Multiple crack growth simulation for lap-joints based on three-dimensional finite element analysis

Fibre metal laminates (FMLs)were developed and refined for their superior crack growth resistance and critical damage size that complimented the damage tolerance design philosophy utilized in the aerospace sector. Robust damage tolerance tools have been developed for FMLs. However, they tend to focus on the evolution of an isolated crack. There is also a risk that they will be invalidated overtime as a result of the occurrence of multiple cracks within one structure (one form of widespread fatigue damage). To combat another failure due to widespread fatigue damage, the airworthiness regulations were revised to include the concept of a Limit of Validity (LOV) of the damage tolerance analyses. Consequently, it is crucial to examine fatigue crack growth (FCG) in FMLs containing Multiple-site Damage (MSD) cracks despite their superior damage tolerance merits. The focus of this thesis therefore is to analyse MSD crack growth in FML structures. Mechanically fastened FML joints are potentially weak structural designs that are susceptible to MSD due to the stress rising contributors such as secondary bending, pin loading and open holes subjected to bypass loading. In this thesis, predictive models were developed to address several key mechanisms that affect FCG in FML joints containing MSD, and validated with corresponding experimental work. Then the predictive models were systematically integrated and implemented for FML joints. It was identified that the nature of fatigue in FMLs led to the load redistribution mechanism as the key factor to be modelled in predicting MSD growth in FMLs. The structural stiffness reductions caused by the presence of multiple cracks resulted in load redistribution from the other cracks to the single crack to be analysed, exacerbating the total stress intensity factor (SIF) experienced at the tips of the single crack, increasing the crack growth rate (CGR). The load redistribution mechanism was first substantiated by investigating FCG in FMLs containing discretely notched layers. The prediction model fairly captured the load redistribution mechanism by idealizing the notches in the metal layers as removals of metal strips. The crack acceleration over a major portion of the crack propagation was well predicted with the model; however, the surge in CGR over roughly 3 mm crack length prior to the link-up was underestimated since the plasticity interaction was not accounted for. The capability of modelling the load redistribution mechanism allows the states of multiple cracks to be analysed one by one. It was found that the load redistribution could not be symmetric for every crack and non-symmetric crack configurations therefore developed in FMLs with finite width. Hence, non-symmetric crack growth in FMLs was also investigated in this work. It was also found that both crack tip non-symmetry and delamination shape non-symmetry affected the crack growth in the metal layers. The model for non-symmetric crack growth in FMLs was validated with experimental data. Good correlation was observed. The model for MSD growth in FML panels sequentially analyses each crack state. The other cracks are idealized as removals of metal strips when analyzing the state of a single crack. This non-physical idealization of the cracks led to consistently conservative prediction results in comparison with the test data. Nevertheless, the prediction model provided good predictions of the evolution of MSD configurations. Additionally, it was proven that a very non-conservative predicted fatigue life could be obtained if the load redistribution mechanism was not considered. The effects of pin loading on FCG in FMLs were also investigated. The test data showed very rapid growth of the crack in the vicinity of the pin loading. The CGR decreased with increasing crack length. The model applied the principle of superposition to split the non-symmetric tension-pin loading into simpler tensile loading and a pair of point loads acting on the crack flanks. The SIFs for the simpler loading cases were derived and superposed to obtain the total SIF as a result of the tension-pin loading. The predicted CGR and equivalent delamination shape correlated with the measurements very well, but the model failed to predict the crack path and the measured delamination shape which were trivial issues for this work. The relevance and applicability of the developed models in this thesis for predicting the MSD behaviour in mechanically fastened FML joints was examined. The predicted results captured the trends of the measured CGR in FML joints containing MSD cracks, although there were some discrepancies. The discrepancies are mainly due to the two major shortcomings of the model which are neglecting the load redistribution over multiple fastener rows and neglecting the effects of secondary bending stresses.

As part of the structural integrity research of the National Aging Aircraft Research Program, a comprehensive study on multiple-site damage (MSD) initiation and growth in a pristine lap-joint fuselage panel has been conducted. The curved stiffened fuselage panel was tested at the Full-Scale Aircraft Structural Test Evaluation and Research (FASTER) facility located at the Federal Aviation Administration William J. Hughes Technical Center. A strain survey test was conducted to verify proper load application. The panel was then subjected to a fatigue test with constant-amplitude cyclic loading. The applied loading spectrum included underload marker cycles so that crack growth history could be reconstructed from post-test fractographic examinations. Crack formation and growth were monitored via nondestructive and high-magnification visual inspections. Strain gage measurements recorded during the strain survey tests indicated that the inner surface of the skin along the upper rivet row of the lap joint experienced high tensile stresses due to local bending. During the fatigue loading, cracks were detected by eddy-current inspections at multiple rivet holes along the upper rivet row. Through- thickness cracks were detected visually after about 80% of the fatigue life. Once MSD cracks from two adjacent rivet holes linked up, there was a quick deterioration in the structural integrity of the lap joint. The linkup resulted in a 2.87" (72.9-mm) lead fatigue crack that rapidly propagated across 12 rivet holes and crossed over into the next skin bay, at which stage the fatigue test was terminated. A post-fatigue residual strength test was then conducted by loading the panel quasi-statically up to final failure. The panel failed catastrophically when the crack extended instantaneously across three additional bays. Post-test fractographic examinations of the fracture surfaces in the lap joint of the fuselage panel were conducted to characterize subsurface crack initiation and growth. Results showed evidence of fretting damage and crack initiation at multiple locations near the rivet holes along the faying surface of the skin. The subsurface cracks grew significantly along the faying surface before reaching the outer surface of the skin, forming elliptical crack fronts. A finite element model (FE) of the panel was constructed and geometrically-nonlinear analyses conducted to determine strain distribution under the applied loads. The FE model was validated by comparing the analysis results with the strain gage measurements recorded during the strain survey test. The validated FE model was then used to determine stress-intensity factors at the crack tips. Stress-intensity factor results indicated that crack growth in the lap joint was under mixed-mode; however, the opening-mode stress intensity factor was dominant. The stress-intensity factors computed from the FE analysis were used to conduct cycle-by-cycle integration of fatigue crack growth. In the cycle-by-cycle integration, the NASGRO crack growth model was used with its parameters selected to account for the effects of plasticity-induced crack closure and the test environment on crack growth rate. Fatigue crack growth predictions from cycle-by-cycle computation were in good agreement with the experimental measured crack growth data. The results of the study provide key insights into the natural development and growth of MSD cracks in the pristine lap joint. The data provided by the study represent a valuable source for the evaluation and validation of analytical methodologies used for predicting MSD crack initiation and growth.

Stiffened panels are widely used in aircraft wing and ftiselage structures. As a result of the cyclic nature of the loads associated with each flight, and material and manufacturing defects it is known that wide spread fatigue cracks may develop particularly around high stress regions such as fastener holes. This simultaneous development of relatively small fatigue cracks at multiple sites in the same structural element can give rise to their joining to form one large crack. This main crack, resulting from the multiple site damage (MSD) may cause immediate and complete failure of the structure.The effect of multiple site damage on the fracture strength of a stiffened sheet is examined using the Strip Yield Model of a crack. This model is relatively simple to apply and has contributed significantly to the fracture analysis of unstiffened structures and, to a more limited extent, to the analysis of stiffened structures. Following previous developments the MSD is represented by a discontinuous strip yield zone ahead of the main crack. The solution is extended in the present work to a crack in a stiffened sheet and results are determined for the crack tip opening displacement and the strip yield zone length for a crack in a typical MSD distribution. The model is used to compare the effect of MSD on the main crack for these structural variables. INTRODUCTION The Displacement Compatibility Method (DCM), has been used extensively (see citations in ref 1) for the analysis of cracked, reinforced sheets typical of those used in the aircraft industry. Applications of the DCM have proved both efficient and versatile for the determination of attachment forces and stress intensity factors in stiffened sheet structures. For high strength materials it is possible to use the principles of Linear Elastic Fracture Mechanics (LEFM) and to base the analysis on the Stress Intensity Factor of the crack. For medium and low strength materials where yielding at the crack tip may exceed the limits required for LEFM to apply it is necessary to use the principles of Non-linear Fracture Mechanics (NLFM). One method of doing this is to use a Strip Yield Zone (SYZ) model of the crack for which the fracture analysis is based on the Crack Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 566 Localized Damage Tip Opening Displacement (CTOD) or Energy Release Rate of the crack. The SYZ model [2] has been used in the analysis of reinforced sheets structures [35]. This previous work was restricted the a single lead crack in the stiffened sheet. The model has also been extended to the analysis of multiple cracks [6] in which the interaction between the multiple cracks, such as occurs in MSD, was accounted for by using the displacement and stress field for the single crack together with the crack line Greens Function for a single crack in a Schwarz alternating process. In the present work the MSD is represented by introducing regions of zero traction into the strip yield zone between which are regions of uniform traction having a magnitude equal to the yield strength of the material. This representation of the MSD enables the single SYZ model to be directly entended to take account of the effect of multiple site damage by having the strip yield zone distributed discontinuously. Each gap in the yield zone tractions corresponds to the region of damage and each junction corresponds to the yielded ligament between the damage sites. A similar approach, based on a dislocation model of the MSD, has been used [7]. This model was used to analyze the effect of MSD on a lead crack in an unstiffened sheet and then create a modified single SYZ model for the analysis of stiffened sheets. In the present work the MSD is represented as a discontinuous distribution of tractions for both the unstiffened and stiffened sheet. THEORETICAL FORMULATION AND SOLUTION OF EQUATIONS The analysis is based on the complex variable technique due to Muskhelishvili [8] which states that the stress/displacement state within a multiply connected, two dimensional body subjected to in-plane loading may be completely specified in terms of two complex stress functions which can be written in series form. The system equations are formed by satisfying equilibrium of forces at, and compatibility of displacements between the attachment points, and by satisfying the strip yield crack condition that the stresses be bounded at the tip of the yield zone (Dugdale Condition). The system equations are solved for the unknown distribution of attachment forces and the unknown ratio of the sheet stress to the yield stress of the sheet material.The CTOD of the crack is determined from the attachment forces and the applied stress ratio for a specified distribution of MSD in the yield zone. CONFIGURATION STUDIED The configuration to be studied in the present work is shown in Fig. 1. It consists of an infinite sheet containing a lead crack of length 2a centered at the origin of the coordinates (x = 0,jy = 0). The lead crack has a series of of collinear cracks symmetrically located on either side of each tip which are joined by ligaments at the yield stress of the material the outer ones of which have strip yield zones at their tip. The region of MSD and the outer tip yield zones extend a distance s from the tip of the lead crack. The collinear cracks, which represent the MSD, are located under doubly riveted stiffeners with a stiffener across the Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 Localized Damage 567 centre of the lead crack. The sheet is subjected to a uniform stress a perpendicular to the crack line. Fig. 1 Lead crack and Multiple Site Damage in a Uniformly Stressed Stiffened Sheet In general the sheet is reinforced by arbitrarily spaced stiffeners parallel to the yaxis. The stiffeners are attached to the sheet at discrete points symmetrically either side of the x-axis. The first attachment point is PQ from the x axis and all the other attachment points are a distance p apart . The attachment points are assumed to be represented by localised forces at the center of a rigid insert of diameter d. The sheet has a modulus of elasticity E, Poisson's ratio v and thickness t. The Young's modulus and area of each stiffener is E$ and Aj respectively. The effect of the in-plane and out of plane bending stiffness of each stiffener is assumed negligible compared to its axial stiffness, In the present work only a symmetrical distribution of two equal length MSD cracks, each side of the lead crack, is considered although the formulation allows for an arbitrary length and position of the MSD cracks It is also assumed that the center of the MSD cracks are symmetrically located across the center line of the attachments, Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533 568 Localized Damage The parameters used for modelling the stiffened sheet are given in Table 1 and represent a typical aircraft stiffened structure [3]. The stiffeners were attached at 15 points either side of the crackline along each rivet line. Parameter Sheet Modulus E Sheet Yield Strength <jy Stiff ener Modulus E,. Sheet Poissions Ratio u First Rivet Pitch p. Rivet Pitch p Sheet Thickness t Stiffener Area A Rivet Diameter d Attachment Line Spacing h Stiffener pitch b Lead Crack Length a MSD Crack Size d, and d, Magnitude 73.8 GVm ' 386 MVm 74.5 GNm* 0.3 38.1 mm 38.1 mm 18.1 mm 1710mm' 8 mm 58.4mm 185.4mm 148.2 mm 10 mm Table 1. Dimensions and Material properties for the stiffened sheet containing MSD COMPARISION WITH KNOWN SOLUTIONS Table 2 shows the crack tip opening displacement for the SYZ model normalised with that for a SYZ crack in an unstiffened sheet. The SYZ crack is modeled as a single crack (^ = = 0) and by simulating this single crack by modelling the SYZ with a longer strip yield zone and eliminating part of the zone with contiguous MSD regions to give the same strip yield length as the single crack model. It can be seen that these two models give identical results as is to be expected. a a + s 0.1 0.5 0.9 Unstiffened Sheet

Many military aircraft have reached or exceeded their original design life, and have been subject to significant increase in maintenance and repair cost due to multiple site damage (MSD). In order to assessing the effects of MSD on the structural integrity of aircraft lap joints, the wing lap joint of certain model military aircraft with MSD was analyzed using special code FRANC2D/L. The rivet holes along the top row of the outer skin of lap joint were considered as the independent structural unit for the simulated MSD cracks. The stress intensity factors (SIFs) at each crack tip with different distribution loads at the rivet holes were computed and show that the analysis results have good coherence with the available literature data. It also shows that the SIF at each crack tip s a function of crack length can be calculated by the crack growth simulation capability of FRANC2D/L. The SIF values are not sensitive to the rivet load distribution manner, which has seriously influence on MSD crack growth direction. Rivet loading can be best molded quadratic load distribution over one half of rivet hole relative to uniform load distribution and point load. As a result of this analysis, it is postulated that for MSD in aircraft lap joints, compliance measurements may provide a useful tool for assessing the structural integrity of the lap joints.

Multiple site damage (MSD) cracks are small fatigue cracks that may accumulate at the sides of highly loaded holes in aging aircraft structures. The presence of MSD cracks can drastically reduce the residual strength of fuselage panels. In this paper, artificial neural networks (ANN) modeling is used for predicting the residual strength of aluminum panels with MSD cracks. Experimental data that include 147 unique configurations of aluminum panels with MSD cracks are used. The experimental dataset includes three different aluminum alloys (2024-T3, 2524-T3, and 7075-T6), four different test panel configurations (unstiffened, stiffened, stiffened with a broken middle stiffener, and bolted lap-joints), many different panel widths and thicknesses, and the sizes of the lead and MSD cracks. The results presented in this paper demonstrate that a single ANN model can predict the residual strength for all materials and configurations with high accuracy. Specifically, the overall mean absolute error for the ANN model predictions is 3.82%. Furthermore, the ANN model residual strength predictions are compared to those obtained using the most accurate semi-analytical and computational approaches from the literature. The ANN model predictions are found to be at the same accuracy level of these approaches, and they even outperform the other approaches for many configurations.

On the through-thickness crack with a curve front in center-cracked tension specimens

Accurate stress intensity solutions for multiple site damage (MSD) cracks in riveted stiffened panels are difficult to determine due to geometric complexity along with variations in rivet load transfer and corrosion, especially the interaction of MSD cracks. A methodology was proposed for efficiently depicting rivet in stiffened panel using finite elements. Rivet material properties were determined based on an empirical force-displacement relationship, for highly refined rivet model as well as for idealized spring element representations of rivets. Parametric studies of panels with a middle crack and a central stiffener indicate that rivets can provide comparable load transfer and relative displacement if the rivets closed to the crack are explicit modeled. Using idealized combination of explicitly and spring element representations of rivets, the stress intensity factors (SIFs) for uncorroded and corroded one-bay stiffened panels were predicted. The results show that the effect of MSD and thinning of the sheet is to increase substantially SIFs values compare to that of a single crack without corrosion. But the SIF is insensitive to corrosion of stiffener. The particular rivet material has relatively little effect on SIF values, while the rivet diameter has a significant effect.

As the commercial and military aircraft fleets continue to age, there is a growing concern that multiple-site damage (MSD) can compromise structural integrity. Multiple site damage is the simultaneous occurrence of many small cracks at independent structural locations, and is the natural result of fatigue, corrosion, fretting and other possible damage mechanisms. These MSD cracks may linkup and form a fatigue lead crack of critical length. The presence of MSD also reduces the structure's ability to withstand longer cracks. The objective of the current study is to assess, both experimentally and analytically, MSD formation and growth in the lap joint of curved panels removed from a retired aircraft. A Boeing 727-232 airplane owned and operated by Delta Air Lines, and retired at its design service goal, was selected for the study. Two panels removed from the left-hand side of the fuselage crown, near stringer 4L, were subjected to extended fatigue testing using the Full-Scale Aircraft Structural Test Evaluation and Research (FASTER) facility located at the Federal Aviation Administration (FAA) William J. Hughes Technical Center. The state of MSD was continuously assessed using several nondestructive inspection (NDI) methods. Damage to the load attachment points of the first panel resulted in termination of the fatigue test at 43,500 fatigue cycles, before cracks had developed in the lap joint. The fatigue test for the second panel was initially conducted under simulated in-service loading conditions for 120,000 cycles, and no cracks were detected in the skin of the panel test section. Artificial damage was then introduced into the panel at selected rivets in the critical (lower) rivet row, and the fatigue loads were increased. Visually detectable crack growth from the artificial notches was first seen after 133,000 cycles. The resulting lead crack grew along the lower rivet row, eventually forming an 11.8" long unstable crack after 141,771 cycles, at which point the test was terminated Posttest fractograpic examinations of the crack surfaces were conducted, revealing the presence of subsurface MSD at the critical rivet row of the lap joint. Special attention was also given to the stringer clips that attach the fuselage frames to the stringers, since they also experienced cracking during the fatigue tests. The performance of the different conventional and emerging NDI methods was also assessed, and some of the emerging NDI methods were quite effective in detecting and measuring the length of subsurface cracks. Delta Air Lines conducted a separate destructive investigation on the state of damage along the right-hand side of the fuselage, near stringer 4R. A comparison of these two studies showed that the lap joint on the left hand-side of the aircraft, along stringer 4L, had better fatigue life than the one on the opposite side, along stringer 4R. The cause of the difference in fatigue life was investigated by close examination of the rivet installation qualities, and was found to be a result of better rivet installation along the lap joint at stringer 4L. Finite element models for both the skin and substructures of the panels were developed and geometrically nonlinear finite element analyses were conducted to verify the loading conditions and to determine near-field parameters governing MSD initiation and growth. Fatigue crack growth predictions based on the NASGRO equation were in good agreement with the experimental crack growth data for through-the-thickness cracks. For subsurface cracks, simulation of crack growth was found to correlate better with fractography data when an empirical crack growth model was used. The results of the study contribute to the understanding of the initiation and growth of MSD in the inner skin layer of a lap joint, and provide valuable data for the evaluation and validation of analytical methodologies to predict MSD initiation and growth and a better understanding on the effect of manufacturing quality on damage accumulation along the lap joint.

The shape of a surface crack in a plate based on a given stress intensity factor distribution

The evaluation of stress intensity factors (SIFs) for cracks in mechanically fastened joints is one of the central issues in a damage tolerance analysis. Accurate stress intensity solutions may be difficult to determine due to geometric complexity along with variations in fastener load transfer and fastener interference and material thickness because of corrosion. Detailed finite element models that include specific aspects of fastener for lap joints analysis, but such representations are often impractical for large lap joints involving many fasteners. In order to reduce the number of degrees of freedom in a particular model, a methodology was implemented that efficiently depicts mechanical fasteners in lap joints using finite elements. Uncorroded and corroded lap joints with three crack scenarios were studied by the computationally efficient model. The effects of pillowing corrosion and fastener interference were also included in the model. The results show that the effect of MSD and thinning of the material is to increase substantially stress intensity factors (SIFs) values compare to that of a single crack without corrosion. For a given cyclic stress range, SIF decreases with increasing rivet interference level. This is particularly true for shorter crack lengths. SIF values for the longer crack are not sensitive to the length of shorter crack on the opposite side of the rivet hole. The effects of corrosion pillowing cause SIF values on the faying surface to be larger than those on the opposing surface, and the crack front distorts from the straight front. Moreover, stresses on the faying surface may exceed the yield strength of the material.

This article contains empirical equations for the K I , K II , and K III stress intensity factors (SIFs) for semi-elliptical surface cracks for brittle materials subjected to rolling contact fatigue (RCF) as a function of the contact patch diameter, angle of crack to the surface, max pressure, position along the crack front, and aspect ratio of the crack. The equations were developed from SIFs calculated by parametric three-dimensional (3D) finite element analysis (FEA) for a range of contact patch radii (1b, 2b, and 3b) and angles of the crack to the surface (0°, 45°, and 60°). Calculating mixed-mode SIFs for surface cracks subject to RCF using 3D FEA is computationally complex because of extreme mesh refinement required at multiple levels to capture steep stress gradients. The comprehensive empirical curve fits presented are accurate to within 0.5% of FE simulations and are useful for component design where contact-initiated surface fatigue damage is important such as in gears, roller bearings, and railway wheels. The results are of particular relevance to hybrid silicon nitride ball bearings, which are susceptible to failure from fatigue spalls emanating from preexisting surface cracks, due to crack growth driven by RCF (G. Levesque and N. K. Arakere, An investigation of partial cone cracks in silicon nitride balls. International Journal of Solids and Structures, 2008, 45:6301–6315).

Thermal buckling of steel tube using finite element method

3D simulation of deflection basin of pavements under high-speed moving loads

A commonly used design criterion for predicting the onset of crack link up at a multiple site damage (MSD) is when the sum of the plastic zones of two adjacent cracks is equal to the remaining ligament (Swift 1985, Broek et al 1994). The collapse load predicted by this criterion, however, will differ with the analytical plastic zone and in general, will yield a nonconservative load. Recently, Pyo et al (1997) have shown that the T* integral, which was designed for elastic-plastic fracture mechanics, can predict the extent of stable crack growth and the subsequent collapse load of wide-panel MSD experiments (deWit et al, 1994). The purpose of this paper is to present experimental/numerical results on stable crack growth and linkup of idealized MSD based on the T* integral. Moiré interferometry was used to determine the orthogonal displacement fields surrounding stably growing cracks in 0.8 mm thick 2024-T3 aluminum specimens with two or three cracks. Fatigue precracked cracks extended toward each other from two circular holes, which were 25.4 mm apart to simulate fastener holes in airplane fuselage, close to the outside edges of the specimens. A longer center crack from a center hole in the wider, three-crack specimens with three holes spaced 25.4 mm apart, provided information on the lead crack effect. T*ε integral, where ε is the distance of an elongating integration contour from the stably growing crack, was evaluated from the Moiré data using the procedure established by Okada et al (1996). ε in all studies was equated to the specimen thickness. An elastic-plastic finite element (FE) model of the fracture specimens were executed in its generation mode (Kobayashi, 1979) by inputting the measured Moiré displacement data along the width, 20 mm away from the crackline, of the specimen. T*ε integral was evaluated using an equivalent domain integral (Nikishkov et al, 1987). The experimentally and the FE determined T*ε’s were in excellent agreement with each other. Moreover, the T*ε variation with stable crack growth closely followed the stable crack growth results generated previously using standard fracture specimens (Omori et al, 1998). Thus stable crack growth data generated by standard fracture specimens can be used to predict crack growth of MSD cracks. Collapsed load was reached when the remaining ligament exceeded the tensile strength of the 2024-T3 sheet and the two cracks rapidly propagated toward each other in the two-crack specimens. For the three-crack specimen, the lead crack propagated toward the smaller two MSD cracks.

An artificial neural network (ANN) extracts knowledge from a training dataset and uses this acquired knowledge to forecast outputs for any new set of inputs. When the input/output relations are complex and highly non-linear, the ANN needs a relatively large training dataset (hundreds of data points) to capture these relations adequately. This paper introduces a novel assisted-ANN modeling approach that enables the development of ANNs using small datasets, while maintaining high prediction accuracy. This approach uses parameters that are obtained using the known input/output relations (partial or full relations). These so called assistance parameters are included as ANN inputs in addition to the traditional direct independent inputs. The proposed assisted approach is applied for predicting the residual strength of panels with multiple site damage (MSD) cracks. Different assistance levels (four levels) and different training dataset sizes (from 75 down to 22 data points) are investigated, and the results are compared to the traditional approach. The results show that the assisted approach helps in achieving high predictions’ accuracy (&lt;3% average error). The relative accuracy improvement is higher (up to 46%) for ANN learning algorithms that give lower prediction accuracy. Also, the relative accuracy improvement becomes more significant (up to 38%) for smaller dataset sizes.