Multi-scale analysis of mechanical properties of high-strength steel with heterogeneous characteristics after pre-fatigue damage

Abstract

This study investigates the residual mechanical behavior of Q690 high-strength steel after pre-fatigue damage by explicitly considering the non-homogeneous characteristics of the initial material. A framework combining experiments, molecular dynamics (MD) simulations, and finite element (FE) modeling is established. Monotonic tensile tests and fatigue experiments are first conducted to characterize the initial mechanical properties and the S–N relationship. Tensile tests on specimens subjected to different levels of pre-fatigue damage are then performed to quantify the degradation of elastic modulus, yield strength, ultimate strength, and ultimate strain. At the microscopic level, MD simulations are employed to reveal the damage evolution mechanisms and the atomic-scale origins of residual property degradation under cyclic loading. The obtained degradation laws are further incorporated into FE models with non-homogeneous initial material properties to simulate the fracture process and post-fatigue mechanical response. The results show that pre-fatigue damage has a negligible effect on the elastic modulus. A moderate strengthening effect on yield strength is observed at low damage levels, followed by a clear reduction with increasing fatigue damage. In contrast, ultimate strength and ultimate strain decrease monotonically, with the ultimate strain being more sensitive to fatigue damage. The proposed non-homogeneous multiscale modeling framework provides a more realistic description of fracture behavior and residual performance degradation in high-strength steels subjected to fatigue loading.

Keywords

High-strength steel multiscale analysis pre-fatigue damage residual mechanical properties

Introduction

High-strength steels are widely used in critical engineering structures, such as bridges, buildings, offshore platforms, and heavy machinery, owing to their high strength-to-weight ratio and favorable comprehensive mechanical properties.^1–3 During service, these structures are inevitably subjected to cyclic loading, which leads to the accumulation of fatigue damage.^4,5 As a result, the mechanical properties of the material gradually degrade, posing a serious threat to structural safety and durability. For Q690 and higher-grade high-strength steels, the inherent non-homogeneity of the microstructure plays a crucial role in fatigue damage initiation and evolution, making the post-fatigue mechanical behavior more complex.^6–8 Therefore, investigating the evolution of pre-fatigue damage while explicitly accounting for the initial material non-homogeneity is essential for accurately evaluating the residual load-carrying capacity and service life of damaged structures.

Existing studies on the fatigue behavior of high-strength steels mainly focus on fatigue life prediction, fatigue crack propagation, and fatigue performance under specific conditions, such as high temperature, corrosive environments, and welded joints.^9–11 Typical approaches include establishing S–N curves, observing crack growth behavior, and measuring residual strength and ductility after fatigue loading.^12–14 Mariappan et al.^15–19 evaluated the residual tensile strength of various metallic materials after fatigue loading and demonstrated that both loading conditions and material type significantly influence residual performance. Wu et al.²⁰ investigated the post-fatigue tensile behavior of 45# steel and found that the proportional limit increased with fatigue damage, while the fracture area gradually decreased. For materials such as 304LN stainless steel,²¹ 316L stainless steel,²² AISI 1022 steel,²³ and Ti–6Al–4 V alloy,²⁴ a slight increase in residual tensile strength has been reported due to strain hardening effects. In contrast, the residual tensile strength of AISI 4140-T steel and 9Cr steel decreases after pre-fatigue loading.^25,26 Cockings et al.²⁷studied the static mechanical properties of high-strength steels with yield strengths up to 1400 MPa, including AerMet100, 300 M, and corrosion-resistant MLX-17 steel, after low-cycle pre-fatigue loading. Their results indicated that moderate strain amplitudes could enhance yield and ultimate strengths, whereas excessive fatigue cycles or high strain amplitudes caused cyclic softening and performance degradation. Zhang et al.²⁸conducted multi-stage fatigue loading tests on Q690 high-strength steel and subsequently performed monotonic tensile tests. The results showed significant changes in fracture location and fracture morphology after fatigue damage. In addition, some studies have focused on fatigue damage evolution under different loading modes and high-temperature conditions.²⁹ However, most existing studies rarely establish a systematic multiscale correlation between the initial material non-homogeneity and the degradation of residual mechanical properties after pre-fatigue damage.

High-strength steels inherently exhibit microstructural non-uniformities, such as grain size variation, phase distribution heterogeneity, and defect localization. Under cyclic loading, these non-homogeneous regions may act as preferential sites for fatigue crack initiation and propagation. Consequently, revealing the influence of pre-fatigue damage on the mechanical behavior of Q690 high-strength steel across macro-, meso-, and micro-scales, while explicitly considering initial material non-homogeneity, remains a major challenge.

In this study, an experiment-calibrated and mechanism-informed multiscale analysis framework was established by combining tensile experiments, MD simulations, and FE modeling. The experimental results quantified the degradation of residual mechanical properties under different pre-fatigue damage levels, the MD simulations revealed the atomistic mechanisms responsible for such degradation, and the FE analysis reproduced the corresponding macroscopic stress distribution and fracture evolution. The framework therefore provides cross-scale consistency in understanding pre-fatigue damage effects, although a direct quantitative mapping from MD variables to FE constitutive parameters was beyond the scope of the present study.

The main contribution of this study lies in the establishment of a non-homogeneous multiscale modeling framework that systematically links pre-fatigue damage evolution with residual mechanical performance in Q690 high-strength steel. The findings enhance the fundamental understanding of fatigue-induced degradation mechanisms and provide a more reliable basis for fatigue-resistant design and safety assessment of high-strength steel structures. Moreover, the proposed approach offers potential guidance for the development of advanced high-strength steels with improved fatigue resistance.

Experimental analysis

Experimental program

Q690 high-strength steel was selected as the investigated material to study its mechanical behavior under different pre-fatigue loading conditions. As shown in Figure. 1, all specimens were machined from an 8 mm-thick Q690 steel plate. For each loading condition, five identical specimens were tested to ensure the repeatability of the experimental results, and the reported values represent the average of the measurements. The chemical composition of the Q690 high-strength steel plate is summarized in Table 1.

Figure 1.

Q690 high-strength steel specimen (unit: mm).

Table 1.

Chemical composition of Q690 high-strength steel (%).

Element	S	P	Al	Cu	Si	Nb	Cr	Mo	Ni		V	Mn	Ti	C	Fe
Proportion	0.005	0.01	0.04	0.3	0.35	0.03	0.4	0.02	0.3		0.003	1.5	0.03	0.16	others

Fatigue and tensile tests were conducted using the testing system shown inFigure 2. The machine is capable of both cyclic fatigue loading and monotonic tensile loading, with support for force-controlled and displacement-controlled modes. The available loading frequency ranges from 0.01 to 80 Hz. For monotonic tests, tensile loading was applied at a constant displacement rate of 1 mm/min. A fatigue loading frequency of 20 Hz was adopted in this study. To capture the deformation behavior during loading, a digital image correlation (DIC) system was employed to monitor strain evolution in real time. After fracture, the fracture surfaces of the specimens were examined using scanning electron microscopy (SEM).

Figure 2.

Fatigue and tensile tests.

Experimental procedure and results analysis

The testing process comprised four stages: initially, tensile tests were conducted to determine the initial mechanical properties of Q690 high-strength steel; subsequently, its fatigue life was measured; followed by pre-fatigue testing; finally, post-fatigue tensile tests were performed on specimens exhibiting pre-fatigue damage. The tensile test results are presented in Table 2.

Table 2.

Initial mechanical properties of Q690 high-strength steel.

Test specimen	Elastic modulus $E$ (GPa)	Yield strength $σ_{y}$ (MPa)	Ultimate strain $ε_{u}$ (%)	Ultimate strength $σ_{u}$ (MPa)	Elongation $δ$ (%)
1	212.3	789.4	10.76	894.3	21
2	207.4	775.3	12.38	872.3	15
3	207.3	799.5	11.34	884.7	22
4	204.4	769.5	12.37	867.7	24
5	209.6	785.6	10.12	893.4	18
Mean value	208.2	783.86	11.39	882.48	20

During fatigue loading, the maximum stress was limited to no more than 0.8 $σ_{y}$ . The stress ratio was defined as $R = σ_{m i n} / σ_{m a x}$ , and the stress amplitude was calculated as $σ_{a} = (σ_{m a x} - σ_{m i n}) / 2$ . A sinusoidal waveform was adopted for all fatigue loading cases. As summarized in Table 3, a total of 30 loading conditions were designed. For each condition, five specimens were tested, and the reported results correspond to the average values. In total, 150 specimens (30 × 5) were tested. For clarity, the experimental results listed in Table 3 are also presented graphically inFigure 3.

Figure 3.

Fatigue life curves at different stress ratios.

Table 3.

Experimental conditions and results.

Specimen number	Stress ratio $R$	Stress amplitude $σ_{a}$ (MPa)	Fatigue life
1	0.4	350	1,293,401
2		375	831,367
3		400	537,561
4		425	369,341
5		450	256,236
6		475	182,489
7	0.3	350	2,203,811
8		375	1,431,342
9		400	998,594
10		425	667,932
11		450	456,378
12		475	327,673
13	0.1	350	4,478,802
14		375	2,998,543
15		400	1,998,869
16		425	1,343,786
17		450	976,378
18		475	671,341
19	0	350	7,402,342
20		375	5,134,312
21		400	3,432,736
22		425	2,346,542
23		450	1,712,121
24		475	1,179,236
25	−1	350	#
26		375	#
27		400	#
28		425	#
29		450	9,126,345
30		475	6,356,390

Note: # indicates withstanding 10 million load cycles without fracture.

As indicated in Table 3 and Figure 3, at a constant stress amplitude, the fatigue life increases markedly with decreasing stress ratio R. For example, at a stress amplitude of $σ_{a} = 350$ MPa, the fatigue life is approximately $1.29 \times 10^{6}$ cycles when $R = 0.4$ . When the stress ratio decreases to $R = 0$ , the fatigue life increases to about $7.4 \times 10^{6}$ cycles. Under fully reversed loading ( $R = - 1$ ), no fracture was observed even after $10^{7}$ cycles, indicating a pronounced effect of stress ratio on fatigue life. These results demonstrate that reducing the stress ratio significantly extends the fatigue life of Q690 high-strength steel.

For a given stress ratio, the fatigue life decreases rapidly with increasing stress amplitude, which is consistent with the typical S–N behavior of metallic materials. Taking $R = 0$ as an example, the fatigue life decreases from approximately $7.4 \times 10^{6}$ cycles at $σ_{a} = 350$ MPa MPa to $1.18 \times 10^{6}$ cycles at $σ_{a} = 475$ MPa. Although the stress amplitude increases by about 36%, the corresponding fatigue life is reduced by nearly 84%. Under fully reversed loading ( $R = - 1$ ), specimens subjected to $σ_{a} = 425$ MPa did not fail after $10^{7}$ cycles, suggesting that this stress level is below the fatigue limit. When $σ_{a} \geq 425 MPa$ , finite-life failure still occurs, indicating that Q690 steel exhibits favorable high-cycle fatigue resistance under fully reversed loading conditions.

Overall, Q690 high-strength steel shows excellent fatigue resistance at low stress ratios, particularly for $R < 0$ , making it suitable for structural applications subjected to alternating and fully reversed loads. The fatigue life of Q690 steel is jointly governed by stress ratio and stress amplitude, and its S–N curves follow the typical fatigue behavior of metallic materials. Moreover, the potential fatigue limit observed under fully reversed loading provides valuable experimental evidence for the application of Q690 steel in high-cycle fatigue environments.

Following the Miller criterion, the fatigue damage is defined as^30,31:

D = \frac{n}{N_{f}}

(1)

Where, $n$ : Number of loading cycles under certain conditions; $N_{f}$ : Number of load cycles to failure under identical conditions.

In the present study, the fatigue damage variable $D = n / N_{f}$ was adopted as an engineering-level scalar index to quantify the pre-fatigue state of the specimens under constant-amplitude cyclic loading. It should be noted that this definition is based on the Miner linear damage accumulation concept and therefore does not account for loading sequence effects or the nonlinear nature of fatigue damage evolution. Accordingly, D is used here as a normalized descriptor for classifying different pre-fatigue conditions and linking them to the subsequent residual tensile response, rather than as a physically complete fatigue damage constitutive law.

Specimen No. 15 was selected as a representative case. Different levels of pre-fatigue damage were introduced according to Eq. (1), followed by monotonic tensile tests. The stress–strain curves were obtained using the DIC system, and the results are shown inFigure 4. As illustrated in Figure 4, pre-fatigue damage has a relatively limited influence on the overall shape of the stress–strain response, whereas its effect on the ultimate strain is much more pronounced. To further quantify this behavior, monotonic tensile tests were performed under three maximum stress levels, $σ_{m a x} =$ , 500, and 700 MPa, with varying pre-fatigue damage levels. The elastic modulus, yield strength, ultimate strength, and ultimate strain were extracted and summarized inFigures 5–8, respectively.

Figure 4.

Stress-strain curves at different pre-fatigue damage levels.

Figure 5.

Relationship between yield strength and pre-fatigue damage.

Figure 6.

Relationship between ultimate strength and pre-fatigue damage.

Figure 7.

Relationship between young's modulus and pre-fatigue damage.

Figure 8.

Relationship between ultimate strain and pre-fatigue damage.

Figure 5 shows that, at low levels of pre-fatigue damage, an increase in yield strength is observed at all stress levels. This behavior indicates a cyclic hardening effect during the early stages of fatigue loading. The hardening is primarily attributed to the increase in dislocation density and their mutual interactions, which hinder subsequent plastic deformation and temporarily raise the flow stress. With further accumulation of fatigue damage, damage-induced softening mechanisms dominated by microcrack initiation and propagation become increasingly important, leading to a gradual reduction in yield strength from its peak value. At $σ_{m a x} = 300$ MP, the stress level is relatively low, and the cyclic hardening effect is more pronounced and persistent. The yield strength exhibits a clear trend of initial increase followed by a gradual decrease with increasing damage. This suggests that microstructural strengthening mechanisms can effectively counteract damage accumulation over an extended fatigue period. At $σ_{m a x} = 500$ MP, the competition between hardening and softening becomes more intense. The yield strength shows a shorter or more moderate hardening stage, followed by a transition to softening as damage accumulates, with the turning point occurring earlier than that under low stress conditions. At $σ_{m a x} = 700$ MP, the high stress level significantly accelerates plastic deformation and early damage evolution. Although a slight initial increase in yield strength may still occur due to rapid dislocation multiplication, fatigue damage mechanisms, such as micro-void nucleation and coalescence, quickly become dominant. Consequently, the yield strength decreases a moderate reduction at relatively low damage levels, and the overall mechanical degradation is the most severe.

As shown in Figure 6, at low stress levels, the initiation and propagation of fatigue damage proceed at a relatively slow rate. During the early stage of damage accumulation, microstructural rearrangement induced by cyclic loading may provide partial support to the ultimate strength, resulting in a very gradual initial decrease. With continued increase in the number of fatigue cycles, the cumulative effect of micro-damage becomes dominant, and the ultimate strength exhibits a stable and slow downward trend. At intermediate stress levels, sufficient driving force is provided to promote damage evolution, while a limited degree of plastic hardening may still occur. A nearly linear decrease in ultimate strength with increasing damage is observed. This behavior suggests that, under such conditions, the weakening effect induced by damage accumulation is nearly balanced by the transient hardening effect, or that the hardening stage is extremely short-lived. Consequently, damage evolution becomes the primary factor governing the degradation of ultimate strength. At high stress levels, the fatigue damage process is significantly accelerated. Extensive plastic deformation zones and microcracks rapidly form within the material, leading to a pronounced reduction in the effective load-bearing area. As a result, the ultimate strength shows a moderate reduction trend at very low levels of pre-fatigue damage. The corresponding curves are characterized by a steep initial drop, followed by a slightly reduced degradation rate as damage modes approach saturation. Under these conditions, any potential microstructural hardening effects are quickly overwhelmed by severe macroscopic damage.

Figure 7 indicates that the elastic modulus remains nearly unchanged throughout the pre-fatigue process. From a theoretical perspective, the elastic modulus is primarily governed by interatomic bonding and crystal structure, and is therefore relatively insensitive to discrete micro-defects such as dislocations and micro-voids. As shown in Figure 8, the reduction in ultimate strain directly reflects the loss of material ductility, which is closely associated with microcrack initiation, propagation, and final unstable fracture during fatigue loading. Pre-fatigue damage introduces irreversible micro-defects into the material, which act as local stress concentrators during subsequent tensile loading. These defects promote premature necking or unstable crack growth, significantly reducing the overall deformation capacity. Consequently, the ultimate strain decreases monotonically with increasing pre-fatigue damage, and the degradation rate depends on the applied stress level and damage evolution stage. Higher maximum stress levels lead to an earlier onset and faster rate of ductility degradation, indicating a transition from slow damage accumulation to the coupled action of damage and plastic instability. This behavior is critical for evaluating the residual deformation capacity and fracture resistance of structural components subjected to cyclic loading.

To further examine the influence of pre-fatigue damage on tensile fracture morphology, fracture surfaces were observed using scanning electron microscopy. The corresponding results are presented in Figure 9.

Figure 9.

Tensile fracture morphology following pre-fatigue damage.

As shown in Figure 9, the fracture surface of the specimen without pre-fatigue damage exhibits well-developed dimples and a pronounced 45° shear lip. These features indicate extensive plastic deformation prior to fracture and are characteristic of a typical ductile fracture mode. With the introduction of pre-fatigue damage, a clear transition in fracture morphology is observed. Although well-developed dimples can still be identified at the bottom of the cup-shaped fracture surface, the shear lip angle is reduced. In addition, fine shell-like fatigue propagation markings appear in the upper right region of the fracture surface. This observation suggests that part of the material's plastic deformation capacity has been consumed during cyclic loading, and the overall fracture behavior shifts toward a plane tensile fracture mode. As the pre-fatigue damage level further increases, brittle fracture features become more pronounced. A distinct radial fatigue crack propagation region can be observed in the upper left area of the fracture surface, whereas the subsequent monotonic tensile fracture region shows little evidence of dimple formation. This morphology indicates that significant fatigue crack growth has already occurred prior to the final tensile failure, leaving the material with limited plastic deformation capacity under static loading and resulting in a predominantly brittle fracture response.

As shown in Figure 9, the fracture surface consists of a fatigue crack propagation zone and a final static tensile fracture zone. The final static tensile fracture zone, labeled in the figure, does not show obvious ductile dimples. This absence of dimples indicates that substantial fatigue crack propagation occurred before the final tensile fracture, leaving only a limited remaining ligament to fail under static tension. Therefore, the final fracture exhibits a relatively brittle morphology

Overall, the fracture surface analysis demonstrates that the fracture mechanism of Q690 high-strength steel gradually transitions from ductile to brittle with increasing pre-fatigue damage. The progressive weakening of dimple structures and shear lips, together with the increasingly prominent fatigue propagation features, provides direct microstructural evidence supporting the degradation of plasticity observed in the mechanical test results.

Numerical analysis

Molecular dynamics analysis

Molecular dynamics (MD) is a computational simulation technique based on classical Newtonian mechanics, which aims to reveal the physical and chemical properties of materials at the atomic scale. In MD simulations, atoms are treated as interacting particles, and the trajectories of all atoms in phase space are obtained by numerically solving the equations of motion for a many-body system. This method provides detailed time-resolved information on atomic motion and structural evolution, and serves as an essential bridge between microscopic mechanisms and macroscopic observable properties, such as thermodynamic behavior, kinetics, and mechanical response. To investigate the microstructural mechanisms underlying the degradation of mechanical properties induced by fatigue damage in high-strength steel, a molecular dynamics model was established, as shown inFigure 10. All simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS),³² and atomic-scale visualization and post-processing were conducted using OVITO.³³ An α-Fe body-centered cubic (bcc) lattice was first constructed as the base matrix. Subsequently, alloying elements were introduced through atomic substitution to ensure that the chemical composition of the model was consistent with that listed in Table 1. In the MD framework, for a system consisting of $N$ atoms, the equation of motion for the $i - t h$ atom can be expressed as^34–36:

m_{i} \frac{d^{2} r_{i}}{d t^{2}} = F_{i} = - \nabla_{i} U (r_{1}, r_{2}, \dots, r_{N})

(2)

Figure 10.

Molecular dynamics model.

Where, $m_{i}$ and $r_{i}$ : the mass and position vector of the i-th atom respectively; $F_{i}$ : The total force exerted on the atom; $U$ : The total potential energy function of the system.

To numerically solve the governing equations of motion, the Velocity–Verlet algorithm was employed to discretize time and iteratively update the atomic positions and velocities, thereby generating the dynamical trajectories of the system. The accuracy of molecular dynamics simulations is strongly dependent on the choice of the interatomic potential, which defines the relationship between atomic interaction energy and relative atomic positions. In this study, a fully atomistic machine-learning-based interatomic potential was adopted to ensure an accurate description of atomic interactions under cyclic loading and subsequent tensile deformation.^37–39 Prior to mechanical loading, geometric optimization was performed by energy minimization under the canonical ensemble (NVT) to eliminate residual stresses and stabilize the atomic configuration. Subsequently, pre-fatigue damage was introduced under the isothermal–isobaric ensemble (NPT) following the procedure defined in Eq. (1), after which monotonic tensile loading was applied. The stress–strain responses corresponding to different levels of pre-fatigue damage are presented in Figure 11. The associated phase transformation behaviors under different pre-fatigue damage levels are shown inFigure 12.

Figure 11.

Tensile curves after different pre-fatigue damage levels.

Figure 12.

Microstructural transformations in different pre-fatigued specimens.

Figure 11 presents the uniaxial tensile stress–strain responses of the simulated system after different numbers of pre-fatigue cycles. Overall, the mechanical response exhibits a systematic evolution with increasing pre-fatigue damage. In the low-strain regime, all curves display an approximately linear elastic behavior. However, a slight reduction in the elastic modulus is observed as the pre-fatigue damage increases. This trend indicates that pre-fatigue loading introduces lattice disturbances at the atomic scale, such as point defects and dislocation loops, which weaken the effective interatomic bonding stiffness. The specimen without pre-fatigue damage shows a pronounced stress peak at the onset of yielding, followed by a stable plastic flow regime. With increasing fatigue damage, the yield strength gradually decreases, and the yield plateau becomes less distinct or even disappears. This behavior suggests that fatigue-induced crystal defects promote the early nucleation and motion of dislocations, thereby reducing the resistance to plastic deformation during subsequent tensile loading. In addition, the fracture strain decreases significantly with increasing pre-fatigue damage. Specimens subjected to high-cycle fatigue fail at relatively low strains, exhibiting a brittle fracture response. This observation indicates that fatigue damage markedly consumes the plastic deformation capacity, facilitating the nucleation and rapid propagation of atomic-scale microcracks at damage-concentrated regions.

Figure 12 presents the evolution of local atomic environments during tensile deformation for specimens with different pre-fatigue damage levels. At the initial stage of deformation, most atoms are identified as BCC, indicating that the matrix structure remains dominant. With increasing tensile strain, the fraction of atoms classified as FCC-like, HCP-like, or disordered gradually increases in highly deformed regions, especially near defect clusters, shear-localized regions, and crack initiation sites.

It should be noted that the FCC/HCP atoms identified in the MD simulations do not necessarily correspond to a real bulk BCC-to-FCC or BCC-to-HCP phase transformation in experimental Q690 steel. The classification is based on the local atomic geometry. Under severe plastic deformation, dislocation cores, stacking-fault-like configurations, twin-like local arrangements, and highly distorted BCC lattices may be recognized as FCC/HCP-like local environments by the structural analysis algorithm. Therefore, the FCC/HCP-like regions in Figure 12 are interpreted as indicators of local lattice rearrangement, atomic-scale disordering, and defect-assisted deformation localization rather than direct evidence of massive phase transformation.

With increasing pre-fatigue damage level, the emergence of non-BCC local atomic environments occurs at lower applied strain and becomes more spatially concentrated around pre-existing defect-rich regions. This result suggests that pre-fatigue-induced defects reduce the local structural stability of the lattice and promote earlier deformation localization during subsequent tensile loading. Such local structural instability is consistent with the experimentally observed reduction in residual ductility and accelerated fracture after fatigue pre-damage.

Nevertheless, the MD simulation results should be considered qualitative and mechanism-informed. The high strain rate, nanoscale model size, periodic boundary conditions, interatomic potential, and local structural classification method may all influence the predicted atomic configurations. Therefore, further experimental characterization, such as TEM, high-resolution EBSD, synchrotron XRD, or in-situ diffraction measurements, is required to verify whether similar local atomic-scale structural rearrangements occur in actual pre-fatigued Q690 steel during tensile deformation.

To further elucidate the influence of fatigue loading on damage evolution in steel, detailed analyses of dislocations and defects were performed, as shown inFigure 13. The molecular dynamics simulations systematically reveal the evolution of microstructural defects, including point defects and vacancy clusters, as well as dislocation structures, such as dislocation lines, loops, and entanglements, under different pre-fatigue cycle numbers. These results provide direct atomic-scale evidence for the mechanisms of fatigue damage accumulation and clarify how microstructural degradation governs the subsequent deterioration of mechanical performance.

Figure 13.

Microstructural defects and dislocation evolution processes in different pre-fatigued damages(the gray region denotes the background matrix atoms, while the colored region highlights the localized affected area.).

As shown in Figure 13, a limited number of fatigue cycles introduce sparsely distributed lattice defects accompanied by a small population of isolated dislocation segments. With increasing cyclic loading, the dislocation density increases markedly, and pronounced interactions such as cross-slip, dislocation reactions, and entanglements are observed. These interactions progressively restrict further dislocation storage and mobility, leading to a transient strengthening effect manifested in the subsequent tensile stress–strain response. Upon further accumulation of fatigue cycles, the dislocation structures undergo substantial reorganization, evolving into well-defined dislocation cells or dense dislocation tangles. Concurrently, the spatial distribution of defects transitions from a relatively homogeneous state to a highly localized configuration. Such defect localization provides preferential sites for strain concentration, thereby facilitating the initiation of macroscopic shear bands and microcracks. The combined effects of micro-void coalescence, early-stage microcrack nucleation, and severe strain localization within a limited number of shear bands significantly reduce the material's capacity for uniform plastic deformation, resulting in a pronounced decrease in fracture strain.

Figures 14 and 15 further illustrate the complete fracture evolution of specimens with pre-fatigue damage subjected to subsequent uniaxial tensile loading. These results demonstrate that pre-fatigue damage fundamentally alters the internal defect architecture, which in turn governs deformation localization, crack initiation, and crack propagation paths, ultimately determining the fracture mode and fracture trajectory of the material.

Figure 14.

Tensile fracture process following pre-fatigue damage.

Figure 15.

Evolution of dislocations and defects during tensile fracture following pre-fatigue damage(the gray region indicates the surrounding matrix/background atoms, and the colored region shows the localized affected zone.).

As illustrated in Figure 14, the presence of a high density of mobile dislocations and micro-scale damage introduced during pre-fatigue loading causes the material to undergo only a short stage of uniform plastic deformation during the initial phase of subsequent tensile loading, with macroscopic necking potentially occurring at an early stage. Plastic deformation rapidly localizes within one or several potential softening bands that coincide with pre-fatigue-induced defect zones. Within these regions, pre-existing micro-voids or microcracks become activated under tensile stress, grow, and progressively coalesce. A dominant crack subsequently emerges from the most severely damaged zone and propagates rapidly along paths characterized by concentrated defects. The orientation of the resulting fracture surface may deviate from the direction of maximum shear stress, reflecting anisotropic weakening induced by pre-fatigue damage. The final fracture exhibits pronounced brittle-like characteristics, with a relatively flat fracture surface and an absence of well-developed shear lips.

As shown in Figure 15, dislocation tangles or cell structures formed during pre-fatigue loading are readily activated during subsequent tensile deformation, leading to rapid dislocation multiplication and motion that accommodate the initial plastic strain. Simultaneously, pre-existing vacancy clusters absorb newly generated point defects and undergo gradual growth. Dislocation activity progressively localizes within the softening bands, where dislocations pile up against obstacles such as cell walls and micro-voids, generating high local stress concentrations that promote void growth and linkage. Micro-voids preferentially enlarge by absorbing dislocations and vacancies and become aligned along the softening bands. A positive feedback mechanism is thus established, in which dislocation motion accelerates void growth, while void growth further impedes dislocation motion and intensifies local stress concentrations. Adjacent micro-voids subsequently coalesce through internal necking or shear linkage, forming a continuous microcrack. The intense stress field ahead of the dominant crack tip drives rapid crack advance via dislocation emission, phase transformation, or direct cleavage. At this stage, dislocation activity in regions remote from the crack path is largely suppressed, and plastic deformation becomes fully concentrated within the crack propagation process.

With increasing strain, the MD simulations show the emergence of FCC-like local atomic environments in some highly deformed regions. In the present study, this phenomenon is interpreted as local lattice rearrangement and severe structural distortion under deformation, rather than as definitive evidence of a bulk BCC-to-FCC phase transformation in the experimental material. It should be noted that this simulation-observed structural evolution may be influenced by the machine-learning interatomic potential, the nanoscale model size, and the high strain rates inherent in MD simulations. Therefore, further experimental verification, such as TEM or diffraction-based characterization, is required to assess whether similar local structural evolution occurs in actual pre-fatigued Q690 steel during tensile loading.

Finite element analysis

In conventional finite element analyses, a homogeneous material model is commonly adopted for the entire global structure. However, due to initial material imperfections, manufacturing-induced variability, and other intrinsic factors, mechanical properties may exhibit a certain degree of spatial dispersion across different regions of the structure. When such heterogeneity is neglected, the constitutive behavior of Q690 high-strength steel can be reasonably approximated by a bilinear elastoplastic hardening model, as expressed in Eq. (3).⁴⁰

{\begin{matrix} σ = E \cdot ε σ \leq σ_{y} \\ σ = σ_{y} + E_{t a n} \cdot (ε - ε_{p}) σ_{y} \leq σ \leq σ_{u} \end{matrix}

(3)

When the initial material heterogeneity is taken into account, the key constitutive parameters—namely the elastic modulus E, tangent modulus $E_{t a n}$ , yield strength $σ_{y}$ , ultimate strength $σ_{u}$ , and ultimate strain $ε_{u}$ are assumed to follow Gaussian distributions. Specifically, $E \sim N (200 GPa, 5)$ ， $E_{t a n}$ ∼ $N (12 G P a, 2)$ , $σ_{y} \sim N (783.6 MPa$ $, 20)$ , $σ_{u} \sim N (850 MPa, 20)$ , $ε_{u} \sim N (10.5 %, 1.5 %)$ . It should be noted that the initial non-uniform material model adopted in the FE analysis is an effective stochastic representation of spatial constitutive variability at the continuum scale, rather than a direct reconstruction of the actual microstructure of Q690 steel. The Gaussian-distributed material parameters were introduced to reflect the statistical nonuniformity of local mechanical resistance arising from microstructural heterogeneity and fatigue-induced damage localization. This treatment does not explicitly account for grain morphology, phase topology, crystallographic orientation, or measured metallographic correlation distance. Therefore, the present model is intended to capture the macroscopic influence of heterogeneous residual properties on stress redistribution and fracture evolution, rather than to reproduce the true microstructure in a one-to-one manner. It should be noted that the initial tensile dataset, consisting of five specimens for each pre-fatigue condition, was sufficient to identify the general degradation trend of the mean mechanical properties but limited for statistically robust estimation of variance. To strengthen the stochastic characterization used in the heterogeneous FE model, an additional 125 groups of experiments were subsequently conducted. The expanded dataset provides a more reliable basis for evaluating the scatter of the key constitutive parameters and offers stronger support for the use of Gaussian-distributed material properties as an effective continuum-level approximation of spatial heterogeneity.

After incorporating the effects of pre-fatigue damage, the stress–strain response of Q690 steel can be further simplified and represented by the constitutive model given in Eq. (4).

{\begin{matrix} σ = E \cdot ε σ \leq σ_{y}^{'} \\ σ = σ_{y}^{'} + E_{t a n} \cdot (ε - ε_{p}) σ_{y}^{'} \leq σ \leq σ_{u}^{'} \end{matrix}

(4)

Here, the degraded yield strength $σ_{y}^{'}$ , ultimate strength $σ_{u}^{'}$ , and ultimate strain $ε_{u}^{'}$ are determined from the experimental results shown in Figures 5, 6, and 8, respectively, and are likewise assumed to follow Gaussian distributions.

The damage evolution process is characterized by a ductile damage model. After the material reaches its ultimate stress, it enters the damage stage, and the scalar damage variable $D_{t e n s i l e}$ reflects the degradation of effective load-bearing capacity. The value of $D_{t e n s i l e}$ ranges from 0 to 1, corresponding to the undamaged state and complete failure state, respectively. Damage initiates when the equivalent plastic strain ${\bar{ε}}^{p l}$ reaches the critical value ${\bar{ε}}_{0}^{p l}$ ; after damage initiation, the damage evolution is governed by the equivalent plastic displacement ${\bar{u}}^{p l}$ , whose expression is given in Eq. (5).

{\bar{u}}^{p l} = ({\bar{ε}}^{p l} - {\bar{ε}}_{0}^{p l}) \cdot l_{c}

(5)

Where, $l_{c}$ is the characteristic length of the finite element.

The damage variable $D_{t e n s i l e}$ evolves linearly with the equivalent plastic displacement ${\bar{u}}^{p l}$ :

D_{t e n s i l e} = \frac{{\bar{u}}^{p l}}{d_{failure}}, 0 \leq D_{t e n s i l e} \leq 1

(6)

Where the damage failure displacement $d_{failure}$ is defined as:

d_{f a i l u r e} = ({\bar{ε}}_{t}^{p l} - {\bar{ε}}_{0}^{p l}) \cdot l_{c}

(7)

When ${\bar{u}}^{p l} = d_{f a i l u r e}$ , the damage variable reaches $D_{t e n s i l e} = 1$ , indicating that the material fails completely and loses its load-bearing capacity.

As illustrated inFigure 16, a finite element model incorporating the initial material heterogeneity was developed in Abaqus, with the specimen geometry defined according to Figure 1. To ensure the reliability of the subsequent numerical results, a mesh sensitivity analysis was performed by systematically varying the element size. The optimal mesh density was identified by comparing the convergence of key response quantities between successive refinements, and the corresponding results are presented inFigure 17.

Figure 16.

Finite element model.

Figure 17.

Mesh sensitivity analysis results.

When a uniaxial tensile stress of 300 MPa is applied to the finite element model shown in Figure 16, pronounced stress heterogeneity is observed among the elements, reflecting the explicitly introduced material non-uniformity. As indicated in Figure 17, with decreasing element size (i.e., progressive mesh refinement), the predicted maximum tensile stress exhibits an initial marked variation followed by a gradual stabilization, demonstrating clear convergence behavior. A mesh size of 3 mm provides satisfactory convergence, ensuring that the numerical results are stable within an acceptable error range. This mesh resolution therefore offers a reliable numerical basis for subsequent simulations of the mechanical response and fracture evolution under different pre-fatigue damage states. All subsequent finite element analyses were conducted using this converged mesh to maintain numerical robustness and consistency of the results. Static tensile simulations were then performed for models with different levels of pre-fatigue damage using displacement-controlled loading. The corresponding finite element results are presented in Figure 18.

Figure 18.

Tensile stress-strain curves under different pre-fatigue damage states.

Figure 18 presents the uniaxial tensile stress–strain responses of the material under six levels of pre-fatigue damage (damage factor $D = 0, 0.1, 0.2, 0.3, 0.4$ ,and $0.5$ ). A systematic comparison clearly reveals the pronounced influence of pre-fatigue damage on the elastic response, plastic deformation behavior, strength, and deformation capacity of the material, providing direct evidence of the linkage between damage accumulation and macroscopic mechanical degradation.

With increasing pre-fatigue damage factor D, the stress–strain curves exhibit a progressive and systematic degradation. First, the overall stress level decreases, indicating a continuous reduction in load-carrying capacity. Second, the curves become increasingly flattened, reflecting a pronounced loss of uniform plastic deformation capability and a reduced strain reserve prior to fracture. Third, a slight reduction in the slope of the initial elastic segment is observed, suggesting a modest stiffness degradation induced by accumulated damage. At low levels of pre-fatigue damage, dislocation rearrangement and early-stage microstructural damage begin to suppress uniform plastic flow, promoting a gradual transition toward localized deformation. In contrast, at high pre-fatigue damage levels, the stress–strain curves reach their peak stress at relatively low strain and subsequently drop sharply, with little or no discernible plastic flow stage. This behavior indicates the presence of well-developed damage bands or microcracks within the material, which trigger rapid instability and premature fracture during tensile loading.

Figure 19 further compares, via finite element simulations, the complete fracture processes of specimens without pre-fatigue damage (Figure 19(a)) and with pre-fatigue damage (Figure 19(b)) under uniaxial tension.

Figure 19.

Fracture process of finite element model: (a) without pre-fatigue damage; (b) with pre-fatigue damage.

Figures 20 and 21 present the post-fracture surfaces of the finite element models without and with pre-fatigue damage, respectively, after completion of tensile failure.

Figure 20.

Fracture surface characteristics of the model without pre-fatigue damage.

Figure 21.

Fracture surface characteristics of the model with pre-fatigue damage.

Figure 19 compares the fracture evolution of the finite element models without pre-fatigue damage and with pre-fatigue damage under uniaxial tension. The von Mises stress contours illustrate the general progression from loading to final failure in the two cases. Although the differences in intermediate stress fields are not always very pronounced in the contour plots alone, the two models exhibit different overall failure evolution characteristics. In combination with the results shown in Figures 20 and 21, the specimen without pre-fatigue damage tends to show a more typical necking-dominated failure process, whereas the pre-fatigued specimen exhibits earlier damage localization and a less regular fracture evolution.

The experimental fracture surface of the pre-fatigued specimen exhibits distinct fatigue propagation zones, radial marks, and brittle features, which are in good agreement with the numerical predictions. In particular, the multiple stress concentration sites (“multi-nucleation” behavior) identified in the simulations provide a mechanistic explanation for the presence of multiple fatigue origins or tearing ridges observed on the fracture surface. Overall, the numerical fracture patterns show good qualitative agreement with the scanning electron microscopy observations, further validating the proposed modeling framework.

The element-wise Gaussian property assignment used in this study does not include spatial correlation length and does not explicitly represent grain-scale microstructural features. Therefore, the resulting stress contours should be interpreted as qualitative indicators of the possible influence of initial property scatter rather than direct evidence of actual microstructure-induced localization. A more physically based model, such as an EBSD-informed finite element model, Voronoi grain model, crystal plasticity model, or spatially correlated random-field model, is required to capture the true localization physics associated with metallurgical heterogeneity

Conclusions

This study systematically investigated the residual mechanical behavior and fracture mechanisms of Q690 high-strength steel subjected to pre-fatigue damage, with particular emphasis on the role of initial material non-homogeneity. By experiments, molecular dynamics (MD) simulations, and finite element (FE) modeling, a consistent multi-scale framework was established to link microstructural damage evolution with macroscopic mechanical degradation and fracture behavior. It should be acknowledged that the present study does not establish a rigorous quantitative bridge law between MD-derived atomistic descriptors and FE constitutive/damage parameters. Specifically, variables such as defect density, vacancy fraction, local structural disorder, and dislocation density were not directly mapped onto continuum quantities such as elastic modulus degradation, yield strength evolution, or fracture strain. Instead, the current coupling is experiment-calibrated and mechanism-informed. Establishing a direct atomistic-to-continuum mapping framework through statistical homogenization or internal-variable-based constitutive modeling remains an important topic for future work. The main conclusions can be summarized as follows:

Effect of pre-fatigue damage on residual mechanical properties: Pre-fatigue damage has a negligible influence on the elastic modulus of Q690 steel, whereas its effects on strength and ductility are pronounced. At low damage levels, a moderate increase in yield strength is observed, which can be attributed to cyclic hardening induced by dislocation accumulation and interaction. With increasing damage, damage-softening mechanisms associated with microcrack initiation and growth dominate, leading to a progressive reduction in yield strength. Both ultimate strength and, more significantly, fracture strain decrease monotonically with increasing pre-fatigue damage, indicating a substantial loss of plastic deformation capacity.

Micro-mechanisms revealed by molecular dynamics simulations: MD simulations demonstrate that pre-fatigue loading introduces a high density of lattice defects, including point defects, dislocation tangles, and vacancy clusters. At low fatigue cycles, dislocation multiplication and interaction lead to transient strengthening. With further cycling, defects reorganize into dislocation cells and highly localized defect bands, which promote strain localization, early micro-void nucleation, and microcrack formation during subsequent tensile loading. Pre-fatigue damage also accelerates phase transformation and structural disordering, causing earlier onset of localized softening and ultimately triggering premature brittle fracture at relatively low strains.

Role of initial material non-homogeneity in fracture behavior: Finite element simulations incorporating statistically distributed material parameters successfully capture the experimentally observed non-uniform stress and strain fields. Compared with homogeneous models, the non-homogeneous material representation leads to earlier strain localization, multiple stress concentration sites, and more realistic crack initiation locations. This confirms that initial material non-homogeneity plays a critical role in governing damage accumulation and fracture evolution, particularly in pre-fatigued specimens.

Transition of fracture modes induced by pre-fatigue damage: Both experiments and simulations reveal a clear transition in fracture mechanisms with increasing pre-fatigue damage. Specimens without pre-fatigue damage exhibit stable necking and ductile fracture characterized by shear lips and dimples. In contrast, pre-fatigued specimens show limited uniform plastic deformation, highly localized damage, and tortuous crack paths guided by pre-existing defect bands, resulting in fracture surfaces dominated by fatigue propagation features and quasi-brittle characteristics.

Implications for fatigue-resistant design and life assessment: The results demonstrate that neglecting pre-fatigue damage and initial material non-homogeneity may lead to a significant overestimation of residual strength and ductility. The proposed multi-scale, non-homogeneous modeling framework provides a physically grounded approach for predicting residual mechanical performance and fracture behavior of high-strength steels under cyclic loading histories, and offers valuable insights for the fatigue-resistant design and remaining life assessment of engineering structures subjected to complex service conditions.

Overall, this work highlights the necessity of explicitly accounting for both pre-fatigue damage and initial material non-homogeneity to achieve reliable predictions of fracture behavior in high-strength steels under combined cyclic and monotonic loading.

Footnotes

Acknowledgments

The research for this paper supported by the China Postdoctoral Science Foundation under Grant Number 2025M773286 and Lianyungang Postdoctoral Science Foundation under Grant Number LYGBSH2025017.

ORCID iD

Songling Xue

CRediT authorship contribution statement

Songling Xue: Writing – original draft, Visualization, Methodology, Conceptualization. Dong Tang: Methodology. Ruili Shen: Supervision, Data curation.

Funding

The authors received financial support for the research, authorship, and/or publication of this article: The research for this paper supported by the China Postdoctoral Science Foundation under grant number 2025M773286 and Lianyungang Postdoctoral Science Foundation under grant number LYGBSH2025017.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability

Data will be made available on request.

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