非均质炸药的Eshelby夹杂理论相场方法

doi:10.19596/j.cnki.1001-246x.8859

摘要/Abstract

摘要：

考虑到夹杂-基体界面微结构复杂失效过程对非均质PBX(高聚物黏结炸药)材料损伤起始具有主导作用, 本文提出基于Eshelby夹杂理论的相场损伤模型, 对非均质PBX炸药损伤形核演化进行数值模拟。相场能量由弹性能和夹杂-基体相互作用能构成, 结合Mori-Tanaka方法推导不同级配下PBX炸药等效力学模量, 相场内变量的变化直接反映了非线性脱黏效应下的损伤分布。采用Eshelby夹杂理论相场方法计算高模量比非均质PBX炸药圆形和多边形颗粒夹杂典型结构, 分析加载条件、颗粒形状、体积占比、模型参数对夹杂-基体界面脱黏机制的影响。数值结果表明: 夹杂-基体界面微结构演化加速了界面脱黏与宏观损伤的形成, 与实验观测是一致的。

关键词: 非均质PBX, 夹杂, 损伤演化, 相场模型, Eshelby理论

Abstract:

Taking the advantages of tracking discontinuous material surfaces explicitly within the continuous mechanics framework, the phase field method has been successfully applied to study crack propagation and damage in brittle materials. Considering that the complex micro-structural inclusion-matrix interaction dominates the damage nucleation for heterogeneous PBX, we develop a phase field inclusion model based on the Eshelby's inclusion theory, and carry out the numerical simulation study of damage initiation and evolution. The phase field energy consists of the elastic energy and the inclusion-matrix interaction energy. Combining with the Mori-Tanaka method, the effective elastic moduli of heterogeneous PBXs with different volume fractions are derived. For the proposed phase field inclusion model, the nonlinear debonding effects and damage distribution can be characterized by the phase field order parameter directly. It owns explicity in physical mechanism, and completeness in mathematical theory. We apply this model to compute the high volume fraction heterogeneous PBXs with typical circular and polygonal inclusions, and investigate the influences of loading, inclusion shape, volume fraction and computational parameters on the debonding mechanism. Numerical results indicate that the inclusion-matrix micro-structural evolution promotes interface debonding and the formation of macroscopic material failure, which coincides with experimental observations.

Key words: heterogeneous PBX, inclusion, damage evolution, phase field model, Eshelby theory

中图分类号:

徐云, 龙瑶, 向美珍, 陈军. 非均质炸药的Eshelby夹杂理论相场方法[J]. 计算物理, 2024, 41(5): 559-568.

Yun XU, Yao LONG, Meizhen XIANG, Jun CHEN. Phase-Field Fracture Method Based on Eshelby Theory for Heterogeneous PBX[J]. Chinese Journal of Computational Physics, 2024, 41(5): 559-568.

图/表 11

图1 采用Eshelby本征应变表征夹杂相场模型的脱黏区(a)采用本征应变表征脱黏区；(b)引入长度尺度

Fig.1 Debonding of the inclusion phase field model is characterized by Eshelby's eigenstrain (a) debonding region is characterized by eigenstrain; (b) introduce a length scale

表1 非均质PBX材料计算参数

Table 1 Computational parameters of heterogeneous PBX

	杨氏模量/GPa	剪切模量/GPa	能量释放率/(J·m^-2)	泊松比
夹杂颗粒	32.45	14.19	3.50	0.143 3
粘结剂	2.40	0.80	1.02	0.499 5
等效模量	7.39	2.47	1.16	0.499 1

图2 计算模型的位移-力加载条件(a)不同的夹杂体积占比；(b)不同的相场递降函数计算参数

Fig.2 Force-displacement loading condition for the computational model with (a) different inclusion volume fractions and (b) different computational parameters in the phase field degradation functions

图3 不同位移-力加载条件下均匀尺寸圆形夹杂(模型1)的损伤断裂分布

Fig.3 Damage distribution of model 1 with monodisperse circular inclusions under different loadings

图4 不同位移-力加载条件下均匀尺寸圆形夹杂(模型2)的损伤断裂分布

Fig.4 Damage distribution of model 2 with monodisperse circular inclusions under different loadings

图5 不同位移-力加载条件下不同尺寸圆形夹杂(模型3)的损伤断裂分布

Fig.5 Damage distribution of model 3 with bidisperse circular inclusions under different loadings

图6 不同位移-力加载条件下不同尺寸圆形夹杂(模型4)的损伤断裂分布

Fig.6 Damage distribution of model 4 with bidisperse circular inclusions under different loadings

图7 不同加载速度下多边形夹杂模型1的损伤断裂分布

Fig.7 Damage distribution of model 1 with polygonal inclusions under different velocity loadings

图8 不同加载速度下多边形夹杂模型2的损伤断裂分布

Fig.8 Damage distribution of model 2 with polygonal inclusions under different velocity loadings

图9 不同时刻圆形夹杂模型2的损伤断裂演化

Fig.9 Damage evolution of model 2 with circular inclusions at different times

图10 脱黏强度与夹杂体积占比和微结构分布的关系(a)临界脱黏能量和应力；(b)随着夹杂体积占比的变化关系

Fig.10 Relationship between debonding and energy density and inclusion volume fraction and microstructure (a) critical debonding energy and critical stress; (b) inclusion volume fraction

参考文献 36

1	BALZER J , SIVIOUR C , WALLEY S , et al. Behaviour of ammonium perchlorate-based propellants and a polymer-bonded explosive under impact loading[J]. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2004, 460 (2043): 781- 806. DOI
2	BENNETT J G , HABERMAN K S , JOHNSON J N , et al. A constitutive model for the non-shock ignition and mechanical response of high explosives[J]. Journal of the Mechanics and Physics of Solids, 1998, 46 (12): 2303- 2322. DOI
3	LACONDEMINE T , ROUX-LANGLOIS C , ROUXEL T . Role of poisson's ratio mismatch on the crack path in glass matrix particulate composites[J]. International Journal of Fracture, 2017, 207 (1): 73- 85. DOI
4	TAN H , HUANG Y , LIU C , et al. The Mori–tanaka method for composite materials with nonlinear interface debonding[J]. International Journal of Plasticity, 2005, 21 (10): 1890- 1918. DOI
5	DIENES J K , ZUO Q H , KERSHNER J D . Impact initiation of explosives and propellants via statistical crack mechanics[J]. Journal of the Mechanics and Physics of Solids, 2006, 54 (6): 1237- 1275. DOI
6	KIM S , WEI Yaochi , HORIE Y , et al. Prediction of shock initiation thresholds and ignition probability of polymer-bonded explosives using mesoscale simulations[J]. Journal of the Mechanics and Physics of Solids, 2018, 114, 97- 116. DOI
7	LIU Ming , HUANG Xicheng , WU Yaoqing , et al. Numerical simulations of the damage evolution for plastic-bonded explosives subjected to complex stress states[J]. Mechanics of Materials, 2019, 139, 103179. DOI
8	BRANCO R , ANTUNES F V , COSTA J D . A review on 3D-FE adaptive remeshing techniques for crack growth modeling[J]. Engineering Fracture Mechanics, 2015, 141, 170- 195. DOI
9	BRISARD S , SAB K , DORMIEUX L . New boundary conditions for the computation of the apparent stiffness of statistical volume elements[J]. Journal of the Mechanics and Physics of Solids, 2013, 61 (12): 2638- 2658. DOI
10	KIKUCHI M , WADA Y , SHINTAKU Y , et al. Fatigue crack growth simulation in heterogeneous material using s-version FEM[J]. International Journal of Fatigue, 2014, 58, 47- 55. DOI
11	BELYTSCHKO T , BLACK T . Elastic crack growth in finite elements with minimal remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 45 (5): 601- 620. DOI
12	HUYNH D B P , BELYTSCHKO T . The extended finite element method for fracture in composite materials[J]. International Journal for Numerical Methods in Engineering, 2009, 77 (2): 214- 239. DOI
13	GAO Yue , LIU Zhanli , WANG Tao , et al. Crack forbidden area in the anisotropic fracture toughness medium[J]. Extreme Mechanics Letters, 2018, 22, 172- 175. DOI
14	DUGDALE D S . Yielding of steel sheets containing slits[J]. Journal of the Mechanics and Physics of Solids, 1960, 8 (2): 100- 104. DOI
15	XU X P , NEEDLEMAN A . Numerical simulations of fast crack growth in brittle solids[J]. Journal of the Mechanics and Physics of Solids, 1994, 42 (9): 1397- 1434. DOI
16	CAMACHO G T , ORTIZ M . Computational modelling of impact damage in brittle materials[J]. International Journal of Solids and Structures, 1996, 33 (20/22): 2899- 2938.
17	FRANCFORT G A , MARIGO J J . Revisiting brittle fracture as an energy minimization problem[J]. Journal of the Mechanics and Physics of Solids, 1998, 46 (8): 1319- 1342. DOI
18	BOURDIN B , FRANCFORT G A , MARIGO J J . Numerical experiments in revisited brittle fracture[J]. Journal of the Mechanics and Physics of Solids, 2000, 48 (4): 797- 826. DOI
19	AMOR H , MARIGO J J , MAURINI C . Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments[J]. Journal of the Mechanics and Physics of Solids, 2009, 57 (8): 1209- 1229. DOI
20	MIEHE C , WELSCHINGER F , HOFACKER M . Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations[J]. International Journal for Numerical Methods in Engineering, 2010, 83 (10): 1273- 1311. DOI
21	AMBATI M , GERASIMOV T , DE LORENZIS L . A review on phase-field models of brittle fracture and a new fast hybrid formulation[J]. Computational Mechanics, 2015, 55 (2): 383- 405. DOI
22	TANNE E , LI T , BOURDIN B , et al. Crack nucleation in variational phase-field models of brittle fracture[J]. Journal of the Mechanics and Physics of Solids, 2018, 110, 80- 99. DOI
23	冯其红, 赵蕴昌, 王森, 等. 基于相场方法的孔隙尺度油水两相流体流动模拟[J]. 计算物理, 2020, 37 (4): 439- 447.
24	李建伟, 项璇, 王景栋, 等. 不同温度和扰动应变作用下纳米微裂纹的晶体相场研究[J]. 计算物理, 2022, 39 (6): 717- 726. DOI
25	王进, 马文婧, 刘玉周, 等. 非晶一次晶化过程微观组织演化和生长动力学的相场法研究[J]. 计算物理, 2022, 39 (4): 403- 410. DOI
26	马文婧, 王进, 郭慧, 等. 晶体相场法研究金属微互连结构形变过程对界面Kirkendall空洞生长的抑制机理[J]. 计算物理, 2023, 40 (4): 416- 424. DOI
27	HASHIN Z . The elastic moduli of heterogeneous materials[J]. Journal of Applied Mechanics, 1962, 29 (1): 143- 150. DOI
28	HASHIN Z , SHTRIKMAN S . On some variational principles in anisotropic and nonhomogeneous elasticity[J]. Journal of the Mechanics and Physics of Solids, 1962, 10 (4): 335- 342. DOI
29	HILL R . A self-consistent mechanics of composite materials[J]. Journal of the Mechanics and Physics of Solids, 1965, 13 (4): 213- 222. DOI
30	ESHELBY J . The force on an elastic singularity[J]. Philosophical Transactions of the Royal Society of London Series A, 1951, 244 (877): 87- 112. DOI
31	ESHELBY J . The determination of the elastic field of an ellipsoidal inclusion and related problems[J]. Philosophical Transactions of the Royal Society of London. Series A, 1957, 241 (1226): 376- 396.
32	MORI T , TANAKA K . Average stress in matrix and average elastic energy of materials with misfitting inclusions[J]. Acta Metallurgica, 1973, 21 (5): 571- 574. DOI
33	WEINBERGER C , CAI Wei , BARNETT D . Elasticity of microscopic structures[M]. ME340B Lecture Notes, Stanford University, 2005: 43- 46.
34	XU Yun , XIANG Meizhen , YU Jidong , et al. A variational fracture method based on Eshelby transformation[J]. European Journal of Mechanics- A/Solids, 2023, 97, 104846. DOI
35	MATOUŠ K , GEUBELLE P H . Multiscale modeling of particle debonding in reinforced elastomers subjected to finite deformations[J]. International Journal for Numerical Methods in Engineering, 2006, 65 (2): 190- 223. DOI
36	MATOUŠ K , KULKARNI M , GEUBELLE P . Multiscale cohesive failure modeling of heterogeneous adhesives[J]. Journal of the Mechanics and Physics of Solids, 2008, 56 (4): 1511- 1533. DOI