Mateusz Budnik

Mikail Demirdelen

Guillaume Gravier

A STUDY ON MULTIMODAL VIDEO HYPERLINKING WITH VISUAL AGGREGATION

Keywords: Video hyperlinking, multimodal embedding, similarity search, memory vectors

Video hyperlinking offers a way to explore a video collection, making use of links that connect segments having related content. Hyperlinking systems thus seek to automatically create links by connecting given anchor segments to relevant targets within the collection. In this paper, we further investigate multimodal representations of video segments in a hyperlinking system based on bidirectional deep neural networks, which achieved state-of-the-art results in the TRECVid 2016 evaluation. A systematic study of different input representations is done with a focus on the aggregation of the representation of multiple keyframes. This includes, in particular, the use of memory vectors as a novel aggregation technique, which provides a significant improvement over other aggregation methods on the final hyperlinking task. Additionally, the use of metadata is investigated leading to increased performance and lower computational requirements for the system.

INTRODUCTION

Video hyperlinking appeared recently as the task of organizing large video collections with explicit links between related video fragments. Hyperlinking can be seen as a complement to video retrieval, focusing on the browsing and exploration stages that follow the search: after finding entry points of interest within the collection, users can browse and explore following the links created by the video hyperlinking process [1]. Over the past years, video hyperlinking has been implemented and evaluated in yearly international benchmarks, first within the MediaEval initiative [2], then as part of the TRECVid series of evaluations [START_REF] Awad | Trecvid 2016: Evaluating video search, video event detection, localization, and hyperlinking[END_REF].

Video hyperlinking systems usually start from a set of anchors that define entry points of interest in collections of long videos and are required to provide, for each anchor, relevant targets within the collection. This task is usually implemented as a two-step process, first starting from a segmentation of the long videos into small segments, then selecting relevant segments for a given anchor [START_REF] Apostolidis | Automatic finegrained hyperlinking of videos within a closed collection using scene segmentation[END_REF][START_REF] Galuščáková | Visual descriptors in methods for video hyperlinking[END_REF]. This last step is cast as a video retrieval task relying on video segment comparison, where various multimodal solutions have been proposed. For instance, in the 2016 TRECVid evaluation, many teams investigated late fusion approaches combining transcript-based, visual-based and metadata-based target retrieval systems. The state of the art was, however, achieved with multimodal representation based on bidirectional neural networks (BiDNNs) embedding transcripts and keyframes in a common representation space attainable from text embeddings with average word2vec and/or from image embeddings with the VGG-19 convolutional neural network (CNN) [START_REF] Vukotić | Bidirectional joint representation learning with symmetrical deep neural networks for multimodal and crossmodal applications[END_REF].

While the video hyperlinking task can be cast as a video retrieval task after video segmentation, a major difference is the use of video fragments as queries in hyperlinking. Most of the work in video retrieval focuses on textual or image queries (cross-modal approaches) [START_REF] Yu | End-to-end concept word detection for video captioning, retrieval, and question answering[END_REF][START_REF] Araujo | Temporal aggregation for large-scale queryby-image video retrieval[END_REF], or on near duplicate video retrieval [START_REF] Wu | Practical elimination of near-duplicates from web video search[END_REF]. In hyperlinking, we rather seek to create multimodal embeddings of video fragments to group and link relevant segments together. Most methods used in the video hyperlinking task over the past few years indeed rely on multimodal representations to find relevant video fragments, with joint embeddings performing best [START_REF] Awad | Trecvid 2016: Evaluating video search, video event detection, localization, and hyperlinking[END_REF].

In this paper, we further improve on the BiDNN approach to target selection in video hyperlinking with a systematic study of various input representations. On the one hand, BiDNNs as implemented in the TRECVid 2016 evaluation does not make use of the latest advances in CNN-based features. In [START_REF] Vukotić | Multimodal and crossmodal representation learning from textual and visual features with bidirectional deep neural networks for video hyperlinking[END_REF], authors observe a significant gain after switching from AlexNet to VGG architectures. We thus investigate the impact of changing the representation of the keyframes of each segment to recent very deep CNN architectures such as ResNet [START_REF] He | Deep residual learning for image recognition[END_REF], Inception [START_REF] Szegedy | Going deeper with convolutions[END_REF] and ResNext [START_REF] Xie | Aggregated residual transformations for deep neural networks[END_REF]. At the transcript level, document and LSTM-based embeddings of texts are considered as a replacement to the average word2vec representation. At the visual modality level, we investigate aggregation of the representation of the multiple keyframes that depict a video segment to account for the temporal structure of videos. In addition to pooling strategies such as average or max pooling, we consider a recently introduced technique, namely memory vectors [START_REF] Iscen | Memory vectors for similarity search in high-dimensional spaces[END_REF], which enables the aggregation of multiple descriptors into a single one, yet maintaining good properties for information retrieval. Memory vectors were successfully used as building blocks for efficient indexing structures in image retrieval. We demonstrate in this paper their ability to act as feature aggregators and show their ben-efit in a video hyperlinking task.

The paper is organized as follows. We first describe the global architecture of the full video hyperlinking system and detail the aggregation components that we propose and compare. We then describe the data and the experimental setup, before reporting and commenting on the results in a target reranking setting to assess the benefit of the various representation and aggregation techniques compared. Based on these results, we describe a full video hyperlinking system and assess it in the TRECVid 2017 video hyperlinking task.

AGGREGATION METHODS IN VIDEO HYPERLINKING

Video hyperlinking systems implement a complete pipeline to turn a collection of raw videos with a given set of anchors, i.e., pre-defined entry points in the collection, into a structured collection with a number of hyperlinks departing from the pre-defined set of anchors. At the core of the system is a content comparison algorithm that builds on a multimodal embedding of video fragments that are to be compared, where multimodal embedding is obtained by means of a BiDNN. As multiple keyframes are present in the video fragments to be compared, one needs to aggregate the visual representations over different keyframes in order to use BiDNNs. After a brief overview of the general content matching mechanism that we use, we present the various aggregation strategies considered in this paper.

System overview

The video hyperlinking system starts by segmenting videos into small segments which are seen as potential targets to select from for a given anchor. For retrieval purposes, each segment is represented in a multimodal representation space in which segments will be compared to anchors using standard retrieval methods. Different steps towards the multimodal embedded representation of a segment are illustrated in Figure 1. The video frames and the speech transcript are extracted and, for each modality, a unique embedding is built for further projection in a multimodal representation space using BiDNN. For the visual modality, a descriptor of each frame is obtained by passing the image through a pretrained convolutional neural network. When several frames are present in a video segment, an aggregation step is performed to produce a single vector representation that will serve as input to the BiDNN fusion. Regarding the audio modality, the transcript of the video segment is embedded to produce the second input to the BiDNN fusion. Different embeddings of transcripts and images are compared in the experiments.

Fusion of the two modalities is performed with a BiDNN [START_REF] Vukotić | Bidirectional joint representation learning with symmetrical deep neural networks for multimodal and crossmodal applications[END_REF], a model which creates a crossmodal translation between two modalities. This is done through the use of two separate neural networks for each translation while having the weights tied between the middle layer of each network. This forces the network to learn a common multimodal representation. Formally, the structure of the network is given by

h (1) i = f (W (1) i × x i + b (1) i ) i = 1, 2 (1)
h (2) 1 = f (W (2) × h (1) 1 + b (2) 1 ) (2)
h (3) 1 = f (W (3) × h (2) 1 + b (3) 1 ) (3)
h (2) 2 = f (W (3)T × h (1) 2 + b (2) 2 ) (4) h (3) 2
= f (W (2)T × h (2) 2 + b (3) 2 ) (5)
o i = f (W (4)
i × h

(3) i + b (4) 1 ) (6)
where h

(j) i
denotes the activation of a hidden layer at depth j in the network i (indicating one of the two modalities), x i is the feature vector for a given modality i and y i is the corresponding output of the network. The parameters are the weight matrices W

Aggregation

In the case of anchor video segments, usually several keyframes are extracted. In order to have a single vector representation, an aggregation step is performed. These image representations are fused to deal with different variations across the video segment. Four aggregation approaches were considered and they can be defined as follows. Let X = [x 1 , ..., x n ], where x i ∈ R d , be a d × n matrix representing anchor vectors. A simple average can be used to create an aggregate vector a:

a(X) = 1 n X1 n (7)
where 1 n is a n dimensional vector with all values set to 1.

The second approach uses a maximum response for each corresponding value in the vectors:

a(X) = max j∈D x ji , i = 1, . . . , n (8)
where D = {1, . . . , d} and x is a corresponding value in matrix X. The third approach selects a just single vector and discards the rest:

a(X) = x i (9)
In the case of our experiments, the vector of the first keyframe in the video fragment was selected as its representative.

Memory vectors

The last aggregation approach was done using the Moore-Penrose pseudo-inverse. This aggregation method called memory vectors can be defined in the following way thanks to the Moore-Penrose pseudo-inverse X + as:

a(X) = (X + ) T 1 n = X(X T X) -1 1 n (10)
The name 'memory vector' refers to the ability to summarize a set of vectors into a single vector, while maintaining the distinctiveness of each member vector. This method was initially used to aggregate multiple image descriptors into a single vector representation to speed up image retrieval [START_REF] Iscen | Memory vectors for similarity search in high-dimensional spaces[END_REF]. In this case, the optimal vector representation with respect to the false positive rate is obtained by maximizing the membership score over all member vectors while minimizing the memory vector norm. The solution to this optimization problem can be given by the pseudo-inverse, considering stricter constraints to eliminate between vectors gathered in the same 'memory' and yielding a better balance between rare and frequent features. In this work, we propose to use memory vectors at the video level.

These aggregation techniques are evaluated and the results presented in Section 4.2. The a vector was later used alongside the transcript vector as an input to the BiDNN to create embedded crossmodal representations of the anchors.

DATA AND EXPERIMENTAL SETUP

The experiments were carried out on the BlipTV dataset [START_REF] Awad | Trecvid 2016: Evaluating video search, video event detection, localization, and hyperlinking[END_REF]. It contains 14 838 videos of a mean length of around 13 minutes. The videos present a variety of topics from computer science tutorials and sightseeing guides to homemade song covers. They are provided in many languages, but a vast majority of them are in English.

Additionally, many other sources of information are available for each video: multiple transcripts generated by the LIMSI2016 [START_REF] Gauvain | The limsi broadcast news transcription system[END_REF] speech-to-text system, the timecodes of the shots, keyframes that correspond to the middle frame of each shot and the metadata. The latter contains information on the video provided by the author such as its title, a description of the video, a list of tags that mainly describe its semantic content, its license, information about the author, etc.

Models

A STUDY ON VISUAL AGGREGATION

In this section, the experiments for the modality representation are introduced with emphasis on the visual modality and its aggregation. The evaluation was carried out on a reranking task composed of the development anchors of the BlipTV dataset. Each anchor had a list of annotated target candidates (both correct and incorrect). The annotations were obtained during the 2016 TRECVid Hyperlinking evaluation. The development set is composed of 89 anchors. The total number of annotated video segments is 7216, which gives on average around 81 segments per anchor. The annotation is binary (relevant or not relevant for a given anchor). All the tests in this section were made using this dataset.

Textual representation

To represent the speech of the videos, the transcripts produced by LIMSI2016 were incorporated. Three different textual neural networks were tested: an averaged word2vec [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF] on each words of the segment, doc2vec [START_REF] Le | Distributed representations of sentences and documents[END_REF] and skipthought [START_REF] Kiros | Skip-thought vectors[END_REF]. The procedure was the same as for the visual features, except the measures used were precision at 5 (P@5) and mean averaged precision (MAP). The results are shown in Table 1. Despite carefully tuning the parameters, the standard word2vec outperformed its the newer alternatives. Therefore, an averaged word2vec was chosen for the text representation.

Visual representation

For the visual embeddings, several different deep convolutional neural network (CNN) architectures were tested as well as layers, from which the embeddings were obtained. For each annotated target a single keyframe was extracted and subsequently embedded using different pre-trained CNN models. The same thing was done for the anchors in the development set. However, more than one image was used for each anchor. The fusion of the anchor vectors was done through average aggregation, which is a well established approach that can provide stable results [START_REF] Vukotić | Multimodal and crossmodal representation learning from textual and visual features with bidirectional deep neural networks for video hyperlinking[END_REF]. A cosine distance measure was used to construct the ranking between the anchors in the development set and their corresponding annotated targets.

The results of these experiments can be seen in Table 2. Two evaluation measures were used: precision at 5 (P@5) and precision at 10 (P@10). Next to the name of the network, the name of the layer is shown from which the embedding was taken as well as the dimension of that embedding. There were either average pooling (AP) layers or fully connected layers (FC). A set of different state-of-the-art deep architectures were tested, including VGG19 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], Inception [START_REF] Szegedy | Going deeper with convolutions[END_REF], two different versions of ResNet [START_REF] He | Deep residual learning for image recognition[END_REF] and ResNext [START_REF] Xie | Aggregated residual transformations for deep neural networks[END_REF]. Based on the results in Table 2, the ResNet-200 descriptors give the highest precision. The last fully connected layer was chosen as the base visual descriptor for the hyperlinking evaluation. It seems that the overall performance of a given descriptor in this is linked to its semantic meaning: in both the VGG19 and ResNet-200 the top layers (which indicate presence of a given concept in an image) are outperforming other layers further down. Even though the latter are conmore suitable for more general representation [START_REF] Yosinski | How transferable are features in deep neural networks?[END_REF].

Average

Aggregation over keyframes

In this section, the performance of different aggregation techniques introduced in Section 2.2 is presented. Table 3 provides the results based on the ResNet-200 descriptors, which displayed the highest precision in the evalution as shown in the previous section. Based on the results, it seems that max aggregation gives the best overall results for P@5 and P@10. Because of that it was chosen as a baseline in the other complete system evaluation. Despite its lower scores for the ResNet-200 fully connected layer, the memory vectors give the highest performance for P@1 and outperform the max aggregation at P@5 for the other descriptor. Because of the above and keeping in mind the limitations of this evaluation, the memory vectors were chosen to be also used in the hyperlinking evaluation.

COMPLETE SYSTEM EVALUATION

Despite seemingly interesting results on the reranking evaluation, this set is far from a complete system and the results must be taken with hindsight. In order to have more accurate and representative results, we used the test set given in ResNet-200 FC ResNet-200 AP Agg.

P@1 P@5 P@10 P@1 P@5 P@ the 2017 edition of the TRECVid video hyperlinking task. In this set, the evaluation is done on 25 anchors for which we can make segment suggestion from the whole database and whose relevance was evaluated by human assessors.

Segmentation

As stated before, a first step of the segmentation was done to fragment each video into segments that can better represent a particular topic or context at a given moment of the video. The difficulty of this step is to have a good coverage of each video without being too redundant. Moreover, no segment should cut the speech. Two methods of segmentation were used in order to cover both the number and the quality of the segments. The first method is a sliding window applied to each video that creates segments that have 30 seconds of continuous speech. This process is applied a second time with an offset with already found segments as described in [START_REF] Bois | Irisa at trecvid2016: Crossmodality, multimodality and monomodality for video hyperlinking[END_REF].

While the above method is good to have control over the segment we produce, it scales badly. In order to produce a large number of segments, a constraint programming framework was used. The length of segments was fixed to be between 50 and 60 seconds. When this was too restrictive, it was expanded to between 10 and 120 seconds. The first method that was used gave around 300.000 segments and the second produced an additional 1.1 million segments, to a total of 1.4 million segments.

Metadata

To augment the precision of our system, the metadata associated with the videos was tested as a way to filter out and narrow down the list of possible target candidates. The list of tags seemed particularly relevant to serve as a filter. However, only 77% of the videos have tags and with a mean number of 4.71 tags per videos. These numbers seemed too restrictive and might result in an overfiltering of the results.

The list of tags was expanded using the text of the video descriptions that are present in 86.6% of the videos with a mean number of 39.8 words excluding stopwords. From these descriptions, the nouns, verbs and adjectives were extracted, lemmatized, afterwards the stopwords and hapaxes were removed. This list of keywords-tags and descriptions-was kept and used to select only videos that share at least one word with the anchor. It is worth noting that the filtering was done on the complete video level. The particular segment within a video still needs to be selected.

Experimental setup

Four different approaches and variations are compared and evaluated:

• BiDNNFull represents the BiDNN algorithm with ResNet-200 visual features and max aggregation (for anchors only). This approach serves as the baseline.

• BiDNNFilter the exact same setup as above. However, the metadata is used as a filter as described in Section 5.2.

• BiDNNMemVec replaces the max aggregation with a memory vector for the visual representation for anchors. All the other parameters are analogues to BiDNNFull. The memory vector representation is embedded using the BiDNN algorithm.

• noBiDNNMemVec does not use the BiDNN model, instead, simple concatenation of the two modalities is used. For the visual representation, the memory vector is used for aggregation of the anchor segments.

The BiDNN-based system was trained with stochastic gradient descent, 0.9 momentum and 20% dropout for 300 epochs (even though it seemed to converge earlier than that). The input video and audio representations had of the size 1000 and 100, respectively. The resulting embedding was an L2 normalized 1024-dimensional vector. Cosine distance was used for matching the embedded vectors.

Results and discussion

The scores of the hyperlinking evaluation are given in Table 4 using the precision at 5, 10 and 20 (denoted as P@5, P@10 and P@20, respectively) as well as the mean average precision (MAP).

The approach using the memory vectors (BiDNNMemVec) seems to outperform the baseline at every measure, while having the biggest difference at P@5. It is important to note that both systems use the same trained BiDNN model, so the improvement is due to the use of memory vectors over max aggregation.

The use of the metadata (BiDNNFilter) led to surprisingly good results giving the best precision at 5 out of any approach and comparable result for P@10. The drawback seems to be that too many correct potential targets are filtered out. This can be seen when considering P@20 and MAP scores, which take more targets into account. The BiDNNMemVec seems to handle this problem better, showing more stability of the quality of the results across different metrics.

Approach

MAP P@5 P@10 P@20 BiDNNFull 0.1334 0.6880 0.7120 0.4240 BiDNNFilter 0.1081 0.7600 0.7440 0.3800 BiDNNMemVec 0.1529 0.7520 0.7440 0.4340 noBiDNNMemVec 0.1246 0.7280 0.7320 0.3960 Table 4. The results for the 4 runs using MAP, precision at 5, at 10 and 20.

Additionally, a significant difference between the methods: BiDNNMemVec and noBiDNNMemVec can be observed showing the interest of using the BiDNN model for this task. However, considering the precision at 5 and 10, noBiDNN-MemVec performs better than the BiDNNFull baseline. This seems to indicate the importance of the choice of the input representation on the overall performance of the system.

CONCLUSION

In this paper, a study on the performance of different visual representations was presented as well as several aggregation methods. The results show that the initial choice of the representation has a significant effect on the overall performance of the system. The same is true for the choice of the aggregation approach, especially in the case of the memory vectors, which seem to provide significant gains on the hyperlinking task. In this study the aggregation was performed only on the anchor side. Therefore, one way of potential improvement could be to extract multiple keyframes for each segments, to have a better representativity of the whole segments. However, doing so could be computationally expensive.

It was also shown that both the use of metadata and the use of BiDNN architectures are relevant and lead to better results. Therefore, trying to incorporate the metadata into the neural network architecture can be considered, using it as a potential third modality. It can however be risky as, contrary to the visual and textual representations, the metadata is available only on the video level. There could be a lot of redundancy if this data is used to train a model on the segment level.

[1] Maria Eskevich, Gareth JF Jones, Robin Aly, Roeland JF Ordelman, Shu Chen, Danish Nadeem, Camille Guinaudeau, Guillaume Gravier, Pascale Sébillot, Tom De Nies, et al., "Multimedia information seeking through search and hyperlinking," in Proceedings of the 3rd ACM conference on International conference on multimedia retrieval. ACM, 2013, pp. 287-294.

[2] Maria Eskevich, Robin Aly, David Racca, Roeland Ordelman, Shu Chen, and Gareth JF Jones, "The search and hyperlinking task at mediaeval 2014," 2014.

Fig. 1 .

 1 Fig. 1. The overview of the system including the extraction of different modalities.

  f is a ReLU function. Training seeks to minimize the mean square error of (x 1 , o 2 ) and (x 2 , o 1 ).

Table 1 .

 1 Results for the textual descriptor evaluation.

		P@5 MAP
	Average Word2Vec 44.2	45.3
	Doc2Vec	38.4	39.4
	Skip-Thought	40.2	41.6

Table 2 .

 2 Results for the visual descriptor evaluation. The average aggregation was used.

	Models	Layers Dims P@5 P@10
	VGG19	FC8	1000 43.40 41.60
	VGG19	FC7	4096 42.40 42.10
	VGG19	FC6	4096 41.00 40.60
	Inception	FC	1000 41.00 41.39
	ResNext-101	AP	2048 41.40 40.10
	ResNet-200	FC	1000 47.20 44.37
	ResNet-200	AP	2048 44.80 43.20
	ResNet-152	AP	2048 45.60 41.67

Table 3 .

 3 Results for the visual aggregation evaluation based on the ResNet-200 descriptors.

	10


P Castany

A Ramarolahy

F Prima

P Laheurte

C Curfs

T Gloriant

In situ synchrotron X-ray diffraction study of the martensitic transformation in superelastic Ti-24Nb-0.5N and Ti-24Nb-0.5O alloys !

Keywords: titanium alloys, superelasticity, stress induced martensite, in situ synchrotron XRD

In situ synchrotron X-ray diffraction study of the martensitic transformation in superelastic Ti-24Nb-0.5N and Ti-24Nb-0.5O alloys.

Introduction

Metastable β titanium alloys are currently developed as biomedical Ni-free alloys with shape memory and superelastic properties [1][2][3][4][5][6][7][8][9][10]. These specific properties are due to the occurrence of a reversible martensitic transformation from the β parent phase (bcc) to a α" product phase (C-orthorhombic). Among the potential compositions, Ti-Nb based alloys are the most investigated because of the combination of their good biocompatibility and mechanical properties [3][4][5][6][7][8]. Depending on the Nb content, binary Ti-Nb alloys can display a full α" martensitic microstructure at room temperature and thus exhibit shape memory properties [3,8,11,12]. If the Nb content is higher, the microstructure is fully β at room temperature and the alloys can display a stress-induced martensitic (SIM) transformation leading to superelastic properties [3,5,11]. Addition of ternary or quaternary elements, such as Zr, Sn or Al, can also improve superelasticity [2,[13][14][15][16]. Particularly, addition of interstitial elements (O or N) allows a strong improvement of both superelastic properties and mechanical strength in binary Ti-Nb based alloys [2,7,17,18] or in more complex Ti-Nb based compositions [19][20][21][22]. In superelastic alloys, the study of the SIM transformation is challenging due to its reversibility after the load is released. That is why in situ experiments are needed to study the SIM under loading conditions. For example, conventional in situ X-Ray diffraction (XRD) studies were performed on binary Ti-26Nb or Ti-13Nb-4Mo alloys (at.%) and allowed to detect the apparition of the α" SIM under loading conditions [5,23,24]. The α" phase is shown to be formed from 0.2% until 2.5% of strain and to be partially reversible after unloading from 2.5% of strain [5,23]. But these experiments were performed only until a deformation of 2.5% followed by an unique unloading, whereas several cycles of loadingunloading until several percent of deformation would allow to obtain a better preciseness on the characteristics of the SIM transformation: strain values at which the transformation starts and finishes to operate, domain of reversibility of the transformation, domains of existence of other mechanisms of deformation such as elasticity or mechanisms of plasticity, etc. However, the main peaks of β and α" phases are difficult to separate because of the relatively great wavelength and the presence of both K α1 and K α2 wavelengths of X-ray sources used in laboratories. In order to avoid these limitations, the use of synchrotron X-ray radiation was also used because of the combination of a shorter wavelength and a better monochromaticity. Synchrotron X-Ray diffraction (SXRD) was especially used for in situ experiments on oxygen-added alloys such as Gum Metals [25,26], Ti2448 [22] or TiNbTaZr-based alloys [27]. But, the volume fraction of SIM α" was generally very low because other mechanisms of superelasticity can take place in these alloys due to the presence of oxygen that is known to inhibit the formation of α" [18,20,22]. SXRD was thus never used to study the SIM transformation in alloys of which superelasticity is predominantly due to this mechanism. This paper focus on two Ti-24Nb based compositions (at.%) alloyed with 0.5% of nitrogen and oxygen, respectively. Their microstructure and mechanical properties have been investigated previously and both alloys exhibit superelastic properties [7]. The nitrogen-added alloy presents a classical behavior with a superelasticity that seems due to SIM α" transformation and the oxygen-added alloy presents the specific features of oxygen-added ! alloys. The main objective of this study is thus to investigate the mechanisms of superelasticity of these alloys by in situ Synchrotron X-Ray Diffraction (SXRD) analyses during cyclic loading-unloading tensile tests. Special attention is focused on the role of O and N addition on superelastic properties and domains of occurrence of the different mechanisms of deformation that are evidenced.

Materials and methods

Both Ti-24Nb-0.5O and Ti-24Nb-0.5N alloys (at.%) were synthesized by cold crucible levitation melting technique (CCLM). For the elaboration, ultra-pure raw metals: 99.999% pure titanium and 99.9% pure niobium were used. Oxygen and nitrogen were added by using 99.8% pure TiO 2 powder and 99.5% pure TiN powder, respectively. Ingots were next homogenized at 1223K during 72ks under high vacuum, followed by water quenching. A cold rolling at room temperature was then applied until 90% of reduction in thickness. Tensile specimens were machined in cold-rolled sheets with normalized shapes: 3 mm width, 0.5 mm in thickness and a gage length of 15 mm. Specimens were finally solution-treated in the βphase domain at 1123K during 1.8ks under high vacuum and water quenched in order to restore a fully recrystallized microstructure from the cold-rolled state. After this whole thermo-mechanical process, the microstructure consists of β phase only (bcc structure). More details on microstructure and mechanical properties of these alloys can be found in a previous work [7]. Texture of the β phase was preliminarily measured from conventional X-ray diffraction on a Philips PW3710 system using Cu-Kα1 radiation (λ = 0.154060 nm). Poles figures were then plotted from calculated orientation distribution functions (ODF). In situ synchrotron X-ray diffraction (SXRD) experiments were carried out at the highresolution beam line ID31 of the European Synchrotron Radiation Facility (ESRF) in Grenoble (France) using a 0.040002106 nm wavelength radiation. In order to investigate the mechanisms of superelasticity and their reversibility, loading-unloading cycles were performed: the strain was increased by steps of 0.5% until an elongation of 5% and each step was followed by a total release of the stress. Additional cycles were next made until strains of 6%, 8% and 10%. Cyclic tensile tests were performed with a strain rate of 10 -4 s -1 and the tensile direction was chosen parallel to the rolling direction. Diffraction patterns were recorded for each cycle under load and after unloading. The geometry of the set-up is sketched in Fig. 1: tensile specimen and incident beam are fixed whereas the detector moves for 2θ angles from 8° to 26° in order to collect transmitted diffracted beams. Positions of diffraction peaks were then used to identify the presence of different phases and determine their lattice parameters. Intensities of some specific peaks were also used to estimate the relative proportion of different phases.

!

Results

Initial texture and microstructure

Ti-24Nb-0.5N and Ti-24Nb-0.5O alloys exhibit a microstructure consisting of full β phase equiaxed grains with a typical grain size of about 50 µm and 100 µm, respectively [7]. The smaller grain size in the nitrogen-added alloy is most probably due to a higher β transus temperature than in the oxygen-added alloy because of the stronger α-stabilizing effect of nitrogen [28,29]. Initial crystallographic textures are presented from {110} and {002} poles figures in Fig. 2. Both alloys have the same texture that consists mainly of the {001}<110> component of the α fiber of bcc metals. This texture is more pronounced in the Ti-24Nb-0.5N alloys. This kind of texture is commonly observed in Ti-Nb based titanium alloys after coldrolling/annealing [30][31][32] or warm-rolling/annealing thermo-mechanical treatments [33]. Crystallographic calculations have demonstrated that the maximum transformation strain in superelastic β titanium alloys is obtained from the stress-induced martensitic transformation when β grains are orientated with a <110> direction along the tensile direction [31]. This characteristic was also evidenced from experimental studies [30,31,34]. In the present study, tensile specimens are strained along the rolling direction, i.e. along a <110> direction: in turn, if a stress-induced martensitic transformation will occur during tensile tests, the superelasticity will be maximum in both investigated alloys.

Mechanical properties

Both alloys have an identical high elastic limit value of 665 MPa and Young's moduli of about 50 GPa [7]. It is also worth noting that, for the Ti-24Nb-0.5N alloy, the value of the elastic limit corresponds to the second yield point on the tensile curve, whereas the first yield point at around 130 MPa corresponds to the critical stress to initiate the stress-induced martensitic transformation. The superelasticity, i.e. the total recovery strain, is also similar: 2% for the Ti-24Nb-0.5N alloy and 2.2% for the Ti-24Nb-0.5O alloy [7]. However, cyclic stress-strain curves do not exhibit the same behavior for both alloys (Fig. 3). The Ti-24Nb-0.5N alloy has a "conventional" behavior of superelastic β titanium alloys: a plateau and hysteresis between loading and unloading curves are present (Fig. 3a) that both indicate the existence of a reversible stress-induced martensitic (SIM) transformation. For the Ti-24Nb-0.5O alloy, no plateau is present but hysteresis between loading and unloading curves from 1.5% (Fig. 3b) suggest that such martensitic transformation probably occurs.

In situ synchrotron X-ray diffraction

Fig. 4 displays initial SXRD patterns (top) and final SXRD patterns (bottom) after the entire cyclic tensile test was performed until an elongation of 10% for the Ti-24Nb-0.5N (Fig. 4a) and Ti-24Nb-0.5O alloys (Fig. 4b), respectively. For both alloys, only the {110} β peak and the {220} β second order diffraction peak are observed before the test, that is in accordance with their strong {hkl}<110> texture. Two very small peaks are also detected on both sides ! around the {110} β peak in the Ti-24Nb-0.5N alloy (Fig. 4a). These peaks correspond to a very small amount of α" martensite, which was formed during the quench. But, as it will be shown further, the presence of this martensite has no effect and can be neglected. These α" peaks are not present in the Ti-24Nb-0.5O alloy because of the stronger inhibitor effect of oxygen on the formation of α" martensite [7]. After being deformed, the α" martensite is the main detected phase for both alloys. The principal detected peaks are indexed in Fig. 4. As the most important peaks are {110} β , (020) α" and (002) α" , the evolution of diffracted peaks of the β and α" phases is more precisely visible on a focus in the 9-10° range during the cyclic tensile test (Fig. 5 and Fig. 6). In order to improve the visibility of the less intense peaks of α" martensite, the first diffractograms are truncated, leading to cut {110} β peaks in Fig. 5 and Fig. 6. All entire diffractograms are also given as supplementary materials (Fig. S1 and Fig. S2 for Ti-24Nb-0.5N and Ti-24-Nb-0.5O, respectively). Fig. 5 shows thus the evolution of most important diffraction peaks during the whole cyclic tensile test on loading (a) and after unloading (b) for each cycle in the Ti-24Nb-0.5N alloy. It can be first noticed that the {110} β peak (marked by black triangles) is slightly shifted from its initial position at 0.5% under loading and then remains in the same position by increasing the strain (Fig. 5a). However, its intensity continuously decreases until 3% and disappears at higher strain. At the same time, (020) α" and (002) α" peaks (black squares and black circles, respectively) appears while their intensities are progressively increasing with the strain. It is also worth noting that the peaks due to the very small amount of martensite formed on quenching (open symbols) remains almost at the same position and then vanish: the (020) α" peak (white squares) is at the same position than the (020) α" peak of the stress-induced martensite (black squares) from 1.5% and the (111) α" peak (white stars) disappears from 6% due to its probable reorientation during the plastic deformation. After unloading of each cycle (Fig. 5b), the {110} β peak (black triangles) returns at its initial position but is superimposed with the (002) α" peak (black circles) contrarily to what happens under loading where these two peaks are clearly separated. In the strain range of 0-3.5%, the cumulated intensity of {110} β and (002) α" peaks after unloading is clearly higher than the intensity of the {110} β under loading, what highlights the occurrence of a reversible SIM transformation in the Ti-24Nb-0.5N alloy. For the Ti-24Nb-0.5O alloy, the evolution of diffraction peaks during the cyclic tensile test is somewhat different (Fig. 6). In the early stage of deformation, the stress-induced martensitic transformation seems not to occur extensively until 1-1.5% on loading (Fig. 6a) whereas the {110} β peak (black triangles) continuously shifts to the left instead. From 1.5% to 3%, the {110} β peak continues to shift while the (020) α" peak appears (black squares). Moreover, from 3% until the end of the tensile test, the {110} β peak disappears and the (002) α" peak of martensite (black circles) appears noticeably. After unloading (Fig. 6b), the {110} β peak remains at the same position during the whole cyclic test, suggesting that the shift observed on loading is due to the elasticity of the β phase. Moreover, in the strain range of 1-3.5%, the intensity of this peak is higher after unloading than under loading while inversely the intensity of the (020) α" peak is higher under loading than after unloading, that evidences the occurrence of a reversible stress-induced martensitic transformation for the Ti-24Nb-0.5O ! alloy. But this SIM transformation starts to occur at higher applied strain than in the Ti-24Nb-0.5N alloy.

Lattice parameters

Lattice parameters of β and α" phases were determined from diffraction patterns under loading for both alloys. Their evolution during the whole cyclic tensile test is plotted in Fig. 7, wherein black circles correspond to the Ti-24Nb-0.5N alloy and open circles to the Ti-24Nb-0.5O alloy, respectively. The lattice parameter of the β phase remains almost constant for the Ti-24Nb-0.5N alloy (black circles); a small increase at the early stage of deformation (from the initial value to 0.5% of strain) can however be observed. On the contrary, the lattice parameter of the β phase in the Ti-24Nb-0.5O alloy is continuously increasing when the strain increases until 2.5% (open circles). After 3% of strain, the β phase is no more detected in diffraction patterns of both alloys and, in turn, lattice parameters cannot be measured any more. It can also be noticed that the initial value of the lattice parameter of the β phase is the same in both alloys and that this value is also constant after unloading during the entire tensile test. For the stress-induced martensitic α" phase, the evolution of a α" , b α" and c α" lattice parameters are similar in both alloys. The a α" and c α" parameters are roughly constant when the strain increases while the b α" parameter continuously increases until 5-6% of strain and remains almost constant at higher applied strain. The elastic deformation of the orthorhombic lattice of α" phase is thus not isotropic in the cell. It is also worth noting that lattice parameters cannot be properly determined for applied strain smaller than 1.5% and 2% for Ti-24Nb-0.5N and Ti-24Nb-0.5O, respectively, due to the too small number of peaks of α" martensite that are detected in diffraction patterns.

Discussion

Evolution of lattice parameters

Evolution of the lattice parameter of the β phase (a β in Fig. 7) highlights the ability of the β phase to deform elastically in both alloys. For both alloys, the lattice parameter of the β phase after unloading remains constant during the whole cyclic tensile test, proving that the increase of this parameter observed on loading is actually pure elasticity. For the Ti-24Nb-0.5N alloy, this elastic deformation of the β phase only occurs until less than 0.5% of applied strain. Indeed, from 0.5%, the β phase does not deform elastically any more (i.e. its lattice parameter is constant) and the SIM transformation starts to be detected (Fig. 5a). For the Ti-24Nb-0.5O alloy, the β phase deforms elastically until 3% of applied strain. However, the SIM transformation starts from 1% (Fig. 6a) that means SIM transformation and pure elastic deformation of the β phase are operating simultaneously until 3%. From the values of lattice parameters, the maximum elastic distortion of the lattice cell can be easily valuated to 0.07% and 1.5% in Ti-24Nb-0.5N and Ti-24Nb-0.5O, respectively. Theses values correspond to a ! maximum lattice strain of 0.1% and 2.1% along the tensile direction (i.e. <110> β ), respectively: the elastic deformation of the β phase is thus twenty times higher in Ti-24Nb-0.5O than in Ti-24Nb-0.5N, showing the very high ability of the β phase to be deformed elastically in the oxygen-added alloy in comparison with the nitrogen-added alloy. Conversely, both alloys exhibit a similar evolution of the three lattice parameters of the α" phase that can be explained by considering the crystallography of the SIM transformation. In both alloys, there is the same predominant orientation of β grains (Fig. 2), consisting of a <110> β direction parallel to the rolling direction, i.e. the tensile direction, and a <100> β direction perpendicular to the specimen surface, i.e. parallel to the incident X-ray beam. The stereographic projection of this specific orientation of the β phase is represented in Fig. 8. Application of the α"/β orientation relationship gives 6 equivalent lattice correspondence variants for the martensite from a specific orientation of the β phase [12]. These variants correspond to the different possibilities for which the [100] α" direction coincides with one of the <100> β and both [010] α" and [001] α" coincide with one of the <110> β , respectively. However, if the martensite is formed when a uniaxial stress is applied, a variant selection operates: depending on the initial orientation of the β grains, only the variants that are preferentially oriented will be formed [32,35], i.e. the variants that will give a maximum of strain. In the present tested specimens with a <110> β direction along the tensile direction, there is only one correspondence variant that is activated [32,35]. The orientation of the cell axis of this specific variant is reported on the stereographic projection in Fig. 8. For this α" variant, the a α" and c α" axis ([100] α" and [001] α" , respectively) are perpendicular to the tensile direction and would thus not evolve when the strain increases. On the contrary, the b α" axis ([010] α" ) lies along the tensile direction and would be more sensitive to the strain increase. This assumption is in good agreement with the observed evolution of lattice parameters of the α" martensite, where a α" and c α" parameters are almost constant and the b α" parameter increases continuously with the applied strain. The non isotropicity of the elastic deformation of α" phase is thus due to its preferential orientation.

Evolution of the SIM transformation

In addition to the observation of present peaks on diffractograms, the evolution of the SIM transformation during the cyclic tensile test can be qualitatively illustrated by the evolution of the relative area of the {110} β peak (that is the ratio of the current intensity of this peak by the initial intensity of the same peak). The Fig. 9 displays this ratio on loading (squares) and unloading (triangles) for both Ti-24Nb-0.5N (Fig. 9a) and Ti-24Nb-0.5O (Fig. 9b) alloys. In order to compare with the recovery strain, Fig. 9c shows the ratio of recovery strain of both alloys for each cycle defined as:

!""#$%&!!"#$%& -!"#$%&'(!!"#$%& !""#$%&!!"#$%&
For the Ti-24Nb-0.5N alloy, the relative area of the {110} β peak on loading starts to decrease from 0.5% of applied strain and continues to decrease strongly until 3.5% (squares in Fig. 9a). At the same time, this area after unloading has a similar behavior (triangles in Fig. 9a) but ! with higher values. This behavior illustrates that the volume fraction of the β phase decreases strongly under loading while its volume fraction increases significantly after the load is released. The SIM transformation appears thus to be extensively operating in this 0.5%-3.5% range of applied strain with a high reversibility. By comparing this result with the ratio of recovery strain (black circles in Fig. 9c), one can also remark that the area of the {110} β peak and of the recovery strain follow the same evolution: the SIM transformation exhibits the largest reversibility until 2% (ratio of recovery strain higher than 90%) that corresponds to the domain wherein the difference of the relative area of the {110} β peak between loading and unloading is the highest; the reversibility decreases further with the applied strain simultaneously with the decrease of the relative area of the {110} β peak after unloading. The reversibility of the strain is therefore clearly due to SIM transformation from the β phase to the α" martensite in the Ti-24Nb-0.5N alloy. For applied strain higher than 4%, the relative areas of the {110} β peak do not evolve any more: on loading, this peak is no more detected, but its area is not zero after unloading because this β peak is superimposed with the (002) α" peak (unloading only) and its intensity cannot be individually measured after unloading. As a consequence, the constant value of its area from 3.5% indicates just that the reversibility of the SIM transformation does not evolve anymore. Regarding to the relative intensities of {110} β and (002) α" peaks on loading, the superimposition of these peaks after unloading has a negligible effect on the evaluation of the relative area of the {110} β peak during the first 3% of deformation. The Ti-24Nb-0.5O alloy exhibits a similar general behavior but with some important differences. First, the relative area of the {110} β peak starts to decrease for applied strain higher than 1% (squares in Fig. 9b) and the SIM transformation seems to operate in the 1-3.5% range of applied strain. Secondly, the difference in value of its area between loading and unloading is not so high than in the Ti-24Nb-0.5N alloy, signifying that the SIM transformation has a lesser reversibility in the Ti-24Nb-0.5O alloy. Thirdly, for applied strain higher than 4%, the {110} β peak is never superimposed with the (002) α" peak, allowing a precise estimation of the relative area of the single {110} β peak after unloading (triangles in Fig. 9b): a part of the SIM transformation is still reversible for applied strain higher than 4% in the Ti-24Nb-0.5O alloy and a residual amount of β phase remains after unloading. In addition, the ratio of recovery strain (open circles in Fig. 9c) shows that the reversibility is total until 1.5% of applied strain. As a consequence, the recovery strain is first only due to the elasticity of the β phase while the SIM transformation starts to operate at around 1-1.5%. The reversibility decreases for applied strain higher than 2% even if the SIM transformation occurs simultaneously with elastic deformation of the β phase. This phenomenon is probably due to the onset of plasticity as the yield stress is reached.

Correlation between SXRD results and tensile curves

The combination of results about lattice parameters (Fig. 7) and the relative area of the {110} β peak (Fig. 9) makes it possible to understand the sequence of activation of each ! mechanism in both alloys. This sequence can be summarized on the conventional stress-strain curves of each alloy (Fig. 10).

For the Ti-24Nb-0.5N alloy (Fig. 10a), the elastic deformation of the β phase stops before the 0.5% of applied strain is reached (Fig. 7), that corresponds to the first yielding point. Next, the SIM transformation occurs mainly until about 3.5% of applied strain (Fig. 9), that corresponds to the second yielding point (YS on Fig. 10a). It is also clearly emphasized that the SIM transformation occurs extensively in the 0.5-2.5% range (Fig. 5 and Fig. 9), which corresponds to the stress plateau on the tensile curve (Fig. 10a). For higher applied strain than 3.5%, the SIM transformation stops to occur, except a small amount of reversible transformation, which probably continues to operate (Fig. 9). This domain corresponds thus to the plastic domain wherein dislocation slip and twinning are mainly operating in this alloy [7] and more generally in this alloy family [5,[36][37][38]. As the SIM transformation is not fully reversible from 2% of applied strain (Fig. 9a), one can also supposed that plastic deformation starts to occurs simultaneously with the SIM transformation, even if this former is the main mechanism in the 0.5-3% range of applied strain. This sequence corresponds to what is expected to occur in superelastic metastable β titanium alloys and partially evidenced in previous in situ studies [5,23,24].

For the Ti-24Nb-0.5O alloy, the sequence is less conventional (Fig. 10b). The deformation is first only accommodated by the elastic deformation of the β phase until an applied strain value of about 1% (Fig. 7), which corresponds to the part of the cyclic stress-strain curve wherein the loading and unloading curves are exactly superimposed (Fig. 3b) and wherein the slope of the curve is linear. This value is high in comparison with conventional alloys but similar values were already reported in oxygen-added alloys [20,27,39,40]. The most surprising feature is that the SIM transformation starts to operate around 1% of applied strain (Fig. 9) and that this transformation is reversible after unloading while the non-transformed remaining β phase continues to deform elastically under load (Fig. 7). It is also worth noting that the onset of the SIM transformation makes the slope of the tensile curve non-linear (Fig. 3b) as it was already evidenced by Dynamic Mechanical Analysis [32]. Both reversible mechanisms are thus operating simultaneously until approximately 2.5% of applied strain. However, the elasticity of the β phase only occurs in the residual non-transformed β phase that is not the preponderant phase after the SIM transformation started. The SIM transformation continues next until 4% and, finally, after 4%, the deformation is accommodated by the mechanisms of plastic deformation (twinning and dislocation slip [7]). It can also be remarked that no second yielding point is present because the SIM transformation occurs in the "plastic domain" of the stress-strain curve, i.e. the SIM critical stress has a similar value than the critical stress for activation of twinning and dislocation slip. Present in situ results shows thus that the yielding point on the curve (YS on Fig. 10b) is due to the beginning of the SIM transformation (and probably also to plastic deformation mechanisms). Plastic deformation mechanisms seems thus to operate simultaneously with the reversible SIM transformation in this alloy. SIM transformation was also already observed in the "plastic domain" in other titanium alloys [41][42][43][44]. However, the transformation is not reversible in that case and does not lead to superelasticity, but contributes to high ductility as a TRIP effect (TRansformation-Induced Plasticity) [42,43].

Effect of oxygen on the SIM transformation

The present study suggests that the superelastic deformation of the Ti-24Nb-0.5O alloy is due to the combination of a wide elastic deformation of the β phase and a reversible SIM transformation. However, other reversible mechanisms are mentioned in the literature for oxygen-added alloy. For example, lattice modulations have been found in Gum metal composition (Ti-23Nb-0.7Ta-1.2O, at.%) [45] and in Ti-23Nb-1O (at.%) alloy [24]. These lattice modulations correspond to nanodomains defined by the relaxation mode of the strain field due to oxygen atoms located in the interstitial sites of the crystal. When a stress is applied, the preferential growth of some pre-existing nanodomains would explain the superelasticity of such alloys, this phenomenon being reversible as demonstrated from in situ TEM experiments [24]. The existence of such nanodomains would also inhibit the formation of long-range α" martensite. However, this reversible growth of nanodomains is also characterized by the occurrence of a stress plateau on stress-strain curves and specific peaks of α" seems also not detected from X-ray diffraction under load [24]. As the present Ti-24Nb-0.5O alloy has a lower content of oxygen, does not exhibit stress plateau and clearly present a SIM transformation, this specific mechanism seems not to occur here.

In high oxygen content alloys, a large elasticity of the β phase was sometimes observed from in situ laboratory XRD or SXRD experiments. For example, the β phase can be deformed elastically until 1.2% in solution treated Ti-23Nb-0.7Ta-1.2O alloy (at.%, Gum metal composition) [40] or until 1.6% in the Ti-30Nb-10Ta-5Zr alloy (wt.%, with 0.3% of O) [27]. These values are quite smaller, but of the same order of magnitude than the 2.1% of elastic deformation that can be accommodated by the β phase in the Ti-24Nb-0.5O alloy. However, this value of 2.1% is obtained for an applied strain of 2.5%, the rest of deformation being accommodated by the SIM transformation, whereas the elastic deformation in other alloys is smaller. The peculiarity of this alloy is to combine a very high ability of the β phase to be deformed elastically and a reversible SIM transformation, resulting in high superelastic properties coupled with a high yield stress. However, an increase of the O content can suppress totally the SIM transformation and lead to a high recovery strain only due to pure elasticity of the β phase as already evidenced in high oxygen content alloys such as Gum Metals [40].

Conclusion

In situ cyclic tensile experiments were performed under synchrotron X-ray radiation on Ti-24Nb-0.5N and Ti-24Nb-0.5O alloys in order to investigate their mechanisms of superelasticity. Both alloys exhibit similar recovery strain but with different behavior: the Ti-24Nb-0.5N alloy presents a classical stress-strain curve with a stress plateau due to a SIM transformation whereas the Ti-24Nb-0.5O alloy does not display such a plateau. Analyses of diffraction patterns acquired under load and after unloading for each cycle allowed to determine precise features and domains of existence of the various mechanisms of deformation:

! -For the conventional Ti-24Nb-0.5N alloy, elasticity of the β phase is very limited and the superelasticity is clearly due to the existence of a SIM transformation from the β phase to the α" phase.

-The Ti-24Nb-0.5O alloy exhibits a non-conventional behavior. The β phase has a strong ability to deform elastically until 2.1%. The recovery strain is first only due to elasticity of the β phase until about 1% of applied strain. Between 1 and 2.5% of strain, a SIM transformation occurs simultaneously with elastic deformation of β phase leading to high superelasticity.

-The specific features of the Ti-24Nb-0.5O alloy are due to its intermediate content of O that inhibit not totally the SIM transformation, allowing this transformation to be reversible after the yield point of the tensile curve is reached.

-In both alloys, the elastic deformation of the α" martensite is mainly accommodated by the b α" parameter due to the initial texture of the β phase. the corresponding strain is indicated between the two patterns of each cycle.

!

Fig. 1 .

 1 Fig. 1. Schematic drawing of the geometry of the in situ SXRD tensile experiment.

Fig. 2 .

 2 Fig. 2. Calculated {110} and {002} pole figures of the Ti-24Nb-0.5N (a) and Ti24-Nb-0.2O (b) alloys.

Fig. 3 .

 3 Fig. 3. Cyclic stress-strain curves of the first 5 % of strain of Ti-24Nb-0.5N (a) and Ti24-Nb-0.2O (b) alloys.

Fig. 4 .

 4 Fig. 4. SXRD patterns acquired before starting the tensile test (top) and after the end of the entire cyclic tensile test (bottom) for Ti-24Nb-0.5N (a) and Ti24-Nb-0.2O (b) alloys.

Fig. 5 .

 5 Fig. 5. SXRD patterns zoomed around the {110} β peak (black triangles) acquired during the in situ cyclic tensile test under loading (a) and after unloading (b) for the Ti-24Nb-0.5N alloy; for each cycle, the corresponding strain is indicated beside each pattern. Squared symbols label the (020) α" peaks, circles label the (002) α" peaks and stars label the (111) α" peaks; open symbols correspond to the α" phase formed on quenching.

Fig. 6 .

 6 Fig. 6. SXRD patterns zoomed around the {110} β peak (black triangles) acquired during the in situ cyclic tensile test under loading (a) and after unloading (b) for the Ti-24Nb-0.5O alloy; for each cycle, the corresponding strain is indicated beside each pattern; black squared symbols label the (020) α" peaks and black circles label the (002) α" peaks.

Fig. 7 .

 7 Fig. 7. Evolution of lattice parameters of β and α" phases as a function of strain during in situ tensile tests for both Ti-24Nb-0.5N (black circles) and Ti-24Nb-0.5O (open circles).

Fig. 8 .Fig. 9 .Fig. 10 .

 8910 Fig. 8. Stereographic projection of the predominant orientation of β grains in the specimen; the tensile direction is along the [110] β direction ans the X-ray incident beam along the [001] β direction.

Fig. S1 .

 S1 Fig. S1. Whole SXRD patterns acquired during the in situ cyclic tensile test under loading (a) and after unloading (b) for the Ti-24Nb-0.5N alloy; the corresponding strain is indicated between the two patterns of each cycle.

Fig. S1 .

 S1 Fig. S1. Whole SXRD patterns acquired during the in situ cyclic tensile test under loading (a) and after unloading (b) for the Ti-24Nb-0.5O alloy;

Acknowledgment

This work was supported by the French National Research Agency (N°ANR 08MAPR 0017). We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities (beamline ID31).


A Ramalohary

P Castany

P Laheurte

F Prima

T Gloriant
email: thierry.gloriant@insa-rennes.fr

Superelastic property induced by low temperature heating of a shape memory Ti-24Nb-0.5Si biomedical alloy

Keywords: titanium, biomedical alloy, microstructure, martensite transformation, superelasticity

Superelastic property induced by low-temperature heating of a shape memory Ti-24Nb-0.5Si biomedical alloy

Alloys possessing shape memory or superelastic behavior are of great interest for biomedical functional devices such as stents, osteosynthesis staples, orthodontic arch wires, etc. The alloys commonly used for such devices belong to the NiTi family (e.g. Nitinol) due to their exceptional shape memory and superelastic properties. However, hypersensitivity and toxicity of nickel remain a problem in many clinical cases and the use of nickel must be avoided [1]. Consequently, nickel-free titanium-based alloys composed only of non-cytotoxic alloying elements such as Nb, Ta, Zr are now widely studied [2][3][4]. The reason for this interest is due to the fact that, depending to the chemical composition, metastable β titanium-based alloys can be mechanically unstable. Consequently, they can also exhibit shape memory effect and superelastic behavior. Indeed, a reversible martensite transformation between the parent β-phase (austenite) and the α"-phase (martensite) formed is observed in such alloys [5][6][7]. In these alloys, the shape memory effect is obtained when the quenched microstructure is composed of the self-accommodating α" martensitic phase (orthorhombic phase) at room temperature. When this self-accommodating martensitic microstructure is mechanically deformed into reoriented α" variants, the shape recovery can be achieved by heating, which induces a reversible martensite transformation into the austenic β phase (body-centered cubic phase). Superelastic (or pseudoelastic) behavior is obtained when the quenched microstructure is composed of the β-metastable phase at room temperature. In this case, a stress-induced martensite transformation (β into α") can directly occur under mechanical stimulation and large elastic recovery (superelasticity) can be obtained due to the fact that this transformation is fully reversible once the mechanical stress is released. From tensile tests, both shape memory and superelastic effects can be highlighted by the presence of a stress plateau on their tensile curves, and thus present a characteristic double-yielding behavior. However, the stress plateau is the consequence of the reorientation of the α" martensitic variants in the case of the shape memory alloy while it is due to the reversible martensite transformation in the case of the superelastic alloy. Numerous works carried out on this kind of alloy have focused on alloys belonging to the binary Ti-Nb system. Unfortunately, the superelastic property observed is far less than that of NiTi and does not exceed 2% of elastic recovery at best [3,[5][6][7]. However, it was showed that addition of a third or a fourth element such as Al or Sn improves the elastic recovery and about 3% of elastic recovery can be reached in some cases [8,9]. Furthermore, addition of interstitial alloying elements (O, N) was also observed to be beneficial to enhance significantly both the superelasticity and the mechanical strength [10][11][12].

In this study, we have explored a new way to obtain a superelastic alloy. Unlike the classical method, which consists of obtaining the β microstructure directly by water quenching from the high-temperature β-phase domain, this method consists of obtaining first a shape memory alloy displaying a fully α" martensitic microstructure and then a superelastic behavior after applying a low-temperature heating. This new method has been validated with Ti-24Nb-0.5Si alloy.

The Ti-24Nb-0.5Si (at.%) alloy was synthesized by cold crucible levitation melting under a pure argon atmosphere by using high-purity raw elements of titanium (99.999%), niobium (99.99%) and silicon (99.99%). The obtained ingot was then homogenized at 1223K for 72 ks under high vacuum (10 -7 mbar), quenched in water (at room temperature) and cold rolled until 90% of reduction in thickness. Samples for microstructural analyses and tensile tests were machined from this cold-rolled sheet. Tensile samples were machined to obtain normalized shapes: 3 mm width, 0.5 mm in thickness and a gage length of 15 mm. All samples were finally solution-treated in the high-temperature β-phase domain at 1123 K for 1.8 ks under high vacuum in order to restore a fully recrystallized microstructure from the cold-rolled state, and then water quenched at room temperature.

In this work, microstructures were characterized and observed by X-ray diffraction (Philips, XRD), optical microscopy (Leica, OM) and transmission electron microscopy (JEOL 2100, TEM). XRD analyses were conducted with Cu K a radiation (λ = 0.15406 nm). For the OM observations, samples were mechanically mirror" polished and etched in a 5% HF, 5% HNO 3 , 90% H 2 O solution. TEM samples were thinned down with a twin-jet electropolishing system using a 4% perchloric acid solution in methanol.

Tensile tests were carried out at room temperature (Instron machine, strain rate: 10 -4 s - 1 ). All tensile tests were performed with the tensile direction parallel to the rolling direction. In this study, cyclic tensile tests consisting of applying 0.5% strain increments (each followed by a stress release) were specifically carried out in order to characterize the stress plateau, which is related to the superelastic or the shape memory property. An extensometer was used to precisely measure the deformation of the samples.

Dynamic mechanical analysis (DMA) was performed with a Metravib DMA50 operating in static mode to evaluate the characteristic temperatures (austenite start, A s , and austenite finish, A f ) associated with the shape memory effect. Thus, the length variation associated with the strain recovery of a predeformed tensile sample was followed during a heating/cooling cycle (heating and cooling rate of 5 K min -1 ) between room temperature and 473 K.

Figure 1 displays a typical XRD profile (Fig. 1a) and optical micrograph (Fig. 1b) of the solution-treated and quenched Ti-24Nb-0.5Si alloy microstructure. XRD peaks were all indexed as belonging to the orthorhombic α" phase (space group: Cmcm) without the presence of any β peak. The cell parameters of this orthorhombic α" phase were found to be: aα " =0.318nm, bα " = 0.478 nm and cα " = 0.463 nm. Observations by OM reveal the presence of thin needles inside equiaxed grains, which corresponds to the typical self-accommodating α" microstructure generally observed in this kind of alloy. In fact, the needles correspond to the different martensitic α" variants that were formed during the quench. Therefore, the equiaxed microstructure observed by OM is the signature of the high-temperature β microstructure.

Figure 2a shows a typical tensile engineering stress-strain curve obtained from the solution-treated and quenched Ti-24Nb-0.5Si alloy. As shown on the curve, the tensile test was performed in a cyclic manner up to 3% of strain and then in a conventional manner from 3% to rupture. This tensile curve reveals the presence of a stress plateau at about 180 MPa. As we have shown that the quenched alloy presents a self-accommodating α" martensitic microstructure, this stress plateau is only due to the reorientation of the martensitic variants. In fact, as typically observed in this kind of microstructure, the different α" variants adapt their deformation and some can grow to the detriment of others. This reorientation behavior is not reversible on unloading and it is for this reason that a weak strain recovery, mainly elastic, is obtained. On the other hand, the observation of hysteresis between loading and unloading is due to the reversible movement of twin boundaries occurring in the martensitic microstructure. This phenomenon is referred to as the "rubber-like effect" in shape memory alloys [7].

To characterize the shape memory behavior of this kind of alloy, the α" reoriented martensitic microstructure must be heated to reach the austenitic temperature, which corresponds in fact to the β phase transformation temperature. Therefore, a quenched Ti-24Nb-0.5Si tensile specimen was preliminarily deformed up to 3% strain in the tensile machine and then heated in the dynamic mechanical analyzer in order to follow both the strain recovery and the temperature variation. Figure 2b presents the DMA strain-temperature curve for a heating-cooling cycle between room temperature and 473 K (rate: 5 K min -1 ).

It can be observed on the curve that almost all the strain was recovered on heating. The residual difference can be attributed to the fact that the strain measurement was not done with an extensometer during the DMA experiment. The β-phase transformation is observed to start at ~360 K, which corresponds to the austenitic start temperature, A s , and the alloy becomes fully β from about 400 K, which corresponds to the austenitic finish temperature, A f , when all the α" martensitic phase is transformed into the β phase. After reaching 473 K, the sample was cooled back to the room temperature. It can be seen that there is no variation on cooling although the martensite transformation (β into α") must theoretically occur on cooling. In fact, this transformation gives an α" self-accommodating microstructure, which is not sensitive to any significant length variation and thus cannot be detected by this kind of test. To confirm that such a martensite transformation has really occurred on cooling, the microstructure of the alloy after the heating-cooling cycle was characterized by XRD and OM. The corresponding XRD profile and optical micrograph are shown in Figure 3a andb, respectively. Surprisingly, the XRD profile reveals that only three diffracted peaks are detected (between 30° and 80°) and all could be perfectly indexed with the β phase this time (Fig. 3a). On the other hand, the typical α" thin needles seem not to be present in the optical micrograph where only an equiaxed β microstructure is observed (Fig. 3b). As it was suggested that the thin needles could be submicrometer in size, the sample was also observed by TEM. Figure 3c andd present, respectively, a typical TEM dark-field image and electron diffraction pattern obtained from such alloy after the heat treatment. In fact, the dark-field image reveals the presence of well-dispersed nanometer-scale precipitates but these precipitates correspond to the ω phase (hexagonal phase) in the present case and not to the α" phase. Indeed, both the darkfield image and electron diffraction pattern exhibit the classical two-phase β+ω iso microstructure usually obtained by low-temperature annealing of metastable β titanium alloys. In fact, the formation of ω iso after low-temperature annealing has been reported in a few studies carried out on Ti-Nb and Ti-Nb-Sn alloys [START_REF] Nyayadhish | ICOMAT-08 Conf. Proc[END_REF][START_REF] Takahashi | [END_REF]. Thus, it can be established that the ω iso phase formation occurring on heating prevents the formation of the α" self-accommodating microstructure on cooling in the present alloy. In fact, it has already been reported that the ω iso and α" phases behave differently under thermal treatment and that one is formed at the detriment of the other [15,16]. This phenomenon can be explained by the fact that the β-stabilizing elements (Nb and Si) are rejected towards the β matrix during the formation of ω iso on heating [17,18]. Consequently, the martensitic start temperature, M s , is believed to decrease below room temperature in the present case.

In order to investigate the mechanical behavior of this β+ω iso microstructure, tensile tests were performed on the Ti-24Nb-0.5Si alloy after a low-temperature heating treatment (up to 473 K). Figure 4 presents the typical engineering stress-strain curve obtained.

The tensile test was performed in a cyclic manner up to 5% strain and then in a conventional manner from 5% to rupture. It can be clearly observed that the alloy presents a superelastic behavior this time. Indeed, the tensile curve exhibits a doubleyielding behavior together with the presence of large hysteresis between loading and unloading, which demonstrates that a stress-induced α" martensite transformation has occurred in the alloy. The superelastic effect is particularly high because, as observed in the enlarged view in Figure 4 and 2.7% of mechanical strain recovery can be obtained, which is an excellent value compared to others observed with this kind of alloy in a recrystallized β-state. Thus, it can be concluded that the β+ω iso microstructure formed after the low-temperature heat treatment possesses the right degree of mechanical instability that permits the reversible stress-induced martensite transformation. Also apparent is the beneficial role of the ω iso phase, which does not prevent the stress-induced α" martensite transformation in the present alloy. It should be mentioned that the temperature of heating must be well controlled with this method. Indeed, higher heating temperatures were also used (523 and 573 K) in this study but the mechanical behavior was found to be very conventional and without any superelastic property. Our hypothesis is that the β-phase becomes too rich in βstabilizer elements and consequently the adequate degree of mechanical instability required is no longer reached. On the other hand, the chemical composition of the alloy is also a very important parameter to control. Indeed, the same experiments were carried out on the binary Ti-24Nb alloy, which also presents a self-accommodating α" microstructure. However, the transformation into a β superelastic alloy could not be obtained with this alloy composition. In fact, the temperature of heating necessary to reach the fully β-phase formation is higher than in the case of the Ti-24Nb-0.5Si alloy (~52 K) and is immediately accompanied by the formation of an excess of ω iso -phase, which makes it impossible to obtain a superelastic alloy. This result is corroborated by a recent study carried out on the Ti-24Nb alloy in which the austenite finish temperature was determined to be 477 K while the ω iso phase transformation was found to start at a much lower temperature at ~420 K by differential scanning calorimetry [START_REF] Nyayadhish | ICOMAT-08 Conf. Proc[END_REF]. In this respect, the addition of Si seems to be very judicious because this element is known to increase the temperature of the ω iso -phase formation on the one hand, and to decrease the martensitic start transformation, M S , on the other [19,20]-both conditions fulfilled by the method proposed in the present work.

Fig. 1 .Fig. 2 .

 12 Fig. 1. X-ray diffraction profile (a) and optical micrograph (b) of the solution-treated and quenched Ti-24Nb-0.5Si alloy.

Fig. 3 .

 3 Fig. 3. X-ray diffraction profile (a) and optical micrograph (b) of the β-phase microstructure of the Ti-24Nb-0.5Si alloy after being heated up to 473K. Dark field TEM image (c) and corresponding selected area diffraction pattern (d) ([1 1 3]β zone axis) showing the ω iso nanoprecipitates.

Fig. 4 .

 4 Fig. 4. Stress/strain curve showing the superelastic behavior of the Ti-24Nb-0.5Si alloy after being heated up to 473K.