Containment Mechanism and Structural Optimization Research for Disk Containment of High-Energy Rotor

LIU Zhiqiang; JU Xiaorong; XUAN Haijun; CHEN Liqiang; HE Zekan

doi:10.11858/gywlxb.20220584

Volume 36 Issue 6

Dec 2022

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References

Chinese Journal of High Pressure Physics > 2022 > 36(6): 064101.

CHEN Weishan, TAN Yi, TAN Dayong, XIAO Wansheng. First-Principles Theoretical Study on the Structure Behaviors of NaPO3 under Compression[J]. Chinese Journal of High Pressure Physics, 2024, 38(5): 050106. doi: 10.11858/gywlxb.20240755

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LIU Zhiqiang, JU Xiaorong, XUAN Haijun, CHEN Liqiang, HE Zekan. Containment Mechanism and Structural Optimization Research for Disk Containment of High-Energy Rotor[J]. Chinese Journal of High Pressure Physics, 2022, 36(6): 064101. doi: 10.11858/gywlxb.20220584

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Containment Mechanism and Structural Optimization Research for Disk Containment of High-Energy Rotor

doi: 10.11858/gywlxb.20220584

1.
AECC Commercial Aircraft Engine Co., Ltd., Shanghai 201306, China
2.
College of Energy Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China
3.
AVIC Nanjing Engineering Institute of Aircraft Systems, Nanjing 211106, Jiangsu, China

Received Date: 13 May 2022
Rev Recd Date: 20 Jun 2022

Available Online: 23 Nov 2022

Issue Publish Date: 05 Dec 2022

Abstract

Abstract

In order to study the mechanism for disk containment of high-energy rotor, with test rotor manufactured with precast cracks, containment tests are carried out using a high-speed spin tester, and the nonlinear explicit dynamics commercial software is used to simulate the containment process of the high-energy rotor. It is found that the impacted area and the edge material in the containment case are compressed and sheared respectively after the impact of the disk fragments by test and simulation results. If the local perforation failure does not occur, the penetration of the fragment is determined by the tensile strain energy of the impacted area and the circumferential extension of the case. Then taking some turbine starter disk an example, the thickness and material analysis of the containment ring are discussed. The design method of determining the allowable thickness of the containment ring by the critical containment thickness 1.15 times of the safety factor is proved. By comparing the containment capacity of different materials, it is concluded that using higher ultimate strength and elongation material to achieve significant weight reduction. This study has some significance to the design of the containment structure of the high energy rotor.
- high-energy rotor,
- disk containment,
- containment ring,
- structural optimization

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泡沫金属质轻，具有较高的比刚度和比强度，以及隔热、电磁屏蔽等物理性能^[1]，在汽车交通、铁路、航空航天等领域广泛应用，如用于飞机外壳夹层、汽车防冲档。除此之外，泡沫金属在受到压缩时，由于其应变滞后于应力，压缩应力-应变曲线中有一个很长的低应力平台，可承受较大的塑性变形，因此泡沫金属具有良好的吸能特性，可用于缓和冲击的工程构件、能量吸收和防振构件^[2]。

目前，常温下泡沫金属的静/动态本构关系已经得到广泛的研究。Chen和Lu^[3]提出了一个依赖于特征应力和总应变的应力势，在此基础上建立了一个唯象的可压缩弹塑性本构模型的框架。该模型避免了人为区分应力-应变的弹塑性区带来的影响。王二恒等^[4]利用Chen和Lu^[3]提出的唯象本构模型框架，建立了一个泡沫金属准静态本构模型，得到了泡沫金属在三维等比例压缩和侧向受约束轴向压缩时的宏观应力-应变曲线。王志华等^[5]提出了一个多参数的非线性弹塑性唯象本构模型，可以全面地描述泡沫金属材料线弹性段、应力平台段和密实段的典型三阶段变形特征。

泡沫金属是一种典型的低成本轻质材料，其复合结构有望作为近空间飞行器中的重要结构部件。但是，近空间飞行器苛刻的应用环境不但要求其结构轻质化，而且要求泡沫金属在高温下有较好的承载、隔热和冲击吸能能力。目前，考虑温度效应的泡沫金属力学行为的研究还比较少。Hakamada等^[6]开展了ALPORAS闭孔泡沫铝及其基体材料在温度范围573~ 773 K内的准静态压缩试验，发现闭孔泡沫铝在高温下的变形机制与其基体材料的变形机制本质上是相同的。Aly^[7]开展了ALPORAS闭孔泡沫铝在常温和高温下的压缩实验，研究了相对密度和实验温度的影响，研究发现，胞壁屈曲是闭孔泡沫铝的主要变形机制，增大密度与升高实验温度对泡沫金属力学性能的影响刚好相反。Cady等^[8]研究了ALPORAS泡沫铝在不同应变率(0.001~1 800 s^-1)和不同温度条件(77~295 K)下的力学性能，结果表明，闭孔泡沫铝的力学性能对温度具有很强的依赖性。

考虑泡沫金属温度效应的本构关系相关研究也比较匮乏。习会峰等^[9]开展了-50~300 ℃范围内不同温度下泡沫铝的静态压缩实验，建立了考虑温度效应的泡沫铝静态压缩本构模型。王鹏飞等^[10]基于Sherwood和Frost提出的本构关系框架，分析了泡沫铝本构方程中温度效应与应变率效应的耦合关系，对本构方程中的应变率敏感系数进行了适当修正，修正后的本构关系与实验结果的重合性较好，在此基础上得到了泡沫铝在一定密度范围内包含温度、应变率影响的较为完备的本构方程。

本研究通过开展不同密度(0.322~0.726 g/cm³)的泡沫铝在不同温度(25~500 ℃)下的准静态压缩实验，分析泡沫铝在不同温度下的力学性能，测得不同温度下泡沫铝的单轴压缩应力-应变曲线。基于Liu-Subhash模型^[11]，对不同温度下的实验数据进行拟合，建立考虑温度效应和密度效应的泡沫铝准静态压缩本构模型。

1. 实验方法及方案

实验材料为闭孔泡沫铝，由上海奥深特金属复合材料科技有限公司提供。本研究采用的闭孔泡沫铝材料原尺寸为400 mm×400 mm×600 mm，孔径介于2~5 mm之间。准静态压缩实验采用线切割技术加工圆柱形试件。为了保证均匀性，排除胞孔尺寸影响，试件高度和直径不小于5个胞孔，试件尺寸为Ø32 mm×15 mm。实验前，对每个试样进行称量，得到其真实的相对密度，测得试样密度范围为0.322~0.796 g/cm³。

准静态实验在MTS810材料试验机上进行，加载速率为0.001 s^-1。实验温度分别取25、200、275、350、425和500 ℃，高温实验在MTS810自带的高温箱中进行，温度误差为±5 ℃。

2. Liu-Subhash本构模型

为了准确描述泡沫材料应力-应变曲线的三阶段特征，Liu与Subhash^[11]提出了一维六参数本构模型

$\sigma \text{=}{{p}_{1}}\frac{{{\text{e}}^{{{p}_{2}}\varepsilon }}-1}{{{p}_{6}}+{{\text{e}}^{{{p}_{\text{3}}}\varepsilon }}}+{{\text{e}}^{{{p}_{4}}}}\left( {{\text{e}}^{{{p}_{5}}\varepsilon }}-1 \right)$

(1)

式中：σ为压缩应力，ε为压缩应变，p₁、p₂、p₃、p₄、p₅和p₆为用于描述泡沫材料性质的参数。p₁主要描述压缩时屈服应力的变化；p₂和p₃为无量纲参数，主要描述应力平台阶段的硬化性能；p₄和p₅主要描述密实阶段的起点和密实阶段斜率的大小；p₆主要描述弹性段斜率的大小。从模型中可以看出，参数p₆的作用可以用p₁和p₃代替。习会峰等^[9]提出简化模型，用常数1取代参数p₆，将其简化为五参数模型

$\sigma \text{=}{{p}_{1}}\frac{{{\text{e}}^{{{p}_{2}}\varepsilon }}-1}{1+{{\text{e}}^{{{p}_{\text{3}}}\varepsilon }}}+{{\text{e}}^{{{p}_{4}}}}\left( {{\text{e}}^{{{p}_{5}}\varepsilon }}-1 \right)$

(2)

3. 实验结果与分析

3.1 包含密度效应的泡沫铝本构模型

3.1.1 密度对应力-应变曲线的影响

图 1为不同密度ρ下泡沫铝的准静态压缩应力-应变实验曲线。从实验结果来看，泡沫铝的应力-应变曲线的形状及发展趋势相似，呈典型的三阶段特性，即：较小应变下的线弹性阶段、对应于胞壁塑性坍塌而缓缓上升的应力平台阶段和密实后的应力迅速上升阶段。从图 1中可以看出，泡沫铝材料的初始密度对其应力-应变曲线影响巨大，随着密度的增大，曲线依次抬高，屈服强度也相应增大，但压缩至致密段的最大应变量减小。因此，在基体材料相同的情况下，在一定的密度范围内，泡沫铝材料的力学性能主要由材料的初始密度决定，初始密度越大，材料承载能力越强。

图 1 常温下不同密度泡沫铝的准静态应力-应变曲线

Figure 1. Quasi-static stress-strain curves of aluminum foam with different densities at room temperature

下载: 全尺寸图片幻灯片

3.1.2 基于Liu-Subhash模型的实验数据拟合

基于简化的Liu-Subhash模型，对实验得到的常温下不同密度泡沫铝的准静态应力-应变曲线进行拟合，得到不同密度泡沫铝材料的模型参数值，如表 1所示。实验曲线和拟合曲线如图 2所示，可见拟合效果较好，可采用该模型描述泡沫铝的单轴准静态压缩应力-应变关系。

表 1 不同密度下的模型参数值

Table 1. Parameter values for different densities

Density/(g·cm^-3)	Parameter
Density/(g·cm^-3)	p₁	p₂	p₃	p₄	p₅
0.322	3.08	86.09	86.22	-6.49	11.60
0.481	5.98	90.83	90.74	-4.66	10.98
0.639	9.31	91.20	90.89	-3.00	9.41
0.726	12.01	92.04	92.14	-1.33	7.41

下载: 导出CSV

| 显示表格

图 2 常温下不同密度泡沫铝的应力-应变曲线拟合情况

Figure 2. Fitting of stress-strain curves of aluminum foam with different densities at room temperature

下载: 全尺寸图片幻灯片

3.1.3 考虑密度效应的修正模型

由表 1可知，参数p₁、p₂、p₃、p₄、p₅随密度的变化而变化，显然这5个参数都是密度ρ的函数。因此，(2)式可以写成

$\sigma \text{=}{{p}_{1}}\left( \rho \right)\frac{{{\text{e}}^{{{p}_{2}}\left( \rho \right)\varepsilon }}-1}{1+{{\text{e}}^{{{p}_{\text{3}}}\left( \rho \right)\varepsilon }}}+{{\text{e}}^{{{p}_{4}}\left( \rho \right)}}\left[ {{\text{e}}^{{{p}_{5}}\left( \rho \right)\varepsilon }}-1 \right]$

(3)

(3) 式即为考虑了密度影响的泡沫铝的常温准静态压缩本构模型。图 3为模型中5个参数随密度的变化情况，对实验数据进行拟合，得到5个参数与密度的关系为

$\left\{ \begin{align} & {{p}_{1}}\left( \rho \right)=20.34{{\rho }^{1.69}} \\ & {{p}_{2}}\left( \rho \right)=94.58{{\rho }^{0.08}} \\ & {{p}_{3}}\left( \rho \right)=94.41{{\rho }^{0.08}} \\ & {{p}_{4}}\left( \rho \right)=12.34\rho -10.55 \\ & {{p}_{5}}\left( \rho \right)=-8.6\rho +14.68 \\ \end{align} \right.$

(4)

图 3 常温下参数随密度的变化规律

Figure 3. Variation of parameters with density at room temperature

下载: 全尺寸图片幻灯片

由(3)式和(4)式得到考虑密度效应的闭孔泡沫铝静态压缩本构模型，该模型可用于描述不同密度下泡沫铝的应力-应变曲线，具体形式如下

$\sigma =20.34{{\rho }^{1.69}}\frac{{{\text{e}}^{94.58{{\rho }^{0.08}}\varepsilon }}-1}{1+{{\text{e}}^{94.41{{\rho }^{0.08}}\varepsilon }}}\text{+}{{\text{e}}^{12.34\rho -10.55}}\left[ {{\text{e}}^{\left( -8.6\rho +14.68 \right)\varepsilon }}-1 \right]$

(5)

3.2 包含温度效应的泡沫铝本构模型

3.2.1 温度对应力-应变曲线的影响

图 4是密度为0.322 g/cm³的泡沫铝在不同温度下的准静态应力-应变曲线。由图 4可知，随着温度的升高，材料由硬变软，由脆变韧。材料呈现明显的温度软化效应，当温度从25 ℃上升到500 ℃时，泡沫铝屈服强度从4.70 MPa下降到0.88 MPa。

图 4 不同温度下泡沫铝的准静态应力-应变曲线

Figure 4. Quasi-static stress-strain curves of aluminum foam at different temperatures

下载: 全尺寸图片幻灯片

3.2.2 考虑温度效应的修正模型

为了得到包含温度效应的泡沫铝本构模型，引入温度软化项

$H\left( T \right)=1-{{T}^{*m}}$

(6)

式中：T^*为无量纲温度项，m为指数。

${{T}^{*}}=\frac{T-{{T}_{\text{room}}}}{{{T}_{\text{melt}}}-{{T}_{\text{room}}}}$

(7)

式中：T_room为室温，T_room=298 K；T_melt为铝合金的熔点，T_melt=933 K。

因此，(3)式可进一步写成

$\sigma =\left\{ {{p}_{1}}\left( \rho \right)\frac{{{\text{e}}^{{{p}_{2}}\left( \rho \right)\varepsilon }}-1}{1+{{\text{e}}^{{{p}_{3}}\left( \rho \right)\varepsilon }}}\text{+}{{\text{e}}^{{{p}_{4}}\left( \rho \right)}}\left[ {{\text{e}}^{{{p}_{5}}\left( \rho \right)\varepsilon }}-1 \right] \right\}\cdot \left[ 1-{{\left( \frac{T-{{T}_{\text{room}}}}{{{T}_{\text{melt}}}-{{T}_{\text{room}}}} \right)}^{m}} \right]$

(8)

(8) 式即为考虑温度效应和密度效应的泡沫铝准静态本构模型。基于该模型，对不同温度下得到的准静态压缩应力-应变曲线进行拟合，得到参数m=1.31。不同温度下泡沫铝的应力-应变实验及拟合曲线如图 5所示。从图 5中可以看到，应力平台阶段和压实段拟合曲线与实验曲线吻合较好，说明该模型可用于描述不同温度下泡沫铝的应力-应变曲线。但在弹性段，拟合曲线与实验结果吻合得不太好，主要原因是Liu-Subhash模型不能很好地描述应力-应变曲线中的应力降现象，另一方面是由于实验时温度控制不精确产生的误差。总体上拟合曲线可以反映实验曲线的特征，拟合得到的参数值是可信的。

图 5 不同温度下泡沫铝应力-应变曲线的拟合情况

Figure 5. Fitting of stress-strain curves of aluminum foam at different temperatures

下载: 全尺寸图片幻灯片

4. 结论

利用MTS万能材料试验机研究了不同密度(0.322~0.726 g/cm³)的闭孔泡沫铝在不同温度(25~500 ℃)下的静态压缩力学性能，实验结果表明：泡沫铝材料的初始密度对其应力-应变曲线影响巨大，随着密度的增大，屈服强度也相应增大，材料承载能力增强；随着温度的升高，泡沫铝材料力学特性由硬变软，呈现明显的温度软化效应。利用Liu-Subhash模型对不同密度下的实验数据进行拟合，拟合效果很好，分析并确定了模型中5个参数随密度变化的函数，并代入Liu-Subhash模型，得到了考虑密度效应的本构模型；又引入温度软化项对本构模型进行修正，建立了综合考虑温度效应和密度效应的泡沫铝准静态压缩本构模型。

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沈阳化工大学材料科学与工程学院沈阳 110142

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