Ductile Fragmentation with a Power Law Cohesive Fracture Model

doi:10.12382/bgxb.2022.0049

Abstract

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

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.

Figures/Tables 10

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

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

Fig.3 Evolution curves of cohesive stress with time for different power index k( 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”

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

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

Fig.7 Finite element model of an expanding ring specimen

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

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

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

Fig.9 Average fragment size versus strain rate

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