On the nucleation of deformation twins at the early stages of plasticity

Abstract

Understanding the deformation mechanisms of hexagonal close-packed (HCP) polycrystals at the grain scale is crucial for developing both macro and micro scale predictive models. Slip and twinning are the two main deformation mechanisms of HCP polycrystals at room temperature. In this paper, the development of grain-level stress tensors during nucleation and growth of twins is investigated. A pure zirconium specimen with HCP crystals is deformed in-situ while the centre-of-mass, orientation, elastic strain, and stress of individual grains are measured by three-dimensional synchrotron X-ray diffraction (3D-XRD). The observed microstructure is subsequently imported into a crystal plasticity finite element (CPFE) model to simulate the deformation of the polycrystal. The evolution of stress in twin-parent pairs at the early stages of plasticity, further into plasticity zone, and unload is studied. It is shown that twins do not relax very much at the nucleation step, but the difference between the measured stress in the twin and parent increases further into plastic zone where twins relax. While at the early stages of plasticity all six twin variants are active, a slightly better estimation of active variants is obtained using the measured grain-resolved stress tensors.

Introduction

Understanding the deformation mechanisms of polycrystalline materials has been at the centre of many studies for decades. In metals and alloys, plastic deformation is controlled by the movement of dislocations on a particular plane in a particular direction, i.e. slip. In the absence of “easy” slip systems, deformation twinning may become active where a discrete domain of the crystal reorients to accommodate the applied strain through the twin transformation strain. In hexagonal close-packed (HCP) polycrystals deformation by twinning is often active. When all twinned zones orient towards one unique direction, a large macroscopic strain equal to the twin transformation strain will be observed; however, when different variants of the same twin system become active, the effects of the transformation strain from different twins will be homogenised. While it is known that the formation of a twin alters the local state of stress within the parent grain, it has proven to be challenging to quantify the state of deformation within the parent and the twin. This paper focuses on quantifying the evolution of stress in twin and parent pairs, and on how different twin variants become active while deforming a polycrystalline zirconium specimen.

Since deformation twins nucleate and grow with mechanical loading, it is challenging to measure elastic strains within twins, especially at the early stages of plasticity when the size of twins is small. Diffraction based experimental techniques are mainly used to quantify load partitioning between twins and parents [1], [2], [3], [4], [5], [6], [7], [8], [9]. For example, the development of internal lattice strains during twinning and detwinning of magnesium alloys is studied using neutron diffraction [10], [11], [12]. It is generally shown that changing the direction of applied load directly affects twinning and detwinning. The lattice strains measured with neutron diffraction have significantly improved our understanding of load sharing between twin and parent grains, yet in such measurements, the local interactions between grains is usually homogenized. Such interactions can be characterized using higher resolution techniques. For example, three dimensional synchrotron micro-Laue X-ray diffraction was used to study twinning and de-twinning in Mg alloys where it was shown that lattice strains measured inside a parent decrease towards the twin interface [13]. Using the same technique, Kumar et al. [14] measured the stress tensor within a parent grain and showed that the stress is localized at the vicinity of the twin boundary. While these studies provide valuable insight into understanding twinning, they are mainly conducted on a few twin-parent pairs.

A better statistical analysis of twins can be provided by the use of electron diffraction [15], [16], [17], [18]. For this purpose, the high angular resolution electron backscatter diffraction (HR-EBSD) technique is mainly used [19], [20], [21]. For example, Guo et al. [22] used HR-EBSD to measure localized stress fields around twins in titanium. They showed that, a better estimation of active twin variant can be achieved if the measured local stresses are used for determining Schmid factor. With the use of the same technique, Khosravani et al. [23] showed that, while both first and second predominant twin variants are active in magnesium, slip transfer from a soft grain to a hard grain can trigger formation of twins in the hard grain. In this context, grains that have “easy” slip systems and undergo plastic deformation by prism or basal are called plastically “soft” whereas those that lack easy slip systems are plastically “hard” grains. In addition, nano-beam electron diffraction was recently used to understand how strain fields around twin boundaries are affected by twin morphologies. It was observed that elastic strains accumulate at the vicinity of semi-coherent twin boundaries within the parent grain [24].

In addition to experimental measurements, numerical modelling techniques have been used to understand the interactions between twins and parent grains [25], twins and twins [26], and twins and slip bands [27]. For modelling twins at meso‑scales, crystal plasticity is used in the self-consistent [28], [29], [30], [31], fast Fourier transform (FFT) [32], and finite element frameworks [33,34]. For example, Want et al. [31] have recently developed a self-consistent model for simulating twinning and de-twinning in magnesium. They found that less internal strain develops in hard grains surrounded by hard neighbouring grains. By adapting the self-consistent framework, Barrett et al. [35] studied the deformation behaviour of α-uranium and found that twinning and de-twinning control the response of uranium during a load reversal. In addition, Grilli et al. [36] used crystal plasticity finite element (CPFE) to characterise slip and twin activity in the same material. It was shown that for replicating the experimental data measured by digital image correlation, it was important to consider the interactions between coplanar twins in full-field models. More recently, the CP-FFT full-field modelling scheme was used for studying twins [37,38]. For example Paramatmuni and Kanjarla [39] have developed a CP-FFT model to study the interaction of twins and their corresponding parents. This model shows that the evolution of stress in parents and twins depends on their misorientation with respect to the loading direction.

The further development of full-field numerical models requires the measurement of comprehensive experimental data sets that can explain the interaction between twins and their corresponding parents. In this paper, three-dimensional synchrotron X-ray diffraction is used to measure the evolution of stress in individual twin and parent pairs. The centre-of-mass (COM), orientation, relative volume, elastic strain, and stress for individual grains is measured during in-situ deformation of a pure zirconium specimen. Post-processing procedures are developed to find twins and their corresponding parents and track them during early stages of plasticity, further into the plasticity zone, as well as unload. Special focus is given to evolution of stress within the identified pairs and variant selection at the early stages of macroscopic plasticity.