HMX晶体热致相变对损伤的影响

杨昆; 吴艳青; 黄风雷

doi:10.11858/gywlxb.20220545

HMX晶体热致相变对损伤的影响

doi: 10.11858/gywlxb.20220545

北京理工大学爆炸科学与技术国家重点实验室, 北京　100081

基金项目: 国家自然科学基金（11872119）；中国博士后科学基金（2020M680394，BX20200046）；国防基础科研核科学挑战专题（TZ2016001）

详细信息

作者简介:
杨　昆（1993－），男，博士，博士后，主要从事高能炸药宏细观力-热-化耦合响应研究.E-mail：ykbit123@163.com

通讯作者:
吴艳青（1974－），女，博士，教授，主要从事含能材料细观力学与安全性研究.E-mail：wuyqing@bit.edu.cn

中图分类号: O521.2; O341
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出版历程
- 收稿日期: 2022-03-22
- 修回日期: 2022-04-15
- 刊出日期: 2022-05-30

Effects of Heating-Induced Phase Transition on Damage for HMX Crystal

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: HMX基PBX炸药混合体系中炸药晶体在发生高温熔化和分解反应之前，会率先发生非均匀热膨胀和固相晶型转变，使材料的力学性能和安全性能发生突变。为探究HMX晶体的热致相变对材料内部损伤演化的影响机制，发展了考虑HMX晶体热膨胀和相变等变形机制的热力耦合晶体本构模型，从力学角度揭示了黏结剂包覆HMX晶体相变对体积变形、应力状态以及裂纹成核演化过程的影响机理，量化分析了升温速率对材料相变和裂纹损伤状态的影响规律。结果表明：随着加载温度升高，HMX晶体的热膨胀和$\,\beta $→$\delta $相变导致体积增大，晶体内部形成拉伸应力状态，同时晶体与黏结剂相互挤压形成的局部压剪作用使晶体内部出现裂纹成核和扩展现象。相变温度附近HMX晶体内部裂纹成核和扩展数量显著增加，晶体内部发生不可逆损伤。外界升温速率对晶体内部裂纹形核扩展与损伤造成显著影响，较高的升温速率会加大晶体损伤程度，增加炸药内潜在热点源及意外点火风险。
- HMX单晶 /
- 热致相变 /
- 热膨胀 /
- 裂纹扩展 /
- 损伤
Abstract: At high temperature loading, the thermal expansion and solid-solid phase transition firstly occur in HMX-based PBXs prior to the melting and decomposition of HMX crystal, thereby inducing the abrupt change of mechanical and safety properties. A constitutive model integrating with several deformation mechanisms, including thermal expansion, and phase transition was developed to investigate the effects of heating-induced phase transition on damage evolution. The influence mechanisms of phase transition in binder-bonded HMX single crystal on the volumetric deformation, stress states and crack nucleation and growth were revealed from the viewpoint of mechanics. The effects of heating rate on phase transition and crack related damage evolution were quantitatively analyzed. The calculated results show that, as the increase of loading temperature, tension stress formed due to the thermal expansion and $\,\beta $→$\delta $ phase transition in unilateral-restrained HMX crystal and local shear stress formed due to mutually compression between crystal and binder, contribute to the nucleation and growth of HMX crystal. The number density of cracks exhibits a remarkable growth near the phase transition temperature, thereby inducing the irreversible damage. The heating rate has a significant influence on the nucleation and growth of cracks. Large heating rate will increase the crack related damage level of crystal, thereby increasing the number density of potential hotspots and risks of inadvertent ignition.
- HMX single crystal /
- heating-induced phase transition /
- thermal expansion /
- crack growth /
- damage

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图 1 变形梯度的乘法分解

Figure 1. Multiple decomposition of deformation gradient

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图 2 黏结剂包覆HMX单晶的有限元模型

Figure 2. Finite element model for binder-bonded HMX single crystal

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图 3 $\,\beta $-HMX和 $\delta $-HMX的体积分数-加载温度曲线

Figure 3. Volume fraction of $\,\beta $-HMX and $\delta $-HMX versus loading temperature

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图 4 热膨胀和热致相变对体积应变的影响

Figure 4. Effects of thermal expansion and phase transition on the volumetric strain

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图 5 黏结剂、HMX晶体、界面和晶内的最大应力演化曲线

Figure 5. Maximum Mises stress evolution of binder matrix, HMX crystal, interface and intragranular HMX

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图 6 90 min加热至480 K时黏结剂、HMX晶体和界面的应力云图

Figure 6. Stress contours of binder matrix, HMX crystal and interface at 90 min and 480 K

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图 7 不同时刻裂纹损伤程度演化云图

Figure 7. Crack growth related damage evolution contours at different loading times

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图 8 HMX晶体的统计裂纹损伤演化

Figure 8. Statistical crack related damage evolution in HMX crystal

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图 9 不同升温速率下HMX晶体的相变速率

Figure 9. Rate of phase transition of HMX crystal at different heating rates

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图 10 不同升温速率下HMX晶体内的裂纹损伤

Figure 10. Crack related damage in HMX crystal at different heating rates

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表 1 $\,\beta $-HMX的弹性常数及其温度系数

Table 1. Elastic constants and temperature coefficients of $\,\beta $-HMX

C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₁₅/GPa	C₂₂/GPa	C₂₃/GPa	C₂₅/GPa
22.2	9.6	13.2	−0.1	23.9	13.0	4.7

C₃₃/GPa	C₄₄/GPa	C₅₅/GPa	C₆₆/GPa	C₃₅/GPa	C₄₆/GPa	$\dfrac{ {{\rm d}{C{_{11} } } } }{ {{\rm d}T} }$/(GPa·K⁻¹)
23.4	9.2	11.1	10.1	1.6	2.5	−0.030

$\dfrac{ {{\rm d}{C{_{12}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{13}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{{_{15}} } } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{22}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{23}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{25}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{33}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)
−0.001	−0.012	0.002	−0.023	−0.018	0.005	−0.003

$\dfrac{ {{\rm d}{C{_{44}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{55}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{66}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{35}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{46}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)
−0.009	−0.004	−0.007	0.003	0.004

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表 2 $\delta $-HMX的弹性常数及其温度系数

Table 2. Elastic constants and temperature coefficients of $\delta $-HMX

C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₂₂/GPa	C₂₃/GPa	C₃₃/GPa
14.5	10.6	10.3	14.0	10.3	18.0

C₄₄/GPa	C₅₅/GPa	C₆₆/GPa	$\dfrac{ {{\rm d}{C{_{11} }} } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{12}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{13}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)
4.4	4.4	2.3	−0.014	−0.007	−0.009

$\dfrac{ {{\rm d}{C{_{22} }} } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{23}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{33} }} } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{44}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{55}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)	$\dfrac{ {{\rm d}{C{_{66}} } } }{ {{\rm d}T} }$/(GPa·K⁻¹)
−0.014	−0.009	−0.019	−0.006	−0.006	−0.007

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表 3 HMX单晶模型的物理参数

Table 3. Physical parameters for HMX single crystal model

Phase	$\,\rho $/(kg∙m⁻³)	c_V/(J∙kg⁻¹∙K⁻¹)	α₁₁/K⁻¹	α₂₂/K⁻¹	α₃₃/K⁻¹	α₁₃/K⁻¹
$\,\beta $	1900	667	−2.90×10⁻⁶	1.16×10⁻⁴	1.79×10⁻⁵	−1.26×10⁻⁵
$\delta $	1760	667	6.18×10⁻⁵	6.18×10⁻⁵	2.47×10⁻⁵

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表 4 HMX的$\,\beta $→$\delta $相变模型参数

Table 4. Parameters related to $\,\beta $→$\delta $ phase transition model of HMX

i	Q/(m³∙mol⁻¹)	S^*/(J∙mol⁻¹∙K⁻¹)	H^*/(kJ∙mol⁻¹)	V^*/(10⁻⁵ m³∙mol⁻¹)
1	1.00	144.44	207.691	1.14
−1	1.00	121.68	197.891	0
2	3.0×10⁻¹⁰	149.85	79.700	2.33
−2	3.0×10⁻¹⁰	127.09	69.900	1.19

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表 5 界面与HMX晶体内双线性内聚力模型参数

Table 5. Bilinear cohesive model parameters for interface and HMX granular

Position	K₁₁/(MPa∙m⁻¹)	K₂₂/(MPa∙m⁻¹)	K₃₃/(MPa∙m⁻¹)	T₁₁/MPa	T₂₂/MPa	T₃₃/MPa	G/(J∙m⁻²)
Interface	1.55⁶	1.55⁶	1.55⁶	1.66	1.66	1.66	80.0
Intra-HMX	10⁶	10⁶	10⁶	2.0	3.0	3.0	100.0

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