Assessment of 3D Short Crack Closure in Ti-6Al-4V Alloy U lizing Synchrotron X-ray Microtomography

Synchrotron X-ray microtomography was u lized to observe the complex 3D crack morphology and the closure behavior of a short crack in Ti-6Al-4V alloy. The aim of the study was to inves gate the effect of the crack path evolu on on the 3D short crack closure behavior. In situ fa gue tests at R = 0.1 were carried out using microtomography with a spa al resolu on of 1 μm. The 3D crack morphology was observed in detail consis ng of non-facets (zigzag), branching, and facets with deflec on angles indica ng the presence of mode II and mode III displacements. The crack grows with facet-like paths mainly in α grains as compared to the non-facet paths in the α+β grains. The change in the crack path from facet-like paths to non-facet-like paths in the larger crack front induces an increase in the frac onal area of closed patches.


Introduc on
Fa gue crack closure has been iden fied as the predominant factor controlling the crack growth rates via reducing the effec ve driving force needed for crack propaga on [1][2]. Tradi onally, studies have es mated an average of crack closure along the crack front by using experimental methods such as clip gauges [2]. However, there is a local varia on in crack closure through specimen's thickness which can only be taken into account by the use of destruc ve approaches [3]. Therefore, there is a need to quan fy the crack closure along the crack front using non-destruc ve techniques. As a result, recently X-ray tomography, which enables the visualiza on of the 3D crack front and the microstructure, has been u lized to study 3D crack closure behavior. By using this technique, a variety of local crack paths along the crack front with their respec ve closure behavior can be quan fied within one specimen.
By employing X-ray tomography, Toda et al. tracked par cles inside an aluminum alloy to obtain local crack opening displacement along a large crack front [4]. In their study, they were able to clarify that the loss of crack surface contact is progressive and a single opening load level could not be defined. Moreover, they found out that the closure behavior was strongly influenced by mode III displacement associated with the local crack morphology [5]. A separate study by Limodin et al. reported that the non-uniform distribu on of closure along the crack front generates unsymmetrical crack propaga on rates [6]. However, the effect of the short crack path morphology and its evolu on on crack closure behavior has not been evaluated.
In this study, synchrotron X-ray microtomography has been u lized to observe the 3D crack closure behavior in a short crack in Ti-6Al-4V alloy. The observa on of the complex crack morphology and the crack front geometry was carried out at a spa al resolu on of 1 μm. The frac onal area of closed patches is quan fied for the short crack at two different crack fronts. The effect of the crack paths evolu on on those closed patches is further analyzed.

Material and experiments
The material used in this study was Ti-6Al-4V alloy. From an ini al thickness of 10 mm, the alloy was hot rolled at 800 ℃ and the thickness was reduced by 50%. A�er this, it was tempered for 96 hours at 900 ℃ in a furnace and allowed to cool inside the furnace. A bimodal structured Ti-6Al-4V alloy with the composi on of 65% α-phase and 35% β-phase was obtained a�er the heat treatment. Specimen for the study was then cut out from the heat treated material using EDM machine and notch of (60×20×4) μm made at the specimen's square cross-sec on of (600×600) μm. Fa gue test was then done at R = 0.1 with a maximum stress of 622 MPa and the crack was allowed to grow to a surface length of about 160 μm.
In situ computed microtomography was carried out at the BL20XU beamline in SPring-8, a synchrotron radia on facility in Hyogo, Japan. The material test rig was posi oned 80 m from the X-ray source with the X-ray beam having photon energy of 30 keV. A CCD detector of 2048×2048 pixels was posi oned 53 mm behind the sample. Scanning was performed at load levels star ng from 10% to 100% of the applied load with load increments of 10%. At each stage, 1800 radiographs scanning 180° capturing the whole specimen's cross-sec on were taken with the exposure me of 150 ms for each scan. The sample was then cycled to a crack length of 227 μm. The same imaging procedure for the crack of crack length 160 μm was repeated for the 227 μm long crack to obtain the projec ons.
The images were then reconstructed from the obtained series of projec ons. A�er the reconstruc on, they were converted to 8-bit images which have be�er contrast between α and α+β phases compared to the reconstructed images. The 2D slice images were then volume rendered to obtain a 3D image of the scanned sec on. The 3D images for each load level were matched to have the same loca on of the notch for accurate analysis of the local crack closure level. A linear a�enua on coefficient range was carefully selected to separate the crack from the material. The crack surface was then extracted for every load level using the seed growth technique. For the evalua on of COD, the crack was binarized and the crack images' Cartesian coordinates converted to polar coordinates. Addi onal details of the methods used can be found in the paper by Hassanipour et al. on the behavior of short crack growth and interac on with 3D microstructure [7].

Crack morphology
The complex morphology of the 3D cracks for two crack fronts that will be herea�er referred to as their crack lengths on the surface of 160 μm and 227 μm, are visualized in detail in Fig.1. The 3D crack morphology consists of facet paths, non-facet or zigzag paths, and crack bifurca on. The crack fronts for both crack lengths have irregular shapes implying the strong interac on of the crack with the local microstructure. Crack growth on the surface and inside the alloy varies along the crack front line. Birosca et al. reported that favorable grain orienta ons may lead to higher crack growth while some features such as grain boundaries can impede growth [8]. The crack paths on the le� side of the notch consist mainly of long facet-like paths with lower changes in the deflec on angles through the grains. As a result, the crack growth on the le� side of the notch is higher than on the right side at 160 μm length. Previous studies corroborate the observa on that the growth rate of facet-like paths is higher than those of non-faceted paths [7,9]. In contrast, the larger crack at 227 μm as seen in Fig.1 (a) has higher crack growth on the right side of the notch than on the le�. This is due to the change in crack path morphology from 160 μm to 227 2 MATEC Web of Conferences 321, 11051 (2020) https://doi.org/10.1051/matecconf/202032111051 The 14 th World Conference on Titanium μm which can be clarified by using cross-sec onal slice images A and B shown in Fig.1 (b). These cross sec onal slices are shown in Fig.2 at 160 μm and 227 μm crack surface lengths.
In Fig.2 (a) the crack path changes from mainly facet-like paths at 160 μm to branching at 227 μm as it grows through α+β grain as seen in Fig.2 (b) which impedes crack growth. It has been shown that crack branching reduces the crack driving forces at the crack p [1,10]. On the other hand, the crack in Fig.2 (c) grows to 227 μm with a small deflec on and con nues to grow with a facet-like path as shown in Fig.2 (d). The low change in the crack deflec on angle may be the reason for the high growth.   μm, respec vely to show the distribu on of the closed patches (white). The closed patches close to the crack front are mainly due to plas city at the crack p and those behind the p may be due to contact of asperi es on the crack faces. The different crack path morphologies that arise from the crack's interac on with microstructure leads to the varia on of the distribu on of these contact points on the crack surfaces. The increase in the plas c zone size induces higher near-p closure. As a result, in Fig. 3 (b) more contact points close to the crack front are seen in comparison to those in Fig.1 (a).
The frac onal area of closed patches increases with a decrease in the load as shown in Fig.3 (c). The increase in the crack front size that has larger plas c zone sizes as explained earlier, leads to the higher frac on of closed patches observed for the 227 μm crack length as compared to that of the 160 μm. The inhomogeneous distribu on of the closed patches that was observed in Fig.3 (a) and (b) contributes to the varia on of the frac onal area of closed patches from one load level to another that is seen in Fig.3 (c).

Local crack closure
In order to observe the increase in the local contact points from 100% to 10% load, the frac on of contact points for the crack paths in slice A and slice B at 160 μm and 227 μm lengths were quan fied. The results are shown in Fig.4 where a frac on equal to 1 implies that the crack faces are fully in contact, otherwise the crack is s ll open at some loca ons within the measured distance from the crack p. The crack opening at the p of slice A was 4 MATEC Web of Conferences 321, 11051 (2020) https://doi.org/10.1051/matecconf/202032111051 The 14 th World Conference on Titanium higher than that of slice B due to the path with long facets and few deflec ons. As a result, at the surface crack length of 160 μm in Fig. 4 (a), the crack in slice A has lower frac ons of closed points with decrease in the load in comparison to those in slice B. The behavior of the frac on of closed points for the crack paths in slices A and B changes with crack path evolu on as shown in Fig.4 (b) at 227 μm.
The crack path in slice A changes from facet-like at 160 μm to branching at 227 μm and as a result, there is an increase in the frac on of closed points than the crack in slice B. The crack in slice A fully closes at 40% load implying that branching close to the crack p can significantly increase the frac on of contact points resul ng in a reduc on in the crack p opening. This shows that the crack p behavior significantly affects the subsequent crack's behavior. Slice B has a low deflec on angle as it grows to 227 μm and con nues to grow with a facet-like path. This could be the reason for the low number of contact points seen in Fig.4 (b).

Conclusion
In situ computed microtomography with a spa al resolu on of 1 μm was employed to inves gate the crack closure behavior in Ti-6Al-4V alloy. The complex morphology of the crack was observed including the crack front geometry, the crack paths such as facets, non-facets and regions of branching.
The inhomogeneous crack fronts indicated the strong influence of the microstructure. First, it was observed that the crack growth strongly depends on crack path morphology. The paths that mostly consist of facets have a high growth as compared to non-facet paths. Secondly, the near-p closure increases due to the larger plas c zone size. Moreover, the crack path evolu on from facet-like to non-facet-like paths leads to an increase in the number of contact points at the crack front. From the findings of the study, the near-front crack behavior can change the crack's behavior.

Acknowledgement
The synchrotron radia on experiments were performed at SPring-8 with the approval of Japan Synchrotron Radia on Research Ins tute through proposal number 2017A0076 and 2018A0076. This work was supported through the grant-in-aid for scien fic research from Structural Materials for Innova on (SM41) of the Cross-ministerial Strategic Innova on Program (SIP) and Light Metals Educa on Founda on.