The objective is to introduce large-scale atomistic modeling techniques and motivate its importance for solving problems in modern engineering sciences. We demonstrate how atomistic modeling can be successfully applied to understand how ma terials fail under extreme loading, emphasizing on the competition between ductile and brittle ma terials failure. We will demonstrate the techniques in describing failure of a copper nano-crystal.
We offer lectures covering the theoretical and numerical basics associated with failure of ma terials. After the lectures, students will work on modeling fracture of a copper nano-crystal using atomistic simulation. Participants will learn the basics of atomistic modeling, including setting up the problem, choosing and using interatomic potentials, analysis and visualization of results. We will link our modeling results to continuum mechanics theories of fracture and dislocation plasticity. Ani ma tions of the failure processes will be generated. We will discuss limitations and potentials of atomistic modeling of fracture of materials.
All simulation codes and numerical tools will be explained in detail. The codes are Open Source and will be provided to participants.
Schedule and Topics Covered
Jan. 9 (Monday): Introduction to classical molecular dynamics: Brittle versus ductile materials behavior (basic concepts of MC/MD, interatomic potentials, failure dynamics of materials and brittle versus ductile behavior) ^
Lecture notes (Lecture 1)
Jan. 11 (Wednesday): Deformation of ductile materials like metals using billion-atom simulations with massively parallelized computing techniques (geometry of dislocations, plasticity, dislocation nucleation and propagation, stacking fault, dislocation reactions, work hardening mechanisms, ultra-large scale computing)
Lecture notes (Lecture 2)
Jan. 13 (Friday): Dynamic fracture of brittle materials: How nonlinear elasticity and geometric confinement governs crack dynamics (dynamic fracture in brittle materials and the role of hyperelasticity, crack limiting speed, instability dynamics, cracks at interfaces)
Lecture notes (Lecture 3), Movie of supersonic fracture, Movie of interface fracture
Jan. 17 (Tuesday): Size effects in deformation of materials: Smaller is stronger (size effects in materials, Griffith criterion of fracture initiation, adhesion and size effects, shape optimization, fracture of protein crystals)
Lecture notes (Lecture 4)
Jan. 19 (Thursday): Introduction to the problem set: Atomistic modeling of fracture of copper (code compilation and usage, commands, pre- and post-processing)
Lecture notes (Lecture 5); problem set (due Jan. 29, 2005)
The IAP activity can be taken for credit. Both undergraduate and graduate level students are welcome to participate. Details will be posted on the IAP website (http://student.mit.edu/iap/fc1.html).
References and Reading Material
- Ultra large-scale simulations of dynamic materials failure (review article by Buehler & Gao, to appear 2006)
- Atomistic modeling of dynamic fracture (review article by Buehler & Gao, to appear 2006r)
- Constrained grain boundary diffusion in ultra thin copper films (review article by Buehler et al., to appear 2006)
- The dynamical complexity of work-hardening: a large-scale molecular dynamics simulation (Buehler et al., AMS, 2005)
- Deformation mechanics of twin lamella nanocrystalline copper (Buehler, 2006, unpublished
- Baskes, M.I., Embedded-atom method: Derivation and application to impurities, surfaces and other defects in metals. Phys. Rev. B, 1984. 29 (12): p. 6443-6543.
- Cleri, F., et al., Atomic-scale mechanism of crack-tip plasticity: Dislocation nucleation and crack-tip shielding. Phys. Rev. Lett, 1997. 79 : p. 1309-1312.
- Mishin, Y., et al., Structural stability and lattice defects in copper: Ab-initio, tight-binding and embedded-atom calculations. Phys. Rev. B, 2001. 63 : p. 224106.
- Katagiri, M., et al., The dynamics of surfaces of metallic and monolayer systems: Embedded-atom molecular dynamics study. Materials Science And Engineering A-Structural Materials Properties Microstructure And Processing, 1996. 217 : p. 112-115.
- Heino, P., H. Häkkinen, and K. Kaski, Molecular-dynamics study of mechanical properties of copper. Europhysics Letters, 1998. 41 : p. 273-278.
- Komanduri, R., N. Chandrasekaran, and L.M. Raff, Molecular dynamics (MD) simulations of uniaxial tension of some single-crystal cubic metals at nanolevel. Int. J. Mech. Sciences, 2001. 43 : p. 2237-2260.
- Theory of dislocations, Hirth JP and Lothe J. New York: McGraw-Hill.
- Fractography: Observing, Measuring and Interpreting Fracture Surface Topography, Derek Hull, Cambridge University Press, 1999.