Study of 3D MPFEM simulation for high-velocity compaction of 2024 al alloy powders

Abstract

In powder metallurgy, high-velocity compaction (HVC) is one of the processes used to densify metal powders, to give them a defined shape, size, porosity, and strength. In order to achieve a green compact of 2024 Al with low porosity and high relative density, this study uses the Multi-Particle Finite Element Method (MPFEM) to simulate the 3D HVC of 2024 Al alloy powder with a particle size of 64 μm. The simulation reproduced the displacement and deformation of particles, as well as the filling of pores during the powder pressing process, effectively simulating the HVC process. The study investigates the effects of impact energy per unit mass (E_m), hammer mass (M), compaction velocity (v), and friction coefficient (µ) on the green compact density. The results indicate thatwhen E_m is increased from 45.9 J/g to 173.3 J/g, the relative density of the green compact rises from 0.72312 to 0.97193.Further research shows that, with E_m remaining constant, the impact of the hammer mass on the relative density of the compact is greater than that of the compaction velocity .The relative density of the compact with a hammer mass of M = 25 kg is 0.015952416 higher than that with M = 15 kg. In addition, the smaller µ between particles and between particles and molds during compaction helps to reduce the kinetic energy consumption, thus promoting the transfer of force from top to bottom during compaction.

Introduction

Driven by the demand for lightweight materials, Al alloys have been widely used in various fields of manufacturing and daily life, including aerospace, marine engineering, automotive and construction^1,2. The 2024 Al alloy is an Al-Cu-Mg series alloy, known for its excellent formability, high strength, superior hardness, low density, cost-effectiveness, and excellent fatigue resistance. It is widely used in aircraft structures, including skins, scaffolds, ribs, and bulkheads³. In addition, environmental issues have become a focus of global attention with growing concerns about global warming and the increasing frequency of extreme weather events, Nations are actively developing and utilizing renewable energy sources to reduce environmental pollution. Powder metallurgy, with its near-net-shape processing methods and exceptionally high material utilization rates, offers significant technological and economic advantages. Its applications have expanded across various sectors of the national economy, from general engineering to precision instruments, from everyday life to healthcare, from civil to military industries, and from conventional technologies to cutting-edge innovations^4,5.

To meet the desired performance requirements, the powder must be subjected a forming process, with powder compaction being the most commonly used forming method. However, traditional compaction experiments make it difficult to observe the dynamic changes in the powder compaction process, limiting in-depth studies of the microscopic mechanisms such as particle rearrangement and deformation during the compaction. In contrast, computational numerical simulation techniques not only allow dynamic visualization of the compaction process, predict experimental results, and provide solutions, but also provide deeper insights into the compaction mechanisms. These simulations can quantitatively characterize the distribution of stress, strain, and temperature during the densification process, providing theoretical guidance for compaction experiments, reducing costs, shortening cycles and minimizing unnecessary waste of resources. In recent years, the multi-particle discrete element model based on Newton’s second law, which analyses the motion of particles, has become widely used due to its ability to accurately represent the interactions between powder particles as well as between powder particles and mold walls. This model effectively simulates particle packing and flow and is supported by a range of platforms such as (Matlab, Python, EDEM, and CAD). It has become the preferred model for exploring various powder forming techniques, including quasi-static compaction^6,7, laser shock dynamic compaction⁸, and hot-pressing^9–11. Peng, Cui et al.^12,13 conducted conducted numerical simulation studies of powder forming using the multi-particle discrete element finite element method, and found that the relative density obtained from the simulation results showed excellent consistency with the experimental outcomes of the model. Han et al.¹⁴ employed a 2D MPFEM simulation to model the compaction process of Al-Fe composite powders with different particle size ratios. The study revealed that the stress was mainly concentrated around the Fe particles, forming a network of contact forces that hindered the densification process. Qian et al.¹⁵ analyzed the effects of particle size, initial packing structure, and applied pressure on the relative density during uniaxial compaction. Ahmet et al.¹⁶ investigated the compaction behavior of hollow particles using 3D MPFEM and found that an increase in shell thickness led to a corresponding rise in the punch’s reaction force. While changes in particle size also influenced compaction behavior, a 25% reduction in particle diameter did not result in a significant impact. The force chain, as a critical feature linking the macroscopic and microscopic mechanisms of the compaction process, Zhang et al.¹⁷ using the 2D MPFEM method to explore the relationship between force chain length and probability density distribution, as well as the correlations between the force chain length and other force chain characteristics were investigated.

HVC is a type of powder compaction technology, where the mass of the hydraulically driven hammer ranges from 5 to 1200 kg. The impact velocity can reach 2–30 m/s, generating a powerful shockwave that transfers energy to the powder within 0.02 s, enabling it to be compacted. Compared to conventional compaction (CC) methods, HVC offers faster compaction velocities, shorter processing times, and higher energy consumption. The resulting product exhibits both high and uniform density, with a density increase of 0.3 g/cm³ and a deviation of less than 0.01 g/cm³, leading to superior performance^18,19. For example, Doremus et al.²⁰ found that the radial force in HVC was approximately 10% lower than that in CC, resulting in a rebound rate that was about 0.1% lower for HVC. Yin et al.²¹ compacted Ti-6Al-4 V powder particles under an impact force of 1.867 KN, achieving a relative sinter density of up to 99.88%. The hardness ranged from 364 ~ 483 HV, and the flexural strength varied from 103 ~ 126.78 MPa. The method of multi-particle discrete element finite element analysis is also applicable to the simulation of HVC. For instance, M. Shoaib et al.²² investigated the impact of loading components on the compaction process and the influence of adhesion during the unloading stage. Zhang et al.²³ compared the simulation results of HVC with experimental measurements of the projectile waveforms, analyzing the propagation of particle perturbations and the forces acting on the particles during a single loading cycle. Zhou et al.^24–26 investigated the variation in micro-porosity and densification behavior of Ti-6Al-4 V during the uniaxial HVC process using both 2D and 3D MPFEM particle models, comparing the results with experimental data. They found a notable disparity in the initial relative densities between the two models. The 3D model accurately captured the particle trajectories and deformation behaviors from all three directions (X, Y, Z), whereas the 2D model underestimated the lateral constraint effects. As a result, the 2D model exhibited a higher initial relative density than the 3D model, with the 2D model showing an initial packing density of 0.78 compared to 0.50 in the 3D model. In terms of final green compact relative density, densification occurred more readily in the 2D model; however, the 3D model provided a more accurate prediction. The difference was attributed to variations in the degrees of freedom of the particles and the initial packing density.

Although the 3D MPFEM more accurately reflects the actual powder compaction process and particle movement and deformation within the mold during pressing, compared to the 2D model, it is widely used for simulating powder forming. However, due to the high computational cost of 3D numerical simulations, the number of particles in the model is significantly limited. As a result, most numerical simulations of powder compaction still rely on 2D models, with relatively few studies on 3D simulations, particularly regarding the influence of various parameters in high-speed compaction processes on green compact quality. The aim of this study is to construct a 3D multi-particle discrete element model to simulate the HVC of 2024 Al alloy powder. The simulation will observe the rearrangement, deformation, pore filling, and changes in relative density of the powder particles during the compaction process. Additionally, the study will explore the impact mechanisms of parameters such as E_m, M, v, and µ on the density of the compacted 2024 Al alloy.

3D MPFEM simulation process

In theory, when the particle model used for numerical simulations matches the powder particles in the actual experiment on a 1:1 scale, it can best align with the experimental results. However, due to computational and time constraints, only a small portion of the powder filler was modelled, while efforts were made to maintain consistency with the experiment in terms of initial packing density and particle size. To simulate the actual powder packing behavior of the powder, a CAD-based secondary development plugin was used to generate a 3D discrete element model of the powder naturally settling under gravity. The particle radius was set to 32 μm, and the volume of the cubic box was 0.5 × 0.5 × 0.5 mm, with an initial packing density of 0.4293, the number of particles was 392. After exporting the powder layer, it was imported into Abaqus as a component, while the other components (top punch, bottom punch, and sino mold) were directly modeled within Abaqus. The system was then assembled with the top and bottom punches and the sino mold as shown in Fig. 1.

Fig. 1.

3D MPFEM Modeling Process (a) Generation of naturally settled 3D spheres in CAD, (b) Import into Abaqus, (c) Assembly of 3D spheres with other components.

In the MPFEM model, the powder particles are defined as deformable bodies, while the top and bottom punches and the sino mold are defined as rigid bodies. Reference points are assigned to each component: a mass is applied to the reference point of the top punch to simulate the falling process of the heavy hammer during HVC, while the reference points of the bottom punch and sino mold are used to apply boundary conditions. The powder particles are discretized in more flexible tetrahedral meshes, while the top and bottom punches and the sino mold are meshed with hexahedral elements (since the rigid bodies are not involved in the calculation). HVC is a process characterized by instantaneous impacts, so a central difference method is used for the simulation, which is suitable for dealing with rapid impacts and highly non-linear behavior. Considering the particle’s force compression during the interaction, the change in contact area is modeled using a face-to-face contact approach, with a “penalty” friction formulation and a “hard contact” pressure overclosure applied to define the tangential and normal behavior of the contact, respectively. In this study, µ between particles and between particles and rigid bodies is assumed to be identical, without differentiation. To speed up the computation, mass scaling is used to increase the target time increment, and parallel processing is used to increase the computational efficiency.

In the selection of material parameters, the HVC process transfers energy to the powder in a few milliseconds, the strain rate is very high, and the effect of work-hardening is significant. In order to cope with the plastic deformation, dynamic deformation and destruction of the material that may result from the high strain rate of the material under the action of transient impact, and to accurately and realistically simulate the behavior of the powder particles under HVC, the Johnson-Cook damage was used as the material behavior. Considering that the temperature increase during the pressing process is small compared to the melting point the Johnson-Cook equation with the temperature dependence removed is adopted, Eq. (1) is as follows:

1

A represents the initial yield stress, B is the strain hardening constant, C is the strain rate constant, n is the strain hardening exponent.

In the paper by Fei et al.²⁷, the Johnson-Cook parameters for 2024 Al alloy are reported as shown in Table (1).

Table 1.

The material parameters for 2024 al alloy are as follows.

Elastic Modulus GPa	Density g/cm3	Poisson’s ratio	A MPa	B MPa	C	n
71	2.77	0.3	345	462	0.001	0.25

In the data extraction process, the Abaqus visualization module is used to extract the necessary frame data into an Excel spreadsheet, which is then plotted. The final relative density of the powder is determined by the volume of the geometric elements occupied by the powder in the final compaction frame and the volume of the space after compaction is complete. The formula (2) is as follows:.

2

Where ρ is the relative density, V_p is the volume of the powder particles after compaction, and V is the total volume of the space.

Results and discussion

The densification process and dynamic mechanical responses during HVC

The 3D DEM model allows for a more intuitive observation of the movement of individual powder particles at different time instances. Compared to the 2D model, it more accurately replicates the movement of powder particles within the mold. The finite element analysis software Abaqus not only solves most structural problems, but also effectively handles nonlinear problems such as collisions and impacts. Thus, in this chapter, using MPFEM approach is used to simulate the compaction process of 2024 Al alloy powder under the conditions of E_m = 160.5 J/g, M = 15 kg, v = 56.4 mm/s, and µ = 0.2. The aim is to study the particle motion and the variation of the relative density, where E_m can be calculated using Eqs. (3) and (4).

3

4

E represents the kinetic energy or compaction energy, M is the mass of the hammer, v is the compaction velocity, E_m is the impact energy per unit mass, m is the mass of the powder.

During the loose packing of powder, irregular surface features and surface friction cause particles to interlock, leading to the formation of arching effects. During the compaction process, the particles are subjected to the impact of the hammer, which disrupts the arching pores. This causes particle displacement and deformation, leading to a reorganization and filling of these pores. In this chapter, the 3D MPFEM model is used to approximate the interactions, sliding, separation, and rotation of powder particles during HVC, as demonstrated by pairs of powders (A1 and A2, B1 and B2, C1 and C2, D1 and D2), as shown in Fig. 2. In reality, the displacement occurring under the compression of the powder is far more complex, as multiple types of displacement may occur simultaneously, often accompanied by deformation. This characteristic can also be directly observed in Fig. 2. Similar particle movements and changes in porosity have also been observed by Zhou²⁵, Han¹⁴ and others in their compaction simulations.

Fig. 2.

The motion of powder particles at different times under the same E_m, A represents the contact between powder particles, B represents the sliding of the particles, C represents the separation of the particles, and D represents the rotation of the particles.

During the compaction process, external forces cause the powder particles to rearrange and deform, bringing their atomic surfaces closer together. Once within the range of interatomic attraction, the particles bond together to from a green body with a certain degree of density. As the compaction progresses, the increased contact area between the particles leads to a higher relative density. As shown in Fig. 3(a), the density of the green body increases with time during the compaction process. The density reaches its maximum value of 0.97 at approximately 8.2 ms, which corresponds to the equivalent stress contour plots at six representative moments in Fig. 3(b). This phenomenon is further linked to the decrease in kinetic energy and the increase in internal energy shown in Fig. 3(c), as well as the variation in top punch velocity shown in Fig. 3(d). In Fig. 3(c), it can be observed that as time increases, the kinetic energy gradually decreases. At 0 ms, the kinetic energy is 23.857 mJ, and it drops to nearly zero around 8.2 ms. Meanwhile, the internal energy increases with time, reaching approximately 19.9 mJ at 8.2ms before stabilizing. At this point, the relative density reaches its maximum. The initial kinetic energy can be calculated using formula (3), yielding a value of 23.857 mJ, which matches the kinetic energy at 0 ms as extracted from the numerical simulation curve. This agreement can be used to verify the rationality of the model parameters applied. In Fig. 3(d), it can be seen that the velocity decreases with time, approaching zero at around 8.2 ms. After this point, the system enters the unloading phase, with the top punch rebounding and the bottom pressure rapidly decreasing. Around 8.2 ms (as shown in Figs. 3(a) and 3(b)), the compaction density experiences a slight rebound and the relative density of the sample also decreases slightly. This phenomenon can be observed in Fig. 3(e), where the bottom support reaction force (Fb) and the frictional force on the sidewall (Ft) increase over time during the densification stage, with both forces acting in the same direction. However, at around 8.2 ms, during the unloading phase, these forces decrease sharply, and their direction reverses from upward to downward, indicating that the green body density experiences a rebound. Overall, the density stabilizes around 0.967.

Fig. 3.

(a) The curve of relative density as a function of time; (b) The evolution of the green body at different time instances; (c) The curves of internal energy and kinetic energy as functions of time; (d) The compaction velocity-time curve; (e) The curves of bottom support reaction force (Fb) and frictional force on the sidewall (Ft) as functions of time.

After the HVC process, the stress distribution was observed at different heights of the green body. Initially, at a height of 0.5 mm along the Z axis, the height decreases to 0.225 mm after HVC. The stress distribution maps at various heights are shown in Fig. 4. The stress at the upper portion is greater than that at the bottom, as can be seen from the cross-sectional stress profiles at heights of 0.224 mm and 0.002 mm in Fig. 4. This can be attributed to the friction between the mold and the particles, and between the particles themselves, which causes some of the stress to be dissipated as it is transferred from the upper to the lower part of the green body during compaction. As a result, the regions of higher stress are concentrated primarily near the top punch, in direct contact with the green body. Furthermore, as this transfer relies on particle displacement and deformation, the stress distribution at different heights consistently shows high stress areas concentrated at the particle edges and gradually shifting towards the center.

Fig. 4.

I Stress distribution contour plot of the green body at different heights.

The effect of unit mass impact energy

In the traditional compaction process, the relative density of the green body is divided into three stages: Stage I, Stage II, and Stage III. In Stage I, the particles are displaced to fill the pores, resulting in a rapid increase in the density of the green body. In Stage II, the relative density gradually increases as the pressure increases. However, when the pressure reaches the critical stress level of the metal particles, there is a certain resistance to further compression. Despite an increase in pressure, the relative density shows little change. In Stage III, when the pressure exceeds the critical stress value, the powder particles begin to deform and the density continues to increase, as shown in Fig. 5(b). During HVC, the pressure acting on the powder particles fluctuates continuously, making it an inadequate measure of energy applied. Therefore, impact energy is typically used as a representation of the impact energy involved. However, Yan et al.²⁸, in their study of HVC and process characterization of Ti powders, found that E_m provides a better description of densification during HVC than the impact energy. Therefore, in this chapter, the influence of E_m on the densification of the green body is studied by varying the compaction velocity to change the value of E_m. Here, the µ = 0.2 and M = 15 kg. Figure 5(a) illustrates the relationship between E_m and relative density. From the graph, it can be seen that as E_m increases, the compaction density gradually improves. In the range of E_m around 45.9 ~ 173.3 J/g, the densification increases with higher E_m. When the E_m reaches 173.3 J/g, the relative density reaches its maximum value of 0.97193. The curve of impact energy per unit mass of the forged blank for high velocity compaction of 2024 Al alloy versus relative density follows a parabolic pattern. Unlike the CC curves, it shows distinct Stage I and Stage III, but no clear Stage II, as shown in Fig. 5. This indicates that, during HVC, densification primarily occurs primarily by particle displacement and deformation. A similar phenomenon was observed by Yan et al.²⁸ in their HVC experiments on Ti powders.

Fig. 5.

(a) The relationship between E_m ranging from 45.9 J/g to 173.3 J/g and relative density in high velocity compaction. (b) The relationship between green body density and forming pressure in conventional compaction.

This phenomenon can also be directly observed through changes in the powder during the HVC process. Figure 6 illustrates the changes in porosity at the cross-section of the alloy powder after compaction at the same time and position, under different unit mass impact energies. To facilitate observation, the porosity images under different unit mass impact energies in Fig. 6(a) are labeled with the same particles as 1, 2, 3, and 4, and the same pores are labeled as A. In Fig. 6(b), the porosity images under different unit mass impact energies are labeled with the same particles as 1, 2, 3, and 4, and the same pores are labeled as B and C. From Fig. 6, it can be observed that the particles are closely packed together, and before compaction, a quadrilateral-shaped pore, labeled as A, is formed. During compaction, there is no significant change in the relative positions of the individual particles. However, as the E_m increases, the pores are gradually filled by the deformation of the powder particles. At E_m = 126.2 J/g, the porosity is already significantly reduced, and at E_m = 173.3 J/g, the porosity is almost negligible, with the pore area approaching zero. However, in practical experiments, the pores formed between the particles after packing do not take the shape of simple planar polygons such as triangles, quadrilaterals, or pentagons. Instead, they often develop into spatial polygons, as shown by B and C in Fig. 6(b). This phenomenon is corroborated by the SEM images of the Ti-6Al-4 V powder compact surface at varying impact heights, as reported by Zhou et al.²⁶. Compared to the 2D multi-particle discrete element model, the 3D model can track particle displacement, deformation, and pore filling across the X, Y, and Z axes, providing a more accurate representation of the HVC process²⁵. Figure 6(b) illustrates the changes in particle positions and morphology at the same location and time under different E_m. By examining the variations in powder position and shape around 45.9 ~ 173.3 J/g, it becomes clear that the HVC process does not occur in a simple sequence of displacement followed by deformation, rather, displacement and deformation typically occur simultaneously (Fig. 6). The displacement and deformation of the powder contribute to the filling of the surrounding pores, and higher E_m promotes this combined process. As the specific energy increases, the porosity decreases from 57.07% in the loose packing state to 2.8% at an energy of E_m = 173.3 J/g, resulting in an increase in the relative density of the compacted body.

Fig. 6.

Changes in porosity under high velocity compaction with varying E_m levels.

The impact of hammer mass and velocity on compaction

The compaction energy is directly proportional to the mass of the hammer and the square of the compaction velocity. The compaction energy can be calculated using Eq. (3), and the specific impact energy per unit mass can be determined by dividing the compaction energy by the mass of the metal powder, Eq. (3). By deriving from Eqs. (3) and (4), Eq. (5) is obtained as follows:

5

In the above equation, M denotes the hammer mass, v is compaction velocity, E_m is the specific impact energy, and m is the mass of the metal powder.

Experiments and simulations conducted by Yan, Zhou, and others on high velocity compaction have shown that increasing the relative density of the green body can be achieved by enhancing E_m^28,29. It is evident from the above formula that E_m is closely related to the hammer mass and compaction velocity. E_m can be increased either by enhancing the compaction velocity or by increasing the hammer mass, as illustrated in Fig. 7. (a) When the hammer mass is 15 kg, increasing the velocity can raise E_m from 45.9 J/g to 160.5 J/g. (b) When the compaction velocity is 35 mm/s, increasing the hammer mass can also raise E_m from 45.9 J/g to 160.5 J/g. When E_m is within the range of 45.9 to 160.5 J/g, and with a hammer mass of 15 kg, as the compaction velocity increases from 30.16 mm/s to 56.43 mm/s, the relative density of the green body increases from 0.723 to 0.96225. This phenomenon is consistent with the observations made in previous high velocity compaction experiments on Al-Fe-Cr-Ti, where the relative density was found to increase as the compaction velocity increased^30–32. When the compaction velocity is 35 mm/s, increasing the hammer mass from 11.14 kg to 38.95 kg causes the relative density of the green body to increase from 0.71267 to 0.99954, as shown in Fig. 8. When the hammer mass changes at the same E_m, the compaction velocity also changes accordingly, as shown in Fig. 7. When E_m = 45.9 J/g, it corresponds to six different sets of hammer mass and compaction velocity, as shown in Fig. 7(a). At the same E_m, as the hammer mass increases, the compaction velocity decreases. Similarly, as shown in Fig. 7(b), as the compaction velocity increases, the hammer mass decreases accordingly. Therefore, at the same E_m, there are often multiple sets of hammer mass and compaction velocity corresponding to each other. As shown in Fig. 9, even under the same E_m, different hammer masses and compaction velocities result in different relative densities of the green compacts. The relative densities corresponding to the six sets of hammer mass and compaction velocity for E_m values of 45.9 J/g, 91.8 J/g, and 106.5 J/g are arranged as shown in Table (2). When E_m = 45.9 J/g, for M = 25 kg and v = 23.34 mm/s, the corresponding relative density is 0.739. On the other hand, for M = 6.74 kg and v = 45 mm/s, the corresponding relative density is 0.70058. At the same impact energy per unit mass, a larger hammer mass corresponds to a greater relative density, while a higher compaction velocity does not lead to a larger relative density. A similar phenomenon is observed at impact energy per unit mass of 91.8 J/g and 106.5 J/g. Therefore, at the same impact energy per unit mass, hammer mass has a more significant impact on the final relative density of the green body than compaction velocity. Consequently, the simulation results can be used to guide the design of hammer mass and compaction velocity for the press.

Fig. 7.

(a) The compaction velocity corresponding to hammer masses of 15 kg, 20 kg, and 25 kg within the impact energy per unit mass range of 45.9 to 160.5 J/g; (b) The hammer mass corresponding to initial impact velocities of 35 mm/s, 40 mm/s, and 45 mm/s within the impact energy per unit mass range of 45.9 J/g to 160.5 J/g.

Fig. 8.

The relative densities of the compacted powder corresponding to the impact energy per unit mass range of 45.9 to 160.5 J/g, when M = 15 kg and v = 35 mm/s remain constant.

Fig. 9.

The relative densities corresponding to hammer masses of 15 kg, 20 kg, and 25 kg, as well as compaction velocity of 35 mm/s, 40 mm/s, and 45 mm/s, within the impact energy per unit mass range of 45.9 J/g to 160.5 J/g.

Table 2.

The hammer masses, compaction velocity, and relative densities corresponding to impact energy per unit mass of 45.9 j/g, 91.8 j/g, and 106.5 j/g.

Em	M	v	ρ
45.9	25	23.34	0.73989
	20	26.1	0.73849
	15	30.16	0.72312
	11.14	35	0.71267
	8.53	40	0.70310
	6.74	45	0.70058
91.8	25	33.04	0.87541
	22.27	35	0.86766
	20	36.9	0.86046
	17.05	40	0.85322
	15	42.66	0.84682
	13.47	45	0.83984
160.5	38.95	35	0.99540
	29.82	40	0.98697
	25	43.72	0.98640
	23.56	45	0.98249
	20	48.8	0.97819
	15	56.43	0.96224

The impact under varying coefficients of friction

In addition to adjusting E_m, v and M, improvements can be made by adjusting µ to achieve a more uniform density distribution and higher relative density. Although friction is the primary cause of uneven density distribution, in many cases, this unevenness can be reduced by adjusting the friction between the powder and the mold. Therefore, studying the effect of different values of µ on the compaction densification process is beneficial for improving the powder metallurgy pressing process and achieving high performance alloy products^33,34. In this section, the influence of varying µ is examined while keeping E_m = 149.2 J/g, M = 20 kg, and v = 47.1 mm/s constant. The µ are selected as 0.2, 0.4, and 0.6 to investigate the density variation during the HVC process. As shown in Fig. 9, as the friction coefficient increases, the relative density of the green body decreases from 0.97038 at µ = 0.2 to 0.93888 at µ = 0.4, and further to 0.92934 at µ = 0.6 (Fig. 10(a)). Additionally, by observing the changes in sidewall friction and kinetic energy at different time intervals for varying µ values, it is evident that the sidewall friction increases with the increase in µ (Fig. 10(b)). The kinetic energy shows minimal variation for different µ during the 0–4 ms compaction period. However, around the 4–9 ms mark, the kinetic energy for µ = 0.2 consistently remains higher than that for µ = 0.4 and µ = 0.6 (Fig. 10(c)). The reason for this is that during the downward transfer of kinetic energy, friction between the particles and between the particles and the sidewalls dissipates some of the energy, hindering its transmission and consequently affecting the relative density of the green body³⁵. Due to the energy dissipation, the kinetic energy cannot be fully transferred from the top to the bottom during the compaction process. As a result, the maximum pressure at the bottom decreases as the µ increases during compaction (Fig. 10(d)).

Fig. 10.

(a) Changes in relative density under different coefficients of friction. (b) Variation of sidewall frictional force over time at different coefficients of friction. (c) Kinetic energy changes over time for varying coefficients of friction. (d) The bottom supporting force at different times under various friction coefficients.

Observing the displacement contour maps along the Z and Y axes for different µ (Fig. 11), it can be seen that as the µ increases, the maximum displacement along the Z axis decreases from 0.2768 mm to 0.2634 mm (Fig. 11(a)). Similarly, the maximum displacement along the Y axis decreases from 0.05206 mm to 0.04449 mm (Fig. 11(b)). Examining the equivalent plastic strain contours of the compacted green body after pressing under different µ at the same E_m (Fig. 12), it is observed that a smaller value of µ is more favorable for particle deformation and force transfer form top to bottom during the compaction process. Comparing the equivalent plastic strain maps for µ = 0.2, 0.4, and 0.6, the plastic strain and the degree of force transfer are notably better at µ = 0.2 than at µ = 0.4 and µ = 0.6. From the perspective of the uniformity of the green body, the deformation at µ = 0.2 is more uniform than at µ = 0.4. Although µ = 0.6 also shows a relatively uniform deformation, the force transfer is significantly lower than at both µ = 0.2 and µ = 0.4. This observation directly supports the hypothesis proposed in Sect. "The densification process and dynamic mechanical responses during HVC", which suggests that friction between the sino mold and the powder, as well as between individual powder particles, consumes a portion of the applied force, thereby affecting the uniformity of the compact density. An increase in the friction coefficient leads to higher frictional forces between the sidewalls and the particles, as well as between individual particles, resulting in the dissipation of kinetic energy. Therefore, in practical production, an appropriate amount of lubricant can be added based on the characteristics of the particles to reduce µ without affecting the sintering process. This reduction in friction will promote the flow and deformation of the alloy powder during compaction, improve the transmission of force, and ultimately enhance the relative density and uniformity of the compacted green body.

Fig. 11.

(a) Movement of powder particles along the Z axis under different friction coefficients.(b) Movement of powder particles along the Y axis under different friction coefficients.

Fig. 12.

Equivalent plastic strain diagrams of pressed. blanks after pressing at different µ under the same E_m.

Conclusions

Through simulations of HVC of 2024 Al alloy powder using MPFEM, it was found that this method accurately and realistically captures the displacement and deformation of the powder during the compaction process. It allows for monitoring the variations in particle motion, energy, velocity, force, and relative density at different time intervals, making it an effective approach for studying powder metallurgy processes. This paper investigates the effects of E_m, M, compaction velocity and µ on the relative density of the 2024 Al alloy compact. The following conclusions were drawn:

(1) Increasing E_m can significantly enhance the relative density of the 2024 Al alloy green body. With µ = 0.2 and M = 15 kg, E_m within the range of 45.9 to 173.3 J/g can elevate the relative density of the 2024 Al alloy powder from 0.72312 to 0.97193.

(2) The enhancement of powder densification is not only influenced by the E_m but also closely related to the hammer mass and compaction velocity. Increasing the hammer mass or the compaction velocity both contribute to a higher relative density. However, under the same E_m, the hammer mass has a greater effect on the green body’s relative density than the compaction velocity.

(3) Reducing the µ helps minimize kinetic energy loss, promoting the flow of alloy powder and the transmission of force. This facilitates a more uniform and efficient transfer of force to the bottom, thereby enhancing the homogenization and relative density of the green body. At E_m of 149.2 J/g, hammer mass of 20 kg and compaction velocity of 47.1 mm/s, reducing the µ increases the relative density of the green compacts from 0.92934 at µ = 0.6 to 0.93888 at µ = 0.4, and then to 0.97038 at µ = 0.2.

Author contributions

All co-authors contributed to the research. Xianjie Yuan, Xuanhui Qu, Haiqing Yin conceived the experimental idea and designed the methodology. Yirui Zhang verified the experimental design, analysed the data and wrote the first draft of the paper. Yuanpan Chen contributed to the revision and layout of the draft. Xianjie Yuan, Zhenwei Yan, Zaiqiang Feng and Zhaojun Tan reviewed and revised the data and the first draft. Xianjie Yuan, Zhenwei Yan, Zaiqiang Feng and Zhaojun Tan reviewed and revised the data and the first draft.

Data availability

Data are contained within the article.

Declarations

Competing interests

The authors declare no competing interests.