Molecular Dynamics Simulation of Temperature and Ti Volume Fraction on Compressive Properties of Ti/Al Layered Composites

Abstract

Based on molecular dynamics simulation, this work investigated the influences of temperature and Ti volume fractions on the compressive deformation of Ti/Al layered composites. According to the simulation, the initial dislocations during compression are concentrated on the Al side, dominated by 1/6<211> and 1/6<112> dislocations, and the 1/2<101> and 1/6<211> dislocations cross the Ti/Al interface from the Al side to the Ti side. It is found that an increase in temperature helps dislocations to form at lower strains, which leads to a decrease in the compressive strength and an increase in the plasticity of the structure. As expected, the Ti volume fraction has a significant impact on the compressive properties of Ti/Al layered composites, and the compressive strength of the material increases with the increase in the Ti volume fraction. At temperatures above 400 K, the reduction rate of compressive strength becomes smaller, which is due to the formation of new ordered metal compounds between Ti and Al. When the volume fraction of Ti is lower than that of Al, plastic deformation mainly occurs on the Ti side, dominated by 1/6<112> dislocations. In contrast, the types of dislocations across the Ti/Al interface and on the Al side are dominated by 1/2<110> and 1/2<011>. When the Ti volume fraction becomes comparable with that of Al, the plastic deformation is transferred from the Ti side to the Al side, and the plasticity of the sample decreases. The optimal compressive properties of Ti/Al layered composites are observed at a Ti volume fraction of 40%, which provides guidance for the structural design of Ti/Al layered composites.

1. Introduction

Ti/Al layered composites have a wide range of applications in aerospace, automotive manufacturing, and other fields due to their light weight, high strength, and good high-temperature performance [1,2,3]. To facilitate these engineering implementations, it is crucial to investigate the mechanical properties and formability of Ti/Al layered composites. The study of the compressive behavior of materials helps to evaluate the environmental adaptability and long-term stability of materials [4,5,6], which is essential to ensure structural integrity and safety. Different from a monolayer structure, the existence of an interface in Ti/Al layered composite plate greatly influences its mechanical behavior, especially the plastic deformations.

The temperature and the volume fraction of Ti are key parameters affecting the mechanical properties of Ti/Al layered composites. At present, the performance studies of Ti/Al layered composites mostly rely on finite element simulation and experimental analysis (such as thermal pressure preparation process, hot rolling process, explosion welding and other preparation processes). A different lamellar structure will have an impact on the performance of the material, whereas there are seldom theoretical studies on the design of a Ti/Al layered structure. For example, Zhao et al. [7] investigate the effect of temperature on the forming performance of Ti/Al layered composites using numerical and experimental methods. The results indicated that the maximum limit drawing ratio at 200 °C is consistent with the minimum thickness reduction. The safe forming area narrows with the increase in the drawing ratio. Chen et al. [8] investigated the effect of the wavy profile mechanical properties of Ti/Al layered composites using experiments and finite element simulations. They found wavy interfaces formed between the Al and Ti layers. Similar strength and ductility levels were obtained for Ti/Al layered composites with straight and wavy interfaces when a proper rolling reduction and annealing were applied. Dong et al. [9] investigated the effect of the volume fraction of Ti on the organizational evolution and thermal properties of Ti/Al layered composites and found that the thermal conductivity, thermal diffusivity, coefficient of thermal expansion, and specific heat capacity of Ti/Al layered composites decreased with increasing Ti content. Dong et al. [10] investigated the effect of the Ti volume fraction on the microstructure and mechanical properties of Ti/Al₃Ti layered composites. They found that samples with a volume fraction of 65% Ti exhibited optimum strength, specific strength, and destructive strain when compressed parallel to the layer. However, at the atomic scale, the effects on the properties of Ti/Al layered composites are poorly studied.

Recently, molecular dynamics (MD) simulation has emerged as an important method to study the mechanical behavior of composite interfaces at the nanoscale. Bian et al. [11] investigated the tensile and compressive deformation mechanisms of Cu/Al₂Cu/Al layered composites by MD simulations and observed the asymmetrical characteristics between tensile and compressive deformation. Polyakova et al. [12] studied the effect of atomic interdiffusion at the Al/Cu interface on the mechanical properties of Al/Cu composites and found that Cu atoms diffuse into Al blocks more readily than Al atoms diffuse into Cu blocks. Li et al. [13] investigated the mechanical properties of graphene cement composites and found that the addition of graphene in the x and z directions increased the tensile strength of G/C-S-H in all three directions, whereas the addition of graphene in the y direction decreased the tensile strength of G/C-S-H. Went et al. [14] investigated the compression strengthening mechanism of nanolaminated graphene/Cu composites and found that the stress–strain curve of the sample went through three states, i.e., the elastic state, the plastic strengthening state, and the plastic flow state.

Evidently, MD simulations can reveal the plastic deformation behavior of layered composites at the atomic level, which can provide guidance for the structural design of Ti/Al layered composites. To this end, this works aims to probe the elastic and plastic deformation of Ti/Al layered composites during compression with varying temperature and structural parameters.

2. Computational and Simulation Methods

Ti/Al layered composites were modeled using Atomsk; Ti/Al layered composites were modeled to include mainly single-crystal-oriented Ti and Al. At room temperature, pure titanium had a hexagonal close-packed (HCP) lattice structure with a space group of P63/mmc and lattice constants of a = 2.95 Å and c = 4.68 Å. [15] Al had a face centered cubic lattice with a lattice constant of a = 4.05 Å. The Ti/Al layered composite model is shown in Figure 1. The x-axis, y-axis, and z-axis of the Al layer corresponded to the [$1\stackrel{-}{1}0$] [$11\stackrel{-}{2}$] and [111] crystal directions. The x-axis, y-axis, and z-axis of the Ti layer corresponded to [$1\stackrel{-}{1}00$] [$11\stackrel{-}{2}0$] and [0001]. The model size was 79.65 Å (x) × 40.8764 Å (y) × 113.24784 Å (z), with a total of 20,736 atoms. The size of the Ti model was 79.65 Å (x) × 40.8764 Å × 57.12944 Å (z). The size of the Al model was 79.65 Å (x) × 40.8764 Å × 56.1184 Å (z). The initial volume fraction of Ti was set as 50%.

The mismatch between Ti and Al in the z-direction is less than 3% at the interface. There is an initial gap of 1 Å between the Ti and Al samples in order to reduce the strong interaction force between the two atoms at the interface. The second nearest neighbor modification embedded atom (2NN-MEAM) interatomic potential [16] was applied to describe the atomic interactions between Ti and Al. The Ti/Al layered composites were firstly modeled using Atomsk software (https://atomsk.univ-lille.fr/) and imported into the open-source molecular dynamics package LAMMPS [17] for simulation. The time step was set to 1 fs, and the periodic boundary conditions were applied in the three directions of the model. The Conjugate Gradient (CG) algorithm was employed to minimize the energy of the model. Then, the model was relaxed for 20 ps to reach the dynamic equilibrium of the lowest energy state under the isothermal–isobaric (NPT) ensemble. Finally, the model was deformed with a constant compressive strain of 0.0002 ps⁻¹ under the NPT ensemble. The results were analyzed using the visualization software OVITO (https://www.ovito.org/) [18].

3. Results and Discussion

3.1. Modeling of Compressive Deformation Behavior of Ti/Al Layered Composite

Figure 2 shows the stress–strain curve of the Ti/Al layered composite under compressive deformation in the z-axis direction at 300 K. At the beginning of the deformation, the compressive stress of the Ti/Al layered composite increases almost linearly with the increase in strain, i.e., elastic deformation. When the strain increases to 0.11, the tensile stress reaches its maximum threshold (~15.16 GPa); thereafter, it decreases sharply and the model enters into the plastic deformation stage.

The compressive evolution of the atomic structure of Ti/Al layered composites at 300 K is shown in Figure 3, which is colored according to the common nearest neighbor atomic analysis [19]. At the beginning of the compression deformation, both Ti and Al layers are in the elastic deformation stage, and the lattice size is changed, but the crystal structure remains unchanged. At this stage, the atoms of the Ti/Al laminate composite are well aligned and no dislocations are generated. When the strain increases further, local disordered atoms appear in the Al layer. Afterwards, the disordered atoms aggregate under stress and plastic deformation occurs, with the initial plastic deformation taking the lead on the Al side. With the increase in strain, the plastic deformation starts to cross the interface from the Al side to the Ti side, and slip dislocations start to appear gradually on the Ti side.

To reveal the changes in the type of dislocations occurring in the compressive deformation of Ti/Al layered composites, the dislocation extraction function [20] in the visualization software OVITO is used for the analysis. The evolution of the type of dislocations produced during compression is shown in Figure 4. It is found that 1/6<211> and 1/6<112> dislocations are generated during compression. The dislocations are concentrated on the Al side initially, and the 1/2<101> and 1/6<211> dislocations cross the interface from the Al side to the Ti side.

3.2. Modeling of Temperature Effects on the Compressive Properties of Ti/Al Layered Composites

The yield strength of a bulk sample is affected by several structural factors, such as grain boundaries, voids and impurities. For materials at nanoscale, the existence of these defects will be significantly suppressed. In this work, we focus on the mechanical properties of the Ti/Al layered composites under ideal conditions without structural defects, which serve as the upper limit for experimental measurements [21,22].

The compressive properties of the sample under six different temperatures, including 100, 200, 300, 400, 500, and 600 K, are examined. Figure 5a shows the compressive stress–strain curves of Ti/Al layered composites at different temperatures. In general, the stress–strain curves share a similar profile, while significant differences in yield strength and yield strain are detected. The elastic modulus of the compressive deformation behavior of Ti/Al layered composites at the early stage of compressive deformation increases gradually with decreasing temperature, suggesting that the temperature also impacts the elastic deformation of the model. Such observation aligns with previous works on other nanomaterials, i.e., the higher the temperature, the lower the modulus [23,24]. According to Figure 5b, the sample has a yield strength of 17.48 GPa with a yield strain of 0.12 at 200 K. The yield strength decreases almost linearly with the increase in temperature. However, the reduction rate of compressive strength decreases above the 400 K temperature.

Figure 6 shows the atomic structure evolution of Ti/Al layered composites subjected to compressive loading at different temperatures. It is evident that the increase in temperature causes more disordered atoms to appear in the model, and the initial dislocations nucleate at lower strains. This is reasonable as higher temperature leads to the relative instability of the nanocrystal structure [25,26]. As the strain increases, both Ti and Al deform plastically after the Ti/Al layered composites reach the compressive strength, and the degree of plastic deformation of Al is greater than that of Ti. As plastic deformation occurs at lower strains when the temperature increases, the plastic deformation becomes more and more concentrated on the Al side. In Figure 6, we can also observe that at low temperatures, the HCP structure of Ti and the FCC structure of Al are mainly converted into disordered atomic structures. However, after the temperature reaches 400 K, the FCC structure on the Al side is mainly converted into an ordered HCP structure. This is because at lower temperatures, the diffusion rate of the atoms is relatively smaller, and Ti and Al atoms cannot effectively form ordered intermetallic compounds. Instead, they tend to form disordered solid solutions or mixed atomic arrangements, where the disordered atomic arrangement lacks sufficient energy to migrate to more ordered lattice sites. As the temperature increases, the kinetic energy of the atoms increases, and the diffusion coefficient increases, which promotes the rapid diffusion of Ti and Al atoms between layers. The high temperature provides enough thermal activation energy, allowing atoms to migrate and form more ordered intermetallic compounds [27,28]. The formation of these ordered metal compounds results in a slight increase in the strength of the Ti/Al layered composite, which leads to a decrease in the reduction rate of compressive strength.

Overall, simulation results show that the compressive properties of Ti/Al layered composites are greatly affected by temperature. The ultimate compressive strength of Ti/Al layered composites decreases significantly with increasing temperature, as well as the yield strain.

3.3. Modeling of the Effect of the Ti Volume Fraction on the Compressive Properties of Ti/Al Layered Composites

The Ti/Al layered composites are modeled using Atomsk for three different volume fractions of Ti (25%; 40%; 50%), and the size and parameters of each model are shown in

Table 1. Modeling parameters of Ti/Al layered composites with different Ti volume fractions.

Model Number	1	2	3
Model size ($x\times y\times z$) ${Å}^3$	79.65 × 40.88 × 75.84	79.65 × 40.88 × 94.56	79.65 × 40.88 × 113.25
Ti model size	79.65 × 40.88 × 16.38	79.65 × 40.88 × 37.47	79.65 × 40.88 × 57.13
Al model size	79.65 × 40.88 × 56.12	79.65 × 40.88 × 56.12	79.65 × 40.88 × 56.12
Volume fraction of Ti	25%	40%	50%
Total number of atoms	13,824	17,280	20,736

.

The compressive stress–strain curves of Ti/Al layered composites with different Ti volume fractions are shown in Figure 7a. It is seen that the Ti/Al layered composite with a Ti volume fraction of 25% reaches a compressive strength of 12.75 GPa at the strain ε = 0.12. The Ti/Al layered composite arrives at a compressive strength of 14.08 GPa at the strain ε = 0.13 when the Ti volume fraction is 40%. The Ti/Al laminate composite with a Ti volume fraction of 50% reaches a compressive strength of 15.14 GPa at the strain ε = 0.11. Figure 7b shows the compressive strength versus Ti volume fraction curves for Ti/Al layered composites.

It is obvious that the compressive strength of Ti/Al layered composites increases as the volume fraction of Ti increases. This is reasonable as Ti is harder and stronger than Al; therefore, increasing the volume fraction of Ti results in a significant increase in the compressive strength of Ti/Al layered composites. It is further found that although the compressive strength of Ti/Al layered composites with a 50% Ti volume fraction is greater than that of Ti/Al layered composites with a 40% Ti volume fraction, the strain required to reach the compressive strength is less than that of the Ti/Al layered composites with a 40% Ti volume fraction. This may be due to the difference in the way the Ti/Al layered composite with a Ti volume fraction of 50% deforms plastically in compression compared to the Ti/Al layered composite with a Ti volume fraction of 40%.

Figure 8 shows the atomic structure evolution of Ti/Al layered composites with different Ti volume fractions. It is found that the initial plastic deformation and dislocations of Ti/Al layered composites with Ti volume fractions of 25% and 40% are mainly concentrated on the Ti side after reaching the compressive strength. Figure 3 shows that the initial dislocations and plastic deformation of Ti/Al layered composites with a Ti volume fraction of 50% are mainly concentrated on the Al side. These observations explain different stress–strain curves shown in Figure 7a. Under the applied stress, the deformation of Ti/Al layered composites is always smaller than that of the Al side as Ti has a higher modulus [29,30]. As such, the Al side will exhibit more plastic deformation than the Ti side. However, when the Ti side is too thin, more plastic deformation will be triggered in order to accommodate the strain energy [31]. The interplay between the strain energy and the thickness of the Ti or Al region results in the observation that although the compressive strength of Ti/Al layered composites increases with a higher Ti volume fraction, the sample may exhibit smaller yield strain.

According to Figure 9, the Ti/Al layered composites with Ti volume fractions of 25% and 40% have more dislocations on the Ti side than the Al side. The types of dislocations on the Ti side are mainly dominated by 1/6<112> dislocations, while the dislocations across the Ti/Al interface are also 1/2<110> and the dislocations on the Al side are dominated by 1/2<110> and 1/2<011>.

4. Conclusions

In this work, the effects of the temperature and the volume fraction of Ti on the compressive deformations of Ti/Al layered composite models are assessed by molecular dynamics simulation. The following conclusions can be drawn:

(1)

When the strain rate is 0.0002p⁻¹ and the temperature is 300 K, the Ti/Al layered composite shows an obvious peak in the stress–strain curve under compressive loading perpendicular to the interface. The types of dislocations during compression are mainly dominated by 1/6<211> and 1/6<112> dislocations. Initially, the dislocations are concentrated on the Al side, and during compression, the dislocations 1/2<101> and 1/6<211> cross the interface from the Al side to the Ti side.

(2)

Temperature exerts a significant impact on the compressive properties of the Ti/Al layered composites. The increase in temperature promotes the nucleation of initial dislocations at lower strains, leading to a decrease in the ultimate compressive strength as well as an increase in the plasticity of the Ti/Al layered composites. When the temperature exceeds 400 K, the Ti and Al atoms generate ordered intermetallic compounds, which results in a decreasing compressive strength reduction rate.

(3)

The compressive properties of Ti/Al layered composites vary with the Ti volume fractions. When the Ti volume fraction is 40% and 25%, the plastic deformation during compression mainly concentrates on the Ti side. And the dislocation type is mainly dominated by 1/6<112>. For the sample with a 50% Ti volume fraction, the plastic deformation mainly concentrates on the Al side, resulting in an increase in compressive strength but a decrease in plasticity. Overall, the compressive properties of the Ti/Al layered composites can be effectively modulated by the Ti volume fraction, which provides guidance for the structural design of Ti/Al layered composites.