Twinning in titanium — a wee micromechanics quest

This is the second in a series of Blog Posts reporting on our recent scientific research in the @ExpMicroMech group to capture a bit of “life behind the scenes” of our work and to give you a flavour of what we found exciting / difficult / and maybe a sneak peak of what lies around the corner.

In this work we have used electron diffraction within the scanning electron microscope to study how deformation twins grow, and due to the persistence of “Reviewer #3” we’ve also addressed the ‘unloading problem’ (we measure stress states after the material has been deformed) using some excellent simulation too. This work is important as twins are a major deformation mode, controlling the final microstructure of processed material and the behaviour of the metal in service (such as during bird strike).

Guo, Y., Abdolvand, H., Britton, T.B., and Wilkinson, A.J. Growth of {11–21} twins in titanium: A combined experimental and modelling investigation of the local state of deformation Acta Materialia (2016)

Initial Comments

The work was predominantly carried about by the very talented Yi Guo (who’s currently over at EMPA), as part of his PhD. Yi’s work was part of a larger study of titanium materials in the Oxford micromechanics group (headed by Angus).

Yi’s work followed, in part, from some work in my own PhD, but frankly his work is much cleaner, better analysed and adds more value than the ‘point and shoot’ analysis I initially performed. In particular, Yi managed to get out the local stress state ahead of the twins; a major step above and beyond the simple analysis of stored dislocation content where twins were terminating. This was combined with some nifty modelling by Hamid and in total the analysis was used to understand why twins grow longer and/or fatter, and where they will extend during further deformation to accommodate local strain.

The review of this paper was especially tiresome and painful. In total it took about 18 months to get this fully through review and into the literature, despite the work being some of the highest quality mechanical analysis of twin stress fields in the literature. On the plus side, Yi held his head up high during a messy review process, and as a highlight we managed to celebrate the manuscript’s one year anniversary:

Sometimes addressing papers results in their having their own anniversaries!

The nuts & bolts — what are twins & why are they important?

Metals deform plastically through the operation of either dislocation mediated slip or deformation twinning.

Dislocation slip is related to the motion of small defects on particular crystal planes and this is relatively easy to operate and generates a reasonable homogeneous deformation field. There are two important points here: (1) for each slip system, dislocation activity can happen in both directions according to the local stress state; (2) movement of one dislocations results in a small amount of change in the crystal shape, and so there is unlikely to be a huge build up on stress when a single dislocation runs into another interface (such as a precipitate or grain boundary) in the material.

However, in less symmetric crystals, such as titanium, another deformation mode based upon twinning may operate. Twins enable massive crystal shear due to a local reorientation of the crystal lattice. They are an extremely heterogenous deformation mode and the sense of the applied stress state is important. Unlike slip, twining is: (1) directionally important, the shear from the formation or growth of a twin can only enable the crystal to change shape in one direction; (2) the deformation per twin volume is high. Furthermore, twinning results in massive crystallographic reorientation and so this important in texture formation.

These two points highlight how twinning is a critical deformation mode, especially in understanding the performance and processing of alloy systems of titanium (and other related alloys, like zirconium).

For more about slip and twinning — head over to DoITPoMS: slip and twinning.

What have we found?

The “Local Schmid Factor” — which uses the local shear stress at each point — is critical to show when twin lengthening and twin thickening is encouraged.

Twins grow at their interfaces. The driving force for growth is related to the stress state, which may encourage the material ahead of the interface and twin. Growth of a twin either is either through twin lengthening or twin thickening.

Using high resolution electron backscatter diffraction (HR-EBSD), we have found that the local stress state near the twin interface tells us whether the twin will fatten or lengthen, indicated by high Local Schmid Factor (LSF) values (in red in the graphical abstract above).

The neat ‘trick’ in this paper is that we have transformed this stress state to explore the shear stress resolved into a frame of reference that would enable the twin to grow. We find that the shear stress ahead of this twin front is critically: (1) different to the global stress state; (2) different for different parts of the twin. This means that the locally resolved shear stress controls twin growth.

Local vs Global Schmid Factor

The Schmid Factor is how well the stress state at a material point is aligned to cause plastic deformation. In effect we transform the applied stress tensor into a local form that considers the shear of a particular crystallographic element.

Crystal shear can be related to particular deformation modes.

A “first order” estimation of the deformation can be taken by considering how the macroscopic, i.e. global, stress state is applied to the each grain in turn. In this evaluation we consider that the each grain is not connected to it’s neighbours. This is like squishing a cake and thinking that the filling and sponge will deform similarly.

A “second order” estimation considers how the deformation is resolved into each point within a grain, given that deformation in a “local” region must be accommodated by the collective deformation of all grains. This involves the superposition of the macroscopic strain state, the local grain neighbourhood, and the local deformation within each grain (e.g. strain and stress states due to prior plastic deformation). This is like squishing a cake and noting that the filling will be extruded sideways, as the sponge camps down.

Comparison of the “global” vs “local” Schmid factors indicates that the activation of twinning variants can be more readily understood at a local scale. The blue stars indicate which variant is active.

Our findings show that twin growth can be predicted best through use of the local, rather than global, Schmid factor. This explains why numerous other studies in the past were not showing strong correlation between the macroscopic (i.e. global) stress state and which twins were being formed.

Simulations — why bother?

This paper is mostly exprimental. However, we have a problem — all our experiments are carried out once the sample has been unloaded. The question that we were dogged with in review centred upon this fact and it queried whether the stresses that we measured were useful. This is where Hamid’s contribution was most helpful (note that he also helped with lots of other parts of the analysis too!).

Crystal plasticity simulations demonstrate the the final stresses after unloading (right hand column) represent the stress just after twinning. This was important to get the paper through review.

We used a crystal plasticity finite element representation of twinning — simplified mechanically, but enough to get an idea of how much our local twin structures could relax. Our findings showed that the shear stress around the twin was indeed ‘locked in’ due to the very strong twinning shear strain associated with the reorientation ahead of the twin. This step was critical in persuading Acta Materialia to re-consider our paper as a new submission and made it sail through review.

Stressing about the local behaviour of materials

The presence of individual grains is important to predict material performance. Here the grains are shown as different colours in this polarised light micrograph of a titanium alloy (author’s image).

At the microstructural length scale (below ~100 µm) the behaviour of the material in a local region will be different, depending on the orientations of grains within the grain cluster. This results in anisotropic local responses, where the performance of each cluster of grains is controlled both by the macroscopic stress state (i.e. how a plate of material is bent) but also due to the local constraint of different grains pulling on each other. This is compounded by heterogenous deformation induced by local twinning, which massively alters the local stress state. In effect, each part of the material does not ‘care’ what the global stress state is doing, instead it is how a cluster of atoms ‘feels’ the local stress at a local level that controls the ultimate response.

Ultimately the implication of this paradigm is that: (1) we have to drive understanding of material performance from the crystal scale upwards; (2) the local microstructure will dominate performance, especially in extremes such as fatigue and failure, and this is especially true in hexagonal materials where twins form.

As a sneak peek, the importance of twins in performance and microstructural formation will become apparent with Vivian’s next couple of papers on zirconium.

The whole paper is worth a read — it’s only “in-press” at the moment but can be found here:

Next time you jet around the world — spare a moment for all the neat engineering that makes you fly.

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You can head over to twitter to follow Dr Ben Britton as @BMatB, or keep up to date with the group’s work via @ExpMicroMech.