In-plane Bending Research Articles

Effect of proof loading on the fatigue life of mooring lines

The oil and gas production sector has experienced substantial expansion in recent decades, playing a crucial role in the global economy. To enhance productive efficiency, several extraction operations are carried out on offshore floating platforms over deep waters, which require advanced mooring system technologies to maintain their positional stability. These systems are exposed to cyclic loads throughout their operation and must be properly designed to withstand fatigue. However, recent incidents of premature failures in mooring lines have revealed a new type of fatigue failure in mooring chain links, induced by mechanisms entitled Out-of-Plane Bending (OPB) and In-Plane Bending (IPB), characterized by fatigue phenomena due to moments out of the plane of the link and in the plane of the link. The origin of these bending mechanisms is related to the manufacturing process of the moorings, during which proof loads of approximately 65% to 80% of the Minimum Breaking Load (MBL) are applied, as recommended by technical standards to extend the mooring’s lifetime. This process, however, causes plastic deformations that restrict sliding movement between adjacent links, resulting, along with friction, in significant bending stresses in the links. In this context, various studies have shown that parameters such as operational tension, link diameter, friction coefficient, and the level of proof loading significantly influence the incidence of fatigue damage in mooring lines. Therefore, the present study proposes to conduct a parametric analysis through finite element simulations, focusing on the variation of the proof loading level to assess its effects on parameters directly related to fatigue calculation and, consequently, the lifetime of mooring lines, such as stress concentration factors, OPB angle variation, OPB moment, among others.

Nanoparticle Surface Enhanced Raman Spectra of Nb-Doped TiO2 Single Crystal Electrodes

A fuel cell is a generator that produces electric power by the hydrogen oxidation reaction at a fuel electrode and the oxygen reduction reaction (ORR) at an air electrode. A fuel cell is a clean energy conversion system that produces only water without emission of carbon dioxide. However, Pt (an expensive precious metal) is used as a catalyst of a fuel cell. Reduction of Pt loading in the catalyst or development of alternative materials of Pt is important for the widespread of fuel cells as a primary energy source in the future. Finding out materials that have higher ORR activity is a major target of the development of fuel cells.TiO2, a more abundant resource compared to Pt, is one of the alternative materials of Pt. The ORR activity of TiO2 can be enhanced by metal doping [1]. Theoretical calculation predicts that doping of Pd and Rh reduces the overpotential of the ORR to zero [2]. The ORR activity of Nb doped TiO2 electrodes depends on the crystal orientation as follows: TiO2(100) < TiO2(111) < TiO2(110) [3]. However, the real surface structure and adsorbed species for enhancing the ORR activity have not been determined on TiO2 single crystal electrodes in electrochemical environments.In this study, we have studied the adsorbates on the low index planes of TiO2 single crystals in 0.1 M HClO4 using nanoparticle surface-enhanced Raman spectroscopy (NPSERS). We assigned adsorbed species using DFT calculation.1%Nb-doped rutile TiO2(100), TiO2(110) and TiO2(111) were annealed and chemically polished with a 30w% HF solution. Au nanoparticles of about 50 nm were dispersed on the single crystal surfaces. Raman spectra were measured by stepping the potential positively with the interval of 0.1 V. The electrolyte solution was 0.1 M HClO4. All the potentials were referred to RHE.NPSERS bands were found at 580 cm-1 and 360 cm-1 in Ar saturated HClO4. The onset potentials of the bands were 0.4, 0.6, and 0.7 V(RHE) on TiO2(100), TiO2(110) and TiO2(111), respectively. The Au-O stretching vibration of Au nanoparticles appears from 1.4 V(RHE) at 590 cm-1 [4]. Thus the observed bands originate from surface adsorbates of TiO2. The band at 580 cm-1 was shifted 15 cm-1 to lower frequency in D2O solution, showing that the band is an adsorbed species containing hydrogen. On the other hand, the band at 360 cm-1 is an oxygen species such as Ti-O because no deuterium isotope effect was observed in D2O solution.DFT calculation showed that symmetrical stretching vibrations of Ti-OH-Ti (bridged OH) and Ti-OD-Ti locate at 577 and 564 cm-1, respectively. Ti-O-H out-of-plane bending vibration and in-plane bending vibration also locate at 350 cm-1 and 680 cm-1, respectively, which are close to the above-mentioned 577 cm-1 according to the DFT calculation using the bridged OH model. However, these two vibrations shift more than 100 cm-1 by the substitution with deuterium, which contradicts the experimental result. Other candidates of the adsorbed species containing hydrogen are OH and OOH on 5-coordinated titanium. However, TiO2(100), which has no 5-coordinated titanium, also gave the NPSERS band at 580 cm-1. Therefore, the band at 580 cm-1 is assigned to the symmetric stretching vibration of Ti-OH-Ti (bridged OH).The onset potential of 580 cm-1 band increases as TiO2(100) < TiO2(110) ≤ TiO2(111), whereas the order of the ORR activity is TiO2(100) < TiO2(111) < TiO2(110). No correlation is found between the onset potential and the ORR activity. This result suggests that adsorbed water, which cannot be observed with NPSERS, is involved in the ORR activity. Acknowledgements This study was supported by New Energy and Industrial Technology Development Organization (NEDO).

Non-dimensional linear analysis of one-dimensional wave propagation in tensegrity structures

This study presents a methodology for analyzing wave propagation in tensegrity lattices within a non-dimensional framework. Two strategies are employed to predict pass bands and bandgaps. The first examines wave dispersion through a single representative unit cell, using dispersion curves to identify bandgaps and pass bands. The second models the structure as a finite system, using modal analysis to compute the steady-state response to harmonic loads and plot the frequency response function. Two unit cells are analyzed: a two-dimensional D-bar unit and a three-dimensional tensegrity prism. The study investigates axial and in-plane bending wave propagation in a D-bar chain and axial wave propagation in a prism chain. After non-dimensionalizing the equations of motion, key parameters such as ratios of stiffness per unit length, mass per unit length, and prestress are identified. Its is shown that varying these parameters shifts the bandgap locations and widths. Prestress has minimal effect in the D-bar case, while a slight shift in the first bandgap is observed in the prism. The predictions from unit cell and finite structure analyses show good agreement.

An analytical method for the vibration characteristics of double panel structures with uniform elastic boundary supports

ABSTRACT In this paper, the methods for solving the free vibration and forced vibration of double panel structures under arbitrary boundaries are studied. Based on the Mindlin plate theory, the natural boundary between plates and plates is constrained by artificial springs, and the theoretical model of the structure is derived. The displacement function of in-plane vibration and bending vibration is expressed by a modified Fourier series expansion. The effectiveness and reliability of this method are verified by a series of numerical calculations and comparison with those of the finite element method. Through the parameter analysis, it can be seen that the vibration isolation effect can be increased by properly increasing the coupling height or making the connecting plate closer to the boundary of the bottom plate. The method presented in this paper can be used in vibration absorption and structural design of such structures.

Acetylacetone – 2-methoxyethanol solutions: Fourier transform infrared spectral studies

The H-bond interactions in the solutions of acetylacetone (AcAc) with 2-methoxyethanol (2-MOE) have been investigated using FTIR spectroscopy. Theoretical calculations on monomers (eight enol isomers and one keto form) and dimers of AcAc have been carried out. The results confirm that both the keto and enol forms of AcAc exist as monomers in liquid AcAc. The analysis of the carbonyl and hydroxyl bands indicates the existence of both the AcAc conformers in the solutions. The intensity of the bands due to the hydroxyl stretching and in-plane bending vibrations decreases rapidly with a decrease in 2-MOE concentration.

Investigation of dynamic stall models on the aeroelastic responses of a floating offshore wind turbine

Dynamic stall effects significantly affect the aerodynamic load prediction of wind turbines. In order to investigate the dynamic stall effects on the loads and responses of a 15 MW floating offshore wind turbine (FOWT), a novel dynamic stall model, namely IAG, is implemented within the widely-used simulation software package OpenFAST in this study. The superiority and accuracy of the IAG model are verified by comparisons against experimental data and numerical results from the Beddoes-Leishman (B-L) model. The results have shown that the IAG model is able to more accurately capture edges of the hysteresis loops of aerodynamic coefficients corresponding to various airfoils and operation states. The aeroelastic responses of a 15 MW floating offshore wind turbine under normal and extreme environmental conditions are calculated by employing the IAG model. The impact of dynamic stall models on blade loads and displacements has been analyzed. It is found that the B-L model produces larger loads and displacements under high wind speed and yaw error conditions, attributed to the insufficiently computational robustness of the B-L model under deep stall situations and the seriously dynamic stall circumstances. The 1st-order and 2nd-order bending modes of the blade are expected to be enhanced by the aerodynamic loads that are predicted using the B-L model. Consequently, the bending-torsional coupling effects would be enhanced, leading to an increase up to 64.7 % on the in-plane bending moment. This study has confirmed that the dynamic stall model should be properly selected properly for the fully coupled analysis of FOWTs.

Effect of tungsten carbide interface decoration on thermal and mechanical properties of carbon fiber reinforced copper matrix composites

The use of carbon fiber (CF)/copper (Cu) composites as thermal management materials shows significant promise. However, inadequate interface bonding hinders their thermal properties. This study introduces a novel method to create tungsten carbide–coated CFs (CF(WC)) using the molten salt method. These coated fibers are then used to develop a CF(WC)/Cu composite through vacuum hot-pressing sintering. Results reveal that the WC coating, formed at 1100 ℃ for 60 min with a tungsten trioxide/CF molar ratio of 1/10, is continuous, crack-free, and has an appropriate thickness. The WC coating facilitates excellent interface bonding between Cu and CF, thus effectively improving the initial poor interface bonding. With similar 50 % fiber content, the CF(WC)/Cu composite exhibits better thermal and mechanical properties than the CF/Cu composite. The in-plane direction thermal conductivity and bending strength of the CF(WC)/Cu composite are 398.7 ± 8.1 W m−1 K−1 and 195.3 ± 6.2 MPa, which are 35.3 % and 90.4 % higher, respectively, than those of the CF/Cu composite. Additionally, the in-plane direction coefficient of thermal expansion is 6.5 ± 0.3 × 10−6 K−1, representing a notable reduction of 37.5 %. These exceptional properties, coupled with the simplicity and efficacy of the preparation process, offer valuable insights for the advancement of carbon/Cu thermal management materials.

Enhanced elastic stress solutions for junctions in various pipe bends under internal pressure and combined loading ([formula omitted] pipe bend, U-bend, double-bend pipe)

Piping systems in nuclear power plants normally operate under high pressure and high temperature. To efficiently manage space within these systems, pipe bends are extensively used. However, the welded joints connecting these pipes may be susceptible to flaws due to weld residual stress, transient loads, and operating environments. When flaws are present in such areas, analytical evaluation of flaws is to be carried out based on fracture mechanics parameters such as stress intensity factor. To calculate the stress intensity factor, distributions of the elastic stress are required. Therefore, this paper presents closed-form approximations of elastic stress in the junction between a pipe bend and a straight pipe under internal pressure. Review of the existing elastic stress solutions for estimating the stresses in pipe bends was carried out analyzing their limitations. Based on those limitations elastic stress solutions for thick to thin wall pipe bends were proposed and were validated against finite element (FE) analysis for thick-wall to thin-wall pipe bends under internal pressure and combined loading (i.e. internal pressure, in-plane bending, out-of-plane bending inflicted simultaneously). 90° pipe bend, U-bend and double-bend pipe configurations were considered and showed good agreement with the FE results exhibiting less than 5.8 % discrepancies. The accuracy of the elastic stress solutions for pipe bends provided in the existing code are summarized and validated in the appendix as well.

Experimental testing and plastic strain analysis of high strength steel longitudinal plate to tubular X joints

Applying high strength steels to tubular joints can increase the propensity to fracture failure due to their lower ductility. However, to simulate the fracture behavior in the finite element (FE) analysis, sophisticated material damage model with rigorous fracture criteria should be incorporated. Recently, the latest draft of ISO 14346 has advocated the use of 5 % strain limit in FE analysis of tubular joints. The strain limit concept has been further developed by the authors’ previous work, for its use as a practical alternative to the complicated material damage model. Specifically, a lowered limit of 2.5 % was recommended for longitudinal plate to circular hollow section (CHS) joints subjected to in-plane bending. This study extends the strain limit investigation to longitudinal plate to tubular X joints subjected to tensile loads. An experimental program is first presented which included both CHS and rectangular hollow section (RHS) chord members fabricated from two high strength steels with nominal yield stresses of 460 MPa and 700 MPa. Based on test-validated supplemental numerical analyses, it is suggested that the joint load corresponding to 2.5 % strain limit can be taken as the load-bearing capacity to suppress occurrence of a fracture failure for the tubular joint configurations considered in this study.

Prototyping of vibration-sensing-actuation device which is contained high-power electrodynamic speaker for diagnosis of actual water main network

Water leakage and bursting due to deterioration of water distribution mains lead to water outages and economic losses. To prevent the accidents, we are conducting research to develop measurements and diagnostic methods for buried water mains. In this study, we focused on the shift in eigenfrequencies of in-plane bending vibration of rings because of deterioration. Therefore, we are developing the vibration-sensing-actuation device which detects the frequency changes of in-plane bending mode. The water distribution network is mainly composed from cast iron pipe. Moreover, the attached facilities for example fire hydrant and water valve are contained. Since attached facilities are fabricated from cast iron component, actual water main network is heavy facilities which have high rigidity. In order to excite the desired in-plane bending mode in heavy components, the proposed sensing-actuation device requires the high-power actuator. In this study, we introduce the high-power electromagnetic actuator more than 100W output into the proposed device. Furthermore, the fundamental operational tests were conducted under the various input signals in the laboratory situations. In addition, the field operation confirmation was performed in an actual water main network.

Experimental modal analysis of in-plane bending vibration mode using actual water main network

Accidents of water leakage and bursting due to deterioration of water pipes cause water outages and economic losses in the surrounding areas. We are conducting research to develop measurement and diagnostic methods for buried water pipes. The graphitic corrosion of water pipes in a buried environment causes a reduction in pipe thickness which leads to strength problems. For this reason, methods for detecting pipe thickness are necessary for evaluating pipe deterioration, however, there is no effective way to analyze pipe thickness today because it cannot be visually observed in a buried environment. In this study, we focused on the shift in eigenfrequencies of in-plane bending vibration of rings due to deterioration. At first, we performed an experimental modal analysis by using a water pipe network which is used in a practical water utility. In addition, we conducted a theoretical analysis based on a model of a two-dimensional ring with coupled incidental attachment. As a result, in-plane bending vibration was observed in the water pipe of actual size. Furthermore, in-plane bending vibration was observed when excited through fire hydrants and it is also observed in pipes that are different material and diameters.

Controllable Growing Defects in Cambered Boron Nitride Utilizing a Plane Bending Strategy for Efficient Oxidative Dehydrogenation of Propane

Controllable Growing Defects in Cambered Boron Nitride Utilizing a Plane Bending Strategy for Efficient Oxidative Dehydrogenation of Propane

Hysteretic behavior of eccentric RHS beam-to-column joints under cyclic in-plane bending

This paper conducted experimental and numerical studies on the hysteretic behavior of eccentric rectangular hollow section (RHS) beam-to-column joints under cyclic in-plane bending. The study began with the design of both stiffened and unstiffened joints, followed by hysteresis tests that revealed failure modes like web weld tearing and stiffener fracture. The seismic performance of the joints was evaluated using hysteresis curves, skeleton curves, ductility coefficients, strength degradation coefficients, and energy dissipation coefficients. Compared to unstiffened joints, the stiffened joints exhibited a 30 % increase in peak load and a 18 % improvement in maximum energy dissipation coefficient. Subsequently, finite element (FE) analysis was performed, and the influence of key parameters on the hysteretic behavior was studied using validated FE models. The results indicated that the hysteretic behavior was positively correlated with the flange width ratio of beam to column, the ratio of beam section height to column flange width, and the thickness ratio of beam to column, while it was negatively correlated with the width-to-thickness ratio of the column. Finally, a mathematical model for the hysteretic behavior of both stiffened and unstiffened joints was developed and validated through experimental and FE comparison, offering practical applicability in engineering design.

Spectroscopic Investigation of Pearl Samples from Online Platforms and E-Marketplaces

P urchasing pearls from online platforms and e-marketplaces has been around for years, where buyers could join in the thrill of the show of opening pearls from oysters or mollusks. In exchange for those materials that claim to be pearls, buyers must pay a high price per piece. In this study, the spectroscopic properties of twenty-seven samples purchased from online platforms and e-marketplaces were revealed. The FTIR spectra show the characteristic peaks of aragonite at 1483, 716, 712, and 699 cm-1, while exhibiting the vaterite peaks at 882 and 879 cm-1. Correspondingly, Raman spectra indicate the ν1 symmetrical and ν4 in-plane bending modes of the carbonate at 1083, 701, and 704 cm-1. Thus, it clarified that all the samples are pearls. The SrO/MnO ratio acquired by energy dispersive X-ray spectroscopy (EDXRF) at an average of 0.44 suggested that the samples are freshwater pearls. Apart from the white pearl, the cause of the color of the sample is separated into two factors. The natural color, which is presented in cream and peach, is caused by polyene pigments. In contrast, vivid colors such as blue, violet, purple, and pink are shown as evidence of dyes. The UV-Vis reflectance spectra also present a different absorption between natural and dyed pearls.

Modeling Stress Concentration Factors for Fatigue Design of KT-Joints Subjected to In-Plane Bending Loads Using Artificial Neural Networks

Stress concentration factor (SCF) is an important parameter for the fatigue design of offshore joints. There are many empirical equations for quick estimation of SCF in tubular joints, based on experimental and numerical investigations. However, most of these equations apply at the crown and saddle points only, even though the maximum SCF may not always occur at these points, resulting in overestimated fatigue life. As the maximum SCF location varies due to multiplanar loads, damage, or reinforcement of joints, its location and magnitude are critical for a realistic fatigue life estimation. However, conventional statistical tools cannot approximate the complex behavior of SCF around the brace axis. On the other hand, artificial neural networks (ANN) can efficiently approximate complex phenomena. This study uses ANN to develop empirical models for determining SCF around the weld toe of KT-joints subjected to in-plane bending (IPB) loads. Eighteen hundred and fifty-eight (1858) designs were simulated using finite element analyses to generate data for training the ANN. Two IPB load conditions were focused on, and empirical equations were proposed for SCF around the chord side of the central brace-chord interface. These equations approximate maximum SCF with less than 5% error. This methodology applies to other joints and load configurations also.

Identification of probability distributions of SCFs in three-planar KT-joints

KT-joints are crucial in jacket platforms, providing structural integrity by effectively transferring loads between the main chord and braces. Their robust design ensures stability and durability in harsh offshore environments, preventing structural failures and enhancing the platform's overall safety and performance. This study presents the findings of finite element (FE) analysis conducted on 324 tubular three-planar KT-joints subjected to in-plane bending (IPB) loadings. The purpose of the research was to generate a probability distribution (PD) for the stress concentration factors (SCFs) under bending moments. To the authors' knowledge, no previous research has analyzed the PD of the maximum SCFs in three-planar KT-joints. Consequently, data representing the maximum SCFs were collected from the three-planar KT connections. The maximum likelihood method was used to determine the distribution parameters. The goodness-of-fit of the Generalized Extreme Value distribution was assessed using the Kolmogorov-Smirnov (KS) and Chi-square (CS) tests. The results indicated that this distribution is the most suitable for modeling three-planar KT-joints under IPB loading. In the subsequent stage, well-defined theoretical probability density functions (PDFs) and cumulative distribution functions (CDFs) were developed. Furthermore, probability-probability diagrams demonstrated that the proposed PD closely aligns with the observed data.

Theory of particle beams transport over curved plasma-discharge capillaries

We present a new approach that demonstrates the deflection and guiding of relativistic electron beams over curved paths by means of the magnetic field generated in a plasma-discharge capillary. The active bending plasma (ABP) represents a promising solution that has been recently demonstrated with a proof of principle experiment. An ABP device consists of a curved capillary where large discharges (of the order of kA) are propagated in a plasma channel. Unlike conventional bending magnets, in which the field is constant over the bending plane, in the ABP, the azimuthal magnetic field generated by the discharge grows with the distance from the capillary axis. This features makes the device less affected by the beam chromatic dispersion so that it can be used to efficiently guide particle beams with non-negligible energy spreads. The study we present in the following aims to provide a theoretical basis of the main ABP features by presenting an analytical description of a single-particle motion and rms beam dynamics. The retrieved relationships are verified by means of numerical simulations and provide the theoretical matrix formalism needed to completely characterize such a new transport device. Published by the American Physical Society 2024

Improvement of Fatigue Strength in Additively Manufactured Aluminum Alloy AlSi10Mg via Submerged Laser Peening

As the fatigue properties of as-built components of additively manufactured (AM) metals are considerably weaker than those of wrought metals because of their rougher surface, post-processing is necessary to improve the fatigue properties. To demonstrate the improvement in the fatigue properties of AM metals via post-processing methods, the fabrication of AlSi10Mg, i.e., PBF–LS/AlSi10Mg, through powder bed fusion (PBF) using laser sintering (LS) and its treatment via submerged laser peening (SLP), using a fiber laser and/or a Nd/YAG laser, was evaluated via plane bending fatigue tests. In SLP, laser ablation (LA) is generated by a pulsed laser and a bubble is generated after LA, which behaves like a cavitation bubble that is referred to as “laser cavitation (LC)”. In this paper, LA-dominated SLP is referred to as “laser treatment (LT)”, while LC collapse-dominated SLP is referred to as “laser cavitation peening (LCP)”, as the impact of LC collapse is used for peening. It was revealed that SLP using a fiber laser corresponded with LT rather than LCP. It was demonstrated that the fatigue strength at N = 107 was 85 MPa for LCP and 103 MPa for the combined process of blasting (B) + LT + LCP, whereas the fatigue strength of the as-built specimen was 54 MPa.

Stability design of multi-celled corrugated-plate CFST walls under combined axial and in-plane bending loads

Multi-celled corrugated-plate concrete-filled steel tubular (MC-CFST) walls are innovative steel-concrete composite walls comprising horizontally arranged corrugated steel plates, interval flat steel plates, and infilled concrete. Due to the significantly improved out-of-plane stiffness, the corrugated steel plate provides a considerable confinement effect on the infilled concrete, which enhances the structural efficiency and cost-effectiveness of MC-CFST walls. In this study, the stability performance of MC-CFST walls under combined axial and in-plane bending loads was investigated through extensive numerical simulations. A refined finite element (FE) model was established and validated using existing test results. Moreover, a formula for calculating the bending capacity of MC-CFST walls was also derived and validated against FE results. Additionally, parametric analyses were conducted to evaluate the effects of various factors such as the wall width, wall height, concrete strength, steel strength, and width of individual corrugated cells on the global stability performance. It was found that the stability performance was predominantly affected by the overall width of the wall rather than the width of the individual corrugated cells, with an increase in wall dimensions generally diminishing the stability performance. Furthermore, increasing the concrete strength improved the stability performance, while increasing the steel strength had a negative effect. Finally, a design formula was proposed for evaluating the bearing capacity and stability performance of MC-CFST walls under combined axial and in-plane bending loads. The formula demonstrated good agreement with the FE results, and it could provide a valuable reference for practical designs of MC-CFST walls.

Elastoplastic limit analysis of functionally graded materials pipe elbows to predict the damage under in-plane bending moment using XFEM-Technic

Functionally Graded Materials (FGMs) have become a vast field of research, due to their wide range of applications and numerous advantages. The use of FGMs has recently expanded, particularly in the reinforcement of tubular structures. Pipe elbows are among the most important elements in a piping system, responsible for reducing stresses and balancing pressure inside pipes. However, due to significant deformations, most frequently caused by bending moment loads, elbows are more prone to exceeding their stress limits. It is for this reason that the analysis of these tubular structures has attracted the interest of many researchers. As a result, the study of their reinforcement can only be carried out through the study of their damage. In other words, to unlock the difficulties of numerically predicting their responses. The aim of our study is to use the finite element method with the proposed meshing technique in the ABAQUS calculation code, to analyze the behavior of a 90° elbow tubular structure, attached to two straight sections, made of functionally graded FGM Al/SiC (Aluminum/Silicon Carbide) material, with a continuous gradual variation of properties in the direction of wall thickness, per row of finished elements along the entire geometry of the tubular structure, in order to simulate a real pipe system installation. The structure is loaded by two modes of in-plane bending moment (Closing and Opening), with an imposed rotational displacement. The aim of this analysis is to evaluate, firstly, the effects of different grading concepts for the FGM Al/SiC material couple in the model geometry (Simple and Symmetrical Concepts), and secondly, the effect of different power exponent indices (n) of the volume fraction, on the elasto-plastic response up to the damage of the tubular structure. The constitutive behavioral law of our model is based on Von Mises’ equivalent stress flow theory with a hardening variable in incremental form. In addition, the TTO (Tamura-Tomota-Ozawa) model was used to describe the elastic-plastic behavior of the FGM, and the XFEM technique was also applied for crack initiation and propagation. The results obtained under moment-rotation conditions show a significant effect on the response as well as on the level of damage, the effect is also remarkable on the ovalization at the bend cross-section. The approach and reliability of the results obtained were based on a comparison with experimental results, which show good agreement, compared with our numerical model.