Additively manufactured Ti–Ta–Cu alloys for the next-generation load-bearing implants

Bacterial colonization of orthopedic implants is one of the leading causes of failure and clinical complexities for load-bearing metallic implants. Topical or systemic administration of antibiotics may not offer the most efficient defense against colonization, especially in the case of secondary infection, leading to surgical removal of implants and in some cases even limbs. In this study, laser powder bed fusion was implemented to fabricate Ti3Al2V alloy by a 1:1 weight mixture of CpTi and Ti6Al4V powders. Ti-Tantalum(Ta)–Copper(Cu) alloys were further analyzed by the addition of Ta and Cu into the Ti3Al2V custom alloy. The biological,mechanical, and tribo-biocorrosion properties of Ti3Al2V alloy were evaluated. A 10 wt.% Ta(10Ta) and 3 wt.% Cu(3Cu) were added to the Ti3Al2V alloy to enhance biocompatibility and impart inherent bacterial resistance. Additively manufactured implants were investigated for resistance against Pseudomonas aeruginosa and Staphylococcus aureus strains of bacteria for up to 48 h. A 3 wt.% Cu addition to Ti3Al2V displayed improved antibacterial efficacy, i.e.78%–86% with respect to CpTi. Mechanical properties for Ti3Al2V–10Ta–3Cu alloy were evaluated, demonstrating excellent fatigue resistance, exceptional shear strength, and improved tribological and tribo-biocorrosion characteristics when compared to Ti6Al4V. In vivo studies using a rat distal femur model revealed improved early-stage osseointegration for alloys with10 wt.% Ta addition compared to CpTi and Ti6Al4V. The 3 wt.% Cu-added compositions displayed biocompatibility and no adverse infammatory response in vivo. Our results establish the Ti3Al2V–10Ta–3Cu alloy’s synergistic effect on improving both in vivo biocompatibility and microbial resistance for the next generation of load-bearing metallic implants.

Load-bearing characteristics and energy evolution of fractured rock masses after granite and sandstone grouting

Experiments on grouting-reinforced rock mass specimens with different particle sizes and features were carried out in this study to examine the effects of grouting reinforcement on the load-bearing characteristics of fractured rock mass.The strength and deformation features of grouting-reinforced rock mass were analyzed under different loading manners;the energy evolution mechanism of grouting-reinforced rock mass specimens with different particle sizes and features was investigated;the energy dissipation ratio and post-peak stress decreasing rate were employed to evaluate the bearing stability of grouting-reinforced rock mass.The results show that the strength and ductility of granite-reinforced rock mass(GRM)under biaxial loading are higher than that of sandstone-reinforced rock mass(SRM)under uniaxial loading.Besides,the energy evolution characteristics of grouting-reinforced rock mass under uniaxial and biaxial loading mainly could be divided into early,middle,and late stages.In the early stage,total,elastic,and dissipation energies were quite small with flatter curves;in the middle stage,elastic energy increased rapidly,whereas dissipation energy increased slowly;in the late stage,dissipation energy increased sharply.The energy dissipation ratio was used to represent the pre-peak plastic deformation.Under uniaxial loading,this ratio increased as the particle size increased and the pre-peak plastic deformation of grouting-reinforced rock mass became larger;under biaxial loading,it dropped as the particle size increased,and the pre-peak plastic deformation of grouting-reinforced rock mass became smaller.The post-peak stress decline rate A_(v) was used to assess the post-peak bearing performance of grouting-reinforced rock mass.Under uniaxial loading,parameter A_(v) exhibited reduction as the particle size kept increasing,and the ability of post-peak of grouting-reinforced rock mass to allow deformation development was greater,and the bearing capacity was greater;under biaxial loading,A_(v) increased with the particle size,and the ability of post-peak of grouting-reinforced rock mass to allow deformation development was low and the bearing capacity was reduced.The findings are considered instrumental in improving the stability of the roadway-surrounding rock by granite and sandstone grouting.

Effects of different orthokeratology lens designs on slowing axial length elongation in children with myopia

AIM:To elucidate whether differences exist in the impact on retarding the elongation of axial length(AL)among children with myopia when utilizing orthokeratology(ortho-k)lenses employing the corneal refractive therapy(CRT)design versus those employing the vision shaping treatment(VST)design.METHODS:This retrospective clinical trial aimed to collect and analyze AL data from individuals who wore ortho-k lenses for three years.A total of 654 subjects were enrolled and prescribed one of the three specific brands of ortho-k lenses:CRT,Euclid,and Mouldway.The study’s primary focus was to compare the rates of AL elongation and myopic progression across these three brands of ortho-k lenses.RESULTS:In the 3-year follow-up,the AL elongation exhibited variations of 0.73±0.36 mm in the CRT lens group,0.59±0.37 mm in the Euclid lens group,and 0.63±0.38 mm in the Mouldway lens group.A noteworthy disparity emerged between the CRT and Mouldway groups(P<0.01),as well as between the CRT and Euclid groups(P<0.001).Additionally,it was observed that 32.1%of participants who wore CRT lenses experienced a decelerated progression of myopia,in contrast to 47.2%in the Euclid group and 44.4%in the Mouldway group.Statistical analyses revealed a statistically significant distinction between the CRT and Euclid groups(P<0.01),and similarly,the CRT group demonstrated a statistically significant difference when compared to the Mouldway group(P<0.05).CONCLUSION:Ortho-k lenses represent a pragmatic strategy for mitigating the advancement of myopia.In contradistinction to ortho-k lenses utilizing the CRT design,those employing the VST design exhibited a more favorable impact regarding retarding AL elongation.

Influence of axial stress on rockburst in deep tunnels: insight from model experiment

Frequent rockburst disasters in deep-buried engineering projects severely impact construction. To explore the influence of axial stress on rockburst in deep-buried tunnels, large-scale true triaxial rockburst experiments were conducted under four different axial stress ratio conditions (ηt, axial loading stress/vertical loading stress) using a self-developed true triaxial loading device under the condition of "pre-loading before excavation". The influence of axial stress on the rockburst process and failure characteristics in deep tunnels was studied using a combination of real-time video monitoring, rockburst debris sieving, and acoustic emission monitoring. The results indicate: (1) all four specimens subjected to different axial stress ratio loading conditions exhibited three stages of macroscopic failure: small particle ejection, flake spalling, and large fragment ejection. Ultimately, "V"-shaped notches appeared on both sides of the tunnel. (2) The failure stress, fragment volume, and fragment size distribution of the rockburst specimens exhibited a clear two-stage failure characteristic with increasing axial stress ratio. In the lower axial stress ratio stage (ηt ≤ 0.7), the increase in the axial stress ratio enhances lateral confinement, thereby increasing the crack initiation strength of the surrounding rock, inhibiting crack formation and propagation, and thus suppressing damage to the surrounding rock of the tunnel. In the higher axial stress ratio stage (ηt > 0.7), the increase in axial stress ratio makes the Poisson effect of the surrounding rock more pronounced, promoting the generation and propagation of cracks along the tunnel axis direction, thereby promoting damage to the surrounding rock. (3) Based on the analysis of acoustic emission parameters (fracture properties), it can be concluded that in the lower axial stress ratio stage (ηt ≤ 0.7), an increase in the axial stress ratio leads to a higher proportion of shear fracture in rockburst damage. Conversely, in the higher axial stress ratio stage (ηt > 0.7), the increase in axial stress ratio gradually reduces the proportion of shear fracture in rockburst damage.

A numerical survey of parameters to reach ignition condition for axial compression of a large-sized field reversed configuration

Field reversed configuration(FRC)is widely considered as an ideal target plasma for magnetoinertial fusion.However,its confinement and stability,both proportional to the radius,will deteriorate inevitably during radial compression.Hence,we propose a new fusion approach based on axial compression of a large-sized FRC.The axial compression can be made by plasma jets or plasmoids converging onto the axial ends of the FRC.The parameter space that can reach the ignition condition while preserving the FRC's overall quality is studied using a numerical model based on different FRC confinement scalings.It is found that ignition is possible for a large FRC that can be achieved with the current FRC formation techniques if compression ratio is greater than 50.A more realistic compression is to combine axial with moderate radial compression,which is also presented and calculated in this work.

Impact of multifocal gas-permeable lens designs on short-term choroidal response, axial length, and retinal defocus profile

AIM:To investigate the impact of multifocal gas permeable contact lens(MFGPCL)in various add power and distance/near area allocation on short-term changes of choroidal thickness(ChT),axial length(AL),and retinal defocus profile in young adults.METHODS:Seventeen young adults(2 males and 15 females;age 23.17±4.48y)were randomly assigned to wear two designs binocularly with a one-week washout period in between.Total of four MFGPCL designs were assessed.All designs were distance-center that varied in two add power(+1.50 and 3.00 D)and/or two distance zone(DZ)diameters(1.50 and 3.00 mm;design A:DZ 1.5/add 3.0,B:DZ 1.5/add 1.5,C:DZ 3.0/add 3.0,D:DZ 3.0/add 1.5).ChT,AL,and peripheral refraction data were collected on each subject at baseline,on days 1 and 7 of MFGPCL daily wear.ChT was assessed in four quadrants using a spectraldomain optical coherence tomography.RESULTS:AL was shortened by-26±44μm with lens C,-18±27μm with lens D,-13±29μm with lens A,and-8±30μm with lens B(all P<0.05).A significant overall increase in ChT was observed with all 4 designs(lens A:+6±6μm,B:+3±7μm,C:+8±7μm,and D:+8±7μm).Temporal and superior choroid exhibited more choroidal thickening associated with MFGPCL.All designs induced significant relative peripheral myopia(RPM)beyond the central 20o across the horizontal meridian in both nasal and temporal fields(P<0.05).CONCLUSION:MFGPCLs show a significant influence on ChT and AL,which are associated with significant increase in RPM after short-term wear.The reliability and feasibility of quantifying short-term changes in ChT support its use as a promising marker for the long-term efficacy of myopia-controlling treatments.

Investigation of granite failure precursor under axial load using modified LSTM framework

Granite is usually composed of quartz,biotite,feldspar,and cracks,and the variation characteristics of these components could reflect the deformation and failure process of rock well.Taking granite as an example,the video camera was used to record the deformation and failure process of rock.The distribution of meso-components in video images was then identified.The meso-components of rock failure precursors were also discussed.Moreover,a modified LSTM(long short-term memory method)based on SSA(sparrow search algorithm)was proposed to estimate the change of meso-components of rock failure precursor.It shows that the initiation and expansion of cracks are mainly caused by feldspar and quartz fracture,and when the quartz and feldspar exit the stress framework,rock failure occurs;the second large increase of crack area and the second large decrease of quartz or feldspar area may be used as a precursor of rock failure;the precursor time of rock failure based on meso-scopic components is about 4 s earlier than that observed by the naked eye;the modified LSTM network has the strongest estimation ability for quartz area change,followed by feldspar and biotite,and has the worst estimation ability for cracks;when using the modified LSTM network to predict the precursors of rock instability and failure,quartz and feldspar could be given priority.The results presented herein may provide reference in the investigation of rock failure mechanism.

Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.

A Tabletop Nano-CT Image Noise Reduction Network Based on 3-Dimensional Axial Attention Mechanism

Nano-computed tomography(Nano-CT)is an emerging,high-resolution imaging technique.However,due to their low-light properties,tabletop Nano-CT has to be scanned under long exposure conditions,which the scanning process is time-consuming.For 3D reconstruction data,this paper proposed a lightweight 3D noise reduction method for desktop-level Nano-CT called AAD-ResNet(Axial Attention DeNoise ResNet).The network is framed by theU-net structure.The encoder and decoder are incorporated with the proposed 3D axial attention mechanism and residual dense block.Each layer of the residual dense block can directly access the features of the previous layer,which reduces the redundancy of parameters and improves the efficiency of network training.The 3D axial attention mechanism enhances the correlation between 3D information in the training process and captures the long-distance dependence.It can improve the noise reduction effect and avoid the loss of image structure details.Experimental results show that the network can effectively improve the image quality of a 0.1-s exposure scan to a level close to a 3-s exposure,significantly shortening the sample scanning time.

Effectivity and safety of trifocal intraocular lenses and capsular tension rings implantation for cataract patients with axial high myopia

●AIM:To assess effectivity and safety of trifocal intraocular lenses(IOLs)and capsular tension rings in treating cataract patients with axial high myopia.●METHODS:A prospective nonrandomized controlled clinical trial was conducted.Totally 98 eyes(74 patients)who underwent femtosecond laser-assisted cataract surgery(FLACS)with trifocal IOLs were enrolled in the study and followed up for 2y after surgery:46 eyes(33 patients)with capsular tension ring implantation in the long axial lengths(AL)group(26<AL<29 mm)and 52 eyes(41 patients)in the normal AL group(22<AL<24.5 mm).Postoperative outcomes about effectivity and safety,including the subjective and objective visual quality,and postoperative complications were assessed.●RESULTS:Uncorrected distance visual acuity at 5 m and uncorrected intermediate visual acuity at 60 and 80 cm in the long AL group were significantly worse than those in the normal AL group at 3mo postoperatively(P<0.05).The differences in reading speed,spectacle independence and potential visual complaints between the two groups were not statistically significant(P>0.05).The dysfunctional lens index and total modulation transfer function(MTF)average height were similar between the two groups.The postoperative internal coma aberrations in the axial high myopia eyes were significantly higher than that in the normal AL group(P<0.05).The total satisfaction score in the long AL group(91.32±2.76)was slightly higher than that in the normal AL group(90.36±3.47),but there was no difference(P=0.136).A statistically negative correlation was found between corrected distance visual acuity(CDVA)and dysfunctional lens index(r=-0.382,P=0.009),and between CDVA and the total MTF average height(r=-0.374,P=0.01).But there was no significant correlation between CDVA and total satisfaction score(r=0.059,P=0.696).Postoperative complications mainly presented as posterior capsular opacity(PCO),retinal detachment and cystoid macular edema.There was no difference in the incidence of fundus disease(6.5%vs 3.8%,P=0.663)or PCO(17.4%vs 7.7%,P=0.217)between the two groups at two years.●CONCLUSION:The utilization of trifocal IOL and capsular tension ring implantation is beneficial for cataract patients with axial high myopia undergoing FLACS.This approach not only ensures excellent subjective feelings and objective visual quality,but also does not increase the incidence of postoperative complications.

Experimental Study on the Axial Compression Performance of Bamboo Scrimber Columns Embedded with Steel Reinforcing Bars

In this paper,a new type of bamboo scrimber column embedded with steel bars(rebars)was proposed,and the compression performance was improved by pre-embedding rebars during the preparation of the columns.The effects of the slenderness ratio and the reinforcement ratio on the axial compression performance of reinforced bamboo scrimber columns were studied by axial compression tests on 28 specimens.The results showed that the increase in the slenderness ratio had a significant negative effect on the axial compression performance of the columns.When the slenderness ratio increased from 19.63 to 51.96,the failure mode changed from strength failure to buckling failure,and the maximum bearing capacity decreased by 43.03%.The axial compression performance of the reinforced bamboo scrimber columns did not significantly improve at a slenderness ratio of 19.63,but the opposite was true at slenderness ratios of 36.95 and 51.96.When the reinforcement ratio increased from 0%to 4.52%,the bearing capacity of those with a slenderness ratio of 51.96 increased by up to 16.99%,and the stiffness and ductility were also improved.Finally,based on existing specifications,two modification parameters,the overall elastic modulus Ec and the combined strength fcc,were introduced to establish a calculation method for the bearing capacity of the reinforced bamboo scrimber columns.The calculation results were compared with the test results,and the results showed that the proposed calculation models can more accurately predict the bearing capacity.

Nonlinear dynamic modeling of planar moving Timoshenko beam considering non-rigid non-elastic axial effects

Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipulator consists of an elastic arm,a rotary motor,and a rigid carrier,and undergoes general in-plane rigid body motion along with elastic transverse deformation.To accurately model the elastic behavior,Timoshenko’s beam theory is used to describe the flexible arm,which accounts for rotary inertia and shear deformation effects.By applying Newton’s second law,the nonlinear governing equations of motion for the manipulator are derived as a coupled system of ordinary differential equations(ODEs)and partial differential equations(PDEs).Then,the assumed mode method(AMM)is used to solve this nonlinear system of governing equations with appropriate shape functions.The assumed modes can be obtained after solving the characteristic equation of a Timoshenko beam with clamped boundary conditions at one end and an attached mass/inertia at the other.In addition,the effect of the transverse vibration of the inextensible arm on its axial behavior is investigated.Despite the axial rigidity,the effect makes the rigid body dynamics invalid for the axial behavior of the arm.Finally,numerical simulations are conducted to evaluate the performance of the developed model,and the results are compared with those obtained by the finite element approach.The comparison confirms the validity of the proposed dynamic model for the system.According to the mentioned features,this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms.

The Method of Thermoelectric Energy Generations Based on the Axial and Radial Flux Electromagnetic Inductions*

The traditional thermoelectric energy conversion techniques are explained in detail in terms of the axial flux electromagnetic (AFE) and the radial flux electromagnetic (RFE) inductions, and applications to heat engines for the energy-harvesting technologies are discussed. The idea is induced by the analysis of thermomechanical dynamics (TMD) for a nonequilibrium irreversible thermodynamic system of heat engines (a drinking bird, a low temperature Stirling engine), resulting in thermoelectric energy generation different from conventional heat engines. The mechanism of thermoelectric energy conversion can be categorized as the axial flux generator (AFG) and the radial flux generator (RFG). The axial flux generator is helpful for low mechanoelectric energy conversion and activations of waste heat from macroscopic energy generators, such as wind, geothermal, thermal, nuclear power plants and heat-dissipation lines, and the device contributes to solving environmental problems to maintain clean and sustainable energy as one of the energy harvesting technologies.

Axial load-share ratio testing to assess the healing of open tibial fractures treated with the Taylor Spatial Frame

Background:The Taylor Spatial Frame(TSF)has gained popularity among orthopedic surgeons for treating open fractures.However,a key challenge is the timely and safe removal of the frame.This study assessed the efficacy and safety of axial load-share ratio(ALSR)testing to evaluate callus healing strength after TSF treatment of open tibial fractures.Methods:A retrospective case-control study was conducted,analyzing 180 adult patients with open tibial fractures treated at Tianjin Hospital’s Orthopedic Limb Correction Unit between August 2019 and August 2022.All patients underwent TSF external fixation surgery,and were divided into two groups based on ALSR testing.Group I(92 patients)underwent ALSR testing,with frame removal if the test value fell below 5%.Traditional methods were used for fixator removal guidance in Group II(88 patients).Clinical outcomes,including fixation duration,complications after fixator removal,and Johner-Wruhs functional scores,were compared between the two groups.Results:The groups showed no statistically significant differences(P>0.05)in sex,age,injury side,body mass index,surgery timing,or fracture type.Group I had a significantly shorter fixation duration(25.85±5.57 weeks)compared to Group II(31.82±6.98 weeks)(P<0.05).Following fixator removal,Group I demonstrated superior Johner-Wruhs scores compared to Group II,indicating better outcomes(P<0.05).Complication rates did not differ significantly between the groups at the last follow-up(P>0.05).Conclusion:Regular postoperative ALSR testing could safely and effectively guide TSF removal following open tibial fracture treatment.This method significantly reduced fixation duration compared to traditional guidance methods while maintaining efficacy and safety.

基于轴-Transformer的医学图像分割模型Axial-TransUNet

针对TransUNet中Transformer自注意力机制计算复杂度高、捕获位置信息能力不足的问题,提出一种基于轴向注意力机制的医学图像分割网络Axial-TransUNet。该网络在保留TransUNet网络编码器、解码器以及跳跃连接的基础上,使用基于轴向注意力机制的残差轴向注意力块代替TransUNet的Transformer层。实验结果表明,在多个医学数据集上,相较于TransUNet等其他医学图像分割网络,Axial-TransUNet的Dice系数、交并比IoU有更好的表现。与TransUNet相比,Axial-TransUNet网络的参数量与浮点运算数(FLOPs)分别降低14.9%和30.5%。可见,Axial-TransUNet有效降低了模型复杂度,并增强了模型捕获位置信息的能力。

Extra-Axial Anaplastic Pleomorphic Xanthoastrocytoma Mimicking Meningioma: A Case Report with Literature Review

Background: A number of meningeal neoplastic lesions may radiologically and clinically simulate meningioma, include hemangiopericytomas, solitary fibrous tumors, schwannomas, hematolymphoid lesions, metastases, and others very rarely, also may clinically mimic meningiomas. Case Description: We present the case of A 28-year-old male patient, with no notable medical history, who presented with worsening headaches for 3 months, imbalance, and visual deficits, An initial MRI revealed extra-axial lesion involving the right Parieto-occipital, The tumor was hypointense on T1-weighted MR images, hyperintense signals on T2-weightedMR images, and heterogeneously enhanced suggestive of a meningioma, total resection was achieved, and the histopathological analysis confirmed the diagnosis of an angioblastic meningioma. However, 15 months later, the patient presented with the same initial visual complaints. A subsequent MRI showed lesion recurrence, leading to a second surgical intervention. The histopathological analysis confirmed the diagnosis of an anaplastic xanthoastrocytoma. Conclusion: This represents an unusual location for an anaplastic pleomorphic xanthoastrocytoma, which should broaden the differential diagnosis of extra-axial lesions.

联合Self-attention与Axial-attention的机场跑道裂缝分割

机场跑道裂缝形态多样、方向各异、长短不一且粗细不均,通常不具有统计规律。现有的各类裂缝分割算法难以在此类复杂场景中落地。针对上述问题,提出了联合self-attention与axial-attention的机场跑道裂缝分割网络(CSA-net),通过引入自注意力模块、轴向注意力模块、可变形卷积模块,提取裂缝的局部特征和全局语义特征。通过transformer decoder还原特征图的原始尺寸,融合了不同尺度间的分割结果,保留尽可能多的细节信息,使得CSA-net有更好的分割精度。在机场跑道实拍的数据集上进行的测试表明,针对裂缝的像素级分割指标F1-score达到了78.91%,高于目前各类裂缝分割算法。

ULTIMATE LOAD-BEARING CAPACITY OF CYLINDER DERIVED FROM AUTOFRETTAGE UNDER IDEAL CONDITION

According to the basic theory on autofrettage and according to the 4th strength theory, several parameters and their relations are studied under ideal condition, including σej/σy, the equivalent stress of total stresses at elastoplastic juncture; σei/σy, the equivalent stress of total stresses at inside surface; σej＇/σy, the equivalent stress of residual stresses at elastoplastic juncture; σei＇/σy, the equivalent stress of residual stresses at inside surface; and p/σy, load-bearing capacity of an autofrettaged cylinder. By theoretical study on relations between the parameters, noticeable results and laws are achieved： to satisfy ｜σei＇｜=σy. the relation between kj and k is, k^2lnkj^2-k^2-kj^2＋2=0, when k→∞, kj = √e = 1.648 72, as based on the 3rd strength theory, where k is the outside/inside radius ratio of a cylinder, kj is the ratio of elastoplastic juncture radius to inside radius of a cylinder; If the plastic region covers the whole wall of a cylinder, for compressive yield not to occur after removing autofrettage pressure, the ultimate k is k=-2.218 46 as based on the 3rd strength theory; With k=2.218 46, a cylinder＇s ultimate load-bearing capacity equals its entire yield pressure, or p/σy=21nk/√3; The maximum and optimum load-bearing capacity of an autofrettaged cylinder is just 2 times the loading which an unautofrettaged cylinder can bear elastically, or p/σy=2（k^2-1）/√3 k^2, and the limit of the load-bearing capacity of an autofrettaged cylinder is also just 2 times that of an unautofrettaged cylinder. The conclusions are the same as based on the 3rd strength theory, but some equations are different from each other.

Effect of Optimum Plastic Depth on Stresses and Load-bearing Capacity of Autofrettaged Cylinder

Autofrettage is an effective measure to even distribution of stresses and raise load-bearing capacity for （ultra-）high pressure apparatus. Currently, the research on autofrettage has focused mostly on specific engineering problems, while general theoretical study is rarely done. To discover the general law contained in autofrettage theory, by the aid of the authors’ previous work and according to the third strength theory, theoretical problems about autofrettage are studied including residual stresses and their equivalent stress, total stresses and their equivalent stress, etc. Because of the equation of optimum depth of plastic zone which is presented in the authors’ previous work, the equations for the residual stresses and their equivalent stress as well as the total stress and their equivalent stress are simplified greatly. Thus the law of distribution of the residual stresses and their equivalent stress as well as the total stress and their equivalent stress and the varying tendency of these stresses are discovered. The relation among various parameters are revealed. The safe and optimum load-bearing conditions for cylinders are obtained. According to the results obtained by theoretical analysis, it is shown that if the two parameters, namely ratio of outside to inside radius, k, and depth of plastic zone, kj, meet the equation of optimum depth of plastic zone, when the pressure contained in an autofrettaged cylinder is lower than two times the initial yield pressure of the unautofrettaged cylinder, the equivalent residual stress and the equivalent total stress at the inside surface as well as the elastic-plastic juncture of a cylinder are lower than yield strength. When an autofrettaged cylinder is subjected to just two times the initial yield pressure of the unautofrettaged cylinder, the equivalent total stress within the whole plastic zone is just identically equal to the yield strength, or it is a constant. The proposed research theoretically depicts the stress state of ultra-）high pressure autofrettaged cylinder more accurately and more reasonably and provides the reference for design of （ultra-）high pressure apparatus.