Fracture behavior of TiB2/Al composite under different stress states: Calibration and evaluation of fracture criteria
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摘要: 复杂应力状态下韧性材料的变形和断裂行为与单轴加载通常具有很大差别,因此近年来失效判据的发展及其在仿真领域的应用得到广泛关注,分析不同失效判据模型在较宽应力状态范围内的适用性差异,并选择合适的模型对于精准地预测工程材料断裂行为至关重要。为了探究原位自生TiB2/Al复合材料的断裂行为,在不同应力状态(应力三轴度−0.82~1.03,Lode角参数−1~1)下进行了系统的断裂试验和微观分析,结果表明该材料的断裂行为和微观机制与应力状态密切相关;除了应力三轴度外,失效判据模型中应该进一步考虑Lode角参数影响以更精确预测宽应力状态下的断裂行为。基于系统的试验结果,对5种典型的失效判据模型参数进行标定,并详细对比和评价了这些模型在宽应力状态范围内对断裂行为的预测能力。结果表明,全面考虑应力三轴度、Lode角参数和截断值的失效判据模型能够更准确地描述复合材料在复杂应力状态下的断裂行为。Abstract: The deformation and fracture behaviors of ductile materials under complex stress states are usually quite different from those under uniaxial loading conditions. In recent years, the development of fracture criteria and their application in numerical simulation have attracted great attention in many engineering fields. So, it is quite important to analyze the applicability of different fracture criteria over a wide range of stress states and select an appropriate model to accurately predict the fracture behavior. The fracture behavior of in-situ TiB2/2024 Al composite was investigated systematically over stress triaxialities ranging from −0.82 to 1.03, and lode angel parameters ranging from −1 to 1 by using an experimental approach. The fracture characteristics and underlying mechanisms are closely related to stress state, and both of the stress triaxiality and lode angle parameter should be included in the fracture criterion to predict fracture over a wide range of stress states. Based on the experimental data, five existing fracture criteria were calibrated, and their ability to describe and predict the fracture behavior was evaluated. The result shows that the fracture criteria which consider comprehensively the effects of the stress triaxiality, lode angle parameter and cut-off value can more accurately predict the fracture behavior of in-situ TiB2/2024 Al composite over a wide range of stress states.
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图 11 TiB2/2024Al 复合材料不同失效判据模型预测结果与试验结果对比:(a)
$ \stackrel{-}{\theta }\text{}\text{=}\text{}\text{±1} $ ;(b)$ \stackrel{-}{\theta }\text{}\text{=}\text{} $ 0Figure 11. Comparison of prediction of all fracture criteria relatively with the experimental data of the TiB2/2024 Al composite: (a)
$ \stackrel{-}{\theta }\text{}\text{=}\text{}\text{±1} $ ; (b)$ \stackrel{-}{\theta }\text{}\text{=}\text{} $ 0表 1 6类用于原位自生TiB2/2024 Al复合材料断裂应变标定的试样形式
Table 1. 6 types of specimens for fracture strain calibration of in-situ TiB2/2024 Al composite
Specimen type Specimen shape Lode angle parameter $ \stackrel{-}{\theta } $ Stress triaxiality η Equivalent fracture strain $ \stackrel{-}{{\varepsilon }_{\mathrm{f}}} $ Smooth round bar, tension $1$ 1/3 $2\ln \left( {\dfrac{ { {a_0} } }{ { {a_{\text{f} } } } } } \right)$[24] Notched round bars, tension 1 $\dfrac{1}{3} + \ln \left( {1 + \dfrac{ { {a_0} } }{ {2{R_0} } } } \right)$[13] $2\ln \left( {\dfrac{ { {a_0} } }{ { {a_{\text{f} } } } } } \right)$[24] Pure shear 0 0 $\dfrac{2}{ {\sqrt 3 } }{\sinh ^{ - 1} }\left( {\dfrac{ {\Delta u} }{ {2{L_0} } } } \right)$[26] Flate grooved plane strain specimen, tension 0 $\dfrac{ {\sqrt 3 } }{3}\left[ {1 + 2\ln \left( {1 + \dfrac{ { {\delta _0} } }{ {4{R_0} } } } \right)} \right]$[24] $\dfrac{2}{ {\sqrt 3 } }\ln \left( {\dfrac{ { {\delta _0} } }{ { {\delta _{\text{f} } } } } } \right)$[24] Cylindrical specimen, compression −1 −1/3 $2\ln \left( {\dfrac{ { {a_{\text{f} } } }}{ { {a_0} } } } \right)$[24] Notched round bar, compression −1 $- \dfrac{1}{3} - \ln \left( {1 + \dfrac{ { {a_0} } }{ {2{R_0} } } } \right)$[25] $2\ln \left( {\dfrac{ { {a_{\text{f} } } }}{ { {a_0} } } } \right)$[24] Notes: a0—Initial radius at the minimum cross section of a smooth round bar or a notched round bar; af—Radius at fracture; R0—Initial radius at the notch of a notched round bar or a flat grooved plate; ∆u—Displacement to fracture of a pure shear specimen; L0—Initial gauge width of a pure shear specimen; δ0—Thickness at the minimum cross section of a flat grooved plate; δf—Thickness at fracture. 表 2 Johnson-Cook(J-C)模型失效判据中材料参数值
Table 2. Determined values of the Johnson-Cook (J-C) fracture criterion parameters
A1 A2 A3 A4 A5 0.08 0.11 −4.70 − − Note: A1-A5—Material constant. 表 3 Bai-Wierzbicki(B-W)模型失效判据中材料参数值
Table 3. Determined values of the Bai-Wierzbicki (B-W) fracture criterion parameters
B1 B2 B3 B4 B5 B6 0.18 −0.97 0.17 −1.20 0.31 −2.04 Note: B1-B6—Material constant. 表 4 Lou-Yooh(L-Y)失效判据中材料参数值
Table 4. Determined values of the Lou-Yooh (L-Y) fracture criterion parameters
C1 C2 C3 C4 0.71 1.09 0.12 0.28 Note: C1-C4—Material constant. 表 5 修正的Mohr-Coulomb(MM-C)失效判据中材料参数值
Table 5. Determined values of the modified Mohr-Coulomb (MM-C) fracture criterion parameters
K/MPa n c1 c2/MPa $ {{c}}_\theta ^{\text{c}} $ $ {{c}}_{\theta}^{\text{s}} $ 795.0 0.14 0.105 333.8 1.0 0.924 Notes: K—Material constant; n—Strain hardening exponent; c1—Coefficient of friction; c2—Shear strength of ductile material; $c_{\theta }^{\text{c}} $—Effect of hydrostatic pressure on plastic behavior of material; $c_{\theta }^{\text{s}} $—Effect of Lode angle parameter on plastic behavior of material. -
[1] SU J, LI Y, DUAN M, et al. Investigation on particle strengthening effect in in-situ TiB2/2024 composite by nanoindentation test[J]. Materials Science & Engineering A,2018,727:29-37. [2] WANG R, GUO W, WANG J, et al. Effects of stress state, strain rate, and temperature on fracture behavior of in situ TiB2/2024 Al composite[J]. Mechanics of Materials,2020,151:103641. doi: 10.1016/j.mechmat.2020.103641 [3] KARTHISELVA N, BAKSHI S. Carbon nanotube and in-situ titanium carbide reinforced titanium diboride matrix composites synthesized by reactive spark plasma sintering[J]. Materials Science & Engineering A,2016,663:38-48. [4] YANG H, CAI Z, ZHANG Q, et al. Comparison of the effects of Mg and Zn on the interface mismatch and compression properties of 50vol% TiB2/Al composites[J]. Ceramics International,2021,47:22121-22129. doi: 10.1016/j.ceramint.2021.04.234 [5] LI W, YANG Y, LIU J, et al. Enhanced nanohardness and new insights into texture evolution and phase transformation of TiAl/TiB2 in-situ metal matrix composites prepared via selective laser melting[J]. Acta Materialia,2017,136:90-104. doi: 10.1016/j.actamat.2017.07.003 [6] JIANG R, CHEN X, GE R, et al. Influence of TiB2 particles on machinability and machining parameter optimization of TiB2/Al MMCs[J]. Chinese Journal of Aeronautics,2018,31(1):187-196. doi: 10.1016/j.cja.2017.03.012 [7] GENG J, LIU G, WANG F, et al. Microstructural and mechanical anisotropy of extruded in-situ TiB2/2024 composite plate[J]. Materials Science & Engineering A,2017,687:131-140. [8] LIN K, WANG W, JIANG R, et al. Thermo-mechanical behavior and constitutive modeling of in situ TiB2/7050 Al metal matrix composites over wide temperature and strain rate ranges[J]. Materials,2019,12(8):1212. doi: 10.3390/ma12081212 [9] WANG H, ZHANG H, CUI Z, et al. Compressive response and microstructural evolution of in-situ TiB2 particle-reinforced 7075 aluminum matrix composite[J]. Transactions of Nonferrous Metals Society of China,2021,31(5):1235-1248. doi: 10.1016/S1003-6326(21)65574-7 [10] 叶想平, 李英雷, 翁继东, 等. 颗粒增强金属基复合材料的强化机理研究现状[J]. 材料工程, 2018, 46(12):28-37. doi: 10.11868/j.issn.1001-4381.2016.001214YE Xiangping, LI Yinglei, WENG Jidong, et al. Research status on strengthening mechanism of particle-reinforced metal matrix composites[J]. Journal of Materials Engineering,2018,46(12):28-37(in Chinese). doi: 10.11868/j.issn.1001-4381.2016.001214 [11] GAO X, ZHANG T, HAYDEN M, et al. Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy[J]. International Journal of Plasticity,2009,25(12):2366-2382. doi: 10.1016/j.ijplas.2009.03.006 [12] OROWAN E. Notch brittleness and the strength of metals[J]. Transactions of the Institution of Engineers and Shipbuilders in Scotland,1945,89:165-215. [13] BRIDGMAN P. Studies in large plastic flow and fracture with special emphasis on the effects of hydrostatic pressure[M]. New York: McGraw-Hill, 1952. [14] HANCOCK J, MACKENZIE A. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states[J]. Journal of Mechanics Physics of Solids, 1976, 24(2-3): 147-160. [15] HANCOCK J, BROWN D. On the role of strain and stress state in ductile failure[J]. Journal of Mechanics Physics of Solids,1983,31(1):1-24. doi: 10.1016/0022-5096(83)90017-0 [16] MCCLINTOCK F. A criterion for ductile fracture by the growth of holes[J]. Journal of Applied Mechanics,1968,35(2):363-371. doi: 10.1115/1.3601204 [17] RICE J, TRACEY D. On the ductile enlargement of voids in triaxial stress fields[J]. Journal of Mechanics Physics of Solids, 1969, 17(3): 201-217. [18] KIM J, ZHANG G, GAO X. Modeling of ductile fracture: Application of the mechanism-based concepts[J]. International Journal of Solids and Structures,2007,44(6):1844-1862. doi: 10.1016/j.ijsolstr.2006.08.028 [19] BAI Y, WIERZBICKI T. A new model of metal plasticity and fracture with pressure and Lode dependence[J]. International Journal of Plasticity,2008,24(6):1071-1096. doi: 10.1016/j.ijplas.2007.09.004 [20] GANJIANI M. A damage model for predicting ductile fracture with considering the dependency on stress triaxiality and Lode angle[J]. European Journal of Mechanics/A Solids,2020,84:104048. doi: 10.1016/j.euromechsol.2020.104048 [21] JOHNSON G, COOK W. Fracture characteristics of three metals subjected to various strains, strain rates, temper-atures and pressures[J]. Engineering Fracture Mechanics,1985,21(1):31-48. doi: 10.1016/0013-7944(85)90052-9 [22] LOU Y, YOON J, HUH H. Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality[J]. International Journal of Plasticity,2014,54(1):56-80. [23] BAI Y, WIERZBICKI T. Application of extended Mohr-Coulomb criterion to ductile fracture[J]. International Journal of Fracture,2010,161(1):1-20. doi: 10.1007/s10704-009-9422-8 [24] BAI Y, TENG X, WIERZBICKI T. On the application of stress triaxiality formula for plane strain fracture testing[J]. Journal of Engineering Materials and Technology,2009,131(2):13-22. [25] WANG J, GUO W, GUO J, et al. The effects of stress triaxiality, temperature and strain rate on the fracture characteristics of a nickel-base superalloy[J]. Journal of Materials Engineering and Performance,2016,25(5):2043-2052. doi: 10.1007/s11665-016-2049-9 [26] BUTCHER C, ABEDINI A. Shear confusion: Identification of the appropriate equivalent strain in simple shear using the logarithmic strain measure[J]. International Journal of Mechanical Sciences,2017,134:273-283. doi: 10.1016/j.ijmecsci.2017.10.005 [27] HUANG J, GUO Y, QIN D, et al. Influence of stress triaxiality on the failure behavior of Ti-6Al-4V alloy under a broad range of strain rates[J]. Theoretical and Applied Fracture Mechanics,2018,97:48-61. doi: 10.1016/j.tafmec.2018.07.008 [28] ROTH C, MOHR D. Determining the strain to fracture for simple shear for a wide range of sheet metals[J]. International Journal of Mechanical ences,2018,149:224-240. doi: 10.1016/j.ijmecsci.2018.10.007 [29] MIRONE G, CORALLO D. A local viewpoint for evaluating the influence of stress triaxiality and Lode angle on ductile failure and hardening[J]. International Journal of Plasticity,2010,26(3):348-371. doi: 10.1016/j.ijplas.2009.07.006 [30] BAO Y, WIERZBICKI T. On fracture locus in the equivalent strain and stress triaxiality space[J]. International Journal of Mechanical Sciences,2004,46(1):81-98. doi: 10.1016/j.ijmecsci.2004.02.006