Fracture Size Effect of Titanium Sheets in Microforming and Its Meso Damage Criterion

doi:10.3901/JME.2022.16.051

Abstract

Abstract: The fracture size effect of titanium sheet was studied by uniaxial tensile experiments. It was found that the elongation and fracture limit stress decreases significantly with the increase of grain size. Observations made on the fracture morphologies show an evident transition from a typical ductile fracture surface of dense dimples to a river-pattern cleavage with the increase of grain size. It is explained that the high density of dislocation accumulation at grain boundaries have a significant shielding effect on the crack propagation for specimens with a small grain size. However, the shielding effect is weakened with the increase of grain size, leading to the easier crack propagation and the reduction of formability. In order to capture the fracture size effect of titanium sheets, a novel meso-scale damage propagation failure criterion considering the grain size effect on the dislocation shielding is established. Compared with the experimental results, the criterion is found capable in predicting the fracture behavior of ultra-thin titanium sheets at different grain size conditions by reflecting the mesoscopic fracture mechanism.

Key words: titanium sheet, fracture mechanism, meso damage mechanical model, damage fracture criterion, size effect

CLC Number:

TG156

XU Zhutian, SUN Lei, JIANG Tianhao, PENG Linfa, LAI Xinmin. Fracture Size Effect of Titanium Sheets in Microforming and Its Meso Damage Criterion[J]. Journal of Mechanical Engineering, 2022, 58(16): 51-57.

References

[1] LAI Xinmin, FU Mingwang, PENG Linfa. Sheet metal meso-and microforming and their industrial applications[M]. Boca Raton: CRC Press, 2018.
[2] BAO Jianxing, XU Jie, QU Jiazheng, et al. Electrically-assisted micro-forming process of gear structure in TA15 titanium alloy[J]. Journal of Mechanical Engineering, 2021, 57(1): 210-216. 包建兴, 徐杰, 曲家正, 等. TA15钛合金齿轮结构电流辅助微成形工艺研究[J]. 机械工程学报, 2021, 57(1): 210-216.
[3] RAN Jiaqi, XU Li, WANG Jilai, et al. Influence of size effect to constitutive model and damage evolution in micro scaled plastic deformation under different strain rate[J]. Journal of Mechanical Engineering, 2019, 55(16): 69-76. 冉家琪, 徐力, 王继来, 等. 多应变速率下尺寸效应对黄铜微尺度塑性变形本构及损伤演化的影响[J]. 机械工程学报, 2019, 55(16): 69-76.
[4] FU M W, WANG J L. Size effects in multi-scale materials processing and manufacturing [J]. International Journal of Machine Tools and Manufacture, 2021, 167: 103755.
[5] WANG J L, FU M W, RAN J Q. Analysis of size effect on flow-induced defect in micro-scaled forming process [J]. The International Journal of Advanced Manufacturing Technology, 2014, 73(9): 1475-1484.
[6] FURUSHIMA T, TSUNEZAKI H, MANABE K-i, et al. Ductile fracture and free surface roughening behaviors of pure copper foils for micro/meso-scale forming [J]. Int. J. Mach. Tool Manu., 2014, 76: 34-48.
[7] XU Z T, PENG L F, FU M W, et al. Size effect affected formability of sheet metals in micro/meso scale plastic deformation: Experiment and modeling [J]. International Journal of Plasticity, 2015, 68: 34-54.
[8] GUO N, SUN C, FU M. Size effect affected deformation characteristics in micro deep drawing of TWIP domed-bottom cups[J]. Procedia Engineering, 2017, 207: 2072-2077.
[9] ZHAO R, LI X J, WAN M, et al. Fracture behavior of Inconel 718 sheet in thermal-aided deformation considering grain size effect and strain rate influence [J]. Materials & Design, 2017, 130: 413-425.
[10] WANG J, LI C, WAN Y, et al. Size effect on the shear damage under low stress triaxiality in micro-scaled plastic deformation of metallic materials[J]. Materials & Design, 2020, 196: 109107.
[11] LI X, CHEN Z, DONG C. Size effect on the damage evolution of a modified GTN model under high/low stress triaxiality in meso-scaled plastic deformation[J]. Materials Today Communications, 2021, 26: 101782.
[12] ZHENG Q, SHIMIZU T, YANG M. Grain size effect on mechanical behavior of thin pure titanium foils at elevated temperatures[J]. International Journal of Mechanical Sciences, 2017, 133: 416-425.
[13] NIE D, LU Z, ZHANG K. Grain size effect of commercial pure titanium foils on mechanical properties, fracture behaviors and constitutive models[J]. Journal of Materials Engineering and Performance, 2017, 26(3): 1283-1292.
[14] ZHU C, XU J, YU H, et al. Size effect on the high strain rate micro/meso-tensile behaviors of pure titanium foil [J]. Journal of Materials Research and Technology, 2021, 11: 2146-2159.
[15] SUN L, XU Z, PENG L, et al. Effect of grain size on the ductile-brittle fracture behavior of commercially pure titanium sheet metals[J]. Materials Science and Engineering: A, 2021, 822: 141630.
[16] ARMSTRONG R W. The influence of polycrystal grain size on several mechanical properties of materials [J]. Metallurgical and Materials Transactions B, 1970, 1(5): 1169-1176.
[17] NAHSHON K, XUE Z. A modified Gurson model and its application to punch-out experiments[J]. Eng. Fract. Mech., 2009, 76(8): 997-1009.
[18] NAHSHON K, HUTCHINSON J W. Modification of the Gurson model for shear failure[J]. European Journal of Mechanics - A/Solids, 2008, 27(1): 1-17.
[19] NEEDLEMAN A. A continuum model for void nucleation by inclusion debonding[J]. Journal of Applied Mechanics, 1987, 54(3): 525-531.
[20] CHEN Z, DONG X. The GTN damage model based on Hill'48 anisotropic yield criterion and its application in sheet metal forming [J]. Comp. Mater. Sci., 2009, 44(3): 1013-1021.
[21] TENG B, WANG W, LIU Y, et al. Bursting prediction of hydroforming aluminium alloy tube based on Gurson-Tvergaard-Needleman damage model[J]. Procedia Engineering, 2014, 81(Supplement C): 2211-2216.
[22] ZHANG Yanbing, FENG Hui, FANG Qihong, et al. Emissiong criterion fo a screw dislocation from a semi-infinite wedge crack penetrating an inhomogeneity[J]. Chinese Journal of Solid Mechanics, 2013, 34(5): 501-507. 张艳兵, 冯慧, 方棋洪, 等. 穿透夹杂界面的半无限楔形裂纹尖端螺型位错的发射研究[J]. 固体力学学报, 2013, 34(5): 501-507.
[23] HIGASHIDA K, TANAKA M, HARTMAIER A, et al. Analyzing crack-tip dislocations and their shielding effect on fracture toughness [J]. Materials Science and Engineering: A, 2008, 483: 13-18.