FBE Uçak ve Uzay Mühendisliği Lisansüstü Programı  Doktora
Bu koleksiyon için kalıcı URI
Gözat
Sustainable Development Goal "none" ile FBE Uçak ve Uzay Mühendisliği Lisansüstü Programı  Doktora'a göz atma
Sayfa başına sonuç
Sıralama Seçenekleri

ÖgeDeformation behavior of thin walled structures filled with auxetic and nonauxetic core materials(Lisansüstü Bilimleri Enstitüsü, 2021) Usta, Fatih ; Türkmen, Halit Süleyman ; Scarpa, Fabrizio ; 670691 ; Uçak ve Uzay MühendisliğiAir vehicles can be exposed to structural damages and disable integrity due to static and dynamic loads. Windshields of an airplane, i.e., fuselage or wing surfaces, can have a risk of these loads, and therefore, they should withstand these external loads. The skin shape of the air vehicle components, e.g., fuselage/wing/empennage of airplane and blade/canopy of the helicopter, can be considered as the combination of curved or flat panels. Likewise, thinwalled tubular structures, which can be utilized as the forms of landing gears or frames of aircraft, can possess curved or flat surfaces depending on crosssection types. This thesis proposes to increase the indentation and impact resistance of the air vehicles under low and highvelocity impact loading. The structural durability of the aircraft components under compressive loading has a key role in the protection of structural integrity during accidents. We mainly focus on enhancing mechanical performances of integrated structures, e.g., sandwich panels and thinwalled tubes with auxetic (i.e., negative Poisson's ratio) and nonauxetic core. In particular, we focus on the effects of curvature by examining flat, single, and doubly curved sandwich panels and then curved thinwalled tubes throughout the thesis studies. The results are compared in terms of compressive modulus, strength, and energy absorption metrics. In the first part of this thesis, we develop novel auxetic open cell assemblies to provide highperformance core structures for integrated stuctures. We describe the behavior of a novel class of hierarchical slotted and asymmetrical edge cellular shapes honeycombs with auxetic and nonauxetic configurations subjected to edgewise compression. Hierarchical (slotted) and nonhierarchical specimens, including hexagonal, traditional reentrant, and asymmetric reentrant, are produced by the Fused Deposition Modeling (FDM) method, which is the most common method for additive manufacturing. The specimens are 3D printed by using Raise3D N1 3D machine and Polylactic acid (PLA) plastic filament, and then they are tested under edgewise compression along the inplane directions. The number of cells is determined as 5x4, and dimensions of 122x105x10 mm3 are kept constant for each design. A rigid mass is crushed through the top edge surface at an axial quasistatic speed of 3 mm/min by using an Instron Roell Amsler test machine. An Imetrum Video GaugeTM system is also used to capture the images of the test samples during crushing and to determine the Poisson's ratio of the samples. The material properties of the PLA plastics are determined via tensile tests following the ASTM D63814 test standard. FE analyses have been performed using the LSDYNA code to benchmark forcedisplacement curves with the experimental results. The numerical models are validated by comparing the loaddisplacement responses with the experimental results for each sample. Linear elastic properties, crashworthiness, and energy absorption capability of the novel honeycomb structures are evaluated from the experimental and numerical standpoint. Specific metrics like normalized compressive modulus, compressive strength, and specific energy absorption (SEA) are evaluated. The Poisson's ratio of the hierarchical honeycomb configurations is compared to the bulk ones. In this section, we also introduce a novel type of composite open cells honeycombs with the PLA plastic reinforcements, hydrogel, and polyurethane foam over a hierarchical cellular platform. The first class is represented by a hybrid architecture combining a hierarchical honeycomb with polyurethane foam filler, while the second is a multiphase structure produced by injecting a sodium alginate hydrogel into the hierarchical voids of the honeycomb metamaterial. The hydrogel formulation consists of sodium alginate (alginate) and a nonionic surfactant, Pluronic F127. Gelcontaining PLA structures are immersed in a 100mM CaCl2 bath prepared by dissolving calcium chloride powder in deionized water. The resulting gel structure is injected into the voids of PLA structures by using syringes. Semireticulated polyurethane rigid (PUR) foam blocks (density 69 kg m3) are processed by using a CNC machine in accordance with the dimensions of gaps in the architectural structures. Then twelve different auxetic and nonauxetic metamaterial architectures are subjected to edgewise compression loading at the same test speed. A parametric numerical analysis is also performed using validated FE models to identify the best metamaterial architecture configurations. Second, we conduct the studies on flat, single, and doubly composite sandwich panels under low and highvelocity impact loading. Sandwich panels are composed of two thin stiff and strong face sheets and a thick lightweight core. The geometrical configuration has a key role to be able to absorb more energy and have more impact resistance. The interface angle, stacking sequence, ply orientation, ply thickness, and material type are the important parameters for manufacturing composite sandwich panels. Here we mainly focus on the effects of different types of auxetic and nonauxetic core structures and curvature of composite panels. In addition, the effects of thickness and stacking sequence of the composite panels are examined, and then an optimization study of the impact behavior of curved plates is performed by using multiobjective optimization techniques. Impact resistance of composite sandwich panels with different types of auxetic (reentrant, double arrowhead, and hexachiral) and nonauxetic core structures are investigated by using Instron 9340 drop test machine. In the experimental studies, sandwich panels are manufactured with the constituents of UD carbon fiber reinforced epoxy resin (CFRP) composite face sheets and PUR foam core and 3D printed PLA plastic cellular core. Composite face sheets consisting of three plies with the [0/45/90] stacking sequence are manufactured with wet/hand layup method. A Heatcon vacuum press test machine is used to cure the epoxy resin and ensure a uniform flatness on both sides of the face sheets. The material properties of the constituents have been determined via tensile and compression tests in accordance with the relevant ASTM test standards. The cellular core topologies are fixed to have the same dimension of wall thickness and number of cells (39x4 except hexachiral topology). A rigid striker with a hemispherical head tip is dropped on the specimens with a speed of 2.6 m/s. A set of numerical analyses with different impact energies are performed using validated FE models to identify the best core design. Then, we indicate how an open cellular core topologies (reentrant lattice) and a PUR lightweight foam core structures affect the highvelocity impact behavior of the doubly curved CFRP sandwich panels. Composite face sheets are manufactured with the dimensions of 250mm radius, 30mm core thickness, and 1.05mm face sheet thickness by using a doubly curved mould made of aluminum alloy. Highvelocity impact tests are carried out by using an air gas gun test machine capable of maximum 40bar compressed air. Frames and fasteners of the gas gun are renewed considering the connection surface of the specimens. Frames are designed and produced with the same radius of curvature of the sandwich panel. In the experimental studies, a 10mm diameter spherical steel projectile is launched to the centre of the specimens with a speed of 100 m/s. The FE models are developed by using the LSDYNA software to simulate the highvelocity impact behavior of the specimens. The strain values measured by using strain gauges are recorded via a data acquisition system. The penetration depth of the projectile is measured by using a digital caliper. Moreover, the effects of curvature on the impact behavior of composite panels are examined by using numerical methods. The doubly curved surfaces are investigated and classified according to the Gaussian curvature coefficient. The impacted surface is extracted from the surfaces of torus, ellipsoids, spheres, and cylinders. We evaluate twelve different doubly and one single curved panels impacted by a spherical projectile at a velocity of 100 m/s. The results are firstly discussed by considering the effects of the curvature on the backplane displacement and the energy absorption of the panels. In addition to these, a multioptimization study based on the Genetic algorithm and Response Surface method is carried out in order to determine the optimum designs of curved plates under highvelocity impact loading. Third, we conduct the studies on crash tubes subjected to axially quasistatic compression and lowvelocity impact loading. Crash tubes are important safety components used as thinwalled structures owing to their lightweight. Here we investigate the effects of filler types, curvature, tube numbers, crosssection, and imperfection on the single and multitube systems' crashworthiness performance. Reentrant and hexagonal configurations are chosen as unit cell shapes of the filler. The numerical studies are conducted using LSDYNA software. Material properties of tubes made of aluminum alloy and auxetic lattices utilizing Acrylonitrile butadiene styrene (ABS) plus and PLA plastics are determined by using tensile tests according to ASTM E8/E8M and ASTM D63814 test standards. The effects of imperfection on the tube and using auxetic filler on the crushing behavior of circular crash tubes are examined by using numerical methods. FE analyses are performed at 5 m/s impact velocity. Two different trigger shapes are suggested and compared to each other and discussed the advantages and disadvantages over nontriggered tubes. In order to indicate the effects of auxeticity, circular crash tubes with and without reentrant lattices are examined under dynamic loads by using experimental and numerical techniques. The tubes in the specified length are cut from the extruded cylindrical aluminum profiles. Then, each specimen is placed in the special grooves on the aluminum plate and bonded using adhesive. Impact tests are conducted by using the Instron Dynatup 8150 test machine. As a special case of integrated thin walled structures, nested tubes are also examined in this section. The effects of using hexagonal honeycomb filler, increasing the numbers of tubes, and changing the lengths of the tubes on the nested tube structures are examined both experimentally and numerically. In the experimental study, a mass is dropped at 2.75 m/s impact velocity onto the multitubular crash tubes by a drop test machine. The results of single, double, triple, quadruple, and quintuple tubular structures with and without the honeycomb filler are compared in terms of collapse mechanism and common crashworthiness indicators. Furthermore, the effects of taper angle, imperfection, and crosssection types on the impact behavior of nested tubes are investigated numerically. Lastly, we present a crashworthiness optimization of nested and concentric circular tubes under impact loading which is performed by coupling FE model, Response Surface models, and Genetic algorithm. Length and thickness of three concentric tubes, as well as the radius of one tube, are adopted as design variables, which are effective parameters on crashworthiness and energy absorption. To reduce the computational cost of the optimization procedure, simple and computationally cheap Response Surface models are created to replace FE analyses in further calculations. The Nondominated Sorting Genetic Algorithm –II (NSGAII) is applied to obtain the Pareto optimal solutions.

ÖgeDigitaltwin flight modelling through machine learning for trajectory error estimation and recovery(Fen Bilimleri Enstitüsü, 2021) Uzun, Mevlüt ; İnalhan, Gökhan ; Demirezen, Mustafa Umut ; 670702 ; Uçak ve Uzay Mühendisliği Ana Bilim DalıHigh fidelity aircraft performance models are essential for the precise estimations of 4D trajectories and fuel consumption. A correct fuel flow model is critical for flight planning purposes, especially in calculating the fuel load required for a trip. Airlines use manufacturers' performance models to calculate fuel consumption for flight planning rather this be at the integrated operations center or at the cockpit level. As such, within the scope of Air Traffic Management (ATM), for problems such as trajectory planning/estimation for separation assurance and capacity and demand balancing, performance models such as the Base of Aircraft Data (BADA) by Eurocontrol are utilized. These baseline models are structured around polynomial approximations of Original Equipment Manufacturer (OEM) performance tables within generic aircraft models. However, flight data strongly suggest that the aircraft tend to deviate from these baseline models as they age and as, are exposed to maintenance, and are operated in diverse regions. Current groundbased flight planning systems utilize aircraft typespecific performance tables to determine fuel flows for given flight conditions and parameters such as altitude, mass, and speed. A performance factor corrects these tables as the aircraft ages. Despite this update, planned fuel consumption may indeed not overlap with the actual one. In addition to the aircraft performance model, wind uncertainty affects fuel consumption by its impact on ground speed. Because ground speed changes trip time, it determines how much fuel is to be consumed for a travel distance. This thesis focuses on the flight planning at the ground level and propose a datadriven machine learning approach to develop a datadriven aircraft digitaltwin model using the most fundamental and airborne recorded flight trajectory and flight parameters data set. In particular, this thesis considers on two distinct problems: uncertainties in aircraft performance models and uncertainties in the wind. In this sense, this thesis proposes methodologies to improve baseline models for fuel flow, and wind estimations via operational data. In particular, this study has investigated introducing neural network architectures to estimate tailnumber specific updates to the aircraft baseline fuel flow model through deep learning for climb, cruise, and descent phases of flight. For training our neural network models, this study has utilized a QAR data set from 30 different tailnumbers with more than 2 million flight segments in total from a fleet of a widebody aircraft operated by a major European flag carrier airline. The proposed architecture is designed to retain the compatibility to the flight planning applications by using the same features that the baseline aircraft models do for computing flight trajectory and the fuel flow. Throughout an extensive feature engineering, the thesis reveals the parameters with a significant impact on fuel flow. The analysis shows that the discrepancy between the modeled and the actual fuel flows stems from a) parametric biases in fuel flows and b) operational variations in the actual implementation of the flight modes. As such, the estimation errors in throttle and the corresponding thrust and excess thrust levels, play a key role in error dynamics. This fact is utilized to further refine the neural network architecture into a novel cascaded structure, which embeds estimation of critic engine related parameters that are not available within baseline models for flight planning. Furthermore, the study has implemented a physicsguided deep neural network framework to improve datadriven models' consistency in flight regimes that are not covered by data. In particular, we guide the neural network with the equations that represent fuel flow dynamics. In addition to the empirical error, we embed this physical knowledge as several extra loss terms. In wind uncertainty part, historical Global Forecast System (GFS) predictions are utilized as baseline estimations. Wind measurements in QAR footprints are considered as groundtruth. Stateoftheart deep learning algorithms are deployed to map baseline estimations for fuel flow and wind to their ground truths. A comparison of the models with real flight data shows that precise estimation of fuel flow with mean absolute errors lower than %0.7 can be achieved at all the flight modes. We further tested these models on different tail numbered aircraft to show the generalization capability of the algorithm. Results on the wind side also show that we can achieve a considerable reduction in wind uncertainty both from a mean error and variance sense. Finally, our fuel flow models are compared with the Airline groundbased planning fuel flow models on the actual flight plans generated by the groundbased system. Total trip fuel comparisons show discrepancies up to %3.5 total fuel loading weight, which will result in potential fuel savings by decreasing the fuel load during takeoff for flights with unnecessary excess fuel load. An example of a specific tailnumber suggests that for typical operation of 200 longhaul flights per day, yearly savings on the order of 17 million USD can be achieved at current jet fuel prices. This "tailnumber specific" performance modeling approach is projected to open considerable frontiers, including further reduction of fuel load safety margins and inflight update of performance models through machine learning methods.

ÖgeHighspeed trajectory replanning and trajectory tracking for collision avoidance(Fen Bilimleri Enstitüsü, 2021) Hasanzade, Mehmet ; Koyuncu, Emre ; 670701 ; Uçak ve Uzay MühendisliğiNot long ago, the operations or the applications requiring highperformance guided and navigation would have required the use of tacticalsize unmanned aerial vehicles. The main reason for this was that highperformance algorithms required bigger or heavier avionics with high computing capabilities or reliable communication buses linked with the ground systems. However, with the development of technology, these capabilities can now be achieved in smaller avionics, making it possible onboard for smallsize unmanned aerial vehicles. New lightweight sensory systems enabled small unmanned systems to have advanced "situational awareness" and allow them to be capable of performing complex missions. Yet, guidance, navigation, and motion planning methodologies are still mostly "conservative" and "usecasespecific," render the UAVs incapable of performing multipurposeoperations. There are many studies on route planning algorithms for situations where the map of the environment is known. Since these studies can operate in the initial phase of the operation, where a response is not expected to be very fast, it can guide the vehicle from the starting point to the end point safely, which is feasible and safe for the vehicle. However, in cases where unknown obstacles occur which can be sensed by any sensor, replanning of the trajectory is necessary in order to avoid obstacles. It is expected that the algorithms will be able to generate the replanned trajectory since the vehicle has less time to avoid it. Therefore, The time efficiency of the replanning phase is directly related to the speed and the aggressiveness of the trajectory followed by the vehicle. it is crucial to utilize an algorithm that generates an evasive maneuver in real time and ensures safety and dynamical feasibility. In this thesis, studies were carried out on two topics, trajectory replanning and trajectory tracking. The first study, this thesis proposes a fast replanning strategy based on deep reinforcement learning for highly agile aerial vehicles. First, the differential flatness model of an air vehicle is utilized, allowing us to directly map the desired output trajectory, which is parameterized with bspline curves, into required input states to track trajectory. Moreover, perception model is used with fixed range and FOV on the vehicle, and as soon as the vehicle detects the obstacle, it performs the realtime evasive action through repetitive replanning over an infinite trajectory. Specifically, the algorithm is initialized with a flight trajectory plan, then performs optimal control point vector update and knot insertion to generate a dynamically feasible conflictfree trajectory. Through this modification, the regenerated trajectory provides feasible evasive maneuvers for the vehicle, where the location and the number of the added control points form the "agility" of this evasive maneuver. The control point insertion considering dynamic constraints and the defined agility metrics is transformed into a trajectory optimization problem, which is solved through deep reinforcement learning (DRL). The proximal policy optimization (PPO) method is utilized to train the replanner with the random forest generation environment. The agent produces replanned dynamically feasible conflictfree trajectories with modified control points approximately in 400us, which enables the realtime flight trajectory generation for highly agile aerial vehicles. The second study proposes a deep reinforcement learningbased trajectory tracking controller, enabling to minimize the positional and velocity track error for aerial vehicles based on a Proximal Policy Optimization (PPO) algorithm where the controller is trained through randomly generated feasible trajectories. PI controller is utilized for the attitude controller and PID for the attitude rate controller as the aerial vehicle's lowlevel controllers. The trajectory generator based on the dynamic model guarantees the flat outputs, such that they do not exceed the given dynamical limitations of the vehicle, and produces pitch and roll references to the attitude controller. Simulation results show the root mean square error of the trajectory tracking performance. Also, DRL agent performance is compared with LQR and LQI based trajectory tracking controllers.

ÖgeInvestigation of interacting multiple fatigue cracks propagation using twodimensional boundary cracklet method(Lisansüstü Eğitim Enstitüsü, 2021) Talal, Ahmed ; Türkmen, Halit Süleyman ; Yavuz, Abdulkadir ; 675445 ; Uçak ve Uzay MühendisliğiAircraft structures experience fatigue loading emanating from different sources e.g. variation of aerodynamic loads on wings and repetitive pressurizing and depressurizing the cabin of the aircraft etc. It is a wellknown fact that fatigue loading is more responsible for the failure of aircraft structures as compared to static loading because a single surface crack can lead to a catastrophic failure due to fatigue loading. At the early stages of the life of aircraft, these surface cracks have no effect on the structural integrity of the aircraft, but with the passage of time, environmental effect, and nature of loading these cracks propagate and interact with each other. These cracks propagate, up to the point where the remaining crosssection of the component is not being capable of carrying the loads and the component will be subjected to sudden fracture. The failures due to fatigue usually start at small surface cracks which act as local stress raisers and propagate and interact with each other and turn into large damageproducing cracks. In practice, these micro surface cracks are always likely to be present in many aircraft structural components even the newly made components can have these cracks due to certain imperfections in machining processes during the manufacturing of aircraft. To produce a damage tolerance design and to meet the certain requirements of certifications applicable in the aerospace industry, it becomes very important to know the behaviour of aerospace structures in the presence of these inevitable surface cracks under fatigue loading. Thus, a fast and accurate method of predicting the behaviour of these cracks under fatigue loading plays a vital role. This fact forces engineers to develop new methods and models which can simulate the effects of existing cracks so that they can predict the remaining useful life of aircraft structure more accurately. Such methods and simulation techniques not only reduce the high cost of physical testing of the aerospace structures but also play a crucial role in producing a better design of these structures. For the analysis of planar cracks, different commercial tools are available, which are mostly based on the analytical formulations and different handbook solutions e.g. NASGRO and AFGROW. These software packages can simulate the fatigue crack growth (FCG) problems of predefined cracks under modeI loading conditions only, but most of the real problems in the industry are under the influence of mix mode loading where crack tip grows under the effect of both modeI and modeII loading conditions. Therefore, these software packages cannot handle such complex problems of mix mode crack growth. Finite element methods are also being used from a long time for the study of FCG. These methods can simulate the interactions of cracks with reasonably good accuracy. But, due to the requirement of fine mesh at the crack tip, generation of a representation of the crack advancement and regeneration of FE mesh after each iteration of FCG, make these methods challenging to adopt. To overcome these difficulties of FEM, in 1999, a meshindependent method called ExtendedFEM (XFEM) with minimal remeshing was developed and since then a continuous improvement has been seen in the implementation of these methods. However, the accuracy of these methods decreases as the complexity of the problem increases and still a lot of research efforts are underway to overcome this shortcoming. By considering the abovementioned limitations of the conventional methods to analyse the FCG of problems involving multiple cracks under mixedmode conditions, there is always room to develop such methods which can mitigate the deficiencies of these methods. Recently, in 2006, a fast and accurate semianalytical method called Boundary Cracklet Method (BCM) is developed by Prof. Dr. A. K. Yavuz (coadvisor of this study) and Prof. Dr. S. L. Phoenix at Cornell University, to find the overall stress field and the stress intensity factor (SIF) for crack tips and crack singular wedges at the crack kinks. This method is based on the dislocation distribution approach which approximates the crack opening displacement profiles by using certain power series that satisfy the tractionfree condition on crack faces. Unlike the conventional mesh dependent methods, where a very fine mesh is required to overcome the stress singularities around crack tips, BCM takes care of crack tip singularities by including wedge eigenvalues in power series and makes sure that all integrals necessary to calculate stress fields are in closed form to give fast solutions. The solution of these integrals is the most timeconsuming part in other meshdependent methods such as FEMs and BEMs. Moreover, only a few numbers of allocation points are used around the crack tips to satisfy tractionfree boundary conditions instead of using more elements. These factors make the algorithm of BCM more reliable and fast as compared to other methods and enable us to solve difficult fatigue crack growth problems. Therefore, the main objective of this thesis is to analyse the multiple cracks interaction under mix mode fatigue loading by using BCM in the twodimensional domain and to show the accuracy and versatility of the method to different fatigue crack growth problems that are difficult to solve by using the conventional methods. Throughout the thesis, it has been proved that the proposed scheme is a reliable and accurate method to simulate the fatigue crack propagation (FCP) involving multiple cracks in complex plate geometries under different conditions of fatigue loading. The accuracy of the method is established through the results presented by different researchers which were already available in the literature. Crack tip SIFs, fatigue crack propagation paths and the number of loading cycles required to produce a given crack length extension are used as a parameter for the comparison. A good agreement among the results of each mentioned parameter is achieved for every problem. Further, this proposed method is used to simulate the FCP in different plate geometries involving single as well as multiple cracks under different conditions of fatigue loading which are typical and difficult problems to solve in aerospace structural components. For this purpose, three different studies are conducted, and the findings of each study are published in different international prestigious forums. In the first study, fatigue crack growth in an infinite plate having two rivet holes separated at some distance and crack emanating from a certain location and orientation from one hole are analyzed under three different farfield fatigue loadings i.e. loading in Xdirection, loading in Y direction and shear loading. The maximum tangential stress (MTS) criterion is used to predict the trajectories of crack growth. Paris's Law along with the approach of equivalent stress intensity factor is used to compute the number of loading cycles to produce a required crack length. It is concluded that after some initial number of loading cycles, the fatigue crack growth path becomes perpendicular to the direction of applied loading in case of farfield applied tensile stress (whether in X or Y direction), and similarly, in the case of shear loading, cracks propagate perpendicular to the direction of maximum principal stress. Almost ten times fewer loading cycles are required to reach at a certain crack size under shear loading as compared to the normal applied stress, which shows that the rate of crack propagation is ten times higher under shear stress. Therefore, among the given three loading conditions, cycling shear stress is the worst one and needs more attention while designing the structures having rivet holes. In the second study, fatigue crack growth simulations of interacting multiple cracks in perforated plates with multiple holes are discussed. To show the versatility of the proposed method, emphasis is given to study such complicated problems which cannot be solved by conventional methods to analyse the FCG. Three different studies with multiple cases of initial cracks emanating from side edges, the center of the plate and the outer periphery of holes in the plate at different orientations are simulated. It has been concluded that the FCG of complicated problems e.g. plate with six holes having seven precracks can be computed fast by the proposed scheme. The conventional methods of analysing FCG have limitations in solving such complex problems. Moreover, the effect of a newly added crack in the vicinity of already present crack is also analyzed and concluded that when two coplanar cracks approach each other, they exhibit an overconstraining phenomenon, which causes the neartip stress field to be significantly higher than that near a single crack and hence ultimately increases the rate of crack growth. To show the efficiency of a computational method in fatigue problems a new and very useful parameter is also introduced: Yavuz's fatigue computational efficiency factor, YCF = µN/t, which is the number of computed million loading cycles per hour (CPU time). In the third study, FCG behaviour of symmetric cracks emanating at different locations at the outer periphery of the hole in an infinite plate with different orientations under inphase tensiontension biaxial loading is presented. As the effects of initial crack orientation under uniaxial fatigue loading are well reported in the literature but the same under the effect of different conditions of biaxial loading has not been investigated. The rate of FCG is computed using Walker's equation, whereas the direction of propagation of crack tip is predicted using the minimum strain density (MSED) criterion. Our results show that BCM is equally effective in predicting the FCG behaviour under complex cases of fatigue loading. It is concluded that cracks tend to propagate perpendicular to the direction of dominant stress in the case of biaxial load where biaxiality ratio λ≠1 and there is no effect of location and orientation of initial crack on the crack trajectory. For equibiaxial loading where λ = 1, the crack tends to propagate diagonally, and its path depends upon the location and orientation of the initial precrack. As far as the number of loading cycles for a given crack extension are concerned, equal load cycles are computed for λ = 0, 0.5, 1 whereas it is concluded that for λ = 1.5, the rate of crack growth increases, and fewer loading cycles are required to produce the given crack length. It is also concluded that there is no change in crack trajectories under different stress ratios (R). For a given effective stress intensity factor (ΔKeff) the rate of crack propagation is increased with the increase in R, but for a given value of stress, the value of ΔKeff is lower for a higher Rvalue, which results in a higher number of required loading cycles to produce the same crack extension.