Multi-Scale Numerical Simulation of Short Tungsten Fiber Reinforced Tungsten–Copper Composites: Influence Mechanisms of Fiber Parameters

Abstract

Tungsten fiber reinforced tungsten–copper (W_f/W-Cu) composites have broad application prospects in fields such as electronic packaging due to their excellent comprehensive properties. However, the correlation between fiber parameters (content, aspect ratio, orientation) and the mechanical behavior of the materials is not yet clear. In this study, a combination of numerical simulation and experimental research was employed to construct a three-dimensional microstructural mechanic model and systematically investigate the influence of fiber parameters on the tensile properties and mechanisms of W_f/W-Cu composites. The results show that: (1) The critical fiber aspect ratio is 7.6. When below this value, fiber pullout dominates, and when above this value, fiber tensile fracture is the main mechanism. (2) As the fiber content increases from 1% to 6%, the tensile strength of the composite increases by 9.6%, the yield strength increases by 10.2%, while the elongation after fracture decreases by 18.6%. (3) As the fiber orientation angle increases from 0° to 90°, the material strength first increases and then decreases, while the toughness first decreases and then increases. (4) Short fibers achieve interface toughening through fiber pullout, crack deflection, and fiber bridging, while long fibers improve the strength and toughness of the composite through load transfer and fiber bridging effects. (5) The damage evolution mechanism reveals the regulation effect of fiber parameters on the multi-scale mechanical behavior of the material. The research results can guide the composition and structure optimization design of W_f/W-Cu composites, provide new ideas for the research of high-performance fiber composites, and have important significance for their engineering applications in extreme environments.

1. Introduction

Metal matrix composites (MMCs) have been widely applied in various fields, such as aerospace, electronic information, energy conservation, and environmental protection, due to their excellent comprehensive properties [1,2,3]. As an important functional MMC, tungsten–copper (W-Cu) composites possess outstanding electrical and thermal conductivity and reliable high-temperature mechanical properties. They show broad application prospects in electrical contacts for high voltage switching, electronic packaging and thermal management, microwave and plasma applications, and aerospace and defense components, such as shaped charge liners and kinetic energy penetrators [4,5,6,7]. However, the mechanical properties of traditional W-Cu composites, especially the strength and plasticity under high-temperature conditions, cannot fully meet the requirements of harsh service environments.

As is known, the influence mechanisms of different reinforcement methods on the mechanical behavior of composites differ significantly. The mechanical properties of particle-reinforced composites mainly depend on the particle volume fraction and the particle/matrix interfacial bonding strength. However, particles have limited ability to bear large loads and have a limited strengthening and toughening effect on composites [8]. Fiber reinforcement is a technical approach that significantly improves the mechanical properties of composites by introducing high-strength, high-modulus fibers into the matrix. Compared with particle reinforcement, the unique geometric structure of fibers allows them to maximize their reinforcing effect along the load-bearing direction, greatly enhancing the specific strength and specific modulus of the material. Meanwhile, the fiber/matrix interface can achieve efficient load transfer between the two phases through stress transfer, further improving the damage tolerance of the composite [9]. Continuous fibers have a high aspect ratio and can fully exert their reinforcing effect in the fiber direction. However, continuous fibers are difficult to use in the preparation of complex-shaped components, and their mechanical properties exhibit high anisotropy, which to some extent limits their engineering applications [10,11]. Compared to continuous fibers and fiber mesh networks, short fibers offer advantages such as low-cost processing, flexible forming, and relatively weaker anisotropic mechanical properties, making them suitable for applications involving complex-shaped components and large-scale production. However, it is important to note that rationally designing the spatial distribution of short fibers is crucial for ensuring the optimal performance of short fiber reinforced composites in specific loading directions [12]. Numerous studies have shown that factors such as fiber content, aspect ratio, and orientation distribution have significant effects on the mechanical properties of composites, and the interfacial bonding strength between fibers and matrix is a key factor in determining material properties [13]. A. Kelly et al. [8] proposed the concept of critical fiber length based on the shear lag theory, pointing out that fibers can only effectively exert their reinforcing effect when their length exceeds the critical length. J.L. Thomason et al. [14] systematically investigated the influence of fiber content and aspect ratio on the mechanical properties of glass fiber/polypropylene composites and found an optimal matching range for fiber content and aspect ratio. These research works have provided important theoretical foundations and experimental evidence for the design and optimization of short fiber composites. In a recent review article on fiber-reinforced MMCs [15], various composite systems, such as SiC fiber-reinforced Ti-based and Al-based composites, stainless steel fiber-reinforced Al-based composites, Al₂O₃ fiber-reinforced NiAl-based composites, and Kevlar fiber-reinforced Mg-based composites, were summarized. Through single fiber pull-out experiments combined with finite element simulations, the fiber/matrix interfacial strength and its influencing factors were investigated. It was found that residual stress, interface thickness, shear strength, and fiber content have important effects on the interfacial properties and mechanical properties of composites, providing important references for the design and preparation of fiber-reinforced MMCs. However, it can be clearly seen that the above-mentioned work mainly focuses on light alloy matrix composites, while there are few reports on high-performance refractory metal matrix composites, such as W-Cu composites. In 1973, Professor Kelly comprehensively summarized the mechanical behavior of short fiber reinforced metal matrix composites in his classic work ’Strong Solids’ [16]. Based on the shear lag theory, he proposed Kelly’s model, which provides universal theoretical guidance for the design and optimization of short fiber composites. However, Kelly’s theory mainly relies on elastic mechanics analysis, and further refinement is needed to characterize mechanical behaviors such as plastic deformation and yield fracture. Moreover, the strengthening mechanisms and failure behaviors of different fiber reinforcement systems exhibit significant differences. Therefore, conducting systematic research on the strengthening and toughening mechanisms of short fibers in high-performance refractory metal matrices (such as tungsten–copper composites) is of great scientific significance and practical value for further developing multi-scale mechanical models and improving the quantitative characterization and prediction methods of mechanical properties of short fiber composites. In our previous study [17], we prepared short tungsten fiber (W_f) reinforced WCu composites and found that W_f with a preferential <110> orientation significantly enhanced the tensile strength of WCu composites, reaching a tensile strength of 549 MPa and plasticity of 10.2%. Preliminary three-dimensional finite element simulations revealed the influence of fiber fracture and interface debonding on material failure, but the effect of fiber parameters on the mechanical behavior of the material was not deeply analyzed. In summary, although some progress has been made in the field of short fiber-reinforced MMCs, and the effects of fiber parameters (content, aspect ratio) and interfacial bonding strength on the mechanical properties of materials have been preliminarily revealed, there is still a lack of systematic and in-depth research on short tungsten fiber-reinforced W-Cu composites, which have broad application prospects. Therefore, it is necessary to develop a multi-scale constitutive model based on physical mechanisms to quantitatively describe the influence of fiber parameters on the mechanical properties of materials and provide theoretical guidance for the structural design and performance optimization of short fiber-reinforced W-Cu composites.

In view of this, short tungsten fiber-reinforced W-Cu composites were selected as the research object in this study to systematically evaluate the influence of fiber content, aspect ratio, orientation, and other factors on the microstructure and macroscopic mechanical properties of the materials. Based on experimental research, we further constructed a three-dimensional numerical model containing the fiber/matrix interface. This model employs cohesive elements to describe the interfacial bonding performance and considers the nonlinear mechanical behavior of fibers and matrix, thus achieving a high-fidelity characterization of the microstructure and mechanical properties of short fiber composites. Through finite element numerical simulations, the effects of key parameters such as fiber content, aspect ratio, and orientation on the mechanical properties and failure behavior of the composites were quantitatively analyzed, revealing the multi-scale cooperative reinforcement mechanism of short fibers. Here, the selection of fiber volume fractions in composite materials requires a comprehensive consideration of various factors, including mechanical performance requirements, process feasibility, and cost. In general, a higher fiber volume fraction leads to increased specific strength and specific modulus of the composite. However, it also increases the tendency for fiber agglomeration and results in higher discreteness of the composite’s mechanical properties [18]. Moreover, excessively high fiber content can significantly reduce the processability of the composite, causing issues such as insufficient matrix infiltration and increased residual stress [19]. Therefore, the selection of fiber volume fraction necessitates a balance between mechanical performance and processability. Considering the aforementioned research findings and the high-density characteristics of the tungsten–copper matrix used in this study, we selected a short tungsten fiber addition range of 1–6 wt.%. This content range not only fully exploits the strengthening and toughening effects of short fibers but also ensures good processability of the composite. Additionally, by analyzing the stress–strain distribution and damage evolution behavior during the tensile deformation of the composites, the failure mechanisms under different fiber parameters were clarified. The research results can provide an important theoretical basis for the structural design and performance optimization of short fiber-reinforced composites and have significant implications for expanding their engineering applications in fields such as electronic packaging.

2. Simulation Methods and Settings

In this study, the finite element method was employed to systematically investigate the mechanical and electrical properties and their influencing factors of short tungsten fiber-reinforced tungsten–copper composites. For the simulation of mechanical properties, Digimat-FE software [20] was used to generate the representative volume element (RVE) models [21] of the composites containing randomly oriented short fibers. Through comparative analysis, considering the complexity of the fiber network structure, tetrahedral elements were used to discretize the model. An average mesh size of 1 μm and an appropriate RVE size of 0.5 mm × 0.5 mm × 0.5 mm were selected to ensure that the model could accurately reflect the mechanical behavior of the composites. Subsequently, the RVE model was imported into ABAQUS for pre-processing operations such as finite element mesh generation, load and boundary condition application. Using this mechanical model, the effects of fiber content, aspect ratio, orientation angle, and other factors on the tensile properties of the composites were systematically simulated and analyzed. Specifically, this study focused on W_f/W-Cu composites with a fiber mass fraction of 4%. To accurately describe the microstructural characteristics of the composites, a three-dimensional geometric model containing randomly oriented fibers was established using Digimat-FE software and imported into ABAQUS for subsequent analysis. The W-Cu matrix was prepared using a random uniform distribution powder metallurgy process, so the size of the RVE model needed to be large enough to include the microstructural features of the material. Through Boolean operations, the fiber model was embedded into the matrix to obtain the fiber/matrix composite structure. Considering the important influence of the fiber/matrix interface bonding state on the properties of the composites, cohesive elements were used to describe the interfacial bonding properties. Unlike idealized rigid connections, cohesive elements can accurately simulate the damage initiation and evolution process of the interface. In the previous study [17], we obtained samples by ball-milling a mixture of short tungsten fibers with an average diameter of 10 μm and a length of 1 mm with W-15 wt.%Cu mixed powder and then using powder metallurgy techniques. The basic data used in the simulation comes from the experimental results. Please refer to Ref. [17] for detailed information. In terms of boundary conditions and loading, one end of the model was fixed, while a displacement load was applied to the other end until macroscopic fracture occurred. To avoid the influence of stress concentration on the results, a coupling constraint was applied to the surface where the displacement load was imposed to ensure uniform load distribution. Moreover, to accurately describe the elastoplastic deformation behavior of the materials, true stress–strain constitutive relationships were constructed for the fibers and matrix, respectively, based on tensile test data.

To accurately predict the mechanical behavior of the composites, an elastoplastic constitutive model considering damage evolution was adopted in this study. The elastic deformation stage of the material was controlled by the elastic modulus, and after yielding, it entered the plastic deformation stage. To simulate the damage and fracture behavior of the material, a ductile damage model was introduced. Figure 1a shows the stress–strain curve of the material considering damage evolution. The solid line in the figure represents the true stress–strain relationship considering damage effects, while the dotted line corresponds to the ideal elastoplastic curve without damage. σy0 and ε0pl are the yield stress and equivalent plastic strain corresponding to the moment of damage initiation, respectively. When the equivalent plastic strain increases ε0pl, the material enters the damage evolution stage, and a damage variable D (0 ≤ D ≤ 1) is introduced to characterize the degradation degree of material properties. D_max is taken as the critical value of 1. When D = D_max, the material element is considered to be completely failed and is deleted from the finite element model, thus simulating the initiation and propagation of cracks. The fiber/matrix interface is described using a bilinear cohesive model, as shown in Figure 1b. The cohesive elements are assumed to be elastic and do not undergo plastic deformation. The damage initiation criterion adopts the maximum nominal stress criterion [22,23], that is, interface damage begins to occur when the normal component or tangential component of the cohesive force reaches the critical value. The mathematical description of the maximum nominal stress criterion is as follows:

$$max\left\{{\displaystyle \frac{t_n}{t_n^o}}, {\displaystyle \frac{t_s}{t_s^o}}, {\displaystyle \frac{t_t}{t_t^o}}\right\}=1,$$

(1)

where $t_n^o, { t}_s^o, t_t^o$ correspond to the peak values of the contact stress of the interface elements in the normal direction, the first shear direction, and the second shear direction, respectively. The three parameters of t_n, t_s, t_t represent the contact stresses of the interface elements at a certain moment in the normal direction, the first shear direction, and the second shear direction, respectively. Once damage is initiated, the cohesive force gradually degrades until complete failure. The energy consumed at complete separation is the interfacial fracture energy. Referring to the fiber pull-out energy formula proposed in the literature [17,18]:

$${\omega }_{po}={\displaystyle \frac{{\sigma }_f^3{d}^2{V}_f}{96l{\tau }_i^2}} ,$$

(2)

where l is the fiber length, σ_f is the fiber strength (taken as 2.97 GPa), τ_i is the fiber/matrix interfacial shear strength, d is the fiber diameter, and V_f is the fiber volume fraction. Substituting the relevant parameters into Equation (2), the interfacial fracture energy ω_c of the composites studied in this paper was calculated to be approximately 0.005 J/m².

In this work, fiber entanglement and agglomeration are not considered initially, and the fiber spacing is controlled to be one fiber diameter apart. The main reason is that when the fibers are too close to each other, the mesh generation of the model will greatly increase the computational requirements, cost, and difficulty. When the mesh density is properly designed, there is no significant impact on the results. Therefore, in this paper, six groups of predicted stress–strain curves of W_f-reinforced W-Cu composites with different mass fractions were calculated. The fiber mass fraction ranged from 1% to 6%, and the aspect ratio was 20. The composite models are shown in Figure 2a.

To investigate the influence of fiber aspect ratio on the mechanical properties of W_f/W-Cu composites, a series of microstructural mechanics models with different fiber aspect ratios were constructed in this study. The fiber diameter was fixed at 0.02 mm, and the fiber aspect ratios were set as 5, 10, 15, and 20, respectively. Figure 2b shows the representative volume elements of four randomly oriented short fiber-reinforced composites. In actual preparation processes, short fibers of different lengths can be obtained through slicing techniques. To comprehensively consider computational efficiency and result accuracy, the size of the RVE was uniformly selected as 0.5 mm × 0.5 mm × 0.5 mm. One face (X = 0) of the model was set as the fixed end of the load, and a tensile displacement load was applied to the opposite face (X = 0.5 mm). The displacement loading rate was 0.000575 mm/s. The cohesive parameters of the fiber/matrix interface were taken from the literature [24]. In this paper, t_n = 500 MPa, t_s = 200 MPa, t_t = 200 MPa, and the fracture energy was w = 0.005 J/m².

Fiber orientation is another important factor affecting the mechanical properties of composites. To quantitatively analyze the influence of fiber orientation angle on the tensile strength of W_f/W-Cu composites, a series of microstructural mechanics models with different orientation angles (φ) were constructed based on a fixed fiber aspect ratio (L/D = 20). As shown in Figure 2c, the angle between the fiber axis and the tensile load direction is defined as φ, and the fiber axis is always parallel to the XOZ plane. φ = 0° corresponds to the fiber axis being parallel to the load direction, while φ = 90° means they are perpendicular. In this paper, five typical fiber orientation angles were considered: φ = 0°, 22.5°, 45°, 67.5°, and 90°. The corresponding microstructural models of the composites are shown in Figure 2d. The other parameters of the model were consistent with the previous text, with the fiber aspect ratio fixed at 20 and the content at 4%.

3. Results and Discussion

3.1. Investigation of the Mechanical Properties of W-Cu Composites Reinforced with Short Fibers of Different Aspect Ratios

Before analyzing the influence of fiber aspect ratio on the mechanical properties of composites, it is necessary to introduce the concept of critical fiber length. The critical length refers to the minimum fiber length required for composites to achieve fiber reinforcement. According to the shear lag theory proposed by B.W. Rosen [25], the critical fiber length Lc can be expressed as:

$$L_c=d_{fb}{\displaystyle \frac{{\sigma }_{fu}}{2{\tau }_s}},$$

(3)

where σ_fu denotes ultimate strength of the fiber (MPa); d_fb denotes fiber diameter (mm); L_c denotes critical fiber length (mm), independent of the magnitude of the applied stress; τ_s is the shear yield stress of the matrix. When the fiber length is greater than the critical length, the fiber plays a tensile load-bearing role; otherwise, the fiber undergoes interface debonding and pullout and cannot fully exert its reinforcement effect.

For the W-Cu matrix material studied in this paper, they have a certain degree of plasticity, and the shear stress along the fiber/matrix interface is non-uniformly distributed. Figure 3 shows the distribution characteristics of fiber axial tensile stress and interfacial shear stress. It can be seen that the interfacial shear stress reaches its maximum value at the fiber ends and gradually decreases to zero along the fiber axial direction. This is mainly because of the stress concentration at the fiber ends and the additional shear stress generated by the coordinated deformation with the matrix. Taking the fiber strength as σ_fu = 3058 MPa and the shear yield strength of the matrix as τ_s = 200 MPa, substituting into Equation (3), it can be calculated that the critical fiber aspect ratio (L_c/d_f) is approximately 7.6. This means that when the fiber aspect ratio is greater than 7.6, the fiber can effectively play a tensile load-bearing role; otherwise, the fiber will fail due to interface debonding and pullout.

To systematically study the influence of the fiber aspect ratio on the mechanical properties of composites, a series of microstructural mechanics models of W_f/W-Cu composites with a fiber content of 4% and aspect ratios of 5, 10, 15, and 20 were constructed in this paper. Figure 4 shows the tensile stress–strain curves of composites with different aspect ratios. The results show that when the fiber aspect ratio is 5, the tensile strength of the composite is 523.9 MPa and the elongation is 5.13%, both of which are lower than other conditions. This is mainly because the fiber length is lower than the critical length at this time, and the stress concentration at the fiber ends causes plastic deformation of the matrix and induces fiber/matrix interface debonding and fiber pullout, as shown in Figure 5a. When the fiber aspect ratio increases to 10, 15, and 20, the tensile strength of the composites increases to 526.7 MPa, 533.8 MPa, and 544.2 MPa, respectively, and the elongation also correspondingly increases to 4.87%, 4.95%, and 5.05%. Figure 5b–d shows that at this time, the fiber length has exceeded the critical length, and the long fibers can effectively transfer the tensile load, and the fiber axial tensile stress gradually increases until the fiber undergoes tensile fracture. Longer fibers are conducive to stress redistribution between the fibers and the matrix, and the fibers fully exert their reinforcement effect and bear most of the external load. Comprehensive analysis shows that the fiber aspect ratio has a significant influence on the mechanical properties of composites. When the fiber length is less than the critical length (such as L/D = 5), the mechanical properties of the composite are poor; when the fiber length is greater than the critical length, as the aspect ratio increases from 10 to 20, the strength and plasticity of the composite show obvious improvements. Therefore, in the design of short fiber reinforced composites, the optimization of the fiber aspect ratio is crucial, and it should be ensured that the fiber length exceeds the critical aspect ratio to fully exert the reinforcement effect of the fibers.

To further reveal the influence mechanism of fiber aspect ratio on the mechanical properties of composites, Figure 6 shows the evolution of fiber Mises stress cloud diagrams of composites with different aspect ratios during the tensile deformation process. When the strain is 2.3% (Figure 6a,d,g,j), the fiber stresses in all conditions are significantly lower than their strength limit (3058 MPa), indicating that the fibers have not undergone significant damage or fracture. With further development of the deformation (strain 4.6%), the fibers begin to show local damage. For short fiber composites with an aspect ratio of 5 (Figure 6b), the fiber ends are the first to be damaged, resulting in a sudden drop in fiber stress. This is because the fiber length is short, the load transfer efficiency is low, and the fiber ends become stress concentration points. However, when the fiber length is longer (Figure 6e,h,k), the fibers can effectively transfer the load, and damage mainly occurs in the middle region of the fibers. With the fracture of local fibers, the load is distributed to adjacent intact fibers, resulting in stress adjustment. Eventually, when the strain reaches 5.75% (Figure 6c,f,i,l), most of the fibers suffer severe damage, and the composite rapidly fails. Fiber fracture induces matrix cracking, leading to macroscopic fracture of the composite.

Based on the above analysis, it can be seen that the fiber aspect ratio affects the macroscopic mechanical properties of the composite by influencing the fiber damage mode. For short fiber composites (L/D < 7.6), the fibers mainly induce matrix plastic deformation and interface debonding through end stress concentration, making it difficult to fully exert their reinforcement effect. In long fiber composites (L/D > 7.6), the fibers can effectively transfer the load, and damage mainly initiates in the middle region of the fibers. The fibers fully exert their reinforcement effect, and with the increase in aspect ratio, the strength and plasticity of the composite show significant improvements. Therefore, the rational utilization of the fiber aspect ratio effect and optimization of fiber length are crucial for improving the mechanical properties of short fiber reinforced composites.

From the perspective of fiber reinforcement mechanisms, the strengthening effects of short fibers on metal matrix composites can be divided into the following three categories: direct load-bearing type, yield transfer type, and microcrack bridging type. For direct load-bearing type reinforcement, the fibers undergo axial tensile deformation until fiber fracture, and most of the load is borne by the fibers. In yield transfer type reinforcement, the matrix first undergoes plastic deformation and transfers the load to the fibers through shear stress until the fiber/matrix interface peels off. Microcrack bridging refers to the fibers hindering and slowing down the expansion of matrix cracks, improving the fracture toughness of the composite through the fiber bridging effect. Combining the simulation results of this paper, it can be found that fibers with different aspect ratios have different reinforcement mechanisms. Figure 7 shows the microscopic morphology of the fracture surface of W_f/W-Cu composites. When the fiber aspect ratio is less than the critical value (such as L/D = 5, Figure 7a), the fibers mainly achieve reinforcement through the pullout mechanism. Under the action of tensile load, the fiber/matrix interface first peels off, and then the fibers are pulled out of the matrix. This corresponds to the yield transfer type reinforcement mechanism, and short fibers are difficult to effectively transfer the load. As the fiber aspect ratio exceeds the critical value (L/D = 10−15, Figure 7b,c), tensile fracture of the fibers can be clearly observed, indicating that the fibers can effectively transfer the load until they fracture beyond their own strength. This corresponds to the direct load-bearing type reinforcement, which is the main strengthening mechanism of long fiber composites. When the fiber aspect ratio further increases (L/D = 20, Figure 7d), the fracture toughness of the composite is significantly improved. The bridging effect of the fibers helps to hinder crack propagation, and a large number of fibers are pulled out, corresponding to the microcrack bridging type reinforcement mechanism. In summary, the fiber aspect ratio is a key factor affecting the mechanical properties of short fiber reinforced composites. Fiber length not only affects the stress state and damage mode of the fibers but also determines the mechanism by which the fibers exert their reinforcement effect. The critical fiber length (L/D = 7.6) is an important basis for the rational design of short fiber composites. Only when the fiber length is greater than the critical length can the fibers fully exert their direct load-bearing effect. With the increase in aspect ratio (L/D = 10−20), the strength and plasticity of the composite show significant improvements. Appropriately increasing the fiber aspect ratio (L/D = 20) also helps to exert the crack bridging effect of the fibers and improve the toughness of the composite. Therefore, for practical engineering applications, a balance between strength, toughness, and processability can be achieved by optimizing the fiber aspect ratio, thereby obtaining short fiber reinforced composites with excellent mechanical properties.

3.2. Investigation of the Mechanical Properties of W-Cu Composites Reinforced with Short Fibers of Different Contents

In this section, the microstructural mechanics model is used to systematically study the influence of fiber mass fraction on the tensile mechanical properties of W_f/W-Cu composites. Considering the computational cost and convergence of the results, the model does not consider fiber entanglement and agglomeration phenomena, and the spacing between adjacent fibers is controlled to be above one fiber diameter. This is because excessively close fibers will severely increase the difficulty of mesh generation, leading to a sharp increase in the computational scale. Experience shows that when the mesh density is reasonable, appropriately simplifying the fiber distribution form will not have a significant impact on the computational results. Figure 8 shows the tensile stress–strain curves of composites with different fiber contents (mass fractions from 1% to 6%), where the fiber aspect ratio is fixed at 20 and randomly distributed in the matrix. All composites exhibit typical mechanical behavior of elastic deformation followed by plastic deformation until fracture. With the increase in fiber content, the tensile strength and yield strength of the composites gradually increase, while the fracture strain and elongation after fracture gradually decrease. This is mainly due to the increase in fiber content, which relatively weakens the load-bearing capacity of the matrix and decreases the plastic deformation ability of the composites.

Quantitative analysis reveals that as the tungsten fiber content increases from 1% to 6%, the tensile strength of the composites gradually increases from 513.5 MPa to 562.5 MPa. Compared to the 1% fiber content model, the tensile strengths of the 2% to 6% models increased by 1.6%, 2.4%, 6.0%, 7.0%, and 9.6%, respectively. This result indicates that the addition of short fibers can significantly enhance the mechanical properties of the composites, and the strengthening effect increases with the increase in fiber content. At the same time, the yield strength also increases with the increase in fiber content, showing a similar trend to the tensile strength. It should be noted that the 9.55% strength improvement in our study is relatively small, mainly due to the lower reinforcement efficiency of random short fibers compared to aligned fibers. The model temporarily does not consider fiber entanglement and agglomeration, reducing fiber dispersion at high contents, and the high contribution of the plastic copper matrix to the mechanical properties. Nevertheless, our results are consistent with the expectations of classic short fiber reinforcement theory. In future research, the short fiber reinforcement effect can be maximized to obtain composites with even more excellent mechanical properties by further increasing the fiber content, optimizing the fiber dispersion and employing high-strength and high-toughness fibers and high-performance coatings. It is worth noting that the elongation after fracture of the composites generally shows a decreasing trend, but a slight rebound occurs at a fiber content of 4%. The elongation decreases from 8.26% at 2% to 7.41% at 3%, and then rebounds to 7.63% at 4%, but is still lower than the level at 2%. The reason for this phenomenon is that when the fiber content increases from 3% to 4%, the number of fibers increases significantly, and their distribution in the matrix becomes more uniform, reducing the existence of pure matrix regions. The plastic deformation of the matrix regions is the main source of elongation in the composites. A moderate increase in fiber content leads to an improvement in the uniformity of the matrix distribution, thus resulting in a slight rebound in elongation. However, when the fiber content further increases (>4%), the constraining effect of the fibers on matrix deformation becomes dominant, and the elongation of the composites decreases again. In summary, it can be concluded that the addition of short fibers can significantly improve the mechanical properties of tungsten–copper composites, and the strengthening effect increases with the increase in fiber content. However, excessively high fiber content will lead to a decrease in the plasticity and toughness of the composites. Therefore, in practical engineering applications, a balance needs to be struck between strength, plasticity, and process cost to obtain the optimal mechanical properties.

To gain a deeper understanding of the failure mechanism of short fiber reinforced tungsten–copper composites, this paper further analyzes the damage evolution process of W_f/W-Cu composites with a fiber content of 4% under tensile loading. Figure 9 shows the equivalent plastic strain cloud diagrams and Mises stress cloud diagrams of the composites at different deformation stages. When the tensile strain reaches 4.95% (Figure 9a), some fibers have already undergone damage and fracture (red circled areas), while cracks begin to initiate in the matrix (black circled areas). High strain regions often correspond to a higher probability of matrix cracking. Figure 9d shows the corresponding Mises stress distribution cloud diagram, where the crack initiation regions also correspond to stress concentration regions, while fiber fracture leads to local unloading, and the stress level in the regions near the fibers is relatively low.

With further development of the deformation (strain 5.06%, Figure 9b,e), the plastic deformation of the matrix gradually accumulates, and new crack initiation sources appear. Due to the stress redistribution caused by matrix cracking, the stress level in the regions near the crack tips is significantly reduced. At the same time, existing cracks will propagate towards the strain concentration regions, and the crack tips become the excitation points for stress concentration. Eventually, when the strain increases to 5.18% (Figure 9c,f), numerous cracks begin to intersect and coalesce, forming penetrating macroscopic fractures. The load-bearing capacity of the composites drops sharply, and the stress–strain curve decreases rapidly. The macroscopic fracture path is often formed through the interconnection of different crack tips. Figure 9c shows a typical crack propagation and coalescence path. This is mainly because the crack tip regions often correspond to high strain regions (Figure 9c) and high stress regions (Figure 9f). Propagation along the crack tip direction can effectively release the internal strain energy of the material, thus becoming the preferred direction for crack propagation.

In summary, the damage and failure process of short fiber reinforced tungsten–copper composites can be divided into three stages: (1) Fiber fracture and matrix crack initiation stage. Randomly distributed fibers first undergo damage and fracture, inducing the initiation of multiple cracks in the matrix. (2) Matrix plastic deformation and crack propagation stage. The plastic deformation of the matrix continuously accumulates, existing cracks gradually propagate, and new crack initiation sources appear. Crack tips become stress concentration points, and cracks propagate along high strain regions. (3) Macroscopic fracture formation stage. Numerous microcracks coalesce and interconnect to form penetrating macroscopic cracks, and the load-bearing capacity of the composites rapidly decreases. Cracks preferentially propagate along high strain sand high stress regions until the final failure of the material. Therefore, for short fiber reinforced composites, suppressing fiber damage and fracture and delaying matrix plastic deformation are key to improving their damage tolerance and increasing their failure toughness. Optimizing the design of the fiber/matrix interface strength and rationally controlling the fiber orientation and distribution can effectively avoid stress concentration, improve the crack propagation resistance of the composites, and thus obtain excellent mechanical properties.

3.3. Investigation of the Mechanical Properties of W-Cu Composites Reinforced with Short Fibers of Different Orientations

Figure 10 shows the tensile stress–strain curves of composites with different orientation angles. It can be seen that the fiber orientation angle has a significant influence on the mechanical behavior of the composites. When φ = 0°, i.e., the fiber axis is parallel to the load direction, the elongation after fracture of the composite reaches the maximum value of 5.2%, but the tensile strength is not the highest. This may be because parallel fibers can maximize their reinforcement effect, and the fibers undergo significant plastic deformation and interface slip, allowing the composite to exhibit better ductility.

When φ = 22.5°, the tensile strength of the composite reaches the highest value of 554.4 MPa. This indicates that moderate fiber inclination helps to exert the fiber reinforcement effect, generating additional shear stress between the fibers and the matrix, and improving the tensile resistance of the composite. As φ further increases, the tensile strength and elongation of the composite generally shows a decreasing trend. When φ = 90°, i.e., the fibers are perpendicular to the load direction, the tensile strength and elongation of the material are reduced to the lowest values of 533.2 MPa and 4.7%, respectively. This is mainly because perpendicular fibers have difficulty effectively transferring the load and are prone to peeling and brittle fracture of the fiber/matrix interface during the tensile process.

Considering both tensile strength and ductility, the tensile performance of the composite is optimal when φ = 22.5°, achieving a good balance between strength and toughness. As φ deviates from the optimal angle, the tensile performance gradually decreases, and both strength and toughness are reduced to the lowest level when φ = 90°. Therefore, in the structural design of W_f/W-Cu composites, rational control of the fiber orientation distribution is crucial. Moderate fiber inclination helps to form effective load transfer between the fibers and the matrix while leveraging the plastic deformation ability of the fibers, which is key to obtaining high-performance composites.

To further reveal the influence of fiber orientation on the failure behavior of composites, Figure 11 and Figure 12 show the evolution processes of fiber Mises stress and equivalent plastic strain at φ = 0° and 90°, respectively. When φ = 0°, the tensile load is mainly borne by the fiber axial direction. In the early stage of deformation (ε = 2.3%, Figure 11a), the fiber stress is mainly concentrated in the middle region of the fibers, and the matrix stress level is relatively low and uniformly distributed. With further development of deformation (ε = 4.6%, Figure 11b), the middle region of the fibers begins to undergo local fracture, causing redistribution of fiber stress. Stress concentration regions begin to appear in the matrix, corresponding to high-probability regions of crack initiation. Eventually, matrix cracks connect the fiber fracture regions, forming macroscopic fractures (Figure 11c,d). Cracks preferentially propagate along the fiber alignment direction, resulting in the lowest crack propagation resistance in the matrix.

When φ = 90° (Figure 12), the load is mainly transferred between the fibers and the matrix through radial tensile stress, and the load borne by the fiber axial direction is small. In the early stage of deformation (ε = 2.3%, Figure 12a), the axial distribution of fiber stress is relatively uniform. With the further development of deformation (Figure 12b–d), the fibers begin to undergo local yielding and discrete fracture. Matrix cracking is mainly controlled by the stress concentration caused by fiber radial fracture. Cracks rapidly propagate along the direction perpendicular to the fiber axis until macroscopic fracture of the material occurs. The above process fully demonstrates that when the fibers are perpendicular to the load direction, the fibers have difficulty effectively transferring the load, and the composite is more prone to brittle fracture. This is also the main reason for the significant reduction in strength and toughness of the composite when φ = 90°.

The evolution process of equivalent plastic strain in Figure 11 and Figure 12 further reveals the regulatory effect of fiber orientation on matrix plastic deformation and crack propagation. When φ = 0°, plastic deformation is mainly limited to the fiber ends and fracture regions, and matrix deformation is relatively uniform. Cracks preferentially propagate along the fiber axial direction, corresponding to high strain regions. When φ = 90°, the fibers have difficulty constraining matrix deformation, and matrix plastic deformation becomes more significant. Cracks rapidly propagate perpendicular to the fiber direction, and the material undergoes brittle fracture along high strain bands.

In addition to affecting the macroscopic mechanical properties of composites, fiber orientation also significantly changes their microscopic fracture mechanisms. Figure 13 shows the fracture morphology of W_f/W-Cu composites with different orientation angles. When φ = 0° (Figure 13a), the fiber axis is parallel to the load direction, and the composite has relatively high tensile strength and fracture strain (Figure 10). The fracture surface is dominated by fiber tensile fracture, and the fiber fracture cross-section is flat, exhibiting cleavage fracture characteristics. This indicates that the fibers bear the main load and undergo macroscopic cleavage along the fiber fracture regions. The matrix plastic deformation induced by fiber fracture is small, and fiber pullout pits are observed only in local regions. When φ = 0°, fiber tensile fracture is the main failure mechanism of the composite.

When φ = 22.5° and 45° (Figure 13b,c), the composite strength reaches the highest while the plasticity slightly decreases (Figure 10). Fiber oblique fracture and local fiber pullout begin to appear on the fracture surface. As φ increases, the stress state of the fibers gradually transitions to shear loading, and fiber oblique fracture helps to improve the material toughness. At the same time, the load transfer efficiency of the fiber/matrix interface decreases, and interface debonding and fiber pullout begin to become important failure modes. Further increasing φ to 67.5° (Figure 13d), the composite strength decreases but the plasticity significantly improves. Fiber pullout becomes the main failure characteristic, with a large number of fibers pulled out from the matrix, leaving circular holes on the matrix surface. The fibers have difficulty transferring axial load, and the fiber/matrix interface first undergoes shear delamination, followed by fiber pullout, and the material fails by shear along the interface. When φ = 90° (Figure 13e), the fiber axis is perpendicular to the load direction, and both the strength and plasticity of the composite are reduced to the lowest level (Figure 10). Interfacial shear delamination dominated by fiber pullout becomes the main failure mode, and the fracture surface exhibits a honeycomb structure. Secondary shear fracture of fibers can be observed in local regions, mainly due to the compressive and shear loads perpendicular to the fiber axis during the pullout process.

Combining the mechanical property test results in Figure 10, it can be seen that fiber orientation significantly affects the microscopic fracture mechanisms of W_f/W-Cu composites. As φ increases from 0° to 90°, the tensile strength of the composite first increases and then decreases, the fracture toughness first decreases and then increases, and the fracture mechanisms successively undergo three stages of fiber tensile fracture, fiber shear yielding, and fiber pullout: (1) When φ = 0°, fiber tensile fracture dominates, and both the strength and toughness of the material are relatively high. (2) When φ = 22.5°, fiber tensile fracture and shear yielding coexist, the strength reaches the highest while the toughness slightly decreases. (3) When φ = 45° to 67.5°, fiber oblique fracture and local pullout coexist, the strength decreases but the toughness significantly improves. (4) When φ = 90°, fiber pullout dominates, and both strength and toughness are reduced to the lowest level. This indicates that fiber orientation significantly changes the microscopic fracture mechanisms of composites by influencing fiber/matrix load transfer, fiber deformation mode, and interface debonding. In the design of short fiber composites, the fiber orientation distribution can be optimized to balance various failure modes such as fiber tension, shear, and pullout, achieving the best match between strength and toughness, and obtaining composites with excellent comprehensive mechanical properties. Based on the systematic RVE simulations, this study has made a preliminary attempt at a numerical analysis of macroscopic mechanics, but the current macroscopic model is still relatively simplified and needs further improvement and modification. On the one hand, it is necessary to develop a more refined constitutive model to better reflect the anisotropy and nonlinear characteristics of the composite material. On the other hand, it is necessary to correct the key parameters in the model through more comprehensive experimental characterization and verification (such as fracture analysis, fatigue experiments, etc.) to improve the accuracy and applicability of the predictions. This will be the focus of our next step of research.

To summarize, based on physical mechanisms, a multi-scale mechanical constitutive model was constructed to quantitatively analyze the influence of fiber parameters such as content, aspect ratio, and orientation on the mechanical properties of composites, revealing the synergistic reinforcement mechanism of short fibers. However, the current research mainly focuses on theoretical simulations and lacks direct comparison and validation with experimental results. In subsequent research, we will focus on strengthening work in both simulation and experimentation. On the one hand, we will further improve the microstructural mechanics model, considering the influence of practical factors such as fiber entanglement and agglomeration, to improve the accuracy and applicability of the model. On the other hand, we will obtain performance data of composites with different fiber parameters through mechanical property testing experiments such as tensile, compression, and fracture toughness tests, and systematically compare them with simulation results. The close integration of simulation and experimentation can more comprehensively and deeply reveal the intrinsic correlation between fiber parameters and material mechanical behavior, providing theoretical and experimental basis for composition optimization and structural design of W_f/W-Cu composites.

4. Conclusions

In this paper, a three-dimensional microstructural mechanic model containing the fiber/matrix interface was constructed to systematically investigate the influence of aspect ratio (5–20), fiber content (1–6%), orientation (0–90°), and other factors on the mechanical properties and failure mechanisms of the material. The main conclusions are as follows:

(1)

There exists a critical value (7.6) for the fiber aspect ratio. When below this value, fiber pullout dominates, and when above this value, fiber tensile fracture is the main mechanism, corresponding to yield transfer type interface strengthening and load transfer type direct reinforcement, respectively. Rational matching of short/long fibers can significantly improve the comprehensive mechanical properties of composites.

(2)

As the fiber content increases from 1% to 6%, the tensile strength of the composite increases by 9.6%, the yield strength increases by 10.2%, while the elongation after fracture decreases by 18.6%, indicating that the short fiber content significantly affects the strength and plasticity of the composite. Excessively high fiber content leads to increased fiber yielding and fracture, weakening the deformation ability of the matrix.

(3)

As the fiber orientation angle increases from 0° to 90°, the tensile strength of the composite first increases and then decreases, and the fracture toughness first decreases and then increases. The strength is highest when φ = 22.5°, and the toughness is best when φ = 0°. Fiber orientation regulates load transfer, fiber deformation mode, and interface debonding, significantly changing the microscopic fracture mechanisms of the material.

(4)

The multi-scale damage evolution mechanism of short fiber composites is revealed: fiber fracture induces matrix crack initiation, followed by matrix plastic deformation, crack propagation, and interconnection, ultimately leading to macroscopic fracture. The higher the fiber content, the more severe the fiber yielding and fracture; the closer the fiber orientation is to perpendicular, the more significant the interfacial shear damage.

(5)

This research innovatively constructs a three-dimensional microstructural mechanic model, achieves high-fidelity simulations of the entire deformation and damage process of short fiber composites, and quantitatively reveals the multi-scale synergistic mechanism of fiber parameters regulating the mechanical behavior of the composite. The research results can provide an important theoretical basis for the structural design and performance optimization of short fiber reinforced composites. The constitutive model and multi-scale analysis method established in this study can also serve as a reference for studying the mechanical properties of other short fiber composite systems. Future research can investigate the influence of fiber spatial distribution, interfacial chemical bonding, and other factors on the material behavior, further improve the multi-scale simulation method, and provide theoretical guidance for the engineering application of short fiber composites in extreme environments.