Mechanical properties of basalt fiber foam concrete based on microscopic numerical simulation
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摘要: 为研究不同密度和纤维掺量的玄武岩纤维泡沫混凝土(BFRFC)的孔隙特征与单轴压缩力学性能，本文对两种密度下三种纤维掺量的试样进行X-CT与单轴压缩试验，分析实测孔隙和纤维分布特征，利用Matlab软件二次开发了BFRFC微观结构的三维重构模型，基于Hashin失效准则和损伤变量建立BFRFC的渐进损伤模型，并采用Comsol有限元软件进行单轴压缩试验仿真模拟。研究发现，BFRFC的孔隙直径服从对数正态分布，孔隙率和平均孔径随着密度的增加及纤维掺量的增多而减小；BFRFC内部的纤维极角主要集中在15°~90°之间，而方位角则在0°~360°之间均匀分布；基于微观结构所建立的BFRFC试样仿真模型，结合材料软化特性的渐进损伤模型，可以有效模拟BFRFC单轴压缩过程；BFRFC中玄武岩纤维的添加显著提升了材料的力学性能，包括峰值强度和吸能能力，且单轴压缩过程中材料内部力学响应从外层向内层进行逐层传递。Abstract: To explore the pore characteristics and uniaxial compression mechanical properties of basalt fiber reinforced foam concrete (BFRFC) with varied densities and fiber mixtures, this study carries out X-ray computed tomography (X-CT) and uniaxial compression tests on samples featuring three types of fiber mixtures at two different densities. It examines the pore and fiber distribution within these samples and leverages MATLAB to develop a three-dimensional reconstruction model of BFRFC's microstructure. Additionally, a progressive damage model, grounded in Hashin's failure criteria and damage variables, has been formulated. The uniaxial compression test simulations were executed using Comsol's finite element software. The findings indicate that BFRFC's pore diameter follows a lognormal distribution. Notably, both porosity and average pore diameter exhibit a decrease with increasing density and fibre content; within BFRFC, the polar angle of the fibers predominantly ranges from 15° to 90°, whereas the azimuthal angle is uniformly distributed across 0° to 360°. The microstructure-based simulation model of BFRFC, integrated with the progressive damage model that accounts for the material's softening characteristics, proves effective in simulating the material's progressive damage. Furthermore, the microstructure-based simulation model, when coupled with the progressive damage model that considers the softening traits of the material, accurately simulates the uniaxial compression behavior of BFRFC. The incorporation of basalt fibers into BFRFC notably enhances its mechanical properties, such as peak strength and energy absorption capacity. Moreover, during the uniaxial compression process, the material's mechanical response is progressively relayed from the outer to the inner layers, enhancing its structural integrity and resilience.
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Key words:
- basalt fiber reinforced foam concrete /
- microstructure /
- X-CT /
- Comsol /
- pore structure /
- mechanical simulation
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图 3 不同BFRFC试样的孔径分布特征
Figure 3. Features of pore size distribution for different BFRFC specimens
图 4 各密度等级BFRFC的孔隙形状特征统计
Figure 4. Statistics of BFRFC pore shape characteristics for each density class
图 6 参数控制的BFRFC建模流程及结果示意
Figure 6. Parameter-controlled BFRFC modeling process and results
图 7 BFRFC数值模型的网格划分示意图
Figure 7. Schematic mesh delineation of the numerical model of BFRFC
图 9 BFRFC材料本构关系
Figure 9. BFRFC material ontological relationship
Point A represents the onset of material damage, point B corresponds to the damage state at any given moment, and point C represents the moment when the material is completely degraded; Ei0 and Eid denotes the initial elastic modulus and the hardening modulus of the material after yielding. εeq0, εeq and εeqf represents the yield strain, strain, and ultimate strain
图 10 各BFRFC试样的应力-应变关系曲线
Figure 10. Stress-strain relationship curves for each BFRFC specimen
图 12 BFRFC单轴压缩结果示意图
Figure 12. Schematic diagram of BFRFC uniaxial compression results
表 1 玄武岩纤维增强泡沫混凝土的配合比及密度(kg/m3)
Table 1. Mix ratio and density of basalt fiber reinforced foam concrete (kg/m3)
Sample No. Cement Water Basalt fiber Foam Wet density Dry density A08-0 416.67 208.33 0 35.49 944.31 868.03 A08-0.15% 416.67 208.33 4.2 35.49 959.33 840.00 A08-0.30% 416.67 208.33 8.4 35.49 1002.33 891.33 A08-0.45% 416.67 208.33 12.6 35.49 965.33 846.00 A10-0 743.05 371.53 0 21.83 1187.60 1075.05 A10-0.15% 743.05 371.53 4.2 21.83 1240.33 1138.00 A10-0.30% 743.05 371.53 8.4 21.83 1226.00 1073.00 A10-0.45% 743.05 371.53 12.6 21.83 1235.67 1131.33 Notes: Sample number A08-0.15% represents the design of dry density of 800 kg/m3 and the volume of basalt fiber mixed with 0.15%. 
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表 2 各组玄武岩纤维增强泡沫混凝土的孔隙率(%)
Table 2. Porosity (%) of each group basalt fiber reinforced foam concrete
Density grade Fiber content X-CT analysis Saturated water absorption A08 0 15.43 15.87 0.15% 14.91 15.29 0.30% 14.44 14.84 0.45% 14.02 13.75 A10 0 10.94 11.51 0.15% 10.39 10.45 0.30% 10.54 10.92 0.45% 9.93 10.75
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表 3 BFRFC代表试样的孔隙尺寸特征
Table 3. Pore size features of representative BFRFC specimens
Sample No. Fiber content Porosity/% Pore diameter/μm Distribution parameters Max Min Average $\mu $ $\sigma $ A08 0 15.43 4480.61 44.54 425.15 5.99 0.34 0.15% 14.91 4503.13 44.54 437.94 5.98 0.37 0.30% 14.44 4534.57 44.54 447.85 6.11 0.34 0.45% 14.02 4556.17 44.54 458.14 6.03 0.40 A10 0 10.94 3000.06 44.54 244.18 5.71 0.29 0.15% 10.39 3035.25 44.54 245.92 5.66 0.30 0.30% 10.54 3094.54 44.54 294.85 5.75 0.27 0.45% 9.93 3136.87 44.54 307.14 5.77 0.32 Notes: The minimum pore diameter of the measured BFRFC specimens is 44.54 μm due to the limitation of testing accuracy and resolution of the X-CT equipment. In fact, the minimum pore diameter of each specimen should be less than 44.54 μm and different from each other
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表 4 计算机性能表
Table 4. Computer Performance Specifications
Component Specifications Processor (CPU) AMD Ryzen Threadripper 3990 X<br> 32 cores / 64 threads<br> Base frequency :
3.7 GHz<br>Max boost frequency: 4.5 GHzGraphics Processor (GPU) NVIDIA RTX 4090<br>VRAM: 24 GB GDDR6 X Memory (RAM) 256 GB DDR4 ECC<br>Frequency: 3200 MHz Primary Storage 2 TB NVMe SSD (Samsung 980 PRO) Secondary Storage 4 TB NVMe SSD (Samsung 970 EVO Plus) Mass Storage 10 TB HDD (Seagate IronWolf Pro) Operating System Windows 11 Pro or Ubuntu 22.04 LTS Motherboard ASUS ROG Zenith II Extreme Alpha<br>Supports multiple GPU slots (PCIe 4.0)<br>8 DIMM slots<br>USB 3.2<br>Wi-Fi 6<br>10 G Ethernet
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表 5 三维Hashin失效准则判断标准
Table 5. Three-dimensional Hashin Failure Criteria
Failure mode Standard of judgment Fiber tension ${\hat \sigma _{11}} \geqslant 0$ $F_{\text{f}}^{\text{t}} = {\left( {\dfrac{{{{\hat \sigma }_{11}}}}{{{X^{\text{T}}}}}} \right)^2} + \alpha {\left( {\dfrac{{{{\hat \tau }_{12}}}}{{{S^{\text{L}}}}}} \right)^2} \leqslant 1$ Fiber compression${\hat \sigma _{11}} < 0$ $F_{\text{f}}^{\text{c}} = {\left( {\dfrac{{{{\hat \sigma }_{11}}}}{{{X^{\text{C}}}}}} \right)^2} \leqslant 1$ Cement matrix tension ${\hat \sigma _{22}} \geqslant 0$ $F_{\text{m}}^{\text{t}} = {\left( {\dfrac{{{{\hat \sigma }_{22}}}}{{{Y^{\text{T}}}}}} \right)^2} + {\left( {\dfrac{{{{\hat \tau }_{12}}}}{{{S^{\text{L}}}}}} \right)^2} \leqslant 1$ Cement matrix compression ${\hat \sigma _{22}} < 0$ $F_{\text{m}}^{\text{c}} = {\left( {\dfrac{{{{\hat \sigma }_{22}}}}{{2{S^{\text{T}}}}}} \right)^2} + \left[ {{{\left( {\dfrac{{{Y^{\text{C}}}}}{{2{S^{\text{T}}}}}} \right)}^2} - 1} \right] \cdot \dfrac{{{{\hat \sigma }_{22}}}}{{{Y^{\text{C}}}}} + {\left( {\dfrac{{{{\hat \tau }_{22}}}}{{{S^{\text{L}}}}}} \right)^2} \leqslant 1$ Notes:$X_{\text{T}}^{}$ and ${X_{\text{C}}}$ represent the longitudinal tensile and compressive strengths, respectively; ${Y_{\text{T}}}$and ${T_{\text{C}}}$ denote the transverse tensile and compressive strengths of the specimen, respectively; ${S_{\text{L}}}$and${S_{\text{T}}}$ are the longitudinal and transverse shear strengths of the specimen, respectively; $\alpha $ is the coefficient of contribution of shear stress to fiber tension ($0 \leqslant \alpha \leqslant 1$); $\hat \sigma $ is the assessment coefficient for material damage.
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表 6 各类损伤变量
Table 6. Impairment variables by category
Damage pattern Value of the damage variable Fiber material damage $D{}_1 = \phi \left( {\max \left\{ {F_{\text{f}}^{\text{t}},F_{\text{f}}^{\text{c}}} \right\}{\text{ }}} \right)$ Cement matrix damage $D{}_2 = \phi \left( {\max \left\{ {F_{\text{m}}^{\text{t}},F_{\text{m}}^{\text{c}}} \right\}{\text{ }}} \right)$ Composite shear damage ${D_3} = 1 - (1 - {D_1})(1 - {D_2})$
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表 7 各BFRFC试样的峰值强度差异(MPa)
Table 7. Differences in peak strength of each BFRFC specimen (MPa)
Density grade Fiber content Simulation results Actual results Absolute error Relative error A08 0.15% 4.17 4.01 0.16 3.99% 0.30% 5.02 5.50 0.48 8.73% 0.45% 6.36 6.59 0.23 3.49% A10 0.15% 7.44 7.04 0.40 5.68% 0.30% 8.12 8.33 0.21 2.52% 0.45% 10.59 11.18 0.59 5.25%
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