• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.7
• /
• pp.2159-2166
• /
• 1996

The stochastic properties of variation in fatigue crack growth are important in reliability and stability of structures. In this study,the stochastic model for the variation of fatigue crack growth rate was proposed in consideration of nonhomogeneity of materials. For this model, experiments were ocnducted on 7075-T6 aluminum alloy under the constant stress intensity factor range. The variation of fatigue crack growth rate was expressed by random variables Z and r based on the variation of material coefficients C and m in the paris-Erodogan's equation. The distribution of fatigue life with respect to the stress intensity factor range was evaluated by the stochastic Markov chain model based on the Paris-Erdogan's equation. The merit of proposed model is that only a small number of test are required to determine this this function, and fatigue crack growth life is easily predicted at the given stress intensity factor range.

• Journal of the Korean Society of Safety
• /
• v.23 no.5
• /
• pp.61-66
• /
• 2008

It is important to calculate the exact crack opening area in the cracked pipe subjected to axial force and bending moment. Among many solutions for obtaining the crack opening displacement, Paris-Tada's expression, which is derived from energy method, is open used in fracture analysis for piping crack problems because of its simplicity. But Paris-Tada's equation has conservativeness when radius over thickness ratio(R/t) is ten or less, for it is based on the stress intensity factor solution having a compliance function derived from a simple shell theory. In this paper we derived a new expression using a different stress intensity factor solution which is able to consider the variation of compliance through wall thickness in a cracked pipe. Conservativeness of both equations was examined and compared to finite element analysis results. Conservativeness of the new equation is decreased when R/t > 10 and increased slightly when R/t < 10 compared with Paris-Tada's. But Both equations were highly conservative when R/t < 10 compared with finite element analysis results.

• Nuclear Engineering and Technology
• /
• v.49 no.6
• /
• pp.1259-1268
• /
• 2017

The alpha eigenvalue problem in multigroup neutron diffusion is studied with particular attention to the theoretical analysis of the model. Contrary to previous literature results, the existence of eigenvalue and eigenflux clustering is investigated here without the simplification of a unique fissile isotope or a single emission spectrum. A discussion about the negative decay constants of the neutron precursors concentrations as potential eigenvalues is provided. An in-hour equation is derived by a perturbation approach recurring to the steady state adjoint and direct eigenvalue problems of the effective multiplication factor and is used to suggest proper detection criteria of flux clustering. In spite of the prior work, the in-hour equation results give a necessary and sufficient condition for the existence of the eigenvalue-eigenvector pair. A simplified asymptotic analysis is used to predict bands of accumulation of eigenvalues close to the negative decay constants of the precursors concentrations. The resolution of the problem in one-dimensional heterogeneous problems shows numerical evidence of the predicted clustering occurrences and also confirms previous theoretical analysis and numerical results.

• Journal of applied mathematics & informatics
• /
• v.41 no.2
• /
• pp.295-309
• /
• 2023

The Richards' equation attracts the attention of several scientific researchers due to its importance in the hydrogeology field especially porous soil. This work presents a numerical method to solve the two dimensional Richards' equation. The pressure form and the mixed form of Richards' equation are solved numerically using a bivariate diamond finite volumes scheme. Euler explicit scheme is used for the time discretization. Different test cases are done to validate the accuracy and the efficiency of our numerical model and to compare the possible numerical strategies. We started with a first simple test case of Richards' pressure form where the hydraulic capacity and the hydraulic conductivity are taken constant and then a second test case where the hydrodynamics parameters are linear variables. Finally, a third test case where the soil parameters are taken according the Van Gunchten empirical model is presented.

• Proceedings of the Korean Reliability Society Conference
• /
• 2004.07a
• /
• pp.161-166
• /
• 2004

A method of estimating B$_{\alpha}$ life of crack growth is proposed based on the linear elastic fracture mechanic model. It is assumed that the coefficients in the Paris-Erdogan equation are random variables and their distributions are estimated by the method of 2-stage estimation from the fatigue crack growth data. A case study is also given. is also given.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.14 no.6
• /
• pp.1552-1560
• /
• 1990

A general form of the mathematical function in the fatigue crack growth rate law for CT specimens was determined by means of the dimensional analysis at elevated temperatures. The experimental results can be rigorously described by the combination of rate theory and fracture mechanics. The rate theory approach extends the scope of fracture mechanics through the consideration of the temperature. The fatigue crack growth rates are represented by the Arrhenius type equation. This equation explains fairly well the experimental data for Cr-Mo-V rotor steel and A517-F steel in the comparatively wide temperature regions as affected with the temperature and the stress intensity factor range interaction.

• Journal of Welding and Joining
• /
• v.7 no.1
• /
• pp.51-58
• /
• 1989

The purpose of this study is to investigate the corrosion fatigue crack growth of PWTHT specimens(SS41, SM53B) which are the compact tension ones extracted from the muti-passed weldment and weld block. The corrosion fatigue test was done at the cyclic stress frequency of 3Hz in 3.5% NaCl solution. The results are as follows. 1. Corrosion fatigue crack growth of as-weld was slower than that of base metal. 2. In the low .DELTA.K region, the effect of corrosion environment on crack growth was obvious. However, the corrosion effect decreased with the .DELTA.K slowly. 3. The behaviour of fatigue and corrosion fatigue crack growth depended on the material, heat treatment as well as experimental conditions. 4. Corrosion fatigue crack growth of PWHT specimens(SS41, SM53B) subjected to 1/4hr, was increased compared with that of as-weld. 5. There was a tendency that the exponent value(m) obtained in 3.5% NaCl solution was decreased in comparison with that in air, and the material constant(C)was increased for Paris equation, da/dN=C((.DELTA.K))$^{m}$ , compared with that in air considerably.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.10
• /
• pp.1694-1701
• /
• 1997

The residual safety assessment of steel structures, an important subject in practice, is given to much attention. Life prediction in the planning course of steel structures under fatigue loading is mainly based on fatigue design criteria resulting from S-N curves. But for any reason cracks have to be assumed due to fabrication failures or fatigue loading in service which can lead total fracture of structures. The life prediction can be carried out by means of fracture mechanics using Paris-Erdogan equation($da/dN=C {\cdot}{\Delta}K^m$). The paper presents results from charpy test to interpret transition behaviour of charpy energy($A_V$) in a wide temperature range and from constant-load-amplitude test to measure fatigue crack growth of various steels widely used in steel bridges since beginning of 20 centuries in Europe. In the normal service temperature range of steel bridges, the steel S355M shows higher maximum charpy energy($A_{Vmax}$) and lower transition temperature($T_{AVmax/2}$) than other steels considered. The C and m of Paris-Erdogan equation on the steels appear to be correlated, and to be affected by the R-ratios due to crack closure, especially at a low fatigue crack growth rate. Scanning electron microscopy analysis was carried out to interpret an influence of the crack closure effects on the correlation of C and m.

• Journal of Ocean Engineering and Technology
• /
• v.1 no.2
• /
• pp.83-92
• /
• 1987

Inorder ot estimate the running life of turbine rotors, fatigue crack propagation low, da/dN = C(${\DELTA}K)^m$, proposed by paris et al. has been widely applied. In this study, fatigue crack propagation rates for 16 samples of 1% Cr-Mo-V rotor steel were measured and statistical characteristics of m and C values in above equation were reviewed. The results are summarized as follows. 1. C and m follow a log-normal distribution and normal distribution, respectively. And the relation of C and shows a strong negative correlation. 2. Fatigue crack propagation equation can be expressed as da/dN=$4.11{\times}10^{-4}({\Delta}K/153.8)^m$, introducing the ralationship C=$C_oK_o^{-m}$. In this case, contribution of $C_o$ distribution to the distribution of log C shows very small compared to degrees of contribution by m.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.39 no.7
• /
• pp.693-700
• /
• 2015

To estimate the fatigue crack propagation behavior of compact tension shear (CTS) specimen under mixed-mode loads, crack path prediction theories and Tanaka's equation were applied. The stress intensity factor at a newly created crack tip was calculated using a finite element method via ANSYS, and the crack path and crack increment were then obtained from the crack path prediction theories, Tanaka's equation, and the Paris' equation, which were preprogrammed in Microsoft Excel. A new method called the finite element crack tip updating method (FECTUM) was developed. In this method, the finite element method and Microsoft Excel are used to calculate the stress intensity factors and the crack path, respectively, at the crack tip per each crack increment. The developed FECTUM was applied to simulate the fatigue crack propagation of a single-edge notched bending (SENB) specimen under eccentric three-point bending loads. The results showed that the number of cycles to failure of the specimen obtained experimentally and numerically were in good agreement within an error range of less than 3%.