Effect of Loading Paths on Hydroforming Tubular Square Components

The influence of loading path on tube hydroforming process is discussed in this paper with finiteelement simulation. Four different loading paths are utilized in simulating the forming process of square tubular component with hydroforming and the result of different loading path is presented. Among the result. the thickness distribution of bilinear loading path is the most uniform one. It shows that the increase of punch displacement in the stage of high pressure is beneficial to the forming of component for optimized Stress condition.

Deformation Mechanism of AZ31B Magnesium Alloy Under Different Loading Paths

Deformation and texture evolution of AZ31 B magnesium（Mg） alloy sheet under uniaxial tension, compression, and reverse loading after different pre-strain（compression and tension） were investigated experimentally. The results indicate that the pre-compressive strain remarkably affects the reverse tensile yield stress and the width of the detwinning-dominant stage during inverse tension process. Similar to stress–strain curve of the uniaxial compression, the curve of reverse tensile yield value also has ‘S＇ shape, and its minimum value is only 38 MPa. The relationship between pre-compressive strain and the width of detwinning-dominant stage presents a linear growth, and the greater the precompressive strain is, the smaller the strain hardening rate of the detwinning-slip-dominant stage is. Compared with the reverse tension under pre-compression, the influence of the pre-tension deformation on the deformation mechanism of subsequent compression is relatively simple. With the increase in pre-tension strain, the yield stress of the reverse loading is rising.

Optimizing loading path and die linetype of large length-to-diameter ratio metal stator screw lining hydroforming

In order to meet the high temperature environment requirement of deep and superdeep well exploitation, a technology of large length-to-diameter ratio metal stator screw lining meshing with rotor is presented. Based on the elastic-plasticity theory, and under the consideration of the effect of tube size, material mechanical parameters, friction coefficient and loading paths, the external pressure plastic forming mechanical model of metal stator screw lining is established, to study the optimal loading path of metal stator lining tube hydroforming process. The results show that wall thickness reduction of the external pressure tube hydroforming(THF) is about 4%, and three evaluation criteria of metal stator screw lining forming quality are presented: fillet stick mold coefficient, thickness relative error and forming quality coefficient. The smaller the three criteria are, the better the forming quality is.Each indicator has a trend of increase with the loading rate reducing, and the adjustment laws of die arc transition zone equidistance profile curve are acquired for improving tube forming quality. Hence, the research results prove the feasibility of external pressure THF used for processing high-accuracy large length-to-diameter ratio metal stator screw lining, and provide theoretical basis for designing new kind of stator structure which has better performance and longer service life.

Modeling of the loading path dependent magnetomechanical behavior of Galfenol alloy

The magnetomechanical behavior of single-crystal Galfenol alloy was found to be strongly dependent on the loading paths. An energy-based anisotropic domain rotation model, assuming that the interaction between domains can be ignored and the probability of the magnetic moment pointing along a particular direction is related to the free energy along this direction, is used to simulate the magnetostriction versus magnetic field and stress curve and to track the magnetic domain motion trail. The main reason for loading path dependent effect is the rotation/flipping of the magnetic domains under different loading paths. The effect of loading and unloading paths on 90° magnetic domain motion was studied by choosing different loading and unloading state and paths. The results show that prior loading magnetic field can make the 90° magnetic domains flip to the directions of 45°domains because the magnetic field is the driving force to make the domains rotate, and the final loading state and the loading path both have great influence on the motion of 90° magnetic domains.

Experimental observations on the nonproportional multiaxial ratchetting of cast AZ91 magnesium alloy at room temperature

The nonproportional multiaxial ratchetting of cast AZ91 magnesium (Mg) alloy was examined by performing a sequence of axial-torsional cyclic tests controlled by stress with various loading paths at room temperature (RT).The evolutionary characteristics and path dependence of multiaxial ratchetting were discussed.Results illustrate that the cast AZ91 Mg alloy exhibits considerable nonproportional additional softening during cyclic loading with multiple nonproportional multiaxial loading paths;multiaxial ratchetting presents strong path dependence,and axial ratchetting strains are larger under nonproportional loading paths than under uniaxial and proportional45°linear loading paths;multiaxial ratchetting becomes increasingly pronounced as the applied stress amplitude and axial mean stress increase.Moreover,stress-strain curves show a convex and symmetrical shape in axial/torsional directions.Multiaxial ratchetting exhibits quasi-shakedown after certain loading cycles.The abundant experimental data obtained in this work can be used to develop a cyclic plasticity model of cast Mg alloys.

Progressive Collapse Resistance of a New Staggered Story Isolated System

A new staggered isolated system developed from the mid-story isolated system is the new staggered story isolated system. There are not many studies on this structure currently. In this study, an 18-story new staggered story isolated system model is established using SAP2000. The dynamic nonlinear dynamic alternate method is used to analyze the structure against progressive collapse. Results show that the structure has good resistance to progressive collapse, and there is no progressive collapse under each working condition. The progressive collapse does not occur for the case of removing only one vertical structural member of the new staggered of isolated system. The side column has big influence on this isolated structures’ progressive collapse;the removal of vertical structural member of the isolation layer has less impact on the structure than the removal of the bottom vertical structural member. After the removing of the member, the internal force of the structure will be redistributed, and the axial force of the adjacent columns will change obviously, showing a trend of “near large and far small”.

Coefficients of earth pressure at rest in thick and deep soils

The effect of test methods and stress paths on the experimental value of the coefficient of earth pressure at rest, K0, was investigated under high pressures. The results indicate that the rigid pressure chamber and flexible lateral confining pressure medium method gives a stress ratio at the initial stage that is not the real K0. Moreover, K0 increases during the loading process becoming greater at high pressures. In the unloading process, however, K0 increases only at the initial stage but decreases thereafter. In addition, the incremental magnitude definition, K0=dσ3/dσ1, gives higher values than the total magnitude definition, K0=σ3/σ1, under loading. This is also true during initial stages of unloading. The experiment results also indicate that earth pressure at rest in deep and thick soils can be estimated by a power function of axial and confining pressures. It is necessary to choose the appropriate Kn to avoid some accidents.

INFLUENCE OF COMPRESSION-BENDING COUPLING ON THE STABILITY BEHAVIOR OF ANISOTROPIC LAMINATED PANELS

Dynamic-Relaxation Method (DRM) is applied to studying the influence of compression-bending coupling on nonlinear behavior of cylindrically slightly curved panels of unsymmetric laminated composite materials subjected to uniform uniaxial Compression during loading and unloading. Numerical results are given for cross-ply plates and panels under S4S4 and S4S2 boundary conditions. The results show that the effects of absolute value and the sign of the coupling coefficient on the stability behavior of the panles are significant.

Multi-axial Fatigue of 2024-T4 Aluminum Alloy

Only the fatigue initiation is considered by the safe-life design approach,while fatigue crack propagation is paid more attention by the damage tolerance approach.The reasonable fatigue design method and durability assessment standard should give these two phases equivalent concerns.To develop a unified model of fatigue initiation and crack propagation,a great deal of baseline fatigue properties of a material should be obtained by fatigue experiments.However,there is lack of thorough and comprehensive experiment study on the fatigue properties of 2024-T4 aluminum alloy,which is widely used as load-bearing components in aircraft industry.In this paper,strain-controlled uniaxial,torsion,and combined axial-torsion fatigue experiments are conducted on 2024-T4 aluminum alloy in ambient air.Fully reversed uniaxial and pure torsion experiments employ solid cylindrical specimens.Fatigue experiments under the fully reversed shear loading with a static axial stress,proportional axial-torsion loading,and 90°out-of-phase axial-torsion nonproportional loading are conducted by using thin-walled tubular specimens.The experimental results show that the mean stress has a significant influence on the fatigue strength of the material.A tensile mean stress decreases the fatigue life dramatically,while a compressive mean stress increases the fatigue life.The strain-life fatigue results obtained from the fully reversed uniaxial fatigue experiments can be represented by one smooth curve of a three-parameter equation.However,two fitting curves are needed for characterizing the results of the fully reversed pure torsion fatigue tests because of the existence of an obvious kink.The baseline fatigue properties of 2024-T4 aluminum alloy obtained from the fatigue experiments have applications for the fatigue design and safe assessment of engineering components.

Shakedown Criterion Employing Actual Residual Stress Field and Its Application in Numerical Shakedown Analysis

Construction of the static admissible residual stress field and searching the optimal field are key tasks in the shakedown analysis methods applying the static theorem. These methods always meet dimension obstacles when dealing with complex problems. In this paper, a novel shakedown criterion is proposed employing actual residual stress field based on the static shakedown theorem. The actual residual stress field used here is produced under a specified load path, which is a sequence of proportional loading and unloading from zero to all the vertices of the given load domain. This ensures that the shakedown behavior in the whole load domain can be determined based on the theorem proposed by K6nig. The shakedown criterion is then implemented in numerical shakedown analysis, The actual residual stress fields are calculated by incremental finite element elastic-plastic analysis technique for finite deformation under the specified load path with different load levels. The shakedown behavior and the shakedown limit load are determined according to the proposed criterion. The validation of the criterion is performed by a benchmark shakedown example, which is a square plate with a central hole under biaxial loading. The results are consistent with existing results in the literatures and are validated by full cyclic elastic-plastic finite element analysis. The numerical shakedown analysis applying the proposed criterion avoids processing dimension obstacles and performing full cyclic elastic-plastic analysis under arbitrary load paths which should be accounted for appearing. The effect of material model and geometric changes on shakedown behavior can he considered conveniently.

Theoretical and experimental analysis on the mechanism of the Kaiser effect of acoustic emission in brittle rocks

The Kaiser effect is formally described as the absence of detectable acoustic emission （AE） events until the load imposed on the material exceeds the previous applied level and is usually used to estimate geostress. By focusing on the heterogeneity of rock material, the mechanism of the Kaiser effect under cyclic loading is analyzed based on statistic damage mechanics. Two groups of granite specimens have been cyclically loaded with two different loading paths to verify the theoretical results. The heterogeneity of rock is the real reason that causes irrecoverable damage on the Kaiser effect of acoustic emission in cyclic loading. The Kaiser effect reflects the damaged state in rocks rather than the previous stress imposed on it. Applications for using the Kaiser effect to estimate geostress were discussed here. It is shown that the commonly used uniaxial loading method for estimating geostress is not in accor- dance with the theoretical and experimental results. The analysis is of importance to use the Kaiser effect correctly for estimating geostress or in other fields. 2008 University of Science and Technology Beijing. All rights reserved.

Prediction and Verifcation of Forming Limit Diagrams Based on a Modifed Shear Failure Criterion

The forming limit diagram plays an important role in predicting the forming limit of sheet metals.Previous studies have shown that,the method to construct the forming limit diagram based on instability theory of the original shear failure criterion is efective and simple.The original shear instability criterion can accurately predict the left area of the forming limit diagram but not the right area.In this study,in order to improve the accuracy of the original shear failure criterion,a modifed shear failure criterion was proposed based on in-depth analysis of the original shear failure criterion.The detailed improvement strategies of the shear failure criterion and the complete calculation process are given.Based on the modifed shear failure criterion and diferent constitutive equations,the theoretical forming limit of TRIP780 steel and 5754O aluminum alloy sheet metals are calculated.By comparing the theoretical and experimental results,it is shown that proposed modifed shear failure criterion can predict the right area of forming limit more reasonably than the original shear failure criterion.The efect of the pre-strain and constitutive equation on the forming limits are also analyzed in depth.The modifed shear failure criterion proposed in this study provides an alternative and reliable method to predict forming limit of sheet metals.

Deformation and defects in hydroforming of Y-shaped tubes

Hydroforming process of a Y-shaped stainless steel tube was investigated through numerical simulation and experiments. The forming process and reasons of typical defects were analyzed with three different loading paths. Thickness distribution of formed Y-shaped tube was obtained. It is shown by numerical and experimental results that the transition regions are depressed in the forming condition of low inner pressure and wrinkles occur, while fracture occurs in the forming condition of high inner pressure. After forming, the thickness in left transition fillet region is the largest, that in fight transition fillet region is thinner, and the thinnest thickness is at the top of the protrusion. The original thickness line is below the top of the protrusion. The thinning area occurs above this line, while the thickening area is below this line. The maximum thinning rate is significantly increased as the calibration pressure increases, while the maximum thickening rate remains almost unchanged.

Perturbation analysis on post-buckling behavior of pile

The nonlinear large deflection differential equation, based on the assumption that the subsoil coefficient is the 2nd root of the depth, was established by energy method. The perturbation parameter was introduced to transform the equation to a series of linear differential equations to be solved, and the deflection function according with the boundary condition was considered. Then, the nonlinear higher-order asymptotic solution of post-buckling behavior of a pile was obtained by parameter-substituting. The influencing factors such as bury-depth ratio and stiffness ratio of soil to pile, slenderness ratio on the post-buckling behavior of a pile were analyzed. The results show that the pile is more unstable when the bury-depth ratio and stiffness ratio of soil to pile increase, and although the buckling load increases with the stiffness of soil, the pile may ruin for its brittleness. Thus, in the region where buckling behavior of pile must be taken into account, the high grade concrete is supposed to be applied, and the dynamic buckling behavior of pile needs to be further studied.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Modeling parameters for predicting the fire-induced progressive collapse in steel framed buildings

Fire is one of the extreme loading events that a building may experience during its service life and can have severe consequences on the safety of its occupants,first responders,and the structure.Steel framed buildings under severe fires can experience high levels of instability at a local or global level,which in turn can lead to the partial or progressive collapse of the structure.However,in current practice,fire resistance of structures is obtained without due consideration to a number of critical factors,and this is mainly due to the high level of complexity in undertaking advanced analysis of structures under fire exposure.This paper presents a parametric study on a ten-story braced steel framed building subjected to fire exposure wherein six different parameters are evaluated:fire severity,fire spread,load paths,temperature-induced creep,local instability,and analysis regime.Results from validated finite element models are utilized to evaluate the influence of the different parameters and recommend critical parameters to be incorporated in the analysis.Results show that the susceptibility of fire-induced progressive collapse significantly depends on the severity of the fire exposure scenario,including fire intensity,fire spread,and extent of burning.Also,accounting for the full effects of transient creep in fire-induced progressive collapse analysis is needed to obtain conservative failure times under severe to very intense fire exposure.Additionally,results from the parametric study infer that the sectional classification of a steel section based on local instability can alter under fire exposure and this effect is more critical in steel columns located in the higher stories of the building;a nonslender column at ambient conditions can transform to a slender section at elevated temperatures.This can induce temperature-induced local instability in the column and lead to an early onset of instability at member and structural levels.

Examining the influence of the loading path on the cracking characteristics of a pre-fractured rock specimen with discrete element method simulation

Damage in a rock mass is heavily dependent on the existence and growth of joints,which are also influenced by the complex stress states induced by human activities(e.g.,tunneling and excavation).A proper representation of the loading path is essential for understanding the mechanical behaviors of rock masses.Based on the discrete element method(DEM),the influence of the loading path on the cracking process of a rock specimen containing an open flaw is examined.The effectiveness of the model is confirmed by comparing the simulation results under a uniaxial compression test to existing research findings,where wing crack initiates first and secondary cracks contribute to the failure of the specimen.Simulation results confirm that the cracking process is dependent upon both the confining pressure and the loading path.Under the axial loading test,a higher confining pressure suppresses the development of tensile wing cracks and forces the formation of secondary cracks in the form of shear bands perpendicular to the flaw.Increase of confining pressure also decreases the influence of the loading path on the cracking process.Reduction of confining pressure during an unloading test amplifies the concentration of tensile stress and ultimately promotes the appearance of a tensile splitting fracture at meso-scale.Confining pressure at the failure stage is well predicted by the Hoek-Brown failure criterion under quasi-static conditions.

An accurate loading experimental measurement device for superplastic free bulging

Superplastic alloy has very strong structure sensitivity. Superplastic bulging with a die of the plate is related not only to stress state but also closely to loading paths. It is an important basis for bulging forming with a die to study deformation law and experimental apparatus for superplastic free bulging, because the boundary of test piece is fixed and friction is insignificant for free bulging. In the paper, a pure high-pressure argon gas source is used as the loading media after it is heated by the heating system outside the furnace, which improves the heating efficiency and temperature uniformity of the test piece. The photoelectric non-contact measurement device can avoid negative influence on the additional stress and uneven temperature at the peak of bulging part caused by push rod in the contact measurement. The temperature and pressure of the test piece in cylindrical insulation furnace with blank holder give feedback control to improve the control precision. In loading gas channels, the pressure is adjusted by accurately measuring and controlling the rotation angle of the stepping motor, and is loaded by an electro-magnetic valve. It significantly increases the response characteristics of the control pressure. This paper also introduces steps and methods to realize several typical loading paths, such as constant pressure, jump pressure and additional back & differential pressure loading. These provide a new way to measure the strain rate sensitivity index m value and improve the deformation speed of superplastic free bulging.

Characterization of the asymmetric evolving yield and flow of 6016-T4 aluminum alloy and DP490 steel

6016-T4 aluminum alloy and DP490 steel were systematically tested under 24 proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive and simple shear tests with a 45°increment,and biaxial tensile tests using cruciform specimens.Cruciform specimens in the rolling/transverse and 45°/135°sampling directions were tested with seven and four different stress ra-tios,respectively.The normal and diagonal planes plastic work contours and the yield stresses under uniaxial tension and compression were measured to investigate the anisotropic yield.Meanwhile,the normal and diagonal planes directions of plastic strain rate and the rα-values under uniaxial tension and compression were characterized to confirm the plastic flow.Several existing asymmetric yield crite-ria under the associated and non-associated flow rules were comprehensively evaluated to describe the asymmetric plastic anisotropy of 6016-T4 aluminum alloy and DP490 steel.The results suggest that in the investigated yield criteria,the non-associated models can predict the tension and compression asym-metry of materials more accurately than the associated models,and the function of stress triaxiality can more effectively describe the asymmetric yield behavior than the first stress invariant.In addition,the pure shear stress states are helpful in assessing the validity and applicability of advanced asymmetric yield stress functions,and the inspection of diagonal plane plastic work contours containing more pure shear stress states should prioritized over that of normal plane plastic work contours.The evaluation of plastic potential functions should not only consider the prediction accuracy of the normal plane di-rections of plastic strain rate,but also further check the diagonal plane directions of plastic strain rate.Expressing mechanical properties as a function of equivalent plastic strain to calibrate parameters of the yield criterion allows the continuous capture of anisotropic evolution of the asymmetric yield surface and the changes in the asymmetric plastic potential surface.

Investigations on MBSE modelling and dynamic performance assessment of an electrical trimmable horizontal stabilizer actuator

With the development of power-by-wire technology for more electric aircraft,the electromechanical actuator(EMA)has the advantages to replace the conventional hydraulic servo actuator in some aerospace flight controls.Conventional hydraulically powered trimmable horizontal stabilizer actuation(THSA)system is nowadays developed to be electrically supplied.Given their safety-criticality,no-back mechanism and redundant load paths are utilized to meet the flight control requirements.However,rare literatures have introduced these functions and addressed the virtual prototyping activities from system-level point of view.This paper proposed such a model of a THSA system with dual electric power sources and fault-tolerant mechanical load paths.The nonlinear effects of components are considered with realism,and system-level simulation test is conducted to support the model-based system engineering(MBSE)approach.The models are developed with a power view instead of a pure signal view.Focusing on the friction effect and compliance effect with backlash or preload,some improved and novel approaches are adopted for these crucial components and validated via experimental results.Meanwhile,the implemented systemlevel model enables injection of crucial faults.Finally,the simulation of the proposed model shows that it is an efficient resource to investigate the actuator’s dynamic performance,to virtually prove that the actuator meets the fail/safe constraint,and to demonstrate the soundness of the fault monitoring functions.