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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.

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.

The distribution of rainflow range is investigated for the Gaussian random process using 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 estimates the distribution of range with high accuracy even, in the case of a random wave with a large irregularity factor. 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.

Probabilistic life prediction is needed in structural reliability analyses of structures because considerable scatter is often observed in fatigue crack growth data. The primary source of this scatter is material inhomogeneity which causes the variability of a material's resistance against fatigue crack growth. One of the useful ways to analyze stochastic fatigue crack growth due to random crack growth resistance is the Tsurui-Ishikawa solution which is derived from the generalized Fokker-Planck equation based on the Markov approximation method. However, no practical methods to determine the parameter of their solution, which determines the distribution of crack growth fatigue life, have been reported. Thus, this paper presents a simplified method to determine the parameter of the Tsurui-Ishikawa solution. The proposed method requires only a few constant ΔK-controlled fatigue crack growth tests and the procedure is quite simple. In order to confirm the proposed method, Monte-Carlo simulations are also performed and satisfactory results are obtained.

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.

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).

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.

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.

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.

Although the finite element method has come into wide use in the field of structural and continuum mechanics, its error characteristics are not well known. This paper discusses the error characteristics of the finite element method in the case of triangular elements with a linear shape function generally used in plane stress analysis. The paper analyzes the discretization errors of finite element method using the technique proposed by Walz et al., with some generalizations. Here approximations included in the calculations of finite element method are discussed with various element patterns in comparison with the equilibrium equations of the field. The analysis reveals that the approximations in finite element method do not converge to the field equations in almost all the element patterns checked here as the element size is made infinitesimal. From this point of view, it interprets what kind of element patterns should be applied. Errors caused by the approximate strain-displacement relation are also discussed by a similar technique.