The elliptic integral method(EIM) is an efficient analytical approach for analyzing large deformations of elastic beams. However, it faces the following challenges.First, the existing EIM can only handle cases with kn...The elliptic integral method(EIM) is an efficient analytical approach for analyzing large deformations of elastic beams. However, it faces the following challenges.First, the existing EIM can only handle cases with known deformation modes. Second,the existing EIM is only applicable to Euler beams, and there is no EIM available for higher-precision Timoshenko and Reissner beams in cases where both force and moment are applied at the end. This paper proposes a general EIM for Reissner beams under arbitrary boundary conditions. On this basis, an analytical equation for determining the sign of the elliptic integral is provided. Based on the equation, we discover a class of elliptic integral piecewise points that are distinct from inflection points. More importantly, we propose an algorithm that automatically calculates the number of inflection points and other piecewise points during the nonlinear solution process, which is crucial for beams with unknown or changing deformation modes.展开更多
The ductility and toughness of peak-aged(PA)Mg-RE alloys are significantly influenced by their grain structure characteristics.To investigate this issue,we examined PA Mg-8.24Gd-2.68Y(wt.%)alloys with two distinct gra...The ductility and toughness of peak-aged(PA)Mg-RE alloys are significantly influenced by their grain structure characteristics.To investigate this issue,we examined PA Mg-8.24Gd-2.68Y(wt.%)alloys with two distinct grain structures:an extruded-PA sample with dynamic recrystallized(DRXed)fine grains and coarse hot-worked grains,and an extrusion-solution treated and PA sample with grown large equiaxed grains.The results showed that the extruded-PA sample demonstrated a favorable combination of tensile strength(426 MPa)and ductility(7.0%).Although intergranular microcracks nucleated in the DRXed region due to strain incompatibility,crack propagation was impeded by the DRXed fine grains,inducing intrinsic and extrinsic toughening mechanisms.On the other hand,the hot-worked grains in the extruded-PA sample initiated transgranular cracks after a relatively high strain,attributed to the strain partitioning effect,ultimately leading to failure.In comparison,the solution-treated-PA sample exhibited lower tensile strength and ductility(338 MPa and 3.7%,respectively).Intergranular cracks nucleated in the CG sample before necking,and the readily formed critical crack,facilitated by the large grain size,exhibited unstable crack growth,resulting in premature failure.This work offers valuable insights for designing high-performance PA Mg-RE alloys and preventing premature failure in practical applications.展开更多
The microstructure,fracture mechanisms,deformation modes,and their correlation with the mechanical properties of Mg-Zn-Gd alloys were analyzed,considering the influence of Y and Nd additions.Increasing Y content and d...The microstructure,fracture mechanisms,deformation modes,and their correlation with the mechanical properties of Mg-Zn-Gd alloys were analyzed,considering the influence of Y and Nd additions.Increasing Y content and decreasing Nd content resulted in an increase in grain size from 17.2 to 29.2μm,and two types of LPSO phases,14 H and 18 R,formed in the alloy.The mechanical properties of the alloys were predominantly influenced by the LPSO phase,with the grain size effect being relatively minor.Based on this analysis,higher Y and lower Nd contents enhanced the tensile strength,yield strength,and elongation of the alloys,with additional improvements observed following solid solution treatment.Changes in Y and Nd content caused a shift in fracture patterns,transitioning from ductile fracture to brittle fracture and then to mixed fracture.Following solid solution treatment,the alloy progressively transitions from intergranular to a combination of ductile and deconvolutional fracture.The deformation modes observed at each stage are as follows:an increase in LPSO phases and twins activates pyramidal slip and suppresses prismatic slip.展开更多
With the development of high-speed railway in China, composite foundation with rigid piles has become a stamdard solution of meeting the high requirements of stability and post-construction settlement of embankment on...With the development of high-speed railway in China, composite foundation with rigid piles has become a stamdard solution of meeting the high requirements of stability and post-construction settlement of embankment on soft subgrade. Among several im- provement pattems, plain concrete piles have been extensively used to treat soft ground supported embankment. To investigate the deformation and failure modes of unimproved soft ground and soft ground reinforced by sub-embankment plain concrete piles, and to learn the influences of track and vehicle load, the effect of pile spacing, as well as the compression moduli of soil layers and upper load condition on the failure modes, a series of centrifuge model tests were performed. Test results indicate that the dis- placement of unimproved soft ground under the embankment increases continuously as embankment, track and train loading, and slip circle failure takes place. The deformation law of soft ground reinforced by sub-embankment plain concrete piles depends on pile spacing, compression modulus of the soft ground, and loading conditions. It was also found that plain concrete piles show displacement and failure patterns depending on its location, compression modulus of soft soil around the pile, and loading condi- tions. Furthermore, the evaluation of improved ground stability as well as the model test procedure is also presented.展开更多
The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And...The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.展开更多
This paper introduces a three-dimensional concave hexagonal honeycomb structure(3D-CHH) with enhanced impact resistance, developed from a two-dimensional concave hexagonal honeycomb structure(2D-CHH), to advance the a...This paper introduces a three-dimensional concave hexagonal honeycomb structure(3D-CHH) with enhanced impact resistance, developed from a two-dimensional concave hexagonal honeycomb structure(2D-CHH), to advance the application of metamaterials in ship protection structures. Both structures were fabricated using additive manufacturing techniques and subjected to quasi-static compression testing to evaluate their deformation modes and energy-absorbing capabilities. Combined experimental and numerical simulation results revealed that 2D-CHH exhibited a “<” mode,while 3D-CHH demonstrated an inward concave “I” mode, with 3D-CHH showing superior negative Poisson's ratio characteristics. The deformation behavior of both structures progresses through four distinct phases: elastic zone,stress plateau zone, plateau stress enhancement zone, and densification zone characterized by rapid stress elevation.The 3D-CHH structure exhibits superior energy absorption compared with both 2D-CHH and conventional honeycomb structures, achieving nearly twice the specific energy absorption of 2D-CHH. Additionally, 3D-CHH shows an 8.4%improvement in energy absorption efficiency compared with 2D-CHH. The enhanced negative Poisson's ratio effect and superior energy absorption properties of 3D-CHH enable effective ship protection while reducing structural weight.展开更多
Lotus-type porous copper was fabricated by unidirectional solidification, and compressive experiments were subsequently conducted in the strain rate range of 10-3-2400 s-1 with the compressive direction parallel to th...Lotus-type porous copper was fabricated by unidirectional solidification, and compressive experiments were subsequently conducted in the strain rate range of 10-3-2400 s-1 with the compressive direction parallel to the pores. A GLEEBLE-1500 thermal-mechanical simulation system and a split Hopkinson pressure bar （SHPB） were used to investigate the effect of strain rate on the compressive deforma-tion behaviors of lotus-type porous copper. The influence mechanism of strain rate was also analyzed by the strain-controlling method and by high-speed photography. The results indicated that the stress-strain curves of lotus-typed porous copper consist of a linear elastic stage, a plateau stage, and a densification stage at various strain rates. At low strain rate （〈1.0 s^-1）, the strain rate had little influence on the stress-strain curves; but when the strain rate exceeded 1.0 s^-1, it was observed to strongly affect the plateau stage, showing obvious strain-rate-hardening characteristics. Strain rate also influenced the densification initial strain. The densification initial strain at high strain rate was less than that at low strain rate. No visible inhomogeneous deformation caused by shockwaves was observed in lotus-type porous copper during high-strain-rate deformation. However, at high strain rate, the bending deformation characteristics of the pore walls obviously differed from those at low strain rate, which was the main mechanism by which the plateau stress exhibited strain-rate sensitivity when the strain rate exceeded a certain value and exhibited less densification initial strain at high strain rate.展开更多
The discrete element method is used to simulate specimens under three different loading conditions（conventional triaxial compression,plane strain,and direct shear）with different initial conditions to explore the und...The discrete element method is used to simulate specimens under three different loading conditions（conventional triaxial compression,plane strain,and direct shear）with different initial conditions to explore the underlying mechanics of the specimen deformation from a microscale perspective.Deformations of specimens with different initial void ratios at different confining stresses under different loading conditions are studied.Results show that the discrete element models successfully capture the specimen deformation and the strain localization.Particle behaviors including particle rotation and displacement and the mesoscale void ratio distributions are used to explain the strain localization and specimen deformation.It is found that the loading condition is one of the most important factors controlling the specimen deformation mode.Microscale behavior of the granular soil is the driving mechanics of the macroscale deformation of the granular assembly.展开更多
Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell latt...Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption(EA)performance.Finite element(FE)simulations of in-plane compression are carried out,and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures.Satisfactory agreement is achieved between the FE simulation results and the theoretical results.It indicates that the 30◦oriented lattice has the largest EA capacity.Furthermore,inspired by the polycrystal microstructure of metals,novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together.The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts.This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.展开更多
A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalizati...A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.展开更多
The cooling rate during vitrification is critical for determining the mechanical properties of metallic glasses.However,the structural origin of the cooling rate effect on mechanical behaviors is unclear.In this work,...The cooling rate during vitrification is critical for determining the mechanical properties of metallic glasses.However,the structural origin of the cooling rate effect on mechanical behaviors is unclear.In this work,a systematical investigation of the cooling rate effect on the deformation mode,shear band nucleation,and nanoscale heterogeneous structure was conducted in three Fe-based metallic glasses.The brittle to ductile deformation transition was observed when increasing the cooling rate.Meanwhile,the governing shear band nucleation site from high load site to low load site appears the synchronous tran-sition.By studying the corresponding nanoscale heterogeneous structure,it was found that nanoscale viscoelastic transition from solid-like to liquid-like as increasing cooling rate enables ductile deformation.The current work not only reveals the nanoscale structural origin of the cooling rate effect on the de-formation behaviors,but also provides a new route to design ductile metallic glasses by freezing more nanoscale liquid-like regions during cooling.展开更多
Compressive properties,microstructure features and deformation modes were investigated in binary Ti-(2,4,8)wt%V alloys during quasi-static(1×10^(-3)s^(-1))and dynamic(3×10^(3)s^(-1))compressions.The compress...Compressive properties,microstructure features and deformation modes were investigated in binary Ti-(2,4,8)wt%V alloys during quasi-static(1×10^(-3)s^(-1))and dynamic(3×10^(3)s^(-1))compressions.The compressive behavior shows a strong dependence on the loading strain rate and vanadium content contained in pure Ti,such that the flow stress increases with the increase in strain rate and vanadium content ranging from 2 wt%to 8 wt%.The microstructure features are clearly different from each other for alloys with different vanadium contents or under quasi-static and dynamic loading conditions.An examination of deformation microstructures by optical microscopy and electron backscattered diffraction indicates that twinning behavior occurs during quasi-static and dynamic compressions and the twinning density increases with strain rate increasing but decreases with vanadium addition.The existence of{1012},{1121}and{1122}type twinning was further identified.With the help of the calculated Schmid factor map,the values of critical resolved shear stress of twinning types mentioned above have been obtained and verified to be rarely affected by the loading strain rate but sensitive to the vanadium content.In vanadium-rich alloys(Ti-8V),twins are rarely observed but dislocation slip mechanism is active by transmission electron microscopy investigations.With vanadium content increasing,both the critical resolved shear stress of twinning types and the content ofβphase with abundant slip systems increase,reflecting a suppression of twinning but an active dislocation slip mechanism.展开更多
Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are di...Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are discovered through high-speed photography. A simple equation to evaluate the radial acceleration of the drop surface is derived. The combined use of this equation and outer flow simulation makes it possible for us to reconstruct the profiles of the early deformed drops. The results agree well with the experiments. Further analysis shows that the duration of flow establishment with respect to the overall breakup time shapes the rear side profile of the drop. Thereby the ratio of the two times, expressed as the square root of the density ratio, appears to be an effective indicator of the deformation features.展开更多
The tension-compression asymmetry presents notable challenges for the application of magnesium alloys in many fields.In this study,the solid-solution treated Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy's tension-compression a...The tension-compression asymmetry presents notable challenges for the application of magnesium alloys in many fields.In this study,the solid-solution treated Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy's tension-compression asymmetry was examined using optical microscope(OM),x-ray diffraction(XRD),viscoplastic self-consistent(VPSC)modeling,and electron backscatter diffraction(EBSD).The VPSC hardening parameters were significantly adjusted based on the Schmid factor of deformation modes in rare earth magnesium(Mg-RE)alloy,which came from the EBSD data.Excellent agreement was found between the modified VPSC model's calculation results,especially the stress-strain curves and pole figures.The alloy exhibited good strength with a negligible tension-compression asymmetry and an impressive 0.98 ratio of compressive yield strength to tensile yield strength(CYS/TYS).The main cause could be attributed to the unusual texture of(11-20)<0001>in alloy,which eliminated the imbalance in tension and compression deformation by having a negative effect on the activation of{10-12}twinning in tensile and a positive effect in compressive deformation.The activation level of{10-12}twinning was 0.37 and 0.40calculated by VPSC model,in the plastic deformation of tension and compression,respectively;in the tensile and compression samples,the EBSD data indicated that approximately 31.9%and 31.1%(area proportion)of the grains were deformed with twins,respectively.Both tension and compression deformation showed the{10-12}twinning in the early stage of deformation,which transformed to{11-22}twinning in the later stage.The considerable activation of pyramidal during the later stages of deformation endowed the alloy with good ductility.展开更多
Aging precipitation can effectively enhance the strength of Mg–RE alloys,but it is usually accompanied by a significant decrease in ductility,thus the strength–ductility trade-off is a longstanding challenge.In this...Aging precipitation can effectively enhance the strength of Mg–RE alloys,but it is usually accompanied by a significant decrease in ductility,thus the strength–ductility trade-off is a longstanding challenge.In this study,we report a new strategy that coupled pre-deformation(pre-tension along the extrusion direction(ED)followed by pre-compression along transverse direction(TD))with artificial aging to achieve an exceptional strength–ductility synergy in the WE54 alloy at RT.We analyzed the microstructure,deformation modes and mechanical properties of four samples:T6(artificial aging),PT-T6(pre-tension+artificial aging),PC-T6(pre-compression+artificial aging),and PTC-T6(coupled pre-deformation+artificial aging).The PTC-T6 sample exhibited the superior strength–plasticity synergy,showing a strength increase of 111.9 MPa over the T6 sample and only a slight decrease in elongation to fracture.The PTC-T6 sample features finer and denser precipitates,along with a higher dislocation density,particularly a significant presence of<c+a>dislocations.This microstructural configuration enhances strength and facilitates the activation of pyramidal slip,which is the primary factor underlying its superior strength–ductility synergy.展开更多
Commercial wrought Mg alloys normally contain low alloying contents to ensure good formability.In the present work,high-alloyed Mg-6 Al-4 Zn-x Sn(x=1,2 and 3 wt.%,respectively)alloys were fabricated by extrusion.Herei...Commercial wrought Mg alloys normally contain low alloying contents to ensure good formability.In the present work,high-alloyed Mg-6 Al-4 Zn-x Sn(x=1,2 and 3 wt.%,respectively)alloys were fabricated by extrusion.Hereinto,Sn was proven to play an effective contribution to simultaneous improvement in strength and ductility that are traditional trade-off features of synthetic materials.It was found that the average grain size of those alloys decreases significantly from^11 to^4μm as a function of Sn contents increasing from 0 to 3 wt.%,while the amounts of Mg2 Sn and Mg17 Al12 particles continuously increase.More importantly,the addition of Sn leads to the transformation of dominated deformation modes from{1012}extension twinning(1 wt.%)to pyramidal slip(3 wt.%)during tensile tests along the extrusion direction at room temperature.The advantageous combination of ultimate tensile strength(~366 MPa)and elongation(~19%)in Mg-6Al-4Zn-3 Sn alloy is mainly attributed to the strong strain hardening ability induced by the enhanced activity of non-basal slip.This work could provide new opportunities for the development of high-alloyed wrought Mg alloys with promising mechanical properties.展开更多
Conventional wrought Mg alloys,such as AZ31 and ZK60 rolled plates,usually exhibit significantly low tensile yield strength in the thickness direction.This can be attributed to the high activity of{10-12}tension twinn...Conventional wrought Mg alloys,such as AZ31 and ZK60 rolled plates,usually exhibit significantly low tensile yield strength in the thickness direction.This can be attributed to the high activity of{10-12}tension twinning due to the strong basal texture(<0001>//ND,normal direction).In this work,the tensile yield strength in the ND of the as-rolled(AR)AZ31 plate increased from 50 to 150 MPa(increased by 200%)via simple processing,i.e.,pre-tension and rolling-annealing(PTRA)treatment.The strong basal texture(<0001>//ND)of the AR plate was changed into a weakened fiber texture(<0001>⊥ND).The evolution of microstructures during PTRA treatment and the activated deformation modes during uniaxial tension were studied quantitatively and statistically by the means of intergranular misorientation(IM)and in-grain misorientation axes(IGMA)analysis.The results indicate that various twin variants,as well as{10-12}-{10-12}secondary twins,were activated during pre-tension and rolling,and most residual matrix was consumed by twins after annealing.The dominated deformation modes in tension changed from{10-12}tension twinning(the AR sample)to prismatic slip(the PTRA sample)in the early tensile deformation.The underlying formation mechanism of the fiber texture and corresponding strengthening mechanism were discussed.展开更多
The strongly anisotropic mechanical behaviors commonly observed in Zr-4 sheets typically lead to inferior formability.In this study,the mechanical behavior and texture evolution of a cold-rolled Zr-4 sheet under uniax...The strongly anisotropic mechanical behaviors commonly observed in Zr-4 sheets typically lead to inferior formability.In this study,the mechanical behavior and texture evolution of a cold-rolled Zr-4 sheet under uniaxial tension in various directions were systematically investigated,and the results showed both anisotropic yielding and hardening behavior in the Zr-4 sheet.The microstructure and texture features revealed by electron backscattered diffraction(EBSD)method indicate that this anisotropic mechanical behavior is closely related to the initial texture and its evolution during plastic deformation.In conjunction with experimental observations,a visco-plastic self-consistent(VPSC)model was employed to quantitatively analyze the relationship between the mechanical anisotropy and the texture features and activation of deformation modes.It was found that the yield anisotropy is affected by the distinct activity of prismaticslip,while the different activities of basalslip and extension twinning(ETW)result in anisotropic hardening.The distinct activation of deformation modes is mainly caused by differences in the evolution of the Schmid factor(SF)and critical resolved shear stress(CRSS)with increasing strain.Additionally,the results prove that the limited twinning activation with a fraction of less than 3%plays a non-negligible role in the hardening behavior during tension along the transverse direction.The latent hardening effect caused by the interaction between prismatic slip and tensile twinning is considered to successfully capture the anisotropic hardening behavior of the Zr-4 sheet.The implementation and insights from the predictions are presented and discussed in this work.展开更多
This study experimentally investigated basal texture initiation and development during cold rolling,in combination with simulation using a modified visco-plastic self-consistent(VPSC)model.The results showed that the ...This study experimentally investigated basal texture initiation and development during cold rolling,in combination with simulation using a modified visco-plastic self-consistent(VPSC)model.The results showed that the orientation of extension twins exhibit a random distribution after rolling.In contrast,the matrix grains deformed by slips tend to orientate with their c-axis around the normal direction(ND).Plastic strain concentration induced by dislocation piling up at grain boundaries contributes to plastic deformation inhomogeneity,and promotes the basal-pyramidal and prismatic-prismatic binary slips.Incorporated with the interactions between the basaland pyramidal<c+a>dislocations,and between the prismaticdislocations,the VPSC model replicates the experimental results,effectively demonstrating the process of the basal texture initiation and development.The basal texture initiation is independent of twinning,and results mainly from the development of misorientation induced by the formation of dislocation sub-boundaries via the interaction between the basaland pyramidal<c+a>dislocations.展开更多
This study focuses on the analytical prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum considering the volumetric deformation modes of the soil above the tunnel crown.A series of...This study focuses on the analytical prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum considering the volumetric deformation modes of the soil above the tunnel crown.A series of numerical analyses is performed to examine the effects of cover depth ratio(C/D),tunnel volume loss rate(h t)and volumetric block proportion(VBP)on the characteristics of subsurface settle-ment trough and soil volume loss.Considering the ground loss variation with depth,three modes are deduced from the volumetric deformation responses of the soil above the tunnel crown.Then,analytical solutions to predict subsurface settlement for each mode are presented using stochastic medium theory.The influences of C/D,h t and VBP on the key parameters(i.e.B and N)in the analytical expressions are discussed to determine the fitting formulae of B and N.Finally,the proposed analytical solutions are validated by the comparisons with the results of model test and numerical simulation.Results show that the fitting formulae provide a convenient and reliable way to evaluate the key parameters.Besides,the analytical solutions are reasonable and available in predicting the subsurface settlement induced by shield tunnelling in sandy cobble stratum.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 12172388 and 12472400)the Guangdong Basic and Applied Basic Research Foundation of China(No. 2025A1515011975)the Scientific Research Project of Guangdong Polytechnic Normal University of China (No. 2023SDKYA010)
文摘The elliptic integral method(EIM) is an efficient analytical approach for analyzing large deformations of elastic beams. However, it faces the following challenges.First, the existing EIM can only handle cases with known deformation modes. Second,the existing EIM is only applicable to Euler beams, and there is no EIM available for higher-precision Timoshenko and Reissner beams in cases where both force and moment are applied at the end. This paper proposes a general EIM for Reissner beams under arbitrary boundary conditions. On this basis, an analytical equation for determining the sign of the elliptic integral is provided. Based on the equation, we discover a class of elliptic integral piecewise points that are distinct from inflection points. More importantly, we propose an algorithm that automatically calculates the number of inflection points and other piecewise points during the nonlinear solution process, which is crucial for beams with unknown or changing deformation modes.
基金supported by the Defense Industrial Technology Development Program(No.JCKY2018407C008)the NCST Science Fund for Distinguished Young Scholars(No.JQ201702).
文摘The ductility and toughness of peak-aged(PA)Mg-RE alloys are significantly influenced by their grain structure characteristics.To investigate this issue,we examined PA Mg-8.24Gd-2.68Y(wt.%)alloys with two distinct grain structures:an extruded-PA sample with dynamic recrystallized(DRXed)fine grains and coarse hot-worked grains,and an extrusion-solution treated and PA sample with grown large equiaxed grains.The results showed that the extruded-PA sample demonstrated a favorable combination of tensile strength(426 MPa)and ductility(7.0%).Although intergranular microcracks nucleated in the DRXed region due to strain incompatibility,crack propagation was impeded by the DRXed fine grains,inducing intrinsic and extrinsic toughening mechanisms.On the other hand,the hot-worked grains in the extruded-PA sample initiated transgranular cracks after a relatively high strain,attributed to the strain partitioning effect,ultimately leading to failure.In comparison,the solution-treated-PA sample exhibited lower tensile strength and ductility(338 MPa and 3.7%,respectively).Intergranular cracks nucleated in the CG sample before necking,and the readily formed critical crack,facilitated by the large grain size,exhibited unstable crack growth,resulting in premature failure.This work offers valuable insights for designing high-performance PA Mg-RE alloys and preventing premature failure in practical applications.
基金Project(2024QN05053)supported by the Natural Science Foundation of Inner Mongolia,ChinaProjects(U24A20106,51931005,52171048)supported by the National Natural Science Foundation of ChinaProject(2020ZDLGY12-02)supported by the Key Industry Innovation Chain Project of Shaanxi Province,China。
文摘The microstructure,fracture mechanisms,deformation modes,and their correlation with the mechanical properties of Mg-Zn-Gd alloys were analyzed,considering the influence of Y and Nd additions.Increasing Y content and decreasing Nd content resulted in an increase in grain size from 17.2 to 29.2μm,and two types of LPSO phases,14 H and 18 R,formed in the alloy.The mechanical properties of the alloys were predominantly influenced by the LPSO phase,with the grain size effect being relatively minor.Based on this analysis,higher Y and lower Nd contents enhanced the tensile strength,yield strength,and elongation of the alloys,with additional improvements observed following solid solution treatment.Changes in Y and Nd content caused a shift in fracture patterns,transitioning from ductile fracture to brittle fracture and then to mixed fracture.Following solid solution treatment,the alloy progressively transitions from intergranular to a combination of ductile and deconvolutional fracture.The deformation modes observed at each stage are as follows:an increase in LPSO phases and twins activates pyramidal slip and suppresses prismatic slip.
基金supported by Program for New Century Excellent Talents in University of China (Grant No.NCET-12-0941)the Fundamental Research Funds for the Central Universities of China (Grant No.A0920502051206-3)
文摘With the development of high-speed railway in China, composite foundation with rigid piles has become a stamdard solution of meeting the high requirements of stability and post-construction settlement of embankment on soft subgrade. Among several im- provement pattems, plain concrete piles have been extensively used to treat soft ground supported embankment. To investigate the deformation and failure modes of unimproved soft ground and soft ground reinforced by sub-embankment plain concrete piles, and to learn the influences of track and vehicle load, the effect of pile spacing, as well as the compression moduli of soil layers and upper load condition on the failure modes, a series of centrifuge model tests were performed. Test results indicate that the dis- placement of unimproved soft ground under the embankment increases continuously as embankment, track and train loading, and slip circle failure takes place. The deformation law of soft ground reinforced by sub-embankment plain concrete piles depends on pile spacing, compression modulus of the soft ground, and loading conditions. It was also found that plain concrete piles show displacement and failure patterns depending on its location, compression modulus of soft soil around the pile, and loading condi- tions. Furthermore, the evaluation of improved ground stability as well as the model test procedure is also presented.
文摘The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.
基金financially supported by the National Natural Science Foundation of China (Grant No.52201334)。
文摘This paper introduces a three-dimensional concave hexagonal honeycomb structure(3D-CHH) with enhanced impact resistance, developed from a two-dimensional concave hexagonal honeycomb structure(2D-CHH), to advance the application of metamaterials in ship protection structures. Both structures were fabricated using additive manufacturing techniques and subjected to quasi-static compression testing to evaluate their deformation modes and energy-absorbing capabilities. Combined experimental and numerical simulation results revealed that 2D-CHH exhibited a “<” mode,while 3D-CHH demonstrated an inward concave “I” mode, with 3D-CHH showing superior negative Poisson's ratio characteristics. The deformation behavior of both structures progresses through four distinct phases: elastic zone,stress plateau zone, plateau stress enhancement zone, and densification zone characterized by rapid stress elevation.The 3D-CHH structure exhibits superior energy absorption compared with both 2D-CHH and conventional honeycomb structures, achieving nearly twice the specific energy absorption of 2D-CHH. Additionally, 3D-CHH shows an 8.4%improvement in energy absorption efficiency compared with 2D-CHH. The enhanced negative Poisson's ratio effect and superior energy absorption properties of 3D-CHH enable effective ship protection while reducing structural weight.
基金financially supported by the National Natural Science Foundation(No.50904004)
文摘Lotus-type porous copper was fabricated by unidirectional solidification, and compressive experiments were subsequently conducted in the strain rate range of 10-3-2400 s-1 with the compressive direction parallel to the pores. A GLEEBLE-1500 thermal-mechanical simulation system and a split Hopkinson pressure bar （SHPB） were used to investigate the effect of strain rate on the compressive deforma-tion behaviors of lotus-type porous copper. The influence mechanism of strain rate was also analyzed by the strain-controlling method and by high-speed photography. The results indicated that the stress-strain curves of lotus-typed porous copper consist of a linear elastic stage, a plateau stage, and a densification stage at various strain rates. At low strain rate （〈1.0 s^-1）, the strain rate had little influence on the stress-strain curves; but when the strain rate exceeded 1.0 s^-1, it was observed to strongly affect the plateau stage, showing obvious strain-rate-hardening characteristics. Strain rate also influenced the densification initial strain. The densification initial strain at high strain rate was less than that at low strain rate. No visible inhomogeneous deformation caused by shockwaves was observed in lotus-type porous copper during high-strain-rate deformation. However, at high strain rate, the bending deformation characteristics of the pore walls obviously differed from those at low strain rate, which was the main mechanism by which the plateau stress exhibited strain-rate sensitivity when the strain rate exceeded a certain value and exhibited less densification initial strain at high strain rate.
基金The National Natural Science Foundation of China(No.51079030)
文摘The discrete element method is used to simulate specimens under three different loading conditions（conventional triaxial compression,plane strain,and direct shear）with different initial conditions to explore the underlying mechanics of the specimen deformation from a microscale perspective.Deformations of specimens with different initial void ratios at different confining stresses under different loading conditions are studied.Results show that the discrete element models successfully capture the specimen deformation and the strain localization.Particle behaviors including particle rotation and displacement and the mesoscale void ratio distributions are used to explain the strain localization and specimen deformation.It is found that the loading condition is one of the most important factors controlling the specimen deformation mode.Microscale behavior of the granular soil is the driving mechanics of the macroscale deformation of the granular assembly.
基金Project supported by the National Natural Science Foundation of China(No.11772231)。
文摘Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption(EA)performance.Finite element(FE)simulations of in-plane compression are carried out,and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures.Satisfactory agreement is achieved between the FE simulation results and the theoretical results.It indicates that the 30◦oriented lattice has the largest EA capacity.Furthermore,inspired by the polycrystal microstructure of metals,novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together.The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts.This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.
基金Project supported by the National Natural Science Foundation of China(No.10972188)the Fundamental Research Funds for the Central Universities of China(No.2010121073)the Scientific Program of Fujian Province of China(No.2007F3096)
文摘A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.
基金supported by the National Natural Science Foun-dation of China(Nos.52201194,52222105,52261028,52001269,92163108,52231006)the 3315 Innovation Youth Talent in Ningbo City(No.2021A123G)+3 种基金the Youth Innovation Promotion Association CAS(No.2019296)the Zhejiang Provincial Natural Science Foun-dation of China(No.LR22E010004)the Zhejiang Provincial Natu-ral Science Foundation Regional Innovation and Development Joint Foundation with Quzhou City(No.LZY23E010002)the Nat-ural Science Foundation of Xinjiang Uygur Autonomous Region of China(No.2022D01C383).
文摘The cooling rate during vitrification is critical for determining the mechanical properties of metallic glasses.However,the structural origin of the cooling rate effect on mechanical behaviors is unclear.In this work,a systematical investigation of the cooling rate effect on the deformation mode,shear band nucleation,and nanoscale heterogeneous structure was conducted in three Fe-based metallic glasses.The brittle to ductile deformation transition was observed when increasing the cooling rate.Meanwhile,the governing shear band nucleation site from high load site to low load site appears the synchronous tran-sition.By studying the corresponding nanoscale heterogeneous structure,it was found that nanoscale viscoelastic transition from solid-like to liquid-like as increasing cooling rate enables ductile deformation.The current work not only reveals the nanoscale structural origin of the cooling rate effect on the de-formation behaviors,but also provides a new route to design ductile metallic glasses by freezing more nanoscale liquid-like regions during cooling.
基金financially supported by the National Natural Science Foundation of China(No.51571036)the National-International Science and Technology Cooperation Project of China(No.2015DFR50930)。
文摘Compressive properties,microstructure features and deformation modes were investigated in binary Ti-(2,4,8)wt%V alloys during quasi-static(1×10^(-3)s^(-1))and dynamic(3×10^(3)s^(-1))compressions.The compressive behavior shows a strong dependence on the loading strain rate and vanadium content contained in pure Ti,such that the flow stress increases with the increase in strain rate and vanadium content ranging from 2 wt%to 8 wt%.The microstructure features are clearly different from each other for alloys with different vanadium contents or under quasi-static and dynamic loading conditions.An examination of deformation microstructures by optical microscopy and electron backscattered diffraction indicates that twinning behavior occurs during quasi-static and dynamic compressions and the twinning density increases with strain rate increasing but decreases with vanadium addition.The existence of{1012},{1121}and{1122}type twinning was further identified.With the help of the calculated Schmid factor map,the values of critical resolved shear stress of twinning types mentioned above have been obtained and verified to be rarely affected by the loading strain rate but sensitive to the vanadium content.In vanadium-rich alloys(Ti-8V),twins are rarely observed but dislocation slip mechanism is active by transmission electron microscopy investigations.With vanadium content increasing,both the critical resolved shear stress of twinning types and the content ofβphase with abundant slip systems increase,reflecting a suppression of twinning but an active dislocation slip mechanism.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11102204,11572313 and 11621202the Natural Science Foundation of Anhui Province under Grant No 1608085MA16
文摘Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are discovered through high-speed photography. A simple equation to evaluate the radial acceleration of the drop surface is derived. The combined use of this equation and outer flow simulation makes it possible for us to reconstruct the profiles of the early deformed drops. The results agree well with the experiments. Further analysis shows that the duration of flow establishment with respect to the overall breakup time shapes the rear side profile of the drop. Thereby the ratio of the two times, expressed as the square root of the density ratio, appears to be an effective indicator of the deformation features.
基金financial support provided by Key Research and Development Program of Heilongjiang(Grant No.2022ZX01A01)Natural Science Found of Heilongjiang Province(LH2022E080)。
文摘The tension-compression asymmetry presents notable challenges for the application of magnesium alloys in many fields.In this study,the solid-solution treated Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy's tension-compression asymmetry was examined using optical microscope(OM),x-ray diffraction(XRD),viscoplastic self-consistent(VPSC)modeling,and electron backscatter diffraction(EBSD).The VPSC hardening parameters were significantly adjusted based on the Schmid factor of deformation modes in rare earth magnesium(Mg-RE)alloy,which came from the EBSD data.Excellent agreement was found between the modified VPSC model's calculation results,especially the stress-strain curves and pole figures.The alloy exhibited good strength with a negligible tension-compression asymmetry and an impressive 0.98 ratio of compressive yield strength to tensile yield strength(CYS/TYS).The main cause could be attributed to the unusual texture of(11-20)<0001>in alloy,which eliminated the imbalance in tension and compression deformation by having a negative effect on the activation of{10-12}twinning in tensile and a positive effect in compressive deformation.The activation level of{10-12}twinning was 0.37 and 0.40calculated by VPSC model,in the plastic deformation of tension and compression,respectively;in the tensile and compression samples,the EBSD data indicated that approximately 31.9%and 31.1%(area proportion)of the grains were deformed with twins,respectively.Both tension and compression deformation showed the{10-12}twinning in the early stage of deformation,which transformed to{11-22}twinning in the later stage.The considerable activation of pyramidal during the later stages of deformation endowed the alloy with good ductility.
基金financially supported by the National Key Research and Development Program of China(Nos.2021YFB3701000 and 2022YFB3709304)the National Natural Science Foundation of China(Nos.51575068 and 51501023)+2 种基金the Chongqing Natural Science Foundation(No.cstc2021jcyj-msxmX0699)the Venture and Innovation Support Program for Chongqing Overseas Returnees(No.cx2023090)the“111”Project by the Ministry of Education(No.B16007),the Sichuan Science and Technology Program(No.2024NSFSC0193).
文摘Aging precipitation can effectively enhance the strength of Mg–RE alloys,but it is usually accompanied by a significant decrease in ductility,thus the strength–ductility trade-off is a longstanding challenge.In this study,we report a new strategy that coupled pre-deformation(pre-tension along the extrusion direction(ED)followed by pre-compression along transverse direction(TD))with artificial aging to achieve an exceptional strength–ductility synergy in the WE54 alloy at RT.We analyzed the microstructure,deformation modes and mechanical properties of four samples:T6(artificial aging),PT-T6(pre-tension+artificial aging),PC-T6(pre-compression+artificial aging),and PTC-T6(coupled pre-deformation+artificial aging).The PTC-T6 sample exhibited the superior strength–plasticity synergy,showing a strength increase of 111.9 MPa over the T6 sample and only a slight decrease in elongation to fracture.The PTC-T6 sample features finer and denser precipitates,along with a higher dislocation density,particularly a significant presence of<c+a>dislocations.This microstructural configuration enhances strength and facilitates the activation of pyramidal slip,which is the primary factor underlying its superior strength–ductility synergy.
基金the National Key Research and Development Program(No.2016YFE0115300)the National Natural Science Foundation of China(Nos.51625402,51790483,and 51801069)+1 种基金Partial financial supports come from the Science and Technology Development program of Jilin Province(Nos.JJKH20180129KJ and 20190103003JH)The Changjiang Scholars Program(T2017035)。
文摘Commercial wrought Mg alloys normally contain low alloying contents to ensure good formability.In the present work,high-alloyed Mg-6 Al-4 Zn-x Sn(x=1,2 and 3 wt.%,respectively)alloys were fabricated by extrusion.Hereinto,Sn was proven to play an effective contribution to simultaneous improvement in strength and ductility that are traditional trade-off features of synthetic materials.It was found that the average grain size of those alloys decreases significantly from^11 to^4μm as a function of Sn contents increasing from 0 to 3 wt.%,while the amounts of Mg2 Sn and Mg17 Al12 particles continuously increase.More importantly,the addition of Sn leads to the transformation of dominated deformation modes from{1012}extension twinning(1 wt.%)to pyramidal slip(3 wt.%)during tensile tests along the extrusion direction at room temperature.The advantageous combination of ultimate tensile strength(~366 MPa)and elongation(~19%)in Mg-6Al-4Zn-3 Sn alloy is mainly attributed to the strong strain hardening ability induced by the enhanced activity of non-basal slip.This work could provide new opportunities for the development of high-alloyed wrought Mg alloys with promising mechanical properties.
基金supported by the National Natural Science Foundation of China(Nos.51575068 and 51501023)the State Key Research and Development Program of MOST,China(No.2016627 YFB0701204)+2 种基金the Fundamental Research Funds for the Central Universities(No.2020CDJDPT001)the Chongqing Natural Science Foundation(Nos.cstc2018jcyjAX0364 and cstc2021jcyj-msxmX0699)the“111”Project of the Ministry of Education(No.B16007).
文摘Conventional wrought Mg alloys,such as AZ31 and ZK60 rolled plates,usually exhibit significantly low tensile yield strength in the thickness direction.This can be attributed to the high activity of{10-12}tension twinning due to the strong basal texture(<0001>//ND,normal direction).In this work,the tensile yield strength in the ND of the as-rolled(AR)AZ31 plate increased from 50 to 150 MPa(increased by 200%)via simple processing,i.e.,pre-tension and rolling-annealing(PTRA)treatment.The strong basal texture(<0001>//ND)of the AR plate was changed into a weakened fiber texture(<0001>⊥ND).The evolution of microstructures during PTRA treatment and the activated deformation modes during uniaxial tension were studied quantitatively and statistically by the means of intergranular misorientation(IM)and in-grain misorientation axes(IGMA)analysis.The results indicate that various twin variants,as well as{10-12}-{10-12}secondary twins,were activated during pre-tension and rolling,and most residual matrix was consumed by twins after annealing.The dominated deformation modes in tension changed from{10-12}tension twinning(the AR sample)to prismatic slip(the PTRA sample)in the early tensile deformation.The underlying formation mechanism of the fiber texture and corresponding strengthening mechanism were discussed.
基金financially supported by the National Major Science and Technology Projects of China(No.2019ZX06002001)the National Natural Science Foundation of China(No.52105413)the supports from Institute of Metal Research,Chinese Academy of Sciences(No.E055A501)。
文摘The strongly anisotropic mechanical behaviors commonly observed in Zr-4 sheets typically lead to inferior formability.In this study,the mechanical behavior and texture evolution of a cold-rolled Zr-4 sheet under uniaxial tension in various directions were systematically investigated,and the results showed both anisotropic yielding and hardening behavior in the Zr-4 sheet.The microstructure and texture features revealed by electron backscattered diffraction(EBSD)method indicate that this anisotropic mechanical behavior is closely related to the initial texture and its evolution during plastic deformation.In conjunction with experimental observations,a visco-plastic self-consistent(VPSC)model was employed to quantitatively analyze the relationship between the mechanical anisotropy and the texture features and activation of deformation modes.It was found that the yield anisotropy is affected by the distinct activity of prismaticslip,while the different activities of basalslip and extension twinning(ETW)result in anisotropic hardening.The distinct activation of deformation modes is mainly caused by differences in the evolution of the Schmid factor(SF)and critical resolved shear stress(CRSS)with increasing strain.Additionally,the results prove that the limited twinning activation with a fraction of less than 3%plays a non-negligible role in the hardening behavior during tension along the transverse direction.The latent hardening effect caused by the interaction between prismatic slip and tensile twinning is considered to successfully capture the anisotropic hardening behavior of the Zr-4 sheet.The implementation and insights from the predictions are presented and discussed in this work.
基金the financial support from the National Foundation of Natural Science(No.51371121) of China.
文摘This study experimentally investigated basal texture initiation and development during cold rolling,in combination with simulation using a modified visco-plastic self-consistent(VPSC)model.The results showed that the orientation of extension twins exhibit a random distribution after rolling.In contrast,the matrix grains deformed by slips tend to orientate with their c-axis around the normal direction(ND).Plastic strain concentration induced by dislocation piling up at grain boundaries contributes to plastic deformation inhomogeneity,and promotes the basal-pyramidal and prismatic-prismatic binary slips.Incorporated with the interactions between the basaland pyramidal<c+a>dislocations,and between the prismaticdislocations,the VPSC model replicates the experimental results,effectively demonstrating the process of the basal texture initiation and development.The basal texture initiation is independent of twinning,and results mainly from the development of misorientation induced by the formation of dislocation sub-boundaries via the interaction between the basaland pyramidal<c+a>dislocations.
基金This study was supported by the National Natural Science Foundation of China(Grant Nos.51538001 and 51978019).
文摘This study focuses on the analytical prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum considering the volumetric deformation modes of the soil above the tunnel crown.A series of numerical analyses is performed to examine the effects of cover depth ratio(C/D),tunnel volume loss rate(h t)and volumetric block proportion(VBP)on the characteristics of subsurface settle-ment trough and soil volume loss.Considering the ground loss variation with depth,three modes are deduced from the volumetric deformation responses of the soil above the tunnel crown.Then,analytical solutions to predict subsurface settlement for each mode are presented using stochastic medium theory.The influences of C/D,h t and VBP on the key parameters(i.e.B and N)in the analytical expressions are discussed to determine the fitting formulae of B and N.Finally,the proposed analytical solutions are validated by the comparisons with the results of model test and numerical simulation.Results show that the fitting formulae provide a convenient and reliable way to evaluate the key parameters.Besides,the analytical solutions are reasonable and available in predicting the subsurface settlement induced by shield tunnelling in sandy cobble stratum.
