Compaction simulation of crystalline nano-powders under cold compaction process with molecular dynamics analysis

Highlights

• The cold compaction process of metal nano-powders is modeled by MD method.

• The compaction of nano-powders is studied for nickel and aluminum nano-particles.

• Simulations are performed for various compaction velocities and temperatures.

• Mechanical behavior of nano-powders is studied at different relative densities.

• 3–stages of nano-powder die-pressing are defined according to compaction velocity.

Abstract

In this paper, the uniaxial cold compaction process of metal nano-powders is numerically analyzed through the Molecular Dynamics (MD) method. The nano-powders consist of nickel and aluminum nano-particles in the pure and mixed forms with distinctive contributions. The numerical simulation is performed using the different number of nano-particles, mixing ratios of Ni and Al nano-particles, compaction velocities, and ambient temperatures in the canonical ensemble until the full-dense condition is achieved. In the MD analysis, the inter-atomic interaction between metal nano-particles is modeled by the many-body EAM potential, and the interaction between frictionless rigid die-walls and metal nano-particles is modeled by the pairwise Lennard-Jones inter-atomic potential. The mechanical behavior of metal nano-powders under the compaction process is numerically studied by plotting the relative density–pressure, mean stress-strain, and material characteristics–strain curves. Moreover, the nano-powder behavior is visualized by means of the centro-symmetry contour at various stages of the forming process. Finally, the evolution of top-punch velocity on the final stage of compaction process is studied by plotting the compaction pressure against the total energy at various compaction velocities.

Introduction

Powder metallurgy is proposed as a method of producing the near-to-net shape industrial components from the loose powders under the pressure. In general, the fundamental step in the powder metallurgy technique is the powder compaction process, in which by implementing the pressure, the components with desired characteristics are manufactured. Commonly, the powder compaction process can be categorized into two distinct approaches; the cold die compaction and the hot isostatic pressing. In the cold die compaction, the loose powders are stuck together under the pressure and a dense body with the desired shape, known as the green body, is extracted; although a sintering process is usually implemented as post-processing to obtain the compressed green body. In the hot isostatic pressing, the hydrostatic pressure is exerted simultaneously with the heat on the loose powders that results in an almost homogenous compressed body with the desired shape [1]. Some of the notable privileges of the powder metallurgy method are the precision, cost-effectiveness, capability of manufacturing complex components, minimizing the machining requisite, applicable to a wide variety of metals, alloys, and metal matrix composites. One of the remarkable advantages of this method is the facility in producing the metal matrix composites by mixing various types of powder materials to obtain the required characteristics [2,3]. This capability of powder metallurgy enables to combine various ratios of different metal powders and fabricate the products with variant mechanical features. Basically, the forming process of powders depends on different types of parameters, such as powder particle specifications, compaction die geometry, compaction velocity, and ambient temperature. Since in the powder metallurgy the components are produced by compacting a set of fine powder particles, the forming process is considerably dependent on the structural features, e.g. the hardness, plastic behavior, and surface characteristics, and the geometrical features of powder particles, e.g. the particle size, shape, and distribution. Obviously, due to the vast number of impressive parameters on the powder compaction process, the experimental investigation of all parameters is not affordable. On the other hand, the numerical simulations can be employed as a feasible alternative for parametric investigation of the powder compaction process [4].

In view of the size of powder particles, the numerical simulation of the powder compaction process can be accomplished in three distinct scales; the macro, micro, and nano-scale levels. Traditionally, the discrete (micro-scale) and continuum (macro-scale) methods have been used to analyze the powder compaction process [[5], [6], [7], [8], [9], [10], [11], [12], [13], [14]]. In the discrete method, powder materials are assumed as a collection of particles in contact with each other, and simulation is performed by the discrete-element method (DEM). In this approach, the deformation of powder material is simulated by definition of the inter-particle and particle-die forces [5,6]; however, there are several simplifying assumptions in the DEM method to alleviate the problem complexity and computational cost [[7], [8], [9]]. In the continuum method, the porous domain of powders is conceived as an integrated substance and the finite-element method (FEM) is employed for simulation of the compaction process. In this method, the nonlinear behavior and work-hardening of powder material, large deformation, large strain, and friction between the powder and die must be taken into the numerical simulation. Moreover, an appropriate plasticity model is required in the analysis of the powder forming process by FEM [[10], [11], [12], [13], [14]]. Recently, numerous studies have been carried out to study the compaction of particles at the nano-scale level. In modeling the nano-particles, the ratio of surface to volume of particles is significantly considerable in comparison to the micro- or macro-scale particles, in a way that the nano-particles exhibit distinguished mechanical behavior [15]. Thus, it can be expected that the behavior of nano-particles during the compaction process becomes noticeably different from the behavior of micro-scale particles that highlights the necessity of investigation of the nano-powders compaction process, individually. In this regard, Saha et al. [16] experimentally investigated the size effect of nano-particles as well as the morphology of nano-powders during the compaction process. They presented that the compaction pressure increases as the particle size of nano-powders decreases. Koruza et al. [17] studied the behavior of NaNbO3 nano-powder during the compaction process and highlighted that the compaction of nano-powders leads to the dense green products than the compaction of submicron powders.

There are several numerical simulations reported in the literature for modeling the compaction process of nano-powders. Boltachev et al. [18] modeled the quasi-static uniaxial compaction of nano-powders by employing the granular dynamics method. They investigated the efficiency of particle size and cell size in the quasi-static compaction of nano-powders [19]. Baric et al. [20] presented a discrete element method based on the micro-mechanical model to simulate the densification of nano-particle films under uniaxial and hydrostatic pressing; it was shown that the proposed model can predict the density, densification rate, densification mechanisms and micro-structural characteristics of the nano-particles. Rojek et al. [21] modeled the densification of nano-particles by applying the discrete element method (DEM). One of the most popular techniques proposed by researches to study the behavior of nano-particles is based on the molecular dynamics (MD) method [[22], [23], [24], [25], [26], [27]]. Henz et al. [22,23] performed the MD analysis to obtain the energetic reaction of nickel and aluminum nano-particles. They proposed two distinct models for Ni and Al nano-particles, including the separated and coated nano-particles, and investigated the dependency of reaction time and adiabatic reaction temperature on the particle size. Zhang et al. [24] studied the compaction behavior of various particle sizes, temperatures, and packing arrangements by applying the MD analysis, and deduced that these parameters can affect the mechanical properties of the compacted components. Stone et al. [25] determined the coefficients of inter-particle friction and presented their relations with the particle size and contact angle using the uniaxial compression. Kiselev [26,27] evaluated the external compressive force on the spherical piston comprised of copper and copper‑molybdenum mixture nano-particles using the MD analysis. They presented that because of the surface traction, the copper nano-particles fill the voids and the crystalline structures change into amorphous forms under a small movement of the piston. A comprehensive overview of the MD technique along with its application on the compaction of nano-particles was presented by Tian [28].

Because of the highly nonlinear behavior of nano-particles and structural complexity of nano-powders during the compaction process, it is required to develop a powerful technique in modeling the compaction process of nano-crystalline metals. There are several parameters, such as the nano-particles characteristics, ambient temperature, and compaction velocity, which can significantly influence the compaction process and the final green product; so it is important to perform a comprehensive parametric study over the various impressive parameters. In this study, the molecular dynamics method is employed to study the forming of nano-particles in the rigid surrounding die-walls under the die-pressing process. The nano-crystalline powders consist of nickel, as a brittle metal, and aluminum, as a ductile metal, in the pure and mixed forms. In order to investigate the compaction behavior of combined Ni/Al nano-particles, numerical simulations are performed with different mixing ratios of Ni and Al nano-particles. The MD analysis of the forming process is accomplished by imposing the uniaxial compression on a set of nano-particles at the constant temperature. Moreover, an extensive investigation is fulfilled over some effectual parameters of the forming process, i.e. the number of nano-particles, the mixing ratios, and the compaction velocity. The plan of the paper is as follows; in Section 2, the molecular dynamics method together with the details of numerical simulations are elucidated. The geometrical characteristics of specimens as well as the interatomic potential and the procedure of modeling are described in this section. In Section 3, the results of numerical simulation are presented and the effects of different parameters on the forming process are discussed. Moreover, the influence of various parameters on the nano-powder compaction process is investigated by evolutions of the mean stress-strain, relative density – pressure, nano-powders characteristic – strain, and nano-powders compaction pressure – total energy at different compaction velocities. Finally, some concluding remarks are given in Section 4.