Dynamic Response of TI2ALC Under Radial Confinement at High Temperature

Experiments were performed to evaluate the dynamic mechanical response of MAX phase material Ti2AlC at high temperature (HT) and under radial confinement. A Split Hopkinson Pressure Bar (SHPB) apparatus was employed to conduct experiments at a strain rate of 500 s−1. High speed photography was used to capture the dynamic response of unconfined specimens. An induction coil was used to heat the specimens from 25 to 1000 °C. Nickel–cobalt–ferrous alloy (Kovar) shrink fit sleeves were utilized to produce a mechanical radial pressure of 30–195 MPa. Unconfined room temperature (RT) and HT experiments revealed that Ti2AlC fails in a gradual, brittle manner (also referred to as graceful failure) with a low dependency on temperature up to 800 °C. All experiments conducted with radial confinement produced a fully plastic response without failure. The addition of hydrostatic confinement increased the maximum compressive stress for all temperatures and allowed specimens to reach strains in excess of 8% without failing. Optical and Scanning Election Microscopy (SEM) images were taken of the cross-section of recovered confined specimens. Imaging revealed conical damage patterns on each end of the specimen which facilitate the plastic response.

MAX phases are layered ternary carbides and nitrides with hexagonal structure in the form M n+1 AX n , where n varies from 1 to 3, "M" is an early transition metal, "A" is and A-group elements and "X" is C and/or N [1][2][3][4]. Most MAX phases have a unique combination of material attributes akin to both ceramics and metals. A few of their favorable properties likening them to ceramics are high elastic stiffness and service temperature along with low thermal expansion and low density [5][6][7]. They possess advantageous qualities associated with metals by being good electrical and thermal conductors as well as being relatively soft, easily machinable and damage tolerant [5,[7][8][9].
MAX phases are identified as kinking nonlinear elastic solids and are able to dissipate large amounts of energy by the formation of kink bands (KBs) when compressed due to their layered strong MX bonds and relatively weak MA bonds [1,10]. At room temperature (RT) MAX phases normally fail in a brittle fashion however, they can reach a brittle to plastic transition (BPT) in HT [11,12] and/or under sufficient hydrostatic confining pressure [10,13].

Inspiration
Ti 2 AlC is one particular phase that possesses all the aforementioned favorable characteristics. It has been a popular material to study because of its superior high temperature performance and low cost when compared to other MAX phases [2,3].
With these extraordinary properties, Ti 2 AlC has great potential for use in extreme thermal and mechanical loading environments such as hypersonic jets, structural applications, and protective armor. In order to use MAX phases to potentially develop safer and higher preforming, aircraft, structures and protection, their dynamic mechanical response must be better understood at high temperature and under confinement. The purpose of this study is to characterize the dynamic compressive response of Ti 2 AlC when it is subject to high temperature loadings and under radial confinement.

Review of Literature
In the past 20 years interest in MAX phases has grown rapidly with Ti 2 AlC getting considerable attention [1]. Many experiments have been performed on Ti 2 AlC in various loading configurations and temperatures in these recent studies. Barsoum et al. measured the thermal and electrical properties, including thermal expansion, heat capacity and thermal conductivity, of Ti 2 AlC in the temperature range of 25 to 1000°C [7]. A study by Radovic et al. has characterized the mechanical properties of polycrystalline Ti 2 AlC from 300 to 1573 K using resonant ultrasound spectroscopy [6]. Also, the response of fully dense and 10 vol.% porous polycrystalline Ti 2 AlC in uniaxial compressing at RT was analyzed by Zhou et al. and Poon et al. [9,14]. Furthermore, Ti 2 AlC's compressive performance at high temperatures, up to 900°C, was evaluated by Bai et al. [5]. At temperatures of 1150 and 1300°C, Barsoum et al. showed that Ti 2 AlC's compressive response is completely plastic [8]. These studies only characterize the properties and quasi-static compressive response of Ti 2 AlC.  [15]. The strain rates varied from 500 to 4700 s -1 and a range of specimen L-D ratios from 0.2 to 0.8 were used. Abtula conducted high temperature dynamic experiments also using a SHPB [12]. These tests were completed at strain rates of 1500-4200 s -1 and temperatures ranging from RT to 1050°C. In addition, a study done by Naik Parrikar et al. evaluated the dynamic and quasi-static compressive constitutive behavior and fracture initiation toughness of fine grained Ti 2 AlC [11]. The experiments were conducted using a modified SHPB apparatus with DIC and servohydraulic testing machine. The temperatures ranged from 25 to 1200°C while the strain rates coved 10 -4 to 500 s -1 . Although many studies have been carried out on Ti 2 AlC none have been completed with confinement.
In fact, only Guitton  with both high temperature and confinement. Therefore, this study seeks to explore the dynamic high temperature confined response of MAX phases, specifically Ti 2 AlC.

Basic Theory
The Split Hopkinson Pressure Bar (SHPB) is a testing apparatus that is used to measure the dynamic mechanical properties of materials. It operates at strain rates from 10 2 to 10 4 s -1 , which includes loading rates seen in car collisions and ballistic impacts [20]. The test consists of three bars, a striker, incident, and transmission bar, all of which are in the same axis. The specimen is placed between the incident and transmission bars. The striker bar impacts one end of the incident bar developing a one dimensional elastic strain wave. The compressive longitudinal wave propagates though the incident bar until it reaches the specimen. Upon which, some of the strain is transmitted through the specimen into the transmission bar while a portion is reflected back, creating a tensile strain wave in the incident bar. The strain in the bars is measured by strain gauges attached to the pressure bars, thus the specimen response can be captured using time resolved strain measurements. When equilibrium within the specimen is achieved, that is when Equation (1) is true, the stress, strain, and strain rate of the specimen are given by Equations (2), (3), and (4), respectively: Where εi, εr, and εt are the incident, reflecting and transmitted strains measured by the strain gauges, σs is the stress in the specimen, Eb and Ab are the bar modulus and area, As is the specimen area, s, and ṡ are specimen strain and strain rate, Ls is the length of the specimen, and Cb, is the longitudinal wave speed given by / , where ρb is the bar density.

Specimen Geometry
The specimen length was chosen in order to measure an adequate reflected pulse amplitude for the desired strain rate. By rearranging Equation (4) the specimen length was calculated to be 8 mm using 500 s -1 for a strain rate and 400 με for the desired reflected strain. To ensure that the specimen would have enough time to reach equilibrium, the equilibrium time, te, in Equation (5), must be achieved before the critical strain, tc in Equation (6), is reached.
Where n is the number of times the pulse is reflected within the specimen before equilibrium is achieved, Ls and Cs are the length and wave speed of the specimen, and εc is the critical strain of the specimen. It takes approximately four transits back and forth within a ceramic specimen before equilibrium is reached [21,22]. Given the high stiffness and low density of Ti 2 AlC it's wave speed of 8120 m/s is similar to ceramics.
Assuming it requires 4 transits to reach equilibrium te is just under 4 μs. Ti 2 AlC is brittle and was expected to fail close to 1% strain, thus making tc ~20 μs, suggesting that equilibrium will be easily attainable.
Traditionally, L/D ratios are kept near 3 /4, where νs is the Poisson's ratio of the specimen, to eliminated inertial effects [20,23]. However, this would require a specimen diameter larger than the pressure bars themselves. It has been suggested that a ratio of 2:1 be used, similar to uniaxial compression testing for brittle materials, for high strain rate testing of high stiffness low failure strain specimens [22]. Because the specimen is stiff, small misalignment of the pressure bars can create stress concentrations that will lead to premature failure, which a shorter specimen would be more prone to. In addition, inertial effects are more significant for softer materials because the extra axial stress is on the order of 1 MPa for the strain rates develop by the SHPB [23]. Since inertia induced axial stress is a function of specimen material properties, radius, and strain acceleration, the stress can be further reduce by specimen geometry and loading conditions [23]. For these reasons, a diameter of 4.6 mm was chosen to achieve L/D ratio as close to 2:1 as practically possible for fabrication purposes. Acceleration can be minimized by having a constant strain rate, the method for achieving this will be discussed in the next section.

Loading Conditions
When testing stiff brittle materials on a SHPB many modifications must be made to accurately measure the material's response [24]. Brittle materials are more sensitive to stress dispersion caused by accelerations which can lead to premature failure. Since the material is stiffer than the pressure bars and expected to fail at high stress when confined, special treatment of the bar contact faces is required. In addition, since the specimens will crack and fragment, the samples must only be loaded once for valid postmortem observations to be taken.
A constant strain rate loading minimizes stress dispersion and the time for the specimen to reach equilibrium. This condition can be created by using pulse shapers to modify the incident pulse. A pulse shaper is a small disk of plastically yielding material placed on the striker side of the incident bar to shape the stress wave profile.
Because brittle materials are usually linearly elastic until failure a linear ramp profile is desirable, especially near failure point of the specimen. In this work copper pulse shapers were used and designed using the method outlined in reference [23].
Because the specimen is stiffer than the pressure bars the bar faces without alteration will indent during loading. This will cause stress concentrations in the specimen corners leading to premature failure. For this reason, tungsten carbide (CW) inserts were placed on each side of the specimen to keep the loading surface flat. The inserts were sized to match the impedance of the bars so that no pulse disturbance would occur. Inserts also protect the pressure bars from permeant deformation which could be caused by the high confinement specimens.
In order to make usable postmortem evaluations of the fragmented and/or damaged specimens it is important to only load the sample once. This was done using a moment trap which consisted of a screw on flange on impact end of the incident bar and a steel block acting as a rigid mass. A gap between the flange and the rigid mass was calculated using the incident pulse strain history in equation (7): Just after the incident pulse is transferred through the bar the flange contacts the rigid mass preventing the reflections within the incident bar from reloading the specimen.

Confinement Sleeve Design
A metal shrink fit sleeve was chosen to apply the desired radial confining pressure on the testing samples. The goal of the confining pressure is to produce a brittle to plastic transition of the MAX phase's dynamic compressive response. The pressure values were chosen based on other work where brittle materials reached or did not reach a ductile response [17,18]. The confining pressure was approximated by solving an axisymmetric boundary value problem given by Equations (8) and (9) [16][17][18]. This equation assumes the specimen is an elastic solid cylinder, the sleeve is an elastic perfectly plastic hollow cylinder containing a plastic boundary. The equation also includes a misfit between the outer diameter of the specimen and the inner dimeter of the sleeve shown in Figure 1.
Where δ is the interference between the specimen outer diameter and the sleeve inner diameter, E1, ν1, and r1 are the specimen's elastic modulus, Poisson's ratio, and outer diameter, , E2, ν2, and r2 are the sleeve's yield stress, elastic modulus, Poisson's ratio, and outer diameter, R is the plastic boundary within the sleeve and P is the confining pressure exerted on the specimen by the sleeve. All values in Equation (8) are known except for the plastic boundary, R which can be solved. By inserting the found R value into Equation (9) Specimen (E 1 ν 1 r 1 ) Sleeve (E 2 ν 2 r 2 R ) Figure 1: Schematic of axisymmetric boundary value problem contribution [16][17][18]. This not only takes extra materials and testing, but produces only an approximate sleeve contribution because the singular sleeve is in a different stress state than the assembled sleeve. When an unchamfered sleeve is loaded axially it expands due to poisons ratio thus relaxing the radial pressure. At a certain strain the confining pressure will be equal to zero as shown in Equation (10) [25]: With the selected materials the confining pressure would be zero at ~2% strain which is at or before the maximum stress of the confined specimens. To prevent the sleeve from relaxing a second chamfered sleeve has been used before [18]. Although, again the stress cannot be directly taken from the experimental results and the sleeve still experiences some relaxation.
Abaqus 6.14 was used to verify confinement pressure on the specimen. The MAX phase was modeled as elastic while the sleeve was modeled as elastic perfectly plastic.
Modeling showed that the confining pressure exerted by the sleeve reduces near the ends of the specimen as shown in Figure 2a, 2c, and 2e. However, when the assembly is compressed the oblique sleeve-bar contact creates high radial pressure on the end faces, shown in Figure 2b, 2d, and 2f. This local elevated confinement pressure reduces damage due to stress concentrations at the specimen corners while allowing the majority of the specimen to sustain full confinement pressure.

High Temperature
One concern high temperature poses is the thermal expansion of the sleeve, which reduces the interference mismatch resulting in loss of confining pressure.  [27]. Because the temperature of the assembly would be measured from a thermocouple attached to the outer surface of the sleeve the temperature of the specimen could not be directly measured. To ensure that both the specimen and the sleeve were being heated evenly by induction heating, after assembly the temperature at the center of the specimen face and at the outer surface of the sleeve were measured revealing no more than a 20°C difference for all the HT testing temperatures.
Another material property concern comes from the high heat required to assemble the confined specimens. During the assembly the shrink fit sleeve was exposed to ~1100°C to allow for the Ti 2 AlC specimen to be inserted. Tensile tests were performed on the sleeve material to verify that the properties after heating were accurate for calculating confining pressure. The tests showed little to no degradation in modulus and yield strength.
An additional consideration has to do with the SHPB apparatus. When the thermal loading is applied to the specimen, heat also transfers to the pressure bars though conduction and radiation. A substantial rise in temperature of the bars will alter the properties, thus changing the wave speed and ultimately the experimental results.
To prevent heating of the bars, water circulating copper coils were wrapped around the incident and transmission bars at the CW interface. The CW inserts also act as a thermal cushion preventing a sharp thermal gradient in the bars and increasing the length of the conduction path to the bars.

Material and Specimens
Commercially available Ti 2 AlC (Maxthal 211, Kanthal®, Sweden) was used for all experiments. The average particle size was 10μm with 80% of the grains falling and sleeve inner diameters were taken using a digital micrometer and small hole gage to ensure proper interference. Using an inducting coil, the sleeves were heated to approximately 1100°C so that the Ti 2 AlC specimens could be inserted. Once the assembly cooled the end faces were ground and chamfered. The sleeved specimens are shown in Figure 3.

Experiments
All experiments were performed using a SHPB apparatus at a strain rate of approximately  [26]. Note that the interface mismatch, δ changes with temperature due to thermal expansion.  Figure 3: Ti 2 AlC specimens, from left to right: unconfined, low confinement, medium confinement, and high confinement.  [26]. †Calculated from compression test. ‡Extrapolated from manufacturer data.

Setup
The SHPB setup, shown in Figure

Postmortem Evaluation
The remains of each of the unconfined experiments were observed using a Nikon SMZ-U stereoscopic microscope. The fracture surfaces were also observed using a Zeiss SIGMA VP Field Emission-Scanning Electron Microscope (FE-SEM). Because TI 2 AlC is conducive the specimens did not required any preparation.
A select few of the confined experiments were also observed using the FE-SEM.
The assemblies were sections using a Buehler IsoMetTM 1000 Precision Sectioning Saw with a diamond blade. The sections were then mounted in an epoxy resin and

Unconfined Experiments
Typical incident, transmitted, and reflected pulses recorded by the oscilloscope are shown in Figure 5. The incident pulses developed had a nearly linear incline and a magnitude greater than the peak of the transmitted pulse while the reflected pulses achieved high magnitudes before the specimen reached its maximum stress. Wedge shaped transmitted pulses were developed through the unconfined specimens.
For the RT unconfined experiments, a high speed camera was used to capture the deformation process. The high speed camera images and the true stress-strain response of unconfined Ti 2 AlC at 25°C experiment are shown in Figure 6. As seen in the Figure   6a-d, macroscopic cracks are not apparent on the surface until well after the maximum stress has been reached. Depicted in Figure 6e, the specimen has one major fracture plane splitting it into two sections. This failure behavior was not uncommon for the RT specimens. Figure 6f displays typical RT dynamic compressive behavior of Ti 2 AlC. The rising portion of the stress-strain curves for all the RT plots is nearly linear with the declining portion displaying the characteristic gradual nature, sometimes referred to as graceful, failure of Ti2AlC [1,7]. In this experiment, force equilibrium was maintained until just after 5% strain. In general, force equilibrium was maintained throughout nearly the whole experiment. In Figure 7 a typical force equilibrium plot is shown. Note that there are small deviations in equilibrium, initially, when the camera and flash are triggered by the incident pulse, and when the specimen response relaxes resulting in a slope change.
For the HT unconfined experiments temperatures of 500, 800, and 1000°C were applied to the specimens. The constitutive behavior seen for the HT unconfined specimens is shown in Figure 8. All samples form wedge shaped plots with the rising portion being steeper than the unloading portion. The initial slopes appear to be the  Postmortem images were taken of the specimens using an optical and scanning electron microscope (SEM). Shown in Figure 9 are the optical images of the unconfined specimens. All specimens tested at 25 to 800°C exhibited fragmentation into two to four major pieces.   The extent of delamination observed also increased with temperature as depicted in the insert of Figure 10c which shows a highly angled and delaminated kinking band.

Confined Experiments
A low, medium, and high confinement sleeve designs were used to create confining pressures of 75, 135, and 195 MPa, respectively at RT by varying the wall thickness of the sleeves. The loading pulses for the confined experiments were very similar to those shown in Figure 5 only the incident pulse amplitudes were greater. Figure 11 shows the RT compressive stress-strain response of the confined specimens at a strain rate of 500 s -1 . The unconfined RT plot is included for reference and plots are shifted along the x-axis to make their features more observable. All the confinement sleeves yielded a brittle to plastic transition. It is clearly seen that after the maximum stress, the confined specimens maintain strength and plastically deform until the load is relieved. These tests stopped arbitrarily at the end of loading pulse and the specimens did not fail even after some reached strains greater than 9%. The Figure 11: True compressive stress-strain response of confined Ti 2 AlC at RT and a strain rate of 500 s -1 . No damage was visible on the impact faces of the recovered specimens. Four specimens were sectioned, ground and polished for microscope imaging. The 500°C-75 MPa sectioned specimen is shown in Figure 13. All sectioned specimens reveal symmetrical damage patterns within the specimen similar to the findings of Chen et al. [17,18]. Conical features on each end of the specimen formed an hourglass shape. Within the hourglass cones the surface appears smooth with very few pores while outside the surface is very rough with many cavities. The conical boundaries between the two regions consist of bands of cracks and highly damage grain structure.
Major crack separation was also seen along the interface in some specimens.
Observation of the highest RT confinement and highest temperature tests shows little to no gaps along the cone boundary. The cracks along the damage band are believed to initially propagate due to high stress concentration at the specimen's corners [17].
Notice that some cracks do not originate at the extreme corners of the specimen but instead well inside of the sleeve. SEM images were also taken of the confined sections. In initial images grain boundaries were hard to make out and no cracks or cavities were apparent in the structure except for those already visible optically. To make the boundaries clearer the specimens were etched. Etching removed TiAl x intermetallic from between the grains structures leaving some absences. SEM images for the RT-75 MPa specimen are shown in Figure 14. In Figure 14a the location of the SEM images are marked on an optical microscope image. The insert shows the entire sectioned specimen for reference. Figure 14b shows the damage band within the loop discernible by many cavities and cracks extending towards the center of the specimen. Also observable within the damage band is grain gliding on long grains parallel with the band. The damage bands do not maintain a constant width or reach the center of the specimen.
All portions within the specimen exhibit intragranular cracking. Figure 14c

Discussion of Experiments
MAX phase Ti 2 AlC specimens under unconfined conditions soften as the temperature is increased inhibiting brittle crack propagation. Thus, weakening the material and increasing the formation of KBs and delamination. Since the development of KBs and delaminations requires high strain and is energy intensive, the apparent higher frequency of KBs and delaminations at HTs is likely responsible for the increasingly gradual failure observed.
In the confined experiments, the radial pressure applied by the confinement sleeves increased the stress required for cracks to propagate within the specimen thereby increasing the strength of the specimen. Likewise, the restriction of crack propagation induced a plastic response in the regularly brittle MAX phase. From observation of the specimens, it is apparent that the two cones making up the hourglass profile move inward when compressed. This motion is accommodated by the deformation and gliding of grains along the conical interface in addition to cracking and radial expansion of the material outside of the hourglass against the sleeve. Based on the work of Chen W. et al. [17,18], the cracks along the cone boundary begin to propagate and accumulate damage primarily after the maximum stress is reached. According to Bei et al. [10], the localized damage in the bands is the reason for the plastic response. As observed in the SEM micrographs, at low temperatures the main damage mechanisms are cracking and kinking. Specimens with lower confining pressures and temperature subjected to higher strains showed major crack separation along the conical boundaries. At elevated temperatures, fewer cracks were present and delamination was prominent. The radial confinement prevents the specimen from separating and creates additional friction along the crack surfaces. This friction impedes the growth of sliding cracks thus producing a fully plastic response.
The average maximum stress achieved for each test condition is plotted in Figure   16. As displayed by the unconfined experiments, an increase in temperature causes slight decrease of roughly 12% in strength through 800°C. After which, at 1000°C the maximum failure stress declines significantly by about 25%. These results agree with increased deterioration of Ti 2 AlC which has been observed at over 800-900°C [5,11,12]. All the unconfined specimens failed in a brittle fashion with a progressively gradual post maximum stress response with increasing temperature.
Remarkably, the response of all confined tests was plastic allowing the material to reach strains in excess of 9% without failure. As expected, the addition of a confinement sleeve boosted the maximum stress with increase of confining pressure.
For the confined RT experiments the improvement in load bearing of the specimen seems to escalate with higher confinement. The maximum stress increased by 20% with just over 10% of the unconfined failure stress applied as confinement pressure.