Research Milestones completed (June 2022 - Apr 2023)

A proper parameter study and convergence check was carried out which forms a basis to the selection of the phase field parameters.
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.
Major challenge - Elimination of the unwanted 'stepped' nature of the logarithmic Hurst Exponent curves (succeeded).
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.
Verification with real experimental crack surfaces in 2D.
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.
Comparison between analytical and simulations - a hypothetical SEN(T) with an inclined crack was considered having a toughness distribution ahead of it.

Crack Pattern after introduction of randomness in grain boundary fracture toughness

H = 0.736

H = 0.537

H = 0.541

Plane Strain

Plane Stress

Extraction of crack surface images for MATLAB image processing

Paper specimen

Aluminium specimen

Glass specimen

H = 0.544

H = 0.562 - 0.945

H = 0.43

Crack path governing ODE (function of local Mode-I, Mode-II SIF, material fracture toughness, T-Stress)

Case 1 - No Elastic mismatch (alternating strip fracture toughness)

PFM crack pattern for 5 strips ahead of notch

PFM crack pattern for 50 strips ahead of notch

Analytical vs PFM for 5 strips

Analytical vs PFM for 50 strips

Analytical 5 strips, H = 0.4011

PFM 5 strips, H = 0.8689

Analytical 50 strips, H = 0.97

PFM 50 strips, H = 0.7424

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

Case 2 - Elastic mismatch (alternating strip modulus & fracture toughness)

PFM crack pattern for 5 strips with both elastic and toughness mismatch

Analytical vs PFM for 50 strips with elastic mismatch

Analytical 50 strips, H = 1 (small scale) to H = 0.31 (large scale)

PFM 50 strips, H = 0.7162

PFM 50 strips neglecting boundary effect, H = 0.5176

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)
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.
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.

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.
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