Microvoids Enhance the Low-Cycle Fatigue Resistance of TiAl Alloys

Abstract

Voids have a crucial effect on the fatigue performance of materials. The general viewpoint is that voids, as possible sources of cracks, are harmful to the fatigue performance of materials. However, this study finds that microvoids enhance the low-cycle fatigue resistance of TiAl alloys, both in single crystal and polycrystal, using molecular dynamics simulations. Due to the difference between the simulation and test, the selected strain value is larger. It is found that during cyclic loading, Shockley partial dislocations preferentially nucleate around the microvoid in the single crystal, with stacking fault tetrahedra forming progressively to obstruct dislocation motion. The polycrystal model exhibits the synergistic effect of the microvoid–grain boundary, and the fatigue resistance is substantially enhanced through the combined mechanisms of Lomer–Cottrell lock formation, twin boundary migration, and phase transformation. In addition, simulation models with microvoids exhibit lower plastic strain energy density and enhance fatigue life compared to microvoid-free counterparts. The present study provides significant insights into designing γ-TiAl alloys through controlled microvoids to optimize fatigue resistance. Future work should include experimental validation to substantiate these computational findings.

1. Introduction

Void defects in metallic materials have traditionally been viewed as detrimental to mechanical properties, with even sparse void distributions significantly degrading strength, ductility, and fatigue life [1,2,3]. This degradation primarily stems from stress concentration around voids, which serve as initiation sites for fatigue failure and potentially catastrophic consequences [4,5]. In recent years, extensive experimental and molecular dynamics simulation studies have been conducted to investigate void nucleation, growth, and closure mechanisms [6,7,8]. Tan et al. [9] demonstrated that in-phase thermomechanical fatigue induces dislocation accumulation and recrystallization around voids, while out-of-phase fatigue promotes twinning deformation. Wang et al. [10] revealed that void evolution in nanocrystalline NiTi alloys progresses through three distinct stages: nucleation, growth, and coalescence.

Contrary to conventional understanding, defects exhibit a dual role in material strengthening, where appropriately sized defects can paradoxically enhance mechanical properties. Yan et al. [11] discovered that adding carbon vacancies to (W_0.5Al_0.5)C_1−x boosts its hardness. The hardest material had 35% vacancies, showing 77% higher hardness than vacancy-free samples and even surpassing pure tungsten carbide. Ding et al. [12] demonstrated that nanoscale voids can dramatically enhance material properties. Their nanovoid-sphere model revealed that sub-critical void sizes induce bond contraction, creating ultra-dense interfacial shells. Qi et al. [13] studied void effects in CoCrFeMnNi HEAs through simulations. They found that voids create stress concentrations that form strong dislocation locks, boosting strength. While voids initially weaken the material, they improve work hardening via enhanced dislocation interactions. Gao et al. [14] explored the effect of void defects on the rotating and bending fatigue life of Ti-17 alloy fabricated by forging/additive hybrid manufacturing. The study found that the location of the hole has a great influence on the fatigue life. The void near the surface will damage the fatigue life, even if it is very small, and the void located in the center axis of the sample will be very safe. Chen et al. [15] demonstrated that gold with uniform nanovoids achieves 107% higher yield strength while preserving ductility. The high surface area also enhances surface–dislocation interactions, boosting both strength and strain hardening for improved ductility. This offers new insights for metal optimization. For multi-void systems, Sopu et al. [16] systematically studied the mechanical properties of Cu₆₄Zr₃₆ metallic glass nanoporous structure by means of molecular dynamics. The effects of the density, arrangement, size, and number of holes on the overall mechanical properties were investigated. They simulated three sizes of metallic glass specimens and found that through the rational design of the holes, the shear bands generated from the holes will hinder and interfere with each other, which is conducive to expanding the plastic deformation area of metallic glass, resulting in necking fracture, thereby improving the plastic deformation ability of metallic glass.

As a representative high-temperature structural material, γ-TiAl alloys exhibit exceptional specific strength, specific stiffness, and oxidation resistance, rendering them highly suitable for aerospace and automotive applications [17,18,19]. The effect of microvoids on the tensile and compressive properties of single-crystal γ-TiAl is very obvious. Tang et al. [20] revealed the shear-ring emission mechanism of pore growth during the tensile process of the γ-TiAl single crystal. Xu et al. [21] studied the compression process of a single-crystal γ-TiAl alloy with a microvoid. It was found that when the plastic deformation of the specimen occurred, the microvoid began to collapse in all directions, and local dislocations and plane faults continued to expand. In comparison to TiAl single crystals, the presence of grain boundaries in polycrystal TiAl significantly influences key mechanical properties, including plasticity, strength, and fracture behavior. These microstructural features result in distinct mechanical property differences between polycrystal and single-crystal TiAl alloys. However, the influence of microvoids in polycrystal γ-TiAl systems remains poorly characterized owing to heterogeneous stress distributions at grain boundaries during deformation, warranting additional investigation, particularly for fatigue. Fatigue performance is crucial for the application of TiAl alloys. Xiang et al. [22] clarified the influence of temperature on the low-cycle fatigue performance of TiAl alloys, which is crucial for their application in aviation engines. Current research has predominantly investigated the static mechanical properties of γ-TiAl alloys, whereas the effects of microvoids on both single-crystal and polycrystal systems under cyclic loading conditions remain insufficiently studied. This study investigates the evolution of microvoid defects during low-cycle fatigue in γ-TiAl alloys, with particular emphasis on the influence of pre-existing microvoids on fatigue performance. By analyzing variations in stress amplitude, plastic strain energy, microvoid volume, and dislocation density, new insights are provided for the development and application of high-performance materials.

2. Materials and Methods

In this investigation, the molecular dynamics LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) simulation package was used. The embedded atom method (EAM) potential developed by Zope and Mishin [23] for the γ-TiAl was used. To investigate the evolution of nanovoids in polycrystal γ-TiAl, the open-source software Atomsk (Version beta-0.13.1) [24] was used to create a single-crystal γ-TiAl and polycrystal model comprising 8 randomly oriented Voronoi grains. Due to its face-centered tetragonal structure, γ-TiAl has lattice parameters of a = b = 3.998 Å and c = 4.186 Å, based on experimental data. In the published literature, the same method is used to build the model [25]. The initial model dimensions are 26 nm × 39 nm × 26 nm. The single-crystal model consisted of 1,639,300 atoms, while the polycrystal model contained 1,576,126 atoms. To examine the influence of a microvoid on the mechanical properties of the model, a spherical microvoid was introduced. The microvoid had a radius of 5 nm, as shown in Figure 1. Periodic boundary conditions were applied along the x, y, and z directions to eliminate boundary effects. An isothermal-isobaric ensemble relaxation of 50 ps by a constant timestep of 1 fs at 873 K was used to equilibrate the model.

This study systematically investigates the influence of microvoids on the fatigue behavior of polycrystal TiAl by employing two distinct computational models: a fully dense reference model and a microvoid-containing model. As shown in Figure 2, the simulations adopted a strain-controlled loading approach, with cyclic strain applied along the y-direction under the following conditions: the single crystals demonstrated strain amplitudes of 9% and 13%, whereas the polycrystal models exhibited a strain amplitude of 5.5% with a strain ratio of −1. The polycrystal model simulation was conducted over 100 loading cycles with variable amplitude, while computational limitations restricted the single-crystal simulation to 20 cycles. Each loading cycle incorporated both tensile and compressive phases at a constant strain rate of 5 × 10⁹ s⁻¹. The selected strain and strain rate values were chosen to balance microstructure evolution observability with computational efficiency. Excessively high strain rate will lead to the ambiguity of dislocation dynamic characteristics, while too low a strain rate will make the simulation of the fatigue failure process of superalloys face great computational challenges. The simulation results were visualized and analyzed using OVITO [26]. The dislocation structures in the crystal were identified by dislocation analysis (DXA [27]), and the common neighbor analysis (CAN [28]) was used to color the crystal structure type.

3. Results and Discussions

3.1. Effect of Microvoid on Low-Cycle Fatigue Life

Figure 2 demonstrates that microvoids significantly influence the stress–strain behavior of single-crystal γ-TiAl alloys. The tensile responses differ markedly between single-crystal and polycrystalline models. Compared to microvoid-free models, microvoid-containing models exhibit substantially reduced yield strength, primarily due to stress concentration around voids that facilitates dislocation nucleation and propagation [29]. However, the difference in average flow stress is less pronounced. In the single-crystal model, the microvoid-containing model shows a slightly higher average flow stress (2.25 GPa) than its microvoid-free counterpart (2.21 GPa). Similarly, polycrystal models display comparable values, with 2.55 GPa for microvoid-containing models versus 2.59 GPa for microvoid-free models.

As shown in Figure 3, the peak stress evolution during low-cycle fatigue can be divided into two distinct stages in both single-crystal and polycrystal models. All models, regardless of microvoid content, demonstrate initial cyclic softening followed by stabilization. Figure 3a reveals significant stress amplitude reduction in the single-crystal model upon completing the second cycle. Except during the first cycle, the microvoid-containing model consistently exhibits higher stress amplitudes than its microvoid-free counterparts. As shown in Figure 3b, during the first stage, cycles 1–20, the tensile peak stress progressively decreases until reaching a stable state after 20 cycles. Regarding compressive stress amplitude evolution, the microvoid-free model exhibits an initial increase during cycles 1–10 followed by stabilization, while the microvoid-containing model shows gradual enhancement during cycles 1–50 before stabilization. Both models demonstrate similar low-cycle fatigue behavior characterized by initial cyclic softening followed by stabilization. Notably, the tensile and compressive stress amplitudes differ marginally between the two models, with compressive stresses being significantly higher than tensile stresses in both cases.

During cyclic loading, the area of the hysteresis loop represents the energy dissipation per unit volume, known as the plastic strain energy density. A higher plastic strain energy density indicates greater energy dissipation in the model, demonstrating that a microvoid-free model can dissipate more energy during cyclic deformation. Li et al. [30] concluded that the plastic strain energy density after reaching the cyclic stabilization stage exhibits good effectiveness for fatigue life prediction. Higher plastic strain energy density leads to shorter fatigue life [31,32]. These findings also indicate that, under the current research conditions, microvoid models exhibit longer fatigue lives. Figure 4a reveals that the microvoid-containing model exhibits significantly higher plastic strain energy than its microvoid-free counterpart, with both models demonstrating an initial increase followed by a subsequent decrease and eventual stabilization. Figure 4b reveals distinct plastic strain energy evolution patterns between microvoid-containing and microvoid-free models during cyclic loading. In the initial cycles (1–10), the microvoid-containing model demonstrates higher plastic strain energy accumulation. However, during cycles 10–30, the microvoid-free model shows increasing plastic strain energy while the microvoid-containing model exhibits decreasing values. At stabilization, the microvoid-free model ultimately accumulates greater plastic strain energy, indicating superior fatigue resistance and extended service life for the microvoid-containing model.

The tensile hysteresis energy model, originally proposed by Ostergren [33] in 1976, postulated that low-cycle fatigue damage is governed by the tensile hysteresis energy or strain energy absorbed by the model. This damage function approximates the absorbed energy as the product of the inelastic strain range $\Delta {\epsilon }_p$ and peak tensile stress ${\sigma }_t$:

$$\Delta W_T={\sigma }_t\Delta {\epsilon }_p$$

(1)

The relationship between hysteresis energy and fatigue life follows the power exponential relationship:

$$\Delta W_T{N}_f^{\beta }=C_1$$

(2)

$$C=C_1/\lambda ={\sigma }_t\Delta {\epsilon }_p{N}_f^{\beta }$$

(3)

where $N_f$ is the number of cycles to sample failure, $C$, $\lambda$, $C_1$, $\beta$ are material constants, and ${\sigma }_t\Delta {\epsilon }_p$ is the Ostergren parameter. As shown in

Table 1. Parameters of different models under low-cycle fatigue cyclic loading.

Type	Model	$\mathit{\Delta }{\mathit{\epsilon }}_{\mathit{p}}$ (%)	${\mathit{\sigma }}_{\mathit{t}}$ (GPa)	Ostergren Parameter (GPa)
polycrystal	microvoid	4.40	2.33	10.25
	microvoid-free	4.50	2.37	10.67
single crystal	microvoid	11.66	2.15	25.07
	microvoid-free	20.85	1.87	38.99

, during the low-cycle fatigue loading, both single-crystal and polycrystal models demonstrate that microvoid-free models exhibit a higher Ostergren parameter compared to the microvoid-containing model. It should be noted that the data presented in Table 1 are derived exclusively from molecular dynamics simulations and have not yet been validated against experimental results. As derived from Equation (3), this higher Ostergren parameter directly correlates with reduced fatigue life, demonstrating the superior fatigue resistance of microvoid-containing models.

3.2. Effect of Microvoids on Low-Cycle Fatigue Microstructure

Stress concentration at microvoid sites facilitates dislocation nucleation, as demonstrated in Figure 5. Stacking faults (SFs) initially form in localized regions during the first cycle with limited spatial extent, then progressively expand throughout the specimen with increasing cycles. Various dislocation types emerge, predominantly 1/6 [112] Shockley partial dislocations accompanied by Shockley dislocation loops. This phenomenon primarily arises from the minimal Peierls stress on (111) planes in γ-TiAl alloys, where dislocations preferentially glide along (111) planes with [112] slip directions, promoting the formation of 1/6 [112] Shockley partial dislocations. Notably, stacking fault tetrahedra (SFTs) emerge during cyclic loading. As a typical three-dimensional vacancy defect, SFTs serve as potent obstacles to dislocation motion due to their highly stable three-dimensional configuration [34].

Stress concentration occurs at microvoid–matrix interfaces, as shown in Figure 6d, leading to the formation of Lomer–Cottrell dislocations during the 55th cycle, as shown in Figure 6a. These dislocations hinder the further movement of dislocations, thereby enhancing the work hardening of the material and improving the fatigue resistance of the material [35]. The strengthening mechanism caused by the local stress gradient was first proposed by Xiang et al. [25] in gradient TiAl alloys. Figure 6c demonstrates the dual role of microvoids as both dislocation sources and obstacles that pin dislocations. The stress around the microvoid is highly concentrated, and the surface or interface can effectively excite and emit new dislocations. When the number of cycles increases to 56, due to the strong interaction between the microvoid and dislocations and the resulting local stress field changes, the parallel twin is significantly hindered, and the deformation mechanism is forced to change. The growth of TB is inhibited, and extrinsic stacking faults (ESFs) and intrinsic stacking faults are illustrated in Figure 6b.

The evolution of micro-damage can be quantitatively characterized by monitoring changes in microvoid volume fraction. Curran et al. [36] first proposed the microvoid nucleation and growth (NAG) model, which employs microvoid volume fraction to quantify damage degree. This approach, using porosity to define damage extent, has gained widespread acceptance in the academic community [37,38]. Figure 7a is the variation curve of the microvoid volume fraction of the single-crystal model with the cycle period. In the initial stage, the void volume fraction fluctuates significantly, rises rapidly to close to the peak, and then decreases slightly. The void volume fraction of subsequent cycles reaches a dynamic fluctuation state within a certain range, and does not show an obvious monotonically increasing or decreasing trend. Figure 7b illustrates the variation in microvoid volume fraction with cycle numbers of the polycrystal model. During cycles 1–10, the microvoid volume fraction decreases from 1.93% to 1.82%, fluctuates within a specific range during cycles 10–80, and further declines to 1.77% in cycles 90–100.

Figure 8 presents the atomic evolution at selected cycle numbers, using cyan-colored atoms as reference markers to visualize microvoid migration. The single-crystal model showed minimal microvoid morphological changes during 20 loading cycles. Throughout cyclic deformation, disordered atoms progressively filled the microvoid. HCP phase formation was observed upon completion of the 20th cycle. The HCP phase formation impedes dislocation motion and increases dislocation density in transformed regions, consequently strengthening the alloy [13]. Additionally, intrinsic stacking faults (ISFs) transform into TB, providing supplementary obstacles for dislocation movement.

As shown in Figure 9b, compressive stress dominates during cyclic loading in the polycrystal model. Under compressive stress, microvoid walls experience inward compression, transforming spherical microvoids into flattened configurations that become filled with disordered atoms. These disordered atomic arrangements surrounding the microvoid induce volume contraction. During cyclic loading, microvoids exhibit no expansion with increasing cycles. Instead, SFs at nano microvoids confine microvoid growth within a limited range, leading to progressive microvoid collapse and gradual loss of functionality, thereby reducing their impact on the model. At the 50th cycle, a phase transformation occurs where FCC structures convert to HCP configurations. The microvoid shrinkage mechanism fundamentally represents an energy dissipation process mediated by dislocation regulation and interface constraints in nano twinned structures under cyclic loading. The synergistic interaction between twin boundaries and dislocations induces stress concentration at microvoid peripheries, driving microvoid shape deformation for energy release [39]. As demonstrated in Figure 9f, the resulting stress concentration may trigger twin boundary migration, which absorbs partial strain energy and further compresses microvoid space. These combined effects significantly enhance the material’s fatigue resistance. The synergistic effect of multiple grain boundaries has a significant impact on the properties of TiAl alloys [40]. At the 70th cycle, a key development is the significant widening of twin layers. This thickening process has important micromechanical implications. Wider twin boundaries create stronger obstacles for dislocation motion across grains [39]. Dislocations require additional energy to penetrate these widened twin regions or must alter their slip paths. This enhanced obstruction mechanism effectively maintains the material’s internal resistance, thereby preventing significant flow stress reduction in void-containing models during subsequent deformation. Ultimately, in the final deformation stage, when plastic deformation capacity is exhausted, catastrophic structural instability occurs, manifesting as complete collapse. These atomic-scale observations show excellent agreement with previous findings by Tang et al. [20] in single-crystal γ-TiAl alloys, who similarly reported void evolution through analogous mechanisms leading to fracture, further validating the universality of these deformation mechanisms.

Microvoids serve as dislocation sources that continuously emit dislocations during cyclic loading. As dislocation density increases, intensified lattice distortion around the microvoid promotes atomic rearrangement to reduce system energy, manifesting as microvoid collapse. Figure 10a,b demonstrate that during the 90th cycle, Shockley dislocations interact with spherical microvoid surfaces, and by the 100th cycle, become absorbed by microvoid surfaces, leaving surface steps, as shown in Figure 10c,d. This absorption behavior induces localized microvoid contraction [41]. Furthermore, the low energy barrier in stacking fault regions may accelerate dislocation slip toward microvoid surfaces, thereby increasing the probability of dislocation absorption.

Microstructural defect analysis confirms that dislocations directly control plastic deformation in materials. The correlation between dislocation evolution and mechanical properties during cyclic loading was examined through analysis of dislocation density variation with loading time for different models, as illustrated in Figure 11. Shockley partial dislocations and perfect dislocations emerge as the predominant types, with other dislocation configurations making negligible contributions. The microvoid-free single-crystal model does not enter the cyclic stable state due to the small number of loading cycles, and its dislocation density fluctuates sharply with the extension of loading time, as shown in Figure 11a,b. The dislocation density of single-crystal models is obviously higher than that of polycrystal models. For polycrystal structure, all models display a consistent pattern of initial dislocation density reduction followed by fluctuation within a defined range, as shown in Figure 11c,d. The findings indicate that dislocation multiplication and annihilation progressively achieve equilibrium during cyclic loading through mutual dislocation interactions, resulting in the dynamic stabilization of dislocation density in both models [42]. This initially elevated dislocation density stems from thermally activated slip systems at elevated temperatures, producing greater initial dislocation densities in high-temperature alloy models.

4. Conclusions

In summary, the influence of microvoid defects on the low-cycle fatigue behavior of single-crystal and polycrystal γ-TiAl alloys was systematically investigated using molecular dynamics simulations. The principal findings can be summarized as follows:

(1)

The microvoid-containing model demonstrated superior fatigue performance, manifested by lower plastic strain energy density and extended fatigue life. This is seen in lower plastic strain energy density and extended fatigue life. Multiple mechanisms contribute to this enhancement. Microvoid compression and dislocation absorption alleviate stress concentration. Twin boundary migration absorbs strain energy. HCP phase transformation and fault reorganization strengthen dislocation-pinning effects.

(2)

Microvoids significantly reduce the yield stress of both single-crystal and polycrystal γ-TiAl alloys. However, the difference in average flow stress between microvoid-containing and microvoid-free models is minimal. All models exhibit cyclic softening, followed by stabilization during low-cycle fatigue loading. In the presence of microvoids, single-crystal models show higher stress amplitudes. In the polycrystal model, the microvoid delayed stress softening. This occurs through mechanisms such as twin boundary formation and dislocation interactions.

(3)

Microvoids in single crystals grow via a shear loop mechanism, yet exhibit significant volume fluctuations due to limited lattice constraints. With increasing cycle numbers, SFTs form and effectively impede dislocation motion. In polycrystal systems, the progressive reduction in microvoid volume fraction indicates gradual microvoid collapse and deactivation. This happens through dislocation-mediated and interface-constrained mechanisms. The preferential formation of Lomer–Cottrell locks and twin boundaries around microvoids obstructs dislocation movement. These effects significantly enhance the material’s fatigue resistance.

It should be emphasized that the current conclusions are derived solely from molecular dynamics simulations. To substantiate these findings, systematic fatigue testing must be performed to validate the predicted improvements in fatigue life and damage tolerance observed in void-containing γ-TiAl alloys. Such experimental verification is essential to confirm these computational results and establish their broader applicability to real-world material systems. This constitutes a critical direction for our subsequent research.