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Showing papers by "Westinghouse Electric published in 1976"


Book ChapterDOI
TL;DR: In this paper, an attempt is made to apply the J-integral concept as an elastic-plastic criterion for fatigue crack growth, and the results show correlation with Jintegral values estimated from load versus deflection hysteresis loops.
Abstract: An attempt is made to apply the J-integral concept as an elastic-plastic criterion for fatigue crack growth. Compact tension fracture specimens of A533B steel are subjected to gross cyclic plastic deformations, and fatigue crack growth rates up to 0.01 in./cycle are obtained. The results show correlation with J-integral values estimated from load versus deflection hysteresis loops. Also, agreement is obtained with the extrapolation of linear elastic fatigue crack growth rate data.

395 citations


Book ChapterDOI
TL;DR: In this article, a fracture mechanics approach was used to study high-temperature creep crack propagation, and crack growth rates were correlated with the C*-parameter which is an energy rate line integral.
Abstract: A fracture mechanics approach was used to study high-temperature creep crack propagation. Crack growth rates were correlated with the C*-parameter which is an energy rate line integral. For materials conforming to a nonlinear stress and strain rate relationship in the steady-state creep range, specifically, those which can be properly idealized as purely viscous (negligible elastic and transient creep effects), C* characterizes the crack tip stress and strain rate fields. Crack growth rate tests were conducted in the creep range on a discaloy superalloy at 1200°F (920 K). Two specimen geometries were tested, a center cracked panel and a compact geometry, to establish the geometry independence of this approach. The results showed that crack growth rate correlated with the C*-integral, while other parameters (K and nominal stress) failed to adequately characterize crack growth rate.

355 citations


Journal ArticleDOI
TL;DR: In this paper, the total spectral absorptivities of plasmas of sulfur hexafluoride for wavelengths of 100 to 15,500 A were derived for both line and continuum radiation.
Abstract: Calculations are made of the total spectral absorptivities of plasmas of sulfur hexafluoride for wavelengths of 100 to 15,500 A. Both line and continuum radiation are considered. For the contributions from line radiation, we have calculated the strengths, widths and shifts of both neutral, singly and doubly ionized atoms of S and F , except that we used experimental line strengths where they are available. The theory used was that of Griem, which assumes LS coupling. Curves are given for the emission coefficient of radiation appropriate to the arc center for isothermal cylindrical plasmas of various radii for pressures of 1 and 10 atm and temperatures from 5000 to 35,000°K. It is found that at 1 atm line radiation can be an order of magnitude higher than continuum radiation and radiation >2000 A is less than 10% of the total radiation for temperatures greater than 15,000°K. Predictions are given of volt-ampere characteristics and central temperatures for arcs of various radii in SF 6 at pressures at 1 and 10 atm.

193 citations


Patent
23 Mar 1976
TL;DR: In this article, a bistatic radar system for detecting the presence of a slowly moving target by the use of an arrangement which provides a reduction in the frequency spread of the reflected clutter energy.
Abstract: A bistatic radar system for detecting the presence of a slowly moving target by the use of an arrangement which provides a reduction in the frequency spread of the reflected clutter energy. A radar transmitter and a radar receiver are located aboard separate aircraft which fly with a predetermined speed and direction about the target area. The speed and direction of the two aircraft are such that the angular velocities of the aircraft about the target area are substantially equal and opposite. This arrangement reduces the spread of the reflected clutter energy caused by motion of the radar transmitter and receiver relative to the target area. The radar return signals are filtered and processed to determine when a signal is present which has been shifted in frequency due to the motion of the moving target. In one embodiment, the two aircraft fly directly toward each other at the same speed. In another embodiment, the two aircraft fly directly away from each other at the same speed. Apparatus is included which determines the position of the moving target both with respect to the two aircraft and with respect to the ground.

191 citations


Book
01 Jan 1976
TL;DR: The most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships can be found in this paper, where the derivation of filtering functions, Fourier, Laplace, Hilbert and z transforms, lowpass responses, the transformation of lowpass into other filter types, the all-pass function, the effect of losses on theoretical responses, matched filtering, methods of time-domain synthesis, and digital filtering are discussed.
Abstract: Long regarded as a classic of filter theory and design, this book stands as the most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships. Analysis and theory are supplemented by detailed design curves, fully explained examples and problem and answer sections. Discussed are the derivation of filtering functions, Fourier, Laplace, Hilbert and z transforms, lowpass responses, the transformation of lowpass into other filter types, the all-pass function, the effect of losses on theoretical responses, matched filtering, methods of time-domain synthesis, and digital filtering. This book is invaluable for engineers other than those who are filter design specialists who need to know about the possibilities and limits of the filtering process in order to use filters competently and confidently in their system designs.

183 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the passive oxidation behavior of silicon nitride hot-pressed with 1 wt% MgO in dry oxygen in the temperature range 1000 to 1400 C.
Abstract: The “passive” oxidation behaviour of silicon nitride hot-pressed with 1 wt% MgO has been studied in dry oxygen in the temperature range 1000 to 1400‡ C. The oxidation follows the classical parabolic behaviour with an apparent activation energy of 375 kJ mol−1. Except for minor amounts of a glass and cristobalite, the oxide film consists predominantly of MgSiO3 in which various impurity elements, e.g. Ca, Fe, Al, etc., concentrate. The outward diffusion of Mg2+ and impurity cations from the grainboundary glass phase through the oxide film appears to be oxidation rate controlling.

176 citations


Proceedings ArticleDOI
08 Jun 1976
TL;DR: In this paper, a review of possible methods of VAr generation and control by static thyristor circuits and new approaches in which power frequency changers (cycloconverters) are employed are described.
Abstract: Generally, static VAr generators function as variable reactances (capacitive or inductive impedances) or controllable ac current and voltage sources. This paper reviews possible methods of VAr generation and control by static thyristor circuits and describes new approaches in which power frequency changers (cycloconverters) are employed. Oscillographic recordings illustrate the operation and performance of practical systems, including a 35 MVAR arc furnace compensator.

164 citations


Journal ArticleDOI
TL;DR: In this article, the governing equation for the capillarity-induced shape changes of a surface of revolution by surface diffusion is presented, and a numerical solution to this equation is used to analyse finite cylinders with hemispherical ends.
Abstract: The governing equation for the capillarity-induced shape changes of a surface of revolution by surface diffusion, $$\frac{{\partial n}}{{\partial t}} = \frac{B}{y}\frac{\partial }{{\partial s}}\left( {y\frac{{\partial K}}{{\partial s}}} \right)$$ where∂n/∂t is the normal velocity of the surface,y is measured normal to the axis of revolution,s is arc length,K is the total surface curvature andB is a kinetic parameter which is constant for a given temperature and material, is presented. A numerical solution to this equation is used to analyse finite cylinders with hemispherical ends. A critical length-to-diameter ratio (L/D) of 7.2 is predicted, below which only one spheroidal particle results and above which two or more are formed, and is shown to have experimental support in several systems.

152 citations


Journal ArticleDOI
TL;DR: In this article, the authors showed that the oxidation of silicon carbide, hot-pressed with ∼ 4 wt % Al2O3, in 1 atm dry oxygen follows classical parabolic behaviour with an activation energy of 481 kJ mol−1 in the temperature range 1200 to 1400° C.
Abstract: The oxidation of silicon carbide, hot-pressed with ∼ 4 wt % Al2O3, in 1 atm dry oxygen follows classical parabolic behaviour with an activation energy of 481 kJ mol−1 in the temperature range 1200 to 1400° C. The oxide film consists predominantly of cristobalite and a glassy phase in which additive (Al) and various impurity elements (Fe, Na, K, etc) concentrate. The desorption of CO(g) from the SiC/SiO2 interface appears to be oxidation rate controlling.

147 citations


Journal ArticleDOI
TL;DR: Crack healing and strengthening of thermally shocked alumina are related to pore evolution in the microstructure during annealing grain growth is not necessary for either an increase or a decrease in strength following heat treatment as mentioned in this paper.
Abstract: Crack healing and strengthening of thermally shocked alumina are related to pore evolution in the microstructure during annealing Grain growth is not necessary for either an increase or a decrease in strength following heat treatment

135 citations


Journal ArticleDOI
TL;DR: A thermodynamic analysis of the stability of Si3N4 and SiC is presented in this article, which can be employed to assess their suitability for use at high temperatures in various environments.

Journal ArticleDOI
S. Y. Wu1
TL;DR: In this paper, the memory retention and switching behavior of a metal-ferroelectric-semiconductor transistor using bismuth titanate have been investigated, and it was shown that the device has a fast switching speed and a switching threshold at a field of about 15 to 20 kV/cm.
Abstract: The memory retention and switching behavior of a metal-ferroelectric-semiconductor transistor using bismuth titanate have been investigated. The study made on p-channel transistors shows that the device has a fast switching speed and a switching threshold at a field of about 15 to 20 kV/cm. It also has a good memory retentivity. The low current OFF state is more stable than the high current ON state. The current in the ON state was found to decay logarithmically with time at long elapsed times. This is attributed to a slow trapping of holes at the ferroelectric-semiconductor interface states.

Journal ArticleDOI
TL;DR: The effect of neutron irradiation on the tensile properties of TZM and tungsten has been experimentally determined in this paper, and the results of these tests were correlated with a rate-temperature parameter (T ln A ϵ ) to provide a concise description of material behavior over the range of deformation conditions.

Book ChapterDOI
TL;DR: In this article, the fracture mechanics approach to fatigue crack growth may be extended by the use of the J-integral concept, so that large scale plasticity effects are included.
Abstract: Fatigue crack growth rate data are obtained for center cracked specimens of A533B steel subjected to elastic-plastic cyclic loading. Cyclic J-integral values estimated from load versus deflection hysteresis loops are correlated with these growth rate data. The relationship obtained is in agreement with previous elastic-plastic data on compact specimens and also with linear elastic data on large size compact specimens. These experimental data suggest that the fracture mechanics approach to fatigue crack growth may be extended by the use of the J-integral concept, so that large scale plasticity effects are included.

Journal ArticleDOI
TL;DR: An internal friction technique has been used to measure the viscosity of the grain-boundary amorphous phase in commercial hot-pressed silicon nitride as discussed by the authors, with an activation energy of 163 kcal mol−1.
Abstract: An internal friction technique has been used to measure the viscosity of the grain-boundary amorphous phase in commercial hot-pressed silicon nitride. The viscosity in the region of the glass transition (850 to 900° C) was approximately 5×1015 P per unit thickness (cm) of the grain boundary, with an apparant activation energy of 163 kcal mol−1.

Journal ArticleDOI
TL;DR: In this paper, the authors determined dimensionless stress-intensity factors for single-edge-cracks solid and hollow round bars loaded in bending, and calculated the factors from experimental compliance (inverse slope of load-displacement curve) measurements.
Abstract: Dimensionless stress-intensity factors were determined for single-edge-crack solid and hollow round bars loaded in bending These factors were calculated from experimental compliance (inverse slope of load-displacement curve) measurements made on round bars loaded in three-point bending The compliance specimens had span to diameter ratios of 667 and 333, and measurements were made over a range of dimensionless crack lengths from 0002 to 070 The tests were made using 3-in (76-mm) and 6-in (152-mm) solid and hollow round bars notched on one side; the hollow bars had an inner to outer diameter ratio of 033 A comparison was made with data in the literature for rectangular bars; for ana/D of 00001, the dimensionless stress-intensity factor for a solid round bar is 13 vs 20 for a rectangular bar

Patent
01 Oct 1976
TL;DR: In this article, the authors proposed a method for storing a pulse width modulated wave of predetermined pattern for any discrete value of successive desired output voltage levels, where the notches characterizing a particular pattern are stored in the form of a digital representation one level along several possible levels defining subdivisions of a given time interval which is itself a submultiple of the total duration of the stored quandrant.
Abstract: Pulse width modulation is produced by digital means. Pulse width modulated waves are stored digitally in a memory and retrieved under control of a voltage signal in order to generate a pulse width modulated wave of predetermined pattern for any discrete value of successive desired output voltage levels. Optimal waveforms are selected and stored which extend only for one quadrant but an alteration of the addressing code based on symmetry yields the mirror image of the stored quadrant while sign modification provides symmetry about the abscissa axis. Also, only a single phase is stored and phase shifting by code alteration of the coded information provides the other phases after retrieval. The notches characterizing a particular pattern are stored in the form of a digital representation one level along several possible levels defining subdivisions of a given time interval which is itself a submultiple of the total duration of the stored quandrant. A comparator responsive to a series of ramp signals detects in real time the stored levels thereby to effect switching from one state to the other and define one edge of a notch. The notches may extend over several of the ramp signals. The invention provides, with substantially the same hardware, for a fixed pattern mode of operation in the normal frequency range, and for a free running triangulation mode for the lower frequency range. The invention applies to the field of induction motor drives with adjustable speed.

Patent
16 Jan 1976
TL;DR: In this article, the grounding conductors of the power system and the real earth ground return path transmit the carrier communication signals between a substation communication terminal and remote communication terminals at the premises of utility company customers.
Abstract: Carrier current signals are impressed to and detected from grounding conductors connected to the power system and to real earth ground. The communication links provided by the grounded neutral conductors of the power system and by the real earth ground return path transmit the carrier communication signals between a substation communication terminal and remote communication terminals at the premises of utility company customers. The communication signals are coupled to the ground conductors by transformer-type couplers in which the grounding conductor constitutes one winding of the transformer.

Patent
18 Feb 1976
TL;DR: In this paper, a reversible heat pump with three refrigerant coils is presented, one of which is in an air duct for the space to be served, another one is in heat exchange relation with outdoor air, and a third one is adapted to exchange heat with a heat exchange fluid which is circulated from a heat storage location.
Abstract: A heating and cooling system is provided which includes a reversible heat pump with three refrigerant coils, one of which is in an air duct for the space to be served, another of which is in heat exchange relation with outdoor air, and a third of which is adapted to exchange heat with a heat exchange fluid which is circulated from a heat storage location, the system including valve means in the refrigerant lines for connecting any of the three coils to operate as either an evaporator or a condenser and for connecting either one of the other two coils to operate as a condenser or evaporator, respectively, so that heat can be exchanged in any combination between air in the duct serving the space to be heated, outside air, and the storage fluid. The system also preferably includes a solar collector and a second fluid storage tank, and circulating means and fluid valve means as well as a fluid-to-air heat exchanger in the duct so that heat from solar insulation may be used to heat directly or placed in storage, or heat may be provided for the space directly from the storage. Heat from storage may also be used with the heat pump operating. Various other modes of heat pump operation are also available in a cooling operation. The system also includes the provision of a diverting valve arrangement for the three coil heat pump which precludes, through a physical blocking arrangement, the possibility of short circuiting the discharge from the refrigerant compressor to the suction side of the compressor.

Patent
26 Aug 1976
TL;DR: In this paper, an arrangement for closing selective areas of the tip portion of a hollow turbine blade having internal serpentine coolant passages is provided by radially extended wall portions at the tip of the blade along at least two sides of the outer ends of each two adjacent internal passages.
Abstract: An arrangement for closing selective areas of the tip portion of a hollow turbine blade having internal serpentine coolant passages is provided by radially extended wall portions at the tip of the blade along at least two sides of the outer ends of each two adjacent internal passages to be closed at the tip, retaining grooves provided in the facing surfaces of the extended wall portions, cover means overlie the outer ends of the selected adjacent passages and have opposite lateral edges received in the retaining grooves, and bond means secure the cover means along the lateral edges to the wall portions. The cover plate means preferably takes the form of two or more separable plates which can be independently inserted into the retaining grooves from an area on the tip portion of the blade which does not have the radially extended walls with retaining grooves therein.

Journal ArticleDOI
TL;DR: In this paper, the effect of impurities on the high temperature mechanical properties of hot-pressed silicon nitride has been determined, and the impurity additions had no effect on the room-temperature mechanical properties.
Abstract: The effect of impurities on the high temperature mechanical properties of hot-pressed silicon nitride has been determined. Selected impurity additions were made to both relatively pure α-phase and Β-phase silicon nitride starting powders. These powders were hot-pressed to full density using 5 wt % MgO as the pressive additive. The silicon nitride hot-pressed from the α-phase powder exhibited higher strength at both 25 and 1400‡ C than that fabricated from the Β-phase powder. The impurity additions had no effect on the room temperature mechanical properties. The CaO additions had the most significant effect on the high temperature mechanical properties. In both the material hot-pressed from the α-phase and Β-phase powders, increasing CaO additions severely reduced the high temperature strength and increased the amount of non-elastic deformation observed prior to fracture. Although alkali additions (Na2CO3, Li2CO3, K2CO3) also tended to have the same effects as the CaO, the high volatility of these compounds resulted in a much reduced concentration in the hot-pressed material, thus minimizing somewhat their tendency to enhance the high temperature strength degradation. The Fe2O3 and Al2O3 had no apparent effect on the high temperature mechanical properties.

Patent
10 Mar 1976
TL;DR: In this article, a self-calibrating microwave transponder incorporating an amplifier, modulator, instantaneous frequency discriminator, memory and voltage controlled oscillator is described which may generate an RF signal in response to the carrier frequency of received low duty cycle pulse RF signals.
Abstract: A self-calibrating microwave transponder incorporating an amplifier, modulator, instantaneous frequency discriminator, memory and voltage controlled oscillator is described which may generate an RF signal in response to the carrier frequency of received low duty cycle pulse RF signals. The instantaneous frequency discriminator is used to provide an address signal from the pulse RF signals which is used to access a memory that contains the correct tuning data for the voltage controlled oscillator to generate an RF signal.

Journal ArticleDOI
TL;DR: In this paper, the switching properties of (010) epitaxial Bi4Ti3O12 films grown on (110) MgAl2O4 substrates have been investigated.
Abstract: Electro-optic switching properties of (010) epitaxial Bi4Ti3O12 films grown on (110) MgAl2O4 substrates have been investigated. The measurements were carried out on large-area films in situ on the spinel substrate using an inter-digitated electrode array. A contrast ratio higher than 7:1 was obtained. Switching times of less than 5 μsec were measured at fields >60 kV/cm. Due to substrate clamping the field needed for switching the epitaxial film was about seven times higher than that for bulk single crystal at a same switching speed. The films exhibit an apparent switching threshold and grey scale capability. Finally, an experimental X-Y matrix-addressed display has been designed and evaluated.

Patent
17 Feb 1976
TL;DR: In this article, a system for controlling the output power of a transmitter which communicates with a remotely positioned receiving station through a "linear" transponder such that the power level of the input signal to the Transponder is substantially constant is disclosed.
Abstract: A system for controlling the output power of a transmitter which communicates with a remotely positioned receiving station through a "linear" transponder such that the power level of the input signal to the transponder is substantially constant is disclosed. The output signal of the transmitter and the input signal to the transponder includes two carriers having predetermined relative power levels with respect to each other. Typically, one carrier will be 10 dB below the other. Since all linear transponders are slightly non-linear, intermodulation distortion products are generated by the transponder. The intermodulation products and the two carriers are retransmitted to the receiving station by the transponder. The power level of the intermodulation distortion products relative to the low power carrier is measured at the receiving station. From the power level of the intermodulation distortion products and the intermodulation distortion characteristics of the transponder, the power level of the input signal arriving at the transponder is determined and a signal generated to control the power output of the transmitter so that the input signal arriving at the transponder has the desired power level. The carrier having the highest power level is modulated with the data to be transmitted using any convenient modulation technique. The low power carrier is not normally modulated. Its only purpose is to generate the intermodulation products which are used to determine the power level of the input signal to the transponder.

Patent
16 Nov 1976
TL;DR: In this paper, an electrodynamic sensor unit and a drive unit are attached to a member subject to vibration, and the sensor unit provides a signal proportional to the vibration velocity, and this signal is utilized to govern the operation of the drive unit, which acts to reduce the vibration amplitude.
Abstract: An electrodynamic sensor unit and a drive unit are attached to a member subject to vibration. The sensor unit provides a signal proportional to the vibration velocity, and this signal is utilized to govern the operation of the drive unit, which acts to reduce the vibration amplitude.

Journal ArticleDOI
TL;DR: In this paper, the physical processes of photoionization in CO 2, N 2, He gas mixtures containing known concentrations of ionizable impurity were studied in two ways: spectroscopic emission and absorption measurements, and by direct collection of photosensitive electrons.
Abstract: Volumetric photoionization in CO 2 -laser gas mixtures by UV emission from bare sparks was studied in two ways: by spectroscopic emission and absorption measurements, and by direct collection of photoionized electrons. The physical processes were understood sufficiently to permit prediction of initial electron distributions in arbitrary geometries of CO 2 , N 2 , He gas mixtures containing known concentrations of ionizable impurity.

Patent
13 Apr 1976
TL;DR: In this article, a synchronous dynamoelectric machine, such as a turbine generator, which is mechanically coupled to a gas turbine prime mover, is started synchronously to bring the gas turbine up to a speed which exceeds its stall speed under load.
Abstract: Method and apparatus for accelerating a large inertia load from rest to a predetermined speed of rotation by means of a synchronous dynamoelectric machine. A synchronous dynamoelectric machine, such as a turbine generator, which is mechanically coupled to a gas turbine prime mover, is started synchronously to bring the gas turbine up to a speed which exceeds its stall speed under load. The rotor field winding of the synchronous dynamoelectric machine is connected to receive direct current excitation from a rotatable rectifier assembly of a brushless exciter. During starting, a quadrature axis winding disposed around the stator of the brushless exciter is energized by single phase alternating current. Alternating current excitation is induced by transformer action within the rotor armature winding of the exciter and is applied to the rotor field winding after being rectified by the rotatable rectifier assembly. The transformer action operates independently of the rotation of the rotor member of the synchronous dynamoelectric machine so that the brushless exciter develops direct current field excitation for starting purposes when the rotor is at rest. Polyphase alternating current excitation is applied to the synchronous dynamoelectric machine stator winding to establish a dynamic magnetic field which rotates at a speed proportional to the frequency of the applied excitation. Interaction of the static magnetic field of the rotor and the rotating stator field produces the mechanical turning force. The frequency of the synchronously applied stator excitation is increased from substantially zero cycles per second to a higher frequency until the rotor member has accelerated synchronously to the desired speed of rotation.

Journal ArticleDOI
TL;DR: In this paper, Tungsten oxide, WO2.96, was reduced to α-W in hydrogen for various time periods over the temperature range 500°C to 900°C.
Abstract: Tungsten oxide, WO2.96, was reduced toα-W in hydrogen for various time periods over the temperature range 500°C to 900°C. Intermediate oxides were determined using X-ray diffraction analysis of the semireduced powders. Several dopant conditions were used, to find the effect on oxide structures and reaction kinetics of the usual dopants K, Si and Al. The scanning electron microscope was employed to determine the morphology of the crystallites at intermediate and final stages of reduction.

Journal ArticleDOI
TL;DR: In this article, a load-follow demonstration was conducted on Consolidated Edison's Indian Point, Unit 2 plant located in Buchanan, New York, in August and September of 1974.
Abstract: Comprehensive load-follow demonstrations were conducted on Consolidated Edison’s Indian Point, Unit 2 plant located in Buchanan, New York, in August and September of 1974 The purpose was to examin

Book ChapterDOI
TL;DR: In this paper, a two-dimensional finite element method is used to develop stress intensity factor solutions for continuous surface flaws in structures subjected to an arbitrary loading, where the arbitrary loading produces a stress profile σ acting perpendicularly to a given section S of the structure.
Abstract: A two-dimensional finite element method is used to develop stress intensity factor solutions for continuous surface flaws in structures subjected to an arbitrary loading. The arbitrary loading produces a stress profile σ acting perpendicularly to a given section S of the structure. The stress profile is represented by a third degree polynomial σ = A 0 + A 1 x + A 2 x 2 + A 3 x 3 Stress intensity factor solutions are developed for continuous surface flaws introduced in particular sections S in the structure considered. Solutions are developed for a surface flaw in a flat plate, for both circumferential and longitudinal flaws inside a cylindrical vessel, and for circumferential flaws at several locations inside a reactor vessel nozzle. The superposition principle is used, and the crack surface is subjected successively to uniform (σ = A 0 ), linear (σ = A 1 x), quadratic (σ = A 2 x 2 ), and cubic (σ = A 3 x 3 ) stress profiles. The corresponding stress intensity factors (K I ( 0 ) , K I ( 1 ) , K I ( 2 ) , K I ( 3 ) ) are then derived for various crack depths using the calculated stress profile in the region of the crack tip. The total stress intensity factor corresponding to the cracked structure subjected to the arbitrary stress profile is expressed as the sum of the partial stress intensity factors for each type of loading. K I = K I ( 0 ) + K I ( 1 ) + K I ( 2 ) + K I ( 3 ) = √πa[A 0 F 1 + 2a/π A 1 F 2 + a 2 /2 A 2 F 3 + 4a 3 /3π A 3 F 4 ] where, a is the crack depth and F 1 , F 2 , F 3 , and F 4 are the magnification factors relative to the geometry considered. The results are presented in terms of magnification factors versus fractional distance through the wall (a/t) and reveal the strong influence of the geometry of the structure and of the crack orientation. The stress intensity factor solutions obtained using this method are compared to solutions obtained using other methods, when available. In the case of the plate geometry, the solution obtained for the linear loading (σ = A 0 + A 1 x) is shown to agree well with the boundary collocation solution reported by Brown and Srawley. The stress intensity factor solutions for the circumferential and longitudinal cracks in the cylindrical vessel compare well with solutions obtained by Labbens et al using the weight functions method proposed by Bueckner, and are also in good agreement with the solution for uniform loading (σ = A 0 ) obtained using the line spring method proposed by Rice.