A. Alankar, Mechanical Engineering, IIT Bombay
Email: alankar.alankar@iitb.ac.in, Ph. No. 022-2576-9356
Course outline and tentative schedule
A. Single Crystals and Polycrystal Concepts
1. Crystal structures, defects in crystal structure (1) [1]
2. Introduction to Vector and Tensor Algebra (1) [2]
3. Elasticity Constants, Elastic Anisotropy (2) [4]
4. Introduction to dislocations (2) [6]
5. Mathematical description of Burgers vector and Circuit (1) [7]
6. Strain and stress field of a dislocation (2) [9]
7. Elastic interactions of Dislocations (3) [12]
8. Dislocation-point defect interaction (2) [14]
9. Concept of Dislocation Dynamics (2) [16]
10. Hands on Dislocation Dynamics Exercises (3) [19]
11. Dislocation-grain boundary interactions, polycrystals, crystallographic texture (2) [21]
B. Framing a Boundary Value Problem for Crystal Plasticity Modeling
1. Introduction to Continuum Mechanics, Crystal Kinematics (1) [22]
2. Approximation of Deformation Gradient, Decomposition (2) [24]
3. Displacement Gradient, Strain Tensors and Stress Tensors (2) [26]
4. Velocity Gradient, Rate of Deformation Tensor, Spin Tensor (1) [27]
5. Single Crystal Plasticity Formulations (2) [29]
6. Rate dependent vs. Rate Independent Formulations (1) [30]
7. Concept of Yield Surface from First Principles (1) [31]
8. Introduction to Integration Schemes for Crystal Plasticity Models (2) [33]
9. Homogenization and Polycrystal Plasticity (1) [34]
10. Dislocation Density Tensor, Strain Gradient and Size Effects (2) [36]
11. Current Hybrid Crystal Plasticity Models (1) [37]
12. Software and Hardware Technology for Multiscale, Multiphysics Crystal Plasticity Models (1)[38]
Based on the above it will take 38 hours i.e. ~ 25 classes. No. of classes can be adjusted based on actual days available for classes.
Grading: Exams/Tutorials: Midterm, Final, group discussions of journal articles/relevant topics. Small projects using MATLABTM/ABAQUSTM/ANSYSTM/COMSOLTM / LAMMPS or algorithms with sample calculations.
Text books / References
1. M. E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University Press, 2009
2. L. E. Malvern, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall Inc., (First Edition), 1977
3. R. J. Asaro and Vlado A. Lubarda, Mechanics of Solids and Materials, Cambridge University Press, 2006
4. D. Hull and D. J. Bacon, Introduction to Dislocations (Fifth Edition), Butterworth-Heinemann (Elsevier), 2011
5. J. P. Hirth and J. Lothe, Theory of Dislocations, Krieger Publishing Company, 1991
6. A. S. Argone, Strengthening Mechanisms in Crystal Plasticity, Oxford University Press, 2008
7. V. Bulatov and W.Cai, Computer Simulations of Dislocations, Oxford University Press, 2013
List of example projects (not limited to, can also be taken up as a team of two if class size is large)
These can also be pursued as algorithms or sample calculations.
1. MATLAB/FORTRAN/C/C++ : 3D viscoplastic deformation model. Kocks-Mecking / Estrin-Mecking models may be considered for this.
2. MATLAB : Plot crystallographic orientation. Pole and inverse pole.
3. Mathematica/MATLAB : Plot dislocation stress field and simulate the effect of external stress.
4. Mathematica/MATLAB : Represent elastic anisotropy in 3D. Dislocation-vacancy interaction.
5. ParaDis: Create random distribution of dislocations and deform.
6. ParaDis: Create a bicrystal and deform in plane strain.
7. LAMMPS: Create random distribution of dislocations and deform uniaxially.
Presentation for project
This will contain a crisp commentary of your project. Cover page + 10 slides with crisp scientific content.
Auditing this course
Auditing requires all quizzes, homeworks, exams and presentation. Based on the performance in these, AU may be assigned. No exemptions.