Bending Part Research Articles

Variation of elastic modulus of high strength 21-6-9 tube and its influences on forming quality in numerical control rotary draw bending

Elastic modulus is one of the most crucial mechanical property parameters that affects the plastic forming quality of bent parts, especially for springback. Elastic modulus practically varies with plastic deformation, and its precise description is necessary to enhance simulation precision for tube bending and gain steady, high-precision bent components by actual bending. Using repeated loading-unloading tensile tests (RLUTTs), the variation of elastic modulus of high strength 21-6-9 stainless steel tube (21-6-9-HS tube) in terms of plastic strain has been obtained, which its decreases rapidly at the beginning, then decreases tardily and tends to be stable in the end with increasing the plastic strain. The variation can be expressed as a first order exponential decay function. By embedding the variation of elastic modulus with the plastic strain into ABAQUS software to simulate numerical control (NC) rotary draw bending of the 21-6-9-HS tube, the prediction precision for the springback angle, springback radius, maximum cross section distortion ratio and maximum wall thinning ratio can be improved by 11.98%, 7.62%, 35.53% and 11.55%, respectively.

Fabrication and testing of small mock-ups for helium cooled ceramic reflector breeding blanket development

Korea has developed a helium cooled ceramic reflector test blanket module (TBM) for fusion reactors. An advanced reduced activation alloy has been developed as a structural material and various joining methods such as E-beam welding, tungsten inert gas (TIG) welding, laser welding, and hot isostatic pressing have been applied to establish its fabrication method and procedure. Based on the current design of the TBM and breeding blanket, TIG welding was selected as the main joining method, and the U-shaped first wall (FW) was adopted. For welding of the breeding blanket, a special joining technique without a permanent backing strip with simultaneous full penetration welding in accordance with the design rules of class N2RX of RCC-MRx is required for the pressure vessel. For the U-shaped FW, distortion of the drilled cooling hole during the bending should be limited. Three small mock-ups were fabricated in this study to investigate these issues. The joints and bending parts were visually observed after cutting, and the hydrostatic pressure test was performed for regions with low thickness. The results show that the proposed fabrication methods are applicable in the fabrication procedure development for the breeding blanket.

Deposition of DLC films on the inner wall of U-type pipes by hollow cathode PECVD

There are many defects in the bending part of U-type pipe, which will directly affect its safety and service life. DLC (Diamond Like Carbon) film is considered as an effective protective film because of its excellent properties. However, it is very difficult to deposit DLC films on the inner wall of U-type pipes with double stress. The purpose of this paper is to deposit DLC film with high hardness, wear resistance and corrosion resistance on the inner wall of U-type pipes by hollow cathode PECVD. The microstructure, mechanical properties, tribological and corrosive behaviors were characterized by the Raman spectroscopy, ATR-FTIR, SEM, nano-indention, polarization, electrochemical impedance spectroscopy and ball-on-disk tribological tests. Results indicates that the U-type pipe inner DLC films shows the lower stress level. Compared with the bare substrate, it presents the higher hardness (7– 14 GPa), elastic factor (>0.1) and plastic factor (>0.1) and the above DLC film exhibits the lower corrosion current density, which is about 1–2 orders of magnitude lower than the bare substrate. Moreover, the DLC films also possesses the lower friction coefficient (0.04– 0.06) and wear rate (2.67– 5.93E-7 mm3N−1 m−1). Therefore, the DLC films exhibits the greater mechanical, tribological and anti-corrosion performance, indicating that the above DLC films effectively protects U-shaped pipe and prolongs its service life.

Deformation and failure of thin spherical shells under dynamic impact loading: Experiment and analytical model

Thin curved shells are widely used in engineering. A shallow spherical shell is an effective representation of a curved shell affected by local impact loading. Therefore, the dynamic response of spherical shells under impact loading should be investigated to provide a design reference for curved shells applicable to engineering fields. In this study, the dynamic response and perforation of an aluminum spherical shell impacted by a cylindrical projectile were investigated theoretically. An isometric transformation was adopted to describe the major bending deformation of the spherical shell around the impact point. In addition, an edge region between the major bending part and an undeformed part was observed experimentally and described using a deformation mode. Hamilton's principle was adopted to derive the governing equations of the dynamic response of the impacted spherical shell. Furthermore, a viscoplastic strengthened model was introduced to describe the membrane force and bending moment of the perforation, whereas a rigid–plastic model was used to calculate the force and moment of the other parts of the spherical shell. The governing equations combined with the strengthened model were solved using the Runge–Kutta method. A comparison between the theoretical predictions and experimental results indicated a good agreement between them. Finally, the effects of the parameters set in the governing equations of the theoretical prediction were analyzed. We observed that the theoretical model predicted dimple radius more accurately than dimple depth. The dimple depth is linearly proportional to the impact velocity. In addition, the assumed sizes of the shear region of perforation only affect the ballistic limit and deformation generated by a velocity higher than the ballistic limit. The deformation and perforation of the impacted shell are almost independent of the initial width of the edge region of deformation. Additionally, we observed that the ballistic limit of the shell is linearly proportional to the shell thickness.

A Structure for the Control of Geometry and Properties of a Freeform Bending Process

Abstract Today, in production shaping processes, the application of closed loop control is often limited to controlling the geometry. For freeform bending processes the geometric deviations are compensated by numerous experimental iterations, without regarding the mechanical properties. Especially for freeform bent parts also the internal properties are important because, e.g., the residual stresses strongly influence the downstream process steps. In this work a multivariable feedback control structure is proposed that is able to control both, the geometry of the workpiece as well as selected mechanical properties of the material.

Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates

In this paper, a modified single variable shear deformation plate theory is developed for free vibration analysis of rectangular functionally graded plates. By using the equilibrium equations of forces, the relationship between bending and shear parts is established, so that the displacement fields and the governing equation of the modified single variable plate theory contain only one unknown variable. As a consequence, the number of unknown variables is reduced, so it is effective for computation of solid mechanics. The advantage of proposed theory is that it consists of only one unknown variable but it is capable for analysis of heterogeneous plate such as functionally graded plates. The numerical results of the free vibration of functionally graded plates are carried out and compared with other published data to ensure the accurateness and effectiveness of this modification. The paper also explores the impact of some parameters on the free vibration of the functionally graded plates.

Researches, studies and development prospects of the quality of metallic parts made on CNC

The quality of products is an important economic indicator. The paper presents studies, researches and development of prospects execution of bent metal parts on CNC machines. Through these studies we tried to find answers regarding the quality of products, problems that many companies face. Laborious studies and research proposed for the paper, on determining the drawings of metal parts (the flat plane). The quality and precision of the products, may influenced by the other variables: the vibrations of machines, tool usage, tolerance between the surface of the bending tools, variation of the temperature during the processes of punching and bending, their usage and the roughness of the metal sheet. The calculations of the drawing pieces must include the bending coefficients Kî. The bending coefficient obtanaited for de steel parts (OL 37) with a thickness of 1 mm, was the subject of the present paper. This coefficient Kî depends on: the type of the material, the chemical composition, the degree of complexity and the number of bends, the movement between the piece and punching or bending tools, vibrations of the machines and other variables. The bending coefficient was obtained by experimental tests and measurements.

A novel GBT-formulation for thin-walled FGM-beam-structures based on a reference beam problem

This paper proposes an efficient generalized beam theory (GBT) formulation, which accounts for cross-sectional deformations in slender prismatic structures. It was shown by the authors in a recent publication [1] that in-plane distortional deformations and accompanied out of plane warping deformations of the cross-section influence the accuracy of results in beam dynamics especially if thin-walled cross-sections are applied. The GBT formulation proposed in [1] overcomes the inaccuracies of classical beam mechanics, however, requires a two-dimensional plane discretization of the cross-section. The computational complexity can be reduced vastly, if thin-walled cross-sections can be discretized with one-dimensional elements. Consequently, this paper discusses an approach with a line mesh discretizing the cross-section and having six degrees of freedom at each node. The membrane part consists of massless micro-polar rotations (drilling rotations) and can be derived independently from the bending part, where a shear elastic formulation is selected.

FREE VIBRATION OF BFGSW BEAMS PARTIALLY RESTING ON PASTERNAK FOUNDATION BASED ON A SINUSOIDAL THEORY

In this paper, free vibration of a bidirectional functionally graded sandwich (BFGSW) beams partially resting on a Pasternak foundation is studied. The beams with three layers, an axially functionally graded core and two bidirectional functionally graded face sheets, are made from a mixture of metal and ceramic. The material properties of the face sheets are considered to vary continuously in both the thickness and length directions by the power-law distributions, and they are estimated by Mori-Tanaka scheme. A sinusoidal shear deformation theory, in which the transverse displacement is split into bending and shear parts, is employed to derive energy expressions of the beam. A finite element formulation is formulated and employed to compute vibration characteristics. Numerical result reveals that the ratio of foundation support to the beam length plays an important role on the vibration behaviour, and the dependence of the frequencies upon the material grading indexes is governed by this ratio. Numerical investigation is carried out to highlight the effects of the material distribution, the layer thickness ratio, the foundation stiffness on the vibration characteristics of the beams. The influence of the aspect ratio on the frequencies of the beams and is also examined and discussed.

Pullout resistance of crimped reinforcing fibers using cold-drawn NiTi SMA wires

This paper assesses the bond strength of crimped fibers manufactured by a cold-drawn SMA wire using a continuous method. Several pullout tests are conducted to study bond strength and crack-closing ability of crimped SMA wire. Before and after SMA heating, the pullout force–displacement relationships of crimped fibers are compared with different types of end-shapes, namely, straight and paddled end, to measure the bond strength of these fibers in cementitious composite material. The cold drawn fiber with more than 4% area reduction ratio due to cold drawing work should be used for producing crimped fibers to overcome the stretching effect of indentation by heating. The paddled fibers show almost twice energy dissipation capacity than the crimped fibers, while secant stiffnesses of the crimped fibers are larger by 20% on the maximum than those of the paddled fibers. Crack-closing ability of crimped fibers may be evaluated when the stretching effect at the bent parts due to thermal expansion are compared with recovery effect of prestrain due to shape memory effect. The experimental data reveals the efficiency and applicability of the crimped SMA fibers in contrast to other end-shape SMA fibers provided by discontinuous methods.

Major Earthquakes of Southern Calabria, Italy, Into the Regional Geodynamic Context

We analyze the seismicity of southern Calabria, the most active area of Italy from the seismic point of view, and compare it with geodetic data available from literature. Our analysis focuses both on the strongest earthquakes of the last centuries reported in the Italian seismic catalog and on seismicity recorded in the last decades by instrumental networks. The data highlight that strong shallow seismicity of southern Calabria, imputed to normal faulting by previous investigators, corresponds to low values of local, geodetic horizontal strain rate. This situation is quite different from that observed along the Apennines from Umbria to northern Calabria, where normal-faulting strong earthquake activity corresponds to relatively large values of extensional strain rate. On the other hand, the strong earthquake activity of southern Calabria corresponds to marked variation of vertical displacement rates detected from west to east in the same area. We frame these evidences into the regional geodynamic model assuming the coexistence of Africa-Europe NNW-trending plate convergence and SE-ward residual rollback of the Ionian lithospheric slab subducting underneath the Tyrrhenian-Calabria unit. Taking also benefit from the recently found relationship between the two strongest earthquakes of the twentieth century in Italy (the southern Calabria earthquakes of 1905 and 1908 of magnitude 7.5 and 7.1, respectively), we propose that instabilities of the upper bending part of the subduction slab may perturb shallow normal faults in the overriding plate and concur to shallow seismicity of southern Calabria jointly with the dynamics of differential vertical motion marked by geodetic data. The opposite action of lithosphere convergence and rollback may justify low values of horizontal strain rate in the low coupling scenario of the Ionian and Tyrrhenian-Calabria units.

An improved shear deformable theory for bending and buckling response of thin-walled FG sandwich I-beams resting on the elastic foundation

This paper proposes an improved first-order beam theory by separation of variables for bending and buckling analysis of thin-walled functionally graded (FG) sandwich I-beams resting on a two-parameter elastic foundation. By dividing the displacements into bending and shear parts, this model can produce the deflections for both two cases with and without shear effect. The mechanical properties of beams based on the power law distribution of volume fraction of ceramic or metal. Governing equations are established from Lagrange’s equations. The new Ritz’s approximation functions, which are combined between orthogonal polynomial and exponential functions, are proposed to solve problem. The deflections and critical buckling loads of thin-walled FG sandwich I-beams are presented and compared with those available literature to verify the present theory. The effects of material distribution, boundary conditions, length-to-height ratio, shear deformation and foundation parameters on the results are investigated in detail.

Bending response of porous advanced composite plates under thermomechanical loads

The new composite functionally classified materials (FGM) used in plates contain probably a porosity volume fraction which needs taking into account this aspect of imperfection in the thermo-mechanical behavior of such structures. A refined shear deformation theory is developed to investigate the thermo-mechanical bending response of porous advanced composite plates such as functionally graded plates by using Navier solution. This work presents a model that employed a new transverse shear function by decomposing the transverse displacements into two parts, the bending part and shear part, the simplified refined shear deformation theory has less unknowns than the first-order shear deformation theory, the higher-order shear deformation theory, the sinusoidal shear deformation theory and the quasi-3D theory, so its computational expenses are reduced. In addition, the new refined theory needs no shear correction factor. The comparisons of deflection, axial stresses, and transverse shear stresses of the porous FGM plates obtained by the proposed theory, these results are compared with others in the literature.

Effect of roller dies on springback law of profile for flexible 3D multi-point stretch bending

With the increasing demand of the parts with multi-segment curvature, long length, and complex section shape, the required target shape is more and more difficult to meet. In this article, a flexible three-dimensional (3D) multi-point stretch bending processing method for a roller die is proposed, and a flexible 3D stretch bending equipment of a roller die is developed. With the application of flexible 3D stretch bending technology of roller dies, the complex 3D parts can be formed at one time with only two degrees of freedom. In order to better evaluate the springback deformation of 3D parts, the total springback process of the flexible 3D stretch bending parts of a roller die is divided into two parts: horizontal bending springback distance and vertical bending springback distance. The springback law of different length profiles is studied by numerical simulation and compared with the experiment. From the perspective of springback, this study analyzes the parts produced by the 3D FSBRD process and studies the influence of different process parameters on springback.

An experimental approach to the estimation of stiffness changes in RC elements exposed to bending and high temperature

This paper presents the results of tests for possible stiffness changes in bent reinforced concrete elements exposed to simultaneous action of load and high temperature. The above issue plays a critical role in the advanced analysis of complex RC structures subjected to fire.In order to examine this issue, an experimental study of 24 full-size RC beams was performed. All beams were divided into 8 series according to 3 factors: (1) the cross-section zone exposed to high temperature – tension or compression zone, (2) reinforcement ratio – 0.44 or 1.13%, (3) load level in reference to ultimate load capacity at room temperature – 50 or 70%. The pure bending part of the beam was heated. Stiffness changes estimated on the basis of deflection measurement.The cross-section stiffness of the beam with the heated tension zone decreases rapidly at the initial heating stage.A decrease of 60–80% in cross-section stiffness is observed at reinforcement temperature of 200–300 °C. When reinforcement temperature is about 500 °C, the cross-section stiffness may be only 10–15% of its value at room temperature. It has also been found that the model recommended in Eurocode 1992-1-2 characterizing mechanical properties of tensile steel in high temperature may be used for the adequate prediction of stiffness decrease in the cross-section with the heated tension zone.It can be assumed that during heating the stiffness of cross-sections with the heated compression zone will remain approximately constant for some time. It will only start to decrease when the strain of concrete exposed simultaneously to load and high temperature begins to exceed its free thermal strain.This paper presents a simplified method to estimate the cross-section stiffness in bent reinforced concrete elements with the heated tension or compression zone.

The Role of Seismic and Slow Slip Events in Triggering the 2018 M7.1 Anchorage Earthquake in the Southcentral Alaska Subduction Zone

AbstractThe M7.1 2018 Anchorage earthquake occurred in the bending part of the subducting North Pacific plate near the geometrical barrier formed by the underthrusting Yakutat terrane. We calculate the triggering potential related with stress redistribution from deformation sources including the M9.2 1964 earthquake coseismic slip, postseismic deformation, slip from regional M > 5 earthquakes, and the cumulative slip of previously detected slow slip events over the past 55 years. We investigate the deeper shallow depth (20–60 km) seismicity response to these perturbations using an epidemic type aftershock sequence model to describe earthquake‐to‐earthquake interactions. The statistical forecast captures the triggered seismicity during the 1983 M6+ aftershocks in Columbia Bay but performs poorly during the slow slip event period between 1992.0 and 2004.8 that presents a statistically significant rate change (β, Z > 2; M < 4.0). We find that stress effects from the 1964 postseismic source and the 12‐year‐long slow slip event (~M7.8) contribute to the 2018 Anchorage earthquake occurrence and that slow slip events modulate the deeper shallow depth seismicity patterns in the region.

Semi-automatic Knob System for Assisting Flexible Endoscope Steering

In this paper, a semi-automatic knob system for assisting control of flexible endoscope is introduced. For conventional flexible endoscope, the torque to bend the bending part is increased proportionally to the curvature of the insertion tube. As the bending angle increases, the required torque is increased. This characteristic makes a surgeon tired. The proposed semi-automatic knob system consists of a knob controller, a power generation unit, and a bending part. The knob controller includes four FSR (force sensitive resistor) sensors to measure external force applied by the operator. The power generation unit generates the power depending on the signal level of FSR sensors. Using the semi-automatic knob system, a user can control the steering of the flexible endoscope with less power as compared to conventional flexible endoscope. The usefulness of the proposed system is verified through experiments.

Free Vibration of FGSW Plates Partially Supported by Pasternak Foundation Based on Refined Shear Deformation Theories

A refined third-order shear deformation theory (RTSDT), in which the transverse displacement is split into bending and shear parts, is employed to formulate a four-node quadrilateral finite element for free vibration analysis of functionally graded sandwich (FGSW) plates partially supported by a Pasternak foundation. An element based on the refined first-order shear deformation theory (RFSDT) which requires a shear correction factor is also derived for comparison purpose. The plates consist of a fully ceramic core and two functionally graded skin layers with material properties varying in the thickness direction by a power gradation law. The Mori–Tanaka scheme is employed to evaluate the effective moduli. The elements are derived using Lagrangian and Hermitian polynomials to interpolate the in-plane and transverse displacements, respectively. The numerical result reveals that the frequencies obtained by the RTSDT element are slightly higher than the ones using the RFSDT element. It is also shown that the foundation supporting area plays an important role on the vibration of the plates, and the effect of the material distribution on the frequencies is dependent on this parameter. A parametric study is carried out to highlight the effects of the material inhomogeneity, the foundation stiffness parameters, and the foundation supporting area on the frequencies and vibration modes. The influence of the layer thickness and aspect ratios on the frequencies is also examined and highlighted.

Extraction of tunnel center line and cross-sections on fractional calculus, 3D invariant moments and best-fit ellipse

In order to measure and analyze the tunnel 3D deformation accurately, effectively and conveniently, we use the 3D point clouds instead of Total station data. A 63.6 m long tunnel was scanned twice by using a Leica C10 laser scanner (max scanning range is 300 m), for each of the scans, to obtain the accurate data and to avoid to having tunnel bending part, we divide the tunnel into five sections for the measurements, and for each measurement, the data is scanned in one station. Since the original data includes some noise, to remove noise in the point clouds, we study a new Fractional calculus template for data smoothing. After that, we propose a new method to extract the tunnel central axis based on the 3D invariant moments, and then the tunnel posture is rotated to make the central axis parallel to the reference direction, which is rotational invariant and repeatable. Based on the central axis in each section, the cross-sections are detected, and the elliptic features of a cross-section are calculated for analyzing the tunnel convergence. To make cross-section measurement rotational invariant, we apply the zeroth, the first and the second moments to obtain major and minor axes through the cross-section center. The experiment results demonstrate that this method can meet the accuracy requirements, and it can be with an accuracy of 2 mm for cross-section measurement. It is useful for tunnel engineering applications both in the tunnel 3D point cloud analysis and 3D information extraction.

Cross-section deformation behaviors of a thin-walled rectangular tube of continuous varying radii in the free bending technology

Abstract Thin-walled rectangular tube bent parts of continuous varying radii are widely used in aircraft, aerospace, aviation, radar, and several high-tech industries to save space and satisfy the internal structure compact of the specific products. In the previous years, the applications of thin-walled rectangular tubes were hindered because of the distortion in the cross-section area, which occurred during deformation. Nevertheless, due to its unique characteristic, free bending technology is highly suitable to form tubular components with a variable bending radii and bends in several planes. Thus, in this study, the deformation behavior of a thin-walled tube (with a rectangular cross-section area) of continuous varying radii during free bending technology was investigated. Besides, a stress analysis model was proposed to predict the equivalent stress and strain distribution. The proposed model was verified using simulations and experimentation. Furthermore, the influence of two key parameters (feeding speed and fillet radius) on the formability of a thin-walled rectangular tube was discussed. The remarkable results obtained from this study verify that free bending technology is a significant forming technology to manufacture rectangular thin-walled tubes with continuous varying radii.