Since 1963
ARTICLE
Modeling of dynamic growth of a micro-scaled void based on strain gradient elasto-plasticity
| 1 | Jiangsu University, Faculty of Civil Engineering and Mechanics, Zhenjiang, Jiangsu Province, China |
| 2 | Wuhan University of Science and Technology, The State Key Laboratory of Refractories and Metallurgy, Wuhan, Hubei
Province |
| 3 | Institute of Applied Physics and Computational Mathematics, Beijing, China |
CORRESPONDING AUTHOR
Submission date: 2019-10-21
Final revision date: 2020-02-11
Acceptance date: 2020-02-25
Online publication date: 2020-10-15
Publication date: 2020-10-15
Journal of Theoretical and Applied Mechanics 2020;58(4):927–941
KEYWORDS
TOPICS
ABSTRACT
Void initiation and growth serve as an important mechanism in ductile failures in metals.
Particularly, on the micron-level, the extra hardening effect associated with strain gradient
is accounted for by adopting strain gradient elasto-plasticity instead of the conventional
plasticity. Effects of inertial, strain gradient hardening and thermal softening are formulated
analytically for the case where a spherical void expands under external hydrostatic stress.
As demonstrated by our results, the inertia effect firstly tends to hinder but then promotes
the void growth. The threshold stress required for rapid void growth is lifted due to extra
hardening of strain gradient so that the growth of a smaller void is delayed more remarkably.
A considerable thermal softening phenomenon is observed here, which is caused by plastic
work during the deformation process. The final void growth rate is mainly related to the
maximum loading, which is consistent with the prediction based on the classical plastic
theory.
REFERENCES (25)
1.
Benzerga A.A., Leblond J.B., 2010, Ductile fracture by void growth to coalescence, Advances in Applied Mechanics, 44, 169-305.
2.
Chakravarthy S., Curtin W.A., 2011, Stress-gradient plasticity, Proceedings of the National Academy of Sciences, 108, 38, 15716-15720.
3.
Chung D., Horgan C., Abeyaratne R., 1987, A note on a bifurcation problem in finite plasticity related to void nucleation, International Journal of Solids and Structures, 23, 7, 983-988.
4.
Cortés R., 1992, Dynamic growth of microvoids under combined hydrostatic and deviatoric stresses, International Journal of Solids and Structures, 29, 13, 1637-1645.
5.
Czarnota C., Mercier S., Molinari A., 2006, Modelling of nucleation and void growth in dynamic pressure loading, application to spall test on tantalum, International Journal of Fracture, 141, 1, 177-194.
6.
Ehrler B., Hou X.D., Zhu T.T., P’ng K.M.Y., Walker C.J., Bushby A.J., Dunstan D.J., 2008, Grain size and sample size interact to determine strength in a soft metal, Philosophical Magazine, 88, 25, 3043-3050.
7.
Fleck N.A., Hutchinson J.W., 2001, A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49, 10, 2245-2271.
8.
Huang Y., Hutchinson J., Tvergaard V., 1991, Cavitation instabilities in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, 39, 2, 223-241.
9.
Jacques N., Mercier S., Molinari A., 2012, Effects of microscale inertia on dynamic ductile crack growth, Journal of the Mechanics and Physics of Solids, 60, 4, 665-690.
10.
Johnson J., 1981, Dynamic fracture and spallation in ductile solids, Journal of Applied Physics, 52, 4, 2812-2825.
11.
Liu D., He Y., Dunstan D.J., Zhang B., Gan Z., Hu P., Ding H., 2013, Anomalous plasticity in the cyclic torsion of micron scale metallic wires, Physical Review Letters, 110, 24, 244301.
12.
Liu J.X., 2015, Analysis of surface effects on the deformation of a nanovoid in an elasto-plastic material, Applied Mathematical Modelling, 39, 17, 5091-5104.
13.
Liu J.X., Demiral M., El Sayed T., 2014, Taylor-plasticity-based analysis of length scale effects in void growth, Modelling and Simulation in Materials Science and Engineering, 22, 7, 075005.
14.
Liu J.X., Soh A.K., 2016, Strain gradient elasto-plasticity with a new Taylor-based yield function, Acta Mechanica, 227, 10, 3031-3048.
15.
Liu J.X., Sayed T.E., 2013, A variational constitutive model for the distribution and interactions of multi-sized voids, International Journal of Damage Mechanics, 23, 1, 124-152.
16.
Luo Y., Yang G., Shao Y., Yao K., 2018, The effect of void defects on the shear band nucleation of metallic glasses, Intermetallics, 94, 114-118.
17.
Molinari A., Wright T.W., 2005, A physical model for nucleation and early growth of voids in ductile materials under dynamic loading, Journal of the Mechanics and Physics of Solids, 53, 7, 1476-1504.
18.
Navarro P.F., Chiu P.-H., Higgins A., Serge M., Benson D.J., Nesterenko V.F., 2018, Shear band patterning and post-critical behavior in AISI 4340 steel with different microstructure, International Journal of Impact Engineering, 112, 144-154.
19.
Ortiz M., Molinari A., 1992, Effect of strain hardening and rate sensitivity on the dynamic growth of a void in a plastic material, Journal of Applied Mechanics, 59, 1, 48.
20.
Sartori C., Mercier S., Jacques N., Molinari A., 2015, Constitutive behavior of porous ductile materials accounting for micro-inertia and void shape, Mechanics of Materials, 80, 324-339.
21.
Sartori C., Mercier S., Jacques N., Molinari A., 2016, On the dynamic behavior of porous ductile solids containing spheroidal voids, International Journal of Solids and Structures, 97-98, 150-167.
22.
Wilkerson J., Ramesh K., 2014, A dynamic void growth model governed by dislocation kinetics, Journal of the Mechanics and Physics of Solids, 70, 262-280.
23.
Wright T., 2002, The Physics and Mathematics of Adiabatic Shear Bands, Cambridge University Press, Cambridge.
24.
Wu X.Y., Ramesh K.T.,Wright T.W., 2003a, The coupled effects of plastic strain gradient and thermal softening on the dynamic growth of voids, International Journal of Solids and Structures, 40, 24, 6633-6651.
25.
Wu X.Y., Ramesh K.T., Wright T.W., 2003b, The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading, Journal of the Mechanics and Physics of Solids, 51, 1, 1-26.
RELATED ARTICLE
