火箭推进

液体火箭发动机中大量采用延性铜合金,严苛载荷导致其普遍工作于大塑性变形状态。由于无法有效处理拉伸试验颈缩后数据,传统工程强度分析所用材料本构无法充分反映出材料的真实承载能力。针对某延性铜合金开展常温单轴拉伸试验,并从工程强度分析的角度提出通用修正函数与参数拟合原则,随后通过有限元颈缩仿真拟合得到加权因子w=0.75和指数修正因子n=2.4。研究表明,有限元颈缩仿真的载荷-位移响应对模型参数和网格具有收敛性,指数修正方法可更好地描述铜合金试件颈缩后响应,选取n=2.4可得到偏保守的材料性能估计。

Ductile copper alloys are widely used in liquid rocket engines, which are generally subjected to large plastic deformation due to extreme loads. Due to the lack of method to effectively process the post-necking data of tensile tests, traditional material constitutive models used in engineering structural analysis failed to fully reflect the real bearing capacity of materials. Uniaxial tensile tests were carried out at room temperature for a ductile copper alloy, and the universal correction function and parameter fitting principles were proposed from the perspective of engineering structural strength analysis. Then, the weighted factor w=0.75 and the exponential correction factor n=2.4 were obtained through the FEM necking simulation. The results show that the load-displacement response of the finite element necking simulation is convergent to the model parameters and mesh. The exponential correction method can better describe the post-necking response of copper alloy specimens. A conservative material property estimate can be obtained by selecting n=2.4.

引言
1 单轴拉伸试验
2 理论与方法
3 本构数值方法与对比
4 颈缩仿真与分析
5 结论

图1 单轴拉伸试验及试验件<br/>Fig.1 Tensile test and the geometry of specimens

图1 单轴拉伸试验及试验件
Fig.1 Tensile test and the geometry of specimens

图2 单轴拉伸试验结果<br/>Fig.2 Results of the monotonic tensile test

图2 单轴拉伸试验结果
Fig.2 Results of the monotonic tensile test

表1 铜合金单轴拉伸力学性能参数<br/>Tab.1 Mechanical properties obtained from the monotonic tensile test of a copper alloy

表1 铜合金单轴拉伸力学性能参数
Tab.1 Mechanical properties obtained from the monotonic tensile test of a copper alloy

表2 不同平均应力修正因子<br/>Tab.2 Different correction factors

表2 不同平均应力修正因子
Tab.2 Different correction factors

表3 铜合金不同多线性本构模型参数<br/>Tab.3 Parameters of different multilinear constitutive models forcopper alloy

表3 铜合金不同多线性本构模型参数
Tab.3 Parameters of different multilinear constitutive models forcopper alloy

图3 不同本构模型预测应力-应变曲线与试验数据对比<br/>Fig.3 Comparison of stress-strain curves predicted by various constitutive models and obtained from the experiment

图3 不同本构模型预测应力-应变曲线与试验数据对比
Fig.3 Comparison of stress-strain curves predicted by various constitutive models and obtained from the experiment

表4 铜合金双段硬化模型参数<br/>Tab.4 Parameters of dual stage hardening model for the copper alloy

表4 铜合金双段硬化模型参数
Tab.4 Parameters of dual stage hardening model for the copper alloy

图4 标距段二维轴对称有限元模型及边界条件(单位:mm)<br/>Fig.4 The 2D axisymmetric FEM model and boundary conditions adopted in the analysis(unit:mm)

图4 标距段二维轴对称有限元模型及边界条件(单位:mm)
Fig.4 The 2D axisymmetric FEM model and boundary conditions adopted in the analysis(unit:mm)

图5 不同变形阶段时试件的塑性应变仿真结果<br/>Fig.5 The simulated results of plastic strain contour of speciment at various deformation stages

图5 不同变形阶段时试件的塑性应变仿真结果
Fig.5 The simulated results of plastic strain contour of speciment at various deformation stages

图6 有限元模型参数的收敛性验证结果<br/>Fig.6 Results of sensitivity tests of the FEM model

图6 有限元模型参数的收敛性验证结果
Fig.6 Results of sensitivity tests of the FEM model

图7 不同修正w因子对应模型载荷-位移曲线<br/>Fig.7 Load-displacement curves of the model corresponding to different correction factor w

图7 不同修正w因子对应模型载荷-位移曲线
Fig.7 Load-displacement curves of the model corresponding to different correction factor w

图8 不同修正因子n和w对应模型载荷-位移曲线<br/>Fig.8 Load-displacement curves of the model corresponding to different correction factor n and w

图8 不同修正因子n和w对应模型载荷-位移曲线
Fig.8 Load-displacement curves of the model corresponding to different correction factor n and w

图9 不同修正模型的载荷-位移曲线<br/>Fig.9 Load-displacement curves of the model corresponding to different correction methods

图9 不同修正模型的载荷-位移曲线
Fig.9 Load-displacement curves of the model corresponding to different correction methods

图10 不同修正模型的应力-应变曲线与试验曲线对比<br/>Fig.10 Comparison of stress-strain curves predicted by various correction models and the experimental data

图10 不同修正模型的应力-应变曲线与试验曲线对比
Fig.10 Comparison of stress-strain curves predicted by various correction models and the experimental data

图11 常用本构预测应力-应变曲线对比<br/>Fig.11 Comparison of stress-strain curves predicted by commonly used models

图11 常用本构预测应力-应变曲线对比
Fig.11 Comparison of stress-strain curves predicted by commonly used models

[1] ANTOLOVICH S D, ARMSTRONG R W. Plastic strain localization in metals: origins and consequences[J]. Progress in Materials Science, 2014, 59(1): 1-160.
[2]BORJA R. A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 190(11/12): 1529-1549.
[3]ZHU Y Z, KANVINDE A, PAN Z F. Analysis of post-necking behavior in structural steels using a one-dimensional nonlocal model[J]. Engineering Structures, 2019, 180: 321-331.
[4]DOWLING N E. Mechanical behaviour of materials[M]. New Jersey: Pearson Education, Inc, 2013.
[5]BRIDGMAN P. The stress distribution at the neck of a tension specimen[J]. Trans. ASM, 1944, 32:553-574.
[6]BRIDGMAN P. Studies in large plastic flow and fracture[M]. New York: McGraw-Hill, 1952.
[7]DAVIDENKOV W. Mechanical methods of testing analysis of the state of stress in the neck of a tension specimen[C]//Proceedings of the ASTM. [S.l.]:ASTM, 1946.
[8]SIEBEL E, SCHWAIGERE S. Mechanics of tensile test[J]. Arch. Eisenhuttenwes, 1948, 19:145-152.
[9]SHAHRJERDI A, RANJBAR B. Correction of post-necking stress-strain curve of copper using surface strain method[J]. Archive of Applied Mechanics, 2022, 92(1): 199-219.
[10]ZHUANG X C, ZHAO Z, LI H Y, et al. Experimental methodology for obtaining the flow curve of sheet materials in a wide range of strains[J]. Steel Research International, 2013, 84(2): 146-154.
[11]JOUN M, EOM J G, LEE M C. A new method for acquiring true stress-strain curves over a large range of strains using a tensile test and finite element method[J]. Mechanics of Materials, 2008, 40(7): 586-593.
[12]ZHU F P, BAI P X, ZHANG J B, et al. Measurement of true stress-strain curves and evolution of plastic zone of low carbon steel under uniaxial tension using digital image correlation[J]. Optics and Lasers in Engineering, 2015, 65: 81-88.
[13]LING Y. Uniaxial true stress-strain after necking[J]. AMP Journal of Technology, 1996, 5:37-48.
[14]JIA L J, KUWAMURA H. Ductile fracture simulation of structural steels under monotonic tension[J]. Journal of Structural Engineering, 2014, 140(5): 04013115.
[15]GAO Y S, ZHANG P, HUO S H. An investigation on the cyclic deformation and service life of a reusable liquid rocket engine thrust chamber wall[J]. Multidiscipline Modeling in Materials and Structures, 2023, 19(3): 522-543.
[16]张凭, 李斌, 高玉闪,等. 重复使用火箭发动机推力室疲劳分析研究进展[J].火箭推进,2024,50(1):12-27.
[17]中国钢铁工业协会. 金属-材料拉伸试验第1 部分:室温试验方法:GB/T 228.1-2021[S]. 北京:中国标准出版社,2021.
[18]KALPAKJIAN S. Manufacturing engineering and technology[M]. Hoboken: Pearson Education, Inc, 2006.
[19]贾良玖, 葛汉彬. 强震下金属结构的超低周疲劳破坏[M]. 上海: 同济大学出版社, 2019.

备注

引言

1 单轴拉伸试验

2 理论与方法

3 本构数值方法与对比

4 颈缩仿真与分析

5 结论

期刊信息