Crack Link-up Research Articles

Dynamic Reliability Assessment of Multi-cracked Structure under Fatigue Loading via Multi-State Physics Model

The structure strength abruptly decreases due to the propagation of multiple cracks. The crack interaction renders the multiple crack reliability problem being a challenging one. Most of the existing methods cannot fit the whole multiple crack growth process and quantify the crack linkup effects on reliability estimation. To address this problem, we extend the multi-state physics modelling and computation framework to evaluate the dynamic reliability of multi-cracked structure via implementing piecewise deterministic Markov processes (PDMP). The proposed multi-state physics model (MSPM) incorporates the crack propagation state transitions and the Forman model that describes the crack growth rate within the states. For the former, the probability of the linkup of adjacent cracks is calculated to identify the multiple crack systems and define the discrete states of each system. For the latter, the Forman model is employed to calculate the crack growth rate within the states. Therefore, each multiple crack system in the structure can be quantified by PDMP and a Monte Carlo algorithm is presented to evaluate the corresponding dynamic reliability values. Ultimately, the dynamic reliability formulation of the multi-cracked structure is developed. The accuracy of the proposed approach is verified by using the sample data from the literature and simulation example.

Probabilistic Fracture Mechanics Analysis of Multiple Cracks in Cylindrical Pressure Vessel

In this work, a probabilistic fracture mechanics analysis of multiple cracks in a cylindrical pressure vessel was conducted. The analysis was performed to predict service life of a pressure vessel with a certain level of reliability if the vessel has a multiple internal surface cracks that interact each other. The stress intensity factor of multiple cracks configuration was determined from the stress intensity factor of a single surface crack in a plate subjected to uni-axial load and the interaction factor between the cracks. In this work, the Swift’s crack link-up criterion was employed. These parameters together with several other stochastic parameters, i.e. initial crack size, Paris’s crack propagation constants and fracture toughness, were then used to calculate the probability of failure with a certain level of reliability. The failure probability was simulated using guided direct simulation, for cycle-by-cycle crack propagation, to find the expected service life and the mode of failure (leak or break). A case study of a high-pressure vessel having different initial crack sizes have been simulated and the service life with 99,99% reliability were determined.

Crack link-up for multiple site damage using an energy density approach

An energy-based crack link-up criterion for multiple site damage conditions is proposed. It is based on the magnitude of strain energy increase during the fracture of the ligament between two adjacent cracks. For the application and verification of the methodology, experiments from the open literature are used. The energy of interest is calculated using elastic–plastic finite element analysis. Numerical results obtained by the proposed methodology are in correlation with experimental data. In all cases considered the present ligament failure criterion has proved to give better predictions, as compared to alternative link-up prediction methodologies.

Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage

An extensive experimental program was conducted by the Boeing Company under the funding of the Federal Aviation Administration (FAA), National Aeronautics and Space Administration (NASA), and the United States Air Force Research Laboratory (USAF/RL) to investigate the effects of multiple-site damage (MSD) on the residual strength of typical fuselage splice joints. The experimental results were used to validate the analytical prediction using various methodologies, including STAGS (a generalized shell finite element code) with the crack-tip-opening angle and T * fracture criteria. The test specimens consisted of large flat panels, curved panels, and an aft pressure bulkhead. The flat panel specimens included three types of longitudinal splice joints and one type of circumferential splice joint. For each type, one panel contained only a lead crack and the other two panels contained MSD 1.3 and 2.5 mm in size, respectively, at the fastener holes ahead of the lead crack. The curved panels were tested under simulated loads of combined cabin pressure and fuselage down bending. Two skin splice types were tested. For each splice type, one panel contained a lead crack only and the other had a lead crack with various sizes of MSD. A section of an aft fuselage containing a large lead crack and MSD in the pressure dome was also tested to demonstrate the capabilities of the methodologies in analyzing actual aircraft structures. This paper presents the analytical approaches and the comparison of predictions with the experimental results in terms of crack linkup stress and residual strength.

Numerical modeling of crack reorientation and link-up

The FRANC3D/BES software system has been used to simulate the reorientation and link-up of hydraulic fractures in three-dimensional (3D) problems. The adopted technique only needs to discretize the body surface and the crack surface. The crack propagation direction is determined using the minimum strain energy criterion. Crack propagation amount is calculated using the mode I stress intensity factor. In hydraulic fracturing, the number of multiple cracks for a given number of perforations depends on the resulting interaction of the cracks. The interaction may be expressed by the fracture stiffness which has been obtained for 3D problems in this paper.

Crack linkup: An experimental analysis

TheTɛ* integral was used to assess stable crack growth and crack linkup in 0.8 mm thick 2024-T3 aluminum tension specimens with multiple site damage (MSD) under monotonic and cyclic loads. TheTɛ* values were obtained directly from the recorded moire fringes on the fracture specimens with and without MSD. TheTɛ* resistance curves of these fracture specimens of different geometries were in excellent agreement with each other. The results suggest thatTɛ* is a material parameter which can be used to characterize crack growth and linkup in the absence of large overloading.Tɛ* based crack growth and net-section-yield based crack linkup criteria for MSD specimens are proposed. The crack tip opening angle (CTOA) criterion can also be used to correlate crack growth larger than 2 mm.

An experimental and numerical analysis of residual strength of butt-joints panels with multiple site damage

The paper presents a combined experimental and computational study of the residual strength of a butt-joint panel with multiple site damage (MSD). The computational model uses a special strip-yield model adapted to MSD, which is implemented into a geometrically nonlinear finite element model. Crack initiation is modelled by a critical crack opening displacement and tearing by a constant crack opening angle criterion. Centre cracked tension tests were first performed to determine the basic fracture parameters. These fracture parameters were then used in the analysis of butt-joint panels with a large lead crack and smaller MSD cracks inserted along the upper row. The simultaneous propagation of multiple cracks in the tests was monitored continuously by aid of a specially developed image analysis technique. Loads for crack initiation, propagation and subsequent crack link-up and panel failure were computed and compared with test results. The geometrical nonlinear effects and the sensitivity to variations in fracture parameters were quantified. An excellent overall agreement was found for the most refined models.

An energy approach to the link-up of multiple cracks in thin aluminum alloy sheets

An energy approach has been used in the study of the coalescence or linkage of multiple cracks in aluminum alloy sheets. The study was motivated by concern for the structural integrity of aging aircraft. Forty reported tests for 2024-T3 aluminum panels with a major crack and several multiple-site damage (MSD) cracks have been analyzed via a simple computational model with a Dugdale–Barenblatt [D.S. Dugdale, J. Mech. Phys. Solids 8 (1960) 100–104; G.I. Barenblatt, in: H.L. Dryden, Th. VonKarman (Eds.), Advances in Applied Mechanics, vol. II, 1962, pp. 55–130] type of plastic or inelastic deformation. For simplicity, the computational model considers only the plastic interaction between the major crack and two symmetrically adjacent MSD cracks in an infinite sheet under remote tensile stress. By following the approach given in [B. Cotterell, J. K. Reddel, Int. J. Fract. 13 (1977) 267–277], the specific work to cause ligament failure is found to be a linear function of the normal extent of the confined plastic region for most tests considered. A few exceptions to this linear relation are attributed to the limitation of the employed computational model. A new criterion and an engineering method to predict crack link-up in an MSD sheet are proposed based on this specific work concept, and they have been demonstrated through application to stiffened panels.

Risk Analysis of Fuselage Splices Containing Multisite Damage and Corrosion

repair of the components. This technology has been increasingly used in the maintenance and management of aging aircraft e eets to improve e ight safety and reduce costs. The output of risk analysis can be used to optimize the maintenance schedule of aging aircraft while maintaining the POF under an acceptable level. To examine the performance of fatigue critical structures, probabilistic risk analysis has been applied to both military and commercial aircraft, and it is believed to be the approach of choice for the future. 1 Various probabilistic risk analysis methodologies have been developed for aging aircraft structures. Generally, there are two aspects in the probabilistic risk analysis to be noted. First is deterministic damage tolerance and durability analysis, such as the analysis of the median crack growth data, the onset pattern of initial MSD, crack linkup criterion, and failure criterion. Considerable effort has been expended on this issue using fracture

Crack Linkup by Stable Crack Growth

Crack Linkup by Stable Crack Growth

On the linkup of multiple cracks

The coalescence or linkup of multiple cracks is considered in this paper. Moreover, two criteria for multiple crack linkup are proposed which are based on linear elastic models. Analytical predictions of multiple crack linkup are compared with experimental results from flat panel tests. The effect of stable tearing has been included in these predictions. The agreement between analysis and experiment is shown to be reasonable.

Low Cycle Fatigue Behavior of Ti-6AI-2Sn-4Zr-6Mo: Part I. The Role of Microstructure in Low Cycle Crack Nucleation and Early Crack Growth

Widmanstatten + grain boundary (W + GB) α and equiaxed (E) structures of different α particle sizes were produced in smooth bar specimens of a Ti-6Al-2Sn-4Zr-6Mo alloy, heat treated to produce a 0.2 pct yield stress of about 1100 MPa. Specimens were cycled at room temperature under total strain control. For both W + GB and Eα structures at low strains crack initiation occurred at α-β interfaces and in the aged β matrix. Profuse extrusions were found in the W + GBα structure. At higher strains for both structures, crack initiation took place preferentially within slip bands in α. Surface crack nucleation and crack link-up occurred more readily in W + GBα structures, which had a shorter life28 than Eα structures, a phenonmenon thought to be due to the much longer surface lengths of the cracks in W + GBα structures. Larger prior β grain size permitted surface cracks to be developed more readily, but the role of β grain size is an indirect one. At large plastic strains colonies of Wα at large angles to the direction of crack propagation can cause the crack to change directions. An explanation for this behavior is offered.