基于球形压痕响应的各向异性材料等效应变硬化指数（英文）
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摘要
针对各向异性材料,讨论单一方向的应变硬化指数对复杂应力问题求解的局限性,提出了一种基于等效能量法计算各向异性材料等效应变硬化指数的新方法。首先,设置一系列有限元仿真实验,得出残余压痕参数与等效应变硬化指数的无量纲函数关系式;其次,使用此无量纲函数建立等效应变硬化指数与残余压痕的数学表达式;最后,通过对比数值试验结果验证该方法的有效性。另外,为了确定各向异性材料的屈服强度,对其Meyer关系进行扩展。通过数值实例及对TC1M钛合金的实际应用验证了该新方法的有效性和可靠性。
Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element(FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.
Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element(FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.
引文
[1]YONEZU A,TANAKA M,KUSANO R,CHEN X.Probing out-ofplane anisotropic plasticity using spherical indentation:A numerical approach[J].Computational Materials Science,2013,79:336-344.
[2]YONEZU A,YONEDA K,HIRAKATA H,SAKIHARA M,MINOSHIMA K.A simple method to evaluate anisotropic plastic properties based on dimensionless function of single spherical indentation-Application to SiC whisker-reinforced aluminum alloy[J].Materials Science and Engineering A,2010,527(29):7646-7657.
[3]ZHANG H,SCHUSTER B E,WEI Q,RAMESH K T.The design of accurate micro-compression experiments[J].Scripta Materialia,2006,54(2):181-186.
[4]WANG M,WU J,ZHAN X,GUO R,HUI Y,FAN H.On the determination of the anisotropic plasticity of metal materials by using instrumented indentation[J].Materials&Design,2016,111:98-107.
[5]OLIVER W C,PHARR G M.An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[J].Journal of Materials Research,1992,7(6):1564-1583.
[6]DAO M,CHOLLACOOP N V,VANVLIET K J,VENKATESH T A,SURESH S.Computational modeling of the forward and reverse problems in instrumented sharp indentation[J].Acta Materialia,2001,49(19):3899-3918.
[7]MOUSSA C,HERNOT X,BARTIER O,DELATTRE G,MAUVOISIN G.Evaluation of the tensile properties of a material through spherical indentation:Definition of an average representative strain and a confidence domain[J].Journal of Materials Science,2014,49(2):592-603.
[8]ROY T K.Assessing hardness and fracture toughness in sintered zinc oxide ceramics through indentation technique[J].Materials Science and Engineering A,2015,640:267-274.
[9]WANG X,WANG C,ATKINSON A.Interface fracture toughness in thermal barrier coatings by cross-sectional indentation[J].Acta Materialia,2012,60(17):6152-6163.
[10]PETRYK H,STUPKIEWICZ S,KUCHARSKI S.On direct estimation of hardening exponent in crystal plasticity from the spherical indentation test[J].International Journal of Solids and Structures,2017,112:209-221.
[11]TABOR D.The hardness of metals[M].London:Oxford University Press,1951.
[12]MOUSSA C,HERNOTX,BARTIER O,DELATTRE G,MAUVOISIN G.Identification of the hardening law of materials with spherical indentation using the average representative strain for several penetration depths[J].Materials Science and Engineering A,2014,606:409-416.
[13]YONEDA K,YONEZU A,HIRAKATA H,MINOSHIMA K.Estimation of anisotropic plastic properties of engineering steels from spherical impressions[J].International Journal of Applied Mechanics,2010,2(2):355-379.
[14]BOCCIARELLI M,BOLZON G,MAIER G.Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping[J].Mechanics of Materials,2005,37(8):855-868.
[15]YONEZU A,KUWAHARA Y,YONEDA K,HIRAKATA H,MINOSHIMA K.Estimation of the anisotropic plastic property using single spherical indentation-An FEM study[J].Computational Materials Science,2009,47(2):611-619.
[16]VLASSAK J J,NIX W D.Measuring the elastic properties of anisotropic materials by means of indentation experiments[J].Journal of the Mechanics and Physics of Solids,1994,42(8):1223-1245.
[17]NAKAMURA T,GU Y.Identification of elastic-plastic anisotropic parameters using instrumented indentation and inverse analysis[J].Mechanics of Materials,2007,39(4):340-356.
[18]PATEL D K,KALIDINDI S R.Correlation of spherical nanoindentation stress-strain curves to simple compression stress-strain curves for elastic-plastic isotropic materials using finite element models[J].Acta Materialia,2016,112:295-302.
[19]DONOHUE B R,AMBRUS A,KALIDINDI S R.Critical evaluation of the indentation data analyses methods for the extraction of isotropic uniaxial mechanical properties using finite element models[J].Acta Materialia,2012,60:3943-3952.
[20]LEE H,LEE J H,PHARR M.A numerical approach to spherical indentation techniques for material property evaluation[J].Journal of the Mechanics and Physics of Solids,2005,53:2037-2069.
[21]KIND N,BERTHEL B,FOUVRY S,POUPON C,JAUBERT O.Plasma-sprayed coatings:Identification of plastic properties using macro-indentation and an inverse Levenberg-Marquardt method[J].Mechanics of Materials,2016,98:22-35.
[22]WANG M,WU J,HUI Y,ZHANG Z,ZHAN X,GUO R.Identification of elastic-plastic properties of metal materials by using the residual imprint of spherical indentation[J].Materials Science and Engineering A,2017,679:143-154.
[23]HELWANY S.Applied soil mechanics with ABAQUS applications[M].New York:John Wiley&Sons,2007.
[24]HILL R.A theory of the yielding and plastic flow of anisotropic metals[J].Proceedings of the Royal Society of London,1948,193:281-297.
[25]DIETER G E.Mechanical metallurgy[M].New York:McGraw-Hill,1961.
[26]LUBLINER J,MORAN B.Plasticity theory[J].Journal of Applied Mechanics,1990,59(1):245-246.
[27]HIBBIT K.Abaqus/standard users manual[M].Providence:Abaqus Inc,1995.
[28]SCHMALING B,HARTMAIER A.Determination of plastic material properties by analysis of residual imprint geometry of indentation[J].Journal of Materials Research,2012,27(16):2167-2177.
[29]BOWDEN F P,TABOR D,PALMER F.The friction and lubrication of solids[M].London:Clarendon Press,1964.
[30]BUCAILLE J L,STAUSS S,FELDER E,MICHLER J.Determination of plastic properties of metals by instrumented indentation using different sharp indenters[J].Acta Materialia,2003,51(6):1663-1678.
[31]PHADIKAR J K,BOGETTI T A,KARLSSON A M.On the uniqueness and sensitivity of indentation testing of isotropic materials[J].International Journal of Solids and Structures,2013,50(20):3242-3253.
[32]ZHAO M,OGASAWARA N,CHIBA N,CHEN X.A new approach to measure the elastic-plastic properties of bulk materials using spherical indentation[J].Acta Materialia,2006,54(1):23-32.
[33]HERNOT X,MOUSSA C,BARTIER O.Study of the concept of representative strain and constraint factor introduced by Vickers indentation[J].Mechanics of Materials,2014,68:1-14.
[34]FLECK N A.Spherical indentation of elastic-plastic solids[J].Proceedings of Mathematical Physical&Engineering Sciences,1999,455:2707-2728.
[35]FISCHER-CRIPPS A C,JOHNSON K L.Introduction to contact mechanics:Mechanical engineering series[J].Applied Mechanics Reviews,2002,55(3):B51.
[36]NI W,CHENG Y T,CHENG C M,GRUMMON D S.An energybased method for analyzing instrumented spherical indentation experiments[J].Journal of Materials Research,2004,19(1):149-157.
[37]BOWDEN F P,TABOR D,PALMER F.The friction and lubrication of solids[M].London:Clarendon Press,1954.
[38]RICHMOND O,MORRISON H L,DEVENPECK M L.Sphere indentation with application to the Brinell hardness test[J].International Journal of Mechanical Sciences,1974,16(1):75-82.
[39]GEORGE R A,DINDA S,KASPER A S.Estimating yield strength from hardness data[J].Metal Progress,1976,109(5):30-33.
[40]KIM K H,KIM Y C,JEON E C,KWON D.Evaluation of indentation tensile properties of Ti alloys by considering plastic constraint effect[J].Materials Science and Engineering A,2011,528(15):5259-5263.
[41]LEE H,LEE J H,PHARR G M.A numerical approach to spherical indentation techniques for material property evaluation[J].Journal of the Mechanics and Physics of Solids,2005,53(9):2037-2069.
[2]YONEZU A,YONEDA K,HIRAKATA H,SAKIHARA M,MINOSHIMA K.A simple method to evaluate anisotropic plastic properties based on dimensionless function of single spherical indentation-Application to SiC whisker-reinforced aluminum alloy[J].Materials Science and Engineering A,2010,527(29):7646-7657.
[3]ZHANG H,SCHUSTER B E,WEI Q,RAMESH K T.The design of accurate micro-compression experiments[J].Scripta Materialia,2006,54(2):181-186.
[4]WANG M,WU J,ZHAN X,GUO R,HUI Y,FAN H.On the determination of the anisotropic plasticity of metal materials by using instrumented indentation[J].Materials&Design,2016,111:98-107.
[5]OLIVER W C,PHARR G M.An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[J].Journal of Materials Research,1992,7(6):1564-1583.
[6]DAO M,CHOLLACOOP N V,VANVLIET K J,VENKATESH T A,SURESH S.Computational modeling of the forward and reverse problems in instrumented sharp indentation[J].Acta Materialia,2001,49(19):3899-3918.
[7]MOUSSA C,HERNOT X,BARTIER O,DELATTRE G,MAUVOISIN G.Evaluation of the tensile properties of a material through spherical indentation:Definition of an average representative strain and a confidence domain[J].Journal of Materials Science,2014,49(2):592-603.
[8]ROY T K.Assessing hardness and fracture toughness in sintered zinc oxide ceramics through indentation technique[J].Materials Science and Engineering A,2015,640:267-274.
[9]WANG X,WANG C,ATKINSON A.Interface fracture toughness in thermal barrier coatings by cross-sectional indentation[J].Acta Materialia,2012,60(17):6152-6163.
[10]PETRYK H,STUPKIEWICZ S,KUCHARSKI S.On direct estimation of hardening exponent in crystal plasticity from the spherical indentation test[J].International Journal of Solids and Structures,2017,112:209-221.
[11]TABOR D.The hardness of metals[M].London:Oxford University Press,1951.
[12]MOUSSA C,HERNOTX,BARTIER O,DELATTRE G,MAUVOISIN G.Identification of the hardening law of materials with spherical indentation using the average representative strain for several penetration depths[J].Materials Science and Engineering A,2014,606:409-416.
[13]YONEDA K,YONEZU A,HIRAKATA H,MINOSHIMA K.Estimation of anisotropic plastic properties of engineering steels from spherical impressions[J].International Journal of Applied Mechanics,2010,2(2):355-379.
[14]BOCCIARELLI M,BOLZON G,MAIER G.Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping[J].Mechanics of Materials,2005,37(8):855-868.
[15]YONEZU A,KUWAHARA Y,YONEDA K,HIRAKATA H,MINOSHIMA K.Estimation of the anisotropic plastic property using single spherical indentation-An FEM study[J].Computational Materials Science,2009,47(2):611-619.
[16]VLASSAK J J,NIX W D.Measuring the elastic properties of anisotropic materials by means of indentation experiments[J].Journal of the Mechanics and Physics of Solids,1994,42(8):1223-1245.
[17]NAKAMURA T,GU Y.Identification of elastic-plastic anisotropic parameters using instrumented indentation and inverse analysis[J].Mechanics of Materials,2007,39(4):340-356.
[18]PATEL D K,KALIDINDI S R.Correlation of spherical nanoindentation stress-strain curves to simple compression stress-strain curves for elastic-plastic isotropic materials using finite element models[J].Acta Materialia,2016,112:295-302.
[19]DONOHUE B R,AMBRUS A,KALIDINDI S R.Critical evaluation of the indentation data analyses methods for the extraction of isotropic uniaxial mechanical properties using finite element models[J].Acta Materialia,2012,60:3943-3952.
[20]LEE H,LEE J H,PHARR M.A numerical approach to spherical indentation techniques for material property evaluation[J].Journal of the Mechanics and Physics of Solids,2005,53:2037-2069.
[21]KIND N,BERTHEL B,FOUVRY S,POUPON C,JAUBERT O.Plasma-sprayed coatings:Identification of plastic properties using macro-indentation and an inverse Levenberg-Marquardt method[J].Mechanics of Materials,2016,98:22-35.
[22]WANG M,WU J,HUI Y,ZHANG Z,ZHAN X,GUO R.Identification of elastic-plastic properties of metal materials by using the residual imprint of spherical indentation[J].Materials Science and Engineering A,2017,679:143-154.
[23]HELWANY S.Applied soil mechanics with ABAQUS applications[M].New York:John Wiley&Sons,2007.
[24]HILL R.A theory of the yielding and plastic flow of anisotropic metals[J].Proceedings of the Royal Society of London,1948,193:281-297.
[25]DIETER G E.Mechanical metallurgy[M].New York:McGraw-Hill,1961.
[26]LUBLINER J,MORAN B.Plasticity theory[J].Journal of Applied Mechanics,1990,59(1):245-246.
[27]HIBBIT K.Abaqus/standard users manual[M].Providence:Abaqus Inc,1995.
[28]SCHMALING B,HARTMAIER A.Determination of plastic material properties by analysis of residual imprint geometry of indentation[J].Journal of Materials Research,2012,27(16):2167-2177.
[29]BOWDEN F P,TABOR D,PALMER F.The friction and lubrication of solids[M].London:Clarendon Press,1964.
[30]BUCAILLE J L,STAUSS S,FELDER E,MICHLER J.Determination of plastic properties of metals by instrumented indentation using different sharp indenters[J].Acta Materialia,2003,51(6):1663-1678.
[31]PHADIKAR J K,BOGETTI T A,KARLSSON A M.On the uniqueness and sensitivity of indentation testing of isotropic materials[J].International Journal of Solids and Structures,2013,50(20):3242-3253.
[32]ZHAO M,OGASAWARA N,CHIBA N,CHEN X.A new approach to measure the elastic-plastic properties of bulk materials using spherical indentation[J].Acta Materialia,2006,54(1):23-32.
[33]HERNOT X,MOUSSA C,BARTIER O.Study of the concept of representative strain and constraint factor introduced by Vickers indentation[J].Mechanics of Materials,2014,68:1-14.
[34]FLECK N A.Spherical indentation of elastic-plastic solids[J].Proceedings of Mathematical Physical&Engineering Sciences,1999,455:2707-2728.
[35]FISCHER-CRIPPS A C,JOHNSON K L.Introduction to contact mechanics:Mechanical engineering series[J].Applied Mechanics Reviews,2002,55(3):B51.
[36]NI W,CHENG Y T,CHENG C M,GRUMMON D S.An energybased method for analyzing instrumented spherical indentation experiments[J].Journal of Materials Research,2004,19(1):149-157.
[37]BOWDEN F P,TABOR D,PALMER F.The friction and lubrication of solids[M].London:Clarendon Press,1954.
[38]RICHMOND O,MORRISON H L,DEVENPECK M L.Sphere indentation with application to the Brinell hardness test[J].International Journal of Mechanical Sciences,1974,16(1):75-82.
[39]GEORGE R A,DINDA S,KASPER A S.Estimating yield strength from hardness data[J].Metal Progress,1976,109(5):30-33.
[40]KIM K H,KIM Y C,JEON E C,KWON D.Evaluation of indentation tensile properties of Ti alloys by considering plastic constraint effect[J].Materials Science and Engineering A,2011,528(15):5259-5263.
[41]LEE H,LEE J H,PHARR G M.A numerical approach to spherical indentation techniques for material property evaluation[J].Journal of the Mechanics and Physics of Solids,2005,53(9):2037-2069.