Bending Deformation Behavior Research Articles

Fracture behavior of NiNb and NiNbP bulk metallic glasses

While it is known that phosphorous additions enhance the hardness, strength, and glass forming ability of NiNb(P) bulk metallic glasses, nothing is known about the trade-offs regarding the fracture characteristics. The fracture toughness and bending deformation behavior of Ni62Nb38 and Ni59.2Nb38.8P2 BMGs were studied, both of which have been reported to have very high compressive yield strength near 3GPa. The binary NiNb BMG exhibited ~4% plastic bending strain and a precracked fracture toughness of KQ = 50MPa√m which gives an excellent combination of strength and toughness relative to other engineering materials. With the addition of 2at.% phosphorus, the glass forming ability was maximized, but the BMG was hardened and embrittled, fatigue precracking was no longer possible, and micronotched toughness values, which should overestimate the precracked fracture toughness, were in the range of KQ = 19 − 26MPa√m. Additionally, a progressive hardening and bending embrittlement was observed for intermediate P additions of 1 and 1.5at.% phosphorus. Transmission electron microscopy revealed larger medium range order clusters in the relatively softer NiNb BMG which were thought to contribute to easier shear transformations and plastic deformation by shear banding.

Electrothermally actuated network metamaterials with reconfigurable bending deformation modes

Reconfigurable metamaterials with specific deformation modes show great promise in applications such as multifunctional antenna, stretchable electronic device, and reconfigurable soft robot, due to their ability to achieve multiple operational states within a single system. Previous researches on active metamaterials with bending deformation responses revealed two main issues: (1) achieving reconfigurable deformation within the same metamaterial is challenging due to the reliance on uniform external field actuation; and (2) there is a lack of in-depth studies on the microstructure-property relationships for the bending deformation responses of network metamaterials due to the lack of theoretical analysis. To address these issues, this study presents a mechanical design strategy for an electrothermally actuated network metamaterials to realize reconfigurable bending deformation. A theoretical model describing the electrothermally actuated bending deformation responses is developed through a three-level analysis, which offers a comprehensive understanding of the parameter-property relationships and accurately describes the bending deformation behaviors. The validity of these mechanical models is confirmed through finite element analyses (FEAs) and experimental results. These mechanical models provide analytical solutions for crucial mechanical quantities, including the electrothermally actuated bending angles and effective strains for bending deformation responses. The bending behaviors of the reconfigurable metamaterials under electrothermal actuation can be adjusted by the key nondimensional geometric parameters and the actuation strategies. Additionally, experimental results and FE calculations demonstrate that multiple bending responses can be realized within a single metamaterial by different actuation strategies. This study offers comprehensive guideline from theoretical predictions, FE calculations, and experimental demonstrations for future researched of reconfigurable metamaterials to realize required deformation behaviors.

Effect of ultrasonic vibration on the roll bending deformation behavior of ultra-thin-walled corrugated sheets

The ultra-thin-walled corrugated sheet is a crucial component of metal honeycomb structures. Due to the size effect, the traditional roll bend forming process often leads to significant dimensional deviations in ultra-thin-walled corrugated sheets. To address this issue, an ultrasonic vibration-assisted roll bend forming process was proposed. First, an ultrasonic vibration-assisted roll bend forming device was designed, which had a special drive roller structure that can alter the original axial direction of ultrasonic vibration to produce a radial vibration with an amplitude of 0–2 µm. Under the high-frequency impact and acoustic softening effect of ultrasonic vibration, the ultra-thin-walled corrugated sheets formed numerous plastic penetration zones. As a result, the influence of individual grain heterogeneity was weakened and the stress distribution states underwent an interchange. Therefore, the ultra-thin-walled corrugated sheets demonstrated improved edge length uniformity, increased hardness in the deformed areas, reduced surface roughness, and decreased springback angle. However, excessive ultrasonic amplitude resulted in severe thinning or even rupture. Ultimately, high-quality ultra-thin-walled corrugated sheets were successfully fabricated using pure titanium foil with a t/d of 5.4 and an ultrasonic amplitude of 1.6 μm.

A Double Fish‐Shaped Metamaterial with Variable Bending Stiffness and Damping under Elastic Tension

The study of bionic metamaterials with unique properties has gained increasing attention in recent years. This article introduces a double fish‐shaped metamaterial (DFSM) and investigates its elasticity and deformation behaviors. The Poisson's ratio of DFSM is derived from the energy principle and Mohr's theorem. The bending deformation behaviors of DFSM under given elastic strains are observed and tested by using the homemade experimental bench, which is further compared with finite element (FE) methods. The FE results show good agreement with experimental results. The bending vibration of DFSM under elastic tension is recorded and analyzed using a homemade prestrain bench in conjunction with a high‐speed camera. The present study proposes a straightforward and valid approach for incorporating the variable bending stiffness and the variable bending damping into DFSM. The revealed mechanical properties of DFSM in this article demonstrate its potential for engineering applications that require multistiffness and multidamping capabilities.

Flexoelectric and surface effects on bending deformation and vibration of piezoelectric nanolaminates: Analytical solutions

In this paper, a model of double-layer rectangular piezoelectric nanolaminates with different upper and lower surface properties is established. The bending and vibration behavior of the piezoelectric nanolaminates are evaluated and analyzed, taking into consideration the flexoelectric and surface effects. Utilizing the surface piezoelectric model, flexoelectric theory, and Kirchhoff plate theory, this study provides analytical solutions for the bending deflection and natural frequency of rectangular piezoelectric nanolamination materials under various boundary conditions. The results indicate that the effects of flexoelectric and surface influences on piezoelectric nanolaminates are associated with residual surface stress and flexoelectric coefficients. These effects can enhance the bending stiffness and decrease the natural frequency of the piezoelectric nanolaminates. Furthermore, altering the residual stress on the upper and lower surfaces of the laminates separately will result in different trends in bending deflection, while causing a consistent trend in natural frequency change. When the electric potential direction of piezoelectric nanolaminates is different, the bending deflection of piezoelectric nanolaminates will change accordingly. The natural frequency of piezoelectric nanolaminates is determined by the absolute value of the flexoelectric coefficients, and is independent of their positive or negative values. Both the surface effect and the flexoelectric effect are influenced by size-dependent behaviors. When the thickness of the laminates is sufficiently large, both the surface effect and flexoelectric effect can be disregarded. This paper's research methods and results provide theoretical models and analytical methods for the microstructure design, multi-physical field characterization, and bending deformation behavior of intelligent components containing rectangular piezoelectric nanolaminates.

Analysis of Bending Deformation and Stress of 6063-T5 Aluminum Alloy Multi-Cavity Tube Filled with Liquid.

The production of aluminum alloy multi-lumen tubes primarily involves hot bending formation, a process where controlling thermal deformation quality is difficult. Specifically, the inner cavity wall of the tube is prone to bending instability defects under the bending stress field. To address these challenges in the bending deformation of aluminum alloy multi-lumen tubes, a multi-lumen liquid-filled bypass forming method is proposed in this paper. This study focuses on the 6063-T5 aluminum alloy double-lumen tube as the research object. The liquid-filled bending deformation behavior of the aluminum alloy double-lumen tube was investigated, and the deformation theory of the aluminum alloy double-lumen tube was studied. Through experimental and numerical simulation methods, the influence of support internal pressure, bending radius, and tube wall thickness on the liquid-filled bending deformation behavior of the double-lumen tube was examined. The results indicate that when the value of internal pressure was 7.5 MPa, the straightening of the outer wall was improved by 2.51%, the thinning rate of wall thickness was minimized, and the internal concave defect was effectively suppressed. The liquid-filled bending method provides a promising new approach for the integrated bending and forming of multi-lumen tubes.

Effects of Yttrium Addition on Bending Deformation Behavior of Magnesium

Effects of Yttrium Addition on Bending Deformation Behavior of Magnesium

Study on Calculation Method of Bending Performance of Concrete Sandwich Composite Slab.

In order to explore the flexural behavior of a concrete sandwich panel under concentrated boundary conditions, based on Kirachhoff's elastic thin plate theory in this paper, the geometric deformation, physical conditions, and equilibrium relationship of a sandwich panel are deduced by constructing the layered analysis model of the sandwich panel, the basic differential equation of the flexural deformation of the concrete sandwich thin plate is obtained, and the mathematical expression of the internal force and displacement under the boundary condition of concentrated support is given. Combined with an engineering example, the proposed calculation method is verified. The results show that, in the arrangement of reliable connectors for concrete sandwich panels, the concrete wythes bear the load while the contribution of the core layer to the bending capacity of the structure can be ignored. When subjected to a laterally distributed load, the sandwich panel mainly experiences out-of-plane bending deformation, and the bending normal stress in the concrete panel layer shows a linear non-uniform distribution along the thickness direction of the panel. The bending deformation performance and bearing efficiency of a concrete sandwich slab with the change in concentrated support position have significant effects, and the load transfer efficiency can be improved by optimizing the arrangement of supports. Except for small local areas near the supports, the bending stress distribution and deformation behavior of the concrete sandwich panel can be accurately analyzed by the calculation method established in this paper.

Bending deformation behavior and characterization method of flexural stiffness of composite tubes under four-point bending tests

The four-point bending test has inherent errors in measuring the flexural stiffness of tubes. The size of loading noses/supports could affect the response of equivalent bending moment on the tested tubes’ transverse section. The asymmetric axial strain distribution on the tested tubes’ transverse section depends on the tube’s thickness to diameter ratio. Based on the above phenomena, a four-point bending test with small-sized loading noses/supports and a characterization formula of tube’s flexural stiffness were proposed. The proposed methods were conducted on a thin-walled steel tube and a composite tube respectively. The errors between theoretical and experimental results were discussed.

GLARE deformation in low-restraint state: Tensile and bending behavior

Fiber metal laminates (FMLs) possess a better weight reduction effect than traditional metal materials due to the coupling properties of heterogeneous materials, showing promise in the areas of aviation and aerospace. At present, the research on FMLs mainly focuses on the deformation properties after curing while the mechanical properties in the low-restraint state, i.e. the laminates are temporarily not cured and are formed under lower constraint stresses, are not studied in detail. Herein, the low-restraint GLARE is taken as a research object and its deformation characteristics and failure mode are studied using uniaxial tensile, bending experiments and numerical simulation in this paper. Moreover, the influence of key parameters, such as temperature, laminate structure and span length, is investigated, as well as the tensile and bending deformation behavior of GLARE in a low-restraint state is obtained. In addition, based on experimental observations, it is found that the low-restraint GLARE produces the phenomenon of interlayer slip, and the interlaminar residual stress is much smaller than the cured laminate, whereas the deformation limit and performance are improved. This paper provides theoretical bases for the in-depth analysis of deformation properties and forming laws of low-restraint GLARE, guiding further applications of laminates.

Bending deformation behavior of a 1000 MPa grade dual-phase steel with superior bending toughness

Poor bending toughness is still a critical drawback of high-strength ferrite-martensite (F-M) dual-phase (DP) steel, which is unfavorable to their collision safety. In this study, a 1000 MPa grade F-M DP steel with excellent bending toughness was fabricated by reducing the strength difference between ferrite and martensite via introducing solid solution strengthening (Si), precipitation strengthening (VC) and reasonable tailoring high martensite content. The obtained DP steel exhibits a high ultimate tensile strength (UTS) of 1123 MPa, together with a good total elongation (TE) of 16.0 % and an excellent maximum bending angle (αf) of 98°. The αf of the obtained DP steel is obviously higher than that of 62–80° for reported DP steels with similar UTS levels. The related bending deformation and fracture behavior are emphasized and indicate that high bending toughness in obtained DP steel can be attributed to the excellent coordinate deformation between ferrite and martensite, improved martensite deformability and crack blocking by the fibrous deformed martensite.

Bending Deformation Behavior of Eggshell and Eggshell–Polymer Composites

Deformation behavior of the composite “eggshell–polymer plomb” was examined under bending. Hen eggs were taken as a biological material for experiments. It was shown that a viscoelastic polymer coating does not change the type of deformation behavior of the composite, given that the eggshell continued to be brittle despite its mechanical characteristics varying widely for a brittle solid. Joint “polymer plomb–eggshell” never cracked under bending and hence exhibited a high cohesion strength under the stresses applied in these experiments. It seems that the composite “eggshell—polymer plomb” could substitute for the composite “tooth enamel–polymer plomb” under elaboration of novel restorative materials for dentistry, namely, for examination of their mechanical properties, including cohesive strength.

Theoretical Modeling and Experimental Verification of the Bending Deformation of Fiber Metal Laminates.

Fiber metal laminates have been widely used as the primary materials in aircraft panels, and have excellent specific strength. Bending deformation is the most common loading mode of such components. An accurate theoretical predictive model for the bending process for the carbon reinforced aluminum laminates is of great significance for predicting the actual stress response. In this paper, based on the metal-plastic bending theory and the modified classical fiber laminate theory, a modified bending theory model of carbon-fiber-reinforced aluminum laminates was established. The plastic deformation of the thin metal layer in laminates and the interaction between fiber and metal interfaces were considered in this model. The bending strength was predicted analytically. The FMLs were made from 5052 aluminum sheets, with carbon fibers as the reinforcement, and were bonded and cured by locally manufacturers. The accuracy of the theory was verified by three-point bending experiments, and the prediction error was 8.4%. The results show that the fiber metal laminates consisting of three layers of aluminum and two layers of fiber had the best bending properties. The theoretical model could accurately predict the bending deformation behaviors of fiber metal laminates, and has significant value for the theoretical analysis and performance testing of laminates.

Deformation behaviors of flip chip plastic ball grid array packages subjected to temperature change using moiré interferometry

When the temperature of the package assembly is changed, non-uniform deformation and local stress may occur owing to the different thermal expansion coefficients of the constituent materials, while concentrated thermal stress may cause significant failure. In this study, we carry out an experiment and analysis of the thermal deformation of a flip chip plastic ball grid array package with respect to temperature change. Interference fringe patterns representing the displacement distribution of each temperature stage are obtained using a Moiré interferometry and the bending deformation behavior and the strain of the solder ball are analyzed thereafter. We compare the deformation behavior of a single-sided package assembly and a double-sided package assembly. The effective strain, which significantly affects the failure of the solder ball, is found to be the largest in the solder ball just outside the edge of the chip in the case of the single-sided package assembly. In the case of the double-sided package assembly, the maximum effective strain is found in the solder ball just inside the edge of the chip, with a value approximately 50 % larger than in the case of the single-sided package assembly. Wenn sich die Temperatur eines Gehäuses ändert, kann es aufgrund der unterschiedlichen Wärmeausdehnungskoeffizienten der einzelnen Werkstoffe zu ungleichmäßigen Verformungen und lokalen Spannungen kommen, während konzentrierte thermische Spannungen zu erheblichen Ausfällen führen können. In dieser Studie führen wir ein Experiment und eine Analyse der thermischen Verformung einer Flip-Chip Kunststoffkugel Gitteranordnung in Abhängigkeit von der Temperaturänderung durch. Mit Hilfe der Moiré-Interferometrie werden Interferenzstreifenmuster aufgenommen, die die Verschiebungsverteilung jeder Temperaturstufe darstellen und anschließend werden das Biegeverformungsverhalten und die Dehnung der Lötkugel analysiert. Wir vergleichen das Verformungsverhalten einer einseitigen und einer doppelseitigen Gehäusebaugruppe. Es zeigt sich, dass die effektive Dehnung, die das Versagen der Lötkugel maßgeblich beeinflusst, im Fall der einseitigen Baugruppe in der Lötkugel direkt außerhalb des Chiprands am größten ist. Bei der doppelseitigen Baugruppe ist die maximale effektive Dehnung in der Lötkugel direkt innerhalb des Chiprands zu finden, mit einem Wert der etwa 50 % größer ist als bei der einseitigen Baugruppe.

A study on bending deformation behavior induced by shot peening based on the energy equivalence

Shot peening is an essential process for forming large thin-walled components in aerospace industries. However, it is challenging to determine directly the mapping relationship between shot peening parameters and deformation response because of the complex elastic–plastic deformation of shot-peened components. In this paper, a computational model of bending deformation of peened plate samples is established by examining the shot peening behavior from the aspect of energy equivalence, in which the deformation energy of the shot-peened plate is determined by the total kinetic energy input due to the shot impacts and a correction factor that takes into account the influences of oblique impact, shot interaction and shot overlap on the peen forming process in practice. It is proven that the square of curvature radius is proportional to the cube of the thickness but inversely proportional to the indentation coverage and the average kinetic energy input of a single shot. For the effect of a single shot impact in peen forming, the average kinetic energy input of a single shot is a power function with the indentation diameter.

Unusual Spreading of Strain Neutral Layer in AZ31 Magnesium Alloy Sheet during Bending.

In this work, we reported an unusual phenomenon of strain neutral layer (SNL) spreading in an as-rolled AZ31B magnesium alloy sheet during V-bending. The SNL on the middle symmetrical surface perpendicular to the transverse direction (TD) of the sheet extended to the compression region and was accompanied by a mound-like feature. However, the SNL on the side surface perpendicular to the TD was distributed with a parallel band feature. The underlying mechanism was revealed by the finite element (FE) analysis. The results indicate that the three-dimensional compressive stresses in the compression region of the bending samples were responsible for the above phenomenon. Moreover, the area of the SNL in the middle position gradually decreased as the bending test progressed. The findings in this study provide some new insights into the bending deformation behavior of magnesium alloy.

Variation in bending deformation behavior and improvement in bendability of extruded pure Mg through Gd addition

In this study, the twinning and slip behaviors of pure Mg and Mg–1Gd extrudates during bending deformation are investigated by subjecting the extrudates to three-point bending tests. The pure Mg extrudate has a coarse grain structure with a strong basal texture. The Mg–1Gd extrudate has a uniform and fine grain structure with a typical rare-earth (RE) texture because the added Gd causes the suppression of grain-boundary migration and the textural tilting during extrusion. When bending deformation is imposed, cracks are formed in the lower region (tension zone (TZ)) of the bending specimens of both extrudates. However, the bending yield strength and failure bending strain of the Mg–1Gd extrudate are 56% and 68% higher than those of the pure Mg extrudate, respectively. Both the extrudates exhibit similar deformation behaviors in the upper region of the bending specimens, in which {10–12} twinning is activated in most grains. However, because the activation stress for {10–12} twinning is lower in the pure Mg extrudate, its bending yield strength is lower than that of the Mg–1Gd extrudate. In the TZs of both the extrudates, a small amount of {10–12} twinning is caused by the minor tensile stress imposed along the width direction, and the dislocation slip is predominantly caused by the major tensile stress imposed along the longitudinal direction. In the TZ of the pure Mg extrudate, slip is activated to a limited extent during bending because of its strong basal texture, which is unfavorable for basal slip. In contrast, in the TZ of the Mg–1Gd extrudate, basal slip vigorously occurs owing to its RE texture. Furthermore, nonbasal slip also occurs because Gd addition reduces the difference between the critical resolved shear stresses of basal slip and nonbasal slip. Consequently, the bendability of the Mg–1Gd extrudate improves through the effective accommodation of the longitudinal tensile strain in the TZ during bending.

Orientation Dependence on Bending Deformation Behavior of Pure Zinc Single Crystals

Three-point bending tests were performed on pure zinc single crystals with different crystal orientations to investigate orientation dependence on bending deformation behavior. With basal planes parallel to the neutral planes, the specimens deformed due to basal slips and formed a gull shape after deformation. On the other hand, specimens whose neutral planes are perpendicular to the basal planes and neutral axes are perpendicular to [0001] deformed due to second order pyramidal 〈c + a〉 slips, {1012} twinning and basal slips within {1012} twins, displaying a V shape. The bending deformation behavior of pure zinc single crystals was found to show strong orientation dependence. Also, the bending deformation behavior of pure zinc single crystals was found to differ from that of pure magnesium single crystals when the neutral plane and neutral axis are respectively perpendicular to the basal planes and [0001].

The Influence of Microstructure on the Flexural Properties of 3D Printed Zirconia Part via Digital Light Processing Technology.

In recent years, additive manufacturing of ceramics is becoming of increasing interest due to the possibility of the fabrication of complex shaped parts. However, the fabrication of a fully dense bulk ceramic part without cracks and defects is still challenging. In the presented work, the digital light processing method was introduced for fabricating zirconia parts. The flexural properties of the printed zirconia were systematically investigated via a three-point bending test with the digital image correlation method, scanning electron microscopy observation and fractography analysis. Due to the anisotropy of the sample, the bending deformation behaviors of the zirconia samples in the parallel and vertical printing directions were significantly different. The flexural strength and the related elastic modulus of the samples under vertical loading were higher than that of the parallel loading, as the in-plane strength is higher than that of the interlayer strength. The maximum horizontal strain always appeared at the bottom center before the failure for the parallel loading case; while the maximum horizontal strain for the vertical loading moved upward from the bottom center to the top center. There was a clear dividing line between the minimum perpendicular strain and the maximum perpendicular strain of the samples under parallel loading; however, under vertical loading, the perpendicular strain declined from the bottom to the top along the crack path. The surrounding dense part of the sintered sample (a few hundred microns) was mainly composed of large and straight cracks between printing layers, whereas the interior contained numerous small winding cracks. The intense cracks inside the sample led to a low flexural property compared to other well-prepared zirconia samples, which the inadequate additive formulations would be the main reason for the generation of cracks. A better understanding of the additive formulation (particularly the dispersant) and the debinding-sintering process are necessary for future improvement.

Investigation on the influence of weld position on the deformation behavior of welded tube during free bending process

The plastic deformation behavior of welded tube is affected by the non-uniform distribution of the mechanical properties of welded tube during the free bending process. To explore the influence of weld position on the forming quality and axis dimensional accuracy of welded tube, the free bending experiment and numerical simulation of welded tube were conducted in this paper. First, the principle of free bending was theoretically deduced and the stress distribution of bent tube was analyzed. Then, the hardness test and uniaxial tensile test were conducted to obtain the mechanical properties of weld zone and parent zone of welded tube. The material strength in the weld zone of welded tube is significantly higher than that in the parent zone. Finally, the free bending experiment and numerical simulation with different weld positions were carried out, and the influence of weld position on the bending radius, cross-sectional distortion, and wall thickness of bent tube was discussed. All these findings advance the insight into the free bending deformation behavior of welded tube and help to improve the forming quality of welded tubes and facilitate the application of free bending technology in welded tube.