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弹塑性比例叠加的锥压入半解析模型与试验方法

张思宇 蔡力勋 司淑倩 陈辉 刘晓坤

张思宇, 蔡力勋, 司淑倩, 陈辉, 刘晓坤. 弹塑性比例叠加的锥压入半解析模型与试验方法[J]. 工程力学, 2023, 40(2): 232-246. doi: 10.6052/j.issn.1000-4750.2021.09.0684
引用本文: 张思宇, 蔡力勋, 司淑倩, 陈辉, 刘晓坤. 弹塑性比例叠加的锥压入半解析模型与试验方法[J]. 工程力学, 2023, 40(2): 232-246. doi: 10.6052/j.issn.1000-4750.2021.09.0684
ZHANG Si-yu, CAI Li-xun, SI Shu-qian, CHEN Hui, LIU Xiao-kun. SEMI-ANALYTICAL MODEL AND TEST METHOD OF CONE INDENTATION BASED ON ELASTOPLASTIC PROPORTIONAL SUPERPOSITION[J]. Engineering Mechanics, 2023, 40(2): 232-246. doi: 10.6052/j.issn.1000-4750.2021.09.0684
Citation: ZHANG Si-yu, CAI Li-xun, SI Shu-qian, CHEN Hui, LIU Xiao-kun. SEMI-ANALYTICAL MODEL AND TEST METHOD OF CONE INDENTATION BASED ON ELASTOPLASTIC PROPORTIONAL SUPERPOSITION[J]. Engineering Mechanics, 2023, 40(2): 232-246. doi: 10.6052/j.issn.1000-4750.2021.09.0684

弹塑性比例叠加的锥压入半解析模型与试验方法

doi: 10.6052/j.issn.1000-4750.2021.09.0684
基金项目: 国家自然科学基金项目(11872320,12072294)
详细信息
    作者简介:

    张思宇(1997−),女,四川南充人,硕士生,主要从事材料测试理论与技术研究(E-mail: zhang_syyy@163.com)

    司淑倩(1995−),女,河南新乡人,硕士,主要从事材料测试理论与技术研究(E-mail: 2920792196@qq.com)

    陈 辉(1990−),男,湖南衡阳人,副教授,博士,主要从事材料力学性能表征与测试方法研究(E-mail: chen_hui5352@163.com)

    刘晓坤(1991−),男,河南商丘人,博士生,主要从事材料测试理论与技术研究(E-mail: 1010727036@qq.com)

    通讯作者:

    蔡力勋(1959−),男,山东曹县人,教授,硕士,主要从事断裂力学研究,材料测试理论与技术研究(E-mail: lix_cai@263.net)

  • 中图分类号: O34

SEMI-ANALYTICAL MODEL AND TEST METHOD OF CONE INDENTATION BASED ON ELASTOPLASTIC PROPORTIONAL SUPERPOSITION

  • 摘要: 基于能量密度等效,考虑圆锥压入(锥压入)过程中线性律纯弹性和幂律纯塑性的应变能比例叠加,提出了弹塑性应变能比例叠加的锥压入载荷-位移模型(Load vs. Displacement Model based on Proportional Superposition of elastoplastic-energy under conical indenting,LDM-PS),进而提出了获取材料Ramberg-Osgood律(R-O律)应力-应变关系的锥压入试验方法。针对80种设定材料,通过LDM-PS预测的载荷-位移曲线(正向预测)与有限元分析结果密切吻合,并且以有限元分析(Finite Element Analysis,FEA)所得载荷-位移曲线作为试验模拟曲线,采用两种锥角圆锥压头分别对平滑材料表面进行两次单锥压入加载(双锥压入),可通过对双锥压入的两个载荷-位移曲线的加载阶段按抛物律(Kick律)回归可实现R-O律参数的求解。由LDM-PS预测的R-O律应力-应变关系曲线(反向预测)与FEA的条件关系曲线密切吻合;针对8种金属材料完成了双锥压入试验,通过锥压入试验新方法预测的应力-应变关系、弹性模量和强度与传统单轴拉伸试验结果吻合良好。
  • 图  1  不同材料常数的hh/(he+hp)曲线

    Figure  1.  hh/(he+hp) curves of different material constants

    图  2  锥压入有限元对称模型

    Figure  2.  The axisymmetric FEA model under conical indenter loading

    图  3  锥压入计算云图

    Figure  3.  nephogram for conical indenting

    图  4  Ap~1+1/N曲线

    Figure  4.  The curve of Ap~1+1/N

    图  5  压入载荷-位移曲线与FEA比较(纯塑性)

    Figure  5.  Comparisons of load-displacement curves and those from FEA(Pure plastic)

    图  6  压入载荷-位移曲线与FEA比较

    Figure  6.  Comparisons of load-displacement curves and those from FEA

    图  7  预测应力-应变关系与FEA对比{60°,70.3° }组合

    Figure  7.  Comparisons of predicted stress-strain curves and those from FEA({60°,70.3° })

    图  8  预测应力-应变关系与FEA对比{53°,65° }组合

    Figure  8.  Comparisons of predicted stress-strain curves and those from FEA ({53°,65° })

    图  9  试验设备

    Figure  9.  Test equipment

    图  10  压入曲线示意图

    Figure  10.  Schematic diagram of indentation curves

    图  11  多级卸载试验P-h曲线(θ=60°)

    Figure  11.  Multi-stage unloading P-h curves for Aluminum and Steel (θ=60°)

    图  12  多级卸载试验P-h曲线(θ=70.3°)

    Figure  12.  Multi-stage unloading P-h curves for Aluminum and Steel (θ=70.3°)

    图  13  压头系数βh/h*的关系曲线(θ=60°)

    Figure  13.  Relation curve between indenter coefficient and h/h* curves for Aluminum and Steel (θ=60°)

    图  14  压头系数βh/h*的关系曲线(θ=70.3°)

    Figure  14.  Relation curve between indenter coefficient and h/h* curves for Aluminum and Steel (θ=70.3°)

    图  15  压入P-h曲线(θ=60°)

    Figure  15.  Indentation P-h curve for Aluminum and Steel (θ=60°)

    图  16  压入P-h曲线(θ=70.3°)

    Figure  16.  Indentation P-h curve for Aluminum and Steel (θ=70.3°)

    图  17  R-O律预测曲线与单轴拉伸对比

    Figure  17.  Comparisons between predicted curves and those from uniaxial tension for Aluminum and Steel

    表  1  纯塑性锥压入模型参数值

    Table  1.   Parameters of pure plastic conical indenting model

    压头半锥角θ/(°)有效体积系数k1有效应变系数k2
    5326.420.1715
    6024.950.1789
    6523.400.1866
    70.321.010.1997
    下载: 导出CSV

    表  2  弹塑性比例因子c参数值

    Table  2.   Elastoplastic scaling factor c parameter value

    压头半锥角θ/(°)比例系数c1比例指数c2比例指数c3
    530.6225−0.06703−0.05327
    600.6406−0.06287−0.06503
    650.6245−0.06544−0.06877
    70.30.6304−0.06404−0.08170
    下载: 导出CSV

    表  3  材料力学性能与单轴拉伸R-O律塑性参数

    Table  3.   Mechanical properties of materials and plastic parameters of uniaxial tensile R-O law

    材料材料常规力学性能材料R-O律塑性参数
    弹性模量
    E/GPa
    屈服强度
    Rp0.2/MPa
    抗拉强度
    Rm/MPa
    硬化系数
    Κ/MPa
    硬化指数
    N
    6061-T651171.00376.1390.6498.214.310
    7075-T651171.40517.6631.9845.211.970
    5083-H11670.30159.3276.2519.43.623
    6082-T671.50326.4348.1448.214.710
    P92210.0548.3715.110767.337
    16Mn212.0309.9521.1876.84.978
    1Cr12Mo219.9616.6767.111198.446
    2Cr12MoV216.9772.2976.113149.661
    下载: 导出CSV

    表  4  压头系数β模型参数

    Table  4.   Parameters of indenter coefficient β model

    压头半锥角θ/(°)弹性模量E/GPa模型系数e1模型指数e2
    6060~800.8055−0.1958
    180~2200.6258−0.2075
    70.360~800.6929−0.2004
    180~2200.4944−0.2509
    下载: 导出CSV

    表  5  R-O律参数及σ-ε曲线优度

    Table  5.   Parameters of R-O law and σ-ε curve goodness

    材料R-O律参数弹性模量E/GPaσ-ε曲线
    优度/(%)
    弹性模量
    E/GPa
    硬化系数
    Κ/MPa
    硬化指数
    N
    单轴拉伸误差/(%)
    6061-T651168.32563.99.19571.003.77098.0
    7075-T651175.20927.19.20271.405.32098.0
    5083-H11668.74475.35.29170.302.22097.0
    6082-T671.90472.613.23071.500.55796.0
    P92209.101041.07.074210.000.40997.0
    16Mn209.70883.54.633212.001.09097.0
    1Cr12Mo213.001117.010.060219.903.12096.0
    2Cr12MoV219.701277.010.890216.901.29099.0
    下载: 导出CSV

    表  6  抗拉强度与单轴拉伸结果的对比

    Table  6.   Comparison of tensile strength with uniaxial tensile results

    材料抗拉强度Rm/MPa
    锥压入单轴拉伸误差/(%)
    6061-T6511397.3390.61.73
    7075-T6511653.4631.93.40
    5083-H116287.2276.23.98
    6082-T6360.5348.13.57
    P92685.4715.14.16
    16Mn511.4521.11.86
    1Cr12Mo804.3767.14.85
    2Cr12MoV935.8976.14.12
    下载: 导出CSV

    表  7  屈服强度与单轴拉伸结果的对比

    Table  7.   Comparison of yield strength with uniaxial tensile results

    材料屈服强度Rp0.05/MPa屈服强度Rp0.1/MPa屈服强度Rp0.2/MPa
    锥压入单轴拉伸误差/(%)锥压入单轴拉伸误差/(%)锥压入单轴拉伸误差/(%)
    6061-T6511345.9363.54.84347.7364.84.67351.1376.16.65
    7075-T6511582.9590.21.24585.4592.11.13590.1517.614.00
    5083-H116156.2157.81.01161.9159.11.76188.5159.318.30
    6082-T6333.1324.62.62334.5325.92.64337.0326.43.25
    P92497.5529.96.11504.6537.06.03517.1548.35.69
    16Mn246.2275.710.7257.1285.49.92274.4309.911.50
    1Cr12Mo659.0611.87.71665.9618.27.72678.0616.69.95
    2Cr12MoV819.4766.46.91824.5774.16.51833.6772.27.95
    下载: 导出CSV
  • [1] GB/T 22458−2008, 仪器化纳米压入试验方法通则[S]. 北京: 中国标准出版社, 2008.

    GB/T 22458−2008, General rules for instrumented nanometer pressing test methods [S]. Beijing: China Standard Press, 2008. (in Chinese)
    [2] GB/T 37782−2019, 金属材料 压入试验 强度、硬度和应力-应变曲线的测定[S]. 北京: 中国标准出版社, 2019.

    GB/T 37782−2019, Determination of strength, hardness and, stress-strain relationship of metallic materials in pressing test [S]. Beijing: China Standard Press, 2019. (in Chinese)
    [3] 钱秀清, 曹艳平, 张建宇. 采用压痕实验确定线性强化弹塑性材料的弹性模量[J]. 工程力学, 2010, 27(6): 24 − 28.

    QIAN Xiuqing, CAO Yanping, ZHANG Jianyu. Determining the elastic modulus of linearly hardening elastoplasitc materials using indentation tests [J]. Engineering Mechanics, 2010, 27(6): 24 − 28. (in Chinese)
    [4] LIU X K, CAI L X, CHEN H, et al. Semi-analytical model for flat indentation of metal materials and its applications [J]. Chinese Journal of Aeronautics, 2020, 33(12): 3266 − 3277. doi: 10.1016/j.cja.2020.05.007
    [5] 张志杰, 郑鹏飞, 陈辉, 等. 基于能量等效原理的金属材料硬度预测方法[J]. 工程力学, 2021, 38(3): 17 − 26. doi: 10.6052/j.issn.1000-4750.2020.04.0249

    ZHANG Zhijie, ZHENG Pengfei, CHEN Hui, et al. The method for hardness prediction of metal materials based on energy equivalence principle [J]. Engineering Mechanics, 2021, 38(3): 17 − 26. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.04.0249
    [6] GIANNAKOPOULOS A E, LARSSON P L, VESTERGAARD R. Analysis of Vickers indentation [J]. International Journal of Solids & Structures, 1994(31): 2679.
    [7] DAO M, CHOLLACOOP N, VAN VLIET K J, et al. Computational modeling of the forward and reverse problems in instrumented sharp indentation [J]. Acta materialia, 2001, 49(19): 3899 − 3918. doi: 10.1016/S1359-6454(01)00295-6
    [8] BUCAILLE J L, STAUSS S, FELDER E, et al. Determination of plastic properties of metals by instrumented indentation using different sharp indenters [J]. Acta Materialia, 2003, 51(6): 1663 − 1678. doi: 10.1016/S1359-6454(02)00568-2
    [9] CHOLLACOOP N, DAO M, SURESH S. Depth-sensing instrumented indentation with dual sharp indenters [J]. Acta Materialia, 2003, 51(13): 3713 − 3729. doi: 10.1016/S1359-6454(03)00186-1
    [10] CAO Y P, LU J. Depth-sensing instrumented indentation with dual sharp indenters: stability analysis and corresponding regularization schemes [J]. Acta Materialia, 2004, 52(5): 1143 − 1153. doi: 10.1016/j.actamat.2003.11.001
    [11] CAO Y P, QIAN X Q, LU J, et al. An energy-based method to extract plastic properties of metal materials from conical indentation tests [J]. Journal of Materials Research, 2005, 20(5): 1194 − 1206. doi: 10.1557/JMR.2005.0147
    [12] LE M Q. A computational study on the instrumented sharp indentations with dual indenters [J]. International Journal of Solids and Structures, 2008, 45(10): 2818 − 2835. doi: 10.1016/j.ijsolstr.2007.12.022
    [13] LE M Q. Material characterization by dual sharp indenters [J]. International Journal of Solids and Structures, 2009, 46(16): 2988 − 2998. doi: 10.1016/j.ijsolstr.2009.03.027
    [14] 姚博, 蔡力勋, 包陈. 基于70.3°圆锥形压头的材料压入测试方法研究[J]. 工程力学, 2013, 30(6): 30 − 35. doi: 10.6052/j.issn.1000-4750.2012.02.0096

    YAO Bo, CAI Lixun, BAO Chen. The research of indentation test method based on cone indenter of 70.3 degrees [J]. Engineering Mechanics, 2013, 30(6): 30 − 35. (in Chinese) doi: 10.6052/j.issn.1000-4750.2012.02.0096
    [15] 姚博, 蔡力勋, 包陈. 基于锥形压入的材料力学性能测试方法研究[J]. 航空学报, 2013, 34(8): 1874 − 1883.

    YAO Bo, CAI Lixun, BAO Chen. Study on testing method of mechanical properties of materials based on conical pressing [J]. Chinese Journal of Aeronautics, 2013, 34(8): 1874 − 1883. (in Chinese)
    [16] CHEN H, CAI L X. Theoretical model for predicting uniaxial stress-strain relation by dual conical indentation based on equivalent energy principle [J]. Acta Material, 2016, 121: 181 − 189. doi: 10.1016/j.actamat.2016.09.008
    [17] SI S Q, CAI L X, CHEN H, et al. Theoretical model and testing method for ball indentation based on the proportional superposition of energy in pure elasticity and pure plasticity[J]. Chinese Journal of Aeronautics, 2021.
    [18] CHEN H, CAI L X, BAO C. Equivalent-energy indentation method to predict the tensile properties of light alloys [J]. Materials & Design, 2019, 162: 322 − 330.
    [19] CHEN H, CAI L X. Unified elastoplastic model based on a strain energy equivalence principle [J]. Applied Mathematical Modelling, 2017, 52: 664 − 671.
    [20] CHEN H, CAI L X. An elastoplastic energy model for predicting the deformation behaviors of various structural components [J]. Applied Mathematical Modelling, 2019, 68: 405 − 421. doi: 10.1016/j.apm.2018.11.024
    [21] 彭云强, 蔡力勋, 韦利明. 基于等效能量原理的延性材料J (δ)阻力曲线测试新方法研究[J]. 工程力学, 2020, 37(10): 7 − 16. doi: 10.6052/j.issn.1000-4750.2019.11.0706

    PENG Yunqiang, CAI Lixun, WEI Liming. The research of new testing method for obtaining the J (δ) resistance curves of ductile materials based on equivalent energy principle [J]. Engineering Mechanics, 2020, 37(10): 7 − 16. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.11.0706
    [22] GOLDMAN N L, HUTCHINSON J W. Fully plastic crack problems: the center-cracked strip under plane strain [J]. International Journal of Solids and Structures, 1975, 11(5): 575 − 591. doi: 10.1016/0020-7683(75)90031-1
    [23] LOVE A E H. Boussinesq's problem for a rigid cone [J]. The Quarterly Journal of Mathematics, 1939(1): 161 − 175.
    [24] SNEDDON I N. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile [J]. International Journal of Engineering Science, 1965, 3(1): 47 − 57. doi: 10.1016/0020-7225(65)90019-4
    [25] JOHNSON K L. The correlation of indentation experiments [J]. Journal of the Mechanics and Physics of Solids, 1970, 18(2): 115 − 126. doi: 10.1016/0022-5096(70)90029-3
    [26] STILWELL N A, TABOR D. Elastic recovery of conical indentations [J]. Proceedings of the Physical Society, 1961, 78(2): 169 − 179.
    [27] 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.
    [28] HENDRIX B C. The use of shape correction factors for elastic indentation measurements [J]. Journal of Materials Research, 1995, 10(2): 255 − 257. doi: 10.1557/JMR.1995.0255
    [29] 张志杰, 蔡力勋, 陈辉, 等. 金属材料的强度与应力-应变关系的球压入测试方法[J]. 力学学报, 2019, 51(1): 159 − 169.

    ZHANG Zhijie, CAI Lixun, CHEN Hui, et al. Spherical indentation method to determine stress-strain relations and tensile strength of metallic materials [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 159 − 169. (in Chinese)
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  • 收稿日期:  2021-09-02
  • 录用日期:  2021-12-10
  • 修回日期:  2021-11-30
  • 网络出版日期:  2021-12-10
  • 刊出日期:  2023-02-01

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