Random Crack Growth Research Articles

Probabilistic damage tolerance analysis on turbine disk through experimental data

A probabilistic analysis on damage tolerance of turbine disk based on experimental data was performed in this paper. Firstly, the fatigue crack growth rate tests at 600°C on 30 compact tension specimens were conducted to investigate the fatigue crack growth characteristics. Experimental results showed that crack growth life appeared great dispersancy. Then a stochastic fatigue crack growth model was proposed and the probability of random crack growth time to reach a specified crack size as well as the distribution function of crack size at the service time could be obtained. At last, considering the uncertainties, probabilistic analysis on the crack growth life of a turbine disk was achieved.

Random Fatigue Crack Growth Rates of China Railway Grade B Cast Steel Wheel

Fracture surface observations and statistical deriving are applied for the present investigation on the random fatigue crack growth rates of China grade B cast steel wheel. Results reveal that: the crack grows with relative regular initial tip companied fabric like stripes along the growth direction but few of fatigue striations, and then, cleavage flowers appearing on the district of transient fracture with few of dimples. It indicates that sharp notched structural crack behaviour acts as a few of plastic dissipation process. Non-linear statistical modeling covering entire three pieces of fatigue crack growth is constructed for describing the random crack growth rates. Scattered randomness of the growth rates has been well characterized.

Random Fatigue Cracking Thresholds of China Railway Grade B Cast Steel Wheel

Fracture surface observations and statistical deriving are applied experimentally for the present investigation on random fatigue cracking thresholds of China grade B cast steel wheel. Results reveal that: the crack grows with relative regular initial tip companied fabric like stripes along the growth direction but few of fatigue striations and then, cleavage flowers appearing on the district of transient fracture with few of dimples. This indicates that sharp notched structures may be subjected to a little plastic dissipation process. In the same time, non-linear statistical modeling is constructed for describing the random crack growth and then, random fatigue cracking thresholds are measured at specified growth rate. The measurements hold a same growth rate which can not be obtained directly from test results.

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris’ law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena.

不規則き裂進展に対する確率場を用いた新しいモデル

A new probabilistic model describing the random fatigue crack growth is proposed based upon a spatially random differential equation driven by a random field. First, a basic equation to describe the random crack growth is formulated as a system of spatially random differential equations by modeling the random propagation resistance in the well-known Paris law as a homogeneous random field. The probability of failure against the fatigue crack growth is then formulated as a functional integral form by the use of its solution. Next, validity of the proposed model is quantitatively verified by comparing with statistical experimental data reported by Ichikawa et. al. Next, an importance sampling simulation scheme is constructed by the use of the Girsanov theorem to make an efficient esimtation for the probability of failure. A numerical example is finally given, which shows that the proposed simulation scheme can give accurate estimation for extremely small probability of failure.

Stress-intensity factor approximations for two-dimensional curvilinear cracks

Two approximations are introduced and assessed that simplify the analytical and numerical treatment of curvilinear cracks in two-dimensional linear elastic fracture-mechanics analyses. The first involves the approximation of the crack trajectory with three segments that maintain a sufficiently accurate description of the near-tip geometry, including the tip's tangent. The second is associated with the use of only two segments, one of which specifies the tip's tangent. Results calculated for several configurations suggest that both approximations lead to accurate stress intensity factors and energy release rates, and can, therefore, be of great use in Monte Carlo-based characterization of random crack growth in brittle materials. An analytical expression is presented for the stress intensity factors of a curvilinear edge crack subjected to uniform far-field tension.

Reliability analysis of structural components under fatigue environment including random overloads

A method is proposed for estimating the hazard rate and reliability function of structural components under the fatigue environment including random overloads. The fatigue crack propagation process is stochastically analyzed by the use of a Markov approximation method in consideration of the retardation effect due to the overloads. The retardation effect is expressed by the probability distribution of the total delay time for the crack propagation process. Firstly, the theoretical approach on the random crack growth is applied under the condition of random occurrence of overloads. The hazard rate of structural components with respect to the ductile failure as well as the fatigue failure is secondly investigated with the aid of the numerical calculation known as the importance sampling simulation. The reliability function for the failure of structural component is shown as the result of the hazard rate. One of the interesting results is that the possibility of failure by overloads is more dominant than the retardation effect of crack growth due to overloads in the high reliability range.

INFLUENCE OF TRANSFORMATION‐INDUCED CRACK CLOSURE ON SLOW FATIGUE CRACK GROWTH UNDER VARIABLE AMPLITUDE LOADING

Abstract Fatigue crack growth under constant and random loading conditions was investigated for a metastable austenitic‐bainitic steel in comparison with a ferritic chromium steel at very low crack growth rates. Experimentally determined random crack growth was compared with linear Miner calculations on the basis of constant amplitude results. It was found that the measured crack growth rates in transforming material are a factor of 10 lower than the calculated values, whereas the difference is only a factor of 2 for the ferritic steel. The reason for the pronounced crack growth retardation in the metastable alloy is transformation of part of the austenitic phase into martensite in the stress field of the crack tip, accompanied by a volume increase and, consequently, residual compressive stresses. Rare high load cycles in the random sequence increase the closure level, which then leads to pronounced retardation of fatigue crack growth for the numerous successive low amplitude cycles.

A Method to Determine the Parameter of the Tsurui-Ishikawa Stochastic Fatigue Crack Growth Solution

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.

Thickness Effect on the Statistical Properties of Random Fatigue Crack Propagation Resistance.

The statistical properties of crack growth fatigue life are often needed in a reliability-based design of fatigue-critical structures. However, recent research revealed that a decrease in specimen thickness caused an increase in the variability of crack growth fatigue life. In this paper, the dependence of the statistical properties of random crack propagation resistance on specimen thickness is investigated. ConstantΔK fatigue crack growth tests are conducted on 2024-T3 aluminum alloy in four cases of specimen thickness. From the experimental data, there is no negligible influence of thickness on the statistical properties of random crack propagation resistance. Using the random crack growth model proposed in the previous paper, the thickness effect on the distribution of crack growth fatigue life is also investigated, and satisfactory agreement with the experiment is obtained.