带有幂次内聚断裂模型的韧性碎裂

doi:10.12382/bgxb.2022.0049

摘要/Abstract

摘要：

固体在受到冲击载荷作用时常常会断裂成多个碎片(碎裂),对冲击碎裂过程的研究对工程防护和国防军事具有重要意义。影响碎片尺寸的关键参数包括加载速率、材料强度和韧性、断裂形态等因素。采用非线性的幂次内聚力模型来描述材料的断裂过程,分析断裂和卸载波传播的耦合过程,给出断口完全断裂时间、卸载波传播距离及碎片平均尺度的解析表达;采用有限元数值模拟不同损伤断裂路径下的韧性碎裂过程,得到断口形貌和破碎产生碎片的平均尺寸。研究结果表明:随着幂次指数k的减小,卸载波的传播距离单调增加,产生碎片的平均尺寸也增加,并且碎片断口变形更大;在诸多可能的非线性损伤演化路径中,存在一种断口位置以最快速卸载方式的损伤断裂模型,该模型对应于幂次指数k=0.5的情况,更接近刻画断口区的断裂发展过程。

关键词: 韧性碎裂, 幂次内聚力断裂模型, Mott波, 碎片尺寸

Abstract:

Solids often break into fragments (fragmentation) in response to rapid loading. Research on the fragmentation process is thus of great significance to engineering applications and national defense. Key parameters that affect the size of the fragments include loading rate, material strength and toughness, and fracture process. The nonlinear power-law cohesive fracture relationship is used to describe the fracture process of ductile materialsand the coupling process of fracture and unloading wave propagation is analyzed. The theoretical model provides the fracture time, unloading wave propagation distance, and fragment size for different cohesive fracture paths. The finite element model is used to simulate the fragmentation process of ductile rings expanding at a high velocity, to exhibit the effects of loading rate and different damage models on the fragmentation process. The results show that the unloading wave propagation distance and the average size of fragments both increase with the power exponent k. It is further found that among the numerous power-law nonlinear cohesive fracture paths, the material fails at the fastest rate with the power index k=0.5, which well describes the cohesive fracture process in the fracture zone.

Key words: ductile fragmentation, power law cohesive fracture model, mott wave, average fragment size

徐便, 郑宇轩, 杨洪升, 周风华. 带有幂次内聚断裂模型的韧性碎裂[J]. 兵工学报, 2023, 44(5): 1493-1501.

XU Bian, ZHENG Yuxuan, YANG Hongsheng, ZHOU Fenghua. Ductile Fragmentation with a Power Law Cohesive Fracture Model[J]. Acta Armamentarii, 2023, 44(5): 1493-1501.

图/表 10

图1 理想塑性材料在恒应变率拉伸过程中的断裂-卸载分析模型

Fig.1 “Cohesive fracture-Mott unloading” analytical model for ideal plastic materials under tension with a constant strain rate

图2 保持断裂能不变时不同k参数所确定的内聚断裂应力-断口张开位移曲线

Fig.2 “Cohesive stress vs crack opening displacement”curves with different power index k with constant fracture energy

图3 不同k参数下的内聚断裂应力随时间发展曲线 (应变率 ε ·=1000s-1)

Fig.3 Evolution curves of cohesive stress with time for different power index k( ε ·=1000s-1)

图4 非线性幂次指数k在0.1~1.9范围的Mott卸载波阵面随时间变化曲线,曲线终点为“断裂时间-卸载区域”包络线( ε ·=1000s-1)

Fig.4 Curves of Mott wave front with time for different power index k=0.1~1.9( ε ·=1000s-1), with endpoints forming an envelope of the “fracture time-unloading zone”

图5 不同k参数下的断裂时间与应变率关系

Fig.5 Fracture time-strain rate relationship for different k

图6 不同应变率下的“断裂时间-卸载区域”包络线

Fig.6 Envelopes of “unloading zone-fracture time” for different strain rates

图7 膨胀环试件的有限元模型

Fig.7 Finite element model of an expanding ring specimen

表1 TU1无氧铜材料参数

Table 1 Material parameters of OFHC

密度/ (kg·m^-3)	比热/ (J·kg^-1·K^-1)		TQ系数 β		转变温度 θ_t/K		熔点温度 θ_m/K		杨氏模量 E/GPa		泊松比 ν
8960	383		0.9		298		1356		129		0.34
Johnson-Cook本构模型参数
A/MPa		B/MPa		C		n		m		$ε · 0$ /s^-1
90		292		0.027		0.28		1.09		1
Johnson-Cook损伤起始参数及断裂能
d₁		d₂		d₃		d₄		d₅		G_c/(N·m^-1)
0.2		0.04		0.01		0.014		1.12		10000

表1 TU1无氧铜材料参数

Table 1 Material parameters of OFHC

密度/ (kg·m^-3)	比热/ (J·kg^-1·K^-1)		TQ系数 β		转变温度 θ_t/K		熔点温度 θ_m/K		杨氏模量 E/GPa		泊松比 ν
8960	383		0.9		298		1356		129		0.34
Johnson-Cook本构模型参数
A/MPa		B/MPa		C		n		m		$ε · 0$ /s^-1
90		292		0.027		0.28		1.09		1
Johnson-Cook损伤起始参数及断裂能
d₁		d₂		d₃		d₄		d₅		G_c/(N·m^-1)
0.2		0.04		0.01		0.014		1.12		10000

图8 k分别取值为0.5、1.0、1.5时金属环膨胀碎裂形态及碎片特征图

Fig.8 Fragmentized expanding rings and typical fragments for specimens with k=0.5, 1.0, 1.5

图9 平均碎片尺度与应变率关系

Fig.9 Average fragment size versus strain rate

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