1 Introduction

Li-ion batteries(LIBs)play an essential role in the battery market of portable electronics and electric/hybrid electric vehicles due to their high energy densities,small size,and long service life[1–4].However,one of the main problems of current commercial LIBs is capacity fading along with an increase in the cycle time.The degradation mechanisms of LIBs can be either electrochemical[1–3,5]or mechanical[1–3,6],which are the most important and popular mechanisms,and the mechanism manifests itself by capacity loss,power fading,or both[7].Dendrite grow th,which is not discussed in this paper,represents another important degradation mechanism in LIBs[1,2,8,9].Mechanical degradation mechanisms are mainly related to the volume changes and subsequent stress generated in the active material particles of the anode or cathode within lithium de/-intercalation[7].As a consequence of tensile stress,active particles may develop cracks,loss of contact between each other or from the current collector,and isolation[10].Fractures among active particles increase the resistance to electron transport and therefore reduce lithium intercalation or deintercalation[11].Additionally,fractures also generate new free surface areas,which,when they come into contact with the electrolyte,cause new side reactions[12]and a new solid electrolyte interface(SEI)layer is generated[13].These phenomena cause further electrochemical degradation.

从2006年提出培养“新型职业农民”，到2012年“大力培育新型职业农民”，再到2017年“全面建立职业农民制度以及实施新型职业农民培育工程”，党中央、国务院历来高度关注农民的培育与发展问题。“农民”问题作为“三农”领域的核心问题，关系着党和国家的发展全局。习近平总书记明确指出：“农村经济社会发展，说到底，关键在人。”加强新型职业农民“双创”教育，提升新型职业农民“双创”能力作为培育新型职业农民的重要环节，对于促进农民职业化发展、提升农业生产竞争力、推动产业升级及建设社会主义新农村，助力乡村振兴具有重要的现实意义。

Early researchers discussed the evolution of mechanical stress and the Li-ion concentration.For example,Lee et al.[14]investigated the stress evolution within thin plates,hollow cylinders,and composites.Then,Christensen and Newman[15,16]developed a detailed mathematical model for diffusion-induced stress in intercalated active particles and applied a tensile stress failure criterion to predict particle cracking.Furthermore,Zhang et.al[17]studied the interplay between mechanical stress and Li-ion diffusion in active particles.The work of Cheng and Verbrugge[18]studied the evolution of strain energy and stress within host sphere particles of an electrode under potentiostatic and galvanostatic operation.Also,Korsunsky et al.[19]devel-oped explicit formulae for internal stress and concentration within active sphere particles of the cathode during charging and discharging.The study by Zhang et al.[20]developed analytical diffusion-induced stresses for transverse isotropic cylindrical electrodes during intercalation process. The effect of chemo-mechanical coupling,surface reaction and particle size on stress evolution and phase interface mitigation in an elasto-plastic silicon particle with complex geometry was investigated by Lu and Ni[21]by using a phase- filed model.The Li-ion distribution and diffusion-induced stress in porous electrodes was analyzed by Ji and Guo[22].Many researcher shave been investigating the fracture phenomenon and diffusion-induced damage in recent years.For example,Deshpande et al.[13]explained the number of battery cycles with coupled chemical degradation based on Paris’s low formulation of mechanical fatigue.The effect of the aspect ratio and the position of the initial defect on crack propagation within LiMn2O4 elliptical particles during charging and discharging was explored by Zhu et al.[23]by using the extended finite element method(X-FEM).The effect of pressure-gradient dependent diffusion on the distribution of the Li-ion concentration and crack propagation was investigated Grantab and Shenoy[24].Crack growth within active particles in the cathode during the intercalation and de-intercalation processes was simulated by Klinsmann et al.[25,26]by using a phase field model.The effect of the material properties,particle size,and discharge rate on fractures of active particles were studied by Zhao et al.[27]by calculating the energy release rate.Then,Woodford et al.[28,29]proposed an “electrochemical shock”model to calculate the critical cracking conditions from the initial surface semicircular defect and proposed a design criterion for electrochemical shock in Li-ion battery electrodes.The mechano-diffusional driving force behind fractures was analyzed by Gao and Zhou[30]by using a finite element method to calculate the J-integral.Hierarchical crack distribution patterns in their thermal-shock experiment by analogizing the thermal shock and electro chemistry shock was found by Lei et al.[31].

建筑工程企业应该在国家颁布的安全条例办法基础上，结合建筑工程自身的实际情况，制订适合施工现场的安全标准化管理制度与办法，建立完善的施工安全标准化体系，具体要落实到施工的每一个环节，细化到人员安排、设备使用、资金投入等等，将全面安全标准化管理工作落到实处。施工现场的管理人员应该要保证现场施工的机械设备和施工工具都达到标准。

Considerable amounts of research involving experimental observations of particle fractures for LiCoO2[19,32],LiMn2O4[33,34],LiFePO4[35,36],silicon[37],and graphite[38–40]after certain electrochemical cycles,have been reported.To this end,Ebner et al.[41]used X-ray tomography to find many cracked particles of lithium nickel manganese cobalt oxide before electrochemical cycles.Therefore,it can be concluded that the fracturing of active particles,which is a type of mechanical degradation,should receive more attention.Both central[19,38]and surface[37,42,43]cracks are found in micron-sized active particles.However,Harris et al.[44]emphasized that electrode active particles tend to experience internal cracking rather than surface cracking.Thus,in this paper,central cracking rather than surface cracking in active particles is considered.

The present work entailed an extensive study of crack propagation during Li-ion intercalation in active particles.We consider the combined effect of Li-ion diffusion,mechanical stress,and damage mechanics to solve the fracture problem induced by diffusion.The effect of the particle size,C-rate,and initial central crack length on fracture behavior is studied by X-FEM combined with ABAQUS 6.16 software.Our study also took into account the diffusion of Li-ions from the crack surface,a phenomenon that was disregarded in all published papers.Thus,the influence of crack surface diffusion(CSD)on the Li-ion concentration,stress,and fracture behavior of particles is also discussed in this paper.LiMn2O4 particles were chosen because they are widely used in commercial LIBs and because the properties of this material are known[15,17,25,45].The particle size,C-rate,initial central crack length,and CSD have a significant influence on the fracture behavior of LiMn2O4.Three crack growth stages are identified and discussed.Our results showed that it is necessary to change the charge/discharge strategy to reduce the degradation of battery performance by avoiding unstable crack growth in the particle.

2 Theory

2.1 Concentration and diffusion induced stress

Figure 1 depicts a LiMn2O4 particle with a central crack of length 2a.Figure 1a,b illustrates situations in which CSD is either disregarded or taken into account,respectively.The crack direction is along the initial crack direction because the geometry and diffusion boundary are symmetrical along the central horizontal axis,so the lithium ion concentration field and stress field is also symmetrical along the central horizontal axis.During the intercalation process,lithium ions diffuse only from the surface of the electrode particles to the center along the radial direction(Fig.1a).However,if CSD is considered,Li-ions diffuse from both the surface and from the crack surface as shown in Fig.1b.In fact,when the crack propagates,Li-ions intercalate from the surface of the initial central crack,as well as from the newly generated crack surface.Li-ion concentration distribution will influence crack growth and crack growth will influence Liion concentration redistribution.To focus on the influence of r,C-rate,ā,and CSD on fracture behavior,we ignored the influence of a newly generated crack on the Li-ion concentration,stress,and fracture behavior.For simplification,the impact of the Li-ion diffusion process of the lithium concentration on the material properties is ignored.Therefore,the elastic modulus E,Poisson’s ratio ν,and diffusion coefficient D of LiMn2O4 all remain constant throughout the electro-chemical cycle.Furthermore,Mn2O4 is also assumed to be a homogeneous linear elastomeric material[46].

Fig.1 Geometry for Li-ion intercalation with a central crack:a excluding CSD,b including CSD

The diffusion of Li-ions in the electrode particles is expressed as follows[24]:

where c represents the concentration and J represents the diffusion flux.As stated by Fick’s law,the diffusion flux is proportional to the concentration gradient as follows[24]:

where in is the current density and F is Faraday’s constant.The relationship between flux J and the C-rate is[25]:

As the results for r=10µm in Table 2 shown,when the C-rate remains at 0.5,the fracture behavior of the particle is I with=0.02.As increases to 0.05 and 0.1,the crack begins to propagate and stays at II.When continues increasing to 0.2,the fracture behavior changes from II to III.A large value of causes increasing maximum principle tensile stress in front of the crack tip,facilitating cracking,and unstable crack grow th.

Combining Eqs.(1)and(2),we have:

where V is the volume of the particle(are a under two dimensional(2D)condition),and S is the surface area of the particle(perimeter under 2D condition).Further,C denotes the C-rate,i.e.,the theoretically required time in hours until the battery is either fully charged or discharged and c max is the saturated concentration of Li-ions in the host particle.

The stress–strain relationship induced by the concentration gradient is given by:

为切实提升新闻摄影质量，在运用摄影技巧及艺术手法时需善用摄影设备中的闪光灯，以有效改善拍摄画面过度曝光等问题。同时，在闪光灯调节过程中，也可采用增设反光板等方式，使光源能够借助反光板及天花板反射形成漫反射效应，有效改善光源不充分或光照不均匀对新闻摄影作品质量造成的不良影响。具体来说，如果在摄影空间较小、距离拍摄物体较近的情况下，可将闪光灯调整至90度，利用周围墙壁及天花板的反光，使拍摄物体能够得到均匀的打光，提升拍摄作品总体质量。

3.3.1 Influence of C-rate

2.2 Cohesive damage model in X-FEM

Since the governing equations of the Li-ion diffusion are similar to that of heat transfer,2D plane strain problem is solved by the coupled thermal stress modules of ABAQUS in this work.Thus,the transient heat transfer process is used to analogize the process of Li-ion diffusion.The fracture behavior is analyzed by X-FEM,which describes the crack behavior by adding an additional function to the shape function.In X-FEM,the crack surface element uses the Heaviside function as the extended shape function to describe the discontinuous behavior.Figure 2 describes the linear softening cohesive damage traction-separation model,which is used to describe the damage behavior of crack tipelements.The maximum principal tensile stress criterion is used to determine the moment at which damage starts.When the maximum principal tensile stress of an element satisfies the following Eq.(7),the element begins to enter the damage softening stage[47]:

Fig.2 Linear softening cohesive damage traction-separation model

where d is the damage variable,which ranges from 0(for the undamaged stage,the maximum principal tensile stress σ reaches the maximum allowable principal tensile stress σi)to 1(for a completely damaged stage,the separation δ reaches the maximum value δf).It should be pointed out that cracks do not propagate from the tip along the initial crack direction until damage variable d increases to 1.

创始人王勇的命运转折是改革开放40年中的标志性事件，他从未避讳自己的出身，在多次采访中，均表示自己本是邹平电业局的一个临时工。或许是进入体制无望，或许是时代创业浪潮的吸引，也或许是一个偶然的机遇，1986年，36岁的王勇离开电业局当选西王村支部书记，开始在西王村创办企业。

where is the maximum principal tensile stress in the element and is the maximum allowable principal tensile stress,which can be regarded as the tensile strength of the material.Further,f tol is the tolerance error usually taken from 0 to 0.1,which is used to adjust the incremental step to ensure that the damage criterion is met in a certain incremental step.In the present work,f tol is taken as 0.05.The stiffness of the ascending stage curve as K and the stiffness of the declining stage curve in the softening stage as K(which can be regarded as the softening stiffness)are defined in Fig.2.In this way,the relationship between K and K can be expressed by the damage variable d as[47]:

3 Results and discussion

Trypsin has potent proteolytic activity, and its inappropriate activation may lead to peritoneal dissemination of infiltrative gastric cancer by defoliation of cancer cells from the surface of advanced primary tumor, attachment and invasion to extracellular matrix under the mesothelium[46].

Table1 Material properties of Mn2O4

Property Unit Mn2O4 References Young’s module(E)GPa 10 [17]Poisson’s ratio(ν)0.3 [17]Diffusion coefficient(D)m2·s−1 7.08×10−15 [15]Partial molar volume(Ω)m3·mol−1 3.60×10−6 [15]Maximum Li-ion concentration(c max)mol·m−3 2.29×104 [25]Maximum principal tensile stress(σTS)MPa 100 [23]Surface energy(γ)J·m−2 0.66 [45]

3.1 Concentration and stress analysis

Figure 3a,b shows the results of the Li-ion concentration under=0.127 with or without the influence of CSD,and Fig.3cand d show the results when the normalized intercalation time equals 0.849.It can be clearly seen that the surface region of the particle exhibited high Li-ion concentrations,whereas the central region exhibited lower Li-ion concentrations.A comparison of Fig.3a,c or b,d shows that the Li-ion concentration increases when increases from 0.127 to 0.849.A comparison of Fig.3a,b or c,d reveals that the minimum Li-ion concentration no longer occurs at the center point of the particle with CSD,because Li-ions not only diffuse from the surface to the center of a particle but also from the surface of the central crack to the surface of the particle.The Li-ion concentration is redistributed based on the CSD introduced result when the Li-ion concentration gradient decreases.

2013年，新疆生产建设兵团水利事业继续保持又好又快的发展势头，兵团水利系统认真学习贯彻党的十八届三中全会精神、中央援疆工作座谈会精神和2013年全国水利厅局长会议精神，以《中共中央国务院关于加快水利改革发展的决定》《兵团党委、兵团关于加快水利发展改革的意见》为指导，积极服务兵团“城镇化、新型工业化、农业现代化”三化建设，扎实开展各项水利工作，取得了显著成效，为兵团经济社会发展提供了强有力的水利支撑。

Figure 4 shows the Li-ion concentration profile at=0.127 with or without CSD considered.The black solid and dashed lines represent the Li-ion concentration profiles when CSD is not considered and for different values of when CSD is considered,respectively.A comparison of the solid and dashed lines indicates that CSD significantly decreases the Li-ion concentration gradient near the center of the particle,but the effect of CSD is gradually alleviated along the radius direction.A comparison of the results with different values of shows that the effect of a decreasing Li-ion concentration gradient is more significant when is larger.The increase of Li-ion concentration near the center of the particle under larger is also found in Fig.4.When is larger,the increase of lithium ion concentration is more obvious.A larger means larger free crack surface;hence,more Li-ions can diffuse from the central crack surface and CSD is more prominent.

Fig.3 Concentration of Li-ion within a particle at C-rate=1 and r=5µm.CSD is included in a and c,excluded from b and d.a and b Results when=0.127,c and d results when=0.849

Fig.4 Li-ion concentration profile of four different values of and no CSD considered(black solid line)at=0.127.Here=0 represents the center of the electrode particle,and=1 represents the surface of the electrode particle along the crack direction.“W”represents with,“O”represents without

Figure 5a,b shows the results of the maximum principal stress distribution under=0.127 with or without the influence of CSD,whereas Fig.5c,d shows the results when the normalized discharging time equals 0.849.In order to explore the influence of CSD on stress,the no crack growth stage is chosen for the stress analysis.The maximum principal tensile stress appears at the front end of the central crack tip and can be expected to decrease the chemical potential and enhance Li-ion diffusion[24].A comparison of Fig.5a,corb,d shows that the maximum principal tensile stress continues increasing during the intercalation process,but it still does not exceed σi(100 MPa).This means that the element in front of the tip of the central crack tip does not enter the softening stage,and the crack does not propagate.If the maximum principal tensile stress in the crack tip element fulfills Eq.(7),the element will enter the damage softening stage,and d begins to increase from zero.When d increases to 1,the crack begins to propagate.A comparison of Fig.5a,b or c,d indicates that the maximum principal tensile stress in front of the crack tip decreases significantly when CSD is considered.Diffusion from the central crack surface can cause stress redistribution,decrease the maximum principal tensile stress of the crack tip,and even change the fracture behavior.Harris et al.[44]also found that the presence of a new surface,as a result of the presence of even a small internal crack or pores,can decease the stress value near the new surface.

Fig.5 Maximum principal stress distribution in an active particle with C-rate=1 and r=5µm.CSD is included in a and c,excluded from b and d.a and b Results when=0.127,c and d results when=0.849

3.2 Fracture behavior analysis

In order to understand fracture behavior during intercalation more clearly,we analyzed the crack development of a particle as a function of time during Li-ion intercalation process when r equals10µm, equals0.1,and the C-rateequals1(shown in Fig.6).The crack behavior during intercalation from the initial to the final state was found to occur in three stages:no crack grow th(stagestable crack grow th(stage),and unstable crack grow th(stage).Sun et al.[48]who studied the cracks induced by the lithiation/de-lithiation cycles of a graphite electrode by carrying out experiments also identified stable crack growth and unstable crack growth stages.The three types of stage is divided by red dash line in Fig.6,and the corresponding transition time are 0.044(stageto stage)and 0.116(stageto stage.It should be emphasized that the transition time from a different stage can be determined for every certain case(C-rate,r,andIn stage,the maximum tensile principal stress σmax in front of the crack tip is lower than the maximum allowable tensile principal stress σi,the material does not enter the damage stage or enter the damage stage,the damage variable is less than 1,and the crack does not experience grow th.Electrodes can be safely used during this stage.

Fig.6 Crack growth profile during Li-ion intercalation process with r=10µm,=0.1,and C-rate=1 without CSD considered

In stageas the value of σmax in front of the tip of the initial central crack increases gradually,it eventually exceeds σi.The material begins to enter the damage stage,when d increases to 1 and the crack begins to propagate at a relatively low speed.The electrodes can be used during this stage.

In stagethe crack length increases rapidly in a very short time and passes through the entire cathode particle.The fracture behavior enters the stage of unstable crack grow th.The particle fragmentation increases the resistance for electron transport and reduces Li-ion intercalation or deintercalation and also generates a new free surface area in contact with the electrolyte,thereby causing new side reactions and generating new SEI.Under these circumstances the capacity of LIBs is quickly reduced,thus unstable crack growth is unacceptable for LIBs in terms of their cycling life management.

Different particle radii(r=5,10,and 15µm),initial central crack lengths(a/r= 0.02,0.05,0.10,and 0.20),C-rates(0.5C,1C,3C,and 5C),and CSD were studied to explore their effects on the fracture behavior of particles.In the following analysis,the crack length,intercalation time,and horizontal coordinate along the crack direction are normalized as,and=x/R.The material properties of Mn2O4 are summarized in Table 1.

就整体而言，火法回收耗能较大，部分方法污染严重，不符合现代工艺要求，方法较为陈旧，鉴于大规模生产要求，火法回收是首选方法。

3.3 Multi-factor influence on fracture behavior

Table 2 presents the results of the different types of fracture behavior of particles with or without CSD considered for r=5,10,and15µm.Region I represents that the crack does not propagate(i.e.,only stageoccurs)during the entire intercalation process.Region II represents that the crack proceeded through stageand is just entering stageat the end of intercalation process.And region III represents that the crack experienced stagesandduring the intercalation process.The optimal combination of the C-rate,particle radius,and initial crack length with or without CSD can be obtained from Table 2.LIBs can be cycled safely in region I(surrounded by the solid line)and can also be cycled around the dashed line between I and II.Region III represents dangerous conditions(surrounded by the dashed line),which is unacceptable in the cycling life of LIBs.Therefore,the condi-tionsin region III or around the dashed line between II and III should be avoided during our daily use of LIBs.This optimal window enables us to determine the appropriate long-term use C-rate without reducing the capacity of LIBs.

Table 2 Fracture behavior distribution of particle under different conditions

Region I,II,and III represent the conditions under which the crack does not propagate(only stageoccurs),only experiences stagesandand experiences all three stages during the intercalation process,respectively

?

where is the change in the lithium concentration from the initial stress-free status,σij and εij represent stress and strain components,Ω is the partial molar volume of the solute,and δij is the Kronecker delta.The last term in Eq.(6)represents the mismatch stress induced by intercalation.

As the region in which r=5µm in Table 2 indicates,when=0.05(the fourth column),the crack remains in region I when the C-rate=0.5 and 1.As the C-rate increases to 3,the crack begins to propagate,enters fracture behavior,and remains in region II.When the C-rate continues increasing to 5,crack growth enters the unstable crack growth stage and the fracture behavior of the particle changes from II to III.A high C-rate,which results in a large concentration gradient and produces a large amount of stress within the particle,facilitates cracking and unstable crack grow th.This conclusion is also valid for the other values of shown in Table 2.

3.3.2 Influence of normalized length of the initial central crack

虽然2018年三季度厨卫行业多品类零售额线上增长明显高于线下增长，但两者占整体的比重差距在逐渐减小。据奥维云网（AVC）的监测数据显示，烟机线上线下零售额环比分别下降了22.6%和14.0%，燃气灶线上线下零售额环比分别下降了10.6%和9.2%，热水器线上线下零售额环比分别下降了18.9%和11.3%。虽然厨卫行业多品类线上线下零售额环比均在下降，但线上浮动大于线下浮动，可见，整体正趋向融合发展。

The initial boundary condition is c=c0,and the constant current boundary condition is:

3.3.3 Influence of particle radius

A comparison of r=5,10,and 15µm in Table 2 shows that,for the same and C-rate,a large particle radius causes cracking and unstable crack growth to occur easily,i.e.,when r=5µm and C-rate=3,the fracture behavior of the particle is II with=0.05,0.1,and 0.2 and I with=0.02.In comparison,when r=10,15µm and C-rate=3,the crack behavior remains in III regardless of the value of.A larger particle radius results in an increase in both the Li-ion concentration gradient and the maximum principal tensile stress such that cracking and the phenomenon of unstable crack growth easily occur.

3.3.4 Influence of CSD

The influence of CSD differs from that of the other factors we discussed above.As the area in which r=5µm in Table 2 shows,the fracture behavior changes from II to I with C-rate=1 and=0.2 and 0.1.It also changes from III to II with C-rate=5 and=0.2.The CSD can reduce the maximum principle tensile stress near the crack tip(shown in Fig.5)by decreasing the Li-ion concentration gradient(shown in Fig.4)within the particle to prevent the crack from easily propagating or entering the unstable growth stage.Comparing the results with and without CSD in Table 2,the results of the fracture behavior are not changed when the value ofis small(such as 0.02 and 0.05),whereas part of the results changed when the value of is large(such as0.1and0.2).The effects of CSD are more significant as increases,because larger means more Li-ions can diffuse from the central crack surface to decrease the concentration gradient(shown in Fig.4),and then influence the fracture behavior results.

In Table 2,there is a very interesting phenomenon when the crack length changes from 0.02 to 0.1 for r=10µm and C-rate=0.5 with CSD considered.The fracture behavior is I→II→I and it is not monotonous with crack length increasing.As initial crack length increases,the maximum principle stress near the crack tip increases according to the relationship between stress and crack length of fracture mechanics.A larger crack length causes a larger stress increase(we call this factor A).Once CSD is introduced,a larger crack length will decrease the Li-ion concentration gradient obviously(see Fig.4)which causes stress to decrease obviously(see Fig.5)(we call this factor B).The role of factors A and B is reverse with crack length change.When I firstly appears=0.02),crack length is small and both factors affect stress only a little.When II firstly appears(=0.05),the effect of factor A plays a leading role.When the crack length continues increasing(=0.1),the effect of factor B will play a key role,which causes I to appear again.When r=10µm and C-rate=0.5 with CSD considered,III changes I when=0.2;the effect of factor B plays a completely dominant role.

The sensitivity of different particle radii to the CSD is different.The difference between the results of r=5µm with and without CSD is dramatic,but the difference of r=10µm is less than that of r=5µm.The results of r=15µm with and without CSD are completely the same.The Li-ion concentration and maximum principal tensile stress in an electrode particle increases sharply as the particle radius increases.As the particle radius is sufficiently large(e.g.,from 10 to 15µm),the particle is more likely to experience cracking or to enter the unstable crack growth stage at a low C-rate and when the value ofā is small.The radius has a larger influence on the fracture behavior than the CSD when the particle radius is larger.In this case,the radius becomes the new dominant factor affecting the fracture behavior of a particle rather than the CSD.

Fig.7 The changes of normalized crack length over normalized time during Li-ion intercalation process in an active particle with r=5µm and C-rate=5

Figure7 shows the changes in the normalized crack length over time with different initial crack lengths.To focus on the influence of CSD and initial crack length on fracture behaviors,the stage transition time is not discussed in that figure,but is shown in Fig.6.This enables the effect of the CSD on the time required for stable or unstable crack growth to be explored.The dashed and solid lines represent the results with and without considering CSD, respectively. A comparison of the dashed and solid lines in all four colors indicates that both types of normalized transition time(stageto stageand stageto stageare delayed to a different degree.A larger value of increases the delay time,but does not change the three-stage fracture behavior.Particularly,stagedoes not appear during the entire intercalation process when considering CSD at whereas it appears at and 0.1.This is because can increase to approximate 1 in a very short time in stage,which is unacceptable for LIBs.Hence,CSD is the major factor affecting the time at which stageis entered.The results can guide the charge and discharge strategy in a battery management system to prevent the generation of long cracks inside the particle.Reducing the charging or discharging rate should be applied before the time of transition from stageto stage

4 Conclusions

A model that couples Li-ion diffusion,mechanical stress,and damage mechanics is presented to simulate the central crack growth of active particles by using X-FEM and by taking into account the influence of multiple factors.CSD was shown to significantly reduce the Li-ion concentration gradient near the center of the particle,but to alleviate gradually along the radius direction.The effect of decreasing the Li-ion concentration gradient is more significant when the initial crack is longer.CSD can also reduce the maximum principle tensile stress near the crack tip.Crack growth was found to occur in a three-stage process(no crack grow th,stable crack grow th,and unstable crack grow th)during the Li-ion intercalation process.The unstable crack growth stage is unacceptable when a long cycling lifetime is required for LIBs.The optimal combination of the C-rate,particle radius,and initial crack length with or without CSD was obtained.Without considering CSD,a smaller radius,lower C-rate,and shorter initial central crack length can prevent cracking or the unstable crack growth stage from being entered.With CSD considered,the result of fracture behavior is safer than that without CSD.In addition,it can delay the transition time within the three-stage process.In this respect,larger values ofā increase the delay time,but do not change the three-stage fracture behavior.

Our results can be used in a battery management system to avoid unstable crack growth leading to battery capacity degradation.Reducing the charging/discharging rate or changing to potentiostatic charging before the unstable crack growth stage is entered is suggested as a good way to realize charge/discharge strategy optimization.CSD plays an important role in particle fracture analysis.Thus,guidelines need to be accompanied by the statistical analysis of the initial flaw sizes in the active material.

3版美国创新战略的框架体系和发展形式基本相同。由于美国的创新国情基本保持不变，即具有完备的金融体系、充足的创新资金、健全的创新人才培养制度以及完善的法律法规体系，因此3版美国创新战略的部署具有相同的框架体系。从发展形式上看，美国政府在3版创新战略中均在扩大创新投资、促进产业发展、激发市场创新活力等方面进行重点部署，并且通过国家制度、产业发展以及企业管理等多个层面来提升国家创新实力。

Acknowledgements Authors gratefully acknowledge the financial support of the National Natural Science Foundation of China(11472165 and 11332005).

CP是一种癌前病变，近年来随着生活条件和饮食结构的改变，尤其是出海渔民CP发展为癌性病变发生率呈增高趋势。为防止CP恶变，故强化CP患者早期诊断及治疗显得尤为重要[6]。随着现代医疗技术的不断进步，内镜下切除CP操作简单、患者痛苦小、住院时间短、价格低廉，已逐步取代了传统的开腹手术，广泛的被医护人员和患者接受[3-5]。但是内镜下治疗CP存在着术后病情复发，并发症和治疗依从性差，尤其是渔民患者。为了更好地配合结肠镜下电切术治疗CP，本院针对渔民患者治疗依从性差等问题，特在常规医护的基础上实施提前针对性知识宣教，并取得了良好的临床效果。

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