搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

考虑晶粒分布的多晶体材料超声散射统一理论

李珊 李雄兵 宋永锋 陈超

引用本文:
Citation:

考虑晶粒分布的多晶体材料超声散射统一理论

李珊, 李雄兵, 宋永锋, 陈超

Ultrasonic sacttering unified theory for polycrystal material with grain sizes distribution

Li Shan, Li Xiong-Bing, Song Yong-Feng, Chen Chao
PDF
导出引用
  • 现有超声散射统一理论可通过多晶体材料的微观结构和力学特性,实现全频域范围内衰减和相速度的正演建模,但其忽略晶粒尺寸分布的影响,进而降低了正演模型的计算精度.本文对不均匀介质的波动方程进行二阶Keller近似,用全频域格林函数推导介质中的平均波;以截断对数正态分布描述晶粒分布,构建加权的空间相关函数;结合材料的弹性模量协方差,建立含晶粒分布的超声散射统一理论,揭示晶粒分布对超声散射的影响规律;制备304不锈钢试块并开展超声散射实验.结果表明考虑晶粒分布特性后,纵波衰减谱和相速度谱相对于实验结果的相异性降低约49%和64%,横波衰减谱和相速度谱相对于实验结果的相异性降低约12%和4%.可见,本文的统一理论模型能有效修正晶粒分布导致的衰减谱和相速度谱偏差,为晶粒分布反演评价提供理论基础.
    The existing unified theory of ultrasonic scattering can model the attenuation and phase velocity in the frequency domain by using the microstructure and mechanical properties of polycrystalline materials. However, this theory does not consider the influence of grain size distribution, thus degrading the calculation accuracy in the forward modeling. A new unified theory, which is mainly corrected by considering the grain size distribution, is developed. First, the second-order Keller approximation and the full-field Green's function are used to calculate the wave equation of inhomogeneous medium and derive the average wave in the medium, respectively. Second, the method of the truncated lognormal distribution is used to describe the grain size distribution and construct the weighted spatial correlation function. Finally, the new unified theory of ultrasonic scattering is established to reveal the influence of grain distribution on ultrasonic scattering.
    Using the new unified model, the effects of the grain distribution widening on the ultrasonic scattering while the average grain size is unchanged, are analyzed for the longitudinal wave and the shear wave. The attenuation increases in the Rayleigh scattering region and the geometric scattering region, while there is less attenuation variation in the stochastic scattering region and two adjacent transition regions. The phase velocity varies strongly in the stochastic-geometric transition region, while the variation is relatively small in other scattering zones. Experiments are conducted by using a 304 stainless steel specimen. The results show that when the grain distribution characteristics are considered, the discrepancy between the longitudinal wave attenuation spectrum and experimental results, and that between the phase velocity spectrum and experimental results are reduced by 49% and 64%, respectively; for the shear wave, these discrepancies are reduced by 12% and 4%, respectively.
    From all above aspects, the accuracy of the new model is higher than that of the traditional model. The new unified theory proposed in this paper can effectively correct the discrepancy of the attenuation spectrum and phase velocity spectrum caused by the grain size distribution and provide a theoretical basis for inverse problem of grain distribution. Also, the theory can be extended to materials containing elongated grains, macroscopic texture or multiple phases.
    • 基金项目: 国家自然科学基金(批准号:51575541,51711530231)和中央高校基本科研业务费(批准号:2018zzts515)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51575541, 51711530231) and the Fundamental Research Fund for the Central Universities, China (Grant No. 2018zzts515).
    [1]

    Li J, Rokhlin S I 2015 Wave Motion 58 145

    [2]

    Kube C M 2017 J. Acoust. Soc. Am. 141 1804

    [3]

    O'Donnell M, Jaynes E T, Miller J G 1978 J. Acoust. Soc. Am. 63 1935

    [4]

    Mason W P, McSkimin H J 1947 J. Acoust. Soc. Am. 19 464

    [5]

    Mason W P, McSkimin H J 1948 J. Appl. Phys. 19 940

    [6]

    Huntington H B 1950 J. Acoust. Soc. Am. 22 362

    [7]

    Papadakis E P 1965 J. Acoust. Soc. Am. 37 703

    [8]

    Weaver R L 1990 J. Mech. Phys. Solids 38 55

    [9]

    Calvet M, Margerin L 2012 J. Acoust. Soc. Am. 131 1843

    [10]

    Calvet M, Margerin L 2016 Wave Motion 65 29

    [11]

    Stanke F E, Kino G S 1984 J. Acoust. Soc. Am. 75 665

    [12]

    Hirsekorn S 1988 J. Acoust. Soc. Am. 83 1231

    [13]

    Ahmed S, Thompson R B 1992 Nondestr. Test. Eval. 8 525

    [14]

    Sha G, Rokhlin S I 2018 Ultrasonics 88 84

    [15]

    Papadakis E P 1964 J. Appl. Phys. 35 1586

    [16]

    Papadakis E P 1961 J. Acoust. Soc. Am. 33 1616

    [17]

    Nicoletti D, Anderson A 1997 J. Acoust. Soc. Am. 101 686

    [18]

    Smith R L 1982 Ultrasonics 20 211

    [19]

    Ryzy M, Grabec T, Sedlák P, Veres I A 2018 J. Acoust. Soc. Am. 143 219

    [20]

    Arguelles A P, Turner J A 2017 J. Acoust. Soc. Am. 141 4347

    [21]

    Bebu I, Mathew T 2009 Stat. Probabil. Lett. 79 375

    [22]

    Zheng Q, Li J, Huang F 2011 Appl. Math. Comput. 217 9592

    [23]

    Schwartz A J, Kumar M, Adams B L, Field D P 2009 Electron Backscatter Diffraction in Materials Science (Berlin, Heidelberg: Springer) pp53-81

    [24]

    Treiber M, Kim J Y, Jacobs L J, Qu J 2009 J. Acoust. Soc. Am. 125 2946

  • [1]

    Li J, Rokhlin S I 2015 Wave Motion 58 145

    [2]

    Kube C M 2017 J. Acoust. Soc. Am. 141 1804

    [3]

    O'Donnell M, Jaynes E T, Miller J G 1978 J. Acoust. Soc. Am. 63 1935

    [4]

    Mason W P, McSkimin H J 1947 J. Acoust. Soc. Am. 19 464

    [5]

    Mason W P, McSkimin H J 1948 J. Appl. Phys. 19 940

    [6]

    Huntington H B 1950 J. Acoust. Soc. Am. 22 362

    [7]

    Papadakis E P 1965 J. Acoust. Soc. Am. 37 703

    [8]

    Weaver R L 1990 J. Mech. Phys. Solids 38 55

    [9]

    Calvet M, Margerin L 2012 J. Acoust. Soc. Am. 131 1843

    [10]

    Calvet M, Margerin L 2016 Wave Motion 65 29

    [11]

    Stanke F E, Kino G S 1984 J. Acoust. Soc. Am. 75 665

    [12]

    Hirsekorn S 1988 J. Acoust. Soc. Am. 83 1231

    [13]

    Ahmed S, Thompson R B 1992 Nondestr. Test. Eval. 8 525

    [14]

    Sha G, Rokhlin S I 2018 Ultrasonics 88 84

    [15]

    Papadakis E P 1964 J. Appl. Phys. 35 1586

    [16]

    Papadakis E P 1961 J. Acoust. Soc. Am. 33 1616

    [17]

    Nicoletti D, Anderson A 1997 J. Acoust. Soc. Am. 101 686

    [18]

    Smith R L 1982 Ultrasonics 20 211

    [19]

    Ryzy M, Grabec T, Sedlák P, Veres I A 2018 J. Acoust. Soc. Am. 143 219

    [20]

    Arguelles A P, Turner J A 2017 J. Acoust. Soc. Am. 141 4347

    [21]

    Bebu I, Mathew T 2009 Stat. Probabil. Lett. 79 375

    [22]

    Zheng Q, Li J, Huang F 2011 Appl. Math. Comput. 217 9592

    [23]

    Schwartz A J, Kumar M, Adams B L, Field D P 2009 Electron Backscatter Diffraction in Materials Science (Berlin, Heidelberg: Springer) pp53-81

    [24]

    Treiber M, Kim J Y, Jacobs L J, Qu J 2009 J. Acoust. Soc. Am. 125 2946

  • [1] 张凤国, 赵福祺, 刘军, 何安民, 王裴. 延性金属层裂强度对温度、晶粒尺寸和加载应变率的依赖特性及其物理建模. 物理学报, 2022, 71(3): 034601. doi: 10.7498/aps.71.20210702
    [2] 张凤国. 延性金属层裂强度对温度、晶粒尺寸和加载应变率的依赖特性及其物理建模. 物理学报, 2021, (): . doi: 10.7498/aps.70.20210702
    [3] 王鹏, 徐建刚, 张云光, 宋海洋. 晶粒尺寸对纳米多晶铁变形机制影响的模拟研究. 物理学报, 2016, 65(23): 236201. doi: 10.7498/aps.65.236201
    [4] 刘英光, 张士兵, 韩中合, 赵豫晋. 纳晶铜晶粒尺寸对热导率的影响. 物理学报, 2016, 65(10): 104401. doi: 10.7498/aps.65.104401
    [5] 宋永锋, 李雄兵, 史亦韦, 倪培君. 表面粗糙度对固体内部超声背散射的影响. 物理学报, 2016, 65(21): 214301. doi: 10.7498/aps.65.214301
    [6] 杨卫明, 刘海顺, 敦超超, 赵玉成, 窦林名. Fe基纳米晶合金晶粒尺寸反常变化的物理机制. 物理学报, 2012, 61(10): 106802. doi: 10.7498/aps.61.106802
    [7] 付鹏涛, 韩纪锋, 牟艳红, 韩丹, 杨朝文. 瑞利散射法研究超声喷流二氧化碳团簇尺度轴向分布. 物理学报, 2011, 60(5): 053602. doi: 10.7498/aps.60.053602
    [8] 唐冬和, 杜磊, 王婷岚, 陈华, 贾晓菲. 纳米器件电流噪声的散射理论统一模型研究. 物理学报, 2011, 60(9): 097202. doi: 10.7498/aps.60.097202
    [9] 王英龙, 张鹏程, 刘虹让, 刘保亭, 傅广生. 晶粒尺寸及衬底应力对铁电薄膜特性的影响. 物理学报, 2011, 60(7): 077702. doi: 10.7498/aps.60.077702
    [10] 温文媖, 陈小刚, 宋金宝. 三层流体系统非线性界面内波传播理论的研究. 物理学报, 2010, 59(10): 7149-7157. doi: 10.7498/aps.59.7149
    [11] 刘猛, 陆建峰, 韩纪峰, 李佳, 罗小兵, 缪竞威, 师勉恭, 杨朝文. 超声喷流Ar团簇生长演化过程及团簇尺寸轴向分布的实验研究. 物理学报, 2009, 58(10): 6951-6955. doi: 10.7498/aps.58.6951
    [12] 毛朝梁, 董显林, 王根水, 姚春华, 曹菲, 曹盛, 杨丽慧, 王永令. 晶粒尺寸对Ba0.70Sr0.30TiO3陶瓷介电性能的影响规律及机理研究. 物理学报, 2009, 58(8): 5784-5789. doi: 10.7498/aps.58.5784
    [13] 王浩, 刘国权, 栾军华, 岳景朝, 秦湘阁. 晶粒棱长、尺寸与拓扑学特征之间关系的Monte Carlo仿真研究. 物理学报, 2009, 58(13): 132-S136. doi: 10.7498/aps.58.132
    [14] 余柏林, 祁 琼, 唐新峰, 张清杰. 晶粒尺寸对CoSb3化合物热电性能的影响. 物理学报, 2005, 54(12): 5763-5768. doi: 10.7498/aps.54.5763
    [15] 冯维存, 高汝伟, 韩广兵, 朱明刚, 李 卫. NdFeB纳米复合永磁材料的交换耦合相互作用和有效各向异性. 物理学报, 2004, 53(9): 3171-3176. doi: 10.7498/aps.53.3171
    [16] 滕蛟, 蔡建旺, 熊小涛, 赖武彦, 朱逢吾. NiFe/FeMn双层膜交换偏置的形成及热稳定性研究. 物理学报, 2004, 53(1): 272-275. doi: 10.7498/aps.53.272
    [17] 朱鸿茂, 吴艳阳, 黄忠文, 王寅观, 朱 成. 一类弱散射界面背向散射超声散斑一阶统计特性. 物理学报, 2003, 52(6): 1438-1443. doi: 10.7498/aps.52.1438
    [18] 李眉娟, 胡海云, 邢修三. 多晶体金属疲劳寿命随晶粒尺寸变化的理论研究. 物理学报, 2003, 52(8): 2092-2095. doi: 10.7498/aps.52.2092
    [19] 滕蛟, 蔡建旺, 熊小涛, 赖武彦, 朱逢吾. (Ni0.81Fe0.19)1-xCrx作为种子层对NiFe/FeMn交换偏置的影响. 物理学报, 2002, 51(12): 2849-2853. doi: 10.7498/aps.51.2849
    [20] 古堂生, 石舜森, 林光明. 测定纳米晶粒尺寸分布的新方法及其应用. 物理学报, 1999, 48(2): 267-272. doi: 10.7498/aps.48.267
计量
  • 文章访问数:  3261
  • PDF下载量:  58
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-09-22
  • 修回日期:  2018-10-11
  • 刊出日期:  2018-12-05

考虑晶粒分布的多晶体材料超声散射统一理论

  • 1. 中南大学交通运输工程学院, 长沙 410075;
  • 2. 中南大学粉末冶金国家重点实验室, 长沙 410083
    基金项目: 国家自然科学基金(批准号:51575541,51711530231)和中央高校基本科研业务费(批准号:2018zzts515)资助的课题.

摘要: 现有超声散射统一理论可通过多晶体材料的微观结构和力学特性,实现全频域范围内衰减和相速度的正演建模,但其忽略晶粒尺寸分布的影响,进而降低了正演模型的计算精度.本文对不均匀介质的波动方程进行二阶Keller近似,用全频域格林函数推导介质中的平均波;以截断对数正态分布描述晶粒分布,构建加权的空间相关函数;结合材料的弹性模量协方差,建立含晶粒分布的超声散射统一理论,揭示晶粒分布对超声散射的影响规律;制备304不锈钢试块并开展超声散射实验.结果表明考虑晶粒分布特性后,纵波衰减谱和相速度谱相对于实验结果的相异性降低约49%和64%,横波衰减谱和相速度谱相对于实验结果的相异性降低约12%和4%.可见,本文的统一理论模型能有效修正晶粒分布导致的衰减谱和相速度谱偏差,为晶粒分布反演评价提供理论基础.

English Abstract

参考文献 (24)

目录

    /

    返回文章
    返回