Study on the Large Plasticity Model and Fracture Initiation Model Parameters of AISI 4340 Steel Targets

doi:10.12382/bgxb.2023.1210

Abstract

Abstract:

The penetration into steel target is a typical process of large plastic deformation,and the construction of constitutive and damage models for the target material is a crucial prerequisite for achieving finite element simulations.In this study,the static and dynamic tests under different stress states and strain rates,and the multilayer target penetration experiments,are conducted on AISI 4340 steel.To facilitate the finite element simulation of steel target penetration,a Swift-Voce hybrid plasticity model is introduced to describe the stress-strain response of material in the large plastic deformation stage,specifically after necking.Additionally,an extended Hosford-Coulomb fracture initiation model,considering stress triaxiality,Lode angle parameters,strain rate,and temperature,is incorporated.In the parameter identification process,the parameters of the plasticity model are first identified based on experimental data and finite element simulations.The parameters of fracture initiation model are identified using an error function and the linear programming algorithm of the simplex method.Finally,the finite element models for quasi-static tension,dynamic tension,and penetration tests are established to inversely verify the parameters of the plasticity and fracture initiation models.The research results show that AISI 4340 steel exhibits the noticeable strain rate strengthening and thermal softening effects.And the newly developed constitutive and damage models are capable of accurately predicting the deformation and fracture behavior of steel target material.The simulated results are good agreement with the experimental data.

Key words: steel target, mechanical property, plasticity model, fracture initiation model, finite element simulation, penetration

CLC Number:

LI Xianghui, ZHANG Xingyu, HU Jiahao, LIU Yang, MA Bohan, WANG Yonggang, JIANG Zhaoxiu. Study on the Large Plasticity Model and Fracture Initiation Model Parameters of AISI 4340 Steel Targets[J]. Acta Armamentarii, 2025, 46(1): 231210-.

Figures/Tables 34

Fig.1 Specimens size in tension test

Fig.2 Multi-layered target plate of AISI 4340 steel

Fig.3 Quasi-static tensile fracture testing

Fig.4 True stress-strain curves

Fig.5 Selection of data acquisition region and positioning of virtual extensometer reference points in DIC

Fig.6 Force-displacement curves

Table 1 Fracture displacements of specimens mm

$d f N T 6$	$d f N T 20$	$d f S H$
2.086	2.816	1.845

Table 1 Fracture displacements of specimens mm

$d f N T 6$	$d f N T 20$	$d f S H$
2.086	2.816	1.845

Fig.7 SHTB testing system

Fig.8 Signal waveforms of SHTB

Fig.9 True stress-strain curves at different strain rates

Fig.10 True stress-strain curves at different temperatures

Fig.11 25mm caliber ballistic gun

Fig.12 93WHA short-rod penetrator

Table 2 Penetration test results

试验序号	着靶速度/ (m·s^-1)	侵彻深度/ mm	2号靶弹坑直径/mm
1	1733.3	50.52	16.84
2	1714.5	51.43	16.42
3	1765.5	52.00	17.23

Fig.13 Cross-sectional diagrams of target plates

Fig.14 Finite element models of quasi-static tensile fracture test specimens

Fig.15 Finite element model of SHTB dynamic tensiletest

Fig.16 Finite element model of AISI 4340 steel target penetration test

Fig.17 Fitting curves of the Swift and Voce hardening models

Table 3 The plasticity model parameters for AISI 4340 steel

参数	数值	参数	数值
E/GPa	210	C	0.023
υ	0.3	$ε ·$ ₀/s^-1	0.001
A₀/MPa	1111	T_r/℃	25
ε₀	0.0007	T_m/℃	1520
n₀	0.162	m	0.85
k₀/MPa	423.5	η_k	0.9
Q₁/MPa	383	ρ/(kg·m^-3)	7850
β	25	C_v/(J·kg^-1·℃^-1)	477
α	0.6

Table 3 The plasticity model parameters for AISI 4340 steel

参数	数值	参数	数值
E/GPa	210	C	0.023
υ	0.3	$ε ·$ ₀/s^-1	0.001
A₀/MPa	1111	T_r/℃	25
ε₀	0.0007	T_m/℃	1520
n₀	0.162	m	0.85
k₀/MPa	423.5	η_k	0.9
Q₁/MPa	383	ρ/(kg·m^-3)	7850
β	25	C_v/(J·kg^-1·℃^-1)	477
α	0.6

Fig.18 Comparison of simulated and experimental force-displacement curves for differentα values (NT6 test)

Fig.19 Fitting curves of plastic model strain rate and temperature-related parameters

Fig.20 Displacement cloud maps of the FEM (left) and photographs of specimens during fracture initiation time (right)

Fig.21 The evolution of equivalent plastic strain with stress triaxiality and Lode angle parameter

Table 4 Fracture initiation model parameters for AISI 4340 steel and the corresponding Di at the moment of fracture displacement d i f for NT6,NT20 and SH

参数	数值
a	1.38
b	1.213
c	0.0035
D_NT6	0.9927
D_NT20	1.0173
D_SH	1.0013

Fig.22 Fracture surface within the stress triaxiality,Lode angle parameter,and equivalent plastic strain space

Fig.23 Fitting curves of fracture initiation model strain rate and temperature-related parameters

Fig.24 Force-displacement curves from FEM and Experiment

Fig.25 Equivalent plastic strain cloud maps

Table 5 The model parameters of bars

参数	数值
E/GPa	210
υ	0.3
ρ/(g·cm^-3)	7.8

Fig.26 True stress-strain curves from experiment and simulation

Table 6 Model parameters of 93WHA

参数	数值	参数	数值
ρ/(kg·m^-3)	17600	D₁	0.008
G/GPa	160	D₂	0.115
A/MPa	645	D₃	4.26
B/MPa	419	D₄	0.2
n	0.31	D₅	3.74
C	0.05	C_v/(J·kg^-1·℃^-1)	134
m	0.5	C₀/(m·s^-1)	3 850
$ε ·$ ₀/s^-1	0.001	S₁	1.24
T_r/℃	25	γ₀	1.58
T_m/℃	1 479	η_k	0.9

Table 6 Model parameters of 93WHA

参数	数值	参数	数值
ρ/(kg·m^-3)	17600	D₁	0.008
G/GPa	160	D₂	0.115
A/MPa	645	D₃	4.26
B/MPa	419	D₄	0.2
n	0.31	D₅	3.74
C	0.05	C_v/(J·kg^-1·℃^-1)	134
m	0.5	C₀/(m·s^-1)	3 850
$ε ·$ ₀/s^-1	0.001	S₁	1.24
T_r/℃	25	γ₀	1.58
T_m/℃	1 479	η_k	0.9

Fig.27 Comparison of simulated and experimental results of AISI 4340 steel target plate penetration

Fig.28 Cloud maps of stable penetration into AISI 4340 steel target plate

References 45

[1]	İBIŞ M Ö, KAHRAMAN Y, GENEL K. Effect of adhesive on ballistic performance of multi-layered steel[J]. International Journal of Impact Engineering, 2023,176:104559.
[2]	PARK J, JEON J, SEO N, et al. Microstructure and mechanical behavior of AISI 4340 steel fabricated via spark plasma sintering and post-heat treatment[J]. Materials Science and Engineering:A, 2023,862:144433.
[3]	马利, 郑津洋, 胡洋, 等. AISI4340钢的绝热剪切与动态失效准则[J]. 兵工学报, 2010, 31(增刊1):79-83.
	MA L, ZHENG J Y, HU Y, et al. Adiabatic shear and dynamic failure criterion for AISI4340 steel[J]. Acta Armamentarii, 2010, 31(S1):79-83. (in Chinese)
[4]	李晓源, 时捷. 弹丸高速冲击条件下高强度钢板抗弹性能[J]. 钢铁研究学报, 2020, 32(5):429-436. doi: 10.13228/j.boyuan.issn1001-0963.20200012
	LI X Y, SHI J. Ballistic behavior of high strength steel targets during high speed impact of projectile[J]. Journal of Iron and Steel Research, 2020, 32(5):429-436. (in Chinese)
[5]	GHAZALI S, ALGARNI M, BAI Y L, et al. A study on the plasticity and fracture of the AISI 4340 steel alloy under different loading conditions and considering heat-treatment effects[J]. International Journal of Fracture, 2020, 225(1):69-87.
[6]	王建军. 典型金属塑性流动中反常应力峰及其本构关系[D]. 西安: 西北工业大学, 2017.
	WANG J J. Anomalous stress peak in the plastic flow of typical metals and its constitutive model[D]. Xi’an: Northwestern Polytechnical University, 2017. (in Chinese)
[7]	王强, 王建军, 张晓琼, 等. 金属热黏塑性本构关系的研究进展[J]. 爆炸与冲击, 2022, 42(9):091402.
	WANG Q, WANG J J, ZHANG X Q, et al. Advances in the research of metallic thermo-viscoplastic constitutive relationships[J]. Explosion and Shock Waves, 2022, 42(9):091402. (in Chinese)
[8]	JIANG M Y, FAN Z X, KRUCH S, et al. Grain size effect of FCC polycrystal:a new CPFEM approach based on surface geometrically necessary dislocations[J]. International Journal of Plasticity, 2022,150:103181.
[9]	ZHANG J, YANG Q S, LIU X. Peridynamics methodology for elasto-viscoplastic ductile fracture[J]. Engineering Fracture Mechanics, 2023,277:108939.
[10]	PAK H, SIM K H, RI Y C, et al. Comparisons of phenomenological and physically based constitutive models for Ti-6Al-2Zr-2Sn-3Mo-1.5Cr-2Nb alloy[J]. Applied Physics A, 2023, 129(11):738.
[11]	FOLLANSBEE P. Application of MTS model to nickel-base superalloys[M]. Cham, Germany:Springer,2022:377-407.
[12]	袁康博, 姚小虎, 王瑞丰, 等. 金属材料的率-温耦合响应与动态本构关系综述[J]. 爆炸与冲击, 2022, 42(9):091401.
	YUAN K B, YAO X H, WANG R F, et al. A review on rate-temperature coupling response and dynamic constitutive relation of metallic materials[J]. Explosion and Shock Waves, 2022, 42(9):091401. (in Chinese)
[13]	JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains,high strain rates and high temperatures[J]. Engineering Fracture Mechanics, 1983,21:541-548.
[14]	朱磊, 刘洋, 孟锦晖, 等. 激光选区熔化Ti-6Al-4V合金的动态力学性能及其本构关系[J]. 爆炸与冲击, 2022, 42(9):091405.
	ZHU L, LIU Y, MENG J H, et al. Dynamic mechanical properties and constitutive relationship of selective laser melted Ti-6Al-4V alloy[J]. Explosion and Shock Waves, 2022, 42(9):091405. (in Chinese)
[15]	马铭辉, 余毅磊, 蒋招绣, 等. 675装甲钢的静动态力学行为与J-C模型参数拟合确定[J]. 北京理工大学学报, 2022, 42(6):596-603.
	MA M H, YU Y L, JIANG Z X, et al. Static and dynamic mechanical properties of 675 armor steel and determination of J-C model parameters[J]. Transactions of Beijing institute of Technology, 2022, 42(6):596-603. (in Chinese)
[16]	VURAL M, CARO J. Experimental analysis and constitutive modeling for the newly developed 2139-T8 alloy[J]. Materials Science and Engineering:A, 2009, 520(1):56-65.
[17]	DUNAND M, MOHR D. Hybrid experimental-numerical analysis of basic ductile fracture experiments for sheet metals[J]. International Journal of Solids and Structures, 2010, 47(9):1130-1143.
[18]	SUNG J H, KIM J H, WAGONER R H. A plastic constitutive equation incorporating strain,strain-rate,and temperature[J]. International Journal of Plasticity, 2010, 26(12):1746-1771.
[19]	PATIL C S, CHAKRABORTY S, NIEZGODA S R. Comparison of full field predictions of crystal plasticity simulations using the Voce and the dislocation density based hardening laws[J]. International Journal of Plasticity, 2021,147:103099.
[20]	JANKOWSKI A F. On the origin of stress-strain relationships,the evaluation of softening coefficients,and mechanistic models for work hardening[J]. Materials Science and Engineering:A, 2023,882:145472.
[21]	ROTH C C, MOHR D. Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets:Experiments and modeling[J]. International Journal of Plasticity, 2014,56:19-44.
[22]	PHAM Q T, LEE B H, PARK K C, et al. Influence of the post-necking prediction of hardening law on the theoretical forming limit curve of aluminium sheets[J]. International Journal of Mechanical Sciences, 2018,140:521-536.
[23]	LEE W S, SU T T. Mechanical properties and microstructural features of AISI 4340 high-strength alloy steel under quenched and tempered conditions[J]. Journal of Materials Processing Technology, 1999, 87(1):198-206.
[24]	李鹤飞. 高强钢断裂韧性与裂纹扩展机制研究[D]. 合肥: 中国科学技术大学, 2019.
	LI H F. Investigation on fracture toughness and crack growth mechanism of high-strength steels[D]. Hefei: University of Science and Technology of China, 2019. (in Chinese)
[25]	SORY D. Notch sensitivity of AISI 4340 in dynamic tensile testing[D].Brussels, Belgium:ECAM, 2013.
[26]	GHAZALI S, ALGARNI M, BAI Y L. A Micro-macro mixed GTN-MMC model to study plasticity and fracture of AISI 4340 steel[J]. Theoretical and Applied Fracture Mechanics, 2023,127:104059.
[27]	JOHNSON G R, COOK W H. Fracture characteristics of three metals subjected to various strains,strain rates,temperatures and pressures[J]. Engineering Fracture Mechanics, 1985, 21(1):31-48.
[28]	林莉, 支旭东, 范锋, 等. Q235B钢Johnson-Cook模型参数的确定[J]. 振动与冲击, 2014, 33(9):153-158,172.
	LIN L, ZHI X D, FAN F, et al. Determination of parameters of Johnson-Cook models of Q235B steel[J]. Journal of Vibration and Shock, 2014, 33(9):153-158,172. (in Chinese)
[29]	任冀宾, 汪存显, 张欣玥, 等. 2A97铝锂合金的Johnson-Cook本构模型及失效参数[J]. 华南理工大学学报(自然科学版), 2019, 47(8):136-144. doi: 10.12141/j.issn.1000-565X.180554
	REN J B, WANG C X, ZHANG X Y, et al. Johnson-Cook constitutive model and failure parameters of 2A97 Al-Li alloy[J]. Journal of South China University of Technology(Natural Science Edition), 2014, 47(8):136-144. (in Chinese)
[30]	BAI Y L. Effect of loading history on necking and fracture[D].Cambridge,MA, US:MIT, 2007.
[31]	BAI Y L, WIERZBICKI T. Application of extended Mohr-Coulomb criterion to ductile fracture[J]. International Journal of Fracture, 2010, 161(1):1-20.
[32]	LI G Q, WANG Y B. Behavior and design of high-strength constructional steel[M]. Sawston,Cambridge, UK: Woodhead Publishing, 2020.
[33]	LI W C, LIAO F F, ZHOU T H, et al. Ductile fracture of Q460 steel:effects of stress triaxiality and lode angle[J]. Journal of Constructional Steel Research, 2016,123:1-17.
[34]	LIU L X, ZHENG Q L, ZHU J, et al. Effects of stress triaxiality and lode parameter on ductile fracture in aluminum alloy[J]. Rare Metal Materials and Engineering, 2019, 48(2):433-439.
[35]	马东方. 基于空穴聚集的高应变率低应力三轴度拉伸断裂机理研究[D]. 宁波: 宁波大学, 2013.
	MA D F. A study for ductile fracture under high strain rate and low stress triaxiality tension based on void coalescence[D]. Ningbo: Ningbo University, 2013. (in Chinese)
[36]	王礼立. 应力波基础[M]. 第2版. 北京: 国防工业出版社, 2005.
	WANG L L. Foundations of stress waves[M]. 2nd edition. Beijing: National Defense Industry Press, 2005. (in Chinese)
[37]	郭鑫. 大变形霍普金森拉杆实验技术[D]. 宁波: 宁波大学, 2019.
	GUO X. Hopkinson tension bar technique for material testing in large deformation[D]. Ningbo: Ningbo University, 2019. (in Chinese)
[38]	MOHR D, MARCADET S J. Micromechanically-motivated phenomenological Hosford-Coulomb model for predicting ductile fracture initiation at low stress triaxialities[J]. International Journal of Solids and Structures, 2015,67-68:40-55.
[39]	马伯翰. 电阻点焊区域的弹丸冲击响应研究与点焊区材料特性初探[D]. 宁波: 宁波大学, 2021.
	MA B H. The ballistic impact response of resistance-spot-welded(RSW) structure and the preliminary study on material properties in RSW zone[D]. Ningbo: Ningbo University, 2021. (in Chinese)
[40]	NELDER J A, MEAD R. A simplex method for function minimization[J]. The Computer Journal, 1965,7:308-313.
[41]	BROWN C, MCCARTHY T, CHADHA K, et al. Constitutive modeling of the hot deformation behavior of CoCrFeMnNi high-entropy alloy[J]. Materials Science and Engineering:A, 2021,826:141940.
[42]	LI J C, CHEN X W, HUANG F L. FEM analysis on the deformation and failure of fiber reinforced metallic glass matrix composite[J]. Materials Science and Engineering:A, 2016,652:145-166.
[43]	杜成鑫. Wf/Zr基非晶复合材料杆弹准细观侵彻机理及优化设计[D]. 南京: 南京理工大学, 2019.
	DU C X. Research on penetration mechanism and optimization design of Wf/Zr-based bulk metallic glass matrix composite rod[D]. Nanjing: Nanjing University of Science & Technology, 2019. (in Chinese)
[44]	DU C X, SHU D W, DU Z H, et al. Effect of L/D on penetration performance of tungsten fibre/Zr-based bulk metallic glass matrix composite rod[J]. International Journal of Refractory Metals and Hard Materials, 2019,85:105042.
[45]	WRIGHT T W. A survey of penetration mechanics for long rods[C]//Proceedings of the Army Research Office Workshop on Computational Aspects of Penetration Mechanics held at the Ballistic Research Laboratory at Aberdeen Proving Ground.Berlin,Heidelberg, Germany:Springer,1983:85-106.