Evaluating the material strength from fracture angle under uniaxial loading

Abstract

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.

Keywords

strength / fracture / mechanics

References

[1] Schuh C A, Lund A C. Atomistic basis for the plastic yield criterion of metallic glass. Nature Materials, 2003, 2(7): 449–452

[2] Zhang Z F, Eckert J. Unified tensile fracture criterion. Physical Review Letters, 2005, 94( 9): 094301 10.1103/PhysRevLett.94.094301

[3] Qu R T, Zhang Z F. A universal fracture criterion for high-strength materials. Scientific Reports, 2013, 3(1): 1117

[4] Gall K, Sehitoglu H, Chumlyakov Y I, Kireeva I V. Tension-compression asymmetry of the stress-strain response in aged single crystal and polycrystalline NiTi. Acta Materialia, 1999, 47( 4): 1203–1217

[5] Xie H X, Yu T, Yin F X. 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

[6] Revil-Baudard B, Chandola N, Cazacu O, Barlat F. Correlation between swift effects and tension-compression asymmetry in various polycrystalline materials. Journal of the Mechanics and Physics of Solids, 2014, 70: 104–115

[7] Cheng S, Spencer J A, Milligan W W. Strength and tension compression asymmetry in nanostructured and ultrafine-grain metals. Acta Materialia, 2003, 51( 15): 4505–4518

[8] Tucker G J, Foiles S M. Quantifying the influence of twin boundaries on the deformation of nanocrystalline copper using atomistic simulations. International Journal of Plasticity, 2015, 65: 191–205

[9] Lund A C, Nieh T G, Schuh C A. Tension-compression strength asymmetry in a simulated nanocrystalline metal. Physical Review B: Condensed Matter and Materials Physics, 2004, 69( 1): 012101

[10] Gürses E, El Sayed T. On tension-compression asymmetry in ultrafine-grained and nanocrystalline metals. Computational Materials Science, 2010, 50( 2): 639–644

[11] Zhang Z F, Eckert J, Schultz L. Difference in compressive and tensile fracture mechanisms of Zr₅₉Cu₂₀Al₁₀Ni₈Ti₃ bulk metallic glass. Acta Materialia, 2003, 51(4): 1167–1179

[12] Mukai T, Nieh T G, Kawamura Y, Inoue A, Higashi K. Effect of strain rate on compressive behaviour of a Pd₄₀Ni₄₀P₂₀ bulk metallic glass. Intermetallics, 2002, 10(11-12): 1071–1077

[13] Hartl A M, Jerabek M, Freudenthaler P, Lang R W. Orientation-dependent compression/tension asymmetry of short glass fiber reinforced polypropylene: Deformation, damage and failure. Comp. Part A, 2015, 79: 14–22

[14] Hartl A M, Jerabek M, Lang R W. Anisotropy and compression/tension asymmetry of PP containing soft and hard particles and short glass fibers. Express Polymer Letters, 2015, 9( 7): 658–670

[15] Dongare A M, LaMattina B, Rajendran A M. Strengthening behaviour and tension-compression strength-asymmetry in nanocrystalline metal-ceramic composites. Journal of Engineering Materials and Technology, 2012, 134( 4): 041003

[16] Kleiser G, Revil-Baudard B, Cazacu O, Pasiliao C L. 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

[17] Kim H, Park J, Ha Y, Kim W, Sohn S S, Kim H S, Lee B J, Kim N J, Lee S. 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

[18] Zhang Q W, Zhang J, Wang Y. 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

[19] Kurukuri S, Worswick M J, Ghaffari Tari D, Mishra R K, Carter J T. Rate sensitivity and tension-compression asymmetry in AZ31B magnesium alloy sheet. Philo. Trans. Royal Soc. A, 2014, 372(2015): 20130216

[20] Dongare A M, Rajendran A M, LaMattina B, Zikry M A, Brenner D W. Tension-compression asymmetry in nanocrystalline Cu: High strain rate vs quasi-static deformation. Computational Materials Science, 2010, 49( 2): 260–265

[21] Ulacia I, Dudamell N V, Galvez F, Yi S, Perez-Prado M T, Hurtado I. Mechanical behaviour and microstructural evolution of a Mg AZ31 sheet at dynamic strain rates. Acta Materialia, 2010, 58(8): 2988–2998

[22] Revil-Baudard B, Cazacu O, Flater P, Chandola N, Alves J L. 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

[23] Alves J L, Cazacu O. 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

[24] Park S H, Lee J H, Moon B G, You B S. Tension-compression yield asymmetry in as-cast magnesium alloy. Journal of Alloys and Compounds, 2014, 617: 277–280

[25] Gravouil A, Moás N, Belytschko T. 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

[26] Sukumar N, Chopp D L, Moran B. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics, 2003, 70( 1): 29–48

[27] Geniaut S, Galenne E. A simple method for crack growth in mixed mode with X-FEM. International Journal of Solids and Structures, 2012, 49( 15-16): 2094–2106

[28] Mi Y, Aliabadi M H. Three-dimensional crack growth simulation using BEM. Computers & Structures, 1994, 52(5): 871–878

[29] Cisilino A P, Aliabadi M H. Three-dimensional BEM analysis for fatigue crack growth in welded components. International Journal of Pressure Vessels and Piping, 1997, 70( 2): 135–144

[30] Krysl P, Belytschko T. The element-free Galerkin method for dynamic propagation of arbitrary 3-D cracks. International Journal for Numerical Methods in Engineering, 1999, 44(6): 767–800

[31] Duflot M. A meshless method with enriched weight functions for three-dimensional crack propagation. International Journal for Numerical Methods in Engineering, 2006, 65(12): 1970–2006

[32] Areias P, Rabczuk T. 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

[33] Areias P, Rabczuk T, de Sá J C. A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement. Computational Mechanics, 2016, 58( 6): 1–16

[34] Areias P, Msekh M A, Rabczuk T. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143

[35] Song J H, Areias P M A, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering, 2006, 67( 6): 868–893

[36] Rao B N, Rahman S. An efficient meshless method for fracture analysis of cracks. Computational Mechanics, 2000, 26(4): 398–408

[37] Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61( 13): 2316–2343

[38] Zhang Z F, He G, Eckert J, Schultz L. Fracture mechanisms in bulk metallic glassy materials. Physical Review Letters, 2003, 91( 4): 045505

[39] Fan J T,Wu F F, Zhang Z F, Jiang F , Sun J, Mao S X. 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

[40] Fan J T, Zhang Z F, Mao S X, Shen B L, Inoue A. Deformation and fracture behaviours of Co-based metallic glass and its composite with dendrites. Intermetallics, 2009, 17(6): 445–452

[41] Chen Y, Dai L H. Nature of crack-tip plastic zone in metallic glasses. International Journal of Plasticity, 2016, 77: 54–74

[42] Tong X, Wang G, Yi J, Ren J L, Pauly S, Gao Y L, Zhai Q J, Mattern N, Dahmen K A, Liaw P K, Eckert J. Shear avalanches in plastic deformation of a metallic glass composite. International Journal of Plasticity, 2016, 77: 141–155

[43] Bringa E M, Caro A, Wang Y M, Victoria M, McNaney J M, Remington B A, Smith R F, Torralva B R, Van Swygenhoven H. Ultrahigh strength in nanocrystalline materials under shock loading. Science, 2005, 309( 5742): 1838–1841

Acknowledgements

The author, Fan J.T. would like to acknowledge the financial supports from BIT-startup for Young Scholar, Independent Research Project of State Key Laboratory of Explosion Science and Technology with Grant No. QNKT17-03, Fundamental Research Funds for the Central Universities and National Natural Science Foundation of China with Grant No. 11602024. Ms. Liuqing Yang is also acknowledged for her contribution to the computational modeling.

RIGHTS & PERMISSIONS

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature