Effects of the extrusion parameters on microstructure,texture and room temperature mechanical properties of extruded Mg-2.49Nd-1.82Gd-0.2Zn-0.2Zr alloy

Microstructure,texture,and mechanical properties of the extruded Mg-2.49Nd-1.82Gd-0.2Zn-0.2Zr alloy were investigated at different extrusion temperatures(260 and 320℃),extrusion ratios(10:1,15:1,and 30:1),and extrusion speeds(3 and 6 mm/s).The experimental results exhibited that the grain sizes after extrusion were much finer than that of the homogenized alloy,and the second phase showed streamline distribution along the extrusion direction(ED).With extrusion temperature increased from 260 to 320℃,the microstructure,texture,and mechanical properties of alloys changed slightly.The dynamic recrystallization(DRX)degree and grain sizes enhanced as the extrusion ratio increased from 10:1 to 30:1,and the strength gradually decreased but elongation(EL)increased.With the extrusion speed increased from 3 to 6 mm/s,the grain sizes and DRX degree increased significantly,and the samples presented the typical<2111>-<1123>rare-earth(RE)textures.The alloy extruded at 260℃ with extrusion ratio of 10:1 and extrusion speed of 3 mm/s showed the tensile yield strength(TYS)of 213 MPa and EL of 30.6%.After quantitatively analyzing the contribution of strengthening mechanisms,it was found that the grain boundary strengthening and dislocation strengthening played major roles among strengthening contributions.These results provide some guidelines for enlarging the industrial application of extruded Mg-RE alloy.

Intricate interplay between shear stress and extrusion temperature in Mg−Al composite rods

The Mg−Al composite rods of aluminum core-reinforced magnesium alloy were prepared by the extrusion−shear(ES)process,and the microstructure,deformation mechanism,and mechanical properties of the Mg−Al composite rods were investigated at different extrusion temperatures and shear stresses.The experimental results show that the proportion of dynamic recrystallization(DRX)and texture for Al and Mg alloys are controlled by the combination of temperature and shear stress.The texture type of the Al alloys exhibits slight variations at different temperatures.With the increase of temperature,the DRX behavior of Mg alloy shifts from discontinuous DRX(DDRX),continuous DRX(CDRX),and twin-induced DRX(TDRX)dominant to CDRX,the dislocation density in Mg alloy grains decreases significantly,and the average value of Schmid factor(SF)of the basalslip system increases.In particular,partial grains exhibit a distinct dominant slip system at 390℃.The hardness and thickness of the bonding layer,as well as the yield strength and elongation of the Mg alloy,reach their maximum at 360℃as a result of the intricate influence of the combined temperature and shear stress.

Effects of hot extrusion on microstructure and mechanical properties of Mg matrix composite reinforced with deformable TC4 particles

Mg matrix composites were often reinforced by non-deformable ceramic particles.In this paper,a novel Mg matrix composite reinforced with deformable TC4(Ti-6Al-4 V)particles was fabricated and then extruded.The evolutions of microstructure and mechanical properties of the composite during hot extrusion were investigated.Hoi extrusion refined giains and eliminated the segregation of TC4 particles.TC4 particles,as deformable particles,stimulated the nucleation of dynamic recrystallization during extrusion.However,since the deformation of TC4 particles partly released the stress concentrations around them,the recrystallized grains are just slightly smaller around TC4 particles than that away from them,which is evidently different from the case in Mg matrix composites reinforced by non-deformable ceramic particles.Compared with AZ91 matrix composites reinforced by SiC particles,the present composite possesses the superior comprehensive mechanical properties,which are attributed to not only the strong interfacial bonds between TC4p and matrix but also the deformability of TC4 particles.

Effect of extrusion temperature on microstructure and mechanical properties of a low-alloying and ultra-high strength Mg-Zn-Ca-Mn matrix composite containing trace TiC nanoparticles

Mechanical properties of microalloying Mg-2.2Zn-1.8Ca-0.5Mn(wt%)matrix composites reinforced by 0.5 wt%TiC nanoparticles before and after extrusion were investigated based on the detailed microstructural analysis.A uniform distribution of TiC nanoparticles was realized in the nanocomposite by the method of ultrasonic-assisted semisolid stirring.The morphology of eutectic Ca2Mg6Zn3 phases changed from plate-like in the free TiC nanoparticles region to lamellar in the dense TiC nanoparticles region for the as-cast nanocomposite.Both the grain structure and precipitates were obviously refined as the extrusion temperature decreased from 350 to 270℃.The nanocomposite exhibited excellent tensile yield strength(352-428 MPa)which was governed by the extrusion temperature.The grain refinement strengthening with the contribution ratio of^80%to this strength increment was much higher relative to thermal expansion effect,Orowan strengthening and dislocation strengthening.Ultrafine recrystallized grain structure with a substantial of ne precipitates appeared in the nanocomposite extruded at 270℃.The refined grain structure was not only due to dynamic recrystallization,but also the synergistic pinning effect of nano-TiCp,precipitated MgZn2 and α-Mn particles.The tensile toughness value of nanocomposite after extrusion improved with increasing the extrusion temperature.Massive micro-cracks formed along the remnant coarse Ca2Mg6Zn3 led to the structural failure during tension.

Effect of extrusion on the microstructure and mechanical properties of a low-alloyed Mg-2Zn-0.8Sr-0.2Ca matrix composite reinforced by TiC nano-particles

A low-alloyed Mg-2Zn-0.8Sr-0.2Ca matrix composite reinforced by TiC nano-particles was successfully prepared by semi-solid stirring under the assistance of ultrasonic,and then the as-cast composite was hot extruded.The results indicated that the volume fraction of dynamical recrystallization and the recrystallized grain size have a certain decline at lower extrusion temperature or rate.The finest grain size of~0.30μm is obtained in the sample extruded at 200℃ and 0.1 mm/s.The as-extruded sample displays a strong basal texture intensity,and the basal texture intensity increases to 5.937 mud while the extrusion temperature increases from 200 to 240℃.The ultra-high mechanical properties(ultimate tensile strength of 480.2 MPa,yield strength of 462 MPa)are obtained after extrusion at 200℃ with a rate of 0.1 mm/s.Among all strengthening mechanisms for the present composite,the grain refinement contributes the most to the increase in strength.A mixture of cleavage facets and dimples were observed in the fracture surfaces of three as-extruded nanocomposites,which explain a mix of brittle-ductile fracture way of the samples.

Effects of the deep rolling process on the surface roughness and properties of an Al-3vol%SiC nanoparticle nanocomposite fabricated by mechanical milling and hot extrusion

Deep rolling is one of the most widely used surface mechanical treatments among several methods used to generate compressive residual stress. This process is usually used for axisymmetric components and can lead to improvements of the surface quality, dimensional accuracy, and mechanical properties. In this study, we deduced the appropriate deep rolling parameters for Al-3vol%Si C nanocomposite samples using roughness and microhardness measurements. The nanocomposite samples were fabricated using a combination of mechanical milling, cold pressing, and hot extrusion techniques. Density measurements indicated acceptable densification of the samples, with no porosity. The results of tensile tests showed that the samples are sufficiently strong for the deep rolling process and also indicated near 50% improvement of tensile strength after incorporating Si C nanoparticle reinforcements. The effects of some important rolling parameters, including the penetration depth, rotation speed, feed rate, and the number of passes, on the surface quality and microhardness were also investigated. The results demonstrated that decreasing the feed rate and increasing the number of passes can lead to greater surface hardness and lower surface roughness.

Effect of Grain Particle Size on Quality of Multi-grain Chips Under Screw Extrusion Processing

Multi-grain chips processed by screw extrusion processing have high nutrition and production value with a low glycemic index.To analyze the effects of particle sizes on the qualities of multi-grain chips extrusion processing by using a single screw extruder,mesh numbers were selected as 80,100 and 120 to describe different grain particle sizes.It was found that the particle sizes of the raw materials had effects on the basic components,sensory properties,texture properties,antioxidant activities and in vitro digestibilities of extruded chips.The results showed that with the decrease of particle sizes,the moisture contents,starch contents of the chips decreased,and fat contents,dietary fiber contents increased.The edible qualities of the chips increased with the decrease of the grain sizes of raw materials.The antioxidant capacities and estimated glycemic indexes of the three kinds of chips showed a trend of decreasing first,and then increasing with the decrease of particle sizes.Correlation analysis showed that the total antioxidant capacities of chips were negatively correlated with the estimated glycemic indexes.The research results provided valuable guidance for the quality processing of multi-grain chips under extrusion processing.

Predictive factors for coronal and sagittal graft extrusion length after using tendon autograft for medial meniscus reconstruction

BACKGROUND Meniscus extrusion occurs in most elderly individuals and most patients after meniscus allograft transplantation.The risk factors and correlative factors of meniscus extrusion have been extensively studied.However,for using tendon autograft for meniscus reconstruction,both graft type and surgical method are different from those in previous studies on meniscus extrusion.AIM To identify predictive factors for coronal and sagittal graft extrusion length after using tendon autograft for medial meniscus reconstruction.METHODS Ten patients who underwent medial meniscus reconstruction with tendon autograft were selected for this retrospective observational study.The graft extrusions and potential factors were measured and correlation and regression analyses were performed to analyze their relationships.RESULTS The medial graft extrusion correlated with the preoperative bilateral hip-kneeankle angle difference,preoperative Kellgren-Lawrence grade,preoperative relative joint space width,and preoperative bilateral medial edge incline angle difference.The anterior graft correlated with the anterior tunnel edge distance at 1 week after operation.The posterior graft extrusion correlated with the preoperative bilateral hip-knee-ankle angle difference,preoperative relative joint space width,and posterior tunnel edge distance at 1 week after operation.The mean graft extrusion correlated with the preoperative bilateral hip-knee-ankle angle difference and preoperative relative joint space width.The preoperative joint space width and anterior and posterior tunnel edge distance at 1 week can be used to predict the medial,anterior,posterior,and mean graft extrusion length.CONCLUSION The preoperative joint space width and tunnel position can be used to predict the coronal and sagittal graft extrusion length after using tendon autograft for medial meniscus reconstruction.

Investigation into Metal Flow Rule during Extrusion of Spherical Surface Parts

A new process of extrusion forming was used to replace the traditional drilling technics.This kind of forming method may improve the structure of materials and anti-deforming capacity,enhancing the life of parts.It is shown by numerical simulations on the forming process of spherical extrusion on bolt-hole.Effects of technological parameters were discussed on spherical surface of extrusion and the diameter of pre-punching hole was determined.It is revealed that the smaller diameter of pre-punching hole,the larger deforming measurement of hole after extrusion.The extrusion stress determines the development trend of pre-punch hole becomes bigger or smaller and the pre-punching hole diameter is the key to control the size of deforming measurement of hole after extrusion.

Investigation of high rate mechanical flow followed by ignition for high-energy propellant under dynamic extrusion loading

Investigating the ignition response of nitrate ester plasticized polyether(NEPE) propellant under dynamic extrusion loading is of great significant at least for two cases. Firstly, it helps to understand the mechanism and conditions of unwanted ignition inside charged propellant under accident stimulus.Secondly, evaluates the risk of a shell crevice in a solid rocket motor(SRM) under a falling or overturning scene. In the present study, an innovative visual crevice extrusion experiment is designed using a dropweight apparatus. The dynamic responses of NEPE propellant during extrusion loading, including compaction and compression, rapid shear flow into the crevice, stress concentration, and ignition reaction, have been firstly observed using a high-performance high-speed camera. The ignition reaction is observed in the triangular region of the NEPE propellant sample above the crevice when the drop weight velocity was 1.90 m/s. Based on the user material subroutine interface UMAT provided by finite element software LS-DYNA, a viscoelastic-plastic model and dual ignition criterion related to plastic shear dissipation are developed and applied to the local ignition response analysis under crevice extrusion conditions. The stress concentration occurs in the crevice location of the propellant sample, the shear stress is relatively large, the effective plastic work is relatively large, and the ignition reaction is easy to occur. When the sample thickness decreases from 5 mm to 2.5 mm, the shear stress increases from 22.3 MPa to 28.6 MPa, the critical value of effective plastic work required for ignition is shortened from 1280 μs to 730 μs, and the triangular area is easily triggering an ignition reaction. The propellant sample with a small thickness is more likely to stress concentration, resulting in large shear stress and effective work, triggering an ignition reaction.

Deformation mechanisms and microstructural characteristics of AZ61 magnesium alloys processed by a continuous expansion extrusion approach

The unique continuous extrusion-based severe plastic deformation approaches were proposed recently to process high-performance magnesium (Mg) alloys,while the in-depth deformation mechanisms under such complicated thermomechanical conditions were not well understood In the present work,the fundamental deformation behaviors of AZ61 Mg alloy from 25 to 400°C were firstly examined under uniaxial compression deformation.Then the deformation mechanisms and microstructural characteristics of AZ61 Mg alloy during continuous expansion extrusion forming (CEEF) were systematically investigated by microstructural observations,finite element and cellular automata simulations The results showed that the continuous evolutions of temperature,larger strain level and complex stress state with strain rate range of 0~5.98 s-1during CEEF brought the distinctive dynamic recrystallization behaviors and texture development in AZ61 Mg alloy,which were different to that of uniaxial compression deformation.In details,a remarkable grain refinement was achieved via CEEF processing due to the simultaneous actions of continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX).Gradually enhanced CDRX were observed from center to edge region,which had significant effects on the texture distribution and texture strength.The c-axis of most grains rotated under distinctive shear strain following parabolic metal flow,resulting in stable fiber texture.In addition,the evolution of the internal texture of the alloy led to an obvious increase in the Schmid factor for the activation of basal(c+a)slip system.©2022 Chongqing University.Publishing services provided by Elsevier B.V.on behalf of Ke Ai Communications Co.Ltd.

Extrusion 3D printing of carbon nanotube-assembled carbon aerogel nanocomposites with high electrical conductivity

Carbon nanotubes(CNTs)with high aspect ratio and excellent electrical conduction offer huge functional improvements for current carbon aerogels.However,there remains a major challenge for achieving the on-demand shaping of carbon aerogels with tailored micro-nano structural textures and geometric features.Herein,a facile extrusion 3D printing strategy has been proposed for fabricating CNT-assembled carbon(CNT/C)aerogel nanocomposites through the extrusion printing of pseudoplastic carbomer-based inks,in which the stable dispersion of CNT nanofibers has been achieved relying on the high viscosity of carbomer microgels.After extrusion printing,the chemical solidification through polymerizing RF sols enables 3D-printed aerogel nanocomposites to display high shape fidelity in macroscopic geometries.Benefiting from the micro-nano scale assembly of CNT nanofiber networks and carbon nanoparticle networks in composite phases,3D-printed CNT/C aerogels exhibit enhanced mechanical strength(fracture strength,0.79 MPa)and typical porous structure characteristics,including low density(0.220 g cm^(-3)),high surface area(298.4 m^(2)g^(-1)),and concentrated pore diameter distribution(~32.8nm).More importantly,CNT nanofibers provide an efficient electron transport pathway,imparting 3D-printed CNT/C aerogel composites with a high electrical conductivity of 1.49 S cm^(-1).Our work would offer feasible guidelines for the design and fabrication of shape-dominated functional materials by additive manufacturing.

Multifunctional HDPE/Cu biocidal nanocomposites for MEX additive manufactured parts: Perspectives for the defense industry

In this study, we investigated the performance improvement caused by the addition of copper(Cu)nanoparticles to high-density polyethylene(HDPE) matrix material. Composite materials, with filler percentages of 0.0, 2.0, 4.0, 6.0, 8.0, and 10.0 wt% were synthesized through the material extrusion(MEX)3D printing technique. The synthesized nanocomposite filaments were utilized for the manufacturing of specimens suitable for the experimental procedure that followed. Hence, we were able to systematically investigate their tensile, flexural, impact, and microhardness properties through various mechanical tests that were conducted according to the corresponding standards. Broadband Dielectric Spectroscopy was used to investigate the electrical/dielectric properties of the composites. Moreover, by employing means of Raman spectroscopy and thermogravimetric analysis(TGA) we were also able to further investigate their vibrational, structural, and thermal properties. Concomitantly, means of scanning electron microscopy(SEM), as well as atomic force microscopy(AFM), were used for the examination of the morphological and structural characteristics of the synthesized specimens, while energy-dispersive Xray spectroscopy(EDS) was also performed in order to receive a more detailed picture on the structural characteristics of the various synthesized composites. The corresponding nanomaterials were also assessed for their antibacterial properties regarding Staphylococcus aureus(S. aureus) and Escherichia coli(E. coli) with the assistance of a method named screening agar well diffusion. The results showed that the mechanical properties of HDPE benefited from the utilization of Cu as a filler, as they showed a notable improvement. The specimen of HDPE/Cu 4.0 wt% was the one that presented the highest levels of reinforcement in four out of the seven tested mechanical properties(for example, it exhibited a 36.7%improvement in the flexural strength, compared to the pure matrix). At the same time, the nanocomposites were efficient against the S. aureus bacterium and less efficient against the E. coli bacterium.The use of such multi-functional, robust nanocomposites in MEX 3D printing is positively impacting applications in various fields, most notably in the defense and security sectors. The latter becomes increasingly important if one takes into account that most firearms encompass various polymeric parts that require robustness and improved mechanical properties, while at the same time keeping the risk of spreading various infectious microorganisms at a bare minimum.

Method of fabricating artificial rock specimens based on extrusion free forming(EFF)3D printing

Three-dimensional(3D)printing technology has been widely used to create artificial rock samples in rock mechanics.While 3D printing can create complex fractures,the material still lacks sufficient similarity to natural rock.Extrusion free forming(EFF)is a 3D printing technique that uses clay as the printing material and cures the specimens through high-temperature sintering.In this study,we attempted to use the EFF technology to fabricate artificial rock specimens.The results show the physico-mechanical properties of the specimens are significantly affected by the sintering temperature,while the nozzle diameter and layer thickness also have a certain impact.The specimens are primarily composed of SiO_(2),with mineral compositions similar to that of natural rocks.The density,uniaxial compressive strength(UCS),elastic modulus,and tensile strength of the printed specimens fall in the range of 1.65–2.54 g/cm3,16.46–50.49 MPa,2.17–13.35 GPa,and 0.82–17.18 MPa,respectively.It is capable of simulating different types of rocks,especially mudstone,sandstone,limestone,and gneiss.However,the simulation of hard rocks with UCS exceeding 50 MPa still requires validation.

Modeling of recrystallization behaviour of AA6xxx aluminum alloy during extrusion process

An innovative approach was introduced for the development of a AA6063 recrystallization model.This method incorporated a regression-based technique for the determination of material constants and introduced novel equations for assessing the grain size evolution.Calibration and validation of this methodology involved a combination of experimentally acquired microstructural data from the extrusion of three different AA6063 profiles and results from the simulation using the Qform Extrusion UK finite element code.The outcomes proved the agreement between experimental findings and numerical prediction of the microstructural evolution.The trend of the grain size variation based on different process parameters was accurately simulated,both after dynamic and static recrystallization,with an error of less than 25% in almost the whole sampling computations.

Improving the ductility and toughness of nano-TiC/AZ61 composite by optimizing bimodal grain microstructure via extrusion speed

In this study,the nano-TiC/AZ61 composites with different heterogeneous bimodal grain(HBG)structures and uniform structure are obtained by regulating the extrusion speed.The effect of HBG structure on the mechanical properties of the composites is investigated.The increasing ductility and toughening mechanism of HBG magnesium matrix composites are carefully discussed.When the extrusion speed increases from 0.75 mm/s to 2.5 mm/s or 3.5 mm/s,the microstructure transforms from uniform to HBG structure.Compared with Uniform-0.75 mm/s composite,Heterogeneous-3.5 mm/s composite achieves a 116.7%increase in ductility in the plastic deformation stage and almost no reduction in ultimate tensile strength.This is mainly because the lower plastic deformation inhomogeneity and higher strain hardening due to hetero-deformation induced(HDI)hardening.Moreover,Heterogeneous-3.5 mm/s composite achieves a 108.3%increase in toughness compared with the Uniform-0.75 mm/s composite.It is mainly because coarse grain(CG)bands can capture and blunt cracks,thereby increasing the energy dissipation for crack propagation and improving toughness.In addition,the CG band of the Heterogeneous-3.5 mm/s composite with larger grain size and lower dislocation density is more conducive to obtaining higher strain hardening and superior blunting crack capability.Thus,the increased ductility and toughness of the Heterogeneous-3.5 mm/s composite is more significant than that Heterogeneous-2.5 mm/s composite.

Effect of thermo-mechanical conditions during constrained friction processing on the particle refinement of AM50 Mg-alloy phases

Constrained Friction Processing(CFP)is a novel solid-state processing technique suitable for lightweight materials,such Mg-and Al-alloys.The technique enables grain size refinement to fine or even ultrafine scale.In this study,the effect of CFP on the microstructural refinement of AM50 rods is investigated in terms of particle size and morphology of the eutectic and secondary phases originally present in the base material,in particular the eutecticβ-Mg_(17)Al_(12)and Al-Mn phases.For that purpose,as-cast and solution heat-treated base material and processed samples were analyzed.The Al_(8)Mn_(5) intermetallic phase was identified as the main secondary phase present in all samples before and after the processing.A notorious refinement of these particles was observed,starting from particles with an average equivalent length of a few micrometers to around 560 nm after the processing.The refinement of the secondary phase refinement is attributed to a mechanism analogous to the attrition comminution,where the combination of temperature increase and shearing of the material enables the continuous breaking of the brittle intermetallic particles into smaller pieces.As for the eutectic phase,the results indicate the presence of the partially divorcedβ-Mg_(17)Al_(12)particles exclusively in the as-cast base material,indicating that no further phase transformations regarding the eutectic phase,such as dynamic precipitation,occurred after the CFP.In the case of the processed as-cast material analyzed after the CFP,the thermal energy generated during the processing led to temperature values above the solvus limit of the eutectic phase,which associated with the mechanical breakage of the particles,enabled the complete dissolution of this phase.Therefore,CFP was successfully demonstrated to promote an extensive microstructure refinement in multiple aspects,in terms of grain sizes of theα-Mg phase and presence and morphology of the Al-Mn and eutecticβ-Mg_(17)Al_(12).

Development of the rolling extrusion rock bolt with constant resistance and large deformation

With the increasing excavation depth of underground engineering,engineering problems such as large deformation and rock burst caused by high geo-stress brings new challenges to the excavation and reinforcement of surrounding rock in deep underground engineering.The traditional rock bolt is prone to brittle fracture under high geo-stress due to its low elongation.Therefore,this work aims to develop a novel energy-absorbing bolt with constant resistance and large displacement to reinforce the surrounding rock with a risk of large deformation or rockburst.The novel energy-absorbing bolt refereed as rolling extrusion rock bolt(RE bolt)is mainly consists of sleeve tube with a variable cross-section,energy absorption slider with steel balls embedded,steel bar connected with the energy absorption slider.The rolling extrusion is adopted to produce the resistance force of the RE bolt,which avoids the sudden attenuation of resistance force and the abrasion of the energy absorption slider.The static pull test is conducted to study the resistance force and deformation characteristics of the RE bolt with different specifications.Results imply that the RE bolt has higher resistance force,larger deformation capacity and energy absorption capacity.The work of this study provides an effective solution for the reinforcement of surrounding rock in deep rock engineering.

Force analysis and experimental study of pure aluminum and Al-5%Ti-1%B alloy continuous expansion extrusion forming process

The deformation zone of CONFORM extrusion was divided into primary gripping zone,gripping zone,conical expansion chamber zone,cylindrical zone and sizing zone of die,and corresponding force equilibrium equations were established using the Slab method.The deformation force formulae of CONFORM machine at any wrapping angle with an expansion chamber were obtained.Experiment on pure aluminum and Al-5%Ti-1%B alloy was conducted on the CONFORM machine self-designed.The resistance to deformation of Al-5%Ti-1%B alloy at the deformation temperature of 400℃ and the strain rate of 3.07 s-1 was measured to be 50 MPa using Gleeble-1500 thermal simulation machine.The calculation results of deformation forces for CONFORM process with an expansion chamber for pure aluminum and Al-5%Ti-1%B alloy were given.The experimental CONFORM radial force is in agreement with the radial force obtained by theoretical formula.

Continuous extrusion and rolling forming velocity of copper strip

A new copper strip production technology combined with continuous extrusion and rolling technology was proposed. The roll velocity must first be matched with the continuous extrusion velocity to achieve continuous extrusion and roll forming. The bite condition of continuous extrusion was determined, and the compatibility equation between the roll velocity and parameters such as the extrusion wheel velocity, reduction, and strip size was established through mechanical by plastic theoretical calculations. The finite element model of continuous extrusion and rolling was then established by using the TLJ400 continuous extrusion machine with a roll diameter of 200 mm. The relationship between the continuous extrusion and rolling velocities was determined through numerical simulations by software DEFORM-3D, and the accuracy of compatibility equation of velocity was verified.