Full length articleDislocation mediated variant selection for secondary twinning in compression of pure titanium
Graphical abstract
Secondary deformation twins within primary twins of deformed pure titanium and the geometry of the new selection criterion.
Introduction
The wide application of hexagonal close packed (HCP) metals such as α-titanium, magnesium and zirconium in aerospace technology, automotive and nuclear industry requires a deep understanding of their deformation mechanisms. These metals are characterized by a large variety of possible slip systems [1], [2], [3]: basal <a> , prismatic <a> , pyramidal 〈c+a〉 , and pyramidal <a> . Besides slip, deformation twinning plays a significant role in the plastic deformation to accommodate the strain along c-axis of the crystal, especially at low temperatures [4] and high strain rates [5]. At room temperature, several twinning modes have been observed in α-titanium [6]. Extension twins including , and induce a positive strain along the c-axis of the parent grain, while contraction twins, such as , and , cause reduction along the c-axis [7].
The large reorientation caused by primary twinning can reposition initially non-active twinning systems of the parent grain into more favorable orientation, promoting secondary twinning inside the primary twins. The following secondary twin systems are reported in magnesium alloys: twins in primary twins [8], [9], [10], and twins in primary twins [11], [12]. The former can readily appear during uniaxial deformations [13], [14]. Barnett et al. [8] reported that the double twin variants that are favored are those that correspond to minimum compatibility strain in the primary twins. Martin et al. [9] found that the secondary twin variants having the greatest potential for growth and with the highest resolved shear stress are most favorable during the selection of secondary twin variants. double twins were found in AZ31 in uniaxial deformation at 77 K, possibly due to the absence of non-basal slip at low temperature, while they did not appear at room temperature deformation where non-basal slip can take place [11]. Wang et al. [15], [16], [17] declared nucleation mechanism of twinning in HCP metals by using simulation. Beyerlein et al. rationale selection based on nucleation via dislocation reaction at the primary twin interface [18]. In pure titanium, and twins are most frequently observed at room temperature [6], [19], [20], compared to other twinning systems. Christian and Mahajan put forward that a low shear and a small shuffling facilitates the formation of these twins [4]. Several compression tests were carried out on commercially pure titanium to study secondary extension twinning inside primary compression twins in Refs. [21], [22], [23]. Jonas et al. [10], [23], [24] recently employed strain accommodation to evaluate the selection of twin variants. In their work, the generation of secondary twins was explained by inspecting several deformation modes in the adjacent parent grains to accommodate the shear induced by the secondary twins [23]. It was proposed that those secondary twin variants are initiated for which the strain can be accommodated the most easily by prismatic or basal glide in the parent. The displacement gradient tensor of the shear operating in the secondary twin frame was transformed into the crystal fame of the neighboring parent grain to identify the slip system in the parent grain that can accommodate the twinning shear displacement in the twin boundary region. Wang et al. [25], [26] considered twinning accommodated by twinning on the other side of a boundary. They employed the Luster-Morris parameter [26], [27], [28] defined by m' = cosψ•cos κ, where ψ is the angle between the normal of the two planes and κ is the angle between two shear directions of the systems, which can be used to quantify the compatibility of accommodating slip or twinning. Recently, the preferred secondary twins were found with a misorientation relation of 41° around a axis compared to the matrix in commercially pure titanium subjected to cold-rolling [29]. The activation of secondary twinning induced by channel-die compression was recently reported and found to be reasonably consistent with a simplified Schmid factor (SF) criterion [30].
There are evidently a range of findings and interpretations in the literature and the present work aims to test their applicability to secondary twining within primary twins in uniaxially compressed pure titanium. It is found in the present work that the only SF based and also the accommodation based secondary twin selection criteria [23] cannot explain the experimental observations. However, the habit plane orientation based criterion - originally proposed for magnesium [8] - applies also to titanium; i.e., it selects the right group (Group II). It does not, however, select the right variant within the group. The main contribution to the topic in the present work is a new criterion which is also able to reproduce the experimental secondary twinning activity. It is based on the special geometry that applies to Group II secondary twins in titanium: there is a common intersection line between three planes: the active prismatic plane in the primary twin and the primary and secondary twin planes. This special geometry makes possible dislocation reactions that are necessary for producing the partial dislocations of the secondary twin. Nevertheless, the Schmid factor criterion is still needed to choose between the two possible Group II twin variants inside the primary twins.
Section snippets
Experimental procedure
In the current study, the material used was rolled commercially pure titanium T40 sheet (ASTM grade 2) with a thickness of 1.5 mm. The composition is given in Table 1 . It is generally understood that deformation twinning is more active with a larger grain size [31], [32], [33]. Therefore, samples with a large grain size were prepared by annealing in a vacuum furnace at 800 °C for 2 h, leading to a fully-recrystallized microstructure. By using a Zwick 120T machine, the samples were deformed at
Microstructure in the initial and deformed states
Fig. 1 presents the microstructure of the initial material in form of EBSD inverse pole figure (IPF) where the ND axis was projected with the shown color code. The material was fully recrystallized with an average grain size of ∼160 μm and presented no twins. RD and TD represent the rolling and transverse directions, respectively. Fig. 2 a displays the texture of the material in {0002}, and pole figures obtained from Fig. 1. The rolling symmetry appears well satisfied by these
A Schmid factor based evaluation of the secondary {10-12} twins
The Schmid factor (SF) is conveniently used as a reference point for examining variant selection. It is based on the idealized hypothesis that the stress direction in a grain is exactly the same as the one applied on the whole sample. From this hypothesis one obtains the following simple formula for the SF:
Here λ is the angle between the loading direction (LD) and the twin plane normal (TPN) while θ is the angle between the LD and the twin shear direction (SD). It is expected that
Conclusions
An experimental study was conducted in the present work for the combination of primary compression and secondary extension twins that were formed during compression in a pure polycrystalline titanium along the ND. A detailed analysis of the detected 425 secondary twins has led to the following conclusions:
- 1.
The 36 possible secondary twin variants can be classified into three groups in terms of misorientations between the parents and secondary twins: Group I with a
Acknowledgements
S. Xu sincerely thanks Dr. J. Wang from University of Nebraska-Lincoln for valuable advices. Dr. Y.D. Zhang from Université de Lorraine is also greatly appreciated for fruitful discussions. This work was supported by the French State through the program “Investment in the future” operated by the National Research Agency (ANR) and referenced by ANR-11-LABX-0008-01 (LabEx DAMAS).
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