1. A proper parameter study and convergence check was carried out which forms a basis to the selection of the phase field parameters.

2. Introduction of randomness in grain boundary fracture toughness was carried out, thereby gaining full control of the PFM crack pattern and the extent of trans-granularity. Crack patterns were observed for both cases of plane strain and plane stress.

3. Major challenge - Elimination of the unwanted 'stepped' nature of the logarithmic Hurst Exponent curves (succeeded).

4. Test for scalability - Hurst Exponent was observed to depend on the length scale as well as the degree of randomness, with a transition from anti-persistence to persistence and vice versa.

5. Verification with real experimental crack surfaces in 2D.

6. Analytical - Development of a crack path differential equation for a material with an inherent heterogeneity under local mixed mode, which involves small scale linear perturbations in SIFs of straight cracks.

7. Comparison between analytical and simulations - a hypothetical SEN(T) with an inclined crack was considered having a toughness distribution ahead of it. 

Hurst Exponent dependence on 'degree of randomness'

Plane Stress vs Plane Strain

Observation - Prominent boundary effect in PFM simulations leading to ambiguous H values at large scale

1. Having known the material parameters, one can obtain proper PFM parameters for an intergranular fracture problem with a toughness ratio in the range (800-1600)

2. A 2D material under pure Mode-I stable crack growth exhibits local mixed mode behaviour near the crack tip which drives the crack under Principle of Local Symmetry (PLS). Its imperative to ensure PLS is satisfied at every step.

3. A material with an inherent micro-structure or a material heterogeneity (eg, an elastic mismatch) exhibits large scale correlation and a non-universal scaling/Hurst exponent. The scalability also depends on the degree/extent of randomness in the material properties.

1. PFM crack patterns are found to be slightly ambiguous towards the end due to boundary effect. As such, a small scale yielding K-field controlled test may be carried out at the cost of tremendously fine mesh and large simulation size and runtime.

2. A thorough comparison between H values for synthetically generated surfaces with established methods needs to be undertaken.

Place - CSJM University, Kanpur (formerly Kanpur University) 

Workshop conducted - LINUX

Class taught - 2nd year B.Tech CSE

Hours - 30 hours

Nature of work - 2 hour hands on training and problem solving in LINUX based OS, for 3 days a week