基于微纳米压入法提取无铅焊料合金弹塑性力学参数的研究
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摘要
本文通过微纳米压入法结合数值模拟研究了无铅焊料合金SnAg3.5的弹塑性力学性能,分别采用圆柱形压头及两种不同锥角压头对无铅焊料合金进行压入测试:基于圆柱形压头测试过程中接触面积恒定的特点得到了无铅焊料的弹性模量,进一步采用塑性应变梯度理论对两种锥角压头的测试结果予以修正并通过数值模拟反分析得到相应的特征应力值,同时基于压入特征塑性应变与压头锥角的关系式得到两种不同锥角压头下的特征应变值,在此基础上经求解方程组得到焊料合金的初始屈服应力与应变强化因子,进而得到了焊料合金的幂强化弹塑性本构关系.该方法剔除了压入尺度效应的影响并保证了所得本构关系的唯一性,给出了一种通过原位压入测试表征金属材料弹塑性力学性能的有效方法.
In this study, the elastic-plastic mechanical properties of SnAg3.5 lead-free solder alloy were investigated through micro-/nano-indentation tests combined with numerical simulations. The elastic-plastic mechanical parameters of the lead-free solder alloy were tested by using a cylindrical indenter and two pyramid indenters with different equivalent cone angles. The elastic modulus of the lead-free solder was obtained based on the constant characteristics of the contact area during cylindrical indenter testing. The test results of the two pyramid indenters were corrected based on the plastic strain gradient theory and then the corresponding representative stress can be obtained by simulation inversions. Based on the proposed relation between the representative plastic strain and the cone angle, the representative strain under the two pyramid indenters with different equivalent cone angles was given. Further, by solving the equations regarding to the representative stress and representative plastic strain, the initial yield stress and the strain hardening exponent, as well as the power law elastic-plastic constitutive relation of the solder alloy can be determined. This method can eliminate the influence of indentation scale effect and guarantee the uniqueness of the obtained constitutive relation, which provides an effective way of characterizing the elastic-plastic mechanical properties of metal materials through in-situ indentation tests.
In this study, the elastic-plastic mechanical properties of SnAg3.5 lead-free solder alloy were investigated through micro-/nano-indentation tests combined with numerical simulations. The elastic-plastic mechanical parameters of the lead-free solder alloy were tested by using a cylindrical indenter and two pyramid indenters with different equivalent cone angles. The elastic modulus of the lead-free solder was obtained based on the constant characteristics of the contact area during cylindrical indenter testing. The test results of the two pyramid indenters were corrected based on the plastic strain gradient theory and then the corresponding representative stress can be obtained by simulation inversions. Based on the proposed relation between the representative plastic strain and the cone angle, the representative strain under the two pyramid indenters with different equivalent cone angles was given. Further, by solving the equations regarding to the representative stress and representative plastic strain, the initial yield stress and the strain hardening exponent, as well as the power law elastic-plastic constitutive relation of the solder alloy can be determined. This method can eliminate the influence of indentation scale effect and guarantee the uniqueness of the obtained constitutive relation, which provides an effective way of characterizing the elastic-plastic mechanical properties of metal materials through in-situ indentation tests.
引文
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[16]MOUSSA C,BARTIER O,HERNOT X,et al.Mechanical characterization of carbonitrided steel with spherical indentation using the average representative strain[J].Materials and Design,2016,89(5):1191-1198.
[17]LUCAS B N,OLIVER W C.Indentation power-law creep of high-purity indium[J].Metallurgical and Materials Transactions A,1999,30(3):601-610.
[18]OLIVER W C,PETHICA J B.Method for continuous determination of the elastic stiffness of contact between two bodies[P].U.S.Patent No.4848141,1989.
[19]XIAO G S,YUAN G Z,JIA C N,et al.Strain rate sensitivity of Sn-3.0Ag-0.5Cu solder investigated by nanoindentation[J].Materials Science and Engineering:A,2014,613:336-339.
[20]OLIVER W C,PHARR G M.Measurement of hardness and elastic modulus by instrumented indentation:advances in understanding and refinements to methodology[J].Journal of Materials Research,2004,9(1):3-20.
[21]CHEN X,OGASAWARA N,ZHAO M,et al.On the uniqueness of measuring elastoplastic properties from indentation:the indistinguishable mystical materials[J].Journal of the Mechanics and Physics of Solids,2007,55(8):1618-1660.
[22]KING R B.Elastic analysis of some punch problems for a layered medium[J].International Journal of Solids and Structures,1987,23(12):1657-1664.
[23]张泰华.微/纳米力学测试技术及其应用[M].北京:机械工业出版社,2004.
[24]DURSK K,FRANKE O,B?HNER A,et al.Indentation size effect in Ni-Fe solid solutions[J].Acta Materialia,2007,55(20):6825-6833.
[25]NAGAHISA O,NORIMASA C,CHEN X.Erratum:“Representative strain of indentation analysis”[J.Mater.Res.20,2225(2005)]and“Limit analysis-based approach to determine the material plastic properties with conical indentation”[J.Mater.Res.21,947(2006)][J].Journal of Materials Research,2006,21(10):2699-2700.
[2]牛晓燕,李娜,树学峰.温度和应变率对低银无铅焊料力学行为的影响[J].稀有金属材料与工程,2014,43(9):2166-2171.
[3]ABTEW M,SELVADURAY G.Lead-free solders in microelectronics[J].Materials Science and Engineering R,2000,27(5):95-141.
[4]SURASKI D,SEELING K.The current status of lead-free solder alloys[J].IEEE Transactions on Electronics Packaging Manufacturing,2001,24(4):244-248.
[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]PI J,WANG Z,HE X,et al.Hardness and modulus of Cu-based bulk metallic glasses via nanoindentation[J].Rare Metal Materials and Engineering,2018,47(2):479-484.
[7]胡欣怡,孙莹莹,宋旼.退火时间对FeCuSiBAl纳米晶/非晶复合材料的纳米压痕力学行为的影响[J].粉末冶金材料科学与工程,2017,22(4):590-594.
[8]张东生,李新涛,夏汇浩,等.纳米压痕技术表征T800碳纤维的弹性模量和硬度[J].宇航材料工艺,2017,34(6):1340-1346.
[9]DAO M,CHOLLACOOP N,VLIET K J V,et al.Computational modeling of the forward and reverse problems in instrumented sharp indentation[J].Acta Materialia,2001,49(19):3899-3918.
[10]ANTUNES J M,FERNANDES J V,MENEZE L F,et al.A new approach for reverse analyses in depth-sensing indentation using numerical simulation[J].Acta Materialia,2007,55(1):69-81.
[11]NAGAHISA O,NORIMASA C,CHEN X.Representative strain of indentation analysis[J].Journal of Materials Research,2005,20(8):2225-2234.
[12]CHEN X,VLASSAK J J.Numerical study on the measurement of thin film mechanical properties by means of nanoindentation[J].Journal of Materials Research,2001,16(10):2974-2982.
[13]王月敏,闫相桥,李垚.Pile-up现象对材料本构关系反演计算的影响[J].哈尔滨工程大学学报,2018,39(5):825-830.
[14]NIX W D,GAO H.Indentation size effects in crystalline materials:a law for strain gradient plasticity[J].Journal of the Mechanics and Physics of Solids,1998,46(3):411-425.
[15]CHENG Y T,CHENG C M.Scaling,dimensional analysis,and indentation measurements[J].Materials Science and Engineering R-Reports,2004,44(4):91-149.
[16]MOUSSA C,BARTIER O,HERNOT X,et al.Mechanical characterization of carbonitrided steel with spherical indentation using the average representative strain[J].Materials and Design,2016,89(5):1191-1198.
[17]LUCAS B N,OLIVER W C.Indentation power-law creep of high-purity indium[J].Metallurgical and Materials Transactions A,1999,30(3):601-610.
[18]OLIVER W C,PETHICA J B.Method for continuous determination of the elastic stiffness of contact between two bodies[P].U.S.Patent No.4848141,1989.
[19]XIAO G S,YUAN G Z,JIA C N,et al.Strain rate sensitivity of Sn-3.0Ag-0.5Cu solder investigated by nanoindentation[J].Materials Science and Engineering:A,2014,613:336-339.
[20]OLIVER W C,PHARR G M.Measurement of hardness and elastic modulus by instrumented indentation:advances in understanding and refinements to methodology[J].Journal of Materials Research,2004,9(1):3-20.
[21]CHEN X,OGASAWARA N,ZHAO M,et al.On the uniqueness of measuring elastoplastic properties from indentation:the indistinguishable mystical materials[J].Journal of the Mechanics and Physics of Solids,2007,55(8):1618-1660.
[22]KING R B.Elastic analysis of some punch problems for a layered medium[J].International Journal of Solids and Structures,1987,23(12):1657-1664.
[23]张泰华.微/纳米力学测试技术及其应用[M].北京:机械工业出版社,2004.
[24]DURSK K,FRANKE O,B?HNER A,et al.Indentation size effect in Ni-Fe solid solutions[J].Acta Materialia,2007,55(20):6825-6833.
[25]NAGAHISA O,NORIMASA C,CHEN X.Erratum:“Representative strain of indentation analysis”[J.Mater.Res.20,2225(2005)]and“Limit analysis-based approach to determine the material plastic properties with conical indentation”[J.Mater.Res.21,947(2006)][J].Journal of Materials Research,2006,21(10):2699-2700.