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Deformation twinning in fatigue crack tip plastic zone of Ti-6Al-4V alloy with Widmanstatten microstructure
Accepted Manuscript Deformation twinning in fatigue crack tip plastic zone of Ti-6Al-4V alloy with Widmanstatten microstructure
Yingjie Ma, Qi Xue, Hao Wang, Sensen Huang, Jianke Qiu, Xin Feng, Jiafeng Lei, Rui Yang PII: DOI: Reference:
S1044-5803(17)31662-5 doi: 10.1016/j.matchar.2017.08.029 MTL 8813
To appear in:
Materials Characterization
Received date: Revised date: Accepted date:
21 June 2017 23 August 2017 24 August 2017
Please cite this article as: Yingjie Ma, Qi Xue, Hao Wang, Sensen Huang, Jianke Qiu, Xin Feng, Jiafeng Lei, Rui Yang , Deformation twinning in fatigue crack tip plastic zone of Ti-6Al-4V alloy with Widmanstatten microstructure, Materials Characterization (2017), doi: 10.1016/j.matchar.2017.08.029
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ACCEPTED MANUSCRIPT Title Deformation Twinning in Fatigue Crack Tip Plastic Zone of Ti-6Al-4V Alloy with Widmanstatten Microstructure
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Author names and affiliations
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Yingjie Ma1, Qi Xue1,2, Hao Wang1, Sensen Huang1,2, Jianke Qiu1, Xin Feng3, Jiafeng
Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016,
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Lei1*, Rui Yang1
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China
Northeastern University, Shenyang 110089, China
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AECC Beijing Institute of Aeronautical Materials, Beijing 100095, China
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Corresponding authors
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Dr. Jiafeng Lei
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Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China. E-mail: [email protected]
ACCEPTED MANUSCRIPT Abstract Titanium alloys with Widmanstatten microstructure usually exhibit remarkable resistance to crack propagation and high fracture toughness, which has been rarely relevant to mechanical twins. In this study, the deformation twinning which was
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commonly observed in fatigue crack tip plastic zone of α/β titanium alloy with
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Widmanstatten microstructure, was firstly investigated by electron backscatter
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diffraction techniques. With fatigue crack propagating, large-scale twins were generated due to periodic loading and the crystallographic feature of Widmanstatten
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microstructure, ultimately consumed the major volume of the parent α colony. The
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development of twins with various rank of Schmid factor (SF) was characterized. Twins with relatively high rank SF grew sufficiently, even restricted the development
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of twins with low rank SF. The activation of the very low rank SF twin (including
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primary and secondary twins) was mainly attributed to the non-uniform local stress distribution induced by the plastic deforming compatibility between the neighbouring
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units. Finally the influence of deformation twinning on mechanical properties
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concerning crack of HCP α-Ti was discussed.
ACCEPTED MANUSCRIPT Deformation Twinning in Fatigue Crack Tip Plastic Zone of Ti-6Al-4V Alloy with Widmanstatten Microstructure
Abstract: Titanium alloys with the Widmanstatten microstructure usually exhibit
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high resistance to crack propagation and high fracture toughness. However, this has
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rarely been connected to mechanical twins. In this study, deformation twinning, which
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is popular in the fatigue crack tip plastic zone of α/β titanium alloys with the Widmanstatten microstructure, was systematically investigated with the electron
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backscatter diffraction technique. With the propagation of the fatigue crack,
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large-scale twins were generated due to the periodic loading and the crystallographic feature of the Widmanstatten microstructure, and they ultimately consumed the major
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volume of the parent α colony. Twin development with various ranks of Schmid
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factors (SF) was characterized, while ordinary deformation twins with relatively high rank SF grew most, extraordinary twins with very low rank SF were also activated,
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although restricted by the ordinary twins. The occurrence of extraordinary twins
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(including primary and secondary twins) were mainly attributed to the non-uniform local stress distribution induced by the plastic deformation compatibility between the neighbouring units. Lastly, the influence of deformation twinning on the mechanical properties concerning crack propagation in hexagonal α-Ti alloys was discussed.
Keywords: Titanium alloy; Widmanstatten microstructure; Twinning; CTPZ
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1.
Introduction
Titanium alloys are extensively used in aerospace systems and marine industries due to their high specific strength (strength/density) and unique corrosion resistance
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[1, 2]. The damage tolerance properties of structural titanium alloys, mainly evaluated by fracture toughness (KIC) and fatigue crack growth rate (da/dN), are considered as
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critical factors dictating safe services [1, 3]. Therefore, titanium alloys with high
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fracture toughness and low fatigue crack growth rate have received considerable
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attentions.
Relevant studies on titanium alloys revealed that, KIC and da/dN are highly
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sensitive to microstructure due to the influence of the crack tip plastic zone (CTPZ) [4-7]. In this sense, Widmanstatten microstructure, consisting of α lamella with the
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hexagonal close packed (hcp) structure and minor residual β phase with the body-centred cube (bcc) structure between α lamellas (Fig.1), contributes to damage
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tolerance, as the large CTPZ and circuitous crack propagating route therein decrease the da/dN and enhance KIC. Hence titanium alloys with the Widmanstatten
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microstructure exhibit remarkable properties of damage tolerance and are extensively used to produce the key structural components of civil aircrafts [2]. In Widmanstatten microstructure, large-sized α colonies consisting of α lamellas with of close crystal orientations provide a smaller amount of slip within unit volume compared with those in equiaxed microstructure, which necessitates deformation twinning to accommodate the strain of plastic deformation. However in titanium alloys, available literatures [8-13] concerning deformation twinning rarely focused on
ACCEPTED MANUSCRIPT Widmanstatten microstructure, except for our previous work [14] that initially reported the appearance of twins in the Widmanstatten microstructure without systematical characterization. Also, the discussions of the outstanding fatigue crack resistance and fracture toughness of the Widmanstatten microstructure mainly focus
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on fatigue crack path and dislocation slip, excluding deformation twining in the
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fatigue CTPZ which is indispensable for plastic deformation.
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In fact, for such lamellar structure with strong anisotropy, appropriate control of twinning can simultaneously improve strength and ductility. In α-Ti, since there are
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only four independent slip systems on the basal and the prismatic planes, plastic
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deformation along the c–axis necessitates < c + a > slip on the pyramidal plane or deformation twinning while the former requires a significantly high critical resolved
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shear stress. Thus {10-12} twinning, with a critical resolved shear stress close to the
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basal slip, is an important mode for c–axis straining [15, 16], and also plays a crucial role in determining mechanical properties and texture evolution due to the scarcity of
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“easy slip” systems in materials with hcp structure [17-19]. It has been observed that
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the combination of mechanical twins and dislocation slip is an effective approach for enhancing ductility and strength, especially in titanium alloys. And the twinning-induced plasticity (TWIP) effect has been considered for the composition design of titanium alloys to induce the twinning mechanism [20-23]. Therefore in this work, we studied in details the deformation twinning in the fatigue CTPZ of Ti-6Al-4V alloy with the Widmanstatten microstructure. The size and morphology of twins with different crack lengths were firstly introduced to reveal the development of twins with crack
ACCEPTED MANUSCRIPT propagating. The evolution of large-scale twins was investigated by discussing the influence of the microstructural parameters, Schmid factors (SF) and periodical stress. Twin variants were distinguished, and the formation of primary twins with low SF and secondary twins was studied. Finally the influence of twins on mechanical properties, especially the resistance to crack
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Experimental procedure
α lamellae Residual β α colony
Prior β grain
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2.
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propagation, of titanium alloys with the Widmanstatten microstructure was discussed.
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100μm
Fig.1 Optical morphology and schematic representation of Ti-6Al-4V alloy with Widmanstatten
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microstructure.
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1.5 25
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250
Initial crack
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Fig.2 Single-edge specimen with prepared initial crack for fatigue crack propagation
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and CTPZ observation, dimensions in millimeters (mm).
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Ti-6Al-4V (Ti64) alloy with a chemical composition (in wt.%) of Al 6.05, V
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4.10, O 0.06, Fe 0.05 and Ti balance was employed for this study. The β transus temperature (Tβ) of this alloy was determined metallographically to be 970 ± 5ºC.
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After heat-treatment at 1000 ºC for 60 min followed by furnace cooling,
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Widmanstatten microstructure was obtained with coarse prior β grains and α colonies consisting of α lamellas as shown in Fig.1. The average size of the prior β grains was about 550 μm and the width of the α platelets was close to 2 μm under the above heat-treatment. Single-edge specimen (Fig. 2) with an initial crack of 2 mm in length was prepared for the observation of CTPZ during fatigue crack propagation (FCP). The FCP experiments were carried out by the MTS 810 system with a sinusoidal waveform at 20 Hz and R = 0.1, where R denotes the ratio of the minimum to the
ACCEPTED MANUSCRIPT maximum stress. The observation of deformation twining in the fatigue CTPZ with different crack lengths was undertaken by employing scanning electron microscope (SEM). The SEM samples were mechanically ground, polished, and etched in the solution
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composed of 100 ml of water, 3 ml of nitric acid and 2 ml of Hydrofluoric acid for
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50-60 s. The characterization of deformation twinning was conducted by using
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electron back-scattered diffraction (EBSD), and the EBSD samples were mechanically ground and electro-polished. EBSD analysis was conducted on FEI
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Nova NanoSEM 430 equipped with Channel 5 system, using a step size of 0.5 μm.
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The Schmid factor based on slipping or twinning, the 3D crystal viewer of twins and parent were confirmed with the EBSD map. The twin variants were identified by
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comparing the observed twin orientation with the theoretical orientations of the six
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twin variants based on the parent grain orientation [24].
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3.
Results and discussion
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3.1. Deformation pattern: twinning and slipping
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Twins α colony
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Fig.3 Typical morphology of deformation twinning in fatigue CTPZ of Ti64 alloy with 20μm
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Widmanstatten microstructure.
Fig.4 Schematic procedure of plastic zone generation ahead of crack tip: (a) monotonic plastic zone induced by far-field load P; (b) distribution of stress caused by the decrease of load; (c) reversed plastic zone induced by the superposition of (a) and (b) [25].
Fig.3 shows the typical SEM morphology of the deformation twinning in the fatigue CTPZ of Ti64 alloy with Widmanstatten microstructure, exhibiting a specific angle between the two twinning variants in a single parent α colony. The twins pass
ACCEPTED MANUSCRIPT through the α/β interface and grow to large sizes. The activation of twins is relevant to
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the stress condition in the CTPZ.
Fig.5 The deformation twinning and slipping in two α colonies, showing the influence of the
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crystal orientation on the deforming pattern, (a) SEM image, (b) EBSD image showing two
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twinning variants in parent colony P1, the red line in (c) representing {10-12} twining plane, (d) Schmid factors distribution based on prismatic slip {1-100} <11-20>, (e) 3D crystal viewer of the corresponding parent and deformation twinning.
Under cyclic loading, two types of plastic zones ahead of fatigue crack tip have been distinguished: the monotonic and reversed ones developed respectively whilst approaching the maximum and minimum stresses as shown in Fig.4 [25-27]. At R ＞
ACCEPTED MANUSCRIPT 0, the sizes of the monotonic and reversed plastic zones, rp and rc, respectively, were estimated with the ratio of rc / rp around 1/4 [25]. In the CTPZ, the option of twinning or slipping in α lamella mainly depends on the relationship between the crystallographic orientation and the loading direction. Fig.5a-c show the twinning and
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slipping respectively activated in the left (P1) and right (P2) α colony. The SF
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distribution map (Fig.5d) based on the prismatic slip {1-100} <11-20> shows the low
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rank SF of the left colony P1 because the c-axis is approximately parallel to the load direction (Fig.5e). Thus, twins are developed to accommodate the strain along the
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c–axis. Slips are activated in the right colony P2 which exhibits relatively higher rank
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SF based on slipping, and eventually evolve to micro cracks.
Fig.6 Misorientation (point-to-point) of α lattice between twins and parent in Fig.5b, both the T1 (a) and T2 (b) twinning variants approximately showing 85° misorientation which is consistent with {10-12} twinning mode.
The EBSD map (Fig.5b) indicates two twinning variants, T1 and T2, in the
ACCEPTED MANUSCRIPT parent colony P1. And the misorientation (point-to-point) of the α lattices between the twins and the parent is approximately 85° for the two twinning variants (as shown in Fig.6), indicating the {10-12} <10-1-1> tensile twinning mode which is consistent with the twin planes marked by the red lines in Fig.5c. It should be noted that the
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observed twins in this study are entirely {10-12} twinning that needs less shear
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deformation compared with {11-21} and {11-22} twinning. The {10-12} twinning
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can be activated by tension along the c-axis or compression perpendicular to the c-axis of the HCP lattice [28, 29]. Considering the orientations of the colonies
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containing twins in the present study (e.g., P1 in Fig.5e), the {10-12} twins in the
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CTPZ should be mainly activated by the tensile stress in the monotonic plastic zone during the load rising stage. The size and strain level of the CTPZ increase with the
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propagation of the fatigue crack, indicating that deformation twinning should be
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relevant to the length of fatigue crack.
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Fig.7 SEM morphology of deformation twinning in fatigue CTPZ under different crack length, showing the evolution of twinning from acicular to large-scale with crack propagating, (a) the overall appearance of FCG specimen while the points “b” – “g” represent twinning position with various crack length as following: (b) 7.23mm, (c) 10.72mm, (d) 11.15, (e) 12.4mm, (f) 13.13mm, (g) 14.7mm, white arrows pointing out the twins.
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Fig.8 The length (a) and width (b) of the prominent deformation twinning in fatigue CTPZ versus
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fatigue crack length.
3.2. Deformation twinning accompanying crack propagation
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The size and morphology of the twins accompanying crack propagation are
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characterized in Fig.7. No twin was observed in the fatigue CTPZ under SEM
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examination until the crack propagating to site “b” with the crack length of 7.23 mm (Fig.7a). With such a relatively small crack length, the acicular twins are activated
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around the crack (Fig.7b) or at the grain boundary (GB) (Fig.7c). The strain in the CTPZ will gradually increase as approaching crack surface, which leads to a stress
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exceeding the critical resolved shear stress (CRSS) of deformation twinning around fatigue crack. TEM studies have indicated that slip precedes twin formation [10]. Both dislocation pile-ups and stress concentration at GB induced by the compatible deformation provide beneficial conditions for the activation of mechanical twins in the CTPZ. Fig.7 indicates that the size of twins rises with the increase of crack length. With
ACCEPTED MANUSCRIPT crack propagating, the size, total plastic strain and strain rate of the fatigue CTPZ increase [30, 31]. The development of large-scale twins (Fig.7e-g) is driven by the increasing requirement of accommodated plastic strain in the CTPZ. Also, the improved strain rate could promote the development of twins [11], especially after
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site “b” in Fig.7a. Fig.8 shows the variation of the measured length and thickness of
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the prominent twins in the CTPZ versus fatigue crack length. Twins size increase as
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the crack propagates until the twins reach the GB or colony boundary (Fig.7f, g), then twin growth is restricted inside a single α colony, resulting in the upper limitation of
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twin size.
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3.3. Evolution of large-scale deformation twinning
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Fig.9 Large-scale deformation twinning in fatigue CTPZ showing the lengthening, thickening and
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combining features, (a) SEM image, (b) EBSD image showing T1 and T2 twinning variants in P1
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and P2 parent colony respectively, the red line in (c) representing {10-12} twining plane, (d) 3D crystal viewer of the corresponding parent and deformation twinning.
Deformation twinning in the Widmanstatten microstructure shows uniquely larger size than that in the equiaxed or bi-modal microstructure of titanium alloys. Fig.9 shows the large-scale deformation twinning in the CTPZ at site “h” in Fig.7a. The EBSD map (Fig.9b) shows that lathy twins at GB grow toward the inside of the parent colony P1. The lengthening and thickening of twins proceed synchronously
ACCEPTED MANUSCRIPT while the lengthening of twins is dominant before reaching the other side of GBs [32]. The combination of twins occurs once neighboring twins meet, then the large-scale twinning bands are generated, and they consume the major volume of the parent grains or colonies. The residual parent inside the twinning bands (Fig.9b) indicates the
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trace of the thickening and combining of twins. Fig.10 schematically shows the
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thickening and combining processes successively.
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development of large-scale deformation twinning, including the initiation, lengthening,
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(c)
Fig.10 Schematic representation of the developing process of large-scale deformation twinning, (a) initiating at grain or colony boundary, (b) and (c) the lengthening and thickening process, (d) the combining of the neighboring twins leading to large-scale deformation twinning.
The large-scale deformation twinning in the CTPZ of the Widmanstatten
ACCEPTED MANUSCRIPT microstructure is relevant to the crystallographic feature of this structure. The large-size of α colonies, where α lamellas exhibit close crystal orientation, provides the beneficial crystallographic spaces for twins growth. In addition, each single load rising during the cyclic process provides the stress condition which promotes the
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twins growth in the monotonic plastic zone ahead of fatigue crack.
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3.4. Twin Variants
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3.4.1. Primary twin in different α colonies
As shown in Fig.9, two {10-12} twinning variants, T1 and T2, are generated in
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parent colony P1 and P2, respectively. The twinning SF based on the far-field tensile
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condition, the twinning plane and the shearing direction of the two twinning variants are determined and given in Table 1. Three important features can be summarized
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from Fig.9 and Table 1: (1) the large-scale T1 (01-12) / [0-111] twinning variant with
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high rank SF consumes major volume proportion of its parent colony and exhibits certain lengthening and thickening directions; (2) the T2 (0-112) / [01-11] twinning
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variant with low rank SF exhibits small size and irregular island-chain morphology; (3)
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the twinning plane of the two variants usually connect at the boundary of the two parent colonies, indicating possible interaction between the two variants.
ACCEPTED MANUSCRIPT Table 1 The deformation twining variants in Fig.8 and the corresponding Schmid factors based on far-field stress T1 variant
T2 variant
Misorientation*
SF
Variants
Misorientation*
SF
(-1102)/[1-101]
61.74°
0.419
(-1102)/[1-101]
59.15°
0.042
(1-102)/[-1101]
62.05°
0.386
(1-102)/[-1101]
57.77°
0.055
(-1012)/[10-11]
58.54°
0.391
(-1012)/[10-11]
61.58°
0.431
(10-12)/[-1011]
58.22°
0.421
(10-12)/[-1011]
62.92°
0.466
(0-112)/[01-11]
6.75°
0.317
T2 (0-112)/[01-11]
2.66°
0.146
T1 (01-12)/[0-111]
3.85°
0.379
(01-12)/[0-111]
11.94°
0.167
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Variants
* The “Misorientation” here represents the deviant orientation of twins between the
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theoretically calculated orientation and the observed orientation, the smallest “Misorientation”
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most closely matches twinning variant.
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The twinning SF is the key parameter influencing twins initiation and growth.
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Under far-field tensile stress, the high rank SF of T1 variant provides stable and prominent dynamic source for the initiation and growth of twins. Meanwhile, there is deformation twinning with very low rank SF in the CTPZ, such as the T2 variant (Fig9b and Table1). The activation of the very low rank SF twins was also reported and the autotwinning mechanism, i.e. the shear provoked by a neighboring twin which ‘extends’ across the grain boundary, was discussed [18]. Moreover, the variation of the outline and orientation of neighboring α colonies will result in the non-uniform
ACCEPTED MANUSCRIPT distribution of the local stress and stress gradient at colony boundaries. Here in Fig.9, the shear deformation during the twinning process of parent P1 remarkably affects the local stress distribution in parent P2, which could be obviously different from the far-field stress condition. In other words, it is inappropriate to solely estimate the
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activation of all twins (especially the low rank SF twins) according to the SF based on
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the far-field stress. However, the low rank SF cannot provide stable and forceful
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dynamic source for twin growth, and will just lead to the dispersive island-chain twin (such as T2 twin in Fig.9).
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3.4.2. Primary and secondary twins in a single α colony
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Fig.11 shows the SEM morphology of the large-scale twins at site “i” in Fig.7a, with various twinning variants in a single α colony. Subsequent EBSD analysis
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(Fig.12) shows that four primary {10-12} twinning variants are generated in a single
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parent α colony, accompanying secondary twinning variants T′ in the primary twins. The twinning plane, shear direction and SF of the four primary twinning variants were
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determined and given in Table 2. With the tensile direction approximatively
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paralleling to the c-axis of HCP structure, the SF of the six {10-12} twinning variants in single parent colony exhibit high rank, facilitating the activation of all six twinning variants. As shown in Fig.12d-e, there are two couples of variants including T1/T3 and T2/T4. It shows a small misorientation between T1 and T3, T2 and T4 variant, which is calculated to be 8° approximately. The morphology and range of the four primary {10-12} twinning variants differ, while variant T1 is the largest twin. The SF rank contributes to the diversity of twinning variant development. Variant T1 exhibits
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T2. Likewise, the development of variant T3 precedes T4.
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Fig.11 Large-scale deformation twinning with multi-variants in fatigue CTPZ.
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Table 2 The four deformation twining variants and corresponding SF in Fig.12
Twin variant
SF
T1
(0-112)/[01-11]
0.488
T2
(-1012)/[10-11]
0.485
T3
(01-12)/[0-111]
0.474
T4
(10-12)/[-1011]
0.457
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Fig.12 Characterization of deformation twinning variants in Fig.11 with EBSD analysis, (a) four primary deformation twinning variants in single α colony, the red line in (b) representing {10-12} twining plane, (c) 3D crystal viewer of the corresponding parent and deformation twinning, (d) pole figure of {10-12} twinning plane of parent grain and the four twinning variants, (e) schematic representation of the crystallographic relationship between the parent grain and twin variants.
ACCEPTED MANUSCRIPT As shown in Fig.12, the secondary twin variants, T1′ and T3′, are respectively activated in the T1 and T3 primary twin parent. The morphology of the secondary twins in the T1 primary twin parent and the corresponding EBSD map are shown in Fig.13. The calculated twin variants of T1′ and T3′ are {10-12} twins, the same as the
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primary twins shown in Fig.13 and Table 3. Similar to variant T2 in Fig.9b, the
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secondary twins T1′ and T3′ (Fig.12, Fig.13) with low rank SF appear with the
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“island-chain” morphology too. Likewise, the local stress distribution in the primary twin parent is remarkably affected by the re-orientation of the parent lattice, and the
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SF based on the far-field stress is not accurate enough to estimate the activation of
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secondary twins.
Table 3 The secondary deformation twining variants in Fig.11 and the corresponding Schmid
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In T1 twinning parent
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factors based on far-field stress
In T3 twinning parent
Misorientation
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Variants
Misorientation
SF
SF
*
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58.19°
0.447
(-1102)/[1-101]
58.86°
0.447
(1-102)/[-1101]
59.68°
0.473
(1-102)/[-1101]
59.99°
0.473
(-1012)/[10-11]
62.58°
0.175
(-1012)/[10-11]
61.69°
0.175
(10-12)/[-1011]
61.13°
0.192
(10-12)/[-1011]
60.58°
0.192
(0-112)/[01-11]
12.45°
0.052
(0-112)/[01-11]
10.64°
0.052
T1′ (01-12)/[0-111]
2.83°
0.043
T3′ (01-12)/[0-111]
1.09°
0.043
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(-1102)/[1-101]
Variants
* The “Misorientation” has been defined in Table1.
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Fig.13 The primary and secondary deformation twinning in fatigue CTPZ, (a) EBSD image, the red line in (b) representing {10-12} twining plane, (c) 3D crystal viewer showing the crystallographic evolution from parent to secondary twins with two different twining planes.
ACCEPTED MANUSCRIPT The activation of the low rank SF twins, including T2 twin in Fig.9b and secondary twins in Fig.13, are extraordinary compared with the ordinary twins with high rank SF, and they highly depend on the deforming compatibility of neighboring colonies, which is affected by the morphology and the crystal orientations of the
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corresponding regions. For example, secondary twins in Fig.12 are generated in both
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variant T1 and T3 (showing close crystal orientation of the two variants), while no
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secondary twin was activated in primary twins T2 and T4. It means that, under far-field stress the relationship of crystal orientations between T1 (or T3) and parent
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colony can induce the locale stress in primary twins to activate the secondary twin.
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3.5. Influence of deformation twinning on mechanical properties The fatigue CTPZ in titanium alloys plays a remarkably role in the mechanical
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properties regarding crack. The large-scale deformation twinning in the fatigue CTPZ
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of the Widmanstatten microstructure of titanium alloys expands the plastic zone, promotes the deflection of fatigue crack, and finally improves the resistance to the
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propagation of fatigue crack.
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The {10-12} twinning is an important mode for accommodating strain along the c–axis in HCP structure, especially for the Widmanstatten microstructure which provides much fewer number of slips in unit volume compared with that of the exquiaxed or bi-modal microstructure. Accompanying deformation twinning, the re-orientation of α lattice results in an elevated rank of SF based on slipping in twin bands (Fig.3d). Thus, deformation twinning not only contributes directly to the plastic deformation, but also provides beneficial crystallographic condition for dislocation
ACCEPTED MANUSCRIPT slip by the re-orientation of α lattice. Deformation twinning effectively refines microstructure by partitioning grains or colonies (Fig.5, Fig.9 and Fig.12), which will improve strength and ductility. In brief, the large-scale twins in the Widmanstatten microstructure of titanium alloys could enrich the plastic deformation in the CTPZ,
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generate the TWIP effect and increase the energy absorption (toughness) in the plastic
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zone. However, the optimal design of composition and microstructure of titanium
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alloys based on the TWIP effect is still in a preliminary stage due to the insufficient
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Conclusions
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In this study, deformation twinning in the fatigue CTPZ of the Widmanstatten
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microstructure of Ti64 alloy was studied. The evolution of large-scale twins with
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crack propagation and the influence of SF on twin variants were characterized. The influence of deformation twinning on the mechanical properties was discussed. The
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following conclusions are drawn.
(1) Only {10-12} twins were observed in the fatigue CTPZ in this study.
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Accompanying crack propagation, deformation twinning changes from acicular to large-scale deformation twinning, and finally consumes the major volume of the parent grain or colony. The large-sized α colony provides beneficial crystallographic space for the large-scale twinning band, while each single load rising can promote twin growth. (2) The SF is the key parameter influencing the initiation and growth of twins. Ordinary twinning variants with high rank SF grow most, restricting the growth of
ACCEPTED MANUSCRIPT extraordinary twinning variants with relatively low rank SF. (3) Based on the far-field stress condition, extraordinary twins with very low rank SF (including primary and secondary twins) could be activated, and exhibit irregular island-chain morphology. Deformation compatibility of the neighboring
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units (including α colony, primary twin) can result in the non-uniform local stress
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distribution and stress gradient at the interfaces (colony boundary or twin boundary).
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Thus, the SF based on the far-field stress is not sufficient to estimate the activation of all twins.
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(4) Deformation twinning not only contributes directly to the plastic deformation,
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but also provides beneficial crystallographic condition for dislocation slip by α lattice re-orientation. The large-scale twins in the Widmanstatten microstructure expand the
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plastic zone, enrich the plastic deformation, generate the TWIP effect and increase the
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energy absorption (toughness) in the CTPZ.
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Acknowledgements
This work is co-supported by Natural Science Foundation of China (51401221
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and 51671195). The authors acknowledge Prof. Dongsheng Xu, Prof. Qingmiao Hu and Prof. Shijian Zheng for the very useful discussion.
ACCEPTED MANUSCRIPT References [1] J.C. Williams, E.A. Starke, Progress in structural materials for aerospace systems, Acta Mater, 51 (2003) 5775-5799. [2] R.R. Boyer, An overview on the use of titanium in the aerospace industry, Mat Sci Eng a-Struct,
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Propagation, American Society for Testing and Materials, Philadelphia, 1967, pp. 247-309.
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[27] J.R. Rice, Special technical publication 415,
Fatigue Crack Propagation, American Society for
Testing and Materials, Philadelphia, 1967, pp. 247-309. [28] S.H. Park, S.G. Hong, C.S. Lee, Activation mode dependent {10-12} twinning characteristics in a polycrystalline magnesium alloy, Scripta Mater, 62 (2010) 202-205.
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ACCEPTED MANUSCRIPT 4.1. Graphical abstract The large-scale deformation twinnings in the CTPZ were developed due to cyclic load and the crystallographic feature of Widmanstatten microstructure, showing remarkable interactions among twinning variants. The large-scale twins expand the plastic zone, enrich the plastic deformation,
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generate TWIP effect and increase the energy absorbed in the CTPZ.
100μm
ACCEPTED MANUSCRIPT Highlights
Large-scale {10-12} twins were observed in the fatigue CTPZ in the Widmanstatten microstructure.
Twins initiation and growth is mostly influenced by the Schmid factor; whereas
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Deformation twinning provides beneficial crystallographic condition for
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dislocation slip by α lattice re-orientation.
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twins with very low rank Schmid factor may also be activated.
Yingjie Ma, Qi Xue, Hao Wang, Sensen Huang, Jianke Qiu, Xin Feng, Jiafeng Lei, Rui Yang PII: DOI: Reference:
S1044-5803(17)31662-5 doi: 10.1016/j.matchar.2017.08.029 MTL 8813
To appear in:
Materials Characterization
Received date: Revised date: Accepted date:
21 June 2017 23 August 2017 24 August 2017
Please cite this article as: Yingjie Ma, Qi Xue, Hao Wang, Sensen Huang, Jianke Qiu, Xin Feng, Jiafeng Lei, Rui Yang , Deformation twinning in fatigue crack tip plastic zone of Ti-6Al-4V alloy with Widmanstatten microstructure, Materials Characterization (2017), doi: 10.1016/j.matchar.2017.08.029
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ACCEPTED MANUSCRIPT Title Deformation Twinning in Fatigue Crack Tip Plastic Zone of Ti-6Al-4V Alloy with Widmanstatten Microstructure
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Author names and affiliations
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Yingjie Ma1, Qi Xue1,2, Hao Wang1, Sensen Huang1,2, Jianke Qiu1, Xin Feng3, Jiafeng
Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016,
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1
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Lei1*, Rui Yang1
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China
Northeastern University, Shenyang 110089, China
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AECC Beijing Institute of Aeronautical Materials, Beijing 100095, China
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Corresponding authors
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Dr. Jiafeng Lei
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Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China. E-mail: [email protected]
ACCEPTED MANUSCRIPT Abstract Titanium alloys with Widmanstatten microstructure usually exhibit remarkable resistance to crack propagation and high fracture toughness, which has been rarely relevant to mechanical twins. In this study, the deformation twinning which was
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commonly observed in fatigue crack tip plastic zone of α/β titanium alloy with
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Widmanstatten microstructure, was firstly investigated by electron backscatter
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diffraction techniques. With fatigue crack propagating, large-scale twins were generated due to periodic loading and the crystallographic feature of Widmanstatten
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microstructure, ultimately consumed the major volume of the parent α colony. The
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development of twins with various rank of Schmid factor (SF) was characterized. Twins with relatively high rank SF grew sufficiently, even restricted the development
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of twins with low rank SF. The activation of the very low rank SF twin (including
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primary and secondary twins) was mainly attributed to the non-uniform local stress distribution induced by the plastic deforming compatibility between the neighbouring
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units. Finally the influence of deformation twinning on mechanical properties
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concerning crack of HCP α-Ti was discussed.
ACCEPTED MANUSCRIPT Deformation Twinning in Fatigue Crack Tip Plastic Zone of Ti-6Al-4V Alloy with Widmanstatten Microstructure
Abstract: Titanium alloys with the Widmanstatten microstructure usually exhibit
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high resistance to crack propagation and high fracture toughness. However, this has
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rarely been connected to mechanical twins. In this study, deformation twinning, which
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is popular in the fatigue crack tip plastic zone of α/β titanium alloys with the Widmanstatten microstructure, was systematically investigated with the electron
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backscatter diffraction technique. With the propagation of the fatigue crack,
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large-scale twins were generated due to the periodic loading and the crystallographic feature of the Widmanstatten microstructure, and they ultimately consumed the major
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volume of the parent α colony. Twin development with various ranks of Schmid
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factors (SF) was characterized, while ordinary deformation twins with relatively high rank SF grew most, extraordinary twins with very low rank SF were also activated,
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although restricted by the ordinary twins. The occurrence of extraordinary twins
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(including primary and secondary twins) were mainly attributed to the non-uniform local stress distribution induced by the plastic deformation compatibility between the neighbouring units. Lastly, the influence of deformation twinning on the mechanical properties concerning crack propagation in hexagonal α-Ti alloys was discussed.
Keywords: Titanium alloy; Widmanstatten microstructure; Twinning; CTPZ
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1.
Introduction
Titanium alloys are extensively used in aerospace systems and marine industries due to their high specific strength (strength/density) and unique corrosion resistance
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[1, 2]. The damage tolerance properties of structural titanium alloys, mainly evaluated by fracture toughness (KIC) and fatigue crack growth rate (da/dN), are considered as
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critical factors dictating safe services [1, 3]. Therefore, titanium alloys with high
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fracture toughness and low fatigue crack growth rate have received considerable
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attentions.
Relevant studies on titanium alloys revealed that, KIC and da/dN are highly
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sensitive to microstructure due to the influence of the crack tip plastic zone (CTPZ) [4-7]. In this sense, Widmanstatten microstructure, consisting of α lamella with the
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hexagonal close packed (hcp) structure and minor residual β phase with the body-centred cube (bcc) structure between α lamellas (Fig.1), contributes to damage
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tolerance, as the large CTPZ and circuitous crack propagating route therein decrease the da/dN and enhance KIC. Hence titanium alloys with the Widmanstatten
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microstructure exhibit remarkable properties of damage tolerance and are extensively used to produce the key structural components of civil aircrafts [2]. In Widmanstatten microstructure, large-sized α colonies consisting of α lamellas with of close crystal orientations provide a smaller amount of slip within unit volume compared with those in equiaxed microstructure, which necessitates deformation twinning to accommodate the strain of plastic deformation. However in titanium alloys, available literatures [8-13] concerning deformation twinning rarely focused on
ACCEPTED MANUSCRIPT Widmanstatten microstructure, except for our previous work [14] that initially reported the appearance of twins in the Widmanstatten microstructure without systematical characterization. Also, the discussions of the outstanding fatigue crack resistance and fracture toughness of the Widmanstatten microstructure mainly focus
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on fatigue crack path and dislocation slip, excluding deformation twining in the
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fatigue CTPZ which is indispensable for plastic deformation.
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In fact, for such lamellar structure with strong anisotropy, appropriate control of twinning can simultaneously improve strength and ductility. In α-Ti, since there are
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only four independent slip systems on the basal and the prismatic planes, plastic
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deformation along the c–axis necessitates < c + a > slip on the pyramidal plane or deformation twinning while the former requires a significantly high critical resolved
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shear stress. Thus {10-12} twinning, with a critical resolved shear stress close to the
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basal slip, is an important mode for c–axis straining [15, 16], and also plays a crucial role in determining mechanical properties and texture evolution due to the scarcity of
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“easy slip” systems in materials with hcp structure [17-19]. It has been observed that
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the combination of mechanical twins and dislocation slip is an effective approach for enhancing ductility and strength, especially in titanium alloys. And the twinning-induced plasticity (TWIP) effect has been considered for the composition design of titanium alloys to induce the twinning mechanism [20-23]. Therefore in this work, we studied in details the deformation twinning in the fatigue CTPZ of Ti-6Al-4V alloy with the Widmanstatten microstructure. The size and morphology of twins with different crack lengths were firstly introduced to reveal the development of twins with crack
ACCEPTED MANUSCRIPT propagating. The evolution of large-scale twins was investigated by discussing the influence of the microstructural parameters, Schmid factors (SF) and periodical stress. Twin variants were distinguished, and the formation of primary twins with low SF and secondary twins was studied. Finally the influence of twins on mechanical properties, especially the resistance to crack
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Experimental procedure
α lamellae Residual β α colony
Prior β grain
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2.
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propagation, of titanium alloys with the Widmanstatten microstructure was discussed.
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Fig.1 Optical morphology and schematic representation of Ti-6Al-4V alloy with Widmanstatten
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microstructure.
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1.5 25
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250
Initial crack
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Fig.2 Single-edge specimen with prepared initial crack for fatigue crack propagation
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and CTPZ observation, dimensions in millimeters (mm).
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Ti-6Al-4V (Ti64) alloy with a chemical composition (in wt.%) of Al 6.05, V
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4.10, O 0.06, Fe 0.05 and Ti balance was employed for this study. The β transus temperature (Tβ) of this alloy was determined metallographically to be 970 ± 5ºC.
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After heat-treatment at 1000 ºC for 60 min followed by furnace cooling,
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Widmanstatten microstructure was obtained with coarse prior β grains and α colonies consisting of α lamellas as shown in Fig.1. The average size of the prior β grains was about 550 μm and the width of the α platelets was close to 2 μm under the above heat-treatment. Single-edge specimen (Fig. 2) with an initial crack of 2 mm in length was prepared for the observation of CTPZ during fatigue crack propagation (FCP). The FCP experiments were carried out by the MTS 810 system with a sinusoidal waveform at 20 Hz and R = 0.1, where R denotes the ratio of the minimum to the
ACCEPTED MANUSCRIPT maximum stress. The observation of deformation twining in the fatigue CTPZ with different crack lengths was undertaken by employing scanning electron microscope (SEM). The SEM samples were mechanically ground, polished, and etched in the solution
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composed of 100 ml of water, 3 ml of nitric acid and 2 ml of Hydrofluoric acid for
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50-60 s. The characterization of deformation twinning was conducted by using
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electron back-scattered diffraction (EBSD), and the EBSD samples were mechanically ground and electro-polished. EBSD analysis was conducted on FEI
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Nova NanoSEM 430 equipped with Channel 5 system, using a step size of 0.5 μm.
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The Schmid factor based on slipping or twinning, the 3D crystal viewer of twins and parent were confirmed with the EBSD map. The twin variants were identified by
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comparing the observed twin orientation with the theoretical orientations of the six
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twin variants based on the parent grain orientation [24].
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3.
Results and discussion
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3.1. Deformation pattern: twinning and slipping
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Twins α colony
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Fig.3 Typical morphology of deformation twinning in fatigue CTPZ of Ti64 alloy with 20μm
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Widmanstatten microstructure.
Fig.4 Schematic procedure of plastic zone generation ahead of crack tip: (a) monotonic plastic zone induced by far-field load P; (b) distribution of stress caused by the decrease of load; (c) reversed plastic zone induced by the superposition of (a) and (b) [25].
Fig.3 shows the typical SEM morphology of the deformation twinning in the fatigue CTPZ of Ti64 alloy with Widmanstatten microstructure, exhibiting a specific angle between the two twinning variants in a single parent α colony. The twins pass
ACCEPTED MANUSCRIPT through the α/β interface and grow to large sizes. The activation of twins is relevant to
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the stress condition in the CTPZ.
Fig.5 The deformation twinning and slipping in two α colonies, showing the influence of the
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crystal orientation on the deforming pattern, (a) SEM image, (b) EBSD image showing two
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twinning variants in parent colony P1, the red line in (c) representing {10-12} twining plane, (d) Schmid factors distribution based on prismatic slip {1-100} <11-20>, (e) 3D crystal viewer of the corresponding parent and deformation twinning.
Under cyclic loading, two types of plastic zones ahead of fatigue crack tip have been distinguished: the monotonic and reversed ones developed respectively whilst approaching the maximum and minimum stresses as shown in Fig.4 [25-27]. At R ＞
ACCEPTED MANUSCRIPT 0, the sizes of the monotonic and reversed plastic zones, rp and rc, respectively, were estimated with the ratio of rc / rp around 1/4 [25]. In the CTPZ, the option of twinning or slipping in α lamella mainly depends on the relationship between the crystallographic orientation and the loading direction. Fig.5a-c show the twinning and
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slipping respectively activated in the left (P1) and right (P2) α colony. The SF
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distribution map (Fig.5d) based on the prismatic slip {1-100} <11-20> shows the low
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rank SF of the left colony P1 because the c-axis is approximately parallel to the load direction (Fig.5e). Thus, twins are developed to accommodate the strain along the
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c–axis. Slips are activated in the right colony P2 which exhibits relatively higher rank
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SF based on slipping, and eventually evolve to micro cracks.
Fig.6 Misorientation (point-to-point) of α lattice between twins and parent in Fig.5b, both the T1 (a) and T2 (b) twinning variants approximately showing 85° misorientation which is consistent with {10-12} twinning mode.
The EBSD map (Fig.5b) indicates two twinning variants, T1 and T2, in the
ACCEPTED MANUSCRIPT parent colony P1. And the misorientation (point-to-point) of the α lattices between the twins and the parent is approximately 85° for the two twinning variants (as shown in Fig.6), indicating the {10-12} <10-1-1> tensile twinning mode which is consistent with the twin planes marked by the red lines in Fig.5c. It should be noted that the
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observed twins in this study are entirely {10-12} twinning that needs less shear
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deformation compared with {11-21} and {11-22} twinning. The {10-12} twinning
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can be activated by tension along the c-axis or compression perpendicular to the c-axis of the HCP lattice [28, 29]. Considering the orientations of the colonies
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containing twins in the present study (e.g., P1 in Fig.5e), the {10-12} twins in the
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CTPZ should be mainly activated by the tensile stress in the monotonic plastic zone during the load rising stage. The size and strain level of the CTPZ increase with the
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propagation of the fatigue crack, indicating that deformation twinning should be
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relevant to the length of fatigue crack.
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Fig.7 SEM morphology of deformation twinning in fatigue CTPZ under different crack length, showing the evolution of twinning from acicular to large-scale with crack propagating, (a) the overall appearance of FCG specimen while the points “b” – “g” represent twinning position with various crack length as following: (b) 7.23mm, (c) 10.72mm, (d) 11.15, (e) 12.4mm, (f) 13.13mm, (g) 14.7mm, white arrows pointing out the twins.
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Fig.8 The length (a) and width (b) of the prominent deformation twinning in fatigue CTPZ versus
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fatigue crack length.
3.2. Deformation twinning accompanying crack propagation
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The size and morphology of the twins accompanying crack propagation are
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characterized in Fig.7. No twin was observed in the fatigue CTPZ under SEM
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examination until the crack propagating to site “b” with the crack length of 7.23 mm (Fig.7a). With such a relatively small crack length, the acicular twins are activated
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around the crack (Fig.7b) or at the grain boundary (GB) (Fig.7c). The strain in the CTPZ will gradually increase as approaching crack surface, which leads to a stress
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exceeding the critical resolved shear stress (CRSS) of deformation twinning around fatigue crack. TEM studies have indicated that slip precedes twin formation [10]. Both dislocation pile-ups and stress concentration at GB induced by the compatible deformation provide beneficial conditions for the activation of mechanical twins in the CTPZ. Fig.7 indicates that the size of twins rises with the increase of crack length. With
ACCEPTED MANUSCRIPT crack propagating, the size, total plastic strain and strain rate of the fatigue CTPZ increase [30, 31]. The development of large-scale twins (Fig.7e-g) is driven by the increasing requirement of accommodated plastic strain in the CTPZ. Also, the improved strain rate could promote the development of twins [11], especially after
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site “b” in Fig.7a. Fig.8 shows the variation of the measured length and thickness of
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the prominent twins in the CTPZ versus fatigue crack length. Twins size increase as
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the crack propagates until the twins reach the GB or colony boundary (Fig.7f, g), then twin growth is restricted inside a single α colony, resulting in the upper limitation of
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twin size.
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3.3. Evolution of large-scale deformation twinning
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Fig.9 Large-scale deformation twinning in fatigue CTPZ showing the lengthening, thickening and
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combining features, (a) SEM image, (b) EBSD image showing T1 and T2 twinning variants in P1
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and P2 parent colony respectively, the red line in (c) representing {10-12} twining plane, (d) 3D crystal viewer of the corresponding parent and deformation twinning.
Deformation twinning in the Widmanstatten microstructure shows uniquely larger size than that in the equiaxed or bi-modal microstructure of titanium alloys. Fig.9 shows the large-scale deformation twinning in the CTPZ at site “h” in Fig.7a. The EBSD map (Fig.9b) shows that lathy twins at GB grow toward the inside of the parent colony P1. The lengthening and thickening of twins proceed synchronously
ACCEPTED MANUSCRIPT while the lengthening of twins is dominant before reaching the other side of GBs [32]. The combination of twins occurs once neighboring twins meet, then the large-scale twinning bands are generated, and they consume the major volume of the parent grains or colonies. The residual parent inside the twinning bands (Fig.9b) indicates the
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trace of the thickening and combining of twins. Fig.10 schematically shows the
(b)
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thickening and combining processes successively.
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development of large-scale deformation twinning, including the initiation, lengthening,
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Fig.10 Schematic representation of the developing process of large-scale deformation twinning, (a) initiating at grain or colony boundary, (b) and (c) the lengthening and thickening process, (d) the combining of the neighboring twins leading to large-scale deformation twinning.
The large-scale deformation twinning in the CTPZ of the Widmanstatten
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twins growth in the monotonic plastic zone ahead of fatigue crack.
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3.4. Twin Variants
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3.4.1. Primary twin in different α colonies
As shown in Fig.9, two {10-12} twinning variants, T1 and T2, are generated in
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parent colony P1 and P2, respectively. The twinning SF based on the far-field tensile
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condition, the twinning plane and the shearing direction of the two twinning variants are determined and given in Table 1. Three important features can be summarized
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from Fig.9 and Table 1: (1) the large-scale T1 (01-12) / [0-111] twinning variant with
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high rank SF consumes major volume proportion of its parent colony and exhibits certain lengthening and thickening directions; (2) the T2 (0-112) / [01-11] twinning
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variant with low rank SF exhibits small size and irregular island-chain morphology; (3)
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the twinning plane of the two variants usually connect at the boundary of the two parent colonies, indicating possible interaction between the two variants.
ACCEPTED MANUSCRIPT Table 1 The deformation twining variants in Fig.8 and the corresponding Schmid factors based on far-field stress T1 variant
T2 variant
Misorientation*
SF
Variants
Misorientation*
SF
(-1102)/[1-101]
61.74°
0.419
(-1102)/[1-101]
59.15°
0.042
(1-102)/[-1101]
62.05°
0.386
(1-102)/[-1101]
57.77°
0.055
(-1012)/[10-11]
58.54°
0.391
(-1012)/[10-11]
61.58°
0.431
(10-12)/[-1011]
58.22°
0.421
(10-12)/[-1011]
62.92°
0.466
(0-112)/[01-11]
6.75°
0.317
T2 (0-112)/[01-11]
2.66°
0.146
T1 (01-12)/[0-111]
3.85°
0.379
(01-12)/[0-111]
11.94°
0.167
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Variants
* The “Misorientation” here represents the deviant orientation of twins between the
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theoretically calculated orientation and the observed orientation, the smallest “Misorientation”
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most closely matches twinning variant.
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The twinning SF is the key parameter influencing twins initiation and growth.
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Under far-field tensile stress, the high rank SF of T1 variant provides stable and prominent dynamic source for the initiation and growth of twins. Meanwhile, there is deformation twinning with very low rank SF in the CTPZ, such as the T2 variant (Fig9b and Table1). The activation of the very low rank SF twins was also reported and the autotwinning mechanism, i.e. the shear provoked by a neighboring twin which ‘extends’ across the grain boundary, was discussed [18]. Moreover, the variation of the outline and orientation of neighboring α colonies will result in the non-uniform
ACCEPTED MANUSCRIPT distribution of the local stress and stress gradient at colony boundaries. Here in Fig.9, the shear deformation during the twinning process of parent P1 remarkably affects the local stress distribution in parent P2, which could be obviously different from the far-field stress condition. In other words, it is inappropriate to solely estimate the
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activation of all twins (especially the low rank SF twins) according to the SF based on
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the far-field stress. However, the low rank SF cannot provide stable and forceful
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dynamic source for twin growth, and will just lead to the dispersive island-chain twin (such as T2 twin in Fig.9).
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3.4.2. Primary and secondary twins in a single α colony
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Fig.11 shows the SEM morphology of the large-scale twins at site “i” in Fig.7a, with various twinning variants in a single α colony. Subsequent EBSD analysis
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(Fig.12) shows that four primary {10-12} twinning variants are generated in a single
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parent α colony, accompanying secondary twinning variants T′ in the primary twins. The twinning plane, shear direction and SF of the four primary twinning variants were
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determined and given in Table 2. With the tensile direction approximatively
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paralleling to the c-axis of HCP structure, the SF of the six {10-12} twinning variants in single parent colony exhibit high rank, facilitating the activation of all six twinning variants. As shown in Fig.12d-e, there are two couples of variants including T1/T3 and T2/T4. It shows a small misorientation between T1 and T3, T2 and T4 variant, which is calculated to be 8° approximately. The morphology and range of the four primary {10-12} twinning variants differ, while variant T1 is the largest twin. The SF rank contributes to the diversity of twinning variant development. Variant T1 exhibits
ACCEPTED MANUSCRIPT the highest SF rank and grows sufficiently, especially restricting the growth of variant
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T2. Likewise, the development of variant T3 precedes T4.
100μm
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Fig.11 Large-scale deformation twinning with multi-variants in fatigue CTPZ.
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Table 2 The four deformation twining variants and corresponding SF in Fig.12
Twin variant
SF
T1
(0-112)/[01-11]
0.488
T2
(-1012)/[10-11]
0.485
T3
(01-12)/[0-111]
0.474
T4
(10-12)/[-1011]
0.457
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ACCEPTED MANUSCRIPT
Fig.12 Characterization of deformation twinning variants in Fig.11 with EBSD analysis, (a) four primary deformation twinning variants in single α colony, the red line in (b) representing {10-12} twining plane, (c) 3D crystal viewer of the corresponding parent and deformation twinning, (d) pole figure of {10-12} twinning plane of parent grain and the four twinning variants, (e) schematic representation of the crystallographic relationship between the parent grain and twin variants.
ACCEPTED MANUSCRIPT As shown in Fig.12, the secondary twin variants, T1′ and T3′, are respectively activated in the T1 and T3 primary twin parent. The morphology of the secondary twins in the T1 primary twin parent and the corresponding EBSD map are shown in Fig.13. The calculated twin variants of T1′ and T3′ are {10-12} twins, the same as the
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primary twins shown in Fig.13 and Table 3. Similar to variant T2 in Fig.9b, the
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secondary twins T1′ and T3′ (Fig.12, Fig.13) with low rank SF appear with the
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“island-chain” morphology too. Likewise, the local stress distribution in the primary twin parent is remarkably affected by the re-orientation of the parent lattice, and the
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SF based on the far-field stress is not accurate enough to estimate the activation of
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secondary twins.
Table 3 The secondary deformation twining variants in Fig.11 and the corresponding Schmid
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In T1 twinning parent
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factors based on far-field stress
In T3 twinning parent
Misorientation
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Variants
Misorientation
SF
SF
*
*
58.19°
0.447
(-1102)/[1-101]
58.86°
0.447
(1-102)/[-1101]
59.68°
0.473
(1-102)/[-1101]
59.99°
0.473
(-1012)/[10-11]
62.58°
0.175
(-1012)/[10-11]
61.69°
0.175
(10-12)/[-1011]
61.13°
0.192
(10-12)/[-1011]
60.58°
0.192
(0-112)/[01-11]
12.45°
0.052
(0-112)/[01-11]
10.64°
0.052
T1′ (01-12)/[0-111]
2.83°
0.043
T3′ (01-12)/[0-111]
1.09°
0.043
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(-1102)/[1-101]
Variants
* The “Misorientation” has been defined in Table1.
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ACCEPTED MANUSCRIPT
Fig.13 The primary and secondary deformation twinning in fatigue CTPZ, (a) EBSD image, the red line in (b) representing {10-12} twining plane, (c) 3D crystal viewer showing the crystallographic evolution from parent to secondary twins with two different twining planes.
ACCEPTED MANUSCRIPT The activation of the low rank SF twins, including T2 twin in Fig.9b and secondary twins in Fig.13, are extraordinary compared with the ordinary twins with high rank SF, and they highly depend on the deforming compatibility of neighboring colonies, which is affected by the morphology and the crystal orientations of the
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corresponding regions. For example, secondary twins in Fig.12 are generated in both
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variant T1 and T3 (showing close crystal orientation of the two variants), while no
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secondary twin was activated in primary twins T2 and T4. It means that, under far-field stress the relationship of crystal orientations between T1 (or T3) and parent
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colony can induce the locale stress in primary twins to activate the secondary twin.
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3.5. Influence of deformation twinning on mechanical properties The fatigue CTPZ in titanium alloys plays a remarkably role in the mechanical
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properties regarding crack. The large-scale deformation twinning in the fatigue CTPZ
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of the Widmanstatten microstructure of titanium alloys expands the plastic zone, promotes the deflection of fatigue crack, and finally improves the resistance to the
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propagation of fatigue crack.
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The {10-12} twinning is an important mode for accommodating strain along the c–axis in HCP structure, especially for the Widmanstatten microstructure which provides much fewer number of slips in unit volume compared with that of the exquiaxed or bi-modal microstructure. Accompanying deformation twinning, the re-orientation of α lattice results in an elevated rank of SF based on slipping in twin bands (Fig.3d). Thus, deformation twinning not only contributes directly to the plastic deformation, but also provides beneficial crystallographic condition for dislocation
ACCEPTED MANUSCRIPT slip by the re-orientation of α lattice. Deformation twinning effectively refines microstructure by partitioning grains or colonies (Fig.5, Fig.9 and Fig.12), which will improve strength and ductility. In brief, the large-scale twins in the Widmanstatten microstructure of titanium alloys could enrich the plastic deformation in the CTPZ,
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generate the TWIP effect and increase the energy absorption (toughness) in the plastic
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zone. However, the optimal design of composition and microstructure of titanium
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alloys based on the TWIP effect is still in a preliminary stage due to the insufficient
4.
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understanding on the mechanisms of deformation twinning.
Conclusions
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In this study, deformation twinning in the fatigue CTPZ of the Widmanstatten
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microstructure of Ti64 alloy was studied. The evolution of large-scale twins with
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crack propagation and the influence of SF on twin variants were characterized. The influence of deformation twinning on the mechanical properties was discussed. The
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following conclusions are drawn.
(1) Only {10-12} twins were observed in the fatigue CTPZ in this study.
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Accompanying crack propagation, deformation twinning changes from acicular to large-scale deformation twinning, and finally consumes the major volume of the parent grain or colony. The large-sized α colony provides beneficial crystallographic space for the large-scale twinning band, while each single load rising can promote twin growth. (2) The SF is the key parameter influencing the initiation and growth of twins. Ordinary twinning variants with high rank SF grow most, restricting the growth of
ACCEPTED MANUSCRIPT extraordinary twinning variants with relatively low rank SF. (3) Based on the far-field stress condition, extraordinary twins with very low rank SF (including primary and secondary twins) could be activated, and exhibit irregular island-chain morphology. Deformation compatibility of the neighboring
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units (including α colony, primary twin) can result in the non-uniform local stress
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distribution and stress gradient at the interfaces (colony boundary or twin boundary).
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Thus, the SF based on the far-field stress is not sufficient to estimate the activation of all twins.
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(4) Deformation twinning not only contributes directly to the plastic deformation,
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but also provides beneficial crystallographic condition for dislocation slip by α lattice re-orientation. The large-scale twins in the Widmanstatten microstructure expand the
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plastic zone, enrich the plastic deformation, generate the TWIP effect and increase the
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energy absorption (toughness) in the CTPZ.
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Acknowledgements
This work is co-supported by Natural Science Foundation of China (51401221
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and 51671195). The authors acknowledge Prof. Dongsheng Xu, Prof. Qingmiao Hu and Prof. Shijian Zheng for the very useful discussion.
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ACCEPTED MANUSCRIPT 4.1. Graphical abstract The large-scale deformation twinnings in the CTPZ were developed due to cyclic load and the crystallographic feature of Widmanstatten microstructure, showing remarkable interactions among twinning variants. The large-scale twins expand the plastic zone, enrich the plastic deformation,
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generate TWIP effect and increase the energy absorbed in the CTPZ.
100μm
ACCEPTED MANUSCRIPT Highlights
Large-scale {10-12} twins were observed in the fatigue CTPZ in the Widmanstatten microstructure.
Twins initiation and growth is mostly influenced by the Schmid factor; whereas
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Deformation twinning provides beneficial crystallographic condition for
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dislocation slip by α lattice re-orientation.
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twins with very low rank Schmid factor may also be activated.