超声激励纳米复相陶瓷非局部本构关系及延性域磨削机理研究
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摘要
超声加工陶瓷材料的去除过程伴随着各种行为效应如力学效应、化学效应、电磁效应和热学效应等，使得问题的研究由单一领域转化为多学科、多领域、宏微观结构交织在一起。此时为了解释加工性能改善的现象，本文基于非局部理论，着重于探索超声波与ZTA纳米复相陶瓷材料的微观作用机理，从材料本构特性、宏观力学特性和磨削表面微观形貌等方面阐述了超声激励对纳米陶瓷加工特性的影响，揭示超声加工时所产生的延性高效现象的理论本质，为进一步完善超声加工的理论奠定基础。本文主要研究内容如下：
基于脆性材料断裂的非局部力学理论，考虑超声激励参量的影响因素建立非局部弹性核参量和弹性核函数公式，推导含有超声激励影响因素的非局部本构模型。讨论了超声振动振幅和频率对核函数的影响，基本上呈现下开口抛物线性形状，在临界振幅和临界频率以前它们对核函数的影响呈递增趋势，在临界值附近时影响最为明显，非局部效应最强烈，此后振幅和频率对核函数的影响呈衰减现象。通过核函数建立宏-微观联系，建立了陶瓷材料超声激励裂纹尖端的非局部弹性解析应力场，发现发生在裂纹尖端的最大应力是有限的，理论上消除了物理上不现实的裂纹尖端应力奇异性，显示了裂纹尖端应力场的本来面目。为超声振动加工延性去除机理的研究提供理论保证和指导。
通过超声激励轴向拉伸试验，考虑不同超声参数下非局部弹性核函数与长程作用域的关系，得出断裂应力随着振幅和频率的增加先减小后增加，呈上开口抛物线性形状，在临界振幅(30kHz，15.3218μm)和临界频率(75W，35kHz)附近时，衰减率最小，非局部效应也最强烈。通过拉伸强度试验结果，对非局部核参量的影响参数进行拟合，求出了频率的影响系数为1.2，从而获得了超声激励下的非局部弹性核函数和非局部本构模型。通过对试件拉伸断口物相分析，说明超声激励作用在很大程度上改善了陶瓷材料的力学性能，ZrO2在应力诱导下发生t→m相变从而吸收应变，有较好的塑性力学性能。对拉伸断口的电镜观察表明，超声拉伸下的断口有明显的晶粒断面，在大量的晶粒上有裂纹出现，说明ZTA陶瓷发生了穿晶/沿晶混合断裂。随着超声激励振幅和频率的增大，断口的空隙逐渐增多，平整度也得到很大的改善，在(30kHz，15.3218μm)和(75W，35kHz)附近时，断面最为齐整，在试验上验证了非局部衰减率的理论变化规律并对超声振动参数进行优化。
基于非局部弹性理论和最大拉应力准则推得了裂纹平面应变断裂韧性的理论公式，从微观力学机理上反映陶瓷材料断裂的解理机制。通过超声激励下的显微硬度和断裂韧性测试试验，发现超声下的材料硬度值约为普通无超声下材料硬度值的70.4%~58.7%，而普通情况下的断裂韧性K IC值约为超声振动下断裂韧性KIC值的68.7%~85.1%。通过试验结果，分析了不同超声频率下临界切削深度的变化规律，研究了超声振动对材料去除性能的影响。并通过磨削力试验及表面微观形貌观察，发现在试验所用的精密平面磨床上，普通磨削ZTA纳米复相陶瓷的延性域磨削深度约为2μm，超声磨削塑性去除临界磨深在20kHz下约为4μm，30kHz下约为8μm，在35kHz下约为12μm，40kHz下的塑性去除临界磨深约为10μm，试验结果和理论推导一致。
依据非局部能量平衡理论和内聚力理论，推导出了物理意义更加明确的超声激励断裂表面能和动态裂纹扩展速度公式。通过超声激励作用下裂纹尖端处的TEM和SEM照片，从“能量角度”和“微观测试”探讨了超声延性域加工的本质，分析了超声激励对裂纹扩展的微观作用机制：发现超声激励造成主裂纹周围产生位错云、微裂纹云、裂纹分叉或者偏转等现象，形成能量吸收机制，裂纹扩展速度降低，材料的表观断裂表面能增大。这种机制通过在裂纹尖端形成对外加超声载荷的屏蔽作用而对裂纹扩展驱动力产生显著影响，从而起到了扩大延性域的作用。并通过应力强度因子、机械能释放率和断裂表面能把非局部本构模型和超声激励裂纹屏蔽效应联系起来。
研究表明非局部本构模型对于超声振动加工陶瓷硬脆材料力学特征的适用性，符合其显著增加延性域切削深度的现象。超声磨削对硬脆材料而言是一种有效的加工方法，扩大了材料塑性域去除的范围，提高了材料的韧性。
The machining process of ceramics materials is followed with various behavioraleffects under ultrasonic excitation such as the mechanical effects, chemical effects,electromagnetic effects and thermal effects, etc. And it turns the study of the problemfrom a single area to multi-areas which are multi-disciplinarians, multi-fields, andintertwined areas between the macro and micro structures. At this point, in order toexplain the ameliorative phenomenon of processing performance, the research which isbased on nonlocal theory pays more attention to the microcosmic acting mechanismbetween ultrasonic and ZTA ceramics, and illustrates the affects of ultrasonic excitationon grinding characteristics of ZTA nano-composite ceramics from aspects of materialconstitutive properties, microscopic mechanical properties and SEM of grinding surfaceetc. The theory essence of the high efficiency and ductility phenomenon is disclosedunder ultrasonic machining, and it lays the foundation for improving the theory ofultrasonic machining. The main work and the achievements of this paper are list asfollows:
Based on nonlocal mechanics theory of brittle material fracture and throughconsidering the influence factors of ultrasonic excitation parameters, nonlocal elastickernel parameters and the formula of elastic kernel function are established andnonlocal constitutive model which contains the influence parameters of ultrasonicexcitation is deduced. The influence of ultrasonic vibration frequencies and amplitudesto kernel function is discussed which mainly presents parabolic shape with open sidedown. The kernel function shows increasing trend before the critical amplitude andfrequency. It is the most obvious near the critical amplitude and frequency and thenonlocal effects are also the strongest. Since then the influences of frequencies andamplitudes to the kernel function present decay phenomenon. The connection betweenmacro and micro is built through the kernel function, and the nonlocal elastic analysisstress field which is near the crack tip of ceramics materials under ultrasonic excitationis established. The maximum stress that occurs near the crack tip is limited. The stresssingularity of crack tip which is unrealistic in physics is eliminated theoretically and thetrue features of stress field near the crack tip are revealed. It provides theoretical guarantee and guidance to the ductile removal mechanism under the ultrasonic vibrationmachining.
Through axial tensile experiments of ultrasonic excitation and considering therelationship between nonlocal elastic kernel function and long-range scope, it can beobtained that fracture stress decreases at first and then increases which presentsparabolic shape with open side up when amplitudes and frequencies increase. When theamplitudes are near the critical value (30kHz,15.3218μm) and the frequencies are nearthe critical value (75W,35kHz), the decay rate is the minimum and the nonlocal effectsare strongest. The influence parameter of nonlocal kernel parameters is fitted throughthe results of tensile test. The influence coefficient of frequency is given to equal to1.2,and the nonlocal elastic kernel function and the nonlocal constitutive model areobtained under ultrasonic excitation. Through the phase analysis of tensile fracture, itsays that the mechanical properties of ceramic materials are improved significantlyunder ultrasonic excitation. The ceramic materials present phase transition t→m whichis induced by stress and it shows better plastic mechanical properties. From the SEMobservation of tensile fracture, it can be seen that there are obvious grain cross-sectionin tensile fracture under ultrasonic excitation and cracks are emerged in a lot of grains.And it says that ZTA ceramics present transgranula and intergranular mixed fracture.Along with the increase of frequencies and amplitudes under ultrasonic excitation, thegap of fracture increases gradually, and the roughness also gets a lot of improvement.Near the amplitude (30kHz,15.3218μm) and frequency (75W,35kHz), the section is thetrimmest. The theoretical change rule of nonlocal decay rate is verified in theexperiment and ultrasonic vibration parameters are optimized.
Based on the nonlocal elastic theory and the maximum tensile stress criterion, thetheoretical formula of the strain fracture toughness in crack plane is deduced, and thecleavage mechanism of fracture in ceramics materials is reflected from the micromechanical mechanism. Through testing experiments of hardness and fracturetoughness under ultrasonic excitation, it can be found that the hardness value underultrasonic excitation is as low as70.4%~58.7%of that in ordinary situation. And thefracture toughness value in ordinary situation is68.7%~85.1%of that under ultrasonicexcitation. Through the test results, the change rule of critical depths in different ultrasonic frequencies is analyzed and the influences of ultrasonic vibration on materialremoval performance are studied. Through the tests of grinding force and theobservation of the surface morphology, it can be found that, the ductile grinding depthof ZTA is about2μm in ordinary grinding, it is4μm in the frequency of20kHz, it is8μm in30kHz, it is12μm in35kHz and it is10μm in40kHz. The results are consistentwith the theory.
According to cohesion theory and nonlocal energy balance theory, the fracturesurface energy formula and the velocity formula of dynamic crack propagation arederived whose physical significance is more definite. Through the photos of TEM andSEM at the crack tip under ultrasonic excitation, the essence of ultrasonic machining inductile domain is discussed from the angle of energy and microscopical testing. Themicroscopic mechanism of crack propagation under ultrasonic excitation is analyzed. Itcan be found that ultrasonic excitation causes many phenomena around the main cracksuch as dislocation clouds, micro cracks clouds and crack bifurcation or deflection, andthe mechanism that can absorb energy is formed. Crack propagation rate decreases andthe fracture surface energy of materials increases. This mechanism makes significanteffects on the diving force of crack propagation by forming shield effect on outerultrasonic load at crack tip, thereby it plays a role of expanding the ductile domain. Andthe nonlocal constitutive model is connected with the shield effect of cracks underultrasonic excitation through the stress intensity factor, mechanical energy release rateand fracture surface energy.
The applicability of the nonlocal constitutive model which has been established tomechanics characteristic of ceramics materials under ultrasonic vibration machiningcorrespond with the phenomenon that the cutting depths are increased significantly inductile domain. Ultrasonic grinding is an effective processing method to hard and brittlematerials which can expand ductile removal domain and improve the toughness of thematerials.
基于脆性材料断裂的非局部力学理论，考虑超声激励参量的影响因素建立非局部弹性核参量和弹性核函数公式，推导含有超声激励影响因素的非局部本构模型。讨论了超声振动振幅和频率对核函数的影响，基本上呈现下开口抛物线性形状，在临界振幅和临界频率以前它们对核函数的影响呈递增趋势，在临界值附近时影响最为明显，非局部效应最强烈，此后振幅和频率对核函数的影响呈衰减现象。通过核函数建立宏-微观联系，建立了陶瓷材料超声激励裂纹尖端的非局部弹性解析应力场，发现发生在裂纹尖端的最大应力是有限的，理论上消除了物理上不现实的裂纹尖端应力奇异性，显示了裂纹尖端应力场的本来面目。为超声振动加工延性去除机理的研究提供理论保证和指导。
通过超声激励轴向拉伸试验，考虑不同超声参数下非局部弹性核函数与长程作用域的关系，得出断裂应力随着振幅和频率的增加先减小后增加，呈上开口抛物线性形状，在临界振幅(30kHz，15.3218μm)和临界频率(75W，35kHz)附近时，衰减率最小，非局部效应也最强烈。通过拉伸强度试验结果，对非局部核参量的影响参数进行拟合，求出了频率的影响系数为1.2，从而获得了超声激励下的非局部弹性核函数和非局部本构模型。通过对试件拉伸断口物相分析，说明超声激励作用在很大程度上改善了陶瓷材料的力学性能，ZrO2在应力诱导下发生t→m相变从而吸收应变，有较好的塑性力学性能。对拉伸断口的电镜观察表明，超声拉伸下的断口有明显的晶粒断面，在大量的晶粒上有裂纹出现，说明ZTA陶瓷发生了穿晶/沿晶混合断裂。随着超声激励振幅和频率的增大，断口的空隙逐渐增多，平整度也得到很大的改善，在(30kHz，15.3218μm)和(75W，35kHz)附近时，断面最为齐整，在试验上验证了非局部衰减率的理论变化规律并对超声振动参数进行优化。
基于非局部弹性理论和最大拉应力准则推得了裂纹平面应变断裂韧性的理论公式，从微观力学机理上反映陶瓷材料断裂的解理机制。通过超声激励下的显微硬度和断裂韧性测试试验，发现超声下的材料硬度值约为普通无超声下材料硬度值的70.4%~58.7%，而普通情况下的断裂韧性K IC值约为超声振动下断裂韧性KIC值的68.7%~85.1%。通过试验结果，分析了不同超声频率下临界切削深度的变化规律，研究了超声振动对材料去除性能的影响。并通过磨削力试验及表面微观形貌观察，发现在试验所用的精密平面磨床上，普通磨削ZTA纳米复相陶瓷的延性域磨削深度约为2μm，超声磨削塑性去除临界磨深在20kHz下约为4μm，30kHz下约为8μm，在35kHz下约为12μm，40kHz下的塑性去除临界磨深约为10μm，试验结果和理论推导一致。
依据非局部能量平衡理论和内聚力理论，推导出了物理意义更加明确的超声激励断裂表面能和动态裂纹扩展速度公式。通过超声激励作用下裂纹尖端处的TEM和SEM照片，从“能量角度”和“微观测试”探讨了超声延性域加工的本质，分析了超声激励对裂纹扩展的微观作用机制：发现超声激励造成主裂纹周围产生位错云、微裂纹云、裂纹分叉或者偏转等现象，形成能量吸收机制，裂纹扩展速度降低，材料的表观断裂表面能增大。这种机制通过在裂纹尖端形成对外加超声载荷的屏蔽作用而对裂纹扩展驱动力产生显著影响，从而起到了扩大延性域的作用。并通过应力强度因子、机械能释放率和断裂表面能把非局部本构模型和超声激励裂纹屏蔽效应联系起来。
研究表明非局部本构模型对于超声振动加工陶瓷硬脆材料力学特征的适用性，符合其显著增加延性域切削深度的现象。超声磨削对硬脆材料而言是一种有效的加工方法，扩大了材料塑性域去除的范围，提高了材料的韧性。
The machining process of ceramics materials is followed with various behavioraleffects under ultrasonic excitation such as the mechanical effects, chemical effects,electromagnetic effects and thermal effects, etc. And it turns the study of the problemfrom a single area to multi-areas which are multi-disciplinarians, multi-fields, andintertwined areas between the macro and micro structures. At this point, in order toexplain the ameliorative phenomenon of processing performance, the research which isbased on nonlocal theory pays more attention to the microcosmic acting mechanismbetween ultrasonic and ZTA ceramics, and illustrates the affects of ultrasonic excitationon grinding characteristics of ZTA nano-composite ceramics from aspects of materialconstitutive properties, microscopic mechanical properties and SEM of grinding surfaceetc. The theory essence of the high efficiency and ductility phenomenon is disclosedunder ultrasonic machining, and it lays the foundation for improving the theory ofultrasonic machining. The main work and the achievements of this paper are list asfollows:
Based on nonlocal mechanics theory of brittle material fracture and throughconsidering the influence factors of ultrasonic excitation parameters, nonlocal elastickernel parameters and the formula of elastic kernel function are established andnonlocal constitutive model which contains the influence parameters of ultrasonicexcitation is deduced. The influence of ultrasonic vibration frequencies and amplitudesto kernel function is discussed which mainly presents parabolic shape with open sidedown. The kernel function shows increasing trend before the critical amplitude andfrequency. It is the most obvious near the critical amplitude and frequency and thenonlocal effects are also the strongest. Since then the influences of frequencies andamplitudes to the kernel function present decay phenomenon. The connection betweenmacro and micro is built through the kernel function, and the nonlocal elastic analysisstress field which is near the crack tip of ceramics materials under ultrasonic excitationis established. The maximum stress that occurs near the crack tip is limited. The stresssingularity of crack tip which is unrealistic in physics is eliminated theoretically and thetrue features of stress field near the crack tip are revealed. It provides theoretical guarantee and guidance to the ductile removal mechanism under the ultrasonic vibrationmachining.
Through axial tensile experiments of ultrasonic excitation and considering therelationship between nonlocal elastic kernel function and long-range scope, it can beobtained that fracture stress decreases at first and then increases which presentsparabolic shape with open side up when amplitudes and frequencies increase. When theamplitudes are near the critical value (30kHz,15.3218μm) and the frequencies are nearthe critical value (75W,35kHz), the decay rate is the minimum and the nonlocal effectsare strongest. The influence parameter of nonlocal kernel parameters is fitted throughthe results of tensile test. The influence coefficient of frequency is given to equal to1.2,and the nonlocal elastic kernel function and the nonlocal constitutive model areobtained under ultrasonic excitation. Through the phase analysis of tensile fracture, itsays that the mechanical properties of ceramic materials are improved significantlyunder ultrasonic excitation. The ceramic materials present phase transition t→m whichis induced by stress and it shows better plastic mechanical properties. From the SEMobservation of tensile fracture, it can be seen that there are obvious grain cross-sectionin tensile fracture under ultrasonic excitation and cracks are emerged in a lot of grains.And it says that ZTA ceramics present transgranula and intergranular mixed fracture.Along with the increase of frequencies and amplitudes under ultrasonic excitation, thegap of fracture increases gradually, and the roughness also gets a lot of improvement.Near the amplitude (30kHz,15.3218μm) and frequency (75W,35kHz), the section is thetrimmest. The theoretical change rule of nonlocal decay rate is verified in theexperiment and ultrasonic vibration parameters are optimized.
Based on the nonlocal elastic theory and the maximum tensile stress criterion, thetheoretical formula of the strain fracture toughness in crack plane is deduced, and thecleavage mechanism of fracture in ceramics materials is reflected from the micromechanical mechanism. Through testing experiments of hardness and fracturetoughness under ultrasonic excitation, it can be found that the hardness value underultrasonic excitation is as low as70.4%~58.7%of that in ordinary situation. And thefracture toughness value in ordinary situation is68.7%~85.1%of that under ultrasonicexcitation. Through the test results, the change rule of critical depths in different ultrasonic frequencies is analyzed and the influences of ultrasonic vibration on materialremoval performance are studied. Through the tests of grinding force and theobservation of the surface morphology, it can be found that, the ductile grinding depthof ZTA is about2μm in ordinary grinding, it is4μm in the frequency of20kHz, it is8μm in30kHz, it is12μm in35kHz and it is10μm in40kHz. The results are consistentwith the theory.
According to cohesion theory and nonlocal energy balance theory, the fracturesurface energy formula and the velocity formula of dynamic crack propagation arederived whose physical significance is more definite. Through the photos of TEM andSEM at the crack tip under ultrasonic excitation, the essence of ultrasonic machining inductile domain is discussed from the angle of energy and microscopical testing. Themicroscopic mechanism of crack propagation under ultrasonic excitation is analyzed. Itcan be found that ultrasonic excitation causes many phenomena around the main cracksuch as dislocation clouds, micro cracks clouds and crack bifurcation or deflection, andthe mechanism that can absorb energy is formed. Crack propagation rate decreases andthe fracture surface energy of materials increases. This mechanism makes significanteffects on the diving force of crack propagation by forming shield effect on outerultrasonic load at crack tip, thereby it plays a role of expanding the ductile domain. Andthe nonlocal constitutive model is connected with the shield effect of cracks underultrasonic excitation through the stress intensity factor, mechanical energy release rateand fracture surface energy.
The applicability of the nonlocal constitutive model which has been established tomechanics characteristic of ceramics materials under ultrasonic vibration machiningcorrespond with the phenomenon that the cutting depths are increased significantly inductile domain. Ultrasonic grinding is an effective processing method to hard and brittlematerials which can expand ductile removal domain and improve the toughness of thematerials.
引文
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