Uniaxial and biaxial compressive response of a bulk metallic glass composite over a range of strain rates and temperatures

Abstract

The uniaxial and biaxial compressive responses of Zr57Nb5Al10Cu15.4Ni12.6–W composite were investigated over a range of strain rates (∼10−3 to 103 s−1) using an Instron universal testing machine (∼10−3 to 10° s−1), drop-weight tower (∼200 s−1), and split Hopkinson pressure bar (103 s−1). The temperature dependence of the mechanical behavior was investigated at temperatures ranging from room temperature to 600 °C using the instrumented drop-weight testing apparatus, mounted with an inductive heating device. The deformed and fractured specimens were examined using optical and scanning electron microscopy. Stopped experiments were used to investigate deformation and failure mechanisms at specified strain intervals in both the drop weight and split Hopkinson bar tests. These stopped specimens were also subsequently examined using optical and scanning electron microscopy to observe shear band and crack formation and development after increasingly more strain. The overall results showed an increase in yield strength with strain rate and a decrease in failure strength, plasticity, and hardening with strain rate. Comparison of uniaxial and biaxial loading showed strong susceptibility to shear failure since the additional 10% shear stress caused failure at much lower strains in all cases. Results also showed a decrease in flow stress and plasticity with increased temperature. Also notable was the anomalous behavior at 450 °C, which lies between the Tg and Tx and is in a temperature regime where homogeneous flow, as opposed to heterogeneous deformation by shear banding, is the dominant mechanism in the bulk metallic glass.

I. Introduction

Strain-rate sensitivity in bulk metallic glasses (BMGs) has been the subject of several studies. Vitreloy-1 BMG (Zr41.25Ti13.75Cu12.5Ni10Be22.5) has been found to be relatively insensitive to strain rate,1, 2, 3 whereas other BMGs exhibit positive strain-rate sensitivity.4, 5 However, most studies on this topic have drawn the conclusion that BMGs exhibit negative strain-rate sensitivity, with the fracture stress decreasing as strain rate increases.6, 7, 8, 9, 10, 11, 12, 13 The mechanistic explanation given by Gu et al.8 for the negative strain-rate sensitivity of these materials is that adiabatic processes occur during failure of BMGs and higher strain rates favor adiabatic processes, thus leading to a lower failure strength at higher loading rates when adiabatic processes are more prevalent. Another explanation has been provided by Li et al.7 suggesting that shear bands in a BMG initiate well below the yield stress and grow upon continued quasi-static loading. Under dynamic loading conditions, cracks initiate immediately upon shear band initiation due to the excess energy that is available; these cracks lead to fracture of the specimen, and thus a lower fracture stress. This explanation for the negative strain-rate sensitivity of BMGs was further supported by work done by Mukai et al.,11 in which they observed that although the quasi-statically tested specimens were failing at an “apparent” yield stress of ∼1.7 GPa, they began to show serrations indicative of shear band formation, which is the mechanism for accommodation of deformation in BMGs. As strain rate was increased, the specimens could no longer accommodate the deformation quickly enough, and the failure strength approached ∼1.4 GPa, which is the stress level when shear band initiation began.

The strain-rate sensitivity of BMG-matrix composites has also been investigated in a few studies.6, 10, 14 In a study by Jiao et al.,14 Zr57Nb5Al10Cu15.4Ni12.6 reinforced with 60 vol% tungsten (W) particles showed strain-rate hardening behavior with a strain-rate hardening exponent of m = 0.016, which is close to a rule of mixtures approximation using the strain-rate sensitivity of the two respective phases.14 As expected, the rate-dependence in this composite is more characteristic of the body-centered-cubic (bcc) tungsten phase, which dominates because of the large volume fraction of tungsten as well as the restraint of the failure mode of the amorphous matrix. Mechanistically, it was found that shear bands develop in the amorphous matrix, and the W particles provide obstacles to shear band propagation, which leads to formation of multiple shear bands and allows for development of large plastic strains. Similarly, Li et al.6 studied W preform-reinforced BMGs and found positive strain-rate sensitivity for W and all composites, but negative strain-rate sensitivity for the monolithic BMGs.

Several studies have investigated the temperature dependence of the deformation and mechanical properties of BMGs,2, 15, 16, 17, 18 although the effects of temperature on BMG-matrix composites have not been investigated. In general, as the temperature is raised past the glass transition of the BMG, a change in the stress–strain response from brittle to ductile behavior can be observed as the deformation mechanism changes from inhomogeneous (failure along a single shear plane) to homogeneous (uniform macroscopic deformation, no macroscopic shear). Falk and Langer19 have used molecular dynamics simulations to propose the theory describing the deformation behavior considering viscoelastic response at low applied stresses, dynamically transitioning to viscoplastic response above the yield stress, and continuing with strain hardening and plastic ratcheting on the basis of the “shear transformation zones” participating in the deformation process.

This study aimed to investigate the strain-rate sensitivity of the BMG composite containing 70% W particles in the LM106 metallic glass matrix. In addition to probing the effects of strain rate, different stress states were also investigated over the range of strain rates by using a cylindrical specimen for uniaxial loading and a 6° inclined cylindrical specimen for biaxial loading. Additionally, the temperature dependence of the composite material was investigated for both stress states.

II. Experimental Details

The mechanical behavior of Zr57Nb5Al10Cu15.4Ni12.6 (LM106) BMG and its composite with tungsten was investigated over a wide range of strain rates and loading conditions. The experimental procedures and details for the mechanical testing performed on the composite material in the low to intermediate strain-rate regimes (10−3 to 103 s−1) are described below.

A. Materials and specimen preparation

The material under investigation was a BMG-matrix composite consisting of an LM106 matrix with 70 vol% crystalline tungsten reinforcement particles (∼5 μm nominal size). The samples were fabricated by Liquidmetal Technologies, Inc. (Rancho Santa Margarita, CA) using a pressure infiltration technique (described in detail by Li et al.6) and were provided by the Army Research Laboratory. All experiments were performed on specimens prepared in the same batch. The composite rods had a density of 15.58 ± 0.09 g/cm3, which was determined using the Archimedes method. A micrograph of the microstructure of this composite is shown in Fig. 1. It should be noted that the W particles form a contiguous phase, allowing for significant reinforcement of the BMG as well as providing an effective and prevalent obstacle to shear band propagation.

The stress and strain distributions in materials are often inhomogeneous during high-strain-rate scenarios, leading to localized regions of increased shear deformation.20 Furthermore, adiabatic shear failure often occurs in high-strength materials during uniaxial compression tests. Pure shear or pure compression states are rare; therefore, it is important to study material response under not only uniaxial, but also biaxial loading to understand the susceptibility of a material to adiabatic shear failure. Behavior of LM106-W specimens under biaxial loading is of particular interest due to the tendency of BMGs to deform by adiabatic shear banding.15, 21, 22

FIG. 1.
figure1

Scanning electron micrograph showing the microstructure of the BMG–W composite in its as-received form. The light gray phase is the crystalline W particles and the dark gray phase is the amorphous BMG.

LM106-70W specimens for compression and compression-shear experiments conducted under low and intermediate strain-rate conditions were 6 mm in height and 6 mm in diameter. Compression-shear specimens were oriented with an inclination of 6° off the loading axis, as shown in the schematic in Fig. 2, which illustrates the uniaxial and biaxial specimen configurations. All specimens were precision machined using electrical discharge machining to insure proper dimensions and tilt. Specimen ends (uniaxial specimens only) were prepared by turning against a coarse pad to create shallow circular grooves, which reduced friction effects. Specimens were then cleaned in an ultrasonic bath with acetone. Two foil strain gauges were applied to each uniaxial compression specimen (for testing at all strain rates), exactly opposite each other (9.4 mm apart around circumference of sample).

FIG. 2.
figure2

Schematic showing the uniaxial and biaxial (6° off-axis) specimen configurations. The biaxial specimens resulted in 10.4% additional shear loading.

As shown by Meyer and Krueger,20 the 6° inclination results in additional shear loading of ∼10.4% of the axial compression load:

$${\tau \over \sigma } = {{{F \over {{A_0}}}\cos \theta \cos \phi } \over {{F \over {{A_0}}}}} = \cos \left( {6^\circ } \right)\cos \left( {84^\circ } \right) = 10.4\% $$

The inclined specimen provides a dynamic biaxial stress state, allowing the material to respond with its specific sensitivity to adiabatic shear failure. An example of the effect of the degree of inclination of the stress–strain responses of Ti–6Al–4V can be seen in Ref. 20.

B. Quasi-static compression and compression-shear testing (∼10−3 to 10° s−1)

Quasi-static mechanical testing for evaluation of the properties of the composite both under uniaxial compression and biaxial compression-shear was performed using an Instron (Norwood, MA) 8503 servo-hydraulic universal testing machine with a 250 kN load capacity. This technique was used for testing at strain rates of 10−3, 5 × 10−2, and 1 s−1, which corresponded to loading rates of 0.006, 0.3, and 6 mm/s, respectively. The specimen was centered between two hardened steel platens, which were lubricated with MoS2 to reduce friction. An inductive (electronic proximity) sensor was placed on either side of the platens to detect cross-head motion and displacement by sensing of the current flowing through an inductive loop. The strain gauges were set up in a half Wheatstone bridge configuration, in which the total resistance was measured over a bridge consisting of four resistors, two of which (the strain gauges) had unknown values. The recorded data included the time, load, cross-head displacement (set s.t. 1 V = 1 mm) measured with the average of the two inductive sensors, and the voltage measured from the average of the two strain gauges. Two of each of the inductive sensors and strain gauges were used to compensate for any bending so that if bending did occur the two complimentary measuring devices would have opposite signals that would average out.

Data analysis was performed using FAMOS software (IMC Systems, Buckinghamshire, UK) to convert load to stress and displacement to strain. The strain gauge signal was converted to strain according to

$${\varepsilon _{SG}} = {{B{U_b}} \over {{U_i}{K_{amp}}{K_{SG}}}} \cdot 100\% $$

where B is the type of the Wheatstone bridge (in this case, B = 2 for half bridge), Ub is the measured voltage signal, Ui is the voltage running through the circuit immediately before the start of the test, Kamp is the amplification (100×), and KSG (=1.98) is the proportionality factor between the relative change of the resistance. The strain gauges typically measured up to ∼5% strain, and these data were used for determination of elastic modulus. After the strain gauge expired, the data from the inductive sensors were used, after correcting it for the compliance of the testing machine. Strain gauges were not used for the compression-shear specimens, because it has been observed in previous work23 that the elastic portion of the curves from the uniaxial and biaxial specimens is identical, so it was unnecessary. The data from these experiments were likewise corrected for compliance.

C. Drop weight compression and compression-shear testing (∼200 s–1)

A drop-weight tower consists of a 600-kg weight that drops on a specimen, which is resting on an anvil.20 Below the weight, a small hammer head is affixed to ensure precise loading conditions. An advantage of this experimental configuration is that large amounts of stored energy can be applied so that strain-rate history of the specimen material is not influenced by its strain hardening. For this study, drop weight tests were performed at a strain rate of 200 s−1, which required a drop height of ∼80 mm, according to and , so that where V is impact velocity, g is the gravitational constant, h is fall height, is strain rate, and h0 is sample height. Strain gauges were affixed on the hammer head to record load-time history. Displacement was measured with a light gate system in which each gate passed generated a peak in the signal, and the distance between peaks was proportional to a known displacement. The optical gate system also served as the trigger for the Tektronix (Richardson, TX) TDS744A Oscilloscope, which recorded the data. Strain rate was calculated from the recorded measurements. Data analysis was performed using FAMOS software. This setup also allowed for specimen recovery during any stage of deformation because it is equipped with high-speed brakes and special stopping devices. After analysis of the initial data, stopped tests were performed approximately at yield, failure, and at stages in between for both the uniaxial and biaxial specimens. The dropped weight was stopped, thus preventing further specimen deformation using precision‐thickness, hardened steel blocks.

Investigations of the compressive mechanical behavior of both uniaxial and biaxial specimens were also explored as a function of test temperature using the drop weight testing facility at a strain rate of 200 s−1. These tests were performed using the same procedure as those at room temperature (RT), but the specimens had a thermocouple point-welded onto their surface to measure specimen temperature. The specimens were heated with inductive heating coils, which were positioned around the area where the sample was set up and where impact took place. Experiments were performed at test temperatures of 200, 380, 450, 550, and 600 °C. These temperatures were measured by the thermocouple welded to the specimen so they reflected actual specimen temperatures, not set temperatures inductive heater or environment temperatures. These test temperatures allowed for investigation of the changes in compressive mechanical behavior over a range of temperatures, below the glass transition temperature (Tg ≈ 405–414 °C24, 25), in the undercooled region between Tg and the crystallization temperature (Tx ≈ 478–480 °C24, 25), and above Tx of LM106. Therefore, the effects of these thermodynamic transitions on the mechanical behavior of the composite could be evaluated. The heating rate was ∼3 °C/s, which is faster than the time scale of the crystallization kinetics in LM106, and precludes crystallization in the undercooled region.

D. Split Hopkinson pressure bar (SHPB) experiments (∼1400–1800 s−1)

The Hopkinson (Kolsky) Bar, commonly used for probing material behavior in the intermediate to high strain-rate regimes,26, 27 employs a striker bar to impact the incident bar, which produces a pulse in the incident bar that has a large length with respect to the specimen size. A small piece of lead (3 mm diameter, <1 mm thick) was placed on the end of the incident bar with grease to provide damping in the signal. After traveling through the incident bar, the elastic wave reaches the specimen, which was lubricated with MoS2 on its ends and held between the incident and transmitted bars. Removable hardened steel platens were used on the ends of the incident and transmitted bars (on either side of the sample) to prevent damage of the bars. These platens were replaced between each experiment. The plastic wave was imparted to the specimen due to the amplitude of the wave. Strain gauges on the incident and transmitted bars allowed for measurement of a direct incident pulse, a reflected pulse, and a transmitted pulse that were recorded using an LDS (Middleton, WI) Nicolet Digital Oscilloscope Workstation, which was triggered by the force increase in the input bar. From these three pulses, specimen stress, strain rate, and strain were derived as follows28:

where E0,A0, and C0 are the elastic modulus, cross-sectional area, and elastic wave speed of the bars, respectively, L is the length of the specimen, and εT and εR are the strains in the transmitted and reflected bars, respectively.

The deformation and failure during impact were imaged using a Redlake (Cheshire, CT) MotionXtra high-speed camera to record 250 images at a rate of 30,000 frames/s (33 μs interframe time) using two Dedocool (Munich, Germany) lights to enhance the imaging. The camera was triggered by the oscilloscope.

For the uniaxial specimens, a pair of foil strain gauges was mounted on opposite sides of the specimen to obtain accurate stiffness and correct for the compliance of the testing apparatus. The signal from the strain gauge was used to calculate strain according to the same procedure described for the quasi-static tests. Data analysis was performed using FAMOS software.

After analysis of the initial data, stopped tests were performed approximately at yield, failure, and at stages in between for both the uniaxial and biaxial specimens. The incident bar was stopped, thus preventing further specimen deformation using precision-machined hardened steel rings, which were placed around the sample (using glue to attach to the platen) and were machined in 0.1 mm increments to stop tests at nearly any strain increment desired.

Because of the high ductility of LM106-70W and the large strains experienced by the specimens under some testing conditions, engineering stress and strain data (for all strain rates) was converted to true stress and strain.

III. Results and Discussion

A. Stress–strain response as a function of strain rate

Compression tests were performed on both uniaxial and biaxial (6° off-axis) specimen configurations at nominal strain rates of 10−3, 5 × 10−2, 1, 200, and 103 s−1. Figure 3 shows the true stress–strain response of both (a) uniaxial and (b) biaxial specimens. It can be seen that the uniaxial and biaxial flow stresses are generally the same. Uniaxial and biaxial specimens typically show similar flow stresses until the point when more force becomes concentrated on the shear plane, which is exaggerated in the biaxial specimens, and as a result the flow stress of the biaxial geometry is less than that of the uniaxial geometry. At low rates, uniaxial failure occurs at a lower stress and strain than biaxial failure, whereas at intermediate to high rates, uniaxial and biaxial failures occur at similar stress levels, but the biaxial specimens fail after less plasticity. Furthermore, although failure occurred in the specimens, it was not observed in the data collected from the experiments performed at 1 s−1 (true strain rate of 0.79 s−1). This is believed to be a result of being at the upper limit of the sensitivity of the Instron load cell.

FIG. 3.
figure3

True stress–strain response of (a) uniaxial and (b) biaxial LM106-70W over a range of strain rates. These plots reveal that with increasing strain rate there is an increase in yield stress, a decrease in failure stress (except from drop weight to SHPB), a decrease in plasticity, and a decrease in strain hardening, with the data at intermediate and high rates showing some softening behavior. Multiple tests were performed at each strain rate, but data from only one of each are shown for simplicity. All specimens failed, although failure was not evident in the data from the 1 s−1 experiments due to being at the upper limit of sensitivity of the Instron. As such, a strain/plasticity limit could not be determined for this strain rate.

The plots shown in Fig. 3 reveal that with increasing strain rate there is an increase in yield stress, a decrease in failure stress (except from drop weight to SHPB), a decrease in plasticity, and a decrease in strain hardening, with the data at intermediate and high rates showing some softening behavior. Figure 4, which shows log σ as a function of log dε/dt with stresses measured at 5% strain in each case, shows the strain-rate sensitivity of LM106-70W over the range of ∼10−3 to 103 s−1. The uniaxial specimens show a consistently higher stress than the biaxial specimens at each strain rate. Both the uniaxial and biaxial specimens show a slope of 0.015. For materials exhibiting a power law relationship for flow stress, σf ∝ (dε/dt)m, dε/dt is the strain rate and the slope defines the strain-rate sensitivity exponent, m. This is comparable to the value m = 0.016 determined by Jiao et al.14 for a composite of LM106 and 60% W. We would expect the 70% tungsten composite to show higher strain-rate sensitivity due to the larger content of bcc tungsten, but the difference is believed to be within experimental error. Several investigators have observed negative strain-rate sensitivity of the monolithic BMG,6, 7, 12 but no strain-rate sensitivity values have been reported. If the rule of mixtures is used in reverse to solve for the strain-rate sensitivity of the BMG phase, this yields a strain-rate sensitivity, m, of −0.008 to −0.009 for the LM106 BMG.

FIG. 4.
figure4

Strain-rate sensitivity of LM106-70W. Plot shows log σ as a function of log and the stresses plotted are measured at 5% strain in each case. Both the uniaxial and biaxial specimens show a strain-rate sensitivity of 0.015, but the uniaxial specimens show a consistently higher stress than the biaxial specimens at each strain rate.

Figure 5 shows the dependence of 0.2% flow stress and strain, and failure stress and strain, on strain rate. At 7.2 × 10−4 s−1 (quasi-static), the 0.2% yield stress was measured to be 1082 ± 21 MPa, which agrees well with a rule-of-mixtures value of 1065 MPa (0.7*750 MPa + 0.3*1800 MPa29). The stress and strain at yield both increase with strain rate, with the biaxial specimens showing more strain-rate sensitivity. Failure stress and strain both decrease with increasing strain rate [except from drop weight (0.79 s−1) to SHPB (1400/1800 s−1), where an increase in failure stress is seen]. The uniaxial and biaxial specimens show similar strain-rate sensitivity with respect to failure stress, but biaxial specimens show a more rapid decrease in failure strain with increasing strain rate than uniaxial specimens do. Figure 6 shows the 0.2% yield stress and failure stress plotted together as a function of strain rate. Yield stress increases with strain rate and failure stress decreases with strain rate, so the two are approaching one another. At a strain rate of 103 s−1 the two stress values are nearly the same, particularly in the case of the biaxial specimens, which show a more rapid increase in yield stress than the uniaxial specimens.

FIG. 5.
figure5

(a) Plot of 0.2% flow stress and strain as a function of strain rate. The stress and strain at yield both increase with strain rate, with the biaxial specimens showing a higher degree of strain-rate sensitivity. (b) Plot of failure stress and strain as a function of strain rate. Failure stress and strain both decrease with increasing strain rate [except from drop weight (0.79 s−1) to SHPB (1400/1800 s−1), where an increase in failure stress is seen, indicated with a gray circle]. The uniaxial and biaxial specimens show similar strain-rate sensitivity with respect to failure stress, but biaxial specimens show a more rapid decrease in failure strain with increasing strain rate than uniaxial specimens do.

FIG. 6.
figure6

Plot of yield stress and failure stress as a function of strain rate. Yield stress increases with strain rate and failure stress decreases with strain rate, so the two are approaching one another. By a strain rate of 103 s−1 the two stress values are nearly the same, particularly in the case of the biaxial specimens, which show a more rapid increase in yield stress than the uniaxial specimens.

The natural log of true stress as a function of natural log of true strain was used to determine the hardening exponent, n, in the power law σ ∝ εn. The dependence of n on strain rate is shown in Fig. 7. For each rate, n was measured from ln ε values of −4 to −2, which correspond to strains of 1.8% to 13.5%. The trend shows a decrease in hardening with increasing strain rate. Although the ln σ-ln ε relationship is not perfectly linear and the power law fit is not perfect, the overall trend illustrates decreasing hardening with increasing strain rate. This indicates that the ability of LM106-70W (specifically the W particles) to accommodate dislocations decreases as strain rate increases. The 10−3 and 5 × 10−2 s−1 experiments show hardening at all strains, and experiments at rates of ≥1 s−1 show softening after 10% strain. The decrease in hardening with increasing strain rate can be explained by the increased temperature generation at higher rates of deformation, which causes increased softening behavior.

FIG. 7.
figure7

Hardening exponent, n, as a function of true strain rate. In all cases, n was measured from ln ε of −4 to −2, which corresponds to strains of 1.8% to 13.5%. The trend shows a decrease in hardening with increasing strain rate. The decrease in hardening with increasing strain rate can be explained by the increased temperature generation at higher rates of deformation, which causes increased softening behavior.

B. Microstructural analysis

Uniaxial specimens tested at strain rates from 10−3 to 1 s−1 showed vertical cracking around the outside of the specimen and failure in the form of a forging cross, or 45° shear planes that originated at the outer edges of the top and bottom of each specimen and intersected in the center of the specimen’s height, as shown in Fig. 8(a). Examination of the cross sections of these specimens showed extensive shearing, as can be seen in the last image in Fig. 8(a). Biaxial specimens tested in this same strain rate regime showed parallel, diagonally-oriented shear cracks around the specimen peripheries, as illustrated in the photograph in Fig. 8(b). There are also notable differences in the cross sections of the biaxial specimens [last image in Fig. 8(b)]. The biaxial cross sections shown in Fig. 8(b) reveal qualitatively less damage than the unixial in Fig. 8(a), and all visible damage in the biaxial specimen are localized into the maximum shear stress region. Further examination of a cross section of a uniaxially tested specimen (tested at ∼1 s−1) is shown in Fig. 9. The macroscopic cross-sectional views show that the shear has been localized into symmetric regions at ∼45° from the loading axis, and the higher magnification micrographs show extensive shear deformation of the W particles.

FIG. 8.
figure8

(a) Uniaxial and (b) biaxial specimens recovered after compressive testing on the Instron at ∼1 s−1. Uniaxial specimens show forging‐cross features from 45° shear fracture and vertical cracks around the periphery of the specimen resulting from tensile stress. Biaxial specimens show parallel shear cracks originating from the 96° corners of the specimens.

FIG. 9.
figure9

Examination of the microstructure of the cross section of a specimen tested at ∼1 s−1 under uniaxial compression. The macroscopic cross-sectional views show that the shear has been localized into symmetric regions at ∼45° from the loading axis, and the higher magnification micrographs show extensive shear deformation of the W particles.

To learn about the deformation and failure mechanisms, stopped experiments were performed on both uniaxial and biaxial specimens using the drop weight and SHPB techniques. After the experiments, which were stopped at varying strain levels, specimens were sectioned, polished, and examined using microscopy. The results from the stopped experiments performed using the drop-weight tower are shown in Fig. 10, and the results from the stopped experiments performed using the SHPB technique are shown in Fig. 11. Specimens stopped at strains near the onset of failure showed shear bands in the expected locations (based on specimen geometry). The uniaxial specimens each showed two 45° bands connecting opposite corners and the biaxial specimens showed a single band connecting the 96° corners of the specimens. In general, the shear bands were found to be more pronounced at higher strain rates, and the shear bands in the biaxial specimens were more pronounced than those in the uniaxial specimens. Higher magnification views show a shear band width on the order of 100 μm develops at a (nominal) strain rate of 200 s−1 and ∼10–20 μm at a strain rate of ∼1400–1800 s−1, regardless of specimen geometry. At 200 s−1, failure in uniaxial specimens begins with a tensile crack in the top center of the specimen, and the crack propagates mostly through the BMG matrix and around the W particles, as illustrated in Fig. 10. After the onset of failure, the shear bands evolve into cracks, and the tensile crack in the center of the specimen continues to grow. It appears that the simultaneous shear cracking from the corners and tensile cracking through the center (lengthwise) cause failure in the uniaxial specimens, whereas the shear deformation alone is responsible for failure in the biaxial specimens.

FIG. 10.
figure10

Stress–strain curves obtained from drop weight testing. Circles along the curves show strain levels at which the tests were stopped, and the specimen was examined for microstructural evidence of the deformation and failure processes. Micrographs of stopped specimen sections, which revealed shear bands, are shown as well as photographs of failed specimens. The top two micrographs reveal a shear band in the uniaxial specimen just before failure and the beginning of a crack in the center of the specimen. The two micrographs in the middle show shear bands that have evolved into cracks after the onset of failure. The last micrograph shows a shear band in a biaxial specimen just before failure. The white lines indicate the approximate boundaries of the shear bands. The width of shear bands developed during drop weight testing was on the order of ∼50 to 100 μm.

FIG. 11.
figure11

Stress–strain curves obtained from SPHB testing. Circles along the curves show strain levels at which the tests were stopped and the specimen was examined for microstructural evidence of the deformation and failure processes. Micrographs of stopped specimen sections, which revealed shear bands, are shown as well as photographs of failed specimens (indicated with stars on curves). The width of shear bands developed during SHPB testing were on the order of ∼10 to 20 μm.

C. Temperature dependence of compressive response

The temperature dependence of the uniaxial and biaxial compressive behavior of LM106-70W was investigated at a nominal strain rate of 200 s−1 using the drop-weight tower setup with inductive heating and specimen temperature measurement. Tests were performed on both uniaxial and biaxial specimens at RT as well as at temperatures of 200, 380, 450, 550, and 600 °C. The stress–strain curves generated from the high temperature tests are shown in Fig. 12. The specimens tested at RT showed softening behavior, whereas the specimens tested at higher temperatures showed almost no softening, which is contrary to what would be expected for a monolithic BMG.2, 15 This is perhaps related to the transition from dislocation nucleation limited processes to dislocation mobility limited processes in tungsten with increasing temperature,30 which is discussed further later in this section. As illustrated in FIG. 12, the uniaxial specimen tested at 450 °C shows unique behavior in comparison to the responses observed at other test temperatures. The 450 °C test temperature falls between the glass transition and crystallization temperatures of LM106 BMG, which is the only range where the BMG will deform homogeneously, and not by localized shear banding (when tested at high strain rates). Although the BMG is still in its amorphous state, it has gone through its “brittle to ductile” transition, and is behaving in more of a ductile (“rubbery”) manner, as evidenced by the different trend evident in its stress–strain response [Fig. 12(a)]. As the test temperature was increased further (550 °C), the crystallization temperature was surpassed and the BMG transformed to a crystalline phase (although probably not fully due to the fast heating rate). At this test temperature, the composite again showed behavior analogous to that at lower test temperatures. Because the behavior at all temperatures (except 450 °C) is similar in response, although not in magnitude, it appears as if the tungsten may be dominating the mechanical response of the composite, except in the temperature range (between Tg and Tx) where the BMG exhibits more ductile or “rubbery” behavior, and therefore dominates the material response. All compression-shear specimens recovered after high temperature testing show shear failure in the form of a crack connecting the 96° corners of the specimen. A vertically-oriented tensile crack also formed at all test temperatures.

FIG. 12.
figure12

Stress–strain curves generated during high temperature testing of (a) uniaxial and (b) biaxial specimens at ∼200 s−1. The specimens tested at RT showed softening behavior, whereas the specimens tested at higher temperatures showed almost no softening. The uniaxial specimen tested at 450 °C shows unique behavior in comparison to the responses observed at other test temperatures. The 450 °C is between the glass transition temperature and crystallization temperature of LM106 BMG, and between these two transitions is the only temperature range where the BMG will deform homogeneously, and not by localized shear banding (when tested at high strain rates). Multiple tests were performed at each test temperature, but only one is shown for simplicity.

When comparing the uniaxial and biaxial stress–strain response for each test temperature, the similarity in flow stress between the uniaxial and biaxial cases can be seen for most temperatures. At RT, however, the flow stress of the biaxial specimens is somewhat lower than that of the uniaxial specimens. This can be attributed to the development of shear bands in the BMG at stresses below yield,7 which is more prevalent in the 6° specimen due to its stress state and susceptibility to shear. At higher temperatures there was no significant difference between the flow stresses measured for the uniaxial and biaxial specimens, so the increase in temperature of the glass phase must be causing a transition toward more homogeneous deformation and less heterogeneous and localized deformation by shear band formation. If the response is more homogeneous, it would be similar to that of the uniaxial specimen since the tendency to develop shear bands would be expected to decrease, therefore making the additional shear stress less significant. At 450 °C, the biaxial specimen shows a higher flow stress than the uniaxial case, which is unusual, but the difference is not considered to be enough to be significant.

Plots of the 0.2% yield stress and failure stress as well as yield and failure strains are shown in Fig. 13. Because of the lack of clearly defined failure points in the true stress–strain curves, the engineering stress–strain curves were used to investigate trends in yield and failure since these curves show hardening up to a maximum stress, which could be consistently measured, followed by failure. Therefore, although the values reported are in engineering stress and strain, the trends are the same in true stress and strain. Several obvious trends emerge from the yield and failure data. As shown in Fig. 13(a), the uniaxial and biaxial specimens yield at the same stress throughout the entire temperature range investigated. For both uniaxial and biaxial specimens, yield stress decreases with increasing test temperature, as expected, and this decrease occurs at the same rate, regardless of specimen configuration. Furthermore, failure stress decreases with increasing test temperature, again as expected, but the uniaxial failure stress, which is always above that of the corresponding biaxial specimen, decreases at a much higher rate so that at 600 °C the uniaxial and biaxial failure stresses are approximately the same. Both the failure stress and failure strain measured for the 450 °C test temperature deviated from the otherwise nearly linear trend; these data points are circled in the plots shown in Figs. 13(a) and 13(b). This deviation can be explained from the difference in the deformation mechanism of the glass in that temperature range, as discussed earlier.

FIG. 13.
figure13

Temperature dependence of mechanical behavior of uniaxial and biaxial LM106-70W specimens tested at ∼200 s−1. (a) Yield and failure stresses as a function of test temperature and (b) yield and failure strains as a function of temperature. In (a) and (b) the data from the 450 °C tests (circled) deviate from the otherwise linear trend. For both uniaxial and biaxial specimens, yield stress decreases with increasing test temperature, and this decrease occurs at the same rate, regardless of specimen configuration. Additionally, failure stress decreases with increasing test temperature, but the uniaxial failure stress, which is always above that of the corresponding biaxial specimen, decreases at a much higher rate so that at 600 °C the uniaxial and biaxial failure stresses are approximately the same. As seen in (b), strain to failure decreases with increasing test temperature. Both the failure stress and failure strain measured for the 450 °C test temperature deviated from the otherwise nearly linear trend; these data points are circled. This deviation can be explained from the difference in the deformation mechanism of the glass in that temperature range.

As shown in Fig. 13(b), strain to failure decreases with increasing test temperature. This trend was the opposite of what was expected since an increase in test temperature typically results in an increase in strain to failure for metals. However, in an investigation of W single crystals with various crack orientations, Gumbsch30 showed that the fracture toughness reaches a maximum at ∼100–200 °C after which it decreases. The mechanistic explanation provided for this behavior was a transition from a process limited by dislocation nucleation to one limited by dislocation mobility. At the peak fracture toughness (∼100–200 °C), dislocation nucleation is at a maximum, but mobility is at a minimum so that dislocations are keeping cracks from propagating. However, as temperature continues to increase, dislocation mobility increases, which allows cracks to propagate and as a result fracture toughness decreases. Although the work by Gumbsch was done on a single crystal, the decrease in fracture toughness with increasing temperature provides a plausible explanation for the analogous decrease in plasticity of the BMG–W composite. Additionally, in the case of tungsten heavy alloys (95W–3.5Ni–1.5Fe), Islam et al.31 found a considerable decrease in ductility at high temperatures (>500 °C), which they attributed to a loss of bonding between the tungsten grains and the matrix and an increase in the percentage of intergranular cleavage. Both the increase in dislocation mobility in the tungsten allowing cracks to propagate and the loss of bonding at the W/BMG interfaces could be contributing to the decrease in plasticity with increasing temperature.

Figure 14 shows the dependence of elastic modulus (obtained from slope of elastic portion of stress–strain curves from drop weight testing at 200 s−1) on test temperature. An overall decrease in elastic modulus was observed. The elastic modulus at RT was 220 GPa, and at 200 °C it dropped to ∼190 GPa, where it plateaued, with no obvious decrease above the glass transition temperature. However, a drastic decrease in elastic modulus was observed above the crystallization temperature of the BMG.

FIG. 14.
figure14

Temperature dependence of elastic modulus showing an overall decrease in E with increasing temperature. A plateau was observed from ∼200° to 450°; therefore, the glass transition temperature was exceeded without any apparent effect on E. However, a drastic decrease in elastic modulus was observed above the crystallization temperature of the BMG. All measurements were taken from drop weight test data (200 s−1); however, no deviation was seen in RT elastic modulus as a function of strain rate. Error bars represent standard deviation of multiple measurements at each temperature, all at the same strain rate.

IV. Conclusions and Summary

Investigation of the compressive behavior of LM106-70W over a range of strain rates (10−3 to 103 s−1) showed an increase in yield strength and a decrease in failure strength, plasticity, and hardening with increasing strain rate. Comparison of uniaxial and biaxial loading gave evidence of a strong susceptibility of this material to shear failure since the additional 10% shear stress inherent with biaxial loading caused failure at much lower strains in all cases. Investigation of the compressive response of LM106-70W over a range of temperatures (up to 600 °C) showed a decrease in flow stress and plasticity with increased temperature. Also notable was the anomalous behavior at 450 °C, which lies between the Tg and Tx and is in a temperature regime where homogeneous flow, as opposed to heterogeneous shear banding, is the dominant deformation mechanism in the BMG. It can be generalized that the tungsten dominates the deformation behavior of the composite given the hardening and large degree of plasticity, which are characteristic of the bcc metal and not the BMG. This is not surprising given that the tungsten is 70 vol% of the composite. However, the additional shear stress during biaxial loading causes the BMG to play a strong role. Additionally, at temperatures between Tg and Tx, the BMG deforms homogeneously, and this mechanistic change is so significant that the deformation of the BMG plays a significant role in the overall deformation of the composite despite its minor volume content (30%).

References

  1. 1.

    H.A. Bruck, A.J. Rosakis, W.L. Johnson: The dynamic compressive behavior of beryllium bearing bulk metallic glass. J. Mater. Res. 11, 503 1996

    CAS  Article  Google Scholar 

  2. 2.

    J. Lu, G. Ravichandran, W.L. Johnson: Deformation behavior of the Zr41.2Ti31.8Cu12.5Ni10Be22.5 bulk metallic glass over a wide range of strain-rates and temperatures. Acta Mater. 51, 3429 2003

    CAS  Article  Google Scholar 

  3. 3.

    G. Subhash, R.J. Dowding, L.J. Kecskes: Characterization of uniaxial compressive response of bulk amorphous Zr–Ti–Cu–Ni–Be alloy. Mater. Sci. Eng., A 334, 33 2002

    Article  Google Scholar 

  4. 4.

    Y. Kawamura, T. Shibata, A. Inoue, T. Masumoto: Workability of the supercooled liquid in the Zr65Al10Ni10Cu15 bulk metallic glass. Acta Metall. 46, 253 1998

    CAS  Google Scholar 

  5. 5.

    L.F. Liu, L.H. Dai, Y.L. Bai, B.C. Wei, G.S. Yu: Strain rate-dependent compressive deformation behavior of Nd-based bulk metallic glass. Intermetallics 13, 827 2005

    Article  Google Scholar 

  6. 6.

    H. Li, G. Subhash, L.J. Kecskes, R.J. Dowding: Mechanical behavior of tungsten preform reinforced bulk metallic glass composites. Mater. Sci. Eng., A 403, 134 2005

    Article  Google Scholar 

  7. 7.

    H. Li, G. Subhash, X-L. Gao, L.J. Kecskes, R.J. Dowding: Negative strain rate sensitivity and compositional dependence of fracture strength in Zr/Hf based bulk metallic glasses. Scr. Mater. 49, 1087 2003

    CAS  Article  Google Scholar 

  8. 8.

    X. Gu, T. Jiao, L.J. Kecskes, R.H. Woodman, C. Fan, K.T. Ramesh, T.C. Hufnagel: Crystallization and mechanical behavior of (Hf,Zr)–Ti–Cu–Ni–Al metallic glasses. J. Non-Cryst. Solids 317, 112 2003

    CAS  Article  Google Scholar 

  9. 9.

    J-F. Sun, M. Yang, J. Shun: High strain rate induced embrittlement of Zr-based bulk metallic glass. Trans. Nonferrous Met. Soc. China 15, 115 2005

    CAS  Google Scholar 

  10. 10.

    F. Dalla Torre, A. Dubach, M. Siegrist, J. Loffler: Negative strain rate sensitivity in bulk metallic glass and its similarities with the dynamic strain aging effect during deformation. Appl. Phys. Lett. 89, 1 2006

    Article  Google Scholar 

  11. 11.

    T. Mukai, T. Nieh, Y. Kawamura, A. Inoue, K. Higashi: Effect of strain rate on compressive behavior of a Pd40Ni40P20 bulk metallic glass. Intermetallics 10, 1071 2002

    CAS  Article  Google Scholar 

  12. 12.

    T.C. Hufnagel, T. Jiano, Y. Li, L-Q. Xing, K.T. Ramesh: Deformation and failure of Zr57Ti5Cu20Ni8Al10 bulk metallic glass under quasi-static and dynamic compression. J. Mater. Res. 17, 1441 2002

    CAS  Article  Google Scholar 

  13. 13.

    T. Masumoto, R. Maddin: The mechanical properties of palladium 20 a/o silicon alloy quenched from the liquid state. Acta Metall. 19, 725 1971

    CAS  Article  Google Scholar 

  14. 14.

    T. Jiao, L.J. Kecskes, T.C. Hufnagel, K.T. Ramesh: Deformation and failure of Zr57Nb5Al10Cu15.4Ni12.6/W particle composites under quasi-static and dynamic compression. Metall. Mater. Trans. A 35, 3439 2004

    Article  Google Scholar 

  15. 15.

    F. Spaepen: A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Mater. 25, 407 1977

    CAS  Article  Google Scholar 

  16. 16.

    G. Wang, J. Shen, J.F. Sun, Z.P. Lu, Z.H. Stachurski, B.D. Zhou: Compressive fracture characteristics of a Zr-based bulk metallic glass at high test temperatures. Mater. Sci. Eng., A 398, 82 2005

    Article  Google Scholar 

  17. 17.

    M. Heilmaier, J. Eckert: Elevated temperature deformation behavior of Zr-based bulk metallic glasses. Adv. Eng. Mater. 7, 833 2005

    CAS  Article  Google Scholar 

  18. 18.

    Q. Wang, J. Pelletier, J. Blandin, M. Suery: Mechanical properties over the glass transition of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass. J. Non-Cryst. Solids 351, 2224 2005

    CAS  Article  Google Scholar 

  19. 19.

    M.L. Falk, J.S. Langer: From simulation to theory in the physics of deformation and fracture. MRS Bull. 25, 40 2000

    CAS  Article  Google Scholar 

  20. 20.

    L. Meyer, L. Krueger: Drop weight compression-shear testing, in Mechanical Testing and Evaluation. ASM Handbook, Vol. 8 ASM International Materials Park, OH 2000 452 454

    Google Scholar 

  21. 21.

    J.X. Li, G.B. Shan, K.W. Gao, L.J. Qiao, W.Y. Chu: In situ study of formation and growth of shear bands and microcracks in bulk metallic glasses. Mater. Sci. Eng., A 354, 337 2003

    Article  Google Scholar 

  22. 22.

    P.E. Donovan: Compressive deformation of amorphous Pd40Ni40P20. Acta Mater. 37, 445 1988

    Article  Google Scholar 

  23. 23.

    L.W. Meyer, E. Staskewich, A. Burblies: Adiabatic shear failure under biaxial dynamic compression/shear loading. Mech. Mater. 17, 203 1994

    Article  Google Scholar 

  24. 24.

    J.G. Loffler, S. Bossuyt, S.C. Glade, W.L. Johnson, W. Wagner, P. Thiyagarajan: Crystallization of bulk amorphous Zr–Ti(Nb)–Cu–Ni–Al. Appl. Phys. Lett. 77, 525 2000

    CAS  Article  Google Scholar 

  25. 25.

    H. Choi-Yim, R. Busch, U. Koster, W.L. Johnson: Synthesis and characterization of particulate reinforced Zr57Nb5Al10Cu15.4Ni12.6 bulk metallic glass composites. Acta Mater. 47, 2455 1999

    CAS  Article  Google Scholar 

  26. 26.

    B. Hopkinson: A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets. Roy. Soc. Phil. Trans., A 213, 437 1914

    CAS  Google Scholar 

  27. 27.

    G. Sunny, F. Yuan, J.J. Lewandowski, V. Prakash: Dynamic stress-strain response of Zr41.25Ti13.75Ni10Cu12.5Be22.5 bulk metallic glass, in Proceedings of the 2005 SEM Annual Conference and Exposition on Experimental and Applied MechanicsSociety for Experimental Mechanics Bethel, CT 2005 157 164

  28. 28.

    M.A. Meyers: Experimental techniques: Methods to produce dynamic deformation Dynamic Behavior of Materials John Wiley & Sons, Inc. New York 1994 305 310

    Google Scholar 

  29. 29.

    R.D. Conner, H. Choi-Yim, W.L. Johnson: Mechanical properties of Zr57Nb5Al10Cu15.4Ni12.6 metallic glass matrix particulate composites. J. Mater. Res. 14, 3292 1999

    CAS  Article  Google Scholar 

  30. 30.

    P. Gumbsch: Brittle fracture and the brittle-to-ductile transition of tungsten. J. Nucl. Mater. 323, 304 2003

    CAS  Article  Google Scholar 

  31. 31.

    S. Islam, M. Tufail, X. Qu: Mechanical properties variation with test temperature for liquid phase sintered 95W–3.5Ni–1.5Fe alloys. Mater. Sci. Forum 561, 647 2007

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank Liquidmetal Technologies, Inc., for providing the materials. The authors also thank Norman Herzig, David Musch, Christoph Wollschlaeger, Stefan Syla, and Gunther Muth at the Technical University of Chemnitz (TUC) for their help with performing experiments. This research is funded by Army Research Office (ARO) Grant No. E-48148-MS-000-05123-1 (Dr. Mullins program monitor) and was performed at TUC under a German Academic Exchange Service (DAAD) Research Grant. Morgana Martin is a recipient of a NASA Jenkins Fellowship.

Author information

Affiliations

Authors

Corresponding author

Correspondence to N. N. Thadhani.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Martin, M., Meyer, L., Kecskes, L. et al. Uniaxial and biaxial compressive response of a bulk metallic glass composite over a range of strain rates and temperatures. Journal of Materials Research 24, 66–78 (2009). https://doi.org/10.1557/JMR.2009.0003

Download citation