# Nanoscale Undulation of Elastic Fields During Deformation Twinning in FCC Metals

## TL;DR

This paper uses advanced modeling to show how elastic fields undulate at the nanoscale during deformation twinning in metals, influencing the formation of twinned microstructures.

## Contribution

The study introduces a geometrically nonlinear phase-field model to reveal nanoscale elastic undulations during deformation twinning in FCC metals.

## Key findings

- Critical shear stresses of ~7 GPa for Ni and ~4 GPa for CoCrFeMnNi trigger elastic undulations.
- Elastic undulations have a nanoscale wavelength of 1–2 nm and precede the formation of twinned microstructures.
- Nonlinear modeling reveals undulations absent in linear approaches, influencing crystal orientation patterns.

## Abstract

What are the main findings?
Geometrically nonlinear phase-field modeling is developed to investigate deformation twinning at finite strains.Critical shear stresses of ~7 GPa for Ni and ~4 GPa for CoCrFeMnNi high-entropy alloy are identified for triggering elastic undulations.Predicted elastic undulations exhibit a characteristic nanoscale wavelength of 1–2 nm.

Geometrically nonlinear phase-field modeling is developed to investigate deformation twinning at finite strains.

Critical shear stresses of ~7 GPa for Ni and ~4 GPa for CoCrFeMnNi high-entropy alloy are identified for triggering elastic undulations.

Predicted elastic undulations exhibit a characteristic nanoscale wavelength of 1–2 nm.

What are the implication of the main findings?
Stripelike undulations serve as a mechanistic precursor that governs the formation of finely twinned microstructures.

Stripelike undulations serve as a mechanistic precursor that governs the formation of finely twinned microstructures.

Finely twinned microstructures are widely observed in metals and alloys but the underlying formation mechanisms remain debatable. In particular, the role of internal stresses in promoting these inhomogeneous patterns is still not clear. By incorporating a geometrically nonlinear microelasticity theory into phase-field framework, we study the evolution of elastic fields resulting from the growing deformation twins (DT) at grain boundaries in fcc metals. Simulations in two model systems, i.e., Ni and CoCrFeMnNi (a high-entropy alloy), show that as the external applied stress increases, the internal elastic fields begin to develop undulations with stripelike patterns owing to the significant geometrical nonlinearity associated with DT. This elastic undulation, absent in linear modeling, is initially nonuniform inside the grain and becomes global and coarsened, exhibiting a characteristic wavelength of ~1–2 nm. The predicted elastic inhomogeneity leads to a stack of alternating crystal orientations favored by the undulating local stress fields. The resemblance of our predicted stress undulation and the stripelike patterns in experiments may suggest a universal mechanistic origin of the nanotwinned microstructures widely observed in deformation twinning and displacive transitions.