幂律梯度材料的热弛豫响应行为

谢雨珊 徐松林 袁良柱 陈美多 王鹏飞

谢雨珊, 徐松林, 袁良柱, 陈美多, 王鹏飞. 幂律梯度材料的热弛豫响应行为[J]. 爆炸与冲击, 2024, 44(8): 081421. doi: 10.11883/bzycj-2023-0437
引用本文: 谢雨珊, 徐松林, 袁良柱, 陈美多, 王鹏飞. 幂律梯度材料的热弛豫响应行为[J]. 爆炸与冲击, 2024, 44(8): 081421. doi: 10.11883/bzycj-2023-0437
XIE Yushan, XU Songlin, YUAN Liangzhu, CHEN Meiduo, WANG Pengfei. Thermal relaxation responses of graded materials satisfing power law[J]. Explosion And Shock Waves, 2024, 44(8): 081421. doi: 10.11883/bzycj-2023-0437
Citation: XIE Yushan, XU Songlin, YUAN Liangzhu, CHEN Meiduo, WANG Pengfei. Thermal relaxation responses of graded materials satisfing power law[J]. Explosion And Shock Waves, 2024, 44(8): 081421. doi: 10.11883/bzycj-2023-0437

幂律梯度材料的热弛豫响应行为

doi: 10.11883/bzycj-2023-0437
基金项目: 国家自然科学基金(11672286,11602267,11872361);安徽省自然科学基金(1708085MA05);高压物理与地震科技联合实验室开放基金(2019HPPES01)
详细信息
    作者简介:

    谢雨珊(1998- ),女,博士研究生,sa20005048@mail.ustc.edu.cn

    通讯作者:

    徐松林(1971- ),男,博士,研究员,博士生导师,slxu99@ustc.edu.cn

  • 中图分类号: O382

Thermal relaxation responses of graded materials satisfing power law

  • 摘要: 梯度材料热弛豫响应行为的理论研究对于热分析具有重要意义。结合Cattaneo-Vernotte线性双曲型热传导方程,推导得到幂律梯度材料的一维双曲型非傅里叶热传导方程。通过积分变换法,解得频域内温度场的贝塞尔级数形式解,随后利用极点留数法,得到时间域内温度场的第一类解析解。在第一类解析解的基础上,由简化欧拉方程解得第二类解析解。结合拉普拉斯数值逆变换方法,验证了解析解的准确性。以高温阻热梯度材料Mo-ZrC的应用为例,讨论了一般温度边界条件以及温度脉冲载荷作用下幂律梯度材料的热弛豫响应行为。分析发现,在所研究范围内温度场具备波动和传导衰减的双重特性。响应时间和温度幅值随着热弛豫时间系数的增大而增大,温度场分布和单元波形与梯度结构相关。
  • 图  1  归一化幂函数分布

    Figure  1.  The distribution of normalized power function

    图  2  贝塞尔级数渐近展开可行性验证

    Figure  2.  Feasibility verification of asymptotic expansion of Bessel equation

    图  3  拉普拉斯逆变换数值计算结果和第一类解析结果对比

    Figure  3.  Comparison of numerical results of inverse Laplace transformation and the results of the first analytic solution

    图  4  第一类温度函数的二维分布图像

    Figure  4.  Two-dimensional distribution image of temperature function of the first analytic solution

    图  5  第一类解在不同位置处的温度-时间曲线

    Figure  5.  Temperature-time curves at different positions of the first analytic solution

    图  6  第一类解在不同时刻的温度分布曲线

    Figure  6.  Temperature-position curves at different times of the first analytic solution

    图  7  第一类解在不同弛豫系数下的温度-时间曲线以及响应时间、温度极值与弛豫系数的关系

    Figure  7.  The temperature-time curves corresponding to different relaxation coefficients and the relationships between response time, maximum temperature and relaxation coefficient of the first analytic solution

    图  8  不同温度脉冲对应的温度-时间曲线

    Figure  8.  Temperature-time curves corresponding to the temperature pulses of different widths

    图  9  拉普拉斯逆变换数值计算结果和第二类解析结果对比

    Figure  9.  Comparison of numerical results of inverse Laplace transformation and the results of the second analytic solution

    图  10  第二类温度函数的二维分布

    Figure  10.  Two-dimensional distribution of temperature function of the second analytic solution

    图  11  第二类解在不同位置处的温度-时间曲线

    Figure  11.  Temperature-time curves at different positions of the second analytic solution

    图  12  第二类解在不同时刻的温度分布曲线

    Figure  12.  Temperature-position curves at different times of the second analytic solution

    图  13  第二类解在不同弛豫系数下的温度时间曲线及响应时间、温度极值与弛豫系数的关系

    Figure  13.  The temperature-time curves corresponding to different relaxation coefficients and the relationships between response time, maximum temperature and relaxation coefficient of the second analytic solution

    表  1  Mo和ZrC的热力学参数

    Table  1.   Thermomechanical properties of Mo and ZrC

    材料 密度/(kg·m−3) 比热容/(J·kg−1·K−1) 导热系数/(W·m−1·K−1) 熔点/℃ 杨氏模量/GPa 泊松比
    Mo 10200 230 150 3400 279 0.32
    ZrC 6510 310 10 2620 390 0.191
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出版历程
  • 收稿日期:  2023-12-22
  • 修回日期:  2024-03-03
  • 网络出版日期:  2024-03-14
  • 刊出日期:  2024-08-05

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