Finite Element Alternating Method Research Articles

The Use of High-Performance Fatigue Mechanics and theExtended Kalman / Particle Filters, for Diagnostics andPrognostics of Aircraft Structures

In this paper, we propose an approach for diagnostics and prognostics of damaged aircraft structures, by combing high-performance fatigue mechanics with filtering theories. Fast & accurate deterministic analyses of fatigue crack prop- agations are carried out, by using the Finite Element Alternating Method (FEAM) for computing SIFs, and by using the newly developed Moving Least Squares (MLS) law for computing fatigue crack growth rates. Such algorithms for sim- ulating fatigue crack propagations are embedded in the computer program Safe- Flaw, which is called upon as a subroutine within the probabilistic framework of filter theories. Both the extended Kalman as well as particle filters are applied in this study, to obtain the statistically optimal and semi-optimal estimates of crack lengths, from a series of noisy measurements of crack-lengths over time. For the specific problem, a simple modification to the particle filter, which can drastically reduce the computational burden, is also proposed. Based on the results of such di- agnostic analyses, the prognostics of aerospace structures are thereafter achieved, to estimate the probabilistic distribution of the remaining useful life. By using a simple example of a single-crack near a fastener hole, we demonstrate the concept and effectiveness of the proposed framework. This paper thus forms the scientific foundation for the recently proposed concepts of VRAMS (Virtual Risk-Informed Agile Maneuver Sustainment) and Digital Twins of aerospace vehicles.

노즐 이종금속용접부의 내면 보수용접부에서 수치해석법을 이용한 PWSCC 균열성장해석

In this paper, crack propagation analyses in the inner diameter (ID) repair weld of the dissimilar metal weldment of a nozzle were performed using a finite element alternating method (FEAM). To calculate the theoretical solution for the crack tip stress intensity factor, a weak type singular integral equation consisted of crack surface traction and dislocation density function was constructed and solved in conjunction with the FEAM. A two-dimensional axisymmetric finite element nozzle model was prepared and ID repair welding was simulated. An initial crack, 10% depth of weld thickness, was assumed and crack propagation trajectory from the initial crack to the 75% depth of thickness was calculated using the FEAM. Crack growth versus time curve was also calculated and compared with the curves obtained from ASME code method. With the method constructed in this paper, crack propagation trajectory and crack growth time were calculated automatically and effectively.

수치해석방법을 이용한 이종금속용접부에서의 균열성장해석

In this paper crack propagation analyses in the dissimilar metal weldment of a nozzle were performed using a finite element alternating method (FEAM). A two-dimensional axisymmetric finite element nozzle model was prepared and welding simulation including the thermal heat transfer analysis and the thermal stress analysis was performed. Initial cracks were inserted at weld and heat affected zone in the finite element model which has welding residual stress distribution obtained from the welding simulation. To calculate crack propagation trajectories of these cracks, a new fatigue crack evaluation module was developed in addition to the previous FEAM program. With the new FEAM fatigue crack evaluation module, crack propagation trajectory and crack growth time were calculated automatically and effectively.

Elasto-Plastic Analysis of 3-D Inner Cracks Using the Finite Element Alternating Method

The finite element alternating method (FEAM) was extended to obtain fracture mechanics parameters and elasto-plastic stress fields for 3-D inner cracks. For solving a problem of a 3-D finite body with cracks, the FEAM alternates independently the finite element method (FEM) solution for the uncracked body and the solution for the crack in an infinite body. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. For elasto-plastic numerical analysis, the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri were used after modification. The extended FEAM was examined through comparing with the results of commercial FEM program for several example 3-D crack problems.

Finite Element Alternating Method for Interacting Surface Cracks

The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, can derive the stress intensity factor (SIF) of surface cracks by using the FEA results for an uncracked body. In the present study, the FEAM was applied to evaluations of SIF for noncoplanar multiple surface cracks. The SIF was evaluated for two surface cracks of dissimilar size, and three crack of the same size. The results suggested that the interaction is greatly affected by the relative crack size and negligible when the difference in the crack size is large enough, and the interaction can be evaluated by taking into account the adjacent cracks even if there are many cracks around them. Finally, the crack growth simulations were conducted and a possibility of the direct evaluation of influence of interaction between adjacent crack without using the combination rules was revealed.

Structural integrity evaluation for interference-fit flywheels in reactor coolant pumps of nuclear power plants

This study is concerned with structural integrity evaluations for the interference-fit flywheels in reactor coolant pumps (RCPs) of nuclear power plants. Stresses in the flywheel due to the shrinkage loads and centrifugal loads at the RCP normal operation speed, design overspeed and joint-release speed are obtained using the finite element method (FEM), where release of the deformation-controlled stresses as a result of structural interactions during rotation is considered. Fracture mechanics evaluations for a series of cracks assumed to exist in the flywheel are conducted, considering ductile (fatigue) and non-ductile fracture, and stress intensity factors are obtained for the cracks using the finite element alternating method (FEAM). From analysis results, it is found that fatigue crack growth rates calculated are negligible for smaller cracks. Meanwhile, the material resistance to non-ductile fracture in terms of the critical stress intensity factor(K IC) and the nil-ductility transition reference temperature RTinNDT are governing factors for larger cracks.

Analysis of Surface Crack in Cylinder by Finite Element Alternating Method

The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, is used for evaluating the stress intensity factor (SIF) of surface cracks in a cylinder. The major advantage of this method is that the SIF can be calculated by using the FEA results for an uncracked body. A newly developed system allows the FEAM to be performed by a simple method, which consists of the conventional FEA for an uncracked body and a subroutine for the FEAM alternating procedure. It is shown that the system can derive the precise SIF of circumferential, longitudinal, and inclined surface cracks in a cylinder. The crack growth predictions are performed for an inclined crack and projected longitudinal and circumferential crack in a cylinder. The results suggests that the crack characterizing procedure prescribed in Sec. XI may cause an unconservative evaluation in the crack growth prediction, and that the FEAM is valid for complex problems, to which the SIF evaluation by the FEA cannot be adopted easily.

직교이방성 판 내의 다중 곡선균열 해석

The interactions between curved cracks are examined in an orthotropic plate and the effects of rectilinear anisotropy on the stress intensity factors are analyzed. The finite element alternating method (FEAM) is used in this study to get the stress intensity factors for the multiple curved cracks. To obtain analytical solutions, which is necessary in FEAM, the curved cracks are modeled as continuous distributions of dislocations, and integral equations are formulated for unknown dislocation density functions to satisfy the given resultant forces on the crack surfaces. Several basic problems are solved to verify the accuracy and efficiency of the proposed method and it can be found that present results show good agreements with the previously published results.

Stress intensity factors for circular hole and inclusion using finite element alternating method

A centre cracked plate subjected to remote tensile and shear loading is considered for the analysis. Effect of circular hole and influence of shrunk fit inclusion on stress intensity factors are studied. Multiply connected domain boundary value problem is solved using finite element alternating method (FEAM). Parametric studies involving drilled hole/inclusion sizes and locations are investigated. Energy release rates evaluated using the stress field obtained by FEAM are in good agreement with other methods. The optimum location in reducing the stress intensity factor with hole/inclusion is obtained and located at a distance 20% of semi-crack length from crack tip on the side opposite the ligament for Mode-I loading and it is also observed that the location is almost invariant of hole sizes. For Mode-II loading, the optimum location for the hole is located at a distance about 23% of semi-crack length from the middle of the crack along the transverse direction.

Modeling of weld residual stresses in core shroud structures

This paper presents a computational model to predict residual stresses in a girth weld (H4) of a BWR core shroud. The H4 weld is a multi-pass submerged-arc weld that joins two type 304 austenitic stainless steel cylinders. An axisymmetric solid element model was used to characterize the detailed evolution of residual stresses in the H4 weld. In the analysis, a series of advanced weld modeling techniques were used to address some specific welding-related issues, such as material melting/re-melting and history annihilation. In addition, a 3-D shell element analysis was performed to quantify specimen removal effects on residual stress measurements based on a sub-structural specimen from a core shroud. The predicted residual stresses in the H4 weld were used as the crack driving force for the subsequent analysis of stress corrosion cracking in the H4 weld. The crack growth behavior was investigated using an advanced finite element alternating method (FEAM). Stress intensity factors were calculated for both axisymmetric circumferential (360°) and circumferential surface cracks. The analysis results obtained from these studies shed light on the residual stress characteristics in core shroud weldments and the effects of residual stresses on stress corrosion cracking behavior.

An efficient variable amplitude loading scheme for three-dimensional fatigue crack

The finite element alternating method (FEAM) is an extremely useful and efficient scheme for the accurate calculation of stress intensity factors in complex three dimensional structures. This approach involves the combination of an analytical solution for a crack in an infinite body with a finite element solution for the uncracked component. Previously a three-dimensional fatigue crack growth algorithm has been incorporated into the alternating method for the case of constant amplitude loading. The major accomplishment outlined in this paper is the implementation of an additional numerical scheme for the more difficult case of variable amplitude loading. Test cases, with an emphasis on components taken from the aerospace industry, are used to validate the revised alternating method computer program. Results reveal excellent levels of correlation with existing packages and highlight the suitability of the finite element alternating method for fatigue crack growth analyses in a wide variety of components such as aircraft components, pipelines, offshore structures, pressure vessels, ships, etc.

Applications of the three dimensional finite element alternating method

This paper describes some recent applications of the three dimensional finite element alternating method (FEAM). The problems solved involve surface flaws in various types of structure. They illustrate how the FEAM can be used to analyze problems involving mechanical and thermal loads, residual stresses, bonded to composite patch repairs, and fatigue.

Analysis of cracks in aging aircraft structures, with and without composite-patch repairs

In this paper, the problems of composite-patch repair of (i) center and edge-cracked panels loaded in the far-field; and (ii) cracks emanating from pin-loaded fastener holes, are examined in thorough detail. The effects of various non-dimensional design parameters on the reduction in the stress-intensity factors near the crack-tip are determined, and are presented in the form of design charts. Both analytical and numerical methods are employed in this study. In the analytical method, the cracked metallic plate was considered to be infinitely large, and the composite patch was modeled as a long orthotropic strip of finite height (in the direction perpendicular to the crack axis). Next, by using the Finite Element Alternating Method (FEAM), a more general analysis capability that can treat arbitrary shapes of the cracked metallic sheet, as well as of the composite patches, is developed. This general FEAM is applied to: (i) composite patch repairs of cracks emanating from loaded fastener holes (the MSD problem); (ii) composite patch repairs of semi-elliptical surface flaws in thick plates; and (iii) composite patch repairs of quarter-elliptical surface flaws emanating from fastener holes. Problem (i) is two-dimensional in nature while problems (ii) and (iii) are fully three-dimensional. In all these cases, the effects of various design parameters on the crack-tip (front) stress-intensity factors are fully discussed.

A finite-element alternating method for two-dimensional mixed-mode crack configurations

A finite-element alternating method (FEAM) is presented for two dimensional mixed-mode cracked problems. An analytical solution is presented for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate. This analytical solution is used as the fundamental solution in the alternating method. For the numerical part of the method the finite-element method is used. For problems of edge cracks emanating from internal boundaries, the method is modified to account for the effect of fictitious crack tip. This modification, the origin-shifting method, is explained in detail. The FEAM is applied to a variety of mixed-mode crack problems with different configurations and loadings to assess the validity of the method. The method gave accurate stress-intensity factors with minimal computing effort. As the method needs to model only the uncracked body, finite-element models with large degrees of freedom are not required and therefore, the method has been implemented on personal computers.

Stress intensity factors for coalescing and single corner flaws along a hole bore in a plate

The objective of this paper is to describe the effects of crack interaction on stress intensity factors for two symmetric coplanar corner flaws located along a hole bore. This numerical analysis employes the Finite Element-Alternating Method to determine Mode I stress intensity factors for single and coalescing corner flaws. Using single flaw stress intensity factors as a reference, analysis of crack size and shape effects on K I for coalescing corner flaws indicates the stress intensity factor for crack points along the hole bore increases as the crack tip separation distance decreases. Interaction effects are not experienced by hole bore crack points when the crack tip separation distance is equal to or greater than half of the largest corner flaw dimension.

Analytical solution for embedded elliptical cracks, and finite element alternating method for elliptical surface cracks, subjected to arbitrary loadings

The complete solution for an embedded elliptical crack in an infinite solid and subjected to arbitrary tractions on the crack surface is rederived from Vijayakumar and Atluri's general solution procedure. The general procedure for evaluating the necessary elliptic integrals in the generalized solution for elliptical crack is also derived in this paper. The generalized solution is employed in the Schwartz alternating technique in conjunction with the finite element method. This finite element-alternating method gives an inexpensive way to evaluate accurate stress intensity factors for embedded or elliptical cracks in engineering structural components.

Stress Intensity Factors for Corner Cracked Holes Under General Loading Conditions

A linear elastic analysis is conducted with the finite element-alternating method for quarter-elliptical corner cracks located at fastener holes. Mode-one stress intensity factors are presented along the crack periphery for a crack face pressure loading which can be represented by a third order polynomial. Results are also given for remote tensile loading applied perpendicular to the crack plane. Two example problems describe application of the polynomial crack face pressure solutions to other loading configurations through a simple linear superposition.

Crack face pressure loading of semielliptical cracks located along the bore of a hole

The finite element-alternating method is used to obtain Mode I stress intensity factors for semielliptical surface cracks centered along the bore of a hole in a large plate of finite thickness. The variation in stress intensity factor around the crack perimeter is provided for two loading configurations: remote uniaxial tension and a crack face pressure described by a third order polynomial. It is suggested that the tabulated solutions for the crack face pressure loading represent “general” results which can be used with linear superposition to compute stress intensity factors for many other practical loading configurations. Two example problems describe application of the superposition procedure with the crack face pressure results.

Part-Elliptical Cracks Emanating From Open and Loaded Holes in Plates

A linear elastic analysis using the finite element-alternating method is conducted for problems of single semi-elliptical and double quarter-elliptical cracks near fastener holes. Mode-one stress intensity factors are presented along the crack periphery for cases of open and loaded holes and crack opening displacements are calculated. Results are shown for a variety of crack geometries and loading conditions and for two ratios of hole diameter to plate thickness.

Quarter Elliptical Cracks Emanating From Holes in Plates

The finite element-alternating method, a linear elastic solution technique, is refined and applied to problems of quarter-elliptical cracks in irregular bodies. The method involves the iterative superposition of a finite element solution for stresses in an unflawed body and an analytic solution for stresses in an infinite solid containing a flat elliptical crack. Mode-one stress intensity factors are presented along the periphery of quarter-elliptical cracks emanating from open fastener holes in flat plates. Results are shown for a variety of crack geometries and two hole-diameter to plate-thickness ratios. Comparisons are made with experimental results of other authors.