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PHYS466 Project Kyoungmin Min, Namjung Kim and Ravi Bhadauria

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Contents INTRODUCTION CURRENT RESEARCH OBJECTIVES SIMULATION SETUP RESULT AND DISCUSSION CONCLUSION REFERENCES INTRODUCTION CURRENT RESEARCH OBJECTIVES SIMULATION SETUP RESULT AND DISCUSSION CONCLUSION REFERENCES

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Graphene: Introduction A single layer of sp 2 hybridized carbon atoms in a honeycomb lattice Multiple use in areas of Electronics, Material Science and Mechanical Engineering Extraordinary mechanical properties (fracture strength is 200 times greater than steel) [2] A single layer of sp 2 hybridized carbon atoms in a honeycomb lattice Multiple use in areas of Electronics, Material Science and Mechanical Engineering Extraordinary mechanical properties (fracture strength is 200 times greater than steel) [2] Graphene

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Current research ApproachSheet description Young’s modulus(TPa) Experimental observation [6] Graphene Structural mechanics: Stiffness matrix[6] Zigzag sheet a=9.847nm / b=1.969nm Structural mechanics: Stiffness matrix[6] Zigzag sheet a=20.178nm / b=4.184nm molecular structural mechanics[5] Zigzag sheet a=6.3945nm / b=4.1841nm molecular structural mechanics[5] Armchair sheet a=6.1531nm / b=4.2630nm Young’s modulus ChiralityShear modulus(TPa) Zigzag sheet[5] a=6.3945nm / b=4.1841nm Armchair sheet[5] a=6.1531nm / b=4.2630nm Chiral sheet[5] a=4.7130nm / b=3.2559nm Zigzag sheet[7] # of cells from 4 to ~0.490 Armchair sheet[7] # of cells from 4 to ~0.447 Shear modulus ChiralityPoisson’s ratio Zigzag sheet[7] # of cells from 4 to ~0.190 Armchair sheet[7] # of cells from 4 to ~ Poisson’s ratio ApproachRemarks Indentation loadCritical wrinkling load Wrinkling behavior

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Objectives Investigate the shear properties of finite sized graphene under various shear loading conditions. Chirality effects and size dependence Investigate the wrinkling behavior under shear conditions. Investigate the shear properties of finite sized graphene under various shear loading conditions. Chirality effects and size dependence Investigate the wrinkling behavior under shear conditions.

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Simulation Setup Adaptive Intermolecular Reactive Empirical Bond Order(AIREBO)[11] extends the interaction range by changing cutoff function based on REBO potential [13]. AIREBO potential allows for covalent bond breaking and creation with associated changes in atomic hybridization within classical potential. Adaptive Intermolecular Reactive Empirical Bond Order(AIREBO)[11] extends the interaction range by changing cutoff function based on REBO potential [13]. AIREBO potential allows for covalent bond breaking and creation with associated changes in atomic hybridization within classical potential. POTENTIAL FUNCTION Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) is used as molecular dynamics engine. LAMMPS[12]

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Simulation Setup BOUNDARY CONDITIONS Move and Fix top and bottom Move and Fix top and bottom Fix top and bottom after simple shear Fix top and bottom after simple shear Apply velocity on top Apply velocity on top 1) Apply strain directly2) Displace and relax top atoms3) Apply velocity BC Similar to 2), takes more time Time Step: 0.1 fs Relaxed steps before simulation Displaced 0.05 Å and relaxed steps Easily unstable

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Results and Discussion After 400 steps, temperature, pressure and potential energy reached at the stable state. RELAXATION Temperature Pressure Potential E Relaxation point

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Results and Discussion Temperature, pressure and potential energy show discontinuity to corroborate the fracture. UNDER SHEAR LOAD Temperature Pressure Potential E Fracture

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Shear 1 (Armchair)Shear 2 (Armchair) Shear 1 (Zigzag)Shear 2 (Zigzag) Armchair Zigzag

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Results and Discussion As the size of structure increases, more shear stress and strain can be hold. For small atoms case, chirality affects more on shear modulus comparing to large atoms case. Shear modulus increases as the size of structure increases. As the size of structure increases, more shear stress and strain can be hold. For small atoms case, chirality affects more on shear modulus comparing to large atoms case. Shear modulus increases as the size of structure increases. SHEAR STRESS-STRAIN RELATIONSHIP

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Results and Discussion As the size is increased, shear properties are converged to bulk value(shear modulus = 480GPa(zigzag) and 450GPa(armchair), shear strength=60GPa) The edge effect from different chiralities influences the behavior of the structure, especially in small size. As the size is increased, shear properties are converged to bulk value(shear modulus = 480GPa(zigzag) and 450GPa(armchair), shear strength=60GPa) The edge effect from different chiralities influences the behavior of the structure, especially in small size. SHEAR PROPERTIES Shear Modulus Shear Strength Fracture shear strain Fracture shear strain Shear modulus in bulk case = 480Gpa(zigzag) and 450GPa(armchair) Shear strength in bulk case = 60 GPa

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Results and Discussion The ratio of amplitude and half wave length relationship [10] The ratio of amplitude and half wave length relationship [10] WRINKLING BEHAVIOR AC ZZ Wrinkle view MD result, 836 atoms # of Atoms ν (Armchair)ν (Zigzag) Bulk case [9]0.21 γ γ A / λ THEORETICAL RESULTS

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Conclusion Optimized boundary condition for shear stress was explored. The shear properties and wrinkling behavior of finite size graphene have been studied in this work. Chirality effect and size dependency of shear modulus, shear strength and fracture shear strain are observed. Wrinkles were observed and needed further investigation. Optimized boundary condition for shear stress was explored. The shear properties and wrinkling behavior of finite size graphene have been studied in this work. Chirality effect and size dependency of shear modulus, shear strength and fracture shear strain are observed. Wrinkles were observed and needed further investigation.

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References [1][1] F. Schendin et al., Nature Materials, Vol. 6, pp (2007) [2][2] C. Lee et al., Science, Vol. 321, No. 5887, pp (2008) [3] [3] I. W. Frank et al., Journal of Vacuum Science and Technology B, Vol. 25, No. 6, pp (2007) [4][4] J. Meyer et al., Nature, Vol.446, pp (2007) [5][5] A. Sakhaee-Pour, Solid State Communications, Vol. 149, No. 1-2, pp (2009) [6][6] C. Li and T. W. Chou, International Journal of Solid and Structures, Vol. 40, No. 10, pp (2003) [7][7] R. Faccio et al., Journal of Physics: Condensed Matter, Vol. 21, No. 28, pp (2009) [8][8] H. Bu et al., Physics Letters A, Vol. 373, No. 37, pp (2009) [9][9] H. Zhao et al., Nano Letters, Vol. 9, No. 8, pp (2009) [10][10] Y. W. Wong and S. Pellegrino, Journal of Mechanics of Materials and Structures, Vol. 1, No. 1, pp (2006) [11][11] S. Stuart et al., Journal of Chemical Physics, Vol. 112, No. 14, pp (2000) [12] [12] S. J. Plimpton, Journal of Computational Physics, Vol. 117, pp (1995) [13][13] D. W. Crenner et al., journal of Physics: Condensed Matter, Vol. 14, No. 4, pp (2002) [14][14] K. Min and N. R. Aluru, In preparation (2010) [1][1] F. Schendin et al., Nature Materials, Vol. 6, pp (2007) [2][2] C. Lee et al., Science, Vol. 321, No. 5887, pp (2008) [3] [3] I. W. Frank et al., Journal of Vacuum Science and Technology B, Vol. 25, No. 6, pp (2007) [4][4] J. Meyer et al., Nature, Vol.446, pp (2007) [5][5] A. Sakhaee-Pour, Solid State Communications, Vol. 149, No. 1-2, pp (2009) [6][6] C. Li and T. W. Chou, International Journal of Solid and Structures, Vol. 40, No. 10, pp (2003) [7][7] R. Faccio et al., Journal of Physics: Condensed Matter, Vol. 21, No. 28, pp (2009) [8][8] H. Bu et al., Physics Letters A, Vol. 373, No. 37, pp (2009) [9][9] H. Zhao et al., Nano Letters, Vol. 9, No. 8, pp (2009) [10][10] Y. W. Wong and S. Pellegrino, Journal of Mechanics of Materials and Structures, Vol. 1, No. 1, pp (2006) [11][11] S. Stuart et al., Journal of Chemical Physics, Vol. 112, No. 14, pp (2000) [12] [12] S. J. Plimpton, Journal of Computational Physics, Vol. 117, pp (1995) [13][13] D. W. Crenner et al., journal of Physics: Condensed Matter, Vol. 14, No. 4, pp (2002) [14][14] K. Min and N. R. Aluru, In preparation (2010)

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