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准脆性材料抗压强度能量平衡尺寸效应模型

刘小宇 杨政 张慧梅

刘小宇, 杨政, 张慧梅. 准脆性材料抗压强度能量平衡尺寸效应模型. 力学学报, 2022, 54(6): 1613-1629 doi: 10.6052/0459-1879-21-460
引用本文: 刘小宇, 杨政, 张慧梅. 准脆性材料抗压强度能量平衡尺寸效应模型. 力学学报, 2022, 54(6): 1613-1629 doi: 10.6052/0459-1879-21-460
Liu Xiaoyu, Yang Zheng, Zhang Huimei. Energy balance size effect model of compressive strength for quasi-brittle materials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1613-1629 doi: 10.6052/0459-1879-21-460
Citation: Liu Xiaoyu, Yang Zheng, Zhang Huimei. Energy balance size effect model of compressive strength for quasi-brittle materials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1613-1629 doi: 10.6052/0459-1879-21-460

准脆性材料抗压强度能量平衡尺寸效应模型

doi: 10.6052/0459-1879-21-460
基金项目: 国家自然科学基金(12172280, 51271138), 陕西省自然科学基金(2020Z-53)和陕西省教育厅专项科研计划(19JK0521)资助项目
详细信息
    作者简介:

    杨政, 教授, 主要研究方向: 结构失效破坏及其三维理论. E-mail: zyang@mail.xjtu.edu.cn

  • 中图分类号: O346

ENERGY BALANCE SIZE EFFECT MODEL OF COMPRESSIVE STRENGTH FOR QUASI-BRITTLE MATERIALS

  • 摘要: 针对现有尺寸效应模型难以体现准脆性材料完整的抗压强度尺寸效应变化规律及其内在机理, 本文通过分析准脆性材料单轴压缩破坏过程中能量输入、储存、整体和局部能量耗散, 建立体现整体和局部损伤的力学模型及描述上述能量演化过程的双线性名义和真实应力应变曲线, 在此基础上确定了名义应力最大时输入能量、储存弹性能、整体和局部能量耗散的表达式, 最后基于能量平衡原理建立抗压强度尺寸效应模型. 抗压强度能量平衡尺寸效应模型能完整体现名义抗压强度尺寸效应, 即随试样尺寸增大, 名义抗压强度在试样尺寸小于等于局部损伤区尺寸时为真实强度, 然后逐渐减小, 最终当试样尺寸趋于无穷大时趋于弹性极限强度; 抗压强度能量平衡尺寸效应模型也能同时体现高径比和试样直径对名义强度的影响, 其包含的参数具有明确的物理意义, 可以反映真实强度、弹性极限强度、名义损伤模量非线性、局部损伤区大小和方向对准脆性材料名义抗压强度尺寸效应的影响; 通过把抗压强度能量平衡尺寸效应模型和现有尺寸效应模型应用于预测各种材料尺寸效应试验和数值模拟数据, 结果表明: 抗压强度能量平衡尺寸效应模型能很好描述试验和数值模拟尺寸效应的非线性变化规律及内在机理, 和现有尺寸效应模型相比, 其总体平均误差最小, 且小于5%.

     

  • 图  1  准脆性材料单轴压缩损伤力学模型

    Figure  1.  Damage mechanics model of quasi-brittle material under uniaxial compression

    图  2  双线性准脆性材料单轴压缩名义(OABT)和真实(OACK)应力应变曲线

    Figure  2.  Bilinear nominal (OABT) and true (OACK) stress-strain curves of quasi-brittle material under uniaxial compression

    图  3  不同阶段声发射位置(图4给出A-F阶段)

    Figure  3.  Locations of acoustic emission at different stages (A-F stages are shown in Fig. 4)

    图  4  花岗岩单轴压缩名义应力应变曲线

    Figure  4.  Nominal stress-strain curve of granite under uniaxial compression

    图  5  准脆性材料抗压强度能量平衡尺寸效应模型

    Figure  5.  Energy balance size effect model of compressive strength for quasi-brittle materials

    图  6  不同尺寸单晶钛合金单轴压缩变形破坏形貌[57]

    Figure  6.  Deformation and failure morphology of single crystal titanium alloy with different sizes under uniaxial compression[57]

    图  7  定比例框下不同单晶钛合金试样和局部剪切区尺寸

    Figure  7.  Size of different single crystal titanium alloy samples and local plastic zone under fix proportional frame

    图  8  参数α 对模型影响

    Figure  8.  Effect of the parameter α on model

    图  9  参数n对模型影响

    Figure  9.  Effect of the parameter n on model

    图  10  参数λ对模型影响

    Figure  10.  Effect of the parameter λ on model

    图  11  参数θ 对模型影响

    Figure  11.  Effect of the parameter θ on model

    图  13  参数at = bt对模型影响

    Figure  13.  Effect of the parameter at = bt on model

    图  12  参数at对模型影响

    Figure  12.  Effect of the parameter at on model

    图  14  不同尺寸效应模型预测编号1砂岩和试验数据对比

    Figure  14.  Comparison of experimental values and predicted results of different size effect models for No. 1 sandstone

    图  26  不同尺寸效应模型预测编号13裂隙岩石和模拟数据对比

    Figure  26.  Comparison of simulated values and predicted results of different size effect models for No. 13 crack-rock

    图  15  不同尺寸效应模型预测编号2白云岩和试验数据对比

    Figure  15.  Comparison of experimental values and predicted results of different size effect models for No. 2 dolomite

    图  16  不同尺寸效应模型预测编号3花岗岩和试验数据对比

    Figure  16.  Comparison of experimental values and predicted results of different size effect models for No. 3 granite

    图  17  不同尺寸效应模型预测编号4花岗岩和试验数据对比

    Figure  17.  Comparison of experimental values and predicted results of different size effect models for No. 4 granite

    图  18  不同尺寸效应模型预测编号5花岗岩和模拟数据对比

    Figure  18.  Comparison of simulated values and predicted results of different size effect models for No. 5 granite

    图  19  不同尺寸效应模型预测编号6煤岩和试验数据对比

    Figure  19.  Comparison of experimental values and predicted results of different size effect models for No. 6 coal

    图  20  不同尺寸效应模型预测编号7钛合金和试验数据对比

    Figure  20.  Comparison of experimental values and predicted results of different size effect models for No. 7 titanium alloy

    图  21  不同尺寸效应模型预测编号8完整岩石和模拟数据对比

    Figure  21.  Comparison of simulated values and predicted results of different size effect models for No. 8 intact rock

    图  22  不同尺寸效应模型预测编号9 C20混凝土和试验数据对比

    Figure  22.  Comparison of experimental values and predicted results of different size effect models for No. 9 C20 concrete

    图  23  不同尺寸效应模型预测编号10 C40混凝土和试验数据对比

    Figure  23.  Comparison of experimental values and predicted results of different size effect models for No. 10 C40 concrete

    图  24  不同尺寸效应模型预测编号11 C60混凝土和试验数据对比

    Figure  24.  Comparison of experimental values and predicted results of different size effect models for No. 11 C60 concrete

    图  25  不同尺寸效应模型预测编号12裂隙岩石和模拟数据对比

    Figure  25.  Comparison of simulated values and predicted results of different size effect models for No. 12 crack-rock

    表  1  不同高径比H/D和直径D试样准脆性材料抗压强度试验和数值模拟数据

    Table  1.   Experiment and numerical simulation data of compressive strength for quasi-brittle materials with different height to diameter ratios H/D and diameters D

    Type of test No.RockSample sizesData sources
    1 sandstone 0.5~4 Ref. [63]
    2 dolomite 1.25~4 Ref. [64]
    H/D 3 granite 1.25~4 Ref. [64]
    4 granite 0.5~6 Ref. [29]
    5 simulated granite 0.5~4 Ref. [58]
    D 6 coal 0.02~2.14 m Ref. [31]
    7 titanium alloy 0.24~8 μm Ref. [57]
    8 simulated intact rock 0.2~2 m Ref. [65]
    9 concrete-C20 0.1~1.2 m Ref. [66]
    10 concrete-C40 0.1~1.2 m Ref. [66]
    11 concrete-C60 0.1~1.2 m Ref. [66]
    12 simulated
    crack-rock
    0.6~6 m Ref. [65]
    13 simulated
    crack-rock
    0.05~12 m Ref. [4]
    下载: 导出CSV

    表  2  本文尺寸效应模型-式(16)或式(17)参数值

    Table  2.   Parameter values of size effect model proposed in this paper for Eq. (16) or (17)

    Type of test No.λc/Dcfcefcn
    H/D10.413 10.768 9144.00.803 3
    21.110 0200.2235.80.834 6
    30.222 7236.4988.51.500
    40.410 052.15168.86.792
    50.540 0183.5257.00.350 5
    D60.042 635.20633.100.028 4
    76.916 × 10−7204544100.590 1
    80.05045.4596.183.452 × 10−4
    93.696 × 10−316.1220.355.795 × 10−7
    103.672 × 10−326.1338.886.117 × 10−7
    113.824 × 10−329.7150.795.926 × 10−7
    120.550 11.77815.000.814 2
    133.266 × 10−311.58150.33.296 × 10−7
    下载: 导出CSV

    表  3  Bazant尺寸效应模型-式(1)参数值

    Table  3.   Parameter values of Bazant size effect model for Eq. (1)

    Type of test No.A11A12A13r
    H/D170.20.023 40.095 00.058 6
    2191.60.083 50.128 70.302 8
    3224.94.566 × 10−43.971 × 10−62.508 × 10−3
    443.560.065 40.505 90.049 0
    5164.60.075 91.266 00.092 2
    D61.6730.034 30.394 90.025 6
    71.3880.130 91.323 00.067 8
    834.950.053 50.242 90.115 1
    915.240.024 30.094 00.429 6
    1023.870.011 10.073 90.131 9
    1125.530.013 20.119 30.086 5
    120.853 27.741 × 10−42.349 × 10−34.719 × 10−4
    137.0780.048 40.661 30.021 0
    下载: 导出CSV

    表  4  Weiss尺寸效应模型-式(2)参数值

    Table  4.   Parameter values of Weiss size effect model for Eq. (2)

    Type of test No.A21A22m
    H/D128.490.858 47.204
    250.400.974 7192.7
    345.970.404 0236.3
    447.100.850 349.72
    5175.104.978 059.27
    D61.3130.955 13.649
    71.0491.4351.621
    819.951.38630.69
    91.5441.78914.49
    102.8881.37722.92
    116.4611.58522.78
    122.2840.317 11.694
    1335.781.8981.01 × 10−6
    下载: 导出CSV

    表  5  刘宝琛尺寸效应模型-式(3)参数值

    Table  5.   Parameter values of Lius size effect model for Eq. (3)

    Type of test No.A31A32A33
    H/D1140.01.86479.64
    297.430.956 1203.1
    3219.11.755238.0
    4183.31.23557.25
    5106.20.845 8190.3
    D642.317.5384.82
    73.4231.0201.872
    888.612.92344.32
    96.4274.91216.02
    1021.775.93225.91
    1134.925.33229.27
    12159.34.4031.781
    13176.43.42111.42
    下载: 导出CSV

    表  6  杨圣奇尺寸效应模型-式(4)参数值

    Table  6.   Parameter values of Yangs size effect model for Eq. (4)

    Type of test No.A41A42A43
    H/D12.1883.4990.318 0
    21.3924.9340.232 0
    32.9304.3420.178 9
    41.5463.5460.549 1
    55.6323.5280.165 8
    D61.4112.0300.025 61
    70.691 11.2110.170 7
    82.3162.9250.160 3
    92.2521.9360.029 55
    101.4542.8530.043 72
    111.8882.7250.059 11
    120.315 81.0811.577
    130.518 14.0380.090 04
    下载: 导出CSV

    表  7  不同尺寸效应模型预测平均误差AE

    Table  7.   Prediction average errors (AEs) of different size effect models

    No.Eq. (1)Eq. (2)Eq. (3)Eq. (4)Eq. (16) or (17)
    11.391.380.82min1.811.07
    20.740.740.65min0.730.65min
    30.680.330.30min0.670.33
    42.892.47min2.964.542.55
    51.771.991.453.221.38min
    618.2016.188.0679.837.57min
    75.965.696.8513.853.04min
    88.616.206.14min8.296.83
    90.34min0.470.421.080.98
    100.92min0.980.942.141.61
    111.271.480.85min4.072.14
    1221.1312.41min13.4618.1513.08
    1313.4921.0612.01117.1110.89min
    TAE5.955.494.2234.684.01min
    Note: The superscript of min denotes the minimum average error (AE) or total average error (TAE) of different size effect models in above table.
    下载: 导出CSV
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  • 收稿日期:  2021-09-09
  • 录用日期:  2022-04-02
  • 网络出版日期:  2022-04-02
  • 刊出日期:  2022-06-18

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