Evaluating the material strength from fracture angle under uniaxial loading
Jitang FAN1,2()
1. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China 2. Advanced Research Institute for Multidisciplinary Science, Beijing Institute of Technology, Beijing 100081, China
The most common experimental methods of measuring material strength are the uniaxial compressive and tensile tests. Generally, shearing fracture model occurs in both the tests. Compressive strength is higher than tensile strength for a material. Shearing fracture angle is smaller than 45° under uniaxial compression and greater than 45° under uniaxial tension. In this work, a unified relation of material strength under uniaxial compression and tension is developed by correlating the shearing fracture angle in theory. This constitutive relation is quantitatively illustrated by a function for analyzing the material strength from shear fracture angle. A computational simulation is conducted to validate this theoretical function. It is full of interest to give a scientific illustration for designing the high-strength materials and engineering structures.
. [J]. Frontiers of Structural and Civil Engineering, 2019, 13(2): 288-293.
Jitang FAN. Evaluating the material strength from fracture angle under uniaxial loading. Front. Struct. Civ. Eng., 2019, 13(2): 288-293.
C ASchuh , A CLund. Atomistic basis for the plastic yield criterion of metallic glass. Nature Materials, 2003, 2(7): 449–452 https://doi.org/10.1038/nmat918
R TQu , Z F Zhang. A universal fracture criterion for high-strength materials. Scientific Reports, 2013, 3(1): 1117 https://doi.org/10.1038/srep01117
4
KGall , H Sehitoglu, Y IChumlyakov , I VKireeva . Tension-compression asymmetry of the stress-strain response in aged single crystal and polycrystalline NiTi. Acta Materialia, 1999, 47( 4): 1203–1217 https://doi.org/10.1016/S1359-6454(98)00432-7
5
H XXie , TYu, F X Yin . Tension-compression asymmetry in homogeneous dislocation nucleation stress of single crystals Cu, Au, Ni and Ni3Al. Materials Science and Engineering A, 2014, 604: 142–147 https://doi.org/10.1016/j.msea.2014.03.018
6
BRevil-Baudard , NChandola , OCazacu, FBarlat . Correlation between swift effects and tension-compression asymmetry in various polycrystalline materials. Journal of the Mechanics and Physics of Solids, 2014, 70: 104–115 https://doi.org/10.1016/j.jmps.2014.05.012
7
SCheng , J A Spencer, W W Milligan . Strength and tension compression asymmetry in nanostructured and ultrafine-grain metals. Acta Materialia, 2003, 51( 15): 4505–4518 https://doi.org/10.1016/S1359-6454(03)00286-6
8
G JTucker , S MFoiles. Quantifying the influence of twin boundaries on the deformation of nanocrystalline copper using atomistic simulations. International Journal of Plasticity, 2015, 65: 191–205 https://doi.org/10.1016/j.ijplas.2014.09.006
9
A CLund , T GNieh, C ASchuh . Tension-compression strength asymmetry in a simulated nanocrystalline metal. Physical Review B: Condensed Matter and Materials Physics, 2004, 69( 1): 012101 https://doi.org/10.1103/PhysRevB.69.012101
10
EGürses , TEl Sayed. On tension-compression asymmetry in ultrafine-grained and nanocrystalline metals. Computational Materials Science, 2010, 50( 2): 639–644 https://doi.org/10.1016/j.commatsci.2010.09.028
11
Z FZhang , JEckert, LSchultz . Difference in compressive and tensile fracture mechanisms of Zr59Cu20Al10Ni8Ti3 bulk metallic glass. Acta Materialia, 2003, 51(4): 1167–1179 https://doi.org/10.1016/S1359-6454(02)00521-9
12
TMukai , T G Nieh, Y Kawamura , AInoue , KHigashi . Effect of strain rate on compressive behaviour of a Pd40Ni40P20 bulk metallic glass. Intermetallics, 2002, 10(11-12): 1071–1077 https://doi.org/10.1016/S0966-9795(02)00137-1
13
A MHartl , MJerabek, PFreudenthaler, R WLang . Orientation-dependent compression/tension asymmetry of short glass fiber reinforced polypropylene: Deformation, damage and failure. Comp. Part A, 2015, 79: 14–22 https://doi.org/10.1016/j.compositesa.2015.08.021
14
A MHartl , MJerabek, R WLang . Anisotropy and compression/tension asymmetry of PP containing soft and hard particles and short glass fibers. Express Polymer Letters, 2015, 9( 7): 658–670 https://doi.org/10.3144/expresspolymlett.2015.61
15
A MDongare , BLaMattina, A MRajendran . Strengthening behaviour and tension-compression strength-asymmetry in nanocrystalline metal-ceramic composites. Journal of Engineering Materials and Technology, 2012, 134( 4): 041003 https://doi.org/10.1115/1.4006678
16
GKleiser , B Revil-Baudard, OCazacu , C LPasiliao . Experimental characterization and modeling of the anisotropy and tension-compression asymmetry of polycrystalline molybdenum for strain rates ranging from quasi-static to impact. JOM, 2015, 67(11): 2635–2641 https://doi.org/10.1007/s11837-015-1612-4
17
HKim , J Park, YHa , WKim , S SSohn , H SKim , B JLee, N JKim , SLee . Dynamic tension-compression asymmetry of martensitic transformation in austenitic Fe-(0.4, 1.0)C-18Mn steels for cryogenic applications. Acta Materialia, 2015, 96: 37–46 https://doi.org/10.1016/j.actamat.2015.06.021
18
Q WZhang , JZhang, YWang . Effect of strain rate on the tension-compression asymmetric responses of Ti-6.6Al-3.3Mo-1.8Zr-0.29Si. Materials & Design, 2014, 61: 281–285 https://doi.org/10.1016/j.matdes.2014.05.004
19
SKurukuri , M J Worswick, D Ghaffari Tari, R KMishra , J TCarter . Rate sensitivity and tension-compression asymmetry in AZ31B magnesium alloy sheet. Philo. Trans. Royal Soc. A, 2014, 372(2015): 20130216 https://doi.org/10.1098/rsta.2013.0216
20
A MDongare , A MRajendran, BLaMattina , M AZikry , D WBrenner . Tension-compression asymmetry in nanocrystalline Cu: High strain rate vs quasi-static deformation. Computational Materials Science, 2010, 49( 2): 260–265 https://doi.org/10.1016/j.commatsci.2010.05.004
21
IUlacia , N V Dudamell, F Galvez , SYi , M TPerez-Prado , IHurtado . Mechanical behaviour and microstructural evolution of a Mg AZ31 sheet at dynamic strain rates. Acta Materialia, 2010, 58(8): 2988–2998 https://doi.org/10.1016/j.actamat.2010.01.029
22
BRevil-Baudard , OCazacu , PFlater, NChandola , J LAlves . Unusual plastic deformation and damage features in titanium: Experimental tests and constitutive modeling. Journal of the Mechanics and Physics of Solids, 2016, 88: 100–122 https://doi.org/10.1016/j.jmps.2016.01.003
23
J LAlves , OCazacu. Micromechanical study of the dilatational response of porous solids with pressure-insensitive matrix displaying tension-compression asymmetry. Euro. J. Mech. A, 2015, 51: 44–54 https://doi.org/10.1016/j.euromechsol.2014.11.010
24
S HPark , J HLee, B GMoon , B SYou . Tension-compression yield asymmetry in as-cast magnesium alloy. Journal of Alloys and Compounds, 2014, 617: 277–280 https://doi.org/10.1016/j.jallcom.2014.07.164
25
AGravouil , N Moás, TBelytschko . Non-planar 3D crack growth by the extended finite element and level sets. Part II: Level set update. International Journal for Numerical Methods in Engineering, 2002, 53(11): 2569–2586 https://doi.org/10.1002/nme.430
26
NSukumar , D L Chopp, B Moran . Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics, 2003, 70( 1): 29–48 https://doi.org/10.1016/S0013-7944(02)00032-2
27
SGeniaut , E Galenne. A simple method for crack growth in mixed mode with X-FEM. International Journal of Solids and Structures, 2012, 49( 15-16): 2094–2106 https://doi.org/10.1016/j.ijsolstr.2012.04.015
A PCisilino , M HAliabadi. Three-dimensional BEM analysis for fatigue crack growth in welded components. International Journal of Pressure Vessels and Piping, 1997, 70( 2): 135–144 https://doi.org/10.1016/S0308-0161(96)00031-2
MDuflot . A meshless method with enriched weight functions for three-dimensional crack propagation. International Journal for Numerical Methods in Engineering, 2006, 65(12): 1970–2006 https://doi.org/10.1002/nme.1530
32
PAreias , T Rabczuk. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122 https://doi.org/10.1002/nme.4477
33
PAreias , T Rabczuk, J Cde Sá . A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement. Computational Mechanics, 2016, 58( 6): 1–16 https://doi.org/10.1007/s00466-016-1328-5
34
PAreias , M A Msekh, T Rabczuk . Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143 https://doi.org/10.1016/j.engfracmech.2015.10.042
35
J HSong , P M AAreias, TBelytschko. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering, 2006, 67( 6): 868–893 https://doi.org/10.1002/nme.1652
36
B NRao , SRahman. An efficient meshless method for fracture analysis of cracks. Computational Mechanics, 2000, 26(4): 398–408 https://doi.org/10.1007/s004660000189
37
TRabczuk , T Belytschko. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61( 13): 2316–2343 https://doi.org/10.1002/nme.1151
J TFan , F FWu, Z F Zhang , F Jiang , JSun , S XMao . Effect of microstructures on the compressive deformation and fracture behaviours of Zr47Cu46Al7 bulk metallic glass composites. Journal of Non-Crystalline Solids, 2007, 353( 52-54): 4707–4717 https://doi.org/10.1016/j.jnoncrysol.2007.06.062
40
J TFan , Z FZhang, S XMao , B LShen , AInoue . Deformation and fracture behaviours of Co-based metallic glass and its composite with dendrites. Intermetallics, 2009, 17(6): 445–452 https://doi.org/10.1016/j.intermet.2008.12.004
XTong , G Wang, JYi , J LRen , SPauly , Y LGao , Q JZhai, NMattern , K ADahmen , P KLiaw , JEckert . Shear avalanches in plastic deformation of a metallic glass composite. International Journal of Plasticity, 2016, 77: 141–155 https://doi.org/10.1016/j.ijplas.2015.10.006
43
E MBringa , ACaro, Y M Wang , M Victoria , J MMcNaney , B ARemington , R FSmith, B RTorralva , HVan Swygenhoven . Ultrahigh strength in nanocrystalline materials under shock loading. Science, 2005, 309( 5742): 1838–1841 https://doi.org/10.1126/science.1116723
