are studied using the boundary collocation method. The results are reported in the form of figures and tables. The influence of Poisson’s ratio is discussed in detail. It can be concluded from the numerical data and theoretical considerations that the mode I stress intensity factors and weight functions are independent of Poisson’s ratio ν for mixed boundary conditions at the plate ends, but depend on ν in case of pure displacement conditions.

Stress intensity factors and T-stress inedge-cracked rectangular plates under mixed boundary conditions

Stress intensity factors and T-stress solutions are available in literature predominantly for cracked components under stress boundary conditions. In order to provide solutions for displacement boundary conditions, rectangular plates with various length-to-width ratios and different types of cracks (single and double-edge cracks) are studied by application of the boundary collocation method. the results are reported in the form of figures and tables.

Prediction of fatigue thresholds of cracked components under mean stresses

The propagation behavior of fatigue cracks was investigated under various stress ratios using structural carbon steel specimens containing small pre-cracks. The threshold condition of crack extension from precracks was given by a constant value of the threshold effective stress intensity rang for long cracks, A ^^^. As a crack grew, the crack closure developed and the effective stress intensity range decreased. When the effective stress intensity range dropped below AK^oc the crack was arrested. The cyclic resistance-curve-method was used'to predict the fatigue limits of the pre-cracked components. The predicted values of the fatigue limit for crack extension, the fatigue limit for fracture, and the length of non-propagating cracks agreed very well with the experimental results.

Short circumferential through-wall cracked pipes subjected to stretch-bending load

The methods for assessment of elastic–plastic fracture behaviour of cracked components include the net section plastic collapse concept, the J-integral approach, and the two-parameter R-6 failure assessment diagram, Revision 3. These failure assessment methods are usually used to obtain fracture behaviour prediction with a reasonable degree of accuracy without carrying out complicated full-length numerical fracture analysis. In the current work, fracture experiments on stainless steel pipes with short circumferential through-wall cracks under stretch-bending load were conducted. Stretch-bending load refers to the loading situation where axial load is generated that is proportional or related to the applied bending load. The J-integral values derived from the experimental load-point load–displacement data under stretch-bending and pure bending conditions are compared to investigate the effect of axial load on the J–resistance curves. The results show clear dependence of crack resistance force on axial load for short circumferential cracks. Crack resistance force decreased noticeably for increased stretch-bending loading compared to pure bending loading.

Fracture analyses of surface-cracked pipes and elbows using the line-spring/shell model

The line-spring/shell model proposed by Rice and Levy (1972) and further modified by Parks and co-workers (1981, 1982, 1995) provides an attractive and inexpensive alternative to analyzing surface-cracked structures. This model idealizes the complex three-dimensional surface crack problem in a plate- or shell-like structure as a more tractable two-dimensional problem. Though used in some previous studies, this model has largely been ignored in the study of surface-cracked nuclear piping components. While it is true that the line-spring method has some restrictions, it can provide reasonably accurate predictions of important fracture parameters of cracked components within the domain of its applicability. Through some detailed studies of surface-cracked pipes and elbows, the predictive nature of the line-spring model is demonstrated by comparing its predictions with that of a three-dimensional finite element model as well as with experimental measurements. Excellent comparisons between the predictions of the line-spring/shell and three-dimensional finite element models are shown not only using the three-dimensional finite element calculations performed by the author, but also using the three-dimensional calculations performed by two other independent investigators. It is hoped that the results shown in this paper invalidate the criticisms and reestablish the usefulness and reasonable accuracy of the line-spring mode, within its domain of applicability, in the analyses of surface-cracked structures.

Supercritical Water Cracking and Washing of Used Polymer.

A rubber polymer (EPDM, ethylene-propylene-diene-terpolymer) and its vulcanized rubber were cracked to paraffin oil (PO) in NaOH-containing supercrtitical water (SCW) at 420°C and 30 MPa. PO recovered as a hexane-soluble cracking component could be recycled as the rubber softener because sulfurs added to the rubber for the elasticity were washed out in SCW. The SCW polymer cracking is not oxidative but reductive. The 13C-NMR analysis of PO obtained by SCW D2O cracking demonstrates that the terminal methyl carbons are deuterated as a clear indication of hydrogen supply by SCW.

Dynamic material properties and their application to components

A methodology was developed for safety analyses of dynamically loaded cracked power plant components. For that purpose fracture tests were performed by means of compact tension specimens made from different ferritic fine grained structural steels and an austenitic steel at different loading rates. Experimental and numerical analyses of the influence of increasing loading rate on the near tip displacement field are described. Thereby, strain rate in the process zone of a crack can be estimated. It was possible to determine the state of stress and local displacement and strain rates from numerical analyses of experiments with components and large scale specimens. Time derivatives of stress intensity factor K resp. J-integral can be used as sufficient parameters for characterizing the loading rate of specimens and components.

Three-dimensional BEM analysis for fatigue crack growth in welded components

In this paper a general procedure for the analysis of three-dimensional multiple fatigue crack growth is presented. The crack propagation is simulated using an incremental crack extension analysis based on the strain energy density criterion and the Paris law. For each crack extension the dual boundary element method is used to perform a single region analysis of the cracked component. Stress intensity factors are computed along the crack fronts using a displacement based method. Crack extensions are automatically modelled with the introduction of new boundary elements along the crack fronts and a localized rediscretization in the area where the cracks intersect the free surfaces. The capability of the procedure is demonstrated by solving a number of multiple edge-crack examples.

Local Approach : Numerical Simulations of Creep and Creep-Fatigue Crack Initiation and Crack Growth in 316L SPH Austenitic Stainless Steel

This study deals with the evaluation of local approach to assess the mechanical integrity of cracked components submitted to cyclic and steady load at elevated temperature. In this approach, a fracture criterion based on calculated intergranular damage ahead of the crack tip is introduce to simulate both crack initiation and crack propagation in 316 L type austenitic stainless steel. This numerical method, based on finite element computations is firstly described. Then numerical results are compared with sets of experimental data for two specimen geometries during load controlled tests. A damage criterion in good agreement with previous studies leads to promising load-displacement response, crack initiation and crack growth curves.

Elastic-plastic fracture mechanics assessment of low constraint aluminium test specimens

Recent studies have shown that the near crack-tip stress field at a given J value is dependent on geometry. This dependence has been linked to the degree of constraint in the geometry, with low constraint geometries losing J dominance at very low deformation levels. New approaches centred on the use of a two-parameter description (e.g. J-T and J-Q) of the crack-tip stress-strain state have emerged. However, there is a serious lack of experimental and numerical results for low constraint geometries to quantify the T-stress and Q-value in the literature. This paper describes details of an experimental and numerical program carried out on low and high constraint geometries (CCT and TPB) fabricated from an aluminium alloy. The results show that the experimental and numerical fracture toughness values (J c ) agree within ±10 percent. The T-stress and Q-value two-parameter methodologies are successful at indexing the fracture toughness, ordering the data into a systematic trend of decreasing fracture toughness with increasing T or Q, albeit with some scatter. This allows the use of practical two-parameter failure criteria, in the form of J-T and J-Q loci, to predict the behaviour of cracked components, without the conservatism associated with the use of high constraint test geometries.

Predictions of pour, cloud and cold filter plugging point for future diesel fuels with application to diesel blending models

The increasing demand for diesel fuel has resulted in an increase in the number of blend streams including cracked components from secondary processes using mostly heavy crudes of different origins. Owing to such compositional changes, the existing property blending equations may no longer be sufficiently accurate. Therefore, the development of new correlations was required. In this work, three low-temperature property correlations, viz. pour, cloud and cold filter plugging points, were developed for precise predictions. An improvement in the accuracy of predictions of up to 30% was observed with the new pour point equations compared with the earlier method. Further, the one-parameter cloud point equation, applicable to any refinery streams of diesel cut, with average error of 1.3°C in 104 data points, was developed and compared with the equation of Tsang et al., containing more parameters. Computer software was also developed for periodic updating of these correlations. The effects of different pour point correlations with other property equations on the formulations of a diesel fuel was also demonstrated through blending models.

A method for establishing geometry correction factors by ratio of finite element stresses

When designing stressed-skin structures, one of the prime objectives is to determine accurate stress intensity factors for the specific components in question, which, in turn, depends on the production of accurate geometry correction factors. For an irregularly shaped component, this usually means applying a specific analytical theorem or using a devoted facility such as may be found in relatively sophisticated finite element packages. An alternative technique, however, is proposed whereby stress intensity/geometry correction factors can be readily evaluated using the most rudimentary of finite element programs. The method is potentially very powerful, since it uses the magnitude of the stress at the crack tip which can be obtained using a surprisingly coarse finite element model of the cracked component. It has been found to produce very accurate results when compared with alternative, more widely established methods but is, nevertheless, very easy to apply. In addition, consideration of the relevant theory indicates that although the method is only applied here to the relatively simple case of a thin centre-cracked sheet, it should be sufficiently versatile to be generally applicable to a wide variety of different structural shapes. This paper describes the technique and compares results using different mesh densities with results obtained by other methods.

Fracture analysis of cracked rubber components in two and three dimensions

This paper presents a non-linear fracture analysis of cracked rubber components. The fracture parameter, tearing energy for rubber materials is computed for two- and three-dimensional bodies using the virtual crack extension method. The crack propagation direction is found by a maximum tearing energy fracture criterion. To illustrate the finite element procedures developed, three design applications were studied. The results obtained are compared to those available in the literature. The procedures developed predict the crack propagation direction in cracked rubber solids.

Creep and creep-fatigue cracking behaviour of two structural steels

The present study deals with crack initiation and crack growth, not only under creep and creep-fatigue conditions but also under more complex thermomechanical cyclic loadings, in both 316L and 1Cr-1Mo-0.25V steel. In these creep ductile materials, most studies have focused on the creep crack growth rates, d a /d t and load-geometry parameter C∗ correlations. In this paper, the creep crack initiation time is defined as the time T i necessary for a defect to grow by a small critical distance X c ( X c ≈ 50 μ m for example). This initiation stage may represent a large part of the rupture life of a cracked component. The importance of such studies is discussed in the first part. In the second part, an attempt is made to present a simplified method based on the fracture mechanics of creeping solids to define the relevant load-geometry parameters for crack initiation and crack growth under creep-fatigue loadings. In particular, it is shown that d a /d N - ΔK correlations apply only when the hold time t h is smaller than the transition time t tr between small-scale and large-scale viscoplasticity. Conversely, for long hold times, it is suggested that the T i -C∗ correlation be used to predict the fatigue.

An assessment of a model method for predicting the fracture of cracked components

Three-point-bend (3PB) specimens with real cracks and very sharp notches have been manufactured from Araldite CT200 with HT907 hardener. The plane strain fracture toughness, KIC, has been obtained from cracked specimen tests and the apparent plane strain fracture toughness, KAppIC, has been obtained for various very sharp notched widths. A systematic variation of apparent fracture toughness with notch width has been observed. Burst tests have also been performed on cylinders with similar, very sharp, axially aligned, external, semi-circular notches. It has been shown that the burst pressure for the cylinders, with different depths of crack, can be predicted from the corresponding 3PB apparent fracture toughness data. The notches in the cylinders and 3PB specimens must be very sharp, and manufactured in a similar way, for the predictions to be accurate. Therefore, by loading model components containing very sharp crack-like flaws to obtain the failure loads, the failure loads of similar actual components having a real crack and behaving in a brittle manner can be predicted.

Fracture mechanics evaluation of cracked components with consideration of multiaxiality of stress state

The fracture-mechanics evaluation of cracked components is an essential part of safety analyses. This evaluation is usually based on one-parametric evaluation procedures without taking into account the multiaxiality of the stress state. Considering the multiaxiality of the stress state across the flawed component cross-section, it is possible to recognize and extend the limits of application of fracture mechanics, which among others, are given by the limited transferability of fracture-mechanics material laws. Within the scope of the research project “Phenomenological Vessel Burst Tests-Phase IV”, T-branches and elbows with dimensions like the primary coolant lines of PWR plants were investigated. In addition to the experimental investigations, extensive numerical calculations were performed by means of the finite element method (FEM). To determine the stress and the gradient of multiaxiality across the ligament of the component, 3-D finite-element analyses were carried out concerning elastic-plastic material behaviour. The evaluation with regard to crack initiation has been proven by experimental results as well as the qualitative assessment of the fracture behaviour on the basis of the multiaxiality analyses.

Using a stress ratio method and F. E. analysis for establishing geometry correction factors in fracture mechanics

When designing stressed-skin structures, one of the prime objectives is to determine accurate stress intensity factors for the specific components in question, which, in turn, depends on the production of accurate geometry correction factors. For an irregularly shaped component, this usually means applying a specific analytical theorem or using a devoted facility such as may be found in relatively sophisticated finite element packages. An alternative technique, however, is proposed whereby stress intensity/geometry correction factors can be readily evaluated using the most rudimentary of finite element programs. The method is potentially very powerful, since it uses the magnitude of the stress at the crack tip which can be obtained using a surprisingly coarse finite element model of the cracked component. It has been found to produce very accurate results when compared with alternative, more widely established method buts is, nevertheless, very easy to apply. In addition, consideration of the relevant theory indicates that although the method is only applied here to the relatively simple case of a thin centre-cracked sheet, it should be sufficiently versatile to be generally applicable to a wide variety of different structural shapes. This paper describes the technique and compares results using different mesh densities with results obtained by other methods.

Experimental and analytical fracture assessment of 165-mm diameter AISI 304 seamless piping containing a circumferential through-wall crack

Field engineers often face the need to assess the residual strength and remnant life of cracked components within a limited time. A number of engineering methods for the assessment of elastic-plastic fracture behaviour of cracked components proposed in the past decade may be used for this purpose. These include the net section plastic collapse method, the J- integral estimation method and the R6 (Revision 3) failure assessment method. The primary aim of these methods is to obtain fracture behaviour prediction with a reasonable degree of accuracy without resorting to a complicated full-length numerical elastic-plastic fracture mechanics analysis. Systematic comparison of these different methods for assessing the relative degrees of accuracy and conservatism based on experimental results are still very limited. In the current work, some fracture experiments on 165-mm diameter piping with through-wall cracks were conducted. Based on these data, the predictive capabilities of the three engineering assessment methods are compared. The relative merits and limitations of each method are discussed in the light of these evaluations. The results suggest that the J- integral method has the best overall accuracy but requires the most detailed baseline material properties data. The R6 Revision 3 method offers a number of choices which vary in complexity and amount of data needed; this method tends to give relatively more conservative results than the J- estimation method. The net section method is the simplest among the three and gives reasonable predictions of maximum load in the current case.