Multi-particle Finite Element Method Research Articles

MPFEM investigation on densification and mechanical structures during ferrous powder compaction

Metal powder compaction is a crucial process in powder metallurgy, significantly affecting the final properties of compacts. However, the quantitative characteristics of multi-scale mechanical structures and the microscopic densification behavior, taking into account the influence of friction conditions, remain unclear. This study utilises a two-dimensional multi-particle finite element method to analyse the ferrous powder compaction. The evolution of powder densification, powder deformation and multi-scale mechanical behaviour under different friction coefficient conditions are analyzed quantitatively and qualitatively. Results reveal that powder densification occurs in distinct stages, with lower friction coefficients promoting greater powder densification, as observed from relative density and coordination number. Additionally, as the axial strain increases, plastic strain gradually rises whilst roundness decreases. Higher friction coefficients are associated with higher equivalent plastic strain but lower powder roundness. The Von Mises stress exhibits different stages of increase with the increment of axial strain. Powders with lower friction coefficients exhibit lower levels of Von Mises stress. As axial strain increases, the number, length, strength and direction coefficient of force chains undergo different evolution processes. Force chains exhibit longer length, fewer numbers, lower strength and lower direction coefficients at lower friction coefficients.

Synergistic densification mechanism of irregular Ti powder during CIP: 3D MPFEM simulation with real-shape particles

Achieving high green density is essential for ensuring the mechanical properties of powder metallurgy workpieces. However, the densification behavior of irregular ductile powders remains unclear due to oversimplification in current numerical simulations. To address this, a three-dimensional multi-particle finite element method model incorporating realistic powder morphology, size distribution, and stacking structure is constructed. It is found that a pivotal motion-deformation synergistic stage exists between the conventional particle rearrangement and elastic–plastic deformation stages. In this stage, plastic deformation is driven by the spheroidization of coarse powders, whereas the resulting vacancies in the stacking structure facilitate slight particle motion. Thereafter, plastic deformation is dominated by the flattening of fine particles, and the pore-filling capacity decreases due to the reduction in non-contact surface area. This synergistic and complementary interaction between the spheroidization of coarse powders and the flattening of fine powders enhances mechanical interlocking and promotes micropore closure. As a result, the micropores exhibit a tendency of downsizing and homogenization, substantially boosting the potential for achieving full densification during sintering. Based on these findings, a method for determining the optimal forming pressure is proposed, considering the manufacturing costs of powder compacts and the characteristics of the micropores in both green and sintered bodies.

Numerical Analysis of Powder Compaction and Tensile Test by Using Multi Particle Finite Element Method

Numerical Analysis of Powder Compaction and Tensile Test by Using Multi Particle Finite Element Method

The mesoscale mechanics of compacted ductile powders under shear and tensile loads

A discrete numerical analysis of the yield and damage properties associated with a cohesive granular system composed of ductile particles is hereby presented. Such a modelling approach aims at better understanding damage mechanisms which are often encountered during the powder compaction process, widely used in the metallurgical and pharmaceutical fields. The analysis was based on the micromechanical modelling of an idealised granular system in the framework of the multi-particle finite element method, in which particle deformation was fully taken into account. An adhesive interaction law, presented in Audry et al. (2024), was used in the purpose of estimating the averaged mechanical properties associated with the modelled elementary volume. The focus was put on tensile and highly deviatoric loadings, which are usually related to the failure of powder compacts. The specific contact area developed through inter-particles contacts was used as an indicator of the mechanical strength of the elementary volume. Threshold surfaces corresponding to yielding and contact decohesion mechanisms were plotted in the stress space.

Numerical simulation study on hot pressing of ceramic/metal powders

This study utilizes the multi-particle finite element method (MPFEM) to establish 2D and 3D hot pressing models for particle-reinforced aluminum matrix composites. The hot pressing of 6061Al powder and 10 % volume fraction SiCp/6061Al composite powder are simulated under a temperature range of 430–510 °C and pressures ranging from 15 to 30 MPa. The densification mechanism of the composites is elucidated by analyzing the evolution of density and microscopic particle behavior. The analysis reveals that elevating both the pressing temperature and pressure effectively increases the relative density of the powders, with the maximum growth rate occurring at 25 MPa. Notably, the barrier effect created by SiC particles in the 6061Al matrix restricts the plastic deformation and flow of matrix particles, leading to a lower final relative density for the composite powder compared to pure 6061Al powder. Microscopic observations indicate that particle rearrangement dominates in the initial pressing stage, while plastic deformation and particle flow become crucial factors for enhancing relative density in the later stage. Further stress-strain analysis demonstrates that 6061Al particles effectively fill pores through plastic deformation, resulting in stress concentration primarily on the harder SiC particles.

Particulate scale MPFEM modeling on heat transfer of ni-based tungsten carbide composite coating

In this article, the effect of WC (Tungsten carbide) content on the macroscopic as well as microscopic temperature evolution patterns of nickel-based coatings was analyzed from the particle scale using the multi-particle finite element (MPFEM) method. The results show that the coating temperature decreases gradually in the radial direction and increases and then decreases in the axial direction for different WC contents. When the heat transfer time is ≤ 1 ms, the lower the content of WC particles in the coating and when arranged in structure B (random loose-packed) helps to improve the high temperature resistance of the coating, and when the heat transfer time is > 1 ms, the higher the content of WC particles in the coating and when arranged in structure A (random close-packed), it helps to improve the high temperature resistance of the coating.

Mesoscale mechanical models for active materials in lithium-ion batteries using the multi-particle finite element method

The stability and mechanical integrity of electrode active materials have a significant impact on the safety and performance of lithium-ion batteries (LIBs). The study of mechanical properties of active materials is crucial for the safety design of batteries. Researchers have conducted several models for describing the mechanical behavior of active materials. However, an accurate mechanical model that can reflect the packing structure of active particles and achieve the multiscale mechanical analysis of active materials is still lacking. To bridge this gap, a three-dimensional (3D) mesoscopic model based on the multi-particle finite element method (MPFEM) is proposed in the present study. The numerical simulation results show that the established model is in good agreement with the experimental results for the description of the compression behavior of the active material. Based on the model, the effects of various factors on the mechanical behavior of the active materials are analyzed. The results deepen the understanding of the multiscale mechanical behavior of anode active materials and provide fundamental insights for the future development of safety design for LIBs.

Study on Compressibility According to Mixing Ratio and Milling Time of Fe-6.5wt.%Si.

Recently, researchers have focused on improving motor performance and efficiency. To manufacture motors with performance and efficiency higher than those of motors manufactured through the additive process, compressibility verification through the parameter control of soft magnetic composites (SMCs) is essential. To this end, this study aims to select suitable powders for manufacturing high-performance, high-efficiency motors by exploring powder mixing ratios and milling times. Through physical property tests, the optimal mixing ratio is predicted using the Multi-Particle Finite Element Method (MPFEM) and powder compression molding analysis, and compressibility is predicted in view of the influence of a change in particle size as a function of the powder mixing ratio and milling time. In addition, based on the result of a comparative analysis of density through experiments and an analysis of internal defects through SEM, a 50:50 mixing ratio of hybrid atomizing and gas atomizing powders milled for 3 h provided the best compressibility. Therefore, the use of SMC cores fabricated using powder compression molding is expected to improve motor performance and efficiency.

Metaheuristic Optimization of Powder Size Distribution in Powder Forming Process Using Multi-Particle Finite Element Method Coupled with Artificial Neural Network and Genetic Algorithm

Metaheuristic Optimization of Powder Size Distribution in Powder Forming Process Using Multi-Particle Finite Element Method Coupled with Artificial Neural Network and Genetic Algorithm

Laser shock dynamic compaction of aluminum–copper (Al–Cu) composite metal powder

Laser impact dynamic compaction experiments and 2D multi-particle finite element method (MPFEM) simulations were carried out on aluminum–copper (Al–Cu) binary-based composite powders. Al–Cu compacts with densities of about 95% were successfully prepared at the maximum laser energy of 1.8 J. Research trends indicate that higher power lasers could nearly achieve the theoretical densities. Analysis of the influence laws of laser energy and copper powder mass fraction on the densities of Al–Cu compacts was carried out, and the effects of microstructure and microhardness of Al–Cu compacts on their mechanical properties were investigated, as well as the stresses and velocities in the dynamic compaction process of Al–Cu composite powders were analyzed. The results showed that the relative densities of composite powder compacts of Al-5 wt%Cu gradually exceeded those of Al-10 wt%Cu and Al-15 wt%Cu with the increase of laser energy. In laser impact dynamic compaction the mechanism of inter-particle joining was solid-state press-welding, and the increase in the hardness of the Al–Cu compacts could be attributed to the inherent hardness of the hard particles. The upper particles have a localized maximum velocity of more than 300 m/s, which met the explosion welding velocity, thus localized cold welding occurred and contributed to the inter-particle connection.

Comparison between periodic and non-periodic boundary conditions in the multi-particle finite element modelling of ductile powders

In recent years, the multi-particle finite element method (MPFEM) has demonstrated its suitability for the micromechanical modelling of granular systems made up of highly deformable particles. This method combines the advantages of the finite element method to compute particles’ deformations and of the discrete element method to simulate particles’ interactions. Being computationally expensive, its main drawback is the limitation of the number of particles which can be included in a simulation. However, using a multi-scale approach, it is possible to deduce mesoscopic material properties from the simulation of a relatively small number of particles within an elementary volume, through appropriate averaging techniques. Such simulations are significantly influenced by the boundary conditions (BCs) applied. Periodic BCs are commonly admitted to be the most accurate. However, they are technically rather difficult to implement in the MPFEM because of the multiple contacts which need to be handled in the model. As a result, simplified BCs involving for example, rigid walls, remain used. This study analyses the effect of different types of BCs on the simulated mechanical response of a numerical granular sample, under quasi-static loading. Two different techniques for implementing full or simplified periodic BCs, introduced by Schmidt et al. [1] and Loidolt et al. [2], respectively, were compared with simpler, non-periodic BCs. In the comparison, the same initial microstructure was used; it consisted of an assembly of 50 spherical particles with a periodic topology. The results suggest that considering the additional computational cost induced by the implementation of multi-point constraints, the advantage brought by periodic BCs is relatively limited. The study also highlights the differences between BC types and provides interpretations relative to the particularities of the numerical method used.

Laser shock dynamic compaction of tungsten carbide reinforced-aluminum matrix (WCp/Al) composites

Laser impact can generate high-strain impact loads. On this basis, a laser impact dynamic compaction (DC) of the tungsten carbide particles (WCp)/Al composite powder with large differences in stiffness and plasticity was performed in this study. Then, the influences of laser energy and WCp content on relative density (actual density/theoretical density), mechanical properties, and microstructure of the pressed billet surface, damage surface, and cross section of the Al matrix composites (WCp/Al) were analyzed. Along with the analysis of the high-strain compaction process, the spread of shock wave process in the compacted billets and the densification behavior of the powder compacts were evaluated via 2D multiparticle finite element method (MPFEM). Results showed that relative density of the compacted billets tended to increase and then decrease with the rise in of WCp content (5%, 10%, 15%, and 20%). In the DC of the composite powder by the laser impact, the pore filling was mainly filled by plastic deformation of the relatively soft Al particles, and the hard WCp did not undergo plastic deformation due to its high strength. A composite powder compact with high relative density was successfully prepared with a WCp content of 10% at 1800 mJ of laser energy. The eventual relative density reached 97.72%, and the overall microhardness increased by approximately 23.25%. The 2D MPFEM simulations could sufficiently predict the dynamic mechanical response in the DC by the laser impact and depict the strain and stress variation patterns at the particle-scale level. Finally, the densification mechanism of the composite powder billets was investigated. The simulation results pertaining to the relationship between the final laser energy and relative density were in significant agreement with the experimental results.

Three-dimensional multiparticle finite element simulation of dynamic compaction of copper powder by laser shock

A three-dimensional multiparticle finite element method(3D MPFEM) model of laser shock compaction powder was established, and the forming process and densification mechanism of dynamic compaction were studied. The effects of the laser peak pressure(1–5 GPa) on the powder density was studied. The compaction density increased with the laser peak pressure and reached the highest at 5 GPa. A comparison of the different energies of the system revealed that the increase in powder temperature was mainly due to the plastic deformation. In the process of powder springback, large pressure can induce rebound, and the powder may produce an interparticle separation phenomenon due to the difference in particle velocities in different layers. Analysis of the densification process of the inner particles, revealed that the upper layer particles undergo first plastic deformation, and then the second plastic deformation occurs due to the inertia effect, which contributes to the improvement of the powder density. • 3D MPFEM was used to simulate the laser shock powder dynamic compaction process. • Adiabatic temperature rise effect is related to powder plastic deformation. • Laser shock powder has springback phenomenon and large strain rate.

Laser shock dynamic compaction of aluminum powder

Dynamic compaction establishes shock waves that produces a violent dynamic mechanical response in powder. This process can realize the high-density compaction of powder to fabricate the compact of powder metallurgy parts with excellent performance. A new method for dynamic compaction of powder using laser shock on a small scale is proposed. It exhibits the unique advantages of a pulsed laser, such as high strain rate and dynamic shock force, and suitable for micro-part manufacturing. The experiment on the dynamic compaction of spherical aluminum powder was completed under five different laser energies. The effects of laser energy and powder packing state on the mechanical properties of the final compact and Microstructure of the compact, including the upper, failure, and cross section surfaces, were analyzed. Results showed that the mechanical properties of the aluminum compacts gradually improved with the increase of laser energy. The nearly fully dense aluminum compacts were successfully compressed at 1800 mJ laser energy with a final relative density of 99.72%. Moreover, the Microhardness of the compacts improved by approximately 60%. The simulation results using multi-particle finite element method (MPFEM) show that with the propagation of the generated shock wave in the compact, particles had large plastic deformation that filled the pores during the laser shock dynamic compaction of aluminum powder. The simulation and experimental results show that the main connection mechanism of particles is cold welding. The dense packing of powder before compaction could considerably improve the propagation of shock waves, and the initiation and growth of inter-particle cracks were reduced.

Numerical study on the warm compaction and solid-state sintering of TiC/316L composite powders from particulate scale

Powder compaction and sintering are critical stages of powder metallurgy in manufacturing high performance particle reinforced metal matrix composites. In this paper, particulate scale numerical investigations on the warm compaction and solid-state sintering of TiC/316L composite powders with different particle size ratios (PSRs, R316L/RTiC) and TiC contents were performed using multi-particle finite element method (MPFEM) in two dimensions. The effects of PSR and TiC content, compaction pressure and temperature, and sintering temperature on the compaction and sintering processes were comprehensively analyzed. On this basis, a variety of macro- and microscopic analyses were conducted to further identify the densification dynamics and mechanisms. The results indicate that green compacts with higher relative density and more uniform stress distribution can be readily achieved by warm compaction. The large-scale plastic deformation of 316L particles caused by the cooperative actions of temperature and pressure is the main densification mechanism in warm compaction. During solid-state sintering, the improvement of relative density is mainly achieved by the vanishing or shrinkage of residual pores along with the growth of sintering necks, accompanied by the deformation of 316L particles. Large displacements of particles mainly occur in contacting areas of adjacent particles. Moreover, the equivalent stress in 316L particles is smaller than that in TiC particles. With the increase of PSR and TiC content, lower relative density of green compacts and sintered parts were obtained and more irregular morphologies of 316L particles can be observed.

A Study of Compaction Densification Behavior of Composite Particles by Multiparticle Finite Element Method

In this paper, 3D particulate scale modelling on the die compaction of DEM generated initial packings of both soft and hard particles was conducted by employing the multiparticle finite element method (MPFEM). The effects of initial packing structures as well as the compaction pressure on the macroscopic and microscopic properties of the whole powder mass and local structures were investigated. In addition, corresponding physical experiments were carried out for model validation. The results show that the compact obtained from the initial dense packing under vibration undergoes yielding stage earlier than that with natural initial packing (without vibration), and the relative density is much higher. Pores that are significantly smaller and with more uniform size and homogenous stress distribution are observed in the former case. Highest stress regions occur in most cases at a grain boundary with large curvature after deformation. Moreover, the high stress in the central part of both soft and hard particles during compaction is significantly reduced after pressure unloading, reaching a new force balance. In this case, the stress is concentrated mainly at the corners of the deformed particles, which creates the risk of cracking during subsequent sintering at either the contact region between particles or the corners. The numerical results are found to be in good agreement with those from physical experiments, confirming the robustness and reliability of the numerical model used in the simulations.

MPFEM simulation on hot-pressing densification process of SiC particle/6061Al composite powders

A hot-pressed compact with high density and uniform stress plays a decisive role in improving the quality of sintered composites. The multi-particle finite element method was utilized to simulate the hot-pressing densification process of SiC particle (SiCp)/6061Al composite powders with huge differences in stiffness and plasticity. The densification mechanism was revealed at macro and particulate scales. Two- and three-dimensional finite element models were both constructed to investigate the effects of pressing temperature, SiCp content and size ratio of 6061Al and SiCp on the relative density and stress distribution of the powder mass. Simulation results demonstrate that pressing temperature and the content and distribution of SiCp have significant effects on the required pressing pressure, relative density and stress distribution of the compact. Compared with cold compaction, the pressing pressure required for compaction can be reduced by 2–3 times at 390–515 °C. The intermediate particle size ratio of 6061Al and SiCp is beneficial for relatively high relative density and low stress of the compact. The fitting of the simulation results verifies the robustness of the established finite element model.

Understanding die compaction of hollow spheres using the multi-particle finite element method (MPFEM)

Powder compaction is a complex manufacturing process, even though the procedural description is simple. While different methods are used in the literature, it is still challenging to understand the governing principles. It is especially challenging for empirical studies to investigate particle-level interactions. Thus, computational analyses are required for particle-level understanding. A wide range of computational methods has been developed, such as the discrete element method (DEM) and the multi-particle finite element method (MPFEM), to characterize powder compaction at the particle level. However, a limited number of studies in the literature have analyzed powder compaction using the 3D multi-particle finite element method. Historically, these studies focus only on solid particles. The compaction behavior of hollow spheres, common to pharmaceutical spray drying, was investigated both computationally and experimentally. In the computational analysis, two different particle sizes with different shell-thicknesses were examined using the 3D multi-particle finite element method. In the experimental study, polymer hydroxypropyl methylcellulose acetate succinate (HPMCAS) particles spray-dried at two different outlet temperatures (45 °C and 80 °C) were used. The results showed that particle diameter/shell-thickness (d/w) plays an essential role in powder compaction behavior. Regardless of the particle size, reducing shell-thickness reduced the required global axial stress to reach equivalent levels of relative density. However, with a constant ratio of d/w, changes to particle size (d) did not significantly influence the global compaction behavior. Similar results were observed in experimental studies. Simulation results showed that thinner-shell particles yield early in the compaction stage. Additionally, both experimentally and computationally, a spherical hollow particle buckling effect was observed. In summary, this study provides new information on how powder compaction behavior was influenced by particle size and particle shell-thickness.

Modeling and Simulation of RDX Powder Thermo‐Mechanical Response to Drop Impact

AbstractA computational framework to predict the deformation, flow, and compaction of an energetic material (EM) powder subjected to drop impact is discussed. Explicit dynamic finite element analysis was performed to simulate drop‐weight impact tests for comparison with experimental results and to gain insight into the ignition sensitivity of RDX powder. The computations simulated the Thermo‐Mechanical behavior of a thin layer of energetic powder subjected to drop impact to study the dependence of ignition sensitivity on the anvil material properties. By modeling high strength steel and a low strength copper anvil, a direct comparison is made on how energy dissipation within the EM is influenced by anvil properties. A hybrid finite element model is introduced that captures the mesoscale discrete particle nature of the powder response in regions of interest while using a continuum model elsewhere to reduce computational cost. To capture the mesoscale behavior, a multi‐particle finite element method (MPFEM) approach was used in selected regions in the hybrid model. Powder temperatures were computed to understand how the striker impact energy is dissipated by plasticity and friction into localized heating of the EM that triggers the ignition. Munition designers can use such a framework to study the low‐level impact sensitivity of munitions in a computationally efficient manner. Results of the simulation using the hybrid model suggest that copper anvil undergoes plastic deformation which absorbs a significant portion of the impact energy reducing the energy dissipated within the EM and suppressing ignition.

Multi-particle FEM modeling on hot isostatic pressing of Ti6Al4V powders

The hot isostatic pressing (HIP) of Ti6Al4V powders was systematically simulated in two dimensions by using multi-particle finite element method (MPFEM) from particulate scale. Different initial packing structures formed by three kinds of powders (i.e. mono-sized powder, binary powder, and powder with normal size distribution) were firstly constructed. Subsequently, the effects of capsule shape, HIP procedure, temperature, pressure, as well as the powder type on the densification behavior of different Ti6Al4V compacts were investigated and discussed. The macroscopic property like relative density and various microscopic properties such as coordination number, stress/strain distributions of capsule and particles, deformation degree, pore filling behavior, densification mechanism and so on were quantitatively characterized. The results indicate that a larger aspect ratio (AR) is more likely to induce local order packing structure during particle rearrangement, and the proportion of powder particles with more regular deformation of Ti6Al4V compact increases after HIP. The total strain energy and deformation mechanisms of Ti6Al4V compacts are quite different with different HIP procedures. With the rise of temperature, the equivalent total strain of both the capsule and the particles became larger and the equivalent Von Mises stress decreased after HIP. In addition, Ti6Al4V powders with different size ratios will affect the performance of the compact in HIP process. The larger the particle size, the smaller the strain acting on the particle, the closer the roundness of the particle to 1. The Ti6Al4V compacts with different particle size distributions were found to exhibit different densification mechanisms. For packing of mono-sized powder, particle rearrangement destroyed bridging structure and large pores so as to accelerate the densification process. While for the Ti6Al4V compacts formed by binary powder or the powder with normal size distribution, the densification mechanism can be inferred to the extreme deformation of small particles promoting relative rigid motion of large particles.