非均匀铁弹畴变对离面极化压电陶瓷应力强度因子的影响研究
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摘要
基于文献中报道的试验结果,本文考虑非均匀的畴变过程区,它包含一个位于中心的饱和区和环绕饱和区的渐变区.为了描述外加应力引起的部分铁弹畴变,本文采用一个显式的基于最小能量原理的非均匀畴变准则.考虑离面极化的压电陶瓷,假设其初始极化矢量平行于离面方向.畴变后的电畴位于面内,具体方位由最大释放功来确定.基于非均匀畴变准则,本文给出了裂尖处非均匀畴变区几何及畴变体积分数的分布.并在静止裂纹和稳态扩展裂纹两种特殊情况下计算了铁弹畴变对裂尖处应力强度因子的影响.结果表明:(1)静止裂纹尖端处的畴变减小了材料的起裂强度;(2)准静态稳态裂纹附近的畴变增加了材料的断裂强度.且理论预测的R曲线渐近值与试验结果定量吻合.
Based on experimental observations of papers by others researchers, this paper considers a non-uniform process zone,which consists of a saturated core and a transitional annulus. To depict the effective degree of domain reorientation induced by mechanical load, we adopt an explicit switching criterion based on the principle of minimum energy. For simplicity, it is assumed that initial polarization vector of piezoelectric ceramic in anti-plane poling is parallel to x3-axis of a rectangular coordinate system.The switched polarization lies in the plane of Ox1 x2, its definite orientation is determined on the principle of releasing the maximum mechanical work. Via the non-uniform switching criterion, the switch zone geometry and contour of volume fraction are depicted.And the effect of ferroelastic domain switching on crack-tip stress intensity are investigated for two special cracks: a stationary crack and a quasi-static steady-state growing crack. Theoretical results indicate that(1) the switching zone around a stationary crack lowers the initial fracture strength of ceramic;(2) the switching zone around a steady-state growing crack increases the material's fracture toughness. Specially, the predicted asymptote of R-curve is in complete agreement with experimental result quantitatively.
Based on experimental observations of papers by others researchers, this paper considers a non-uniform process zone,which consists of a saturated core and a transitional annulus. To depict the effective degree of domain reorientation induced by mechanical load, we adopt an explicit switching criterion based on the principle of minimum energy. For simplicity, it is assumed that initial polarization vector of piezoelectric ceramic in anti-plane poling is parallel to x3-axis of a rectangular coordinate system.The switched polarization lies in the plane of Ox1 x2, its definite orientation is determined on the principle of releasing the maximum mechanical work. Via the non-uniform switching criterion, the switch zone geometry and contour of volume fraction are depicted.And the effect of ferroelastic domain switching on crack-tip stress intensity are investigated for two special cracks: a stationary crack and a quasi-static steady-state growing crack. Theoretical results indicate that(1) the switching zone around a stationary crack lowers the initial fracture strength of ceramic;(2) the switching zone around a steady-state growing crack increases the material's fracture toughness. Specially, the predicted asymptote of R-curve is in complete agreement with experimental result quantitatively.
引文
[1]HEYWANG W,LUBITZ K,WERSING W.压电:该技术的发展和未来[M].北京:北京大学出版社,2012.
[2]方岱宁,王骥,陈伟球.压电结构与器件分析:英文版[M].北京:高等教育出版社,2013.
[3]SCOTT J F.Prospects for ferroelectrics:2012-2022[J].ISRN Materials Science,2013,7:187313.
[4]UCHINO K.The development of piezoelectric materials and the new perspective[C]//Advanced Piezoelectric Materials:Science and Technology(2nd Ed.),Woodhead Publishing,2017,1-92.
[5]ZHU T,YANG W.Toughness variation of ferroelectrics by polarization switch under non-uniform electric filed[J].Acta Materialia,1997,45(11):4695-4702.
[6]LU W,FANG D N,LI C Q,et al.Nonlinear electric-mechanical behavior and micromechanics modeling of ferroelectric domain evolution[J].Acta Materialia,1999,47(10):2913-2926.
[7]李尧臣.铁电-铁弹材料的非线性本构关系及其有限元实施[J].中国科学:物理学力学天文学,2007,37(1):106-122.
[8]LUCATO S L S E,LUPASCU D C,R?DEL J.Effect of poling direction on r-curve behavior in lead zirconate titanate[J].Journal of the American Ceramic Society,2010,83(2):424-426.
[9]LANDIS C M.Non-linear constitutive modeling of ferroelectrics[J].Current Opinion in Solid State and Materials Science,2004,8(1):59-69.
[10]HUBER J E.Micromechanical modeling of ferroelectrics[J].Current Opinion in Solid State and Materials Science,2005,9(3):100-106.
[11]KAMLAH M.Ferroelectric and ferroelastic piezoceramics-modeling of electromechanical hysteresis phenomena[J].Continuum Mechanics and Thermodynamics,2001,13(4):219-268.
[12]SCHNEIDER G A.Influence of electric field and mechanical stresses on the fracture of ferroelectrics[J].Annual Review of Materials Research,2007,37(1):491-538.
[13]KUNA M.Fracture mechanics of piezoelectric materials-Where are we right now[J].Engineering Fracture Mechanics,2010,77(2):309-326.
[14]STARK S,NEUMEISTER P,BALKE H.Some aspects of macroscopic phenomenological material models for ferroelectroelastic ceramics[J].International Journal of Solids and Structures,2016,80(2):359-367.
[15]MISHRA R K.A review on fracture mechanics in piezoelectric structures[J].Materials Today:Proceedings,2018,5(2):5407-5413.
[16]杨卫.力电失效学[M].北京:清华大学出版社,2001.
[17]方岱宁,刘金喜.压电与铁电体的断裂力学[M].北京:清华大学出版社,2008.
[18]MCMEEKING R M,EVANS A G.Mechanics of transformation-toughening in brittle materials[J].Journal of the American Ceramic Society,1982,65(5):242-246.
[19]BUDIANSKY B,HUTCHINSON J W,LAMBROPOULOS J C.Continuum theory of dilatant transformation toughening in ceramics[J].International Journal of Solids and Structures,1983,19(4):337-355.
[20]YANG W,ZHU T.Switch-toughening of ferroelectrics subjected to electric fields[J].Journal of the Mechanics and Physics of Solids,1998,46(2):291-311.
[21]FANG F,YANG W.Poling-enhanced fracture resistance of lead zirconate titanate ferroelelctric ceramics[J].Materials Letters,2000,46(2-3):131-135.
[22]YANG W,FANG F,TAO M.Critical role of domain switching on the fracture toughness of poled ferroelectrics[J].International Journal of Solids and Structures,2001,38(10):2203-2211.
[23]YANG W,FANG F.Toughening of ferroelectrics by the out-of-plane poling[J].Acta Mechanica Sinica,2003,19(2):147-153.
[24]FANG F,YANG W,ZHU T.Crack tip 90°switching in tetragonal lanthanum-modified lead zirconia titanate under an electric field[J].Journal of Materials Research,1999,14(7):2940-2944.
[25]F?RDERREUTHER A,THURN G,ZIMMERMANN A,et al.R-curve effect,influence of electric field and process zone in BaTiO3 ceramic[J].Journal of the European Ceramic Society,2002,22(12):2023-2031.
[26]HACKEMANN S,PFEIFFER W.Domain switching in process zones of PZT:characterization by microdiffraction and fracture mechanical methods[J].Journal of the European Ceramic Society,2003,23(1):141-151.
[27]HANNINK R H J,KELLY P M,MUDDLE B C.Transformation toughening in Zirconia-containing ceramics[J].Journal of the American Ceramic Society,2000,83(3):461-487.
[28]CUI Y Q,YANG W.Toughening under non-uniform ferro-elastic domain switching[J].International Journal of Solids and Structures,2006,43(14-15):4452-4464.
[29]CUI Y Q,ZHONG Z.A novel criterion for nonuniform domain switching of tetragonal ferroelectrics[J].Mechanics of Materials,2012,45(2):61-71.
[30]CUI Y Q,ZHONG Z.Nonuniform ferroelastic domain switching driven by two-parameter crack tip stress field[J].Engineering Fracture Mechanics,2012,96(12):226-240.
[31]GAO H.Application of 3-D weight functions-I:formulations of crack interactions with transformation strains and dislocations[J].Journal of the Mechanics and Physics of Solids,1989,37(2):133-153.
[2]方岱宁,王骥,陈伟球.压电结构与器件分析:英文版[M].北京:高等教育出版社,2013.
[3]SCOTT J F.Prospects for ferroelectrics:2012-2022[J].ISRN Materials Science,2013,7:187313.
[4]UCHINO K.The development of piezoelectric materials and the new perspective[C]//Advanced Piezoelectric Materials:Science and Technology(2nd Ed.),Woodhead Publishing,2017,1-92.
[5]ZHU T,YANG W.Toughness variation of ferroelectrics by polarization switch under non-uniform electric filed[J].Acta Materialia,1997,45(11):4695-4702.
[6]LU W,FANG D N,LI C Q,et al.Nonlinear electric-mechanical behavior and micromechanics modeling of ferroelectric domain evolution[J].Acta Materialia,1999,47(10):2913-2926.
[7]李尧臣.铁电-铁弹材料的非线性本构关系及其有限元实施[J].中国科学:物理学力学天文学,2007,37(1):106-122.
[8]LUCATO S L S E,LUPASCU D C,R?DEL J.Effect of poling direction on r-curve behavior in lead zirconate titanate[J].Journal of the American Ceramic Society,2010,83(2):424-426.
[9]LANDIS C M.Non-linear constitutive modeling of ferroelectrics[J].Current Opinion in Solid State and Materials Science,2004,8(1):59-69.
[10]HUBER J E.Micromechanical modeling of ferroelectrics[J].Current Opinion in Solid State and Materials Science,2005,9(3):100-106.
[11]KAMLAH M.Ferroelectric and ferroelastic piezoceramics-modeling of electromechanical hysteresis phenomena[J].Continuum Mechanics and Thermodynamics,2001,13(4):219-268.
[12]SCHNEIDER G A.Influence of electric field and mechanical stresses on the fracture of ferroelectrics[J].Annual Review of Materials Research,2007,37(1):491-538.
[13]KUNA M.Fracture mechanics of piezoelectric materials-Where are we right now[J].Engineering Fracture Mechanics,2010,77(2):309-326.
[14]STARK S,NEUMEISTER P,BALKE H.Some aspects of macroscopic phenomenological material models for ferroelectroelastic ceramics[J].International Journal of Solids and Structures,2016,80(2):359-367.
[15]MISHRA R K.A review on fracture mechanics in piezoelectric structures[J].Materials Today:Proceedings,2018,5(2):5407-5413.
[16]杨卫.力电失效学[M].北京:清华大学出版社,2001.
[17]方岱宁,刘金喜.压电与铁电体的断裂力学[M].北京:清华大学出版社,2008.
[18]MCMEEKING R M,EVANS A G.Mechanics of transformation-toughening in brittle materials[J].Journal of the American Ceramic Society,1982,65(5):242-246.
[19]BUDIANSKY B,HUTCHINSON J W,LAMBROPOULOS J C.Continuum theory of dilatant transformation toughening in ceramics[J].International Journal of Solids and Structures,1983,19(4):337-355.
[20]YANG W,ZHU T.Switch-toughening of ferroelectrics subjected to electric fields[J].Journal of the Mechanics and Physics of Solids,1998,46(2):291-311.
[21]FANG F,YANG W.Poling-enhanced fracture resistance of lead zirconate titanate ferroelelctric ceramics[J].Materials Letters,2000,46(2-3):131-135.
[22]YANG W,FANG F,TAO M.Critical role of domain switching on the fracture toughness of poled ferroelectrics[J].International Journal of Solids and Structures,2001,38(10):2203-2211.
[23]YANG W,FANG F.Toughening of ferroelectrics by the out-of-plane poling[J].Acta Mechanica Sinica,2003,19(2):147-153.
[24]FANG F,YANG W,ZHU T.Crack tip 90°switching in tetragonal lanthanum-modified lead zirconia titanate under an electric field[J].Journal of Materials Research,1999,14(7):2940-2944.
[25]F?RDERREUTHER A,THURN G,ZIMMERMANN A,et al.R-curve effect,influence of electric field and process zone in BaTiO3 ceramic[J].Journal of the European Ceramic Society,2002,22(12):2023-2031.
[26]HACKEMANN S,PFEIFFER W.Domain switching in process zones of PZT:characterization by microdiffraction and fracture mechanical methods[J].Journal of the European Ceramic Society,2003,23(1):141-151.
[27]HANNINK R H J,KELLY P M,MUDDLE B C.Transformation toughening in Zirconia-containing ceramics[J].Journal of the American Ceramic Society,2000,83(3):461-487.
[28]CUI Y Q,YANG W.Toughening under non-uniform ferro-elastic domain switching[J].International Journal of Solids and Structures,2006,43(14-15):4452-4464.
[29]CUI Y Q,ZHONG Z.A novel criterion for nonuniform domain switching of tetragonal ferroelectrics[J].Mechanics of Materials,2012,45(2):61-71.
[30]CUI Y Q,ZHONG Z.Nonuniform ferroelastic domain switching driven by two-parameter crack tip stress field[J].Engineering Fracture Mechanics,2012,96(12):226-240.
[31]GAO H.Application of 3-D weight functions-I:formulations of crack interactions with transformation strains and dislocations[J].Journal of the Mechanics and Physics of Solids,1989,37(2):133-153.