Design and Dynamic Experiment of Al-Cu Graded Materials Impactor with Strain Rate of 1

Abstract

Based on simplified calculations of one-dimensional wave systems, loading pressure platform curves of Al-Cu gradient materials (GMs) impactor were designed. The Al-Cu GMs were prepared using tape-pressing sintering, and their acoustic properties were characterized to match the design path. The parallelism of the Al-Cu GM was confirmed using a three-dimensional surface profilometry machine. A one-stage light-gas gun was used to launch the Al-Cu GM, impacting an Al-LiF target at a velocity of 400 m/s. The results of the experimental strain rate demonstrate that the Al-Cu GMs can realize the precise control of the strain rate within the range of 10⁴‒10⁵/s in the high-speed impact experiments.

Keywords

high strain rate; Al-Cu graded materials; impactor; acoustic impedance; gas gun experiment

1 Introduction

The mechanical properties of materials under various strain rates are pivotal for their application in diverse working environments^[1–3]. Traditional static mechanical property tests typically capture the mechanical response behavior only within lower strain rate ranges of 10^-5–10¹/s. However, understanding material dynamics and solid-state deformation mechanisms under high strain rates is still a significant research area for decades^[4–9]. The response of materials to impacts and other high strain promotes the development of numerous theories, ranging from empirical models to the latest physical models^[10–13]. The duration of loading at ultra-high strain rate is notably brief and the strain stress stability is more important compared to that at low strain rate. Therefore, to achieve precise control of stress, it is necessary to test samples at relatively constant strain rates.

Split Hopkinson pressure bar (SHPB) experiments and gas gun experiments are two common methods used for conducting experiments at relatively high strain rates. In SHPB experiments, the testing strain rate typically falls within the range of 10¹–10³/s^[14–16]. And the strain rate of gas gun experiments is in the range of 10⁶–10⁹/s. However, there is little attention paid to strain rates between 10⁴/s and 10⁵/s, which are widely used in research on explosive welding and blasting proximity^[17–19]. Although the stress-strain curves produced by SHPB experiments closely resemble the ideal elastoplastic behavior with approximately constant strain rates, some researchers argue that the effect of strain rate on metal materials is primarily sensitive to the logarithm of variability. Consequently, they assume that modest changes in strain rate during experiments may not significantly influence the test results^[20]. However, as the demand for more constitutive equations of reliable material increases, there is a growing awareness of the importance of such small differences^[21–22]. Materials such as high polymers and nano-materials exhibit high sensitivity to strain rate, and even slight variations in strain rate can induce significant differences in stress-strain curves and microstructure^[23–24]. Thus, there is an urgent need to conduct experiments with high strain rates of 10⁴–10⁵/s to meet the demands of sophisticated tests.

Graded material (GM) impactors were demonstrated to effectively reduce the strain rates in dynamic experiments^[25–26]. Previous studies focused on preparing several types of GMs, including Mg-Cu, W-Cu, and W-Cu-Mg, to facilitate dynamic impacting^[26–28]. However, designing loading paths to achieve the desired loading strain rate was proven to be a challenge, particularly because element Mg with hexagonal close-packed structure is susceptible to phase transitions. To obtain reliable dynamic experimental results, Al-Cu GMs were selected for dynamic experiments due to the favorable properties and low susceptibility to phase transitions.

2 Experiment

By meticulously controlling the composition and thickness of the GMs using one-dimensional wave calculations, the corresponding loading path was derived, which was characterized by a ramp loading before the initial shock loading. Several loading path curves were designed for impacting an Al target and then transformed into various Al-Cu GM structures using one-dimensional wave calcula-tions. Subsequently, the corresponding Al-Cu GMs were prepared through tape casting and hot press sintering techniques. The physical properties of Al-Cu GMs were predicted based on the monolithic properties, such as density and acoustic impedance. The effectiveness of the graded structures was assessed using a three-dimensional surface profilometry machine. And then the prepared GMs were employed to impact an Al-LiF target at a velocity of 400 m/s using a one-stage light-gas gun. Experimental pressure curves were meticulously measured using a photon Doppler velocimeter and compared to the designed pressure curve.

Al-Cu GMs with diverse loading paths were designed and the impedance-thickness distribution corresponding to each path was derived using the MLEP (2015SR065998) software developed by China Academy of Engineering Physics. And then the variations in loading pressure and strain rate asso-ciated with these different loading paths were calculated. Al-Cu GMs with the designed impedance-thickness distribu-tion were prepared by adjusting the density and acoustic velocity of the single-layer materials in accordance with Eq.(1)^[25]:

Z=ρv

(1)

where Z represents the impedance-thickness distribution; ρ and v are the density and acoustic velocity, respectively. Single-layer thickness was controlled through mass. Firstly, metal powder and dispersant were placed in a zirconia ball milling tank, and then ethanol and butanone solvents were added. The mixture was stirred in a three-dimensional ball mill at 240 r/min for 12 h. Subsequently, corresponding binders and plasticizers were added and mixed for 12 h at the same speed, resulting in Al-Cu casting slurries with various composition. These slurries were used to form Al-Cu casting films using double scrapers. The thickness of the films after drying was controlled by adjusting the height of scrapers. Then, the dried Al-Cu casting films were cut into wafers with predetermined diameter, stacked sequentially, and pressed into cast blanks by a tablet press under the stress of 100 MPa. Finally, the thickness was meticulously controlled through rigorous mass assurance processes. The scanning electron microscope (SEM, Thermo Fisher, Quanta250) was used to characterize the graded structure of Al-Cu GMs. The flatness of the Al-Cu GM was assessed using the three-dimensional optical profiler (ST400, American Nanovea Company), which included measurements of parallelism and detection of internal defects. Subsequently, the Al-Cu GMs served as impactors and were launched at high velocity for dynamic experiments using a gas gun, as depicted in Fig.1. Sample data were collected from the target comprising a Al baseplate with the thickness of 2.0 mm and a LiF window. Changes in pressure and strain rate were recorded at the interface of the Al-LiF window, providing valuable insights into the dynamic behavior of the system.

Fig.1  Schematic diagram of dynamic experimental process

3 Results and Discussion

To demonstrate the effectiveness of the experimental design, we devised several paths aiming to attain the maxi-mum pressure of 5 GPa. The relationship between pressure and time is as follows^[26]:

p(t)=p0+A(t)P

(2)

where p(t) is a function of pressure changed with time, p₀ is the initial pressure, P is the pressure loading index, and A is the proportionality coefficient, which has different values in different pressure paths. Obviously, any loading path can be obtained through the change of P value. The initial pressure p₀ of Al-Cu GMs can be determined from the highest pressure of 3.56 GPa. Fig.2 illustrates several distinct loading paths designed by the principles.

Fig.2  Pressure curves of Al-Cu GMs with different P values

Using one-dimensional wave calculation, the pressure curve can be transformed into an impedance-thickness curve specific to the Al-Cu GMs. Subsequently, the impedance-thickness curve can be further converted into a composition-thickness curve of the Al-Cu GMs according to the mixing rule of impedance calculation, as depicted in Fig.3. Once the composition-thickness curve is established, GMs can be produced in accordance with these curves. The design of the components determines the impedance-thickness distribution, which can be calculated from the corresponding pressure curve by MLEP software.

Fig.3  Impedance-thickness curves of Al-Cu GMs with different P values

Fig.4 depicts the pressure and strain rate curves derived from one-dimensional wave calculations^[26]. Analysis of the results reveals that the initial higher strain rate corresponds to the initial impact pressure of the front Al shock loading. Subsequently, the strain rate of the target falls within the range of 10³–10⁵/s, owing to the pressure platform generated by the Al-Cu stacked structure design. The pressure platform means that the GMs are loaded with each layer appearing a corresponding constant value to the corresponding pressure. When the pressure loading index is 1, the strain rate is confined within a relatively narrow range of 10⁴–10⁵/s. Consequently, the corresponding Al-Cu GMs were prepared and experiments were conducted using the gas gun.

Fig.4  Validation and design pressure curves with different P val- ues (a); strain rate-time curves calculated from GM structure distribution (b)

The microstructures of various Al-Cu GMs are depicted in Fig.5. Cu particles are shown in white and Al particles are shown in gray. Both Al and Cu particles are uniformly distributed with different pressure loading indexes without discernible pores, which indicates that Al and Cu particles have high densification and effective dispersion. The interfaces of the Al-Cu GMs are distinctly defined, facilitating the calculation of impedance-thickness distribution for the GMs based on their respective locations.

Fig.5  Microstructures of Al-Cu GMs with different P values: (a) P=3; (b) P=2; (c) P=1; (d) P=1/2; (e) P=1/3

To assess the impact effect on the target, different curves of the GMs obtained in the experiment are presented in Fig.6. The error between the experimental impedance values and the designed values for the Al-Cu GMs is within 4%. The thickness of the film was meticulously controlled using the density obtained from the homogeneous monolayer materials to adjust the mass and to ensure a constant reduction of mass during the removal of polymer additives. As shown in Fig.5a, the thickness of the nth layer for different Al-Cu GMs is represented by d_n. The average thickness of the films is 50±2.5 μm with the error less than 5%. The thickness of the GMs can be further adjusted based on precise control of mass.

Fig.6  Impedance-thickness curves of Al-Cu GMs with different P values (a); comparison between experimental and theoretical values of wave impedance curves (b); layer thickness of films for Al-Cu GMs obtained by mass measurement (c)

The impact design results and structural characterization findings demonstrate that the strain rate along the loading path can be effectively controlled within the designated range when P=1. Surface parallelism of the corresponding Al-Cu GMs characterized by a three-dimensional profiler is depicted in Fig.7. Apparent differences in flatness of the GMs indicate variations in internal coefficients of thermal expansion and stress levels. From the two-dimensional height difference map of the Al surface in Fig.7a, different colors represent various height differences. The Al surface appears lower in the center and higher around the edges, which indicates the Al surface is concave while the Cu surface appears convex. The curvature of both surfaces is approximately 20 μm. Ensuring good surface parallelism is crucial for maintaining the accuracy of data in impact experiments.

Fig.7  Two-dimensional height difference maps of Cu and Al surface (a); flatness schematic diagram of Al-Cu GMs (b)

Fig.8a illustrates the pressure curve for the Al-Cu GMs, impacting an Al target of 2 mm equipped with a LiF window when the pressure loading index is 1. The pressure within the Al target was derived from initial data obtained via laser probe measurements. Initially, the particle velocity exhibits an abrupt shock impact within 0.1 μs, followed by a pressure plateau of 3.56 GPa, corresponding to the structure of the pure Al layer Subsequently, a smooth wave platform ramps up from 3.56 GPa to 5.0 GPa, representing each layer of GMs up to the Cu layer. The pressure data obtained from the gas gun experiment align well with the initially designed pressure curve. The differences between the designed and experimental pressure data can be attributed to the impedance-thickness data, which exhibit a relatively low uncertainty below 5%, primarily due to impedance changes caused by diffusion at the sintered interface within the Al-Cu GMs. Fig.8b displays the strain rate of the target. The experimental strain rate is confined within a narrow range of 10⁴–10⁵/s. Notably, the experimental strain rate appears smoother than the designed theoretical curve due to interfacial diffusion within the Al-Cu GMs.

Fig.8  Comparison between experimental and theoretical curves of pressure (a) and strain rate (b)

In conclusion, this research demonstrates the feasibility and effectiveness of using Al-Cu GMs to achieve precise control of strain rates in high-speed impact experiments, thereby contributing to advancements in materials testing and characterization under dynamic loading conditions.

4 Conclusions

1) The methodology to achieve a strain rate range of

10⁴–10⁵/s for impacting an Al target using Al-Cu GMs is successfully designed and implemented. Through the conversion from pressure distribution curves into impedance-thickness distribution curves of Al-Cu GMs based on the principle of GM wave system propagation, a suitable curve corresponding to the desired strain rate range is selected.

2) The Al-Cu GMs are meticulously prepared by tape casting method, which ensures the control of wave impedance and thickness with an error under 5%. Although the prepared Al-Cu GMs exhibit low flatness and obvious internal graded structure, they effectively transform the designed pressure curves into experimental results. The pressure curves obtained from experimental samples closely resemble the designed curves, displaying a smooth wave platform rising from 3.56 GPa to 5.00 GPa, while the strain rate remains within the narrow range of 10⁴–10⁵/s.