1.Introduction

Near β titanium has become widely accepted as the metal of choice for manufacturing aircraft components due to its superior properties[1,2].Ti-7333(Ti-7Mo-3Nb-3Cr-3Al,wt%)alloy is a newly developed near β titanium alloy owning outstanding mechanical properties such as high strength,excellent fatigue crack growth resistance,as well as good hardenability[3,4].Establishing the composition-microstructureperformance relationship is of great significance for predicting the mechanical properties of titanium alloys.Therefore,it is essential to obtain elastic and plastic properties of single phase as the basis of further investigation for polycrystalline aggregation.Plastic deformation in polycrystalline microstructures of titanium alloys is strongly dependent on the grain morphology and crystallographic lattice orientation[5].

水力压裂技术产生的裂缝长度通常可达100 m,宽度和长度分别为0.01 m和1 m。为了对油层进行分布式测量,微纳传感节点混在携砂液中(含石英砂)随压裂进程进入裂缝,其在裂缝中的位置因而是随机分布的[4]。体积和功率较大的锚节点通常布置于井筒内部,由外部电源供电,可直接与裂缝内的传感器节点进行磁感应通信,锚节点同时通过磁感应方式为传感节点提供电能;微纳尺寸的传感器节点具有全向线圈天线,同时配置超级电容器储存耦合电能。考虑到供电及传感器通信能力等因素,在面向油藏裂缝的地下无线传感网络中,锚节点和传感节点之间通信(下行链路)是单跳方式,传感节点与锚节点之间通信(上行链路)采用多跳方式[5]。

Nanoindentation has a distinct advantage to mechanically characterize individual phase in titanium alloys with significantly less effort and equipment comparing to micropillars and cantilever beams which require the focused ion beam(FIB)techniques to prepare samples[6].Thanks to its precise load-controlling and displacement-sensing capabilities,nanoindentation has been increasingly used to study the mechanical response of materials such as hardness,elastic modulus,creep parameters and strain-hardening exponent [7]. In addition,nanoindentation, combined with electron backscattered diffraction(EBSD)scan,has been widely applied to investigate deformation mechanism of grains with different orientations and confirmed that the anisotropic mechanical response is consistently observed across various titanium alloys[6,8–10].

Beyond the typical hardness tests,the strain-rate sensitivity(SRS)measurement based on dynamic nanoindentation becomes possible now.Although the local strain field around the indentation is much more complex than the conventional macroscopic Engineering ratesensitivity measurement,nanoindentation test allows investigating the mechanical response to strain rate with different microstructures,such as the ultrafine-grained and nanocrystalline materials[11,12],the fully lamellar microstructures[8]and the multilayered films[13].

UPS的配置应根据发信台设备的用电功率以结合其他因素做精确计算后进行配置，经统计，目前发信台正在运行的设备及所需功率如表2。

In the past few years,the crystal plasticity finite element(CPFE)method achieved great success in modeling and simulating the plastic deformation process of various microstructures,thus building up the relationship between microstructure and mechanical properties[14,15].The predictive capability of CPFE models mostly relies on the accuracy of constitutive laws,which express the slip rate on crystallographic slip planes in terms of resolved shear stress and other solution dependent state variables.Compared to the limitations in generating real samples with various microstructures,it is easier to establish different models with detailed characterization of microstructure features from single crystal to polycrystalline aggregate[16–18].Furthermore,the CPFE method also can provide credible validation for the experimental results,be instructive to predict mechanical performance of materials,and investigate detailed information about slip systems beyond the limitation of experimental conditions.

The purpose of this study is to investigate the micromechanical behavior and SRS properties of β phase in Ti-7333 alloy,using nanoindentation experiments combined with crystal plasticity modeling.The authors believe that the comparative analysis between experimental and numerical nanoindentation results could provide supportive information about mesoscopic mechanical behavior investigation and performance prediction.

2.Nanoindentation simulation and experiments

2.1.Nanoindentation tests

综上所述，推测在脑胶质瘤细胞中miR-543通过激活Caspase凋亡信号通路进而抑制细胞增殖，促进细胞凋亡。本实验为miR-543抑制脑胶质瘤细胞增殖作用机制的进一步研究提供了证据，揭示miR-543可作为新的脑胶质瘤相关基因治疗靶点，为延长脑胶质瘤患者生存期提供新方向。

To reveal the relationship between hardness and orientations the locations of indentations were carefully selected in the middle of grains away from boundaries for specific orientations identified by EBSD map,using a ZEISS SUPRA 55 Scanning Electron Microscope equipped with EBSD detector.The nanoindentation experiments were carried out using Hysitron TI-950 nanoindentation tester equipped with a Berkovich indenter.The spacing between adjacent indentations was over 20 times the maximum width of indentations to make sure that the deformation of one indentation was not interfered by the others.The loading procedure divided into three parts: firstly, loading to the maximum load(2000 μN)in 5 s,then holding for 2 s,and unloading to 0 μN in 5 s.

in which K is a constant with a value of 24.56 for perfect Berkovich indenter,and hc is the contact depth.In addition to the typical nanoindentation tests measuring static hardness,the CSM approach enables the investigation of the SRS properties of β phase in Ti-7333 alloy by the displacement oscillation of indenter.Lucas and Oliver[20]differentiated and simplified the Eqs.(1)and(2),and obtained the expression of indentation strain rate as follows

2.2.Hardness and SRS exponents

Nanoindentation tests are commonly applied to measure hardness and modulus of thin film and bulk materials based on the load-displacement curves.The value of hardness of an individual grain can be calculated from unloading portion of the curve using the method developed by Oliver and Pharr[19]as following expression

where P denotes the applied load and A denotes the projected contact area that can be calculated by

Then,nanoindentation tests under constant strain rate were applied to the sample using a standard continuous stiffness measurement(CSM)method for determining the SRS properties.The rate sensitivity of two selected grains with different orientations was measured through indentations made for three targeted indentation strain rate,varying between 0.2,0.05,and 0.01 s-1.For each grain and strain rate,four repeated indents were made.The peak load was set as 10 mN and the preload P0 set as 500 μN,which were the same for all tests.The preload setting aimed to avoid the useless vibration of indenter in contact with the surface of sample.The surface topography around indents was measured by Bruker Dimensions Icon AFM,and the data analyzed by NanoScope Analysis software.The nanoindentation tests were performed at room temperature.

which indicates that the indentation strain rate can keep constant as long as the ratio of loading rate(P˙)to load(P)remains a constant value.For SRS measurements,Mayo and Nix[21]purposed that the indentation rate could be derived from the concept of true strain,and defined the SRS exponent,m,using a constant loading rate by

规范审计内容的前提是离任审计的相对独立性，加强离任审计工作独立性的措施有很多，例如我国某建勘院在多年的工作与当地政府的帮助下开始逐步规范相关审计内容。地勘单位首先根据当地审计工作人员的指导，有组织有秩序地开展地质勘查相关工作，从内部完善离任审计任务。其次法定负责人从根本上意识到离任审计工作的相对独立性，这样才能使得离任工作不影响整个工程项目的进度。最后离人审计人员完善审计内容，根据地勘单位的特异性为其准备相应的指标数据，确保审计内容的高参考价值，并能更加合理地反映并反馈出地勘单位的工作核心与竞争的优势性。

2.3.Crystal plasticity framework

In present work,the crystal plasticity constitutive model is employed based on the work of Peirce et al.[22].The crystal orientation and activated slip systems are taken into account.The total deformation gradient F of finite strain can be decomposed into elastic part Fe and plastic part Fp according to following equation

The nanoindentation simulation and experiments focused on the mesoscopic mechanical behavior of β phase in titanium.A new type of near β titanium alloy Ti-7333 (Ti-7Mo-3Nb-3Cr-3Al) designed by Northwestern Polytechnical University(NPU)was subjected as the experiment material.The β transus temperature of Ti-7333 alloy was approximately 850 ℃measured by metallographic method.Forged bar of Ti-7333 alloy was solution-treated at the temperature of 900 ℃for 30 min followed by water quenching in order to obtain the single β phase. The samples were from the bar with a dimension of 10 mm×7 mm×5 mm.The specimens were ground with sand papers and polished with OP-S diluted H2O2(with a ratio 1:9 of H2O2:OP-S)by Struers Metallographic Polisher,obtaining high-quality surface required for nanoindentation test and EBSD measurement.The microhardness tester was used to mark a target region with a half of rectangular frame.

where Fe is derived from the elastic stretching and rigid body rotation,and Fp is derived from dislocation slip.Dislocation slip is assumed to the sole mechanism for plastic deformation,and therefore,the evolution of velocity gradient Lp can be given by

[3] 耿红卫：《印尼华文教育的历史沿革与现状》，《云南师范大学学报》(对外汉语教学与研究版)2007年第3期，第68页。

where and mα are plastic shear strain rate,slip direction vector and normal vector to slip plane on the α-th slip system,respectively.The shear rate on each slip system depends on resolved shear τα and slip system resistance gα by a rate-dependent power law as following

Simulated pileup profiles of indented surfaces along AC and BD directions of each grain are assembled in Fig.5.From the curves of different grains,it can be seen that the maximum height of pileup ranged from only 5–10 nm due to the good capability of plastic deformation for BCC crystal.Combined the results of Fig.4 and Fig.5,the width of pileup and the maximum value of height differs among those grains with different orientations,indicating that the morphology of pileup in β phase of Ti-7333 alloy is related to the orientation of indented grains.

The crystal plasticity constitutive model incorporated into the finite element code using user material subroutine.For single crystal model,the current strengths,shear strains,resolved shear stresses,slip directions and normals to slip plane are considered as solution dependent state variables[23].The subroutine automatically updates the solution dependent state variables at the end of each increment step.The values of the material Jacobian matrix∂ Δσ∂ /Δε can also calculate in the subroutine.

The SRS properties were evaluated from the curves of hardness versus displacement of indenter obtained by nanoindentation tests under constant strain rate in Fig.6.The initial measured hardness is inaccurate due to the preloading at early stage of deformation.In order to avoid the error resulting from the instability,the initial part of the curves was neglected.In Fig.6(b),the average values of hardness obtained at the depth of 300 nm assembled to fit the SRS exponent,m.It should be mentioned that these grains numbered 1 and 2 are not the same as the ones in Fig.2.

（1）重视新科技在金融行业的应用。对于清华大学数字货币进校园，我认为应该鼓励，支持学校等机构积极探索新技术的应用。

总之，小学信息技术课堂教学中，教师一定要多鼓励学生勤动脑、多动手，通过多种形式的教学方法，使学生认识到学习信息技术的重要性以及学习信息技术的乐趣。其次加强对学生实践探究能力的培养的重视度，提高学生对所学知识的实践应用能力，同时对实践中遇到的问题能够进行有效的探究与分析，实现信息技术教学的可持续发展。

where h0 is the initial hardening modulus,τ0 and τ0 are initial value and saturation value of the yield strength,respectively.And γ is the Taylor cumulative shear strain on all activated slip systems.The latent hardening modulus can be described as whereq is a constant.

1)初步设计了超前支架的结构，该支架不但具有垂直升降和水平伸缩功能，而且支架在展开时与顶板接触良好，同时分析了支架的受力情况。

Fig.1.Three-dimensional finite element model of nanoindentation:modeled and meshed.(color is required only for online version).

3.Results and discussion

3.1.Three-dimensional finite element model

As shown in Fig.1,a three-dimensional finite element model generated with a dimension of 5.12µm×2.56µm×5.12µm.The whole model includes a cube representing the single crystal and a Berkovich indenter located on the surface of cube.We assumed that there is no Friction between the indenter and materials.

Since the Young's modulus of diamond is much larger than titanium alloy,deformation of the indenter was neglected by assuming that it is a rigid body.And the cubic was set as deformable part consisting of 14,520 eight-node brick elements and 16,236 nodes with reduced integration(C3D8R).The maximum number of elements already verified to guarantee a satisfying compromise between the accuracy and computational costs.Given the real constraint conditions of samples during indentation process,the bottom surface and four surrounding surfaces of the cubic were constrained.

由图2可知，电压互感器1、2、3、4、5、6、7、8、9和11号A相的量测数据序列之间的平均欧氏距离均小于阈值，而电压互感器10的量测数据序列与上述电压互感的量测数据序列的平均欧氏距离大于阈值，由此可以判定电压互感器10，也就是宾叙一线A相的电压互感器发生故障。

The parameters of crystal plasticity constitutive model for β phase of Ti-7333 alloy are assembled in Table 1.It should be mentioned that twelve slip systemsof β phase are considered in the model.

3.2.Effect of orientations on nanoindentation results

From a microscopic point of view,it is essential to investigate the effect of grain orientations on mechanical response in meso-scale.Plastic deformation of crystal inherently derives from the dislocation slipping on slip plane.Therefore,the change of grain orientation determines different loading direction during indentation process,which also leads to the change of activated slip systems.

The HKL channel 5 software is used to analyze the EBSD results in specific region previously marked (Fig. 2(a)), especially for theorientation information.The orientation mapping inserts in the rectangle of Fig.2(a).Fig.2(b)exhibits the inverse pole figure of different orientation.These grains conducted nanoindentation test are numbered and marked in Fig.2(b).

Table 1 The crystal plasticity constitutive parameters of β phase in Ti-7333 alloy.

γ0˙ /s- 1 n h0 /M Paτ0/ M Pa [24] τs /M Pa [24]0.001 15 1500 300 353

Fig.3 integrates the load-displacement curves of six selected grains obtained by their nanoindentation tests.From Fig.3,it can be seen that there are divergence existing in the maximum indent depth,and the slope of unloading part determines hardness of indented materials.Meanwhile,Table 2 lists measured hardness with different orientations varying from 3.78 to 4.27 GPa with an average value of 4.06 GPa.According to the curves in Fig.4 and the data in Table 2,the hardness shows a certain orientation-dependent characteristics.

However,due to its body-centered crystal structure,β phase of Ti-7333 alloy includes up to 48 slip systems,which might activates during plastic deformation.The change of loading direction has little effect on the number of activated slip systems.Thus,grain orientation has slight effect on the load-displacement curves of nanoindentation.

The displacement-controlling loading mode was used to simulate the movement process of indenter,and displacement-time data from experiments were used as input amplitude.The simulated values of hardness calculated by the Oliver-Pharr method using the simulated load-displacement curves are listed in Table 2,existing an acceptable error with 12.89%.The crystal plasticity constitutive parameters in Table 1 show a reasonable accuracy.

Under experimental conditions,the tip of Berkovich indenter was inevitably worn in contrast to the perfectly sharp indenter used in simulation.Even though the maximum indented depth in experiments and simulation were identical,plastic deformation took up a greater proportion during simulation process resulting in a lager residual indented depth.Therefore,the experimental results show better elastic resilience and higher hardness than the simulated results.

3.3.Pileup patterns

The top views of simulated surface morphology for corresponding grains after unloading are shown in Fig.4.It can be clearly observed that a similar distribution of three pileup areas occurs evenly along three sides of Berkovich indents boundaries,reflecting a character of symmetrical plastic deformation mechanism in β phase of Ti-7333 alloy.

Qualitatively,in each case,the height of the pileup was not the same along the three sides.There was a major pileup that was larger than the other two pileup hillocks with the exception of grains numbered 4 and 5.The three-dimensional view of grain 1 in Fig.5(a)is cut along two directions in AC(through one pileup)and BD(through the others pileup).The materials below indented surface had positive displacements,indicating that pileup comes from the internal material plastic accumulation.

Fig.2.(a)SEM image of target area and inserted EBSD orientation map,(b)inverse pole figure showing the orientation of grain with indentations.(color is required only for online version).

Fig.3.Load-displacement curves for nanoindentation of 6 grains numbered in Fig.2.(color is required only for online version).

Table 2 Hardness of 6 grains calculated from experiments and simulation.

Grain Hardness/Gpa Experimental Simulated 1 3.78 3.49 2 4.27 3.72 3 4.19 3.74 4 3.95 3.33 5 4.13 3.52 6 4.02 3.42 Average 4.06 3.54

where denotes the reference value of the slip rate,n represents the reciprocal of SRS exponent.As dislocations accumulating during shear,the materials is work hardened through both self and latent hardening mechanisms,and the rate of change of slip resistance can be given by

3.4.Relationship between orientations and SRS exponents

where hαβ is the hardening modulus.The PAN hardening model is used in this work,and the self-hardening modulus can be given by

小学阶段的学生思维能力还不够成熟，对于抽象事物的理解能力和想象能力较差，通过实物教学的方式帮助学生将学习内容具体化、生动化，可以有效降低教学难度，更加适用于小学数学课堂教学。例如测量教学，学生对于度量单位较为陌生，也很难理解。教师可以发给学生尺子，和学生一起测量身边可以接触到的实物，记录下一组组测量数据，通过这种学生的亲自操作和实践体验，帮助学生理解度量单位，进而对于抽象的知识概念有更加清晰的认识和接受。小学数学课堂教学这种具体化教学的运用可以说是较为常见的，因为它不仅有效降低了学生学习难度，避免学生对于苦涩知识的畏惧情绪，也极大丰富了教师的教学手段，提升课堂教学有效性。

The results show that β grains exhibit different hardness under each constant strain rate,and the higher strain rate it applies,the larger hardness it obtains.In Fig.6(a),the hardness has slightly decline under a rate of 0.2 and 0.05 s-1,in comparison to the obvious decline at a rate of 0.01 s-1 in Fig.6(b).The decrease occurs mainly in the initial stage,and the hardness tends to be stable as the depth of indentation increases.

The m values were evaluated from the plots of hardness against strain rate in log-log form,showing in Fig.6(c)-(d).The hardness rises continuously with increasing strain rate,from about 3.3–4.0.The AFM images of two grains with the strain rate of 0.05 s-1 were added in Fig.6,showing pile-up distribution surrounding the indents.It is noteworthy that there was one prominent pileup in each grain,which is consistent with simulated results shown in Fig.4.Thus,the reliability of CPFE model established in this paper is verified.

Compared between two grains,there is no obvious difference in hardness under the same strain rate,showing that the strain rate has more significant influence than grain orientations on the value of hardness in β phase of Ti-7333 alloy.With similar m value(0.056 and 0.064)for two orientations,the rate sensitivity is independent of grain orientation in terms of β phase.In early researches,the SRS exponent has a strong dependence on the orientation in nano-twin copper[25],which is much higher in the hard loading direction(vertical to twin boundaries).The SRS exponent of dual phase titanium Ti-6242 and Ti-6246[8]exhibits differences in the degree of orientation dependence,which is attributed to the volume fraction and thickness of β lath combined with the ability for dislocation to easily slip across complex microstructures. However, there are no precipitation or twinning structure found in the solution-treated Ti-7333 alloy of single β phase.Besides,the BCC structure of β phase owns greater capability of plastic deformation, in comparison to the HCP structure of α phase determining the soft and hard orientation during slip.Therefore,the grain orientation has nearly no effect on the SRS exponent in β phase of Ti-7333 alloy.Still,the relationship between the m value obtained through nanoindentation tests and the rate sensitive measurement of macrodeformation still needs further investigation.

4.Conclusions

By the combination of instrumented nanoindentation,EBSD and AFM experimental measurements,and CPFE modeling,the deformation process of nanoindentation in near β Ti-7333 titanium alloy is assessed.The crystal orientation dependency of the alloy is characterized by analyzing the pileup topography distribution around indentations,and the rate sensitivity properties investigated with a nanoindentation CSM method using multiple indentations at different constant strain rate.

Fig.4.Simulated pileup morphology of 6 grains from Fig.2(color is required only for online version).

Fig.5.Simulated pileup pattern in(a)3D view and sections in(b)AC and(c)BD paths and simulated pileup profiles of indented surfaces along(d)AC and(e)BD directions.(color is required only for online version).

Fig.6.Individual hardness vs.displacement curves and the hardness vs.strain rate(log-log form)for(a,c)grain 1 and(b,d)grain 2 under different strain rate.(color is required only for online version).

The typical nanoindentation tests have been used to discuss the relationship between hardness and grain orientations in β phase of Ti-7333 alloy.Nanohardness and load-displacement curves of six grains with different orientations show a character of orientation dependence.Based on the results of CPFE simulation for single crystal nanoindentation process,pileup pattern of β phase appears symmetrical distribution because of its body-centered cubic microstructure,while the width and height of pileup relates to grain orientations.Most of grains own one major pileup and two relatively smaller pileup hillocks.Moreover,under a constant strain rate,the value of hardness shows decreasing tendency as the indentation depth increasing,and the SRS exponents m exhibit independence of grain orientation in the β phase.

Acknowledgements

转变工作作风。工会最大的优势是密切联系职工群众，最大的危险是脱离职工群众。各级工会要加强对工会干部的教育、管理、监督，激励广大工会干部事不避难、干事创业，促进工会干部在实践中锻炼成长，增强群众工作本领，打造一支高素质专业化的工会干部队伍。要完善联系职工群众的制度机制，深入基层一线，加强调查研究，坚决防止“四风”特别是形式主义、官僚主义。基层工会要紧紧围绕职工群众转、依靠职工群众干、成效由职工群众来评判，面对面、心贴心、实打实地做工作，让工会工作深深扎根于广大职工群众之中。

The authors gratefully acknowledge the National key Research and Development Program of China(2016YFB0701303)and the“111”Project(No.B08040)for financial support.

Research data

The raw data of individual nanoindentation associated with section 4.3 can be found in the online version at http://dx.doi.org/10.17632/ddxtvjjfdk.4.

Declarations of interest

None.

节能工作作为一项系统工程，已然需要深入医疗业务及医院运行的细节中。因此，更加契合医疗业务运行的综合能源管理平台搭建，集成管理、统一规划将是未来医院节能的趋势所向，也是北医三院节能管理工作一直在积极思考的。

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