Linear Elastic Fracture Mechanics Analysis Research Articles

Critical parameters for ductile fracture of surface flaws

A surface flaw in a section of finite thickness is a problem of practical importance. A number of linear elastic fracture mechanics (LEFM) analyses of this problem have been conducted and have provided descriptive parameters for predicting a fracture stress for LEFM conditions. However, these parameters have not been shown to be effective for predicting the fracture stress under ductile conditions, even though a strong demand exists for such capabilities. This paper describes an experimental approach to defining the critical parameters for surface flaws in ductile materials. A test program was conducted using plate specimens of annealed Type 304 stainless steel containing surface flaws of ellipsoidal, triangular, or rectangular shapes. An empirical approach, based on gross strain, is used to develop equations for predicting initiation of crack growth, conditions for the crack to penetrate the 6.35 mm (0.25 in.) wall thickness, and for plastic instability. These equations provide a means to identify the parameters that quantify the severity of the surface flaw in a ductile material.

Influence of cladding on linear elastic RPV-analysis during loss of coolant accident

This report is dealing with the influence of the cladding layer on linear elastic fracture mechanics analyses of reactor pressure vessels subjected to emergency core cooling situations. The American computer code OCA-I was modified in order to be able to solve the stress distribution produced by thermal and mechanical loading across an undisturbed cylinder wall which is composed of two different materials. A brief description of the analytical approach is given. Analyses of two typical loss-of-coolant accidents, the Large Break LOCA and the Small Break LOCA, in which long axial cracks have been assumed to exist prior to the transient were performed. The results are presented in form of comparisons between calculations without considering cladding effects, with thermal cladding effects included only, and with cladding accounted for in thermal as well as in stress analyses.

Boundary integral equation stress analysis of a rotating disc with a corner crack

The analytical and numerical formulation of the boundary integral equation (BIE) method are outlined for the general case in linear elasticity. Using this method, three-dimensional linear elastic fracture mechanics analyses of a rotating disc with a corner crack at its bore are carried out. The cases considered are for a disc with external to internal radius ratio of 8 and with thickness equal to the diameter of the central bore. Two different crack shapes, namely, a quarter-circular crack and a quarter-elliptical crack with ellipse aspect ratio of 0.75, are analysed. For each of these shapes, corner cracks penetrating 50 per cent and 75 per cent of the disc thickness are treated. Stress intensity factor solutions for these cracks are presented for the centrifugal loading condition, as well as when the disc is subjected to a radial tensile stress at its external circumferential periphery.

The Effect of Induction Heating Stress Remedies on Existing Flaws in Pipes

One method for reducing stress corrosion cracking problems called induction Heating for Stress Improvement (IHSI) has been successful in producing compressive residual stresses on the inside surface of welded pipes. During the time that the induction heating coil is turned on, however, the process causes tensile stresses at the inner wall, raising questions about the effect that the induced tensile stress field may have on existing flaws in the pipe. To provide a basis for comparing as-welded stress distributions with the stress distributions occurring during the IHSI process, stress intensity factors were computed for part-through, axisymmetric, circumferential cracks in pipes using linear elastic fracture mechanics analyses. Results for as-welded stress distributions agree with the field experience that most of the crack pipes in Boiling Water Reactor piping systems are smaller diameter pipes in the 4–12-in. (102–305-mm) range. Stress intensity factors in the smaller diameter pipes for the stresses during IHSI were comparable to those for the as-welded stresses. For the 26-in- (660-mm-) dia pipe, the large changes in the stress distributions during the IHSI process suggest the possibility of a net closing or opening of a flaw existing in the pipe prior to the heat treatment.

THE SHORT CRACK PROBLEM

Abstract— The problem associated with short crack growth, defined as situations in which the intensity of the crack tip field is underestimated by linear elastic fracture mechanics analyses, is briefly reviewed. Two cases are identified, cracks growing in plastically strained materials, such as occurs in high strain fatigue studies and at notch roots, and small cracks growing in single grains as occurs close to the fatigue limit in plain specimens. Important mechanical and metallurgical features of short cracks are discussed with particular reference to the upper and lower bound definition of a short crack.

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K 1 c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions. In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K 1 c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.

The characterization of fracture toughness of two X-70 pipeline steels

The fracture toughness of two acicular ferrite, high strength low alloy (HSLA) pipeline steels was investigated utilizing a linear elastic fracture mechanics analysis (KIC testing according to ASTM E399-74) as well as an elastic plastic fracture mechanics analysis (J-Integral and crack opening displacement COD methods). The tests were conducted at a strain rate of 10-4/s, K= 10 Ksi√in/s (11 MPa√m/s) using 0.5 in. (12.7 mm) thick compact tension specimens. A resistance curve test technique developed by Landes & Begley was employed to obtain the JIC fracture toughness, whereas, the British Standard for COD testing was followed for measuring the δc fracture toughness. It was observed that the semi-killed AF-1 steel possesses anisotropic fracture toughness properties whereas, the AF-2 steel which is rare earth treated steel for sulfide shape control exhibits isotropic fracture toughness properties. The temperature dependence of the fracture toughness was determined to assess the usefulness of these steels for arctic applications. An attempt was made to correlate the linear elastic fracture toughness KIC or KQ values with the elastic-plastic fracture toughness, JIC and COD data for both steels tested in three notch orientations. The data shows that JIC and δQ fracture toughness parameters can be used for specifying the fracture toughness of these steels for service temperatures extending down to −130 °C.

Stress intensity factors for semi-elliptical surface cracks in pressurised cylinders using the boundary integral equation method

Three dimensional linear elastic fracture mechanics analyses of the problem of an internally pressurised thick-walled cylinder with a semi-elliptical surface crack are carried out using the Boundary Integral Equation method. The cases treated are for ratios of external to internal cylinder radii of 2 and 3, with maximum crack depths ranging from 20% to 80% of the wall thickness. For a typical crack, the predicted value of stress intensity factor decreases slightly along the crack front moving away from the point of deepest penetration, reaching a minimum before increasing rapidly as the free internal surface of the cylinder is approached. The results presented will be of considerable use in the prediction of residual or safe life of, for example, chemical reactor tubes known to be cracked to a certain depth.

Fracture mechanics issues for irradiated blanket structures

This paper reviews some of the factors that will affect fracture behavior of fusion reactor structures and summarizes some component life predictions based on linear elastic fracture mechanics analysis. The review includes discussion of the environments to which the components will be subjected, the response of materials to these environments, the time dependent nature of the structural response, and the fracture related failure mechanisms. Radiation environments and complex loading conditions in a fusion reactor cause a variety of material phenomena. These phenomena include irradiation swelling and creep, strength changes due to matrix hardening, helium embrittlement, and surface effects such as sputtering and blistering. The interaction of thermal creep, irradiation creep, and swelling results in complex time, temperature, and neutron fluence dependent stress histories in first wall and blanket structures. These effects reduce compressive thermal stresses during the burn portion of a reactor operating cycle and result in residual tensile stress during the non-burn portion of the cycle. The cyclic nature of these stresses, particularly in a tokamak reactor, and the presence of undetected flaws provide a basis for the application of fracture mechanics. Linear elastic fracture mechanics analysis techniques have been applied to predict component life for several conceptual tokamak fusion reactor designs. These analyses show that the structural life may be limited by growth of initial flaws to a coolant leakage. Results indicate that for neutron wall loadings below 2 to 3 Mw/m 2, life is likely to be controlled by stresses during the burn period and, at higher wall loadings, by residual stresses during the non-burn period. Fracture toughness properties tend to be reduced by irradiation. Therefore, brittle fracture will be a potentially critical failure mode. Fatigue crack growth and fracture characteristics of the design will affect the operating mode of a reactor and influence the performance of different types of reactors. Tests are currently planned to develop material crack growth and fracture toughness data [1] for candidate alloys because these properties have been shown to be important.

ELASTIC-PLASTIC FRACTURE MECHANICS FOR INITIATION AND PROPAGATION OF NOTCH FATIGUE CRACKS

Initiation and propagation are considered to be controlled by the extent of total plastic shear deformation φ. Crack initiation and crack propagation occur when φ, exceeds a critical threshold value which can be equated to threshold conditions determined from linear elastic fracture mechanics analyses. When a crack is in a plastically deformed zone φt=φp+φe. where φp is the component of φt due to notch bulk plasticity and φe, is the component of φt due to a linear elastic fracture mechanics (LEFM) analysis of the crack tip plasticity field. When cracks initiate at notch roots φt > φth. As the crack propagates in the notch plastic zone the rate of decrease of vp will be different from the rate of increase of φe and it is possible for φt to decrease to a level below φth thereby creating a non-propagating crack.

Fatigue under complex stress

Fatigue-crack propagation in biaxially stressed plates has been investigated. The normal stress σx, applied on a plane perpendicular to the crack front, affects the rate of propagation of a Stage II crack extending by a Mode I mechanism. This stress, which does not affect singularity conditions in a linear elastic fracture mechanics analysis, has different effects should it be tensile or compressive, cyclic or constant. The changes in crack-growth rate are related to changes in the size of the plastic shear ears at the tip of the crack. Fatigue-crack propagation is related to two parameters in the plane of the plate, the maximum shear stress range and the stress normal to the plane of maximum shear. Both these parameters will affect the crack-opening displacement and hence crack-growth rate.

The growth of fatigue cracks at high temperatures under predominantly elastic loading

The extent of applicability of linear elastic fracture mechanics (LEFM) to high temperature fatigue-crack growth in 1 2 and 1% Cr-Mo-V turbine-casing steels has been established using a range of specimen geometry and thickness. Crack growth rates exceeded those at room temperature and generally increased with declining frequency. The relation for crack growth was: dL/ dN = CΔK 2, where L was cracuength, N cycle number, C a frequency-dependent term and ΔK the stress intensity amplitude. There was little effect of increasing the maximum stress intensity of the cycle (or mean stress level) provided widespread creep deformation was avoided. A limiting crack tip displacement (C.O.D.) for LEFM analysis was established for the cast Cr-Mo-V steels examined. The relative contributions of creep and oxidation to fatigue-crack growth were examined. Oxidation was found to predominate at high frequencies and low amplitudes, whilst creep effects were significant at low (10 −3 Hz) frequencies.

The temperature wave method of determining fracture toughness values due to crack propagation

A method is presented of determining fracture toughness by measurement of the amount of heat emitted at the tip of a propagating crack. Two thermojunctions placed adjacent to the crack were used to monitor the temperature wave produced at fracture. An electromagnetic fluxmeter was used to integrate the thermojunction output with respect to time and was calibrated to give a direct reading in terms of strain energy release rate G. The temperature wave method is independent of initial crack length and fracture surface area and can be readily used for specimens having complex sections. Values obtained by this method compare favourably with toughness values determined by a linear elastic fracture mechanics analysis. Results of static and dynamic three-point bending tests on specimens at different temperatures within the range −40 to 60° C are reported.

The fracture energy of a glass fibre composite

The fracture energy of a glass fibre-polyester composite has been measured by work of fracture (γf) measurements on bending beams, and by linear elastic fracture mechanics analyses (γi) of the bending beams and edge-notched tensile plates. It was found that for the bend specimens γi< γf. The work of fracture, γf, displayed a strain rate dependence, but there was no such dependence of γi. It is postulated that γi is determined by a debonding mechanism while γf is the sum of a debonding mechanism plus a pull-out contribution. The edge-notched tensile plate experiments showed that γi obtained from thick plates was less than that obtained from side-grooved plates, and that in each case there was a dependence of γi on crack size.

Crack initiation in PVC for subsequent linear elastic fracture mechanics analysis

AbstractReproducible starter‐cracks for subsequent linear elastic fracture mechanics analysis have been grown in PVC by fatigue cycling at 80 Hz. The crack growth rate has been related to the fracture surface markings and to the opening mode stress intensity factor (KI) of the fatigue cycle. Termination of the fatigue crack growth when crack growth rate is constant ensures a smooth mirror fracture surface and a sharp crack tip.

Crack stability in linear elastic fracture mechanics

A linear elastic fracture mechanics analysis of the conditions that produce crack instability is presented. If the initial crack extension causes the change in crack-tip resistance to be negative with respect to the change in crack-tip loading, the crack will continue to propagate even though the loading agent remains stationary, and the crack is defined as unstable. The value of crack-tip load when the crack becomes unstable, G c, is not only a function of the plate material and thickness and fracture mode, but also depends on the specimen geometry and size, and on the compliance of the loading system. The crack-tip resistance, G R, on the other hand, is essentially a property of the plate material and thickness and fracture mode if the crack-propagation is time independent. Once G R has been experimentally determined as a function of crack-propagation distance for a particular plate material and thickness and fracture mode, the value of G e can be calculated for the same material and thickness and fracture mode for any plate configuration for which the elastic stress analysis is known.