Multiple Site Damage Research Articles

Analytical prediction model for fatigue crack growth in Fibre Metal Laminates with MSD scenario

This paper presents a theoretical and experimental study on Multiple-site Damage (MSD) crack growth behaviour in Fibre Metal Laminates (FMLs). The prediction model is developed based on a simplified analysis of the effects of load redistribution on a single crack in FMLs containing multiple cracks. Test results show that the crack growth accelerates as cracks grow towards each other. The tests also show non-symmetric crack growth behaviour and non-symmetric interfacial delamination propagation in case of multiple cracks. The prediction model successfully captures the crack growth acceleration and non-symmetric growth behaviour.

Weight function, stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

AbstractPeriodic collinear edge hole cracks and arbitrary small cracks emanating from collinear holes, which are two typical multiple site damages occurred in the aircraft structures, are studied by using the weigh function method. An explicit closed form weight function for periodic edge hole cracks in an infinite sheet is obtained and further used to calculate the stress intensity factor and crack opening displacement for various loading cases. Compared to finite element method, the present weight function is accurate and highly efficient. The interactions of the holes and cracks on the stress intensity factor and crack opening displacement are quantitatively determined by using the present weight function. An approximate weight function method is also proposed for arbitrary small cracks emanating from multiple collinear holes. This method is very useful for calculating the stress intensity factor for arbitrary small cracks.

Splitting method and hybrid-Trefftz formulation for multisite damage analysis in two-dimensional domains

The aim of this paper is to present a new strategy for multiple-site damage analysis by combining the splitting method and hybrid-Trefftz stress formulation in a two-dimensional domain. The first is a decomposition method originally conceived to obtain the solution of a cracked solid. Accordingly, the given problem is split into three subproblems: an uncracked global problem (PG(0)), a local problem (PL(k)) considering a single crack located in a reduced domain and a global problem (PG(k)) aiming to account for the relative interaction effects among all the cracks. Most subproblems are independent and the solution results from a non-iterative strategy, which is one of the main benefits of this method. The hybrid-Trefftz stress formulation is a non-conventional finite element method where stresses and displacements are approximated, independently, in the domain and boundary of the element, respectively. The stress fields are hereby approximated by a basis function that solves the Navier equation and includes analytical fracture mechanics functions, so that the values of stress intensity factors are computed from the solution of the linear system. The hybrid-Trefftz formulation is used in the local problem PL(k) of the splitting method, therefore improving the performance of the method and providing accurate solutions with very coarse meshes. In conclusion, it is shown through the numerical examples that the splitting method and hybrid-Trefftz formulation framework hereby proposed allows conducing accurate analysis. Once exploring a parallel processing, taking advantage of the independence of each subproblem, the framework can be extended to consider different scenarios of multisite cracked solids with a low computation cost.

Mathematical model for three equal collinear straight cracks: A modified Dugdale approach

The present paper discuss a multiple site damage (MSD) problem of three collinear straight cracks exist in an infinite isotropic elastic perfectly plastic plate. Uniform stress distribution is applied at the infinite boundary of the plate in a direction perpendicular to the faces of the cracks. As a result, yield zones are developed ahead each crack tip. These yield zones are sensitive about the load applied at the boundary of the plate. Since the regions near the crack tips are very week as compared to other parts of the plate, therefore, it is assumed that the behaviour of yield stress of the plate near the yield zones is in linear fashion. Hence, rims of the yield zones are subjected to linearly varying stress distribution to stop further opening of cracks along the real axis. The problem is solved using widely used complex variable technique and closed form expressions are derived for stress intensity factor (SIF), crack tip opening displacement (CTOD) and length of developed yield zones at each crack tip. Under small-scale yielding, numerical results for yield zone length and crack-tip opening displacement as a function of remotely applied stress are obtained and presented graphically.

Modified Dugdale model for four collinear straight cracks with coalesced yield zones

A prelude to the problem of two collinear straight cracks has been considered in this paper. Multiple site damage problem of four cracks with coalesced yield zones under the influence of linear stress distribution is discussed. It is assume that the configuration of cracks considered in this paper is just before the formation of two equal straight cracks. Analytical expressions are obtained for stress intensity factors, crack tip opening displacements(CTODs) at each crack tip using complex variable method. A numerical study is carried out to compare the effects of linear stress distribution on the growth of yield zones for two different crack configurations. Some of the analytical expressions are compared with previously published works as a limiting case. Furthermore, results are compared with the solution of two equal collinear straight cracks under similar mechanical loading conditions.

Probabilistic fatigue integrity assessment in multiple crack growth analysis associated with equivalent initial flaw and material variability

The residual strength of components can be abruptly reduced due to multiple site damage (MSD). In general, the fatigue and fracture performance of MSD contains a significant number of uncertainties. Major uncertainties can be characterized by initial flaw, material variability and crack growth rates, among other factors. To cope with uncertain random variables, some probabilistic methods can be considered. However, these seldom obtain efficient and reliable results because of the complexities included in computations of fatigue and fracture mechanics, and probabilistic approaches. To overcome these difficulties in the life-cycle reliability analysis of MSD, the Gaussian process (GP) response surface model has been assembled with one of the recent multiple crack analysis tools, XFEM, in this study. The assembled GP-XFEM method represents a convenient way to obtain the response surface and sensitivity factors of multiple crack propagation in a structure (or a component) under a complex environment with computational efficiency. The accuracy and advantages of the proposed method were verified by a number of experimental results and numerical examples.

Analytical evaluation of the Stress Intensity Factor in stiffened sheets with multiple side damage

A closed form solution of the Stress Intensity Factor (SIF) for stiffened flat sheets, typically used in aircraft construction, in Multiple Site Damage (MSD) conditions, has been developed. The well-known theory of complex variable functions has been used, through the application of functions specifically developed for the case of cracks equally spaced and of equal length. Moreover, the superposition principle has been applied to evaluate the compression loads transmitted by the stringers through the rivets, by imposing the equilibrium on the crack free surfaces and the compatibility of displacements between sheet and stringers at the rivets location. The results have been compared with solutions available in the literature, obtained by combination of various analytical techniques and experimental methodologies, showing a good agreement. The proposed method is a reference for the validation of other numerical or analytical methods and effectively can replace the Finite Element Method for simple geometries.

Multiple crack propagation by DBEM in a riveted lap-joint

The fatigue behavior of a riveted lap joint is analyzed with the Dual Boundary Element Method (DBEM). A Multiple Site Damage (MSD) scenario is obtained from the simultaneous initiation, from the most loaded holes, and propagation of different cracks. The analysis is bidimensional, with no allowance for secondary bending effects that are judged negligible, due to the reduced thicknesses of the involved plates. The lap joint considered has three rivet rows and undergoes a uniaxial fatigue load. When the cracks are short in comparison to plate thickness and hole diameters the allowance for nonlinear pin-rivet contact condition is provided. Crack faces are meshed using “discontinuous” quadratic elements and Stress Intensity Factors (SIFs) are calculated by the J-integral approach. The crack growth rate is calculated by the well-known Paris’ law, getting a satisfactory correlation between numerical and experimental findings (the latter available from literature).

Dual boundary element analysis of fatigue crack growth, interaction and linkup

Multiple-site and widespread fatigue damage have been an issue to the aircraft and construction industry for a long period. Structural components develop cracks at several locations which grow with crack paths that are difficult to predict. When two cracks approach one another, their stress fields influence each other leading to an enhancing or shielding effect which depends on the position and orientation of the cracks. Since there are no generalized analytical methods for predicting crack stress fields, simulation of multiple-crack growth is an important and challenging task which is still an evolving area of research.This paper describes a two-dimensional application of the dual boundary element method (DBEM) to the analysis of mixed-mode multiple-crack growth in linear elastic fracture mechanics, under fatigue loading. The crack-growth process is simulated with an incremental multiple-crack extension analysis based on the maximum principal stress criterion. For each increment of the analysis, in which crack extensions are modelled with new straight boundary elements, the DBEM is applied to perform a single-region stress analysis of the cracked structure and the J-integral is used to compute the stress intensity factors. The incremental analysis is based on a prediction–correction technique that defines, in each increment of the analysis, the direction and the extension of the multiple interacting cracks, thus taking into account the discreteness of the analysis and ensuring that the requirement of the path uniqueness is satisfied. Based on the ligament yield criterion which assumes that when the plastic zones of two adjacent cracks touch each other, the ligament between the cracks fails and the cracks coalesce, plates with multiple-site damage can be analysed. The fatigue life and residual strength of the structure are introduced as a post-processing procedure on the results of the multiple-crack growth. Results of this incremental analysis are presented for several geometries with multiple-site damage, demonstrating the accuracy and efficiency of the strategies adopted in the analysis.

Experiments and model predictions for fatigue crack propagation in riveted lap‐joints with multiple site damage

AbstractIn this paper, the growth of long fatigue cracks up to failure in aircraft components is studied. A deterministic model is presented, able to simulate the growth of fatigue through cracks located at rivet holes in lap‐joint panels. It also includes criteria to assess the link‐up of collinear adjacent cracks in a MSD scenario. To validate the model, a fatigue test campaign was carried out on riveted lap‐joint specimens in order to produce experimental crack growth and link‐up data. Accurate measurements of naturally occurred surface cracks were automatically performed by the Image Analysis technique, thus allowing the tests to run 24 h a day. The comparison between experimental tests and numerical simulations is good, thus confirming the model as a useful tool for the assessment of fatigue life of aircraft riveted joints.

Study on life and path of fatigue cracks in multiple site damage plates

This paper presents experimental and numerical study of the fatigue crack growth of hollowed pre-notched plates with multiple site damages (MSD). The numerical analyses were performed using finite element method. Experiments were carried out to validate the numerical results. Fatigue tests of aluminum sheets with MSD cracks were conducted to evaluate the effects of some parameters such as the thickness, hole diameter and central distance of the holes. The results show that the distance of the holes has greatest and size of the hole has little effects on the fatigue lives. Nucleation of cracks strongly depends on the thickness, distance and hole size.

Predicting the influence of discretely notched layers on fatigue crack growth in fibre metal laminates

This paper presents an analytical model for fatigue crack growth prediction in Fibre Metal Laminates (FMLs) containing discretely notched layers. This model serves as a precursor in the development of a simplified prediction methodology for modelling the effect of load redistribution on a single crack in FMLs containing Multiple-site Damage (MSD) scenario. The model mainly focuses on capturing the influence of load distribution around discretely notched layers on the growth behaviour of an adjacent crack in a FML panel. The utilized approach in the model is the use of linear elastic fracture mechanics (LEFM) in conjunction with the principle of superposition and displacement compatibility. The proposed model is also validated using experimental data.

Approximate method for stress intensity factors determination in case of multiple site damage

A simple and easy to use approximate procedure, for calculating stress intensity factors, was proposed. The procedure was developed based on existing solution for stress intensity factor in the case of two unequal cracks in an infinite plate subjected to remote uniform stress. The solution for this configuration was used for obtaining interaction effect coefficients which take into consideration the increase of stress intensity factor of analyzed crack tip due to interaction with existing adjacent crack. Accuracy and application of suggested procedure were verified through two different computer programs which are based on two different computational methods: finite element method (FEM) with singularity elements and extended finite element method (X-FEM). The analysis of the results has shown that a very good agreement between solutions was achieved, and that this method can provide stress intensity factors with acceptable accuracy.

Experimental Study on Local Plastic Collapse in a Plate Weakened by Two Collinear Cracks

Fracture and fatigue assessment of structures weakened by multiple site damage (MSD) currently represents a challenging problem. Here, we communicate the outcomes of an experimental study conducted on a plate weakened by two closely-spaced collinear cracks, which represents the simplest form of MSD. The experimental results are used to verify the predictions of a recently developed theoretical approach.

Local plastic collapse conditions for a plate weakened by two closely spaced collinear cracks

Fracture assessment of structures weakened with multiple site damage (MSD), such as two or more interacting cracks, currently represents a challenging problem. Strength calculations of structural components with MSD are still largely based on two-dimensional solutions for single (or isolated) cracks available in various texts and handbooks or derived from a simplified finite element analysis. Such simplifications could often result in non-conservative predictions. Therefore, there is a strong motivation for the development of more advanced modelling approaches, which could incorporate effects of the interaction between multiple cracks, thickness-induced constraints and other nonlinear phenomena. The primary purpose of this work is to develop and validate a simplified three-dimensional analytical model for the evaluation of the residual strength of two through-the-thickness cracks in a plate of finite thickness subjected to uni-axial loading.

A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness

ABSTRACTFatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.

P627: Is precautionary neurophysiological monitoring useful for beta-thalassemia patients?

P627: Is precautionary neurophysiological monitoring useful for beta-thalassemia patients?

Probabilistic Model of Multiple-Site Fatigue Damage of Riveting in Airframes

The probabilistic model of multiple-site damage of riveting in airframes is based on the statistical description of kinetics of the three fatigue fracture factors: time to crack initiation near the rivet hole, dimensional nonuniformity of flaws, and coalescence of counterpropagating cracks from neighboring holes. The probabilistic measure of these factors is used to determine time-dependent performance characteristics of a rivet joint: no-failure operation function and lifetime distribution function. The limiting state of the structure comes if at least one of the ligaments between the holes is fractured.

On the Development of a Prediction Methodology for Crack Growth in Fibre Metal Laminates with MSD Scenario

Multiple-site Damage (MSD) is a dangerous scenario for aircraft structures due to the interaction of adjacent cracks in one structural element. Despite their excellent fatigue crack growth resistance, Fibre Metal Laminates (FMLs) may also encounter this damage scenario. However, only few studies on fatigue crack growth in presence of MSD in FMLs has been reported. An overview of the relevant methods for predicting the crack propagation properties of MSD in FMLs is given and discussed in this paper. The fatigue crack growth of MSD in FMLs was experimentally studied and is reported in this paper. A new analytical methodology, based on the superposition principle and displacement compatibility method, is proposed.

Fatigue and Damage Tolerance of Aging Airplane Structures

The paper highlights key questions in ensuring safe operation of aging civil\transport aircraft in Russia. Presented is the analysis of current requirements to fatigue, fail-safe and damage tolerance for transport aircraft structures stated in FARs, Advisory Circulars (UAS) and Russian Airworthiness Regulations\ AR IAC Aviation Regulations. The paper gives the design goals and actual service life values\ service years of aging aircraft fleet and data on full-scaled fatigue tests, together with methods and approaches to ensure safe operation of aircraft structures in case of multiple site damages, corrosion and materials degradation for Russian aging fleet.