Formation of adiabatic shear band within Ti-6Al-4V: An in-situ study with high-speed photography and temperature measurement

International Journal of Mechanical Sciences 171 (2020) 105401

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Formation of adiabatic shear band within Ti-6Al-4V: An in-situ study with high-speed photography and temperature measurement Shengxin Zhu a,b, Yazhou Guo c,d,∗, Qichao Ruan c,d, Haosen Chen a,b,∗∗, Yulong Li c,d, Daining Fang b a

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China c School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China d Shaanxi Key Laboratory of Impact Dynamics and Engineering Application, Northwestern Polytechnical University, Xi’an 710072, China b

a r t i c l e

i n f o

Keywords: Adiabatic shear localization Temperature rise High speed photography Shear-compression Impact loading

a b s t r a c t Shear failure is frequently accompanied by the formation of an adiabatic shear band (ASB) under dynamic loading conditions. It was widely believed that both the thermal softening and stress state exert great influence on the initiation of the ASB. However, clear knowledge regarding the true mechanisms is still lacking and experimental research is especially needed. In this paper, a novel in-situ experimental setup was developed to observe the deformation localization and temperature evolution of the ASB simultaneously, by using the high-speed photography and high-speed infrared radiation (IR). The effect of the temperature increase on the initiation of the ASB was studied with the modified shear-compression specimens (SCS) of three different degrees. It is found that before the initiation of the ASB, the temperature of the deformed region in the SCS does not increase rapidly. Then, intense increment of temperature was found with the initiation and propagation of the ASB. The typical events—including the peak stress, the initiation of the ASB, and the maximum temperature—for adiabatic shear failure are ordered chronologically. It is proved that temperature increase may not the primary factor that triggers the initiation of the ASB.

1. Introduction Titanium alloys have been widely used as structure materials over the last few decades owing to their excellent combination of good formability, low weight, and high specific strength at high temperatures and corrosive environments. Because of these good features, titanium alloys are used for a wide variety of applications, ranging from aircraft engines and structural components to bio-applications [22]. amongst titanium alloys, Ti-6Al-4 V is extensively applied and hence is the most studied. Ti-6Al-4 V is used in industrial applications such as turbine blades, engine casing, and sports equipment [36]. In these applications, the material may suffer from dynamic loads during sudden events, e.g., ballistic impact, crack propagation, and crashes. Additionally, the material can suffer from dynamic loads during the manufacture procedure, e.g., highspeed machining, metal forming, and forging. Adiabatic shear localization (ASL) is an important dynamic failure mode and is known to as a ductile failure of metallic material under high-strain rate loading. The dynamic failure process is frequently accompanied by the formation of an adiabatic shear band (ASB) and causes the fracture of the material.

∗ ∗∗

Hence, gaining insight into the initiation and evolution of the ASB is of great importance. ASBs in metals and alloys have been widely investigated for decades. There are two main monographs on this subject [4,38], which present detailed background information. The former provides detailed descriptions and discussions on the experiment and physics of the ASB, and the latter concentrates on the analytical modeling of the ASB. Furthermore, there have been review articles on this subject ([1,37]; Y. [42]) in the past decade. The strength evolution of a material is dominated by two opposite mechanisms: hardening, such as strain hardening or strain rate hardening, and softening, such as thermal softening [3,24,46] or microstructure-related softening [13,17,33]. The classical description of ASL was presented by Zener and Hollomon, who regarded ASL as thermal-plastic instability. It is implied that the temperature is a crucial factor affecting the initiation and evolution of the ASB [3,7,24,39– 41]. From this perspective, it is the temperature increase that initially softens the materials and results in the formation of an ASB. However, detailed works involving microstructural investigations of the postmortem bands suggest that dynamic recrystallization (DRX) might be

Corresponding author at: School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China. Corresponding author at: State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China. E-mail addresses: [email protected] (Y. Guo), [email protected] (H. Chen).

https://doi.org/10.1016/j.ijmecsci.2019.105401 Received 28 March 2019; Received in revised form 31 August 2019; Accepted 20 December 2019 Available online 23 December 2019 0020-7403/© 2019 Elsevier Ltd. All rights reserved.

S. Zhu, Y. Guo and Q. Ruan et al.

the trigger of ASB [29,31,35]. Temperature increase and DRX are both implemented in the numerical modeling of the ASB [21,26]. It is suggested that the thermal softening may play a secondary role or no role at all in the initiation of the ASB. They also point out that thermal softening was not the formation mechanism of the ASB. Although analysis and numerical modeling indicate that thermal softening is not a major formation mechanism of the ASB, few experiments have been performed for verifying the effect of thermal softening on the formation mechanism of the ASB. Nevertheless, because of the transient and local features of ASB formation, it is difficult to perform in situ experimental measurements of the temperature and the shear-band evolution simultaneously. Thus, the causal relationship between the temperature increase and the formation of the ASB has not been experimentally dentified. Costin et al. measured a temperature increase of 100 K inside the shear band by using a highspeed single-element infrared (IR) InSb (indium antimonide) detector [8]. The measured temperature increase was an underestimation of the real temperature increase, because the diameter of the single element (1 mm) was much greater than the width of the shear band. Subsequently, different high-speed IR detectors, such as linear array detectors [14,20,23,27,28,32,47] and planar array detectors [11], were utilized for measuring the temperature increase in the ASL process with different experimental apparatuses, such as the split Hopkinson torsion bar and split Hopkinson pressure bar (SHPB). One notable study is that of Duffy [20,23], who used thin-wall tubular specimens for measuring the temperature and shear strain during the formation of an ASB by a split Hopkinson torsion bar. High-speed photographs of fine gridlines deposited on the surface of the specimen were obtained, indicating that a macroscopical deformation process occurred during shear band formation. However, the macroscopical deformation was not in accordance with the temperature history, which was measured using high-speed IR detectors. Other notable studies are those of Zhou [47] and Guduru [11]. A specimen proposed by Kalthoff [18] was employed for examining the shear band propagation and mode-II crack evolution under impact loading. In the study of Guduru, the optical technique of coherent gradient sensing was employed to examine the evolution of the mixed-mode stress intensity factors and to observe the initiation and propagation of the shear band. Simultaneously, a high-speed IR detector was used for recording the temperature history during the initiation and propagation of the shear band. However, owing to the small crack tip plastic zone and the concentrated fringes in the zone, the initial moment of ASB formation could not be observed accurately. Thus, Guduru et al. could not conclusively determine whether thermal softening had a significant impact on the initiation of the ASB. Recently, the adiabatic shear behavior of pure titanium has been investigated by the combining high-speed photography with IR temperature measurement [12]. However, the susceptibility of pure titanium to formation of ASB is lower than Ti-6Al-4 V, because of a larger critical shear strain for ASB in pure titanium [6,20]. The Ti-6Al-4 V is widely used in structures and components sustained to impact loading due to higher mechanical strength of Ti-6Al-4 V, while the lower mechanical strength of the pure titanium is widely used in medical field. Hence, it is important that a detailed study needs to be performed for clarifying the causal relationship between the temperature increase and the formation of the ASB in the Ti-6Al-4 V. Performing high-speed photography and IR temperature measurement simultaneously is very helpful for investigating the formation of the ASB. By examining the key factors—e.g., the strain localization, temperature increase, and ASB initiation—the relationship among those can be intuitively determined. In this study, we investigated the shear localization behavior of Ti-6Al-4 V using an SHPB system combined with a high-speed camera and an IR temperature measurement system. The formation of the shear band during the ASL process was observed by taking a series of high-speed photographs of specimens with grids previously deposited on the surfaces. Simultaneously, the temperature increase during the ASL process was determined. By examining the deformation, temperature increase, and ASB initiation, the causal relation-

International Journal of Mechanical Sciences 171 (2020) 105401

ship between the temperature increase and the formation of the ASB was clarified. 2. Experimental techniques 2.1. Material and specimen The specimen was similar to those proposed in a previous work [10]. It was loaded under dynamic conditions, with an SHPB system. The initiation and propagation of ASB was observed by using two diagnostic techniques. On one side of the specimen, high-speed photography was utilized for obtaining the evolution of the deformation. On the other side, high-speed IR temperature measurements were performed to monitor the evolution of the temperature. These techniques are briefly described below. The specimen is schematically presented in Fig. 1. The dimensions of the specimen are shown in Fig. 1(b). The length of the specimen was 17 mm. It had a 7 × 7mm2 square cross section. The specimen design included two semi-circular slots inclined to the longitudinal axis at an angle of 𝛼. The semi-circle had a radius of 2 mm, and the thickness of the gauge section was 1.6 mm. Three kinds of specimens were tested, with angles of 40°, 45°, and 50° According to this design, the compressive displacement applied to the end faces of the specimen was converted into local shear deformation in the semi-circular gauge section. Another advantage of the design is that there were no sharp edges or stress concentrations on the gauge with large strains (Z. [43–45]). As shown in Fig. 1(c), a grid of lines was engraved on the surface of the specimen’s semi-circular gauge section to show deformation process. Initially, these lines were oriented perpendicular to the direction of shear deformation, hence the slope of lines can provide a shear strain distribution across the gauge section during deformation. The approximate density of the lines was 4–5/mm, and the approximate etching depth was 0.09 mm. The relative orientation of specimens is shown in Fig. 1(d). Owing to the anisotropic mechanical behaviors of the rolled Ti-6Al-4 V plate, all the specimens were machined with two semi-circular slots in the longitudinal rolling direction of the rolled plate. The material used in this work was Ti-6Al-4 V. The chemical composition of the material was presented in Table 1. All the SCSs were obtained via wire electro-discharge machining from a rolled plate with a thickness of 25 mm. 2.2. Mechanical testing The SHPB is conventionally used for dynamic compression tests, and the theory and technique of the SHPB were introduced in detail elsewhere [5]. In this study, the diameter of the bars of the SHPB system was 12.7 mm. The striker bar, the incident bar, and the transmit bar were all made of maraging steel. The testing procedure for the SCS using the SHPB was the same as that for conventional SHPB experiments, except for the data processing. The shear component of the load Fshear is defined at the gliding plane along the direction of the inclined slots. The shear displacement ushear is defined along the gliding direction of the inclined slots. The nominal shear stress 𝜏 is determined as Fshear divided by the area of the inclined gauge section, and the nominal shear strain is determined as the displacement along the direction of the inclined slots divided by the deformed width of the inclined slots. The equations are listed below. 𝐹𝑠ℎ𝑒𝑎𝑟 = 𝐹 ⋅ 𝑐𝑜𝑠𝛼 𝑣 − 𝑣𝑡 𝑣𝑠ℎ𝑒𝑎𝑟 = 𝑖 𝑐𝑜𝑠𝛼

(1) (2)

Δ𝑡

𝑢𝑠ℎ𝑒𝑎𝑟 = ∫ 𝑣𝑠ℎ𝑒𝑎𝑟 𝑑𝑡

(3)

0

𝜏=

𝐹 sin 𝛼 cos 𝛼 𝑎𝑡ℎ

(4)

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 1. Geometric configuration of the SCS with respect to the roll plate. (a) Photograph of a specimen. (b) Dimensions of the specimen(mm) and the arrangement of the IR detector elements. (c) Grid of fine lines deposited on the outside surface of the semi-circular gauge section. (d) Specimens machined with shear direction in the longitudinal rolling direction L.

𝛾̇ =

𝑣𝑖 − 𝑣𝑡 𝑤 cos 𝛼

(5)

Δ𝑡

γ = ∫ 𝛾𝑑𝑡 ̇

(6)

0

Here, F is the average force applied to the specimen; vi and vt are the axial velocities of the two specimen surfaces that contact the incident and transmit bars, respectively; 𝛼 is the angle of inclination of the semicircular slots with respect to the longitudinal axis; a is the width of the square cross section of the specimen; th is the thickness of the semicircular gauge section; Δt is the period of loading. Based on the one-dimensional stress wave theory, F, vi , and vt at the bar/specimen interfaces can be calculated: 𝐹𝑖 + 𝐹𝑡 2 ( ) 𝑣𝑖 = 𝐶 𝜀𝑖 − 𝜀𝑟

(8)

𝑣𝑡 = 𝐶 𝜀𝑡

(9)

𝐹 =

(7)

where, Fi = EA(𝜀i + 𝜀r ) and Ft = EA𝜀t are the forces at the end of the incident and transmit bars, respectively; 𝜀i , 𝜀r , and 𝜀t are the inciTable 1 Chemical composition (weight%) of Ti-6Al-4 V. Element

Fe

Al

V

C

N

H

O

Content

0.3

6.2

4.1

0.1

0.05

0.01

0.2

dent, reflected, and transmitted strains, respectively; E, A, and C are the Young’s modulus, the cross-sectional area, and the longitudinal speed of the stress wave, respectively. 2.3. High-speed IR temperature measurement and photography Fig. 2 shows a schematic illustration of the experimental apparatus utilized in the study. By means of high-speed photography and highspeed IR temperature measurement simultaneously, the mechanical and thermal processes associated with the initiation and propagation of the ASB are studied. The flash, high-speed camera, and IR system are all triggered by the incident pulse of the stress wave. During the experiment, the output signal generated by the NO.1 strain gauge on the incident bar of the SHPB system was utilized to trigger the data-acquisition system, which recorded the signals from the loading signals from the NO.2, 3 strain gauges in the incident and transmit bars and the high-speed IR detectors for measuring the temperatures. The same gauge also triggered the high-speed camera, which captured the initiation and propagation of the ASB. In addition, when the camera captured the images, the feedback signals were recorded by the data-acquisition system. The time sequence for each device can be easily derived by calculating the time intervals during which the stress wave travels from the incident strain gauge to the specimen. Using the aforementioned methods, images were obtained that properly corresponded to the load and temperature histories. The overall experimental processes can be divided into four steps. Firstly, calibration was conducted for determining the relationship

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 2. Schematic of the experimental apparatus.

between the temperature and voltage before the test. Secondly, the specimens were placed between the incident and transmit bars. Alignment was made to allow maximum collection of radiation of the IR detector and good optical image from the high-speed camera at the same time. Thirdly, the IR system and the high-speed photography system were tested without mechanical loading to make sure they worked properly. Last, the striker bar was fired and struck the incident bar to produce stress wave, which triggered the flash, high-speed camera, IR system and data-acquisition system and loaded the specimens. 2.3.1. High-speed IR temperature measurement The high-speed IR temperature measurement system included an optical system with 1:1 magnification and an eight-element IR detector (liquid N2 cooled and InSb linear array). The optical system comprised a convex spherical mirror and a concave spherical mirror. Before each experiment, the alignment of optical system, and the detector is need be accomplished, which allows optimal collection of radiation from a welldefined location where temperatures were to be measured. Because IR is invisible, an optical device was used for the alignment, as shown in the upper portion of Fig. 2. The alignment method used is similar to that employed in a previous study [47]. The linear array of the detector was made up of eight elements. Each element was 150 × 150μm2 in size. The centre distance between two adjacent elements was 200 𝜇m, and the length of the whole array was 1.55 mm. The respond time of detectors was 1 μs approximately. During experiments, the detector signals were recorded by a high-speed digital acquisition system. By means of the predetermined relationship between the output of detector and the

temperature of a heated specimen of the same material, dimension, and surface finish in the actual experimental setup, the temperature curves around the shear band were acquired using the output signals of IR detector. 2.3.2. High-speed photography Images were recorded using a high-speed camera capable of capturing pictures with 768 × 924 pixels and a maximum image frequency of 5 million frames per second. A telecentric lens was installed in the highspeed camera. The image frequency was 2 million frames per second (500 ns temporal resolution) in this work. A high-brightness flash was used for obtaining clear high-speed photographs. But, a high-brightness could affect the IR temperature measurement system. Thus, a setup in which these two systems were completely isolated was employed during the entire test. However, when cracks occurred in the specimens, the light from the flashes entered the isolated space and sharply increased the signals of the detector. The deformation process and shear strain distribution were investigated using the grid of fine lines, which was engraved on the outside surface of the specimen’s semi-circular gauge section. As discussed in the “Introduction” part, many researchers have studied the process of adiabatic shear localization by using high-speed camera (Z. [43,48]) or high-speed temperature measurement [20,28,32]. This work combined these two techniques with SHPB and acquired the deformation image, temperature and load information simultaneously. The advantage is that the time sequence of some important events such as peak stress, ASB initiation, intense temperature rise, etc. can be

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Fig. 3. Typical calibration curves of one detector element for Ti-6Al-4 V. Three repeated tests were conducted.

International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 4. Typical force–displacement curves at the inclined slots with angles of 40°, 45°, and 50°

directly obtained. The causal relationship of these events could be deduced. The major difficulties of this experimental work include the interference between the high-speed photography and the high-speed IR systems, the synchronization of different systems and the acquisition of clear images. These difficulties make the experiment time consuming and low success rate. 3. Results and discussion 3.1. Calibration The relationship between the temperature and voltage needed to be determined before the experiments. The calibration was performed in a direct manner, as previously reported [16,19,28,32,47]. In the present study, each of the eight elements were individually calibrated at the same time. First, the specimen was settled between the incident and transmit bars and the surface of semi-circular gauge section was equipped with a thermocouple to record its surface temperature. Second, the specimen was heated to a desired temperature. Last, accompanied by cooling the specimen, the voltage output signals and temperature were recorded from the IR detector and thermocouple, respectively. This procedure was performed three times to ensure the repeatability of the calibration curves. During the dynamic loading, the plastic deformation affects the roughness of the specimen surface and the emissivity, which introduces errors in the temperature measurement. However, this was not considered in the present study, because for strain of 0.2 in an aluminum alloy [16] and for a slight variation in the emissivity of Ti-6Al-4 V, transitioning from a machined state to a rough state [28], the surface roughness does not significantly influence the calibration curves. In addition to the roughness of the surface, the oxidization of the surface can change the emissivity under heating at high temperatures during calibration processes. To verify that this does not affect the temperature measurement, three repeated cycles of heating the specimen to a desired temperature followed by a temperature reduction, were conducted. Fig. 3 shows that oxidation did not occur (or did not affect calibration) in our temperature range for one of the eight elements in the detector, and the results are identical to those previously reported [28]. 3.2. Mechanical properties Fig. 4 shows the typical force–displacement curves at the inclined slots with angles of 40°, 45°, and 50° The force calculated using Eq. (1) is the shear component of the load Fshear . The displacement calculated using Eq. (3) is defined along the gliding direction of the inclined slots.

Fig. 5. Deformation process and the temperature history of SCS40. Arrows 1–7 indicate the time of the camera shots. Six representative snapshots of the specimen are shown in Fig. 6, which correspond to arrows 2–7 in Fig. 5. s1–s8 represent the signal of IR elements. Temp is the calculated temperature based on the conversion of mechanical work into heat (with 0.5 as the Taylor–Quinney factor). The dashed black line and red arrow 4 both indicate the appearance of ASB.

As shown in Fig. 4, with the increase of the angle, the maximum displacement increases, and the maximum force decreases. The maximum shear stresses calculated using Eq. (4) with angles of 40°, 45°, and 50° are 934, 875, and 975 MPa, respectively. Generally, with the increase of the angle of the inclined slot, the shear stress decreases, and the normal stress increases. This means that the normal stress at the inclined plane could have an influence on the ASL failure. The ASL process with angles of 40°, 45°, and 50° is illustrated and discussed in detail below. 3.3 Results of deformation and temperature evolution simultaneously The thermomechanical results for three different angles (40°, 45°, and 50°) of the inclined slots are shown in Fig. 5, Fig. 11, and Fig. 15. Fig. 6(a)–(f) present images of the deformation processes obtained by the high-speed camera, corresponding to the time indicated by arrows 2–7 in Fig. 5. There are three distinct stages in the deformation process of SCS, including uniform deformation (stage 1), nonuniform deformation (stage 2), and shear localization (stage 3). At stage 1, the stress increased rapidly, and the deformation of the specimen remained relatively

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 6. Six high-speed images showing the deformation process of SCS40. The initiation moments of ASL are shown in Fig. 6(c). The blue frame shows the relative temperature measurement points on the surface of the gauge section. The red dotted lines indicate the propagation of the ASB, corresponding to the mismatched lines (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

homogenous, as evidenced by the straight lines in Fig. 6(a). Subsequently, the deformation was nonuniform in the gauge section, mainly owing to the geometry of the specimen. At stage 3, the lines were mismatched, indicating that the ASB appeared in the gauge section. The blue frame in Fig. 6(c)–(e) shows the relative temperature measurement region on the surface of the gauge section. The actual temperature measurement points were on the other side of the gauge section. As shown in Fig. 5, the lowest measured temperature was approximately 80 °C, rather than room temperature. This is because below 80 °C, the amplitude of the detector’s output signal was equal to or lower than the that of the background noise; thus, the output signals could not be detected. The maximum measured temperature approached 400 °C. The maximum measured temperature for the specimens with the other two angles was approximately 300 °C. A previous study [47] demonstrated that the measured temperature of C-300 was higher than that of Ti-6Al-4 V. The propagation speed of the ASB exhibited the same re-

lationship between C-300 and Ti-6Al-4 V. The authors then concluded that a higher propagation speed can lead to a higher deformation rates, which results in a higher temperature rises. In this work, the speed of ASB propagation can be directly estimated from the high-speed images. The evolution of the speed with respect to time is shown in Fig. 7. Obviously, the ranking of ASB propagation speed is SCS50> SCS40> SCS45, which is inconsistent with the measured temperatures. Therefore, the propagation speed is not the primary factor that determines the temperature rise within ASB. The temperature began to increase rapidly, which corresponds to the initiation of the ASB (stage 3). The temperature at the beginning of this stage was approximately 120 °C. After the initiation of the ASB—corresponding to the visible mismatch of lines—was observed, the ASB propagated along the shear direction and ran through the gauge section within a few microseconds. The formation of the ASB and the temperature evolution will be discussed in detail later.

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Fig. 7. Speed of ASB propagation with respect to time.

By utilizing the high-speed images, the shear strain field of the SCS can be determined. Fig. 8 presents the evolution of the shear strain for SCS40, corresponding to the time point shown in Fig. 5. The shear strain fields for the other two angles are shown in Figs. 13 and 17. Using the acquired deformation patterns, some quantitative information can be obtained. Most of the shear deformation is concentrated in the mid-

International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 9. Shear strain evolution of one line in the gauge section of SCS40. This line is located in the region of temperature measurement. The deformed width is measured along the direction of the lines, which is perpendicular to the direction of the inclined semi-circular slots.

region of the gauge section. Fig. 9 shows the shear strain evolution of one line in the gauge section of SCS40. This line is located in the region of temperature measurement. The deformed width in Fig. 8 is along the direction of the lines, which is perpendicular to the shear direction.

Fig. 8. Shear strain field of the gauge section of SCS40 under impact loading. The time within each contour indicates the loading time at which the picture is taken (see Fig. 6).

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International Journal of Mechanical Sciences 171 (2020) 105401

or the Culver criterion. Employing a constitutive relation 𝜏 = K𝛾 n ; the shear strain leading to the initiation of the ASB is expressed as follows: 𝛾𝑐 =

Fig. 10. Experimental results and critical shear strain for the initiation of the ASB predicted by Eqs. (10) and (11).

𝑛𝜌𝐶𝑣 , 𝜒

(10)

where 𝛾 c is the critical shear strain; n is the strain hardening index; 𝜕𝜏 𝜌 is the density; cv is the specific heat of the material; and 𝜒 = 𝜕𝑇 is • thermal softening coefficient. For Ti-6Al-4 V, cv is 586 J/(kg K) and 𝜌 is 4.43 g/cm3 . The strain hardening index n is 0.05 [25], and the thermal softening coefficient 𝜒 is 0.59 MPa/K. The predicted value of 𝛾 c leading to the initiation of the ASB is 0.219, which underestimates the critical shear strain for ASB initiation. However, it is close to the value of the nominal shear strain. This indicates that the Culver criterion might be used for some engineering applications, but it cannot describe the intrinsic characteristics of the ASB. Bai [2] proposed a criterion for the initiation of the ASB, which is expressed as follows. (𝑚 + 𝑛)𝜌𝐶𝑣 𝑇 𝛾𝑐−𝐵𝑎𝑖 = (11) 𝜏𝜈 𝑛 𝑚 − 𝜈 Here, the constitutive relation 𝜏 = 𝐾 𝛾 𝛾̇ 𝑇 is employed. m is the strain rate hardening index, 𝜈 is the thermal softening index, 𝜏 is the shear stress, and T is the temperature. The strain rate hardening index m is 0.087, and the thermal softening index 𝜈 is 0.059 for Ti-6Al-4 V (Jia, 2016). 𝜏 and T are equal to the value at the initiation of the ASB, which are given by experimental results. The predicted results are shown in Fig. 10. Owing to the different values of the temperature and shear stress at the initiation moment of the ASB, the predicted results differ for SCS40, SCS45, and SCS50. The criterion of Bai considers the effects of temperature and strain rate, which reflects some veritable characteristics of the ASB. However, this criterion could not account for the variation tendency of the critical shear strain with respect to loading angles or stress states. Thus, a new criterion for the initiation of the ASB is still needed. Such a criterion is presented in another work (Adiabatic shear failure of Ti-6Al-4V: Effects of stress state). 3.4. Formation of ASB

Fig. 11. Deformation process and the temperature history of SCS45. Arrows 1–7 indicate the time of the camera shots. Six representative snapshots of the specimen are shown in Fig. 12, which correspond to arrows 2–6 in Fig. 11. s1–s8 represent the signal of IR elements. Temp is the calculated temperature based on the conversion of mechanical work into heat (with 0.5 as the Taylor–Quinney factor). The dashed black line and red arrow 4 both indicate the appearance of ASB.

Then, the average local shear strain can be approximately calculated using Eqs. (5) and (6), where w is equal to the total deformed width. The nominal shear strain is also calculated, with w equal to the original diameter of the semi-circular slots. Apparently, the average local shear strain is higher than the nominal shear strain at the same loading stage. The average local shear strain is 0.53 at the initiation moment of the ASB and is similar to the local shear strain indicated by the high-speed images, indicating that the value calculated using the high-speed images is credible. The local shear strain and nominal shear strain at the initiation moment of the ASB in Fig. 10. The results differ among the three angles of the specimens. Considering the plane stress in the mid-region of the gauge section, the shear stress decreases, and the compressive stress increases in the inclined plane with the increase of the angle. Thus, it is supposed that the stress state affects the shear strain at the initiation moment of the ASB. The effect of the stress state is discussed in another work (Adiabatic shear failure of Ti-6Al-4V: Effects of stress state). As far as the author’s best knowledge, Culver proposed the most common criterion of ASB initiation [9], which is called the maximum stress criterion

The formation of the ASB has been studied by many researchers. However, the full development of the ASB—from initiation to propagation—is still not completely understood. One area of uncertainty is the effect of the temperature increase on the initiation of shear bands. The results of the present study offer a detailed characterization of the deformation and temperature rise during ASL of Ti-6Al-4 V and by examining the deformation processes, mechanics, and temperature information, the role of the temperature increase can be identified. Before the initial appearance of the ASB, the measured temperature does not rise rapidly, and does not exceed 120 °C. The temperature increase before ASB initiation can be calculated using the following equation: 𝛽𝑊𝑝 Δ𝑇 = (11) 𝜌𝑐𝑣 where 𝛽 is the Taylor–Quinney coefficient, Wp the plastic work density, 𝜌 is the density of the material, and cv is the specific heat of the material. During dynamic loading, the SCS undergoes shear and compressive stress in the gauge section, and the plastic work density is expressed as follows. 𝑊𝑃 = ∫ 𝝈 ∶ 𝑑 𝜺 (12) ( )) ( 𝑊𝑃 = ∫ 𝜎11 𝑑 𝜀11 + 𝜎22 𝑑 𝜀22 + 𝜎33 𝑑 𝜀33 + 2 𝜎12 𝑑 𝜀12 + 𝜎23 𝑑 𝜀23 +𝜎31 𝑑 𝜀31 (13) Here, 𝜎 ij and 𝜀ij are the components of the stress and strain tensors, respectively (ignoring the elastic contributions). For the tests in this study, it is assumed that the loading axis is along the direction “1″ and that there is a plane stress state in the gliding plane of the gauge section. Thus, 𝜎 22 = 𝜎 33 = 𝜎 23 = 𝜎 31 = 0. Moreover, the width of the slots on the specimen does not change appreciably after the post-mortem

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 12. Six high-speed images showing the deformation process of SCS45. The initiation moments of ASL are shown in Fig. 11(c). The blue frame shows the relative temperature measurement points on the surface of the gauge section. The red dotted lines indicate the propagation of the ASB, corresponding to the mismatched lines (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

measurement, which means that 𝜀11 is very small and can be neglected. As a result, only the shear component 𝑊𝑃 = 2 ∫ 𝜎12 𝑑 𝜀12 remains. The shear stress and strain used for calculating the temperature increase are both local values corresponding to the region of temperature measurement. The local shear strains are derived from the high-speed images. The calculated temperatures and 𝛽 just before the initiation of the ASB are shown in Table 2. The temperature predicted by using 𝛽 = 0.5 [34] are also given . Furthermore, the 𝛽 calculated using the measured temperature varies for loading angles of 40°, 45°, and 50° The calculated Taylor–Quinney coefficient is far from 0.9, which is a widely accepted value. The fact that Taylor–Quinney coefficient depends on the stress state is the same as that of previous study [34]. For SCS40, When the

Table 2 Calculated temperature and 𝛽 for SCS40, SCS45, and SCS50 . Calculated temperature (°C)

SCS40

SCS45

SCS50

𝛽 = 0.9 𝛽 = 0.5 [34] Measured temperature (°C) Calculated 𝛽

154 95 124 0.66

127 81 95 0.59

145 91 110 0.62

ASB propagates to the measurement points shown in Fig. 6(d)—from 58.45 to 60.45 μs in Fig. 5, a sharp increase in the measured temperature is observed. It is suggested that the shear localization deformation

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 13. Shear strain field of the gauge section of SCS45 under impact loading. The time within each contour indicates the loading time at which the picture is taken (see Fig. 12).

Fig. 14. Shear strain evolution of one line in the gauge section of SCS45. This line is located in the region of temperature measurement. The deformed width is measured along the direction of the lines, which is perpendicular to the direction of the inclined semi-circular slots.

Fig. 15. Deformation process and the temperature history of SCS50. Arrows 1–7 indicate the time of the camera shots. Six representative snapshots of the specimen are shown in Fig. 16, which correspond to arrows 2–6 in Fig. 15. s1–s8 represent the signal of IR elements. Temp is the calculated temperature based on the conversion of mechanical work into heat (with 0.5 as the Taylor–Quinney factor). The dashed black line and red arrow 4 both indicate the appearance of ASB.

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 16. Six high-speed images showing the deformation process of SCS50. The initiation moments of ASL are shown in Fig. 16(c). The blue frame shows the relative temperature measurement points on the surface of the gauge section. The red dotted lines indicate the propagation of the ASB, corresponding to the mismatched lines (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

processes were happening in the gauge section. These processes are also observed in Fig. 9. From 58.45 μs to 60.45 μs, the width in the region, where the deformation can continue happening, is reducing. However, during the time interval between 55.45 μs and 58.45 μs, the deformed width isn’t reduced with increasing deformation continually.

Thus, it is indicated that before 58.45 μs, the shear localized deformation does not occur, and the distribution of the temperature is relatively uniform. Sharp temperature increases were observed during the localized shear deformation. For SCS50, the initiation time of the ASB was 56.85 μs. Again, before the initiation of the ASB, the

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 17. Shear strain field of the gauge section of SCS50 under impact loading. The time within each contour indicates the loading time at which the picture is taken (see Fig. 16).

Fig. 18. Shear strain evolution of one line in the gauge section of SCS50. This line is located in the region of temperature measurement. The deformed width is measured along the direction of the lines, which is perpendicular to the direction of the inclined semi-circular slots.

temperature did not change rapidly. When the ASB propagated to the measurement points in Fig. 16(d), the measured temperature was approximately 150 °C. From 56.85 to 58.35 μs, as shown in Figure 18, the deformed width decreased with the ASB propagation and the temperature increased sharply. Table 3 shows the time sequence of the occurrence of typical events (such as the peak shear stress, the initiation of the ASB, and the maximum temperature) in the shear-compressive failure process for SCS40, SCS45, and SCS 50. The time moment of the peak shear stress is regarded as the base time. The peak shear stress occurred before the initiation of ASB. After that, a very fast increase of the temperature was detected by the high-speed IR detector. Because the ASB has “transient” and “local” characteristics, it is difficult to determine the occurrence of the ASB from a macroscopic perspective without the assistance of other methods. In the present study, the occurrence of the ASB was captured by the visible mismatch of the fine grid lines. When the ASB occurred initially, the measured temperature doesn’t exceed 130°C and lower than 90°C before the temperature increase sharply. Furthermore, there was a short time difference between the sharp temperature starting to rise and the initiation of the ASB. But, the effect of thermal softening can be assessed based on the measured temperature and utilizing the Johnson–Cook constitutive model. Taking SCS40 as an example, the measured temperature is nearly 124 °C, which can lead to an 8% decrease in the stress. Considering the strain-rate hardening, the strain rate is calculated by 𝜀̇ = 𝜀𝑐∕𝑡 , where the subscript c represents 𝑐 the critical moment of ASL initiation. In addition, the calculated result indicates that the strain-rate hardening can lead to a 15% increase in

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International Journal of Mechanical Sciences 171 (2020) 105401

Table 3 Time sequence of the occurrence of typical events in the shear-compressive failure process. Time for typical events occurring

Peak shear stress

Initiation of ASB

Maximum temperature

SCS40 SCS45 SCS50

0 (μs) 0 (μs) 0 (μs)

6.5 (μs) 10.2 (μs) 2.37 (μs)

18 (μs) 17.74 (μs) 11.37 (μs)

stress. It is found that the hardening is still greater than thermal softening. As shown in Table. 2, the calculated temperature (𝛽 = 0.5) are less than the measured temperature. The difference of temperature can be caused by the localized shear deformation within narrower region. According to the evolution of the shear strain shown in Figs. 9,14, and 18, the localized shear deformation is observed owing to the reduction of the deformed width. Further localized deformation leads to a further increase in the local temperature. So, the maximum temperature can be achieved with the propagation of ASB through the inclined slot in the specimen before occurrence of crack. The aforementioned typical events are chronologically ordered as follows: the peak shear stress, the initiation of ASB, and the maximum temperature. The obtained experimental results indicate that the observable sharp temperature increase occurred after the initiation of the ASB, suggesting that the temperature increase did not play a key role in the initiation of the ASB. Thermal softening is not the primary factor that leads to the initiation of the ASB. Possible errors may exist when recording the time of typical events. These errors are mainly determined by the response time of the test apparatus. Since the temporal resolutions of the load acquisition system, high-speed camera and IR temperature measurement system are 0.1μs, 0.5μs and 1μs, respectively, and all these systems are triggered by the same signal, the temporal error is limited to about 1μs. When it comes to the temperature measurement, as pointed out in [15], the error in IR temperature measurement mainly originates from the change of surface condition and the accuracy of calibration. However, these errors are all in acceptable limits in a certain temperature range. In addition, the main purpose of the tests is to clarify the time sequence of intense temperature rise, ASB initiation, etc. The temperature accuracy itself would not affect its time sequence information. 3.5. Microstructural morphology of ASB Interrupted dynamic tests on shear-compression specimens were conducted by SHPB with stop-rings with different lengths. Microstructures of ASB at different evolution stages were obtained. ASB was not observed until the loading displacement is greater than 0.45 mm (22.5% of the width of the gauge section). Fig. 19 presents the microstructure of Ti-6Al-4 V at different deformation stages. As shown in Fig. 19(a), typical lamellar 𝛼+𝛽 phases were observed in the undeformed material of Ti-6Al-4 V. Fig. 19(b) shows an ASB at the early stage of initiation. The ASB is about 1 mm in length and 8 μm in width. Large shearing was observed within the shear band, while the material outside ASB was relatively undeformed. The small deformation of the material suggested little heat was generated before ASB initiation. It should be noted that microvoids were found within ASB at this early stage, indicating that they were closely related to the formation of ASB. The local instability induced by microstructural softening, microvoids for example, may play the primary role for ASB initiation. Macrocracks were observed at the later stage of ASB evolution, as shown in Fig. 19(c). The width of ASB increased to about 20 μm, indicating that ASB width is not a constant but grows with the loading process. Fracture surfaces of the specimens were examined by scanning electron microscope (SEM), shown in Fig 20. The fracture surfaces were characterized by a large number of elongated dimples, typical feature

Fig. 19. Morphology of ASB within Ti-6Al-4 V under impact loading.

of ductile fracture. There is little difference for specimens with different loading angles, except that the flow direction of dimples for SCS50 slightly deviated from the prescribed shearing direction. The out-ofplane displacement of the SCS50 specimen was responsible for this phenomenon.

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International Journal of Mechanical Sciences 171 (2020) 105401

Fig. 20. The fracture morphology of Ti-6Al-4 V under dynamic shear.

4. Conclusion Experiments were conducted on an SCS made of Ti-6Al-4 V to study the deformation localization and temperature evolution of the ASB by utilizing high-speed photography and high-speed IR temperature measurement simultaneously. By combining the strain field and temperature history, the effect of the temperature increase on the initiation of the ASB was investigated in detail. Before the initiation of the ASB, the temperature in the deformed region of the SCS did not increase rapidly. Then, with the initiation and propagation of the ASB, an intense temperature increase occurred. The typical events—including the peak stress, the initiation of the ASB, and the maximum temperature—for adiabatic shear failure are ordered chronologically. It is proposed that the temperature increase does not play a key role in the initiation of the ASB. The microstructural observation also indicated that the shear instability induced by microstructural softening (such as microvoid) may be the trigger of the ASB. Acknowledgments The authors gratefully acknowledge the financial support from National Natural Science Foundation of China (No. 11672354, 11527803, 11922211 and 11802029). This work is also supported by the State Key Laboratory of Explosion Science and Technology (ZDK[30]T18-03). Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijmecsci.2019.105401. References [1] Antolovich SD, Armstrong RW. Plastic strain localization in metals: origins and consequences. Prog Mater Sci 2014;59:1–160. doi:10.1016/j.pmatsci.2013.06.001. [2] Bai YL. Adiabatic shear banding. Res Mech 1990;31:133–203. [3] Bai YL. Thermo-Plastic instability in simple shear. J Mech Phys Solids 1982;30:195– 207. doi:10.1016/0022-5096(82)90029-1. [4] Bai YL, Dodd B. Adiabatic shear localization: occurrence, theories, and applications. Oxford: Oxford; 1992. [5] Chen WW, Song B. Split Hopkinson (Kolsky) bar: design, testing and applications. Springer Science & Business Media; 2010. [6] Chichili DR, Ramesh KT, Hemker KJ. Adiabatic shear localization in alphatitanium: experiments, modeling and microstructural evolution. J Mech Phys Solids 2004;52:1889–909. doi:10.1016/j.jmps.2004.02.013. [7] Clifton RJ, Duffy J, Hartley KA, Shawki TG. On critical conditions for shear band formation at high strain rates. Scripta Metallurg 1984;18:443–8. doi:10.1016/0036-9748(84)90418-6. [8] Costin, L.S., Crisman, E.E., Hawley, R.H., Duffy, J., 1979. On the localisation of plastic flow in mild steel tubes under dynamic torsional loading. [9] Culver, R.S., 1973. Thermal instability strain in dynamic plastic deformation 519– 530. [10] Dorogoy A, Rittel D, Godinger A. Modification of the shear-compression specimen for large strain testing. Exp Mech 2015;55:1627–39. doi:10.1007/s11340-015-0057-6.

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