Математическая модель многоочагового усталостного повреждения заклепочных соединений

Multiple Site Damage (MSD) is one of the significant damaging factors that limit the airworthiness of aging fleet aircrafts. In case of MSD multiple fatigue cracks initiates and propagates at the rivet holes. Those cracks are relatively short in length, but with a sufficiently large number of them and an unfavorable arrangement along the rivet joint, they can join together and form a crack of a dangerous length. To prevent this type of damage it is necessary to have adequate methods for predicting the boundary state of riveted joints during MSD. A useful approach is a numerical experiment based on Monte-Carlo simulation of the MSD main random factors – the formation of initial cracks and their growth. This paper presents a probabilistic model for predicting the initial stage of MSD – destruction of at least one bridge between the adjacent holes. A level I model is considered, which describes the process of fatigue failure of specimens without rivets but with multiple holes, which are typical for riveted joints. The initiation of fatigue cracks and their growth are modeled taking into account the laws of damage development obtained experimentally on specimens with multiple cracks. So, to simulate the random initiation of cracks in time the Weibull distribution is used. The parameters of this distribution depend on the applied stress. The growth of cracks is described by the Paris' equation, taking into account the experimentally confirmed correlation between the coefficients of this equation. The model assumes that each initiated crack propagates according to a random value of the Paris' equation exponent. The distribution of such a random value corresponds to a logarithmically normal law with experimentally obtained parameters. The criterion for the possible join of opposite cracks growing from adjacent holes is the uniting of plastic deformation zones at the tips of such cracks. The results of modeling are presented in the form of multiple site damage realization field of points in the coordinates of the number of cycles before the initiation of cracks vs. the number of cycles before the destruction of the bridge between holes.

Structure, processing and performance of ultra-high molecular weight polyethylene (IUPAC Technical Report). Part 4: sporadic fatigue crack propagation

Fatigue tests were carried out on compression mouldings supplied by a leading polymer manufacturer. They were made from three batches of ultra-high molecular weight polyethylene (UHMWPE) with weight-average relative molar masses, ${\overline{M}}_{\mathrm{W}}$, of about 0.6 × 106, 5 × 106 and 9 × 106. In 10 mm thick compact tension specimens, crack propagation was so erratic that it was impossible to follow standard procedure, where crack-tip stress intensity amplitude, ΔK, is raised incrementally, and the resulting crack propagation rate, da/dN, increases, following the Paris equation, where a is crack length and N is number of cycles. Instead, most of the tests were conducted at fixed high values of ΔK. Typically, da/dN then started at a high level, but decreased irregularly during the test. Micrographs of fracture surfaces showed that crack propagation was sporadic in these specimens. In one test, at ΔK = 2.3 MPa m0.5, there were crack-arrest marks at intervals Δa of about 2 μm, while the number of cycles between individual growth steps increased from 1 to more than 1000 and the fracture surface showed increasing evidence of plastic deformation. It is concluded that sporadic crack propagation was caused by energy-dissipating crazing, which was initiated close to the crack tip under plane strain conditions in mouldings that were not fully consolidated. By contrast, fatigue crack propagation in 4 mm thick specimens followed the Paris equation approximately. The results from all four reports on this project are reviewed, and the possibility of using fatigue testing as a quality assurance procedure for melt-processed UHMWPE is discussed.

A method for determination of the boundaries of the stage of steady fatigue crack growth and parameters of Paris equation

A method and procedures for determining the boundaries of the second stage of the kinetic crack resistance diagram or fracture toughness kinetic diagram, sample formation within the aforementioned boundaries and determination of the parameters С and n of the Paris equation from the sample are presented. The necessity of developing the method is attributed to the lack of rules and procedures for accurate determination of the boundaries of the second stage in the current standards and regulatory document (RD). The proposed method provides a given accuracy of determination of the number of cycles corresponding to the length of the fatigue crack at the upper boundary of the second stage obtained by numerical integration of the Paris equation with the found values of the parameters С and re. The developed method is based on the application of two criteria R2 and %. Statistical criterion R2 characterizes a degree of deviation of the experimental data from the linear fragment of the kinetic fracture toughness diagram. Parametric criterion у specifies the level of accuracy of the parameters С and re of the Paris equation. This level is set through a comparative evaluation of the experimental and calculated crack length I and the number of cycles N, obtained by integration of the Paris equation within the specified lower and upper limits of the interval of the stable growth of fatigue crack. Application of the method is shown by the example of the experimental data obtained when testing samples of VT9 titanium alloy, deformable nickel alloy EI437BU and granular nickel alloy EP741NP (granules up to 140 pm) at room and elevated temperatures. Application of the method indicates that the experimental and calculated curves "I - N" obtained by numerical integration of the Paris equation differ by less than the specified value of the criterion X ^ 3%, in contrast to the results obtained in accordance to the recommendations of the regulatory documents.

Review of Available Probabilistic Models of the Crack Growth Parameters in Paris Equation

Crack growth rate parameters of the Paris equation are crucial inputs in the engineering critical assessment (ECA) of structures containing flaws. In fracture mechanics based reliability analysis, probabilistic models of these parameters are often used. Despite the considerable body of research in this area, there is significant variability among available models. This paper reviews the current available models in the literature and addresses areas requiring further research with a view to assisting probabilistic flaw assessment. The effect of the existing variability in crack growth model parameters is investigated by fracture mechanics analysis of a case study crack.