Modelling and Simulation on the Effect of Hot Forming Damage on Three-Point Bending Performance of Beam Components

The effects of forming damage are analyzed,which occur during hot stamping process,on the load-carrying capacity and failure mode of hot stamped beams.A damage-coupled pre-forming constitutive model was proposed,in which the damage during hot stamping process was introduced into the service response.The constitutive model was applied into the three-point bending simulation of a hot stamped beam,and then the influences of forming damage on the load-carrying capacity and cracks propagation were investigated.The results show that the forming damage reduces the maximum load capacity of the hot stamped beam by 7.5%.It also causes the crack to occur earlier and promotes crack to propagate along the radial direction of the punch.

Three-point bending behavior of aluminum foam sandwich with steel panel

Static three-point bending tests of aluminum foam sandwiches with glued steel panel were performed. The deformation and failure of sandwich structure with different thicknesses of panel and foam core were investigated. The results indicate that the maximum bending load increases with the thickness of both steel panel and foam core. The failure of sandwich can be ascribed to the crush and shear damage of foam core and the delamination of glued interface at a large bending load, The crack on the foam wall developed in the melting foam procedure is the major factor for the failure of foam core. The sandwich structure with thick foam core and thin steel panel has the optimal specific bending strength. The maximum bending load of that with 8 mm panel and 50 mm foam core is 66.06 kN.

A modified Johnson-Cook model for NC warm bending of large diameter thin-walled Ti-6Al-4V tube in wide ranges of strain rates and temperatures

Numerical control（NC） warm bending is a proven strategy to form the large diameter thin-walled（LDTW） Ti-6 Al-4 V tubes, which are typical light-weight and high-performance structural components urgently required in many industries. In virtue of unveiling the thermo-mechanical coupled deformation behaviors, uniaxial tensile tests were conducted on Ti-6 Al-4 V tube within wide ranges of temperatures（25-600 ℃） and strain rates（0.00067-0.1 s～（-1））. Moreover, a modified Johnson-Cook（JC） model is proposed with a consideration of nonlinear strain rate hardening and the interaction between strain hardening and thermal softening. Resultantly, the present model gives more accurate predictions for flow stress over the entire deformation ranges and the maximum error decreases by about 90%. By employing proposed model to NC warm bending, preferable precision is obtained in predicting forming defects including fracture, wrinkling and over thinning. The present work lays foundation for the forming limit prediction and process optimization in NC warm bending of LDTW Ti-6 Al-4 V tubes.

Three-point bending performance of a new aluminum foam composite structure

A new composite structure based on aluminum foam sandwich and fiber metal laminate was proposed. A layer of glass fiber was provided at the interface between the metal panel and the aluminum foam core in this composite structure, using adhesive technology to bond the materials together by organic glue in the sequence of metal panel, glass fiber, aluminum foam core, glass fiber and metal panel. The experimental results show that the new composite structure has an improved comprehensive performance compared with the traditional aluminum foam sandwiches. The optimized parameters for the fabrication of the new aluminum foam composite structure with best bending strength were obtained. The epoxy resin and low porosity aluminum foams are preferred, the thickness of aluminum sheets should be at least 1.5 mm, and the type of glass fiber has little effect on the bending strength. The main failure modes of the new composite structures with two types of glues were discussed.

Electro-chemo-mechanical analysis of the effect of bending deformation on the interface of flexible solid-state battery

Flexible solid-state battery has several unique characteristics including high flexibility,easy portability,and high safety,which may have broad application prospects in new technology products such as rollup displays,power implantable medical devices,and wearable equipments.The interfacial mechanical and electrochemical problems caused by bending deformation,resulting in the battery damage and failure,are particularly interesting.Herein,a fully coupled electro-chemo-mechanical model is developed based on the actual solid-state battery structure.Concentration-dependent material parameters,stress-dependent diffusion,and potential shift are considered.According to four bending forms(k=8/mm,0/mm,-8/mm,and free),the results show that the negative curvature bending is beneficial to reducing the plastic strain during charging/discharging,while the positive curvature is detrimental.However,with respect to the electrochemical performance,the negative curvature bending creates a negative potential shift,which causes the battery to reach the cut-off voltage earlier and results in capacity loss.These results enlighten us that suitable electrode materials and charging strategy can be tailored to reduce plastic deformation and improve battery capacity for different forms of battery bending.

Three-point bending of honeycomb sandwich beams with facesheet perforations

A novel square honeycomb-cored sandwich beam with perforated bottom facesheet is investigated under threepoint bending,both analytically and numerically.Perforated square holes in the bottom facesheet are characterized by the area ratio of the hole to intact facesheet（perforation ratio）.While for large-scale engineering applications like the decks of cargo vehicles and transportation ships,the perforations are needed to facilitate the fabrication process（e.g.,laser welding）as well as service maintenance,it is demonstrated that these perforations,when properly designed,can also enhance the resistance of the sandwich to bending.For illustration,fair comparisons among competing sandwich designs having different perforation ratios but equal mass is achieved by systematically thickening the core webs.Further,the perforated sandwich beam is designed with a relatively thick facesheet to avoid local indention failure so that it mainly fails in two competing modes：（1）bending failure,i.e.,yielding of beam cross-section and buckling of top facesheet caused by bending moment;（2）shear failure,i.e.,yielding and buckling of core webs due to shear forcing.The sensitivity of the failure loads to the ratio of core height to beam span is also discussed for varying perforation ratios.As the perfo-ration ratio is increased,the load of shear failure increases due to thickening core webs,while that of bending failure decreases due to the weakening bottom facesheet.Design of a sandwich beam with optimal perforation ratio is realized when the two failure loads are equal,leading to significantly enhanced failure load（up to 60%increase）relative to that of a non-perforated sandwich beam with equal mass.

Numerical analysis of bending property of bi-modulus materials and a new method for measurement of tensile elastic modulus

In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.

Semi analytical modeling of springback in arc bending and effect of forming load

The analytical model for springback in arc bending of sheet metal can serve as an excellent design support.The amount of springback is considerably influenced by the geometrical and the material parameters associated with the sheet metal.In addition,the applied load during the bending also has a significant influence.Although a number of numerical techniques have been used for this purpose,only few analytical models that can provide insight into the phenomenon are available.A phenomenological model for predicting the springback in arc bending was proposed based on strain as well as deformation energy based approaches.The results of the analytical model were compared with the published experimental as well as FE results of the authors,and the agreement was found to be satisfactory.

Preset model of bending force for 6-high reversing cold rolling mill based on genetic algorithm

The hydraulic roll-bending device was studied, which was widely used in modem cold rolling mills to regulate the strip flatness. The loaded roll gap crown mathematic model and the strip crown mathematic model of the reversing cold rolling process were established, and the deformation model of roll stack system of the 6-high 1 250 mm high crown （HC） reversing cold rolling mill was built by slit beam method. The simulation results show that, the quadratic component of strip crown decreases nearly linearly with the increase of the work roll bending force, when the shifting value of intermediate roll is determined by the rolling process. From the first pass to the fifth pass of reversing rolling process, the crown controllability of bending force is gradually weakened. Base on analyzing the relationship among the main factors associated with roll-bending force in reversing multi-pass rolling, such as strip width and rolling force, a preset mathematic model of bending force is developed by genetic algorithm. The simulation data demonstrate that the relative deviation of flatness criterions in each rolling pass is improved significantly and the mean relative deviation of all five passes is decreased from 25.1% to 1.7%. The model can keep good shape in multi-pass reversing cold rolling process with the high prediction accuracy and can be used to guide the production process.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

A novel rat tail disc degeneration model induced by static bending and compression

Background:A new rat tail intervertebral disc degeneration model was established to observe the morphologic and biologic changes of static bending and compression applied to the discs.Methods:In total,20 Sprague-Dawley rats with similar weight were randomly di-vided into 4 groups.Group 1 served as a control group for a baseline assessment of normal discs.Group 2 underwent a sham surgery,using an external device to bend the vertebrae of coccygeal 8-10.Groups 3 and 4 were the loaded groups,and exter-nal devices were instrumented to bend the spine with a compression level of 1.8 N and 4.5 N,respectively.Magnetic resonance imaging(MRI),histological,and quanti-tative real-time PCR(qRT-PCR)analysis were performed on all animals on day 14 of the experiment.Results:Magnetic resonance imaging and histological results showed that the changes of intervertebral disc degeneration increased with the size of compression load.Some architecture disorganizations in nucleus pulposus and annulus fibro-sus were found on both of the convex and concave side in the groups of 1.8 N and 4.5 N.An upregulation of MM-3,MM-13,and collagen 1-α1 mRNA expression and a downregulation of collagen 2-α1 and aggrecan mRNA expression were observed in the sham and loading groups.Significant changes were found between the loading groups,whereas the sham group showed similar results to the control group.Conclusions:Static bending and compression could induce progressive disc degen-eration,which could be used for biologic study on disc degeneration promoted by static complex loading.

Analysis of Error Caused by Replacing Spherical Shell with an Elastic Plate Model in Studying Bending Deformation of the Lithosphere

To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.

Experimental and theoretical analyses of package-on-package structure under three-point bending loading

High density packaging is developing toward miniaturization and integration, which causes many difficulties in designing, manufacturing, and reliability testing. Package-on-Package （POP） is a promising three-dimensional high- density packaging method that integrates a chip scale package （CSP） in the top package and a fine-pitch ball grid array （FBGA） in the bottom package. In this paper, in-situ scanning electron microscopy （SEM） observation is carried out to detect the deformation and damage of the PoP structure under three-point bending loading. The results indicate that the cracks occur in the die of the top package, then cause the crack deflection and bridging in the die attaching layer. Furthermore, the mechanical principles are used to analyse the cracking process of the PoP structure based on the multi-layer laminating hypothesis and the theoretical analysis results are found to be in good agreement with the experimental results.

An Inelastic Material Model for Lateral Torsional Buckling and Biaxial Bending of Steel W-Shapes

A new material model for beam elements was developed for use as normalized tangent modulus expressions when performing 3-dimensional second-order inelastic analyses of steel I-section beams.The stiffness matrix of a 14 degree-of-freedom beam element was updated to include the effects of yielding on St.Venant’s torsion and bimoment stiffness at the initial and terminal nodes.A validation study compared the new model’s results with those from published detailed finite element analyses and was found to be in very close agreement.A biaxial end-moment study with two different depth-to-flange-width ratios provided expected and consistent results over a range of moment conditions.

A Method for Evaluating the Maximum Bending Degree of Flexural Toppling Rock Masses Based on the Rock Tensile Strain-Softening Model

Flexural toppling occurs when a series of layered rock masses bend towards their free face.It is important to evaluate the maximum bending degree and the requirement of supports of flexural toppling rock mass to prevent rock mass cracking and even failure leading to a landslide.Based on the rock tensile strain-softening model,this study proposes a method for calculating the maximum curvature(C_(ppmax))of flexural toppling rock masses.By applying this method to calculate Cppmax of 9 types of rock masses with different hardness and rock layer thickness,some conclusions are drawn:(1)the internal key factors affecting C_(ppmax)are E^(⋆)(E^(⋆)=E_(ss)/E_(0),where E_(0)and E_(ss)are the mean deformation moduli of the rock before and after reaching its peak tensile strength,respectively),the strainεt corresponding to the tensile strength of rock,and the thickness(h)of rock layers;(2)hard rock layers are more likely to develop into block toppling than soft rock layers;and(3)thin rock layers are more likely to remain in flexural toppling state than thick rock layers.In addition,it is found that C_(ppmax)for flexural toppling rock masses composed of bedded rocks such as gneiss is related to the tensile direction.

Rice stem lodging properties and bending modeling under the influence of circadian temperature difference

Under diurnal temperature stress,the vascular bundle content of mature rice stems will change which will cause a change in the modulus of elasticity.Therefore,the rice stems will collapse with the reduction in bending resistance because of the change in the modulus of elasticity.In order to reveal the distribution of vascular bundle gradients in rice stems under different climatic temperatures and explore the locations where stems are prone to bending and the form of stem damage,this study established a model of stem stiffness under free loading based on observing microstructure of the rice.The lodging characteristics of rice stems was explored seldom in different environmental temperatures from a micro structure of rice stems.So,the statistical analysis and t-tests were carried out on stems 1 to 4 in combination for cantilever bending tests at room temperature on stem internodes 3,versus three-point bending tests at-10℃ to 65℃ temperature treatment.Results showed that the bending resistance of the stem can be well predicted by using the vascular bundle distribution regression model and the variable stiffness mechanical model.The bending resistance of No.3 stem was established by using the results obtained from the three-point bending test in a temperature range between 10℃-65℃.The correction coefficient TF of stem bending resistance under temperature difference induced stress was established based on the Gauss regression model.Statistical analysis showed that the bending resistance of No.3 stem was relatively large in a temperature range of 16℃-34℃.This study elucidated the variations of the mechanical properties of rice stems under temperature difference induced stress and provided a theoretical foundation for understanding the lodging characteristics of rice during mechanized harvesting.

Influence of heat treatment conditions on bending characteristics of 6063 aluminum alloy sheets

Bending deformation behaviors of solution treated(ST),natural aged(NA)and T6tempered6063aluminum alloy sheetswere studied by three-point bending tests.The changes of bending force,interior angle,bending radius and sheet thickness in thefillet region were analyzed by experimental measurements and numerical simulations.The results showed that the bendingcharacteristics were strongly dependent on the heat treatment conditions.The T6alloy sheets were bent more sharply and localplastic deformation occurred severely in the fillet region.However,the ST and NA alloy sheets exhibited relatively uniform bendingdeformation and large bending radius.The bending force of T6alloy was the highest,followed by the NA alloy and that of the STalloy was minimum.After unloading,as compared with the ST and NA alloys,the springback of T6alloys was markedly larger.Theaging time showed a positive sensitivity on the springback and non-uniform bending deformability.The bending characteristics areattributed to the combined effects of yield strength,yield ratio and coefficient of neutral layer.

A Multiscale Model of Mass-Functionally Graded Beam-Fluid System Under Bending and Vibration Responses

In this paper,a multiscale model is developed for the mass functionally graded(FG)beam-fluid system to investigate its static and dynamic responses based on 3D printed porous beam free vibration tests,which are determined by two aspects.At the microstructural level,the gradient variation is realized by arbitrary distribution of matrix pores,and the effective moduli under specific distribution are obtained using the micromechanics homogenization theory.In the meantime,at the structural level,the mechanical responses of FG porous beams subjected to mass loading are considered in a static fluid environment.Then,the explicit expressions of local finite-element(FE)expressions corresponding to the static and dynamic responses are given in the appendices.The present results are validated against numerical and experimental results from the literature and mechanical tests of 3D printed structures,with good agreement generally obtained,giving credence to the present model.On this basis,a comprehensive parametric study is carried out,with a particular focus on the effects of boundary conditions,fluid density,and slenderness ratio on the bending and vibration of FG beams with several different gradations.

Analysis of bending on the front end of sheet during hot rolling

The analysis of bending in finishing rolling was performed. An asymmetrical rolling force model was established, and the upper and lower neutral points were determined. Thc bending which resulted from the asymmetrical rolling force at the roll gap was studied and related flexibility equations were proposed according to elastic mechanics. Moreover, material mechanics was used to analyze the effects of temperature difference and self-weight on the bending out of the roll gap, and the flexibility equations were constructed. The main factors on bending were summed up, and the bending rule in the rolling could be obtained. In addition practical calculation was made with the production data of ribbon steel from Laiwu Iron ＆ Steel Group Co. Ltd.

Numerical modeling of flow in continuous bends from Daliushu to Shapotou in Yellow River

The upper reach of the Yellow River from Daliushu to Shapotou consists of five bends and has complex topography. A two-dimensional Re-Normalisation Group （RNG） k-ε model was developed to simulate the flow in the reach. In order to take the circulation currents in the bends into account, the momentum equations were improved by adding an additional source term. Comparison of the numerical simulation with field measurements indicates that the improved two-dimensional depth-averaged RNG k-e model can improve the accuracy of the numerical simulation. A rapid adaptive algorithm was constructed, which can automatically adjust Manning＇s roughness coefficient in different parts of the study river reach. As a result, not only can the trial computation time be significantly shortened, but the accuracy of the numerical simulation can also be greatly improved. Comparison of the simulated and measured water surface slopes for four typical cases shows that the longitudinal and transverse slopes of the water surface increase with the average velocity upstream. In addition, comparison was made between the positions of the talweg and the main streamline, which coincide for most of the study river reach. However, deviations between the positions of the talweg and the main streamline were found at the junction of two bends, at the position where the river width suddenly decreases or increases.