304不锈钢纤维/ZL104铝合金复合泡沫的孔结构、力学、吸声性能及其机理

doi:10.11901/1005.3093.2021.675

304不锈钢纤维/ZL104铝合金复合泡沫的孔结构、力学、吸声性能及其机理

苗琪¹, 左孝青^,¹, 周芸¹, 王应武¹^,², 郭路¹, 王坦¹, 黄蓓¹

1.昆明理工大学材料科学与工程学院昆明 650093

2.云南省科学技术院高新技术中心昆明 650051

Pore Structure, Mechanical and Sound Absorption Performance for Composite Foam of 304 Stainless Steel Fiber/ZL104 Aluminum Alloy

MIAO Qi¹, ZUO Xiaoqing^,¹, ZHOU Yun¹, WANG Yingwu¹^,², GUO Lu¹, WANG Tan¹, HUANG Bei¹

1.School of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China

2.Centre of Advanced Technology, Yunnan Provincial Academy of Science and Technology, Kunming 650051, China

通讯作者: 左孝青，教授，zxqdzhhm@kmust.edu.cn，研究方向为多孔金属材料、金属基复合材料及有色金属材料

责任编辑: 黃青

收稿日期: 2021-12-07 修回日期: 2022-03-10

基金资助:

国家自然科学基金(52261009)
国家自然科学基金(51861020)
国家自然科学基金(51741103)
云南省重大科技专项(2019ZE008)

Corresponding authors: ZUO Xiaoqing, Tel: 13108899276, E-mail:zxqdzhhm@kmust.edu.cn

Received: 2021-12-07 Revised: 2022-03-10

Fund supported:

National Natural Science Foundation of China(52261009)
National Natural Science Foundation of China(51861020)
National Natural Science Foundation of China(51741103)
Key Science and Technology Project of Yunnan Province(2019ZE008)

作者简介 About authors

苗琪，男，1996年生，硕士

摘要

用渗流铸造法制备ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫，对比研究了两种泡沫的孔结构、力学和吸声性能及其机理。结果表明，调控盐(次盐)的作用使合金泡沫和复合泡沫的孔壁上出现次孔结构而生成多孔孔壁结构；纤维复合后的泡沫以孔壁纤维、穿孔纤维和孔间纤维三种状态存在，与相同孔隙率的合金泡沫相比，复合泡沫的孔隙率为77%~86%、主孔径为0.35 mm、纤维直径为0.1 mm，具有更高的压缩性能和吸声性能。复合泡沫的压缩性能和吸声性能，都随着孔隙率和纤维含量的提高先提高后降低。孔隙率为82%的复合泡沫，纤维含量(体积分数)为5%时力学性能达到2.6 MPa，纤维含量为8%时其平均吸声系数(吸声性能)为0.893。有限元分析结果表明，复合泡沫受力时，孔壁纤维和穿孔纤维能传递和分散应力，并通过位移和偏转等方式消耗能量，使其强度提高；J-A模型分析结果表明，突出到孔隙中的纤维使复合泡沫的表面粗糙度和比表面积和声波在泡沫内的损耗增大，是其吸声性能较高的原因。

关键词： 复合材料; 304不锈钢纤维/ZL104复合泡沫; 渗流铸造; 吸声性能; 力学性能; 孔隙率

Abstract

Foam materials of ZL104 alloy and 304 stainless steel fiber/ZL104 alloy composite were prepared by the infiltration casting method, and their pore structure, mechanical performance, sound absorption properties and the relevant mechanisms were investigated. The results show that within the prepared foam materials, there exist interconnected larger pores, and on the wall of which, there are many smaller sub-pores. The formation of such sub-porous structure may be ascribed to the effect of the second moderating salt adopted for the infiltration casting. Moreover, the fibers present in three states in the composite foam: pore wall fiber, perforated fiber, and inter-porous fiber. The typical composite foam with fiber diameter of 0.1 mm and porosity of 77-86%, while the mean diameter of 0.35mm for the main pores. The composite foam has better compression yield strength and sound absorption performance rather that those of the alloy foam with the same porosity. The compression and sound absorption properties of composite foams increased first and then decreased with the increasing porosity and fiber content. It is wealthy noted that among others the compression yield strength reaching the peak value of 2.6 MPa for the foam with porosity of 82% and fiber content of 5%, accordingly, the average sound absorption coefficient reaching the peak value 0.893 for the composite foam with porosity of 82% and fiber content of 8%, respectively. Finite element analysis shows that when being pressed, the pore wall fibers and perforated fibers can transfer and disperse stress, and the energy can be consumed by displacement and deflection of the fibers, thus enhancing the strength of the composite foam. J-A model analysis shows that the fibers protruded into the pores increase the surface roughness and specific surface area of the foam, resulting in an increasing acoustic wave loss of the composite foam, which is the reason for the higher sound absorption property of the composite foam.

Keywords： composites; 304 stainless steel fiber/ZL104 composite foam; infiltration casting; sound absorption performance; mechanical performance; porosity

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本文引用格式

苗琪, 左孝青, 周芸, 王应武, 郭路, 王坦, 黄蓓. 304不锈钢纤维/ZL104铝合金复合泡沫的孔结构、力学、吸声性能及其机理[J]. 材料研究学报, 2023, 37(3): 175-183 DOI:10.11901/1005.3093.2021.675

MIAO Qi, ZUO Xiaoqing, ZHOU Yun, WANG Yingwu, GUO Lu, WANG Tan, HUANG Bei. Pore Structure, Mechanical and Sound Absorption Performance for Composite Foam of 304 Stainless Steel Fiber/ZL104 Aluminum Alloy[J]. Chinese Journal of Materials Research, 2023, 37(3): 175-183 DOI:10.11901/1005.3093.2021.675

渗流泡沫铝独特的开孔结构，使其具有低密度、高比强度、耐温、不吸湿和可回收等特性^[1~5]。这种泡沫铝对频率高于800Hz的噪声有良好的吸收性能^[6]，有广阔的应用前景^[7~12]。

渗流泡沫铝的孔隙率，对其吸声性能有显著的影响^[13~19]。低孔隙率(孔隙率低于70%)渗流泡沫铝在1000~5800 Hz的平均吸声系数低于0.7^[6]。随着孔隙率的提高其吸声性能提高，但是力学性能严重降低^{[20, 21]}。Wang Hui等^[22]发现，孔隙率从61.5%提高到65.5%时，泡沫铝的吸声系数增大了11.24%；Liu^[23]制备的孔隙率为85%~96%的高孔隙率渗流泡沫铝，其屈服强度只有0.13~0.28 MPa；Wu^[21]采用熔模铸造法制备的孔隙率为85%~93.5%的开孔泡沫铝，其屈服强度也只有0.086~0.102 MPa。改性处理和T6热处理使泡沫铝的屈服强度有所提高(0.235 MPa)，但是仍然不能满足作为结构材料使用的要求。

制备兼具高力学性能及高吸声性能的渗流泡沫铝，是重要的研究方向。提高渗流泡沫铝力学性能最有效方法，是对泡沫基体进行复合化处理，用颗粒、晶须或纤维等材料使其强化^[24~31]。Altinkök^[24]研究了Al₂O₃/SiCp复合材料，发现起抗拉强度随着SiCp粒径的减小而提高；郭成等^[25]制备了MgAl₂O₄晶须增强铝基复合泡沫材料，发现MgAl₂O₄晶须使其压缩性能大大提高；Zhang等^[27]制备了编织碳纤维增强铝基复合材料，发现纤维复合使其力学性能明显提升；Mu等^[28]制备了碳纤维/泡沫铝复合材料，发现纤维含量(体积分数)为5%的复合泡沫其压缩性能比纤维含量为1%的复合泡沫明显提高。本文制备ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫，研究孔隙率和纤维含量对复合泡沫力学性能和吸声性能的影响并分析其机理。

1 实验方法

1.1 试样的制备

基体材料为ZL104铝合金(9.3%Si，0.25%Mg和0.32%Mn)，渗流前驱体为NaCl颗粒，其直径分别为0.35 mm(主盐)和0.12 mm(调控盐)，比例为7∶1.2，增强体为304不锈钢纤维( $ϕ$ 0.1 mm×5 mm)。将前驱体颗粒和不锈钢纤维均匀混合后压制成预制体，然后将其加热到650℃，保温30 min后用ZL104合金熔体进行压力渗流(渗流压力0.4~0.8 MPa)。渗流体凝固后用水将其中的盐颗粒溶除，通过工艺调控制备的试样参数列于表1。试样的孔隙率范围为77%~86%，制备的合金泡沫(不含纤维的泡沫，1#~5#)及复合泡沫(6#~13#)纤维含量(体积分数)分别为0%、2%、5%、8%和11%。

表1 合金泡沫和复合泡沫试样的参数

Table 1 Sample parameters of alloy foams and composite foams

Sample	Pore size/mm	Porosity/%	Fiber content/volume fraction, %	Fiber size/mm²
1#	0.35+0.12	77	0	…
2#	0.35+0.12	80	0	…
3#	0.35+0.12	82	0	…
4#	0.35+0.12	84	0	…
5#	0.35+0.12	86	0	…
6#	0.35+0.12	77	8	$ϕ$ 0.1×5
7#	0.35+0.12	80	8	$ϕ$ 0.1×5
8#	0.35+0.12	82	8	$ϕ$ 0.1×5
9#	0.35+0.12	84	8	$ϕ$ 0.1×5
10#	0.35+0.12	86	8	$ϕ$ 0.1×5
11#	0.35+0.12	82	2	$ϕ$ 0.1×5
12#	0.35+0.12	82	5	$ϕ$ 0.1×5
13#	0.35+0.12	82	11	$ϕ$ 0.1×5

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1.2 性能表征

(1) 用SEM(S-3400N型)表征孔结构，包括孔形貌、纤维分布以及纤维-基体结合情况；用盐颗粒粒径、结合扫描电镜表征孔径；用纤维与复合泡沫基体的体积比表征纤维含量；孔隙率为

ϕ = (1 - \frac{ρ_{1}}{ρ_{0}}) ∙ 100 % = (1 - \frac{M}{V} ∙ \frac{1}{ρ_{0}}) ∙ 100 %

(1)

式中 $ϕ$ 为泡沫孔隙率； $ρ_{0}$ 为ZL104铝合金密度(2.65 g/cm³)； $ρ_{1}$ 为泡沫试样密度，用排水法测量； $M$ 为泡沫试样质量； $V$ 为泡沫试样体积。

(2) 用Autograph AG-X100KN万能试验机测试泡沫试样(直径和厚度为30 mm)的压缩性能，对试样准静态压缩的速率为3 mm/min。

(3) 根据国家标准GB/T 18696.2-2002，基于传递阻抗法，在刚性背衬条件下用SW-477阻抗管测试泡沫试样(直径和厚度为30 mm)在1000~5800 Hz频率范围内的垂直入射吸声系数。

(4) 有限元模拟：使用COMSOL Multiphysics ®有限元软件对复合泡沫压缩过程进行有限元模拟，结合复合泡沫的力学性能分析纤维复合对复合泡沫力学性能的影响机理。

(5) J-A模型分析：采用J-A模型表征复合泡沫的吸声性能，结合测量的复合泡沫的吸声系数分析纤维影响复合泡沫吸声性能的机理。

2 结果和讨论

2.1 ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫的孔结构

图1给出了ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫的孔结构。由图1a可见，合金泡沫的孔结构均匀，孔径偏差较小，大部分孔隙呈扁圆形，孔隙间彼此贯通，几乎看不到闭孔结构；由图1b、c可见，纤维复合后孔壁的粗糙度和孔结构的复杂程度明显提高，部分孔壁变为纤维/合金复合孔壁，孔壁也比合金泡沫的更薄；另外，在合金泡沫和复合泡沫孔壁上都有次孔结构(图1a、b)。其原因是，在预制体混合和压制过程中粒径为0.12 mm的调控盐颗粒填充在粒径为0.35 mm主盐颗粒间隙中，渗流后去除预制体形成了多孔孔壁结构。

图1

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图1 ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫的孔结构以及复合泡沫中纤维的状态

Fig.1 Pore structure of ZL104 alloy foam (a) and 304 stainless steel fiber/ZL104 alloy composite foam (b) and fiber in the composite foam (c~f)

由图1c、d、e可见，纤维不规则地分布在孔壁和孔隙与孔隙之间的合金基体上，有(i)孔壁纤维、(ii)穿孔纤维和(iii)孔间纤维(部分嵌入孔壁、端头部分延伸到孔隙中)三种形态。嵌入孔壁中的纤维(i)和(ii)有利于复合泡沫保持较高的强度，而声波与孔壁和孔壁上的纤维(ii)和(iii)产生的摩擦增大可提高吸声性能。

2.2 力学性能

2.2.1 孔隙率对合金泡沫和复合泡沫压缩性能的影响

图2给出了孔隙率为77%~86%的合金泡沫(图2a，1#~5#)和纤维含量为8%(体积分数)的复合泡沫的应力-应变曲线(图2b，6#~10#)，表2列出了不同孔隙率泡沫试样的屈服强度。由图2可见，合金泡沫和复合泡沫的压缩曲线都有金属泡沫典型的压缩三阶段特征：线弹性阶段、塑性应变阶段以及致密化阶段。可以发现，复合泡沫的塑性变形阶段的曲线比合金泡沫的平滑，表明复合泡沫具有比合金泡沫更高的压缩稳定性。另外还可见，在相同的应变条件下复合泡沫致密化阶段的应力值远比合金泡沫的大，可归结于纤维的增强作用。从表2可见，孔隙率由77%提高到86%，合金泡沫相应的屈服强度从1.9 MPa下降到0.5 MPa，复合泡沫相应的屈服强度从2.15 MPa下降到0.7 MPa，合金泡沫和复合泡沫的屈服强度都随着孔隙率的增大而降低，而复合泡沫的屈服强度高于相同孔隙率的合金泡沫。还可以看出，在孔隙率相同的条件下复合泡沫的屈服强度均高于合金泡沫，表明复合泡沫能承受更大的变形量而不至于压塌。

图2

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图2 孔隙率不同的合金泡沫和复合泡沫试样的压缩应力-应变曲线

Fig.2 Stress-strain curves of alloy foam (a) and composite foams (b) with different porosity

图3

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图3 纤维含量不同的复合泡沫的应力-应变曲线

Fig.3 Stress-strain curves of composite foams with different fiber contents

图4

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图4 合金泡沫和复合泡沫试样的吸声系数与频率的关系

Fig.4 Relationship between sound absorption coeffic-ient and frequency of composite foams with diff-erent porosity (a) composite foam; (b) Compar-ison of 82% porosity alloy foam and composite foam

图5

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图5 纤维含量不同的复合泡沫的吸声系数与频率的关系

Fig.5 Relationship between sound absorption coefficient and frequency of composite foam with different fiber contents

图6

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图6 合金泡沫和复合泡沫的压缩应变

Fig.6 Compressive strain of alloy foam (a) and composite foam (b)

表2 孔隙率不同的泡沫试样的屈服强度

Table 2 Yield strength of composite foam with different porosity

Porosity/%	77	80	82	84	86
Alloy foam/MPa(1#~5#)	1.90	1.30	0.80	0.70	0.50
Composite foam/MPa(6#~10#)	2.15	1.50	1.63	1.10	0.70

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2.2.2 纤维含量对复合泡沫压缩性能的影响

图3给出了孔隙率为82%、纤维含量不同的复合泡沫试样(8#、11#~13#)的应力-应变曲线，表3列出了相应的屈服强度数据。由图3和表3可见，复合泡沫的屈服强度随着纤维含量的提高先提高后降低，最大屈服强度对应的纤维含量即为最佳纤维添加量。纤维含量小于5%的复合泡沫其屈服强度随着纤维含量的提高而提高；纤维含量为5%的复合泡沫(11#)屈服强度最高(2.6 MPa)，比合金泡沫(3#)提高了225%；纤维含量高于5%时屈服强度随着纤维含量的继续提高而逐渐降低，强化效果减弱，导致复合泡沫抵抗外力变形破坏能力降低、屈服强度下降，整体仍比合金泡沫的高。

表3 纤维含量不同的复合泡沫的屈服强度

Table 3 Yield strength of composite foams with different fiber contents

Sample	11#	12#	8#	13#
Fiber content/%	2	5	8	11
Yield strength/MPa	0.60	2.60	1.63	0.90

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2.3 吸声性能

2.3.1 孔隙率对合金泡沫和复合泡沫吸声系数的影响

图4a给出了纤维含量为8%、孔隙率不同的复合泡沫试样(6#~10#)的吸声系数与频率的关系，图4b比较了孔隙率为82%的合金泡沫试样(3#)和复合泡沫试样(8#)的吸声系数，表4列出了试样的平均吸声系数。由图4a可见，在1000~5800 Hz的声频范围内复合泡沫的吸声系数随频率呈振荡变化，出现吸声峰和吸声谷，并且随着孔隙率的提高吸声峰和吸声谷向高频方向移动。由表4可见，复合泡沫的平均吸声系数随着孔隙率的提高先增大后减小，孔隙率为82%的复合泡沫吸声性能最佳，平均吸声系数为0.893。图4b和表4比较了孔隙率同为82%的复合泡沫与和合金泡沫的吸声性能。与相同孔隙率的合金泡沫(3#)相比，复合泡沫(8#)的吸声峰向低频方向移动并具有更高的平均吸声系数，复合泡沫(8#)的平均吸声系数比合金泡沫(3#)提升了10.2%，说明纤维复合能提高复合泡沫的吸声性能。

表4 孔隙率不同的泡沫试样的平均吸声系数

Table 4 Average sound absorption coefficient of composite foam with different porosity

Porosity/%	77	80	82	84	86
Alloy foam(1#~5#)	-	-	0.810	-	-
Composite foam(6#~10#)	0.829	0.870	0.893	0.888	0.832

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2.3.2 纤维含量对复合泡沫吸声系数的影响

图5给出了孔隙率为82%、纤维含量不同的复合泡沫试样(6#~10#)的吸声系数与频率的关系，表5列出了相应的平均吸声系数。由图5和表5可见，复合泡沫的吸声曲线达到峰值频率后，随着纤维含量的提高吸声峰向低频方向移动、峰值增大，吸声性能提高；复合泡沫的平均吸声系数呈先增后减的趋势。纤维含量≤5%时，虽然纤维网络不完整，但是吸声性能比合金泡沫显著提高；纤维含量为8%的复合泡沫(8#)吸声性能最佳，平均吸声系数高达0.893；但是纤维含量高于8%的复合泡沫，吸声性能随着纤维含量的提高逐渐降低。这表明，孔隙率为82%的复合泡沫其最佳吸声性能对应的最优纤维添加量为8%。

表5 纤维含量不同的复合泡沫的平均吸声系数

Table 5 Average sound absorption coefficient of composite foam with different fiber contents

Sample	3#	11#	12#	8#	13#
Fiber content/%	0	2	5	8	11
Average sound absorption coefficient	0.810	0.882	0.884	0.893	0.872

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3 机理分析

3.1 力学性能的机理

使用COMSOL Multiphysics ®有限元软件，对复合泡沫压缩过程进行有限元模拟，图6给出了合金泡沫和复合泡沫(纤维含量5%)压缩前后的应变分布。图6a给出了合金泡沫的应变分布，图6b给出了复合泡沫的应变分布。在图6a及图6b的椭圆区域，在相同应力条件下对比了孔结构变形前(黑色)、后(蓝色)的形态变化。可以看出，未加纤维区域的应变幅度较大，而有纤维区域的演变幅度较小。其原因是，复合泡沫中的纤维受载荷作用时纤维发生位移和偏转(图6b箭头部分)抵耗了部分压缩能量从而增大了对变形的抗力，使复合泡沫的应变较小。

纤维含量为8%的复合泡沫不同位置(A、B、C、D、E、F、G和H)的应力分布，如图7所示。随机选取4个不含纤维和4个含有纤维的孔壁较薄位置进行应力分析，8个位置的应力值列于表6。结合图7和表6可知，复合泡沫受到外力时纤维区域E、F、G、H处的应力值总体上小于无纤维区域的A、B、C、D处。这表明，纤维能将压应力传递和分散，使孔壁的受力均匀化程度提高、降低了应力集中，从而提高了复合泡沫的屈服强度。

图7

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图7 纤维含量为8%的复合泡沫不同位置的应力分布

Fig.7 Stress of alloy composite foams with fiber content 8% at different positions

表6 纤维含量为8%的复合泡沫不同位置的应力

Table 6 Stress values of composite foam with fiber content of 8% at different locations

Position	A	B	C	D	E	F	G	H
Stress /×10⁹ Pa	9.26	8.40	1.98	4.65	3.09	0.746	0.651	1.31

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有限元分析结果表明，在外加载荷相同的条件下复合泡沫的应变和应力均小于合金泡沫，纤维提高复合泡沫力学性能的效果显著；由图1可见，纤维在复合泡沫中的状态主要有孔壁纤维(图1c)、穿孔纤维(图1d)和孔间纤维(图1e)。孔壁纤维和穿孔纤维能在复合泡沫受到外力时产生偏转和位移抵耗部分压缩能量；此外，纤维还能传递和分散应力，降低局部应力集中；纤维还能钉扎裂纹和抑制裂纹扩散、阻碍压缩应变并改变压缩塌陷路径，从而提高复合泡沫抵抗外力变形的能力^{[28, 32]}。随着纤维含量的提高孔壁纤维和穿孔纤维数量、纤维-基体合金结合界面增加，使纤维的增强作用逐渐增大；但是，纤维含量高于5%后，其在泡沫基体中的占比增加使合金基体对纤维的包裹程度降低，降低了纤维增强效果。

3.2 吸声性能的机理

3.2.1 孔隙率的影响

在孔径相同的条件下，随着孔隙率的提高泡沫孔壁变薄、孔隙数量增多、多孔化程度提高和比表面积增大，入射到泡沫内部的声波与孔壁间的摩擦、反射和衍射程度提高，使声能的衰减加剧。另外，孔壁上的次孔结构还能改变穿过其中的空气流速、扰乱或改变声波的传播，使声波与孔壁摩擦增多从而提高泡沫的吸声性能。但是，由图8可见，孔隙率由82%提高到86%使孔壁的厚度减小并使孔隙合并、孔隙增大和孔壁变薄，导致泡沫的通透性过高和比表面积减小，使声波的传播路径线性化，对声波的摩擦、粘滞和反射等效应减弱，从而使泡沫的吸声性能下降。

图8

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图8 孔隙率不同的ZL104合金泡沫的局部孔结构

Fig.8 Local pore structure of ZL104 alloy foam (a) porosity 82% (b) porosity 86%

3.2.2 纤维复合的影响

纤维复合泡沫的吸声性能可用J-A模型^[33]描述：

α = 1 - {|\frac{Z - ρ_{0} c_{0}}{Z + ρ_{0} c_{0}}|}^{2}

(2)

Z = - j \frac{Z_{c}}{ϕ} c o t k t

(3)

Z_{c} = \sqrt[]{K (ω) ρ (ω)}

(4)

k = ω \sqrt[]{ρ (ω) / K (ω)}

(5)

ρ (ω) = ρ_{0} α_{\infty} [1 + \frac{σ ϕ}{j ω ρ_{0} α_{\infty}} {(1 + \frac{4 j α_{\infty}^{2} η ω ρ_{0}}{σ^{2} Λ^{2} ϕ^{2}})}^{1 / 2}]

(6)

K (ω) = γ P_{0} / \{γ - (γ - 1) {[1 + \frac{σ ϕ}{j B^{2} ω ρ_{0} α_{\infty}} {(1 + \frac{4 j α_{\infty}^{2} η ω ρ_{0}}{σ^{' 2} Λ^{' 2} ϕ^{2}})}^{1 / 2}]}^{- 1}\}

(7)

Λ = \frac{1}{c} {(\frac{8 α_{\infty} η}{σ ϕ})}^{1 / 2}

(8)

Λ' = \frac{1}{c'} {(\frac{8 α_{\infty} η}{σ ϕ})}^{1 / 2} = {(\frac{8 α_{\infty} η}{σ' ϕ})}^{1 / 2}

(9)

σ = \frac{8 μ}{ϕ d^{2}}

(10)

式中 $α$ 为吸声系数， $Z$ 为泡沫金属表面阻抗， $Z_{c}$ 为泡沫金属的特性阻抗，k泡沫金属中的声波传播常数，t为泡沫金属厚度，α_∞ 为曲折因子； $ρ_{0}$ 为空气密度；c₀为空气的声速；σ为静流阻率； $ϕ$ 为孔隙率；ω为声波角频率；γ为绝热常数；P₀为空气压强；B² 为空气的prandtl数；η为空气粘滞系数；Λ为粘性特征尺度，表征粘滞损耗占主要时孔隙网络的压缩截面的尺度；Λ′为热特征尺度，表征以热损耗为主时孔隙内表面积较大区域的尺度；d为孔径；μ为表征孔壁表面粗糙度的常数。

孔径、孔隙率、声频和材料的厚度一定时，复合泡沫的吸声系数主要受孔壁粗糙度μ和曲折因子α_∞ 影响。纤维复合后，由于复合泡沫中纤维的含量有限，纤维对曲折度α_∞ 的影响较小，因此其影响可以忽略；孔间纤维和穿孔纤维(图1d，e)使复合泡沫孔壁表面的粗糙度μ和泡沫静流阻率 $σ$ 增大(式10)，于是复合泡沫的粘性特征尺度 $Λ$ (式8)、热特征尺度 ${Λ'}^{}$ (式9)减小、有效弹性模量 $K (ω)$ (式7)、有效密度 $ρ (ω)$ (式6)、特性阻抗 $Z_{c}$ 减小(式4)、表面阻抗 $Z$ (式3)减小，吸声系数 $α$ (式2)增大。

纤维复合后，声波通过孔隙时受到穿孔纤维和孔间纤维以及多孔孔壁的阻碍而发生衍射或绕流，使声波与孔壁之间的碰撞次数增加，还可能带动孔隙中的纤维振动，导致声能损耗的增大。另外，增强体与基体合金之间的微塑性变形、热膨胀失配甚至界面区域周围的高密度位错也能使声能的损耗增大^[26]，从而使吸声性能提高。同时，随着纤维含量的提高，穿孔纤维和孔间纤维数量增多，泡沫的曲折度^[34]、孔壁粗糙度、比表面积以及孔隙中空气的流动阻力都随之增大，摩擦和粘滞性损耗增大，使吸声性能提高；但是，过高的纤维含量(高于8%)时吸声性能下降。其原因是，纤维含量过高使纤维的团聚加剧^[6]、孔隙数量减少(团聚的纤维结合铝液阻塞孔隙)、次孔尺寸增大和孔隙合并。

4 结论

(1) 采用渗流铸造法可制备主孔径为0.35 mm、次孔径为0.12 mm的高孔隙率(77%~86%)ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫；泡沫孔结构中的次孔分布在主孔壁上形成了多孔孔壁，复合泡沫孔结构中的纤维以孔壁纤维、孔间纤维和穿孔纤维三种状态存在。

(2) 纤维复合提高了复合泡沫的力学性能。孔隙率一定时，复合泡沫的屈服强度随着纤维含量的提高先提高后降低；复合泡沫受力时孔壁纤维和穿孔纤维能降低应力集中，纤维以位移和偏转等方式消耗能量而使其力学性能提高。

(3) 纤维复合提高了复合泡沫的吸声性能。在1000~5800 Hz复合泡沫的吸声系数随着孔隙率和纤维含量的提高先提高后降低。根据J-A模型，孔隙率、孔径、曲折因子、声频及材料厚度一定的复合泡沫，纤维复合使其孔壁粗糙度提高和比表面积增大，摩擦和粘滞作用使声波的损耗增大，多孔孔壁结构进一步增大声能损耗从而使其吸声性能提高。

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2019

... 渗流泡沫铝独特的开孔结构，使其具有低密度、高比强度、耐温、不吸湿和可回收等特性^[1~5].这种泡沫铝对频率高于800Hz的噪声有良好的吸收性能^[6]，有广阔的应用前景^[7~12]. ...

Polymer infused composite metal foam as a potential aircraft leading edge material

2020

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2018

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2020

Numerical modelling of the sound absorption spectra for bottleneck dominated porous metallic structures

2019

A comparative analysis of sound absorption performance of ZL104/aluminum fiber composite foam

2019

... 渗流泡沫铝的孔隙率，对其吸声性能有显著的影响^[13~19].低孔隙率(孔隙率低于70%)渗流泡沫铝在1000~5800 Hz的平均吸声系数低于0.7^[6].随着孔隙率的提高其吸声性能提高，但是力学性能严重降低^{[20, 21]}.Wang Hui等^[22]发现，孔隙率从61.5%提高到65.5%时，泡沫铝的吸声系数增大了11.24%；Liu^[23]制备的孔隙率为85%~96%的高孔隙率渗流泡沫铝，其屈服强度只有0.13~0.28 MPa；Wu^[21]采用熔模铸造法制备的孔隙率为85%~93.5%的开孔泡沫铝，其屈服强度也只有0.086~0.102 MPa.改性处理和T6热处理使泡沫铝的屈服强度有所提高(0.235 MPa)，但是仍然不能满足作为结构材料使用的要求. ...

... 纤维复合后，声波通过孔隙时受到穿孔纤维和孔间纤维以及多孔孔壁的阻碍而发生衍射或绕流，使声波与孔壁之间的碰撞次数增加，还可能带动孔隙中的纤维振动，导致声能损耗的增大.另外，增强体与基体合金之间的微塑性变形、热膨胀失配甚至界面区域周围的高密度位错也能使声能的损耗增大^[26]，从而使吸声性能提高.同时，随着纤维含量的提高，穿孔纤维和孔间纤维数量增多，泡沫的曲折度^[34]、孔壁粗糙度、比表面积以及孔隙中空气的流动阻力都随之增大，摩擦和粘滞性损耗增大，使吸声性能提高；但是，过高的纤维含量(高于8%)时吸声性能下降.其原因是，纤维含量过高使纤维的团聚加剧^[6]、孔隙数量减少(团聚的纤维结合铝液阻塞孔隙)、次孔尺寸增大和孔隙合并. ...

Sound absorption properties of Al foam

2005

The rheology of polymer solution elastic strands in extensional flow

2010

Microstructure-based experimental and numerical investigations on the sound absorption property of open-cell metallic foams manufactured by a template replication technique

2018

Primary investigation on sound absorption performance of highly porous titanium foams

2015

Influences of compression ratios on sound absorption performance of porous nickel-iron alloy

2018

A Spherical-pore foamed titanium alloy with high porosity

2015

一种具有球形孔隙的高孔率泡沫钛合金

2015

Sound absorption characteristics of aluminum foams treated by plasma electrolytic oxidation

2015

Thermal and acoustic properties of aluminium foams manufactured by the infiltration process

2013

Sound absorption characteristics and structure optimization of porous metal fibrous materials

2015

Bottom-up approach for microstructure optimization of sound absorbing materials

2008

A simplistic unit cell model for sound absorption of cellular foams with fully/semi-open cells

2015

A statistical method for predicting sound absorbing property of porous metal materials by using quartet structure generation set

2015

Effects of cell parameters at low strain rates on the mechanical properties of metallic foams of Al and 7075-T6 alloy processed by pressurized infiltration casting method

2018

Enhancing the flow resistance and sound absorption of open-cell metallic foams by creating partially-open windows

2021

Effects of modification and heat treatment on energyabsorption capacities of aluminum alloy foams

2011

... [21]采用熔模铸造法制备的孔隙率为85%~93.5%的开孔泡沫铝，其屈服强度也只有0.086~0.102 MPa.改性处理和T6热处理使泡沫铝的屈服强度有所提高(0.235 MPa)，但是仍然不能满足作为结构材料使用的要求. ...

变质处理及热处理对泡沫铝合金压缩吸能性的影响

2011

Sound absorption properties of open-cells aluminum foams prepared by infiltration casting methods

2013

渗流铸造法制备的开孔泡沫铝的声学性能

2013

Preparation of low density open-cell aluminum foam by soluble plaster mould

2010

用可溶石膏型预制块制备低密度开孔泡沫铝

2010

Investigation of mechanical and machinability properties of Al₂O₃/SiCp reinforced Al-based composite fabricated by stir cast technique

2015

... 制备兼具高力学性能及高吸声性能的渗流泡沫铝，是重要的研究方向.提高渗流泡沫铝力学性能最有效方法，是对泡沫基体进行复合化处理，用颗粒、晶须或纤维等材料使其强化^[24~31].Altinkök^[24]研究了Al₂O₃/SiCp复合材料，发现起抗拉强度随着SiCp粒径的减小而提高；郭成等^[25]制备了MgAl₂O₄晶须增强铝基复合泡沫材料，发现MgAl₂O₄晶须使其压缩性能大大提高；Zhang等^[27]制备了编织碳纤维增强铝基复合材料，发现纤维复合使其力学性能明显提升；Mu等^[28]制备了碳纤维/泡沫铝复合材料，发现纤维含量(体积分数)为5%的复合泡沫其压缩性能比纤维含量为1%的复合泡沫明显提高.本文制备ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫，研究孔隙率和纤维含量对复合泡沫力学性能和吸声性能的影响并分析其机理. ...

... [24]研究了Al₂O₃/SiCp复合材料，发现起抗拉强度随着SiCp粒径的减小而提高；郭成等^[25]制备了MgAl₂O₄晶须增强铝基复合泡沫材料，发现MgAl₂O₄晶须使其压缩性能大大提高；Zhang等^[27]制备了编织碳纤维增强铝基复合材料，发现纤维复合使其力学性能明显提升；Mu等^[28]制备了碳纤维/泡沫铝复合材料，发现纤维含量(体积分数)为5%的复合泡沫其压缩性能比纤维含量为1%的复合泡沫明显提高.本文制备ZL104合金泡沫和304不锈钢纤维/ZL104合金复合泡沫，研究孔隙率和纤维含量对复合泡沫力学性能和吸声性能的影响并分析其机理. ...

Compressive properties and energy absorption of aluminum composite foams reinforced by in-situ generated MgAl₂O₄ whiskers

2015

Damping and sound absorption properties of particle reinforced Al matrix composite foams

2003

Fabrication of carbon fibers reinforced Al-matrix composites in pulsed magnetic field

2021

Strain-rate effects on the compressive response of closed-cell copper-coated carbon fiber/aluminum composite foam

2011

... 有限元分析结果表明，在外加载荷相同的条件下复合泡沫的应变和应力均小于合金泡沫，纤维提高复合泡沫力学性能的效果显著；由图1可见，纤维在复合泡沫中的状态主要有孔壁纤维(图1c)、穿孔纤维(图1d)和孔间纤维(图1e).孔壁纤维和穿孔纤维能在复合泡沫受到外力时产生偏转和位移抵耗部分压缩能量；此外，纤维还能传递和分散应力，降低局部应力集中；纤维还能钉扎裂纹和抑制裂纹扩散、阻碍压缩应变并改变压缩塌陷路径，从而提高复合泡沫抵抗外力变形的能力^{[28, 32]}.随着纤维含量的提高孔壁纤维和穿孔纤维数量、纤维-基体合金结合界面增加，使纤维的增强作用逐渐增大；但是，纤维含量高于5%后，其在泡沫基体中的占比增加使合金基体对纤维的包裹程度降低，降低了纤维增强效果. ...

Carbon materials reinforced aluminum composites: a review

2014

Processing and properties of copper-coated carbon fibre reinforced aluminium alloy composites

2009

Research progress on preparation methods and energy absorption properties of hollow particles/metal matrix syntactic foams

2020

空心微珠/金属基复合泡沫制备方法与吸能性能的研究进展

2020

Impact resistance, flexural and tensile properties of amorphous metallic fiber-reinforced cementitious composites according to fiber length

2021

2009

... 纤维复合泡沫的吸声性能可用J-A模型^[33]描述： ...

A review on the taxonomy, factors associated with sound absorption and theoretical modeling of porous sound absorbing materials

2019

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