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 材料工程  2019, Vol. 47 Issue (7): 35-49 PDF
http://dx.doi.org/10.11868/j.issn.1001-4381.2018.001411
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#### 文章信息

LIU Pei-sheng, XIA Feng-jin, CHENG Wei

Study on property model for porous materials 2: experimental verification

Journal of Materials Engineering, 2019, 47(7): 35-49.
http://dx.doi.org/10.11868/j.issn.1001-4381.2018.001411

### 文章历史

Study on property model for porous materials 2: experimental verification
LIU Pei-sheng, XIA Feng-jin, CHENG Wei
Key Laboratory of Beam Technology of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
Abstract: The "octahedral structure model" is introduced for three-dimensional reticulated porous materials, as well as the mathematical relations of their basic physical and mechanical properties. On this basis, the verification works about some performance relations, including the conductivity and tension, etc, are reviewed in this paper. A number of issues were discussed with the emphases on the practicality of these mathematical and physical relations, the rationality of the correction coefficients, the significant influence on the calculation results, and the allowable stress and the plastic index value of the corresponding dense body were also analyzed in details. According to this mathematical and physical relationship, the performance indexes such as the electrical resistivity of porous products can be calculated by the easily measurable basic parameters like the porosity. The experimental results prove this way feasible. Therefore, this method can be superior to the finite element and other complex computational methods.
Key words: porous material    property model    experimental verification

1 多孔材料的电阻率 1.1 电阻率的数理表征

 (1)

1.2 模型理论验证及分析 1.2.1 实验样品

1.2.2 测试结果与验证分析

 图 1 测试片状泡沫金属制品电阻的试样 Fig. 1 Samples for testing the electrical resistivity of metal foam plate

 No θ/% ρ1/(nΩ·m) ρ2/(nΩ·m) Δρ/(nΩ·m) |Δρ/ρ1|/% 1 88.60 1523.0 1648.0 125.0 8.2 2 89.66 1590.8 1820.6 230.0 14.4 3 90.19 2017.5 1921.0 -96.5 4.8 4 92.55 2235.1 2542.4 307.3 13.7 5 93.52 3033.1 2929.7 -103.4 3.4 6 95.79 4040.4 4537.1 496.7 12.3 7 95.83 4782.0 4581.2 -200.8 4.2 8 97.15 7174.9 6732.4 -442.5 6.2 9 98.38 12621.8 11904.9 -717.0 5.7 10 98.84 19579.3 16665.7 -2913.6 14.9 Average 8.8

 图 2 泡沫镍样品电阻率与孔率的关系 Fig. 2 Relationship between electrical resistivity and porosity of the nickel foam samples

2 多孔材料的抗拉强度 2.1 抗拉强度的数理表征

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2.2 模型理论验证及分析 2.2.1 实验样品

 图 3 泡沫镍抗拉强度试样的形状及尺寸 Fig. 3 Shape and size of the nickel foam samples for tensile strength test
2.2.2 测试结果与验证分析

 No θ/% σ′/MPa σ/MPa ︱Δσ/σ′︱/% 1 88.60 6.75 6.91 2.3 2 89.66 6.45 6.12 5.2 3 90.19 5.40 5.73 6.0 4 92.55 4.16 4.06 2.4 5 93.52 3.23 3.41 5.6 6 95.79 2.48 1.98 16.6 7 95.83 2.00 1.97 1.7 8 97.15 1.28 1.22 4.6 9 98.38 0.63 0.60 4.0 10 98.84 0.38 0.40 4.5 Average 4.0

 图 4 泡沫镍样品的抗拉强度实测数据与本模型理论公式曲线 Fig. 4 Measured data and the theoretical formula curves for tensile strength of the nickel foam samples

2.2.3 模型理论讨论 2.2.3.1 本理论模型的适用性

2.2.3.2 本关系表达的可行性

2.2.3.3 本理论关系的计算精度

3 多孔材料的伸长率 3.1 伸长率的数理表征

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3.2 模型理论验证及分析 3.2.1 实验样品和测试方法

3.2.2 数理关系验证及分析

 No θ/% δ/% 1 88.60 9.14 2 89.66 9.99 3 90.19 11.10 4 92.55 13.14 5 93.52 12.47 6 95.79 13.96 7 95.83 14.91 8 97.15 16.35 9 98.38 10.22 10 98.84 15.04
 图 5 电沉积型泡沫镍伸长率与孔率的关系 Fig. 5 Relationship between elongation and porosity of electrodeposited nickel foam

3.2.3 泡沫金属拉伸断裂行为

4 多孔材料的双向拉伸 4.1 双向拉伸的数理关系

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4.2 模型理论验证及分析 4.2.1 实验样品和测试方法

 图 6 泡沫镍双向拉伸试样的形状和尺寸 Fig. 6 Shape and size of the nickel foam samples for biaxial tensile test
4.2.2 数理关系验证及分析

 No θ/% vx/(mm·min-1) vy/(mm·min-1) σx/MPa σy/MPa σd/MPa σd′/MPa ︱[(σd′-σd)/σd]︱/% K ︱[(K-k)/K]︱/% 1 89.3 8.0 8.0 5.31 5.54 5.43 6.07 11.8 0.296 10.1 2 90.0 8.0 8.0 5.50 5.62 5.56 5.56 0.1 0.329 0.0 3 90.4 6.5 9.0 4.32 5.31 4.89 5.31 8.6 0.304 7.6 4 90.7 6.5 9.0 4.08 5.01 4.62 5.11 10.8 0.300 9.2 5 91.3 8.5 7.5 4.86 3.66 4.38 4.71 7.4 0.308 6.5 6 92.0 6.5 9.0 3.56 4.13 3.88 4.25 9.6 0.312 8.2 7 92.2 8.0 8.0 4.23 4.10 4.17 4.10 1.7 0.335 1.7 8 93.1 8.5 7.5 3.77 3.10 3.48 3.53 1.3 0.325 1.2 9 94.4 8.0 8.0 2.99 3.13 3.06 2.71 11.4 0.369 12.3 10 94.7 8.5 7.5 3.06 2.28 2.75 2.54 7.6 0.355 7.8 11 95.2 6.5 9.0 1.77 2.41 2.16 2.26 4.7 0.315 4.3 12 97.0 8.0 8.0 1.27 1.33 1.30 1.26 2.9 0.339 3.2 13 97.2 9.0 6.5 1.57 0.85 1.36 1.16 14.8 0.386 17.3 14 98.3 8.0 8.0 1.67 0.67 1.46 (0.61) (57.9) (0.763) (132.0) 15 98.5 8.0 8.0 0.61 0.47 0.55 0.54 3.2 0.339 3.0 Average 6.8 0.329 6.6

K=0.329、[σ]=317MPa[11]、金属镍塑性指标m≈1.25代入式(6)，计算得出偏应力值σd′，一同列于表 4中。将σd′与直接通过实验数据获得的偏应力值σd进行对照，可见总体上两者还是比较接近的。计算值σd′对实验值σd的相对波动幅平均为6.8%，也是一个较小的量。由此可见，该式的计算精度较高，可较好地表达泡沫金属在双向拉伸过程中对应不同孔率指标的总体载荷水平。

4.2.3 模型理论的讨论 4.2.3.1 塑性指标m的取值

m取值1.25获得了良好的计算效果，只能说明对电沉积法所制泡沫镍适用，而对其他工艺方法所制多孔镍或泡沫铝的适用程度尚不确定。根据数理关系的相关推演分析，推测其值也在1~1.5之间，且于1.25附近。

4.2.3.2 模型理论结果的应用

4.2.4 经典理论公式应用对比分析 4.2.4.1 代表性理论关系应用分析

4.2.4.2 总结性评述

5 多孔材料的疲劳性能 5.1 疲劳性能指标的数理表征 5.1.1 类应力疲劳

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5.1.2 类应变疲劳

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5.2 模型理论应用及检验 5.2.1 疲劳实验方法

5.2.1.1 类应力疲劳

 图 7 循环加压实验装置图 Fig. 7 Experimental installation diagram for cyclically pressing the sample
5.2.1.2 类应变疲劳

 图 8 循环弯曲实验装置图 Fig. 8 Experimental installation diagram for cyclically bending the sample
5.2.2 实验结果与分析 5.2.2.1 类应力疲劳

 No θ/% w/mm ρ /(nΩ·m) ρ′/(nΩ·m) (Δρ/ρ)/% Fσ/Kσ 1 88.1 2.94 1267.69 1266.22 -0.12 0.144 2 89.0 2.74 1316.57 1334.38 1.35 0.159 3 90.6 2.64 1912.68 2064.48 7.94 0.191 4 93.8 2.79 2646.66 2934.03 10.86 0.326 5 95.5 2.52 3459.17 3398.69 -1.75 0.480 6 99.1 2.44 19353.78 23725.04 22.59 3.658

5.2.2.2 类应变疲劳

 No θ/% d/mm w/mm ρ/(nΩ·m) ρ′/(nΩ·m) (Δρ/ρ)/% Fε/Kε 1 89.7 0.57 2.62 1590.79 1641.07 3.16 0.062 2 92.6 0.60 2.71 2235.07 2291.11 2.51 0.053 3 93.5 0.64 2.60 3033.09 3100.02 2.21 0.052 4 95.8 0.68 2.91 4040.42 4122.39 2.03 0.043 5 97.2 0.72 2.46 7174.91 7247.70 1.01 0.037 6 98.4 0.76 2.71 12621.83 12739.84 0.93 0.028

5.3 模型理论总体性讨论 5.3.1 孔隙因素的影响问题

5.3.2 材料制备和边缘效应

5.4 相关工作对比分析

Schultz等[48]对用于直升机的泡沫铝的疲劳行为进行了研究。试样包括熔体发泡法所得产品和粉末烧结法所得产品。结果显示，如果应力幅一定，则试样的密度越大(即孔率越小)，载荷周次就会越大，即泡沫铝试样的疲劳性能越好。这一结果与类应力疲劳模型关系一致[41]

6 多孔材料的比表面积 6.1 比表面积的数理关系

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6.2 计算公式验证

6.2.1 电沉积工艺制备的泡沫镍

 No θ/% d/mm SV/(cm2·cm-3)(from test result) SV/(cm2·cm-3)(from eq.(10)) 1 88.60 0.5602 1098.68 1093.55 2 89.66 0.5735 1197.38 1195.75 3 90.19 0.5707 1275.72 1276.02 4 92.55 0.6008 1637.48 1648.33 5 93.52 0.6413 1782.20 1797.60 6 95.79 0.6802 2649.22 2675.69 7 95.83 0.6458 2818.19 2846.21 8 97.15 0.7242 3727.77 3748.20 9 98.38 0.7553 6367.34 6309.11 10 98.84 0.7378 9146.05 8949.45

n取值-1.41不但使计算值与实测值的平均偏差仅为0.8%，偏差范围也仅在－2.2%~1.0%之间，而且常数项KS值只在126.9~131.0区间，对其平均值的波动幅度在－1.0%~2.2%之间，平均波动幅度值只有0.8%。

6.2.2 渗流工艺制备的泡沫铝

 No θ/%[51] d/mm[51] SV/(cm2·cm-3)[51] SV/(cm2·cm-3)(from eq.(10)) 1 73.0 2.66 15.7 15.66 2 76.6 2.68 14.7 14.69 3 78.6 2.73 13.8 13.85 4 82.0 2.76 12.5 12.56 5 85.8 2.85 10.7 10.64

6.2.3 表 7表 8中的数据修约问题

6.3 模型分析 6.3.1 验证分析

6.3.2 公式常数问题

nKS的具体取值虽然是通过实验数据拟合而来的，但拟合值用于公式后获得了十分令人满意的结果，无论是计算结果与实验结果的平均偏差还是偏差范围的幅度都非常小，充分说明这种数据处理方式是合理的。

7 结束语

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