Creep Behavior and Deformation Mechanism of Aluminum Alloy: Integrating Multiscale Simulation and Experiments

Abstract

Aluminum (Al) alloys exhibit exceptional mechanical properties, seeing widespread use in various industrial fields. Here, we use a multiscale simulation method combining phase field method, dislocation dynamics, and crystal plasticity finite element method to reveal the evolution law of precipitates, the interaction mechanism between dislocations and precipitates, and the grain-level creep deformation mechanism in 7A09 Al alloy under creep loading. The phase field method indicates that Al alloys tend to form fewer but larger precipitates during the creep process, under the dominant effect of stress-assisted Ostwald ripening. The dynamic equilibrium process of precipitate is not only controlled by classical diffusion mechanisms, but also closely related to the local strain field induced by dislocations and the elastic interaction between precipitates. Dislocation dynamics simulations indicate that the appearance of multiple dislocation loops around the precipitate during the creep process is the main dislocation creep deformation mechanism. A crystal plasticity finite element model is established based on experimental characterization to investigate the macroscopic creep mechanism. The dislocation climb is hindered by grain boundaries during creep, and high-density dislocation bands are formed around specific grains, promoting non-uniform plastic strain and leading to strong strain gradients. This work provides fundamental insights into understanding creep behavior and deformation mechanism of Al alloy for deep-sea environments.

1. Introduction

Creep presents a critical challenge for the structural integrity of deep-sea vessels, where the aluminum (Al) alloy pressure hull endures immense and constant hydrostatic pressure for prolonged durations [1,2,3,4,5]. While operating in an ambient seawater environment, the combination of exceptionally high stress and extended exposure times makes creep a significant design consideration, potentially compromising long-term safety and performance [6,7]. High-strength Al alloys, particularly the 7A09 (Al-Zn-Mg-Cu) type, are prime candidates for these demanding marine pressure hulls due to their excellent strength-to-weight ratio and corrosion resistance [8,9]. Accurately predicting the creep behavior of 7A09 Al alloys under deep-sea conditions necessitates moving beyond purely empirical models to those rooted in fundamental deformation physics models, a goal powerfully enabled by advanced multi-scale simulations [10,11,12].

The performance of 7A09 alloy under deep-sea service hinges critically on its resistance to time-dependent deformation driven by high hydrostatic stress. Microstructural evolution, particularly the interaction of dislocations with strengthening precipitates, grain boundaries, and solute atoms under persistent load, dictates long-term creep resistance [13,14,15]. It is essential to fully understand how these features interact across atomic, micro-, and macro- scales. However, the explicit quantitative relationship between dominant nano-/micro-scale deformation mechanisms (e.g., dislocation glide, climb, and pinning at precipitates) and measurable macroscopic creep rates under high pressure remains inadequately established [16,17,18,19]. Computational multi-scale simulation offers a unique pathway to directly probe these complex, interdependent mechanisms in ways difficult or impossible with experiment alone, enabling fundamental insight for predicting 7A09 alloy life and optimizing material design for deep-sea environments [10,19,20,21].

At present, the creep model of 7A09 Al alloy under deep-sea pressure generally relies on macroscopic observation and phenomenological relationships. These approaches lack a robust physical foundation, making it difficult to link the measurable macroscopic creep strain rate with the potential activity of the deformation mechanism controlled by the evolving microstructure under high stress [22,23,24,25]. Crucially, under high hydrostatic pressure, the mechanisms like the dislocation motion hindered by precipitates, the interaction between lattice distortion effect and dislocation, the potential accommodation process of grain boundary or their relative contributions shift throughout the creep stages have not been clearly quantified [24,26]. Bridging this gap demands a deliberate multi-scale simulation approach, integrating distinct computational methods across different length and time scales to unravel the complex interplay governing time-dependent deformation and explicitly link micro-mechanistic activity to the macroscopic response of the 7A09 alloy under representative deep-sea loading [27,28,29].

The present study aims to establish a physically based understanding of creep in 7A09 Al alloy under deep-sea hydrostatic pressure by conducting a systematic multi-scale simulation investigation into the multiscale deformation mechanisms. This study adopted the collaborative combination of multiple computing techniques: the micrometer-scale phase field method is used to investigate the evolution of the precipitate under pressure; the discrete dislocation dynamics simulation of mesoscale simulation shows the collective dislocation behavior and the interaction of dislocation precipitates under continuous hydrostatic stress equivalent to deep-sea conditions. The creep curve of polycrystalline response is predicted by macroscopic crystal plastic finite element method. The stress, strain distribution, and dislocation density evolution are studied, revealing the creep deformation mechanism of 7A09 alloy at grain level. The simulation results of different scales provide multiple perspectives to reveal the creep deformation mechanism of 7A09 alloy under deep-sea pressure. This study provides basic insights for the life prediction of 7A09 alloy and the material optimization design of deep-sea environment.

2. Experiments

The experimental material is 7A09 Al alloy sheet. The chemical composition of the alloy is: Mg 3.9, Cu 2.0, and the remaining Al (mass fraction, %). In order to eliminate the randomness and improve reproducibility of the experimental results, 5 sets of uniaxial tensile specimens and 3 sets of creep test specimens are constructed. The tensile specimen adapts the internationally common dumbbell-shaped structure design. The geometric dimensions of the 7A09 aluminum alloy tensile specimen are shown in Figure 1a. The gauge length section is 20 mm, the width is 3.4 mm, the thickness is 1.5 mm, the radius of the transition arc is 6.64 mm, and the width of the clamping end is 10 mm. The strain rate is controlled at 2 × 10⁻⁴ s⁻¹.

The microstructure of the sample is characterized using a field-emission scanning electron microscope (SEM, Zeiss Ultra 55, Carl Zeiss Microscopy, Jena, Germany). Samples are mounted on Al stubs with conductive carbon tape and sputter-coated with a 5 nm platinum layer to ensure electrical conductivity. Secondary electron (SE) and backscattered electron (BSE) images are acquired at accelerating voltages of 5–20 kV and working distances of 5–10 mm under high-vacuum conditions (≤10⁻³ Pa). For high-resolution imaging, the in-lens SE detector is utilized at 5 kV with a 3 mm working distance.

Crystallographic orientation mapping is performed using an EBSD system (HKL Channel 5, Oxford Instruments, Abingdon, UK). Samples are mechanically polished to a mirror finish, followed by vibratory polishing with 0.02 μm colloidal silica for 4 h to eliminate surface deformation. The specimen is tilted to 70° relative to the incident beam, and Kikuchi patterns are collected at 20 kV accelerating voltage, 15 nA probe current, and 15 mm working distance. Data acquisition employed a step size of 0.2–0.8 μm across regions of interest, with patterns indexed via Hough transformation (resolution: 70, binning: 4 × 4). Post-processing included grain reconstruction (minimum grain tolerance: 5°, minimum grain size: 2 pixels) and noise reduction by neighbor orientation correlation.

3. Multiscale Simulation Method

3.1. Phase Field Method

The crystal phase field method (PFC) is one of the latest simulation methods in materials science, which is used to solve the problem of atomic and microscale tight coupling. The limit value of the characteristic time scale in molecular dynamics (MD) simulation is in the picosecond range (10⁻¹² s) [30]. The molecular dynamics method is suitable for simulating high stress and high strain rate experiments under extremely short impact loads, which differs significantly from the long-term creep simulation experiments required in this paper [31].

The ideal free energy of an alloy is similar to that of A single-element structure and is represented by A and B, respectively. The ideal free energy of an alloy can be written as [32]:

$$∆F_{id}=k_{B}T\int [{\rho }_{A}ln\left({\displaystyle \frac{{\rho }_A}{{\rho }_0^A}}\right)-\delta {\rho }_A+{\rho }_{B}ln\left({\displaystyle \frac{{\rho }_B}{{\rho }_0^B}}\right)-\delta {\rho }_B]d\overrightarrow{r}$$

(1)

where ${\rho }_A$ and ${\rho }_B$ represent the solute number densities in elements A and B, respectively. ${\rho }_0^{\mathrm{A}}$ is the reference state density of solute A, while ${\rho }_0^{\mathrm{B}}$ is the reference state density of solute B. This is ${\rho }_A\equiv {\rho }_A-{\rho }_0^{\mathrm{A}}$, $\delta {\rho }_B={\rho }_B-{\rho }_0^{\mathrm{B}}$.

The two-point correlation function is utilized to describe the A–A, B–B, or A–B interactions, and the excess free energy density is expanded to the second order of the density, that is:

$$∆F_{ex}=-{\displaystyle \frac{1}{2}}{k}_{B}T{\sum }_j{\sum }_m\delta {\rho }_j\left(\overrightarrow{r}\right)\int C_2^{jm}\left(\overrightarrow{r},{\overrightarrow{r}}^{\prime }\right){\delta \rho }_m\left({\overrightarrow{r}}^{\prime }\right)d{\overrightarrow{r}}^{\prime }$$

(2)

where $C_2^{jm}$ represents all possible combinations of correlations between species j and m. Dimensionless atomic number density is defined as:

$$n={\displaystyle \frac{\rho {-\rho }_0}{{\rho }_0}}$$

(3)

Therefore, the total free energy of binary alloys is expressed as [33]:

$${\displaystyle \frac{\Delta F}{k_{B}T{\rho }_0}}=\int \{{\displaystyle \frac{n^2}{2}}-\eta {\displaystyle \frac{n^3}{6}}+\chi {\displaystyle \frac{n^4}{12}}+\left(n+1\right)∆F_{\mathrm{m}\mathrm{i}\mathrm{x}}-{\displaystyle \frac{1}{2}}n(\int {d{r}^{\prime }C}_{eff}^n{n}^{\prime }+\int {d{r}^{\prime }C}_{eff}^c{c}^{\prime })-{\displaystyle \frac{1}{2}}(c-c_o\left)\right(\int {d{r}^{\prime }C}_{eff}^n{n}^{\prime }+\int {d{r}^{\prime }C}_{eff}^c{c}^{\prime }\left)\right\}dr$$

(4)

where $∆F_{\mathrm{m}\mathrm{i}\mathrm{x}}$ is the mixing entropy. The mixed entropy is expressed as:

$$∆F_{\mathrm{m}\mathrm{i}\mathrm{x}}=\omega \left\{c\mathit{ln}\left({\displaystyle \frac{c}{c_o}}\right)+(1-c)ln\left({\displaystyle \frac{1-c}{1-c_o}}\right)\right\}$$

(5)

where $\omega$ is a coefficient used to correct the mixed entropy that deviates from the reference component. $c_o$ is the reference component.

The expression of the parameters is as follows:

$$\left\{\begin{array}{l}{C}_{eff}^n=c^2{C}_2^{BB}{{+(1-c)}^{2}C}_2^{AA}+c(1-c)(C_2^{BA}+C_2^{AB}),\\ C_{eff}^c=c(C_2^{BB}-C_2^{BA})-(1-c)(C_2^{AA}-C_2^{AB}), \\ C_{eff}^{c_{o}n}=c(C_2^{BB}-C_2^{AB})-(1-c)(C_2^{AA}-C_2^{BA}), \\ C_{eff}^{c_{o}c}=C_2^{BB}+C_2^{AA}-(C_2^{BA}+C_2^{AB}). \end{array}\right.$$

(6)

The free energy function of PFC in binary alloys is described as follows [33]

$$\begin{gathered} {\displaystyle \frac{\Delta F}{{\rho }^o{k}_{B}T}}=\int \{{\displaystyle \frac{n^2}{2}}-\eta {\displaystyle \frac{n^3}{6}}+\chi {\displaystyle \frac{n^4}{12}}+\left(n+1\right)∆F_{\mathrm{m}\mathrm{i}\mathrm{x}} \\ \hspace{1em}\hspace{1em}-{\displaystyle \frac{1}{2}}n\int {d{r}^{\prime }C}_{eff}^n\left(\left|r-r^{\prime }\right|\right)n^{\prime }+\alpha {\left|\overrightarrow{𝛻}c\right|}^2\}dr \end{gathered}$$

(7)

where $\eta$ and $\chi$ are the polynomial expansion parameters of the quasi-rational energy, and α is the gradient energy coefficient, which is used to set the scale and energy of the component interface.

The effective correlation function in the free energy describes the interaction between atoms, which represents the stability of the crystal structure and the topological defects of the crystal phase. The valid association function is defined as:

$$C_{eff}^n=X_1\left(c\right)C_2^{AA}+X_2\left(c\right)C_2^{BB}$$

(8)

where $X_1$ and $X_2$ are interpolation functions related to two directly correlated functions, namely:

$$\left\{\begin{array}{l}{X}_1\left(c\right)=1-3c^2+2c^3 \\ X_2\left(c\right)=1-3{\left(1-c\right)}^2+2(1-{c)}^3\end{array}\right.$$

(9)

where $C_2^{AA}$ and $C_2^{BB}$ are the correlation functions of pure metals, A and B, respectively. $C_2^{AA}$ and $C_2^{BB}$ are weighted according to their local components. The relevant function is established in the Fourier space and written as:

$${\widehat{C}}_2^{ii}\left(k\right)={\sum }_j{\widehat{C}}_{2j}^{ii}={\sum }_j{e}^{-{\displaystyle \frac{{\sigma }^2}{{\sigma }_{Mj}^2}}}{e}^{{\displaystyle \frac{-(k-k_j{)}^2}{{2\alpha }_j^2}}}$$

(10)

where ii = AA and BB, ${\widehat{C}}_2^{ii}$ is the correlation function of different crystal plane families, and each crystal plane family j contributes a peak to the direct correlation function in the unit lattice. σ is the temperature, and ${\sigma }_{Mj}$ is the effective transition temperature. $k_j$ is the position of the peak corresponding to the crystal face family j and is affected by the crystal face spacing.

Under this limit condition, the dynamics of the density and concentration fields are coupled. Furthermore, assuming that the mobility is a constant, the kinetic equation can be expressed as

$${\displaystyle \frac{\partial n}{\partial t}}=M_n\left\{{\overrightarrow{𝛻}}^2\left({\displaystyle \frac{\delta F}{\delta n}}\right)\right\}$$

(11)

$${\displaystyle \frac{\partial n}{\partial t}}=M_c\left\{{\overrightarrow{𝛻}}^2\left({\displaystyle \frac{\delta F}{\delta c}}\right)\right\}$$

(12)

where $M_n$ and $M_c$ are dimensionless mobility parameters. Under periodic boundary conditions, it is transformed into the Fourier space through the semi-implicit Fourier spectrum method. Linear terms are processed implicitly, while nonlinear terms are processed explicitly:

$$\widehat{n}(t+∆t)={\displaystyle \frac{{-k}^2∆t{M}_n[-\eta \frac{{\widehat{n}}^2\left(t\right)}{2}+\chi \frac{{\widehat{n}}^3\left(t\right)}{3}+∆F_{mix}-\int C_{eff}^n{\widehat{n}}^{\prime }\left(t\right)]+\widehat{n}(t)}{(1{+k}^2∆t{M}_n)}}$$

(13)

$$\widehat{c}(t+∆t)={\displaystyle \frac{{\widehat{c}\left(t\right)-k}^2∆t{M}_{\mathrm{c}}[\left(n+1\right)\frac{\delta ∆{\widehat{F}}_{mix}\left(t\right)}{\delta \widehat{c}\left(t\right)}-\frac{1}{2}n\int \frac{{\delta \widehat{C}}_{eff}^n\left(t\right)}{\delta \widehat{c}\left(t\right)}{n}^{\prime }]}{1-k^2∆t{M}_{\mathrm{c}}\alpha }}$$

(14)

It can be noticed that $n(t+∆t)$ and $c(t+∆t)$ is based on $\widehat{n}\left(t+∆t\right)$ and $\widehat{c}(t+∆t)$ inverse Fourier transform. Here, suppose $M_n$ and $M_c$ are 1.

The length and width of the simulated sample are set at 128a × 128a, where a is the lattice constant. The sample contains 16,384 atoms. The initial conditions of the PFC simulation are determined by the temperature and the concentration of the system. Periodic boundary conditions are applied in the simulation. By calculating the free energy curves of different phases and fine-tuning the fitting parameters, the polynomial fitting parameters are $\eta =1.4$, $\chi =1$, the mixed entropy coefficient is ω = 0.005, and the reference composition is $\omega =0.005$. For all solid phases, the widths of the relevant peaks are ${\alpha }_{111}=0.8$ and ${\alpha }_{100}={\displaystyle \frac{2}{\sqrt{3}}}{\alpha }_{111}$, respectively. The main vectors in the reciprocal lattice are $k_{111Al}=2\pi$, $k_{100Al}={\displaystyle \frac{2}{\sqrt{3}}}{k}_{111Al}$, $k_{111\theta }=\left({\displaystyle \frac{81}{38}}\right)\pi$, and $k_{100\theta }={\displaystyle \frac{2}{\sqrt{3}}}{k}_{111\theta }$, respectively. The effective transition temperature of each group in all solid phases is ${\sigma }_{Mj}=0.55$.

Its force application mode is fixed compression creep along the X-axis, and the simulated strain loading is 0.3%. ∆x and ∆y are the initial grid space steps, and $∆x^{\prime }$ and $∆y^{\prime }$ are the deformed grid space steps. The calculation of the changing grid sizes in the x and y directions is as follows

$$∆x^{\prime }=∆x/\left(1+0.3\mathrm{\%}\right)$$

(15)

$$∆y^{\prime }=∆y$$

(16)

During the precipitation process, the phase field crystal model can describe the diffusion and interaction of atoms. Simulate the movement of atoms and phase transitions in materials to reveal the movement mechanism of precipitated microstructures.

3.2. Dislocation Dynamics Simulation

We use the open-source code ParaDiS (v4.0.0) program to simulate the constant stress DDD of the microstructure composed of uniformly arranged precipitate [34]. The DDD framework uses node representation, in which dislocation lines are described by a set of nodes connected by straight segments. The node force ${\mathrm{F}}_i$ at node i is expressed as the sum of all the forces experienced by the segment connected to node i, that is

$${\mathrm{F}}_i={\sum }_j {\mathrm{f}}_{ij},$$

(17)

$${\mathrm{f}}_{ij}={\mathrm{f}}_{ij}^{\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}+{\mathrm{f}}_{ij}^{\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}}+{\mathrm{f}}_{ij}^{\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}}+{\mathrm{f}}_{ij}^{\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}+{\mathrm{f}}_{ij}^{\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{d}}$$

(18)

where ${\mathrm{f}}_{ij}^{\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}$ represents the linear tension (i.e., the force associated with the dislocation core), ${\mathrm{f}}_{ij}^{\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}}$ is the force generated due to the long-range elastic interaction between dislocation segments, and ${\mathrm{f}}_{ij}^{\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}}$ represents the force generated due to the interaction between dislocations and ordered precipitates. ${\mathrm{f}}_{ij}^{\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}$ represents the force generated due to the mismatch strain field associated with the elastic coherent precipitates, and ${\mathrm{f}}_{ij}^{\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{e}\mathrm{d}}$ is the externally applied stress. The fundamental force ${\mathrm{f}}_{ij}$ acting on the dislocation segment due to any source existing in the system can be obtained through the Peach–Koehler equation, which is given as

$${\mathrm{f}}_{ij}=\sigma \cdot {\mathrm{b}}_{ij}\times {\mathrm{l}}_{ij}$$

(19)

where $\sigma$ is the local stress field, and ${\mathrm{l}}_{ij}$ is the line connecting nodes i and j. In the original version of the ParaDis code, ${\mathrm{f}}_{ij}^{\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}$ and ${\mathrm{f}}_{ij}^{\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}}$ are considered using the nonsingular continuum theory of dislocations [35].

We used the reaction force model to describe the interaction forces generated due to the long-range order of precipitates [36,37,38]. Yashiro and his colleagues [38] proposed the reaction force model and implemented it in the multi-scale dislocation dynamics software package. They used the reaction force model to describe the dislocation cutting process, in which the superdislocations form in the precipitates and the APB faults exist between the superdeviated crystals. In particular, the front superbalance will be subject to a repulsive force when passing through the particle, thereby generating an APB, while the trailing superbalance will be subject to an attractive force from the particle. The movement of the trailing superbalance eliminates the APB formed by the leading superbalance. However, in our work, we used a large APB energy so that the dislocation segments only experienced the repulsive force from the particles, making them unaffected by the dislocations. The disassembly–precipitate interaction force ${\mathrm{f}}_{ij}^{\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}}$ is as follows

$${\mathrm{f}}_{ij}^{\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}}=\left\{\begin{array}{l}{\displaystyle \frac{1}{2}}{\displaystyle \frac{{\chi }_{\mathrm{A}\mathrm{P}\mathrm{B}}}{\parallel {\mathrm{b}}_{ij}\parallel }}\parallel {\mathrm{I}}_{ij}\parallel \tanh \left({\displaystyle \frac{3\left(L-d_{min}\right)}{L}}\right)n^s d_{\mathrm{m}\mathrm{i}\mathrm{n}}⩽L,\\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{d}_{\mathrm{m}\mathrm{i}\mathrm{n}}>L,\end{array}\right.$$

(20)

where ${\chi }_{\mathrm{A}\mathrm{P}\mathrm{B}}$. is the inverting boundary energy, $d_{\mathrm{m}\mathrm{i}\mathrm{n}}$. is the normal distance from the dislocation node to the surface of the inclusion, L is the length of the transition measured outward from the surface of the inclusion, at which the interaction decays to zero, and $n^s$. is the outward normal of the inclusion surface connecting the dislocation node. The matrix interface depends on how well we can capture the attenuation of interaction forces as the distance from the surface increases. Since in the current setup, each particle is symmetrically surrounded by six particles, and the particle forces on the dislocation node always follow the outward normal, the superposition of the forces from the opposite surface will result in the cancellation of the interaction forces at a small distance from the particle surface. Here, we choose the transition length L as 10 b. Although our choice of L is arbitrary, one can estimate the transition length L using molecular dynamics simulations. In addition, we assume that the force, ${\mathrm{f}}_{ij}^{\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}}$, is the transition length L of the smooth (continuous) attenuation L from the surface of the precipitates. Here, we do not consider the interaction between the differential discharge and the sediment, which also leads to the shearing of the sediment. This interaction can lead to the force of attraction on the dislocation node. We will include these impacts in our future work.

The interaction force resulting from coherent strain can be expressed as [37,39]

$${\mathrm{f}}_{ij}^{\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}={\displaystyle \frac{1}{2}}{\sigma }^{\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}\cdot {\mathrm{b}}_{ij}\times {\mathrm{l}}_{ij},$$

(21)

where ${\sigma }^{\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}$ is the local stress field associated with coherent precipitates. Here, we do not consider the forces due to coherent strains, although the implementation of these interactions is simple. The stress field σ mismatch can be calculated using the Fourier spectroscopy iterative perturbation method [40] using a uniform 3D mesh covering the simulation chamber. In the DDD framework, σ mismatches at specific dislocation nodes can be obtained by interpolating σ mismatch values from spectral grid points around the nodes. Since we focused on the effects of the stress applied and the interparticle spacing during constant stress creep on the development of IDN, we used a simple reaction force model to describe the dislocation–barrier interaction in this work.

The law of mobility provides a response function that describes how dislocations respond to potential driving forces. Since we assume a quasi-static description of the nodal force, we use the resistance tensor B(ξ) to describe the law of mobility, which is defined as follows

$$B(\xi )=\left\{\begin{array}{l}{B}^{\mathrm{g}}(m\otimes m)+B^{\mathrm{c}}(n\otimes n)+B^{\mathrm{l}}\left(t\otimes t\right) \forall n\in \left\{111\right\},\\ B^{\mathrm{c}}I+(B^{\mathrm{g}}-B^{\mathrm{l}})(t\otimes t) \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\forall n\notin \left\{111\right\},\end{array}\right.$$

(22)

where $B^{\mathrm{g}}$, $B^{\mathrm{c}}$, and $B^{\mathrm{l}}$ represent the slip, climb, and line components of the resistance tensor B(ξ), respectively, n represents the slip surface, t represents the dislocation line vector, and ξ is the tangent vector of the dislocation node, m = n × t. The mobility tensor M is the reciprocal of the resistance tensor $M=B^{-1};M_{\mathrm{e}}=(B^{\mathrm{g}}{)}^{-1};M_{\mathrm{c}}=(B^{\mathrm{c}}{)}^{-1}$.

Dislocation segments located on any {111} slip surface have both slip and climb velocity components. On the other hand, for dislocation segments in the non-octahedral plane, the slip component of the velocity becomes zero. The gliding component of drag tensor B is shown below

$$B^{\mathrm{g}}={\left[(B^{\mathrm{e}\mathrm{g}}{)}^{-2}\parallel b\times t{\parallel }^2+(B^{\mathrm{s}\mathrm{g}}{)}^{-2}(b\cdot t{)}^2\right]}^{-1/2}$$

(23)

where $B^{\mathrm{e}\mathrm{g}}$ and $B^{\mathrm{s}\mathrm{g}}$ are the drag coefficients of the blade misalignment and the screw misalignment along the slip direction.

The climbing component of drag tensor B is given below

$$B^{\mathrm{c}}=B^{\mathrm{e}\mathrm{c}}\parallel b\times t\parallel$$

(24)

where $B^{\mathrm{e}\mathrm{c}}$ is the drag coefficient associated with a segment that has the edge feature along the normal of the slip surface. Note that the blade component of the mixed dislocation can be moved by climbing, while the screw component can be moved by cross-slip.

3.3. Crystal Plastic Finite Element Method

The plastic deformation behavior of Al alloy polycrystalline materials at the mesoscale is illustrated by a rate-dependent crystal plasticity model [41]. The total deformation gradient $\mathbf{F}$ consists of the mechanical part ${\mathbf{F}}^{\mathrm{m}}$ and the thermodynamic part ${\mathbf{F}}^{\mathsf{\theta }}$. The deformation gradient tensor of the mechanical part maps the reference configuration to the deformation configuration, which is decomposed into elastic and plastic components [41]:

$$\mathbf{F}={\mathbf{F}}^{\mathrm{m}}{\mathbf{F}}^{\mathsf{\theta }}={\mathbf{F}}^{\mathrm{e}}{\mathbf{F}}^{\mathrm{p}}{\mathbf{F}}^{\mathsf{\theta }}$$

(25)

where ${\mathbf{F}}^{\mathrm{e}}$ is the elastic deformation gradient, which describes the elastic stretching and rigid rotation of the crystal lattice of the material, and is the plastic deformation gradient, which ${\mathbf{F}}^{\mathrm{p}}$ represents the nonlinear plastic deformation. The total velocity gradient $\mathbf{L}$ is calculated from the mechanical part of the deformation gradient and is decomposed into elastic and plastic components [42]:

$$\mathbf{L}=\mathbf{F}{\mathbf{F}}^{-1}={\mathbf{F}}^{\mathbf{e}}{\mathbf{F}}^{\mathbf{e}-1}+{\mathbf{F}}^{\mathbf{e}}{\mathbf{F}}^{\mathbf{p}}{\mathbf{F}}^{\mathbf{p}-1}{\mathbf{F}}^{\mathbf{e}-1}$$

(26)

The plastic component of the velocity gradient of the crystal structure is expressed as lattice shear along a particular crystal slip direction in different crystal slip planes. The plastic velocity gradient is obtained by converting the slip rate ${\dot{\gamma }}^a$ and then adding the individual contributions of each slip system

$${\mathbf{L}}^{\mathbf{p}}={\dot{\mathbf{F}}}^{\mathbf{p}}{\mathbf{F}}^{\mathbf{p}-1}={\displaystyle {\sum }_{\alpha =1}^{N_{slip}}} {\dot{\gamma }}^a{\mathbf{m}}_0^a\otimes {\mathbf{n}}_0^a$$

(27)

Schmid tensors in the deformation configuration of the slip system a, ${\mathbf{S}}^a$ are shown in the equation below. The Schmid tensor in the slip frame of reference is defined by the deformation slip direction, $s_e^a$, and the deformation slip surface normal, $n_e^a$, and its expression is as follows:

$${\mathbf{S}}^a=s_e^a\otimes n_e^a$$

(28)

where

$$s_e^a={\mathbf{F}}_e{s}^a$$

(29)

$$n_e^a={\mathbf{F}}_e^{-T}{n}^a$$

(30)

When the corresponding threshold is reached, the α-slip system is activated. The critical value is related to the resistance to overcome the dislocation motion process. Second, the relationship between the Piola–Kirchhoff stress tensor and the Green Lagrange strain tensor is given by the generalized Hooke’s law:

$$\mathbf{S}=\mathbb{C}:{\mathbf{E}}^{\mathrm{e}}$$

(31)

where $\mathbb{C}$ is the fourth-order anisotropic elastic stiffness matrix. By referring to the crystal [${\mathbb{C}}^c$], the elasticity in is converted to a sample or deformation reference configuration:

$$\left[\mathbb{C}\right]=\left[G\right]\left[{\mathbb{C}}^c\right][G{]}^T$$

(32)

where [G] is a 6 × 6 special fourth-order transformation matrix that transforms the vector stress from the crystal reference value to the sample reference value using the component [G] of the crystal-to-sample transformation

$$\left.\left[\mathbf{G}\right]=\left[\begin{array}{cccccc}{g}_{11}^2& g_{12}^2& g_{13}^2& 2g_{11}{g}_{12}& 2g_{13}{g}_{11}& 2g_{12}{g}_{13}\\ g_{21}^2& g_{22}^2& g_{23}^2& 2g_{21}{g}_{22}& 2g_{23}{g}_{21}& 2g_{22}{g}_{23}\\ g_{31}^2& g_{32}^2& g_{33}^2& 2g_{31}{g}_{32}& 2g_{33}{g}_{31}& 2g_{32}{g}_{33}\\ g_{11}{g}_{21}& g_{12}{g}_{22}& g_{13}{g}_{23}& g_{11}{g}_{22}+g_{12}{g}_{21}& g_{13}{g}_{21}+g_{11}{g}_{23}& g_{12}{g}_{23}+g_{13}{g}_{22}\\ g_{31}{g}_{11}& g_{32}{g}_{12}& g_{33}{g}_{13}& g_{11}{g}_{32}+g_{12}{g}_{31}& g_{13}{g}_{31}+g_{11}{g}_{31}& g_{12}{g}_{33}+g_{13}{g}_{32}\\ g_{21}{g}_{31}& g_{22}{g}_{32}& g_{23}{g}_{33}& g_{22}{g}_{31}+g_{21}{g}_{32}& g_{21}{g}_{33}+g_{23}{g}_{31}& g_{22}{g}_{33}+g_{23}{g}_{32}\end{array}\right.\right]$$

(33)

For cubic lattice materials with three independent elastic constants C₁₁, C₁₂, and C₄₄, the elastic stiffness matrix in the crystal reference is expressed as:

$$\left.[{\mathbb{C}}^c]=\left[\begin{array}{cccccc}{C}_{11}& C_{12}& C_{12}& 0& 0& 0\\ C_{12}& C_{11}& C_{12}& 0& 0& 0\\ C_{12}& C_{12}& C_{11}& 0& 0& 0\\ 0& 0& 0& C_{44}& 0& 0\\ 0& 0& 0& 0& C_{44}& 0\\ 0& 0& 0& 0& 0& C_{44}\end{array}\right.\right]$$

(34)

The Green-Lagrange strain tensor is expressed as

$${\mathbf{E}}^{\mathrm{e}}={\displaystyle \frac{1}{2}}[{\mathbf{F}}^{\mathrm{e}\mathrm{T}}{\mathbf{F}}^{\mathrm{e}}-\mathbf{I}]={\displaystyle \frac{1}{2}}({\mathbf{F}}^{\mathrm{p}-\mathrm{T}}{\mathbf{F}}^{\mathrm{T}}\mathbf{F}{\mathbf{F}}^{\mathrm{p}-1}-\mathbf{I})$$

(35)

where represents the second-order unit tensor.

The shear stress of the dislocation motion driving force is expressed as:

$${\tau }^a=\left(\begin{array}{c}{\mathbf{F}}^{\mathrm{e}\mathrm{T}}{\mathbf{F}}^{\mathrm{e}}S\end{array}\right):{\mathbf{P}}^a$$

(36)

where $\mathbf{S}$ stands for the second Piola Kirchhoff stress. When ${\tau }^a$ reaches the corresponding critical value, the a-slip system is activated. The critical value is related to the resistance to overcome the dislocation motion process.

The thermally activated slip law is defined as a temperature-dependent exponential form. The plastic strain rate ${\dot{\gamma }}^a$ is determined by the decomposed shear stress and the deformation resistance of the slip system, and is a function of the reference slip rate ${\dot{\gamma }}_0$ and the exponential constants p and q:

$${\dot{\gamma }}^a={\dot{\gamma }}_0\mathrm{e}\mathrm{x}\mathrm{p}\left\{-{\displaystyle \frac{\mathsf{\Delta }F}{k_B\theta }}{\left[1-{\left({\displaystyle \frac{|{\tau }^a-X^a|}{{\tau }_{ceff}^a}}\right)}^p\right]}^q\right\}\mathrm{s}\mathrm{g}\mathrm{n}({\tau }^a-X^a)$$

(37)

where the usual variations of p and q range from 0≤ p ≤1 and 1≤ q ≤2, representing the shape of the statistical obstacle profile; ${\dot{\gamma }}_0$ is the reference plastic strain rate that describes the macroscopic plastic strain rate; ${\tau }^a$ is the decomposition shear stress; $X^a$ is the motion hardening effect caused by the back stress; and ${\tau }_{ceff}^a$ is the deformation resistance of the slip system, and sgn is the signum function. When the corresponding threshold is reached, the a-slip system is activated. The critical value is related to the resistance to overcome the dislocation motion process.

The deformation resistance ${\tau }_{ceff}^a$ of the effective slip system considers lattice friction ${\tau }_c^0$, Taylor’s strength α with geometric factors, and forest dislocation ${\rho }_{for}^a$:

$${\tau }_{ceff}^a=\underset{\mathrm{friction} \mathrm{stress}}{\underbrace{{\tau }_c^0}}+G{b}^a\sqrt{\underset{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{strength}}{\underbrace{{\alpha }^2{\varrho }_{for}^a}}}$$

(38)

Considering statistical storage dislocation and geometrically necessary dislocation density, the forest dislocation is calculated by projection:

$${\rho }_{for}^a={\sum }_b \left|{\mathit{n}}^a\cdot {\mathit{t}}^b\right|\left(\left|{\mathit{\varrho }}_{GNDe}^b\right|+{\mathit{\varrho }}_{SSDe}^b\right)+\left|{\mathit{n}}^a\cdot {\mathit{s}}^b\right|\left(\left|{\mathit{\varrho }}_{GNDs}^b\right|+{\mathit{\varrho }}_{SSDs}^b\right)$$

(39)

The total dislocation density in the slip system is calculated as:

$${\rho }_{tot}^a={\sum }_a {\rho }_{SSD}^a+\left|{\rho }_{GNDe}^a\right|+\left|{\rho }_{GNDs}^b\right|$$

(40)

The dislocation density on the alpha-slip system is evolved according to the following equation [43]:

$${\dot{\varrho }}_{SSD}^a=\left(k_1{\displaystyle \frac{\sqrt{{\varrho }_{for}^a}}{b^a}}-k_2(\dot{ϵ},\theta ){\varrho }_{SSD}^a\right)|{\dot{\gamma }}^a|$$

(41)

The annihilation parameter, $k_2(\dot{ϵ},\theta )$, is calculated as:

$$k_2(\dot{ϵ},\theta )=k_1{\displaystyle \frac{\zeta b^a}{g^a}}\left(1-{\displaystyle \frac{K_{B}T}{D^a(b^a{)}^3}}\mathrm{l}\mathrm{n}{\displaystyle \frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}}\right)$$

(42)

The creep mechanism of 7A09 Al alloy is reflected by the climbing of dislocation, which affects the slip rate. The effect of creep on slip is more significant than the axial strain and volume changes induced by dislocation creepage [44]. Therefore, the creep law is defined as:

$${\dot{\gamma }}^a={\dot{\gamma }}_C\mathrm{e}\mathrm{x}\mathrm{p}\left(b_C|{\tau }^a-X^a|-{\displaystyle \frac{Q_C}{R\theta }}\right)\mathrm{s}\mathrm{g}\mathrm{n}({\tau }^a-X^a)+{\gamma }^a{\dot{\gamma }}_D\mathrm{e}\mathrm{x}\mathrm{p}\left(b_D|{\tau }^a-X^a|-{\displaystyle \frac{Q_D}{R\theta }}\right)\mathrm{s}\mathrm{g}\mathrm{n}({\tau }^a-X^a)$$

(43)

where $b_C$ and $b_D$ represent stress multipliers for creep deformation and creep damage, respectively. $Q_C$ and $Q_D$ are activation energies. ${\dot{\gamma }}_C$ and ${\dot{\gamma }}_D$ are the reference strain rates for creep deformation and creep damage, respectively. $R$ and $\theta$ represent the universal gas constant and temperature, respectively.

4. Results and Discussion

4.1. Mechanical Properties and Microstructure

Figure 1b shows morphological characteristics before and after deformation in the form of actual product. The physical photos of the specimen after fracture show that the fracture indicates the ductile fracture mechanism of the material. Figure 1c shows a representative stress–strain curve under uniaxial tensile. The yield strength of Al alloy samples is distributed in the range of 454.3 MPa, the tensile strength fluctuates in the range of 510.1 MPa, and the strain at break is between 12%. Figure 1d shows the representative evolution of creep plastic strain with time (hour). The steady-state creep rate is 5.9 × 10⁻⁸ s⁻¹.

Figure 2 shows some representative distribution maps for the elements (Al, Cu, and Mg) in the 7A09 Al alloy, determined via SEM-EDS analysis. The SEM image of Figure 2a clearly reveals the diffuse distribution of granular precipitates (white arrows indicate the precipitation of different components). The uniform distribution of granular precipitates indicates that the alloy has formed a high-density precipitated strengthened structure after heat treatment, which plays a key role in improving the strength of the material.

The electron backscatter diffraction (EBSD) mass plot in Figure 3a shows that most of the regions show bright high-contrast characteristics, indicating that the defect density inside the crystal is low, reflecting the overall crystal integrity of 7A09 Al alloy. Figure 3b,c shows the grain orientation distribution along the horizontal (RD), and transverse (TD) directions of the sample by means of an inverted pole figure (IPF) superimposed on the grain boundary features. It is worth noting that the color distribution of the IPF map is highly random and uniform, and there is no specific color. The elongated grains are regularly arranged in a single direction, with a significant length-to-width ratio and a concentrated size distribution, which is a homogeneous equiaxed–sub-equiaxed mixed grain structure that is conducive to coordinating plastic deformation and inhibiting crack propagation, while the high-angle grain boundaries with no obvious annealing twin characteristics indicate that the recrystallization process of the material is sufficient and no abnormal grain growth occurred. The phase distribution in Figure 3d shows a single face-centered cubic (FCC) Al matrix marked in red for the entire scan area, and no diffraction signal from the second phase or the impurity phase is detected, indicating the single-phase solid solution structure of the 7A09 Al alloy.

The grain size distribution (Figure 4a) follows a typical lognormal distribution, with a maximum grain size of ~129.5 $\mathsf{\mu }\mathrm{m}$, a minimum grain size of ~5.4 $\mathsf{\mu }\mathrm{m}$, and an average grain size of ~14 $\mathsf{\mu }\mathrm{m}$. The total number of grains analyzed is 2595, of which 90% of the grain size is distributed in the range of 5.4–105 $\mathsf{\mu }\mathrm{m}$ and presents a bimodal distribution, which may be related to the inhomogeneous grain growth caused by local strain differences during dynamic recrystallization caused by heat treatment and rolling of the material. The grain boundary misorientation distribution (Figure 4b) shows two significant peak regions, indicating the presence of many subcrystalline structures or partially recrystallized regions in the material, which are related to the mechanism of subcrystalline merging during the formation or recovery phase of the dislocation wall during the deformation process. It is worth noting that the 10–15° transition interval accounts for a small proportion, indicating that there is an obvious orientation difference transition mechanism in the grain evolution process of this alloy.

4.2. Evolution of Precipitate

The aggregation and arrangement of atoms, as well as the formation and evolution of precipitates, are observed [45]. It is clearly observed that in the initial state (t = 0 h), there are four discretely distributed precipitate particles in the material, labeled “A”, “B”, “C”, and “D”, which are similar in size and show a stable spatial distribution, as shown in Figure 5a. With the creep time extended to 5000 h, the precipitate phases showed obvious differential evolution behaviors: the precipitate “A” underwent a slow and continuous coarsening process, and its volume gradually increased. The sediment “B” showed a reverse evolution trend, and the size of the sediment continued to decrease. Of particular note is the fact that the adjacent “C” and “D” are driven by an elastic strain field and eventually fuse to form a new oval-shaped precipitate “E” by the Ostwald (diffusion-controlled roughening mechanism) curing mechanism (Figure 5b) [46]. According to deformation Equation (15), the constant compressive strain is 0.3%. Under the action of a small constant compressive strain, the subsequent evolution process (t = 10,000–15,000 h) showed obvious size selection characteristics, in which both “A” and “E” continued to grow, but the former showed faster growth kinetics, which may be due to the difference in interaction energy between the dislocation stress field and the precipitates with different orientations (Figure 5c,d). When entering the late creep stage (t ≥ 20,000 h), the system has a new evolution characteristic: the dominant phase “A” begins to split after reaching the critical size, which may be related to the competition between the interfacial energy and the anisotropic strain energy. The secondary phase “E”, on the other hand, undergoes a continuous dissolution process, gradually decreasing in size until it eventually disappears from the matrix (Figure 5e,f). This non-monotonic evolution of the precipitate reveals that the dynamic equilibrium process of the precipitate in 7A09 Al alloy is not only controlled by the classical diffusion mechanism, but also closely related to the dislocation-induced local strain field and the elastic interaction between the precipitates under persistent stress. The whole evolutionary process vividly demonstrates the complex dynamic behavior of competitive growth and ablation in stress-assisted phase transitions.

Figure 6 shows the effect of compressive creep on the average size and number of precipitates of the 7A09 Al alloy. Figure 6a clearly shows that the coarsening rate accelerates significantly over time as the average size increases. The results showed that the average size of the precipitate increased significantly after the late stage of compressive creep (t = 20,000 h). Figure 6b shows the number of precipitates of the 7A09 Al alloy. It clearly depicts the decrease in the number of precipitates of 7A09 Al alloy as the compression creep time increases. It is shown that the system tends to form fewer but larger precipitates under stress. The deep mechanism of the evolution of the precipitate of 7A09 Al alloy during compressive creep is due to the synergistic effect of multiple physics: the inhomogeneous stress field formed by the dislocation network drives the directional diffusion of solute atoms through the chemical potential gradient, and the dislocation pipe diffusion significantly accelerates the solute migration. The additional chemical potential generated by the co-lattice strain at the precipitate/matrix interface promotes the segregation of solutes to the large-size precipitate, which follows the stress-assisted Ostwald law.

The mechanism of microstructure creep deformation involves the coupling of multiple physical fields: dislocation stress field drives solute directional diffusion (dislocation pipeline diffusion accelerates migration), and interface coherent strain promotes solute segregation towards larger precipitates. Differences in orientation lead to selective evolution, revealing that phase transition under stress is jointly regulated by diffusion, strain field, and elastic interactions. The defects generated by creep deformation and the stored strain energy in the experiment can provide nucleation and growth conditions for the precipitation of TiAl₂ phase [47], which is consistent with the growth of the precipitated phase in this simulation experiment.

4.3. Interaction Between Precipitate and Dislocation

At constant room temperature (Figure 7), the creep strain increases nonlinearly from 0.15% to 0.82% (up to 446%) when the applied stress is increased from 20 MPa to 50 MPa (150% increase), and all curves reach the steady-state creep stage.

Based on the steady-state creep rate data at different stress levels (20–50 MPa), the creep deformation mechanism of the alloy is revealed. The creep behavior of alloys is usually described in terms of the power-law relationship between the creep rate and the modulus-compensated effective flow stress [49]:

$$\dot{ϵ}=A{\left[{\displaystyle \frac{{\sigma }_{\mathrm{e}}}{\mu }}\right]}^n$$

(44)

where A is a constant, ${\sigma }_{\mathrm{e}}$ = $\sigma$−${\sigma }_{\mathrm{b}}$ is an effective flow stress, ${\sigma }_{\mathrm{b}}$ = $f\sigma$ is the maximum back stress [50], where f is the volume fraction of the precipitate. The log-logarithmic plot of strain rate versus stress is fitted with a power-law equation (Figure 8) as follows

$$\mathrm{l}\mathrm{o}\mathrm{g}\left(\dot{ϵ}\right)=\mathrm{l}\mathrm{o}\mathrm{g}\left(A\right)+n\mathrm{l}\mathrm{o}\mathrm{g}({\sigma }_{\mathrm{c}}/\mu )$$

(45)

where the stress index n = 4.8923 is obtained. The stress index is well comparable with the n = 5.1 of 7075-T6 Al alloy and n = 4.6 of 2024-T3 Al alloy reported in the literature, but it is significantly higher than that of pure Al n = 3.2, highlighting the multi-scale interaction effect of the precipitate formed by Zn/Mg/Cu alloying elements and the dislocation motion of solution atoms. Based on this, the cross-scale constitutive relationship will be used as the core input parameter of the dislocation density evolution equation in the crystalline plastic finite element simulation and provide a theoretical basis for composition-process optimization for the design of high-temperature creep-resistant Al alloys.

As shown in Figure 9, based on the three-dimensional discrete dislocation dynamics simulation, the evolution of the dislocation density with the cumulative plastic strain of the 7A09 Al alloy single crystal model (size 5 × 5 × 10 μm³, initial dislocation density 5 × 10¹¹ m⁻², and 200 mixed dislocation sources with Burgers vector [110]/2) is revealed during the creep process at room temperature.

The simulation data show that in the initial stage of creep, the dislocation density increased steadily, and there is no obvious correlation with the applied stress, which is due to the strong pinning effect of the precipitated strengthening phase that needed to be overcome by the activation of the dislocation source at this stage. When the ${\epsilon }_{\mathrm{p}}$ < 0.01% entered the creep acceleration phase, the dislocation proliferation rate showed a significant stress dependence. As applied stress increases, dislocation multiplication with strain accelerates, indicating a higher creep strain rate under high stress (Figure 9a). The error value of dislocation density is less than 10 percent, which shows simulation repeatability (Figure 9b). These cross-scale evolution laws provide key parameters for the construction of creep damage coupling constitutive models, especially the quantitative relationship between the dislocation storage term and the stress sensitivity coefficient, which can be embedded in the crystal plastic finite element framework, and the dynamic equilibrium equation of dislocation nucleus-annihilation-locking in multi-scale simulation is optimized by deep reinforcement learning algorithm, which lays a theoretical foundation for the life prediction of ship parts.

Figure 10 shows a schematic diagram of the evolution of the interaction between dislocations and precipitates in the low plastic strain level range of 0.01–0.03% under applied stress of 30 MPa and 50 MPa in the [001] direction. As the plastic strain increases, the dislocations slide and multiply, interacting with the precipitate to produce a dislocation loop and encapsulate the precipitate. Under higher applied stress, under the same plastic strain, there are more dislocations around the precipitate, and there is a situation of large dislocation loops and small dislocation loops, similar to the orbit of the planets in the solar system. The dislocations on different slip planes will be surrounded on the same precipitate at the same time, resulting in a peculiar structure of heteroplanar dislocation loops alternately surrounding the precipitate. This is mainly attributed to the large size of the precipitated phase, which leads to the dislocations on different slip planes being spatially hindered by the same precipitated phase. As shown in Figure 11, initially, the dislocations on the (111) sliding surface are hindered by the precipitated phase. Over time, the dislocations bend to form dislocation loops. Immediately following is the obstruction of dislocations on the $\left(\overline{1}11\right)$ slip plane, which eventually becomes a dislocation loop. Then, dislocations on the $\left(1\overline{1}1\right)$ and $\left(11\overline{1}\right)$ sliding planes form loops. Some dislocation loops are not wound around the precipitate, that is, the plane where the dislocation loop is located does not pass through the precipitate, which is because there is not only a stress field inside the precipitate, but also because of the mismatch between the modulus and lattice between the precipitate and the matrix, resulting in uneven stress around the precipitate.

Figure 12 shows the evolution of the local amplification of the interaction between dislocations and precipitates during creep under applied stress of 30 MPa. With the increase of plastic strain, the dislocations on the $\left(\overline{1}11\right)$ slip surface slide first, bypassing the precipitate to form a dislocation loop, and then the dislocations on the $\left(\overline{1}11\right)$ slip surface meet the dislocations on the subsequent $\left(1\overline{1}1\right)$ sliding surface and react to produce dislocation knots. As the creep strain continues to increase, the dislocation knot dissociates and re-forms two independent dislocations. The function of the precipitate in the creep process is to hinder the dislocation that slides first to form a dislocation loop, and meets and reacts with the later sliding dislocation to produce a dislocation knot and then dissociates, such a repeated process of forming and dissociating dislocation knots, inducing dislocation creep intensification.

Figure 13 shows the evolution of the local amplification of the interaction between the dislocation and the precipitate during creep under an applied stress of 50 MPa. With the increase of plastic strain, the dislocations on the $\left(\overline{1}11\right)$ slip surface slide first, bypassing the precipitate to form a dislocation loop, and then the dislocations on the $\left(\overline{1}11\right)$ slip surface meet the dislocations on the subsequent $\left(11\overline{1}\right)$ sliding surface and react to produce a dislocation junction. Different from the situation under the action of 30 MPa external stress, due to the higher stress, the dislocations on the $\left(11\overline{1}\right)$ surface continue to slip and proliferate and form more dislocation knots, which are difficult to dissociate, resulting in many dislocation entanglements and accumulation near the precipitate, resulting in a rapid increase in dislocation density.

4.4. Deformation Behavior and Mechanism

The representative volume element (RVE) model for crystal plasticity finite element simulation is constructed to accurately capture the creep deformation mechanism of 7A09 Al alloy under high-pressure environments by writing the Matlab(v2016a) script to convert EBSD data into the RVE model. The distribution of grain size, morphology, and orientation in the RVE model is consistent with the EBSD results. It is worth noting that there are many slight misorientations inside the grains (Figure 14a), which have a slight impact on the simulation results. Therefore, in the modeling process, misorientation with an angle less than 3° in the columnar grains is ignored. Figure 14a,b shows the comparison of grain distribution between EBSD results and the established RVE model. The established model can effectively reproduce the grain microstructure of 7A09 Al alloys. The comparison of the pole figure between EBSD results and the established RVE model is shown in Figure 14c,d. The texture of the RVE model (Figure 14d) is consistent with the experimental results (Figure 14c). The grain morphology and grain orientation of the RVE model is highly consistent with experimental results, which reflects the reliability and accuracy of the model.

The RVE model is imported into Gmsh software (v4.11.1) for meshing. The meshing strategy is optimized according to the grain size: for large grains, a relatively sparse mesh is used to reduce the computational cost. For smaller grains, a denser cell grid is used (Figure 15). This approach is based on the consideration that stress or strain concentrations are more likely to occur in the vicinity of small grains during deformation, so a finer mesh is needed to capture local mechanical behavior, thereby improving the overall accuracy of the simulation model. The model contains 27,903 nodes and 18,374 units. The number of elements and nodes in this model can effectively reflect the complex mechanical response of metal materials and ensure the reliability and accuracy of the simulation results [51]. The crystal plasticity model is implemented in Abaqus finite element software (v2023HF) through the User Material Subroutine (UMAT).

Figure 16 shows the plastic strain vs. time curve of 7A09 Al alloy obtained by crystal plasticity finite element simulation. The plastic strain shows a gradual upward trend with the increase of time. Within the first few hours, the plastic strain increases rapidly, showing a distinct initial creep phase. At this stage, the dislocations within the material begin to multiply rapidly, and the activity of the slip system gradually increases, resulting in a rapid accumulation of plastic strains. With the extension of creep time, the increase rate of plastic strain gradually slows down and enters the steady-state creep stage. The creep deformation of the material tends to be stable, and the accumulation rate of plastic strain remains relatively constant. Currently, the movement and proliferation of dislocations reach a dynamic equilibrium, and the microstructure of the material shows a certain stability. This stability may be related to the interaction between the grains as well as the obstruction of dislocations at grain boundaries, limiting further plastic deformation [15,52].

Figure 17 shows the plastic strain distribution of 7A09 Al alloy at 10, 100, 500, and 1000 h during the creep, respectively, and the white lines represent the grain boundaries. The distribution of plastic strain within the material changes significantly over time. In the early stages (10 h), the plastic strain is mainly concentrated in some specific grains, while the plastic strain near the grain boundary is relatively small. This indicates that in the early stage of creep, the dislocation movement mainly occurs inside the grain. With the increase of creep time, the plastic strain gradually expands to the vicinity of the grain boundaries, and some grain boundaries begin to show obvious strain accumulation. This may be due to the accumulation of dislocations at grain boundaries, resulting in local stress concentrations, which promote the deformation of grain boundaries [10]. During the creep phases of 500 and 1000 h, significant plastic strain is accumulated near grain boundary regions, and even higher strain values in some areas. This indicates that in the long-term creep process, the grain boundaries gradually become the main region of plastic deformation, and the internal deformation of the material is more uneven, and the strain concentration in the local area is more obvious. This phenomenon may be related to dislocation slip, grain boundary diffusion, and grain boundary weakening at grain boundaries, resulting in a gradual decline in the mechanical properties of the material [15].

Figure 18 shows the statistical storage dislocation density (SSD) distribution of 7A09 Al alloy at different creep times of 10, 100, 500, and 1000 h, with the white lines representing grain boundaries. As shown in Figure 18a, the density of SSD is relatively uniformly distributed in the grain at the early stage of creep. With the extension of creep time (Figure 18b), the SSD density begins to increase significantly at some grain boundaries, showing that the grain boundaries hinder the movement of dislocations, resulting in the accumulation of dislocations near the grain boundaries and the formation of dislocation walls. The grain boundaries limit the slip of the dislocations to a certain extent, increasing the local strain gradient of the material [53]. Over longer creep times (Figure 18c,d), the accumulation of SSD density near grain boundaries is further intensified, especially in some specific grain boundary regions, where significant high-density dislocation bands are formed. These dislocation bands may be due to dislocation interactions and accumulation at grain boundaries, further hindering the movement of dislocations, resulting in strain gradients in local areas [5]. Combined with the plastic strain distribution in Figure 17, the density of SSD gradually accumulates with the increase of plastic deformation of the material, especially near grain boundaries. This suggests that the distribution of SSD is closely related to the distribution of plastic strain, and an increase in SSD leads to more plastic deformation. The high SSD density region at the grain boundary is in good agreement with the concentrated region of plastic strain, which further confirms the critical role of grain boundaries in the creep process. The increase in dislocation density and the concentration of plastic strain together promote the creep deformation and damage evolution of the material, which may eventually lead to the failure of the material [54]. As an obstacle to the movement of dislocations, grain boundaries play a key role in the creep process, leading to the accumulation of dislocations and the formation of strain gradients, thereby promoting the accumulation of plastic strains.

5. Conclusions

This work systematically investigates the mechanical properties, microstructural evolution, and creep deformation mechanisms of 7A09 Al alloy, yielding the following key findings:

(1) The alloy exhibits high strength (average yield strength: 464.3 MPa, tensile strength: 526.1 MPa) and moderate ductility (average strain: 11.2%) with minimal data dispersion, confirming exceptional process consistency. Microstructural analysis reveals a homogeneous equiaxed/sub-equiaxed grain structure with random crystallographic orientations and no preferred texture. Precipitates are uniformly distributed, contributing to dispersion strengthening.

(2) During compressive creep, precipitates undergo non-monotonic evolution: coarsening, dissolution, and coalescence, followed by splitting. Average precipitate size increases by >200% over 25,000 h, while their density decreases by ~60%, indicating stress-driven Ostwald ripening.

(3) Creep strain surges 446% when stress increases from 20–50 MPa, with a stress exponent of 4.89, aligning with precipitation-strengthened Al alloys. Dislocation dynamics simulations show dislocations bypass precipitates at 30 MPa, forming loops that later dissociate; high stress induces dislocation entanglement at 50 MPa and rapid density escalation near precipitates.

(4) Crystal plasticity finite element modeling reveals: at early creep (≤100 h), plastic strain localizes within grain interiors; at the long-term creep (≥500 h), strain shifts to grain boundaries, causing dislocation pile-ups and SSD density spikes, accelerating damage accumulation.

(5) The alloy’s high strength consistency, predictable precipitate coarsening, and quantified creep mechanisms support its reliability in marine load-bear components. The constitutive model enables accurate life prediction for high-stress applications.