PhD Studentship: Understanding Crack Branching via Multiscale Mathematical Methods

Research theme: Applied Mathematics, Materials

This 3.5 year PhD project is funded by the MADSIM Project (School of Natural Sciences growth fund). Funding is for Home students and EU students with settled status. Funding covers home tuition fees and provides a stipend at the UKRI rate (£19,237 for 2024/25). The start date is between 1st September - 1st October.

There are many examples of branching in nature: the most celebrated of these is the way that rivers form by the coalescence of many small streams and rivers which build up to form a major river. Working the other way round, a single initial crack inside a material can bifurcate many times and spread out in much the same way that a growing tree forms by branches splitting into small ones. Current understanding of crack growth is that the branching is dictated by a purely a set of local conditions which ‘blindly’ build up the large branched networks that may result.
We want to explore a) the variety of branched structures that we see emerging in different materials and how they occur in 3D b) understand if and how the branched crack network behind the propagating crack front is actually influencing the cracking behaviour. Lastly c) inversely we can investigate what the material properties must be to give rise to the branching behaviour seen.
In particular, we want to examine and characterise the distribution of stress as well as the geometry and scale of the crack branching to bring insights into the crack branching behaviour in different materials. These insights can then be applied to real structures.

The specific aims of the project are:

• Develop an experimentally-validated, multiscale model to help explain the branching behaviour seen in different materials.
• Use the model to investigate macroscale influences on the microscale behaviour of the crack tip.
• Use the model to help separate out ‘symptoms’ and ‘causes’ of crack branching.
• Starting with the observations of cracking from large 3D datasets use the model to explain the parameters of the material systems.
• Use the model simulations to investigate possible methods for controlling crack branching to tune material performance.

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

We strongly recommend that you contact the supervisors for this project before you apply: Prof Andrew Hazel and Prof Timothy Burnett (Andrew.Hazel@manchester.ac.uk, Timothy.Burnett@manchester.ac.uk).

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