ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Manifold adaptive method for thermo-mechanical coupled fatigue phase-field model
Received date: 2025-07-11
Revised date: 2025-08-27
Accepted date: 2025-09-18
Online published: 2025-09-24
Supported by
National Natural Science Foundation of China(U2341238)
Phase-field models can automatically capture crack initiation, propagation, and complex behaviors like branching and coalescence by tracking the evolution of an order parameter. This makes them particularly advantageous for simulating the fatigue fracture of structures. However, the highly nonlinear nature of phase field problems and the high computational cost of fatigue analysis present significant challenges for thermo-mechanically coupled phase-field fatigue simulations. This paper adopts a manifold adaptive finite element based acceleration algorithm. A thermo-mechanically coupled fatigue phase-field model is derived from thermodynamic principles and is used in con-junction with a constant load accumulation method. This approach is then applied to study the behavior of dog-bone specimens, plates with a central hole, and microstructures with spherical defects under thermo-mechanically coupled fatigue loads. The results show that the proposed manifold adaptive thermo-mechanically coupled phase-field model can accurately preserve the curved geometric shapes during mesh refinement and accelerates the computation speed of thermo-mechanically coupled fatigue problems by approximately 90 times. The simulated stress-life curve, when compared with test data, shows that the life prediction error is within a factor of two scatter band. Furthermore, the phase difference of the thermo-mechanically coupled fatigue load significantly affects the fatigue life, with life decreasing as the phase difference decreases.
Key words: phase field; thermo-mechanical fatigue; manifold; adaptive; fatigue life
Chengyu LIU , Yu’e MA , Pengcheng CHEN . Manifold adaptive method for thermo-mechanical coupled fatigue phase-field model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2026 , 47(6) : 232552 -232552 . DOI: 10.7527/S1000-6893.2025.32552
| [1] | 胡小飞, 张鹏, 姚伟岸. 断裂相场法[M]. 北京: 科学出版社, 2022: 2-5. |
| HU X F, ZHANG P, YAO W A. Phase field method for fracture[M]. Beijing: Science Press, 2022: 2-5 (in Chinese). | |
| [2] | FRANCFORT G A, MARIGO J J. Revisiting brittle fracture as an energy minimization problem[J]. Journal of the Mechanics and Physics of Solids, 1998, 46(8): 1319-1342. |
| [3] | BOURDIN B, FRANCFORT G A, MARIGO J J. Numerical experiments in revisited brittle fracture[J]. Journal of the Mechanics and Physics of Solids, 2000, 48(4): 797-826. |
| [4] | WU J Y. A unified phase-field theory for the mechanics of damage and quasi-brittle failure[J]. Journal of the Mechanics and Physics of Solids, 2017, 103: 72-99. |
| [5] | FENG Y, FAN J D, LI J. Endowing explicit cohesive laws to the phase-field fracture theory[J]. Journal of the Mechanics and Physics of Solids, 2021, 152: 104464. |
| [6] | ZHANG P, YAO W A, HU X F, et al. Phase field modelling of progressive failure in composites combined with cohesive element with an explicit scheme[J]. Composite Structures, 2021, 262: 113353. |
| [7] | ZHANG P, TAN S Y, HU X F, et al. A double-phase field model for multiple failures in composites[J]. Composite Structures, 2022, 293: 115730. |
| [8] | TANG W, WEN S Z, HOU H L, et al. Phase-field simulation and machine learning of low-field magneto-elastocaloric effect in a multiferroic composite[J]. International Journal of Mechanical Sciences, 2024, 275: 109316. |
| [9] | 郭雯, 马玉娥, Natarajan Sundar, 等. 基于自适应双相场模型的纤维增强复合材料单层板断裂性能[J]. 复合材料学报, 2024, 41(3): 1505-1515. |
| GUO W, MA Y E, NATARAJAN S, et al. Study on fracture of fiber-reinforced composite single layer laminate based on adaptive double phase-field model[J]. Acta Materiae Compositae Sinica, 2024, 41(3): 1505-1515 (in Chinese). | |
| [10] | TAN Y, LIU C, ZHAO J S, et al. Phase field model for brittle fracture in multiferroic materials[J]. Computer Methods in Applied Mechanics and Engineering, 2023, 414: 116193. |
| [11] | MIN L, WANG Z L, HU X F, et al. A chemo-thermo-mechanical coupled phase field framework for failure in thermal barrier coatings[J]. Computer Methods in Applied Mechanics and Engineering, 2023, 411: 116044. |
| [12] | 马玉娥, 陈鹏程, 郭雯, 等. 基于光滑有限元法的热-弹相场断裂研究[J]. 固体力学学报, 2023, 44(3): 346-354. |
| MA Y E, CHEN P C, GUO W, et al. Study on thermo-elastic phase fracture modeling based on the cell-based smoothed finite element method[J]. Chinese Journal of Solid Mechanics, 2023, 44(3): 346-354 (in Chinese). | |
| [13] | 王博臣, 侯玉亮, 夏凉, 等. 基于子结构法与损伤识别的周期性结构脆性断裂相场模拟[J]. 航空学报, 2022, 43(3): 225159. |
| WANG B C, HOU Y L, XIA L, et al. Phase field modeling of brittle fracture of periodic structures based on ubstructuring and damage identification[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(3): 225159 (in Chinese). | |
| [14] | 张子瑜, 郝林. 扩展有限元法在断裂力学相场模型中的应用[J]. 航空学报, 2022, 43(9): 225976. |
| ZHANG Z Y, HAO L. Application of X-FEM in a phase-field model for crack propagation[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(9): 225976 (in Chinese). | |
| [15] | ALESSI R, VIDOLI S, DE LORENZIS L. A phenomenological approach to fatigue with a variational phase-field model: The one-dimensional case[J]. Engineering Fracture Mechanics, 2018, 190: 53-73. |
| [16] | CARRARA P, AMBATI M, ALESSI R, et al. A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 361: 112731. |
| [17] | SCHREIBER C, KUHN C, MüLLER R, et al. A phase field modeling approach of cyclic fatigue crack growth[J]. International Journal of Fracture, 2020, 225(1): 89-100. |
| [18] | HUANG X, XIE Q K, LI S L, et al. A phase-field fracture model for creep-fatigue behavior[J]. Theoretical and Applied Fracture Mechanics, 2024, 132: 104483. |
| [19] | XU B, KANG G Z, KAN Q H, et al. Phase field simulation on the cyclic degeneration of one-way shape memory effect of NiTi shape memory alloy single crystal[J]. International Journal of Mechanical Sciences, 2020, 168: 105303. |
| [20] | LI J W, HU Y N, AO N, et al. An adaptive cycle jump method for elasto-plastic phase field modeling addressing fatigue crack propagation[J]. Computer Methods in Applied Mechanics and Engineering, 2025, 442: 118074. |
| [21] | SUN S, GONG Q H, NI Y, et al. A micromagnetic-mechanically coupled phase-field model for fracture and fatigue of magnetostrictive alloys[J]. Journal of the Mechanics and Physics of Solids, 2024, 191: 105767. |
| [22] | TANG W, WANG L F, SUN S, et al. Macroscopically modeling fatigue life of additively manufactured metals: Pore-defect informed phase-field model[J]. Journal of the Mechanics and Physics of Solids, 2025, 196: 106008. |
| [23] | DU C Y, CUI H T, ZHANG H J, et al. Phase field modeling of thermal fatigue crack growth in elastoplastic solids and experimental verification[J]. Mechanics of Materials, 2024, 188: 104839. |
| [24] | ZHANG Z H, ZHANG R J, SUN S, et al. A thermo-mechanically coupled phase-field fatigue fracture model[J]. Acta Mechanica, 2026, 237: 709-726. |
| [25] | DING J L, YU T T, FANG W H, et al. An adaptive phase field modeling of fatigue crack growth using variable-node elements and explicit cycle jump scheme[J]. Computer Methods in Applied Mechanics and Engineering, 2024, 429: 117200. |
| [26] | SARGADO J M, KEILEGAVLEN E, BERRE I, et al. A combined finite element-finite volume framework for phase-field fracture[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113474. |
| [27] | KRISTENSEN P K, GOLAHMAR A, MARTíNEZ-PA?EDA E, et al. Accelerated high-cycle phase field fatigue predictions[J]. European Journal of Mechanics-A Solids, 2023, 100: 104991. |
| [28] | KITAMURA K. Crack surface energy: Temperature and force dependence[J]. Materials Transactions, 2008, 49(3): 643-649. |
| [29] | AMOR H, MARIGO J J, MAURINI C. Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments[J]. Journal of the Mechanics and Physics of Solids, 2009, 57(8): 1209-1229. |
| [30] | MOLNáR G, GRAVOUIL A. 2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture[J]. Finite Elements in Analysis and Design, 2017, 130: 27-38. |
| [31] | 《中国航空材料手册》编辑委员会. 中国航空材料手册(第4卷): 钛合金 铜合金[M]. 2 版. 北京:中国标准出版社, 2002: 104-132. |
| Editorial Committee of China Aviation Materials Manual. China aviation materials manual (Vol 4): Titanium alloy, copper alloys[M]. 2nd ed. Beijing: Standards Press of China, 2002: 104-132 (in Chinese). | |
| [32] | GORSKI J, PFEUFFER F, KLAMROTH K. Biconvex sets and optimization with biconvex functions: A survey and extensions[J]. Mathematical Methods of Operations Research, 2007, 66(3): 373-407. |
/
| 〈 |
|
〉 |