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In the reflow soldering process, the IC package is heated over 270°C by the infrared rays. In a delamination interface, the stress field near a crack tip will always be in a mixed-mode state. It was assumed that the initial defects were generated among the corner part of die pad and epoxy molding compound. The 3-D finite element analysis was carried out to evaluate the strain energy release rate of delamination interface in IC packages subjected to non-steady thermal stress. The strain energy release rate of mixed mode was evaluated by the modified crack-closure integral and virtual crack extension method. The maximum difference of strain energy release rate between the modified crack-closure integral and virtual crack extension method was about 8%. Therefore, it is considered that the modified crack-closure integral is useful as a simple evaluation method of the strain energy release rate. The stress intensity factor K was examined from 3-D and 2-D virtual crack extension method. The virtual crack extension method can evaluate stress intensity factors of the interface crack under a mixed-mode loading accurately.

In this paper a crack identification method of plane frame is presented using both genetic algorithm (GA) and FEM. The crack is simulated by an equivalent rotational spring model. On the basis of this approximate model, the stiffness matrices of a cracked element are developed employing the Timoshenko beam thory. In order to calculate the natural frequencies of the frame, which are required to identify of the crack location and depth from frequency measurements, FEM program including the cracked element is written. The depth and the position of the crack in the plane frame are estimated by using these natural frequencies and GA. The proposed method is verified by numerical simulation of some sample problems.

In order to develop life assessment techniques for aged components made of modified 9Cr–1Mo steel, specimens were artificially deteriorated by aging, creep and fatigue tests at elevated temperatures, and associated changes in the microstructure and mechanical properties were examined. It was observed that aging resulted in formation of Laves phase causing a decrease in toughness. The creep damage in base metal could be correlated with decrease in hardness, while creep damage in weldments could be correlated with the area fraction and density of creep voids. Creep rupture in weldments occurred in the fine-grained heat affected zone by the formation and growth of creep voids. The fatigue damage in base metal correlated to the maximum length of a crack among micro-cracks initiated during fatigue cycles.

A crack in a structural member can change the eigenfrequencies of the undamaged structure. The magnitude of change in the eigenfrequencies is a function of the depth and the location of the crack. By relating the eigenfrequencies to the crack location and depth, we proposed a crack identification method for plane frame structures in present paper. In the FEM vibration analysis for the structures, the crack is simulated by an equivalent rotational spring, connecting the two segments of the beam. The matrix elements containing a crack are derived explicitly by combining both the transfer matrix method and the compatibility equation of each segment. The eigenfrequencies computed by FEM are then applied to studying the inverse problem-identification of crack location from frequency measurements. And the crack identification method is performed by using both the finlte element method and the genetic algorithm. In order to confirm the validity of the proposed method, several frame structures with a crack are analyzed.

Fracture tests for the verification of WPS (warm prestressing) effect were carried out by using large flat specimens with very low toughness. Tensile and bending loads and thermal shock were applied simultaneously to the specimens with the realistically postulated flaw and the two times larger one in order to make the maximum K{sub I} cross the lower bound of K{sub IC} data. During the tests, loading was controlled to simulate the shape of K{sub I} versus temperature curve for the postulated PTS transient. Both the specimens did not break within the scatter band of K{sub IC} when K{sub I} was decreased during cooling. K{sub I} values at fracture by reloading were beyond the upper bound of K{sub IC}. That is, the effectiveness of WPS was directly demonstrated for the PTS transients. Also, K{sup I} values at fracture can be predicted by Chell`s theory. As the test results, Japanese PWRs have sufficient temperature margin against PTS.

Pressurized thermal shock (PTS) is a phenomenon that can occur in the reactor pressure vessels (RPVs) with internal pressure and is one of the most severe stress conditions that can be applied to the vessel. Preliminary research has shown that no PTS concern is likely to exist on Japanese RPVs during their design service lives. However, public acceptance of vessel integrity requires analyses and experiment in order to establish an analytical method and a database for life extension of Japanese RPVs. The Japanese PTS integrity study was carried out from FY 1983 to FY 1991 as a national project by Japan Power Engineering and Inspection Corporation (JAPEIC) under contract with Ministry of International Trade and Industry (MITI) in cooperation with LWR utilities and vendors. Here, a crack arrest test was carried out using a toughness gradient steel plate with three layers to study the concept of crack arrest toughness. Four-point bending load with thermal shock was applied to the large flat plate specimen with a surface crack. Five crack initiations and arrests were observed during the test and the propagated crack bifurcated. Finally, cracks were arrested at the boundary of the first and the second layer, except for a smallmore » segment of the crack. The first crack initiation took place slightly higher than the lower bound of K{sub Ic} data obtained by ITCT specimens. That is, the K{sub IC} concept for brittle crack initiation was verified for heavy section steel plates. The first crack arrest took place within the scatter band of K{sub Ia} and K{sub Id} data for the first layer. That is, the K{sub Ia} concept appears applicable for crack arrest of a short crack jump.« less

To evaluate the cumulative fatigue damage under Gaussian random loading, the distribution of rainflow range must be evaluated from the random waves. It is considered difficult to evaluate the distribution of range from the geometry of the PSD of the waves except the narrow band random waves, the range distribution of which becomes Rayleigh distribution. As to the random waves with bimodal PSD, however, the authors have already shown that the range can be derived from the PSD analytically. The distribution of range can be represented by the ratio of two dominant frequencies and the ratio of two corresponding power.In this paper, the property of fatigue damage evaluated by the proposed method is examined. And the fundamental equations necessary for reliability analysis are formulated. The derived equations are compared with the results of Monte-Carlo simulations and good agreements are obtained. Finally, several diagrams, which enable us fatigue design easily, are presented.

Fracture tests for the verification of WPS (warm prestressing) effect were carried out by using large flat specimens and big compact specimens with low toughness. In the case of monotonical KI increasing during cooling, the specimen broke within the scatter band of KIC. On the other hand, when KI was decreasing during cooling, the specimens did not break even if KI values were beyond the scatter band of KIC. That is, WPS effect was confirmed even for the low toughness steel like reactor pressure vessel wall under neutron irradiation. Also, KI values at fracture can be predicted by Chell’s theory. By applying WPS effect and the predictive equations for irradiation embrittlement for Japanese PWR reactor steels to the PTS integrity analysis, much more temperature margin can be expected.

Japanese pressurised thermal shock (PTS) integrity study has been carried out to obtain public acceptance of reactor pressure vessels integrity against PTS events and to provide the data base for their life extension. This paper introduces a research plan and results.

The distribution of rainflow range is investigated for the Gaussian random process under bimodal PSD. The new method evaluates the distribution of range by taking the sum of two Rayleigh distributions which correspond to two dominant frequencies in bimodal PSD. Representative distribution data have been obtained from rainflow analysis for simulated time histories. The applicability of the proposed method is examined for the range distribution generated by the simulation. It is shown that the method evaluates the distribution of range with high accuracy even for the random wave giving a large irregularity factor in some cases. Since range data for unimodal PSD can be evaluated by Rayleigh approximation, the new method for bimodal PSD greatly extends the region of analytical treatment.

Closed-form expressions of the stress intensity factor are so useful in fracture mechanics analysis that a number of expressions have been obtained for various kinds of cracked specimens. However, most of actual structures are statically indeterminate, and stress intensity factors for such statically indeterminate cracked structures cannot be estimated only in terms of the above expressions. Such crack problems in statically indeterminate structures were systematically discussed by Okamura et al., and stress intensity factors for statically indeterminate cracked structures were shown to be estimated in terms of the crack compliance, i. e., the variation of compliance due to the presence of cracks. In this paper, an estimation scheme of closed-form expressions for crack compliance is presented. First, asymptotic properties of the crack compliance are obtained for single edge notched (SEN) specimens under both tension and bending. Then, closed-form expressions are estimated based on the asymptotic properties. The obtained expressions are shown to be quite accurate and useful for not only engineering discussion but also theoretical study.

It has been shown from the results of round robin tests conducted under VAMAS project that the fatigue property may vary from one researcher to another due to the difference of evaluation models used. It is important to clarify the effect of the S-N evaluation model used on the reliability analysis. In this paper, the fatigue data are fitted to five regression models and the goodness of fit is investigated. The fatigue data are picked from the fatigue database which was provided by JSMS. No significant difference could be found concerning the goodness of fit against the models. However, the results differed slightly depending on the factor used in the goodness of fit. Moreover, the effect of the model on the evaluated fatigue life is investigated for the fatigue under random loads. The fatigue life evaluation was formulated for three regression models and the fatigue life under various rms values was calculated for several materials. The effect of the fatigue model on the evaluation life was clarified.

A step B test was carried out as one of the test items using large scale flat plate specimens within the Japanese PTS research project. Its experimental goal was the investigation of the crack behavior in the upper shelf region under combined mechanical and thermal loading. The experimental data were described in detail. By means of numerical simulation of the experiment, time histories of temperature distribution through the thickness, deformation and strain were obtained and compared with experimental data. Also the ductile stable crack growth by the J resistance concept was compared with experimental results. As a result, the stable crack growth of the step B test was conservatively estimated by J resistance curves obtained by 1TCT specimens. Currently, the reason of overestimation is not so clear. Triaxiality near the crack tip may be one of the reasons for the overestimation

For clarifying fracture strength and estimating structural integrity, a simple procedure has been developed to evaluate the stress intensity factors for some cracked structures in our recent studies. This procedure is the application of a matrix method to the analysis of cracked structures, as in the analysis of statically indeterminate structures based on the energy principle. In this paper, the above procedure is extended to nonlinear elastic structures using the fact that the complementary energy of cracked members can be easily calculated using fully plastic solutions. Therefore, it is shown that this procedure enables us to easily carry out some parametric studies systematically without full numerical calculation as in finite-element analysis. Furthermore, this procedure is applied to the evaluation of the J-integral for one or more axial cracks in circular cylinders, where matrix formulation is shown to be useful for both computer-aided calculation and the discussion on some influential parameters: such as external forces, diameter ratios, relative crack depths, and the number of cracks.

In this paper, mixed mode stress intensity factors for one or more symmetric and asymmetric axial cracks in pressurized cylinders are calculated using a simple approach which we proposed in our previous work. Effects of parameters on both KI and KII are investigated systematically concerning ( 1 ) diameter ratios, ( 2 ) relative crack depths, ( 3 ) the number of cracks, ( 4 ) pressure acting on crack face, ( 5 ) the presence of cracks with unequal depth, and ( 6 ) the asymmetric arrangement of cracks. Then, the results obtained are summarized as follows : ( a ) KI for two symmetric internal axial cracks (=KI) is the largest of all that for other axially cracked configurations : ( b ) KII is always negligible in unstable fracture prediction ; ( c ) the differences in KI for various cracked configurations in thin-walled cylinders are so small that KI is not so conservative in fracture evaluation ; and ( d ) accurate closed-form expression of KI is obtained for practical use.

Fatigue crack growth is a major factor that must be considered in the design and life prediction of fatigue-critical structures, yet recent studies suggest that much of fatigue crack growth data exhibit a large amount of statistical variability and deterministic models do not adequately describe the crack propagation behavior. Thus, the need to use probabilistic methods to predict fatigue crack growth becomes evident. In this paper, focus is centered on the formulation of a stochastic fatigue crack growth model. With the use of the diffusion Markov process theory, a partial differential equation called the Fokker-Planck equation which satisfies the probability density of the random time to reach a given crack size is introduced. Then, the equation is numerically solved by the finite differential method, and the statistical properties of crack growth fatigue life are evaluated.

In this paper, the J-value of an axially cracked cylinder under thermal shock, internal pressure and several pressurized thermal shock (PTS) conditions are evaluated over the full range of crack depth ratio (ζ) using a simple estimation scheme based on the deformation theory of plasticity which we proposed in our earlier works. Several parameter studies show characteristic features of the fracture strength under PTS as follows, The effect of internal pressure is predominant upon the J-value and dJ/da under PTS. Under any PTS condition, J-ζ relation shows that the J-value reaches its maximum at a certain ζ, then drops to zero (i.e., the starting point of crack closure) at ζs0.9. The compliance of the cylindrical shell plays an important role in the fracture prediction of a pressure vessel. Under typical PTS conditions, the region at the crack tip dominated by the Hutchinson-Rice-Rosengren singularity is substantially large enough to apply the J-based criterion to predict unstable ductile fracture.

Stress intensity factors for load-controlled C-shaped specimens (LC-CSS) are discussed in some literatures, but those for displacement-controlled C-shaped specimens (DC-CSS), which are often used for environmental fracture toughness testing, are not. In this paper, an analytical procedure is shown by which to estimate mixed-mode stress intensity factors for DC-CSS with some internal and external axial cracks. The results obtained are summarized as follows : (1) Analytical results for LC-CSS show good agreement with the numerical data in the literature. (2) Mode II stress intensity factors are always negligible as compared to mode I stress intensity factors for commonly used thin-walled rings. (3) Explicit formulation of the stress intensity factors obtained in this paper is effective for both practical use and the discussion of influential parameters. (4) Several parameter studies for DC-CSS show that it is important for the analysis of such statically indeterminate structures to consider the variation of the system's compliance due to the presence of cracks.

Fatigue crack propagation can be represented by a stochastic process such as a Markov process, which accounts for the distribution of crack propagation fatigue life. However, since we normally are able to obtain only limited information about the actual stochastic properties of the fatigue crack propagation process, it is necessary to represent the process by an appropriate model. This paper presents a new stochastic model which treats the material's resistance against fatigue crack growth as a spatial stochastic process evolving along the path of the crack. To obtain the stochastic properties of the fatigue crack propagation process, constant ΔK tests were conducted for several ΔK cases, and the parameters of the model were calculated by a spectral analysis using the maximum entropy method (MEM), which accounts for the statistical correlation that has been observed between adjacent fatigue crack growth rates. Using a proposed random crack propagation model, Monte-Carlo simulations were also performed and satisfactory agreement with the results of experiments were obtained.

This paper presents a new scheme for the estimation of unstable ductile fracture of a reactor pressure vessel under thermal shock conditions. First, it is shown that the bending moment applied to the cracked section can be evaluated by considering the plastic deformation of the cracked section and the thermal deformation of the shell. As the contribution of the local thermal stress to the J-value is negligible, the J-value under thermal shock can be easily evaluated by using fully plastic solutions for the cracked part. Next, the phenomena of ductile fracture under thermal shock are expressed on the load-versus-displacement diagram which enables us to grasp the transient phenomena visually. In addition, several parametrical surveys are performed on the above diagram concerning the variation of (1) thermal shock conditions, (2) initial crack length, and (3) J-resistance curve (i.e. embrittlement by neutron irradiation).

The variability of fatigue crack growth rate da/dN should be decomposed into two parts; the inter-specimen variability and the intra-specimen one. Recently, the inter-specimen variability is considered to be more important than the intra-specimen one from a reliability engineering point of view. In order to analyze the statistical prosperity of inter-specimen variability, fatigue crack growth tests must be conducted under the constant ΔK condition and the crack length must be measured at intervals of constant cycles, because the inter-specimen variability depends upon the intervals between measurements of crack length. Then an automated testing system is strongly needed for those statistical analysis. However, it is considered to be difficult to guarantee the measurements of crack length at regular intervals with single task processing, because the process of saving data in floppy disk or managing key-board may force the process of measuring crack length to wait. Thus an automated fatigue crack growth rate testing system using real-time multitask processing has been developed, which enables us to measure crack length at regular intervals. This paper describes in detail a personal computer-based testing system designed to be used with a standard servo-hydraulic test frame. A new algorithm is introduced to perform constant ΔP and constant ΔK fatigue crack growth tests effectively using a multi-tasking method. The system is designed to ease of operation and reduce the chance of operator error. The developed system was examined for the constant ΔK test and the satisfactory results were obtained. In this paper an error analysis was also performed to determine the crack length error. The analysis clarified the effect of an error in load and back face strain on determination of compliance-inferred crack length.

This paper presents a new scheme for the estimation of unstable ductile fracture using the J-integral. The proposed method uses a load-versus-displacement diagram which is generated using fully plastic solutions. By this method, the phenomena of the ductile fracture can be grasped visually. Thus, the parametrical survey can be executed far more easily than before. Then, using the proposed method, unstable ductile fracture is analyzed for single-edge cracked plates under both uniform tension and pure bending. In addition, several parametrical surveys are performed concerning (1) J-controlled crack growth, (2) compliance of the structure, (3) ductility of the material (i. e., J-resistance curve), and (4) scale of the structure (i. e., screening criterion). As a result, it is shown that the proposed method is especially effective for the parametlical study of unstable ductile fracture.

This paper describes an experimental study on pressurized thermal shock, PTS, problem by using a photoelastic technique for the purpose of confirming the validity of application of statically indeterminate fracture mechanics to the problem. The following points are made clear from the test results:(1) Thermal stresses obtained from the photoelastic test results agree well with those given by nonstationary thermal conduction analysis.(2) Bending moments obtained from observation of photoelastic fringes agree well with those given by nonstationary thermal conduction analysis. It was experimentally confirmed that bending moment occurred by constraint in such structure that bending deformation was restricted. The compliance of the end of specimen was quantitatively evaluated.(3) The good agreement was observed between the stress intensity factor obtained from observation of photoelastic fringes near a crack tip and that given by application of statistically indeterminate fracture mechanics which was described in the previous paper. It was confirmed that statically indeterminate fracture mechanics which was valid for theoretical evaluation of the stress intensity factor under PTS. Also by this experimental results, It was made clear that bending moment by constraint influenced significantly the stress intensity factor under PTS.

Safety evaluation of components with crack-like defects must be treated probabilistically because the initial size of defects and other parameters are nondeterministic. In the case of an actual structure, such as a pressure vessel, the most important defect is the surface flaw. But life prediction involving surface flaws is not simple, as the aspect ratio of a crack may change gradually as the crack grows. Therefore, probabilistic analysis is also complicated. This paper presents a simple method of probabilistic life prediction for the fatigue crack propagation of a semiellipitical surface crack, and the influence of several parameters on crack propagation life is discussed.

This paper presents an application of Fracture Mechanics for a statically indeterminate structure to a pressurized thermal shock (PTS) problem of pressure vessel of PWR. This method is efficient to clarify the mechanical characteristics of PTS event. The following results were obtained:1) Stress intensity factor (K) under PTS is affected by the compliance of the shell of pressure vessel.2) The bending moment occurred by flexural constraint is important for K under PTS.3) As a new test method of PTS simulation with high precision, 4-point bending of a plate with axial load is proposed.

This paper presents the analysis of the deformation and the strength of a cracked body, emphasizing a superimposed effect of multiple toads on elastic and plastic deformation of an edge-cracked beam or column under two kinds of loads, bending and axial toads. The analysis has been done about the effect of axial force on the elastic angular deformation, including the effect of half-closure of crack, and also on the angular deformation of a cracked plastic hinge. Finally as a practically important example, the above analyses are applied to the problem of the deformation and the load carrying capacity of the cracked column under an eccentric axial force.

A new algorithm for the improvement of measuring accuracy of ultrasonic attenuation using a spectrum analysis has been developed. Normally, the ultrasonic attenuation is evaluated from 1st and 2nd peak values of the pulse-echo ultrasonic wave. However, the attenuation values evaluated by this method possibly contain some error, because those values are greatly affected by the superimposed noise. The proposed method removes this problem by evaluating the attenuation values from the expected envelope curve of the original ultrasonic wave. The algorithm developed is incorporated in, measuring system which consists of a personal computer with ultrasonic apparatus and a digital storage oscilloscope. Several ultrasonic waves obtained from Monte Carlo simulations and high-temperature fatigue-damaged specimens are analyzed by using both the proposed method and the normal method. It is concluded that the measuring accuracy of ultrasonic attenuation by the present method is higher than that by the normal method.

A crack reduces the flexural rigidity of a column. The effects of the reduced rigidity on the load carrying capacity, the deflection, and the fracture load of a slender column with a single-edge crack have been studied based on the column theory together with the well-known relationship between the compliance and the stress intensity factor of a cracked beam. A crack reduces the load carrying capacity and increases the lateral deflection of a column under an eccentric compressive load. The calculated deflection agrees very well with the values measured by Liebowitz, Vanderveldt and Harris. The increased lateral deflection increases the bending moment at the cracked section. The bending stress intensity factor of a cracked column was also calculated, with the increased bending moment taken into consideration. The net stress intensity factor at the crack tip is the difference between the bending and the compression stress intensity factors. The fracture toughness value obtained from cracked columns agree reasonably well with the value obtained from cracked plate. This study indicates that the superposition of stress intensity factors of the same mode is valid.