面向长寿命设计的航空发动机材料力学性能试验与表征技术进展

Progress in mechanical property testing and characterization technologies of aero-engine materials for long-life design

摘要

随着我国大涵道比涡扇航空发动机向更长服役寿命和更高可靠性方向发展，材料的力学性能试验与表征成为保证其长寿命服役可靠性的关键。本文系统综述了面向长寿命设计的航空发动机材料力学性能的试验技术、损伤表征和服役寿命预测等方面的进展，主要聚焦在转子叶片材料的超高周疲劳、涡轮热端部件的高温长时蠕变、限寿件材料的真实工艺缺陷疲劳裂纹表征三个典型场景，介绍了基于电磁振动台的超高频振动疲劳、基于 DIC 方法的蠕变测量、基于分段模型/物理机制的蠕变寿命预测、基于 SEM/CT 的原位疲劳等技术在该领域的应用。未来，需要进一步深入研究航空发动机材料超高周疲劳裂纹萌生、长寿命蠕变速率应力依赖与微结构演化、真实工艺缺陷损伤演化等物理机制，同时需进一步推动基于迁移学习、强化学习等技术的长寿命智能预测模型，实现航空发动机零部件的组织-性能-寿命一体化评价，以应对未来航空发动机带来的持续挑战。

Abstract

As high bypass ratio turbofan aero-engines develop towards longer service life and higher reliability， the mechanical property testing and characterization of materials have become the key to ensuring their long-term reliable operation. This paper systematically reviews the progress in the testing technologies， damage characterization and service life prediction of aeroengine materials for long-life design，mainly focusing on three typical scenarios：very-high cycle fatigue of rotor blade materials，long-term high-temperature creep of turbine hot-end components and fatigue crack characterization of real process defect-limited-life materials. It introduces the application of technologies such as very-high-frequency vibration fatigue based on electromagnetic vibration tables， creep measurement based on DIC methods，creep life prediction based on segmented models/physical mechanisms and in-situ fatigue based on SEM/CT in this field. In the future，it is necessary to further study the physical mechanisms of very-high cycle fatigue crack initiation，long-life creep rate stress dependence and microstructure evolution and real process defect damage evolution of aeroengine materials. Meanwhile，it is necessary to further promote intelligent life prediction models based on transfer learning，reinforcement learning，attention mechanisms and so on to achieve an integrated evaluation of the microstructure-performance-life of aero-engine components，in order to meet the continuous challenges brought by future aero-engines.

关键词

航空发动机 / 长寿命设计 / 超高周疲劳 / 高温蠕变 / 损伤容限

Key words

aero-engine / long-life design / very-high cycle fatigue / high-temperature creep / damage tolerance

参考文献

[1] SINGH R. Fifty years of civil aero gas turbines[J]. Air-craft Engineering and Aerospace Technology, 1996, 68: 3-19.

[2] 刘大响, 金捷, 彭友梅, 等. 大型飞机发动机的发展现状和关键技术分析[J]. 航空动力学报, 2008, 23(6): 976-980.

[3] LIU D X, JIN J, PENG Y M, et al. Summarization of development status and key technologies for large air-plane engines[J]. Journal of Aerospace Power, 2008, 23(6):976-980.

[4] 李华. 厦航一 CFM56-7 B22 发动机创中国在翼时间记录[EB/OL]. [2026-01-14]. https://news.carnoc.com/list/283/283173.

[5] LI H.Xiamen Airlines’CFM56-7 B22 Engine Sets New China’s In-Flight Time Record[EB/OL]. [2026-01-14]. https://news.carnoc.com/list/283/283173.

[6] CCAR-33-R2 航空发动机适航规定[S].

[7] CCAR-33-R2 Aircraft engine airworthiness regula-tions[S].

[8] 14 CFR Part 33,Amendment 33-32 Airworthiness stan-dards:aircraft engines[S].

[9] 何歆,张弓. 民用航空发动机适航要求解读-结构审定[M]. 北京: 航空工业出版社,2019:41-52.

[10] HE X, ZHANG G. Civil aviation engine interpretation of airworthiness regulations[M]. Beijing: Aviation In-dustry Press,2019:41-52.

[11] 陶春虎. 航空装备失效典型案例分析[M]. 北京: 国防工业出版社, 1998.

[12] TAO C H. Typical case analysis of aviation equipment failure[M]. Beijing: National Defense Industry Press, 1998.

[13] MIL-HDBK-1783B Engine structural integrity program[S].

[14] GJB 241A 航空涡轮喷气和涡轮风扇发动机通用规范[S].

[15] GJB 241A General specifications for aviation turbojet and turbofan engines [S]. behavior of a titanium alloy in the VHCF regime based on a vibration fatigue test[J]. International Journal of Fatigue, 2023, 172:107608.

[16] BATHIAS C, PARIS P C. Gigacycle fatigue in mechan-ical practice[M]. New York: Marcel Dekker, 2005.

[17] BATHIAS C. Piezoelectric fatigue testing machines and devices[J]. International Journal of Fatigue, 2006, 28 (11):1438-1445.

[18] WANG Q Y, KHAN M K, BATHIAS C. Current under-standing of ultra-high cycle fatigue[J]. Theoretical and Applied Mechanics Letters, 2012, 2(3):031002.

[19] 刘汉青, 何超, 黄志勇, 等. TC17合金超高周疲劳裂纹萌生机理[J]. 金属学报, 2017, 53(9):1047-1054.

[20] LIU H Q, HE C, HUANG Z Y, et al. Very high cycle fatigue failure mechanism of TC17 alloy[J]. Acta Met-allurgica Sinica, 2017, 53(9):1047-1054.

[21] XU W, ZHAO Y G, CHEN X, et al. An ultra-high fre-quency vibration-based fatigue test and its comparative study of a titanium alloy in the VHCF regime[J]. Met-als, 2020, 10(11):1415-1423.

[22] XU W, CHEN X, GAO Z Y, et al. Fatigue behaviors of a titanium alloy in the VHCF regime based on a vibra-tion-based bending fatigue test[J]. Fatigue & Fracture of Engineering Materials & Structures, 2022, 45(9):2549-2562.

[23] XU W, YANG X F, ZHONG B, et al. Multiaxial fatigue investigation of titanium alloy annular discs by a vibra-tion-based fatigue test[J]. International Journal of Fatigue, 2017, 95:29-37.

[24] XU W, ZHU B C, CHEN X, et al. Thickness debit effect of Ni-based single crystal superalloy thin-walled speci-mens in the VHCF regime based on a vibration fatigue test[J]. Journal of Materials Research and Technology, 2024, 33:2538-2548.

[25] GAO Z Y, CHEN X, ZHU S Y, et al. Notch fatigue behavior of a titanium alloy in the VHCF regime based on a vibration fatigue test[J]. International Journal of Fatigue, 2023, 172:107608.

[26] 许巍, 杨宪峰, 郭广平. 基于振动的钛合金膜盘材料疲劳性能试验研究[J]. 实验力学, 2018, 33(2):239-244.

[27] XU W, YANG X F, GUO G P. Experimental study of titanium alloy film disc fatigue performance of based on vibration fatigue measurement[J]. Journal of Experi-mental Mechanics, 2018, 33(2):239-244.

[28] 杨宪峰, 许巍, 郭广平. 基于非线性振动的联轴器膜盘振动疲劳试验研究[J]. 实验力学, 2016, 31(6):44-50.

[29] YANG X F, XU W, GUO G P. Experimental study of vibration fatigue of coupling diaphragm based on nonlin-ear vibration[J]. Journal of Experimental Mechanics, 2016, 31(6):44-50.

[30] 许巍, 赵延广, 钟斌, 等. 基于振动台的 TA11 钛合金超高频疲劳实验和验证[J]. 航空材料学报, 2019, 39(4):86-92.

[31] 史振学, 李嘉荣, 韩梅, 等. DD6 单晶高温合金的缺口疲劳性能[J]. 钢铁研究学报, 2011, 23(增刊 2):345-348.

[32] SHI Z, LI J, HAN M. Notched fatigue properties of DD6 single crystal superalloy[J]. Journal of Iron and Steel Research, 2011, 23(Suppl 2): 345-348.

[33] NICOLETTO G. Directional and Notch effects on the fatigue behavior of as-built DMLS Ti6Al4V[J]. Interna-tional Journal of Fatigue, 2018, 106:124-131.

[34] LANNING D B, NICHOLAS T, PALAZOTTO A. The effect of notch geometry on critical distance high cycle fatigue predictions[J]. International Journal of Fatigue, 2005, 27(10/11/12):1623-1627.

[35] 王弘, 高庆. 缺口应力集中对 40Cr 钢高周疲劳性能的影响[J]. 机械工程材料, 2004, 28(8):12-14.

[36] WANG H, GAO Q. Influence of Notch stress-concentra-tion on the ultra-high-cycle fatigue behaviors of 40Cr steel[J]. Materials for Mechanical Engineering, 2004, 28(8):12-14.

[37] NEUBER H. Theory of notch stresses: principles for exact calculation of strength with reference to structural form and material[M]. Berlin: springer, 1958.

[38] TAYLOR D. The theory of critical distances:a new per-spective in fracture mechanics[J]. Mechanical Engineer-ing, 2007, 130(8):49-60.

[39] SUSMEL L. The theory of critical distances: a review of its applications in fatigue[J]. Engineering Fracture Mechanics, 2008, 75(7):1706-1724.

[40] TAYLOR D. Geometrical effects in fatigue: a unifying theoretical model[J]. International Journal of Fatigue, 1999, 21(5):413-420.

[41] SUSMEL L, TAYLOR D. A novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime[J]. Fatigue & Fracture of Engineering Materials & Structures, 2007, 30(7):567-581.

[42] YANG X G, WANG J K, LIU J L. High temperature LCF life prediction of notched DS Ni-based superalloy using critical distance concept[J]. International Journal of Fatigue, 2011, 33(11):1470-1476.

[43] YE W L, ZHU S P, NIU X P, et al. Fatigue life predic-tion of notched components under size effect using criti-cal distance theory[J]. Theoretical and Applied Frac-ture Mechanics, 2022, 121:103519.

[44] FURUYA Y, KOBAYASHI K, HAYAKAWA M, et al. High-temperature ultrasonic fatigue testing of single-crystal superalloys[J]. Materials Letters, 2012, 69:1-3.

[45] GJB Z18A—2020 金属材料力学性能数据处理与表达[S].

[46] GJB Z18A—2020 Data processing and representation of mechanical properties of metallic materials[S].

[47] ASTM E139- 11 Standard test methods for conducting creep, creep-rupture, and stress-rupture tests of metallic materials[S].

[48] GB/T 2039—2012 金属材料轴向蠕变试验方法[S].

[49] GB/T 2039—2012 Test method for axial creep of metal-lic materials[S].

[50] 焦泽辉, 吴安民, 侯金涛, 等. 一种适用于板状试样高温持久蠕变试验夹具: CN106769423B[P]. 2019-05-21.

[51] 王亮, 钟汉萍, 王剑, 等. 一种自动热电偶穿瓷管装置:CN110039290B[P]. 2020-09-22.

[52] ZHANG Y, HU J K, KANG L X, et al. Creep behavior characterization of nickel-based single-crystal superal-loy DD6 thin-walled specimens based on a 3D-DIC method[J]. Materials, 2023, 16(8):3137.

[53] 方园园, 赵杰, 李东明. 9Cr1Mo 型耐热钢持久性能的统计分析及可靠性预测[J]. 机械强度, 2010, 32(5): 750-753.

[54] FANG Y Y, ZHAO J, LI D M. Statistical analysis and reliability prediction of creep rupture property for 9Cr1Mo-type heat-resistant steels[J]. Journal of Mechanical Strength, 2010, 32(5):750-753.

[55] 赵杰, 李东明, 方园园. T91/P91 钢持久性能的统计分析及可靠性预测[J]. 金属学报, 2009, 45(7):835-839.

[56] ZHAO J, LI D M, FANG Y Y. Statistical analysis and reliability prediction of creep rupture property for T91/P91 steel[J]. Acta Metallurgica Sinica, 2009, 45(7):835-839.

[57] 赵杰, 李东明, 方园园. Manson-Haferd 常数的选择及在蠕变持久寿命预测中的应用[J]. 材料工程, 2009(6):30-34.

[58] ZHAO J, LI D M, FANG Y Y. Selection of Manson-haferd constants and its application on rupture life pre-diction[J]. Journal of Materials Engineering, 2009(6): 30-34.

[59] 张效成, 宫建国, 轩福贞. 蠕变断裂寿命外推方法及数据分散性处理研究[J]. 压力容器, 2017, 34(7):11-18.

[60] ZHANG X C, GONG J G, XUAN F Z. Study on extrap-olation methods of creep rupture life and processing of data scattering[J]. Pressure Vessel Technology, 2017, 34(7):11-18.

[61] 于慧臣, 李兴无, 吴学仁, 等. 先进航空发动机设计用金属材料数据手册[M]. 北京: 航空工业出版社, 2022.

[62] YU H C, LI X W, WU X R, et al. Data handbook of metal materials for the design of the advanced aero engines[M]. Beijing: Aviation Industry Press, 2022.

[63] SANDSTRÖM R. Modelling creep properties of alloys without adjustable parameters[J]. Journal of Materials Science, 2025, 60(39):18201-18224.

[64] XU R D, LI Y, YU H C. Microstructure evolution and dislocation mechanism of a third-generation single-crys-tal Ni-based superalloy during creep at 1170 ℃[J]. Materials, 2023, 16(14):5166.

[65] XU R D, LI Y, YU H C. Creep behavior and deforma-tion mechanism of a third-generation single crystal Ni-based superalloy at 980 ℃[J]. Metals, 2023, 13(9) : 1541.

[66] FAN Y N, SHI H J, QIU W H. Constitutive modeling of creep behavior in single crystal superalloys: effects of rafting at high temperatures[J]. Materials Science and Engineering:A, 2015, 644:225-233.

[67] Le GRAVEREND J B, CORMIER J, GALLERNEAU F, et al. A microstructure-sensitive constitutive model-ing of the inelastic behavior of single crystal nickel-based superalloys at very high temperature[J]. Interna-tional Journal of Plasticity, 2014, 59:55-83.

[68] Le GRAVEREND J B. A hardening-based damage model for fast-evolving microstructures: application to Ni-based single crystal superalloys[J]. International Journal of Plasticity, 2019, 123:1-21.

[69] ZHANG Y, XU R D, HU J K, et al. A thickness debit effect characterization parameter for creep rupture behaviors of nickel-based single crystal superalloys[J]. Journal of Materials Research and Technology, 2024, 29:3522-3531.

[70] CHEN J W, CAO T S, XU W, et al. Analysis of thin-wall effect mechanism based on stress rupture proper-ties and fracture characteristics of DD10 Ni-based sin-gle-crystal alloy[J]. Materials Characterization, 2024, 218:114494.

[71] 王永明, 何歆, 张弓, 等. 基于国情与实践的民用航空发动机材料/工艺适航审定技术路径[J]. 航空材料学报, 2025, 45(6):81-88.

[72] WANG Y M, HE X, ZHANG G, et al. Path of airwor-thiness certification for civil aero-engine materials/pro-cesses based on national conditions and certification practices[J]. Journal of Aeronautical Materials, 2025, 45(6):81-88.

[73] AC-33-AA-2024-01R1 航空发动机审定[S].

[74] AC-33-AA-2024-01R1 Aircraft engines airworthiness standards[S].

[75] 游令非, 张建国, 周霜, 等. 航空发动机限寿件疲劳可靠度计算新方法[J]. 航空学报, 2019, 40(12): 104-115.

[76] YOU L F, ZHANG J G, ZHOU S, et al. A new method for fatigue reliability calculation of aero-engine limited life parts[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(12):104-115.

[77] 丁水汀, 周惠敏, 刘俊博, 等. 航空发动机限寿件表面特征概率损伤容限评估[J]. 航空动力学报, 2021, 36(2):421-430.

[78] DING S T, ZHOU H M, LIU J B, et al. Probabilistic damage tolerance assessment of surface features of aero engine life limited parts[J]. Journal of Aerospace Po-wer, 2021, 36(2):421-430.

[79] 何艳丽, 廖焕文, 王禄秀. 商用航空发动机金属增材制造技术及装备应用[J]. 航空制造技术, 2014, 57(22):47-51.

[80] HE Y L, LIAO H W, WANG L X. Application of tech-nology and equipment for metallic additive manufactur-ing in commercial aeroengine[J]. Aeronautical Manu-facturing Technology, 2014, 57(22):47-51.

[81] 张弓. 航空发动机涡轮盘腔多场耦合危险机理研究[D]. 北京: 北京航空航天大学, 2012.

[82] ZHANG G. Research on the multi-field coupling hazard mechanism of the turbine disk chamber in aviation engines[D]. Beijing: Beihang University, 2012.

[83] 王栓程, 杨冰, 廖贞, 等. 金属材料疲劳短裂纹萌生与扩展研究综述[J]. 机械工程学报, 2023, 59(16):32-53.

[84] WANG S C, YANG B, LIAO Z, et al. Research on short fatigue crack initiation and propagation of metallic mate-rials: a review[J]. Journal of Mechanical Engineering, 2023, 59(16):32-53.

[85] JIANG R, KARPASITIS N, GAO N, et al. Effects of microstructures on fatigue crack initiation and short crack propagation at room temperature in an advanced disc superalloy[J]. Materials Science and Engineering: A, 2015, 641:148-159.

[86] PANG H T, REED P A S. Microstructure effects on high temperature fatigue crack initiation and short crack growth in turbine disc nickel-base superalloy Udimet 720Li[J]. Materials Science and Engineering: A 2007, 448:67-79.

[87] WANG X S, LI Y Q. Characteristics of fatigue surface microcrack growth in vicinal inclusion for powder met-allurgy alloys[J]. Acta Mechanica Solida Sinica, 2003, 16:327-333.

[88] 王习术, 梁锋, 曾燕屏, 等. 夹杂物对超高强度钢低周疲劳裂纹萌生及扩展影响的原位观测[J]. 金属学报, 2005, 41(12):1272-1276.

[89] WANG X S, LIANG F, ZENG Y P, et al. Sem in situ observations to the effects of inclusions on initiation and propagation of the low cyclic fatigue crack in super strength steel[J]. Acta Metallrugica Sinica, 2005, 41(12):1272-1276.

[90] WU L L, JIAO Z H, YU H C. Study on small crack growth behavior of laser powder bed fused Ti6Al4V alloy[J]. Fatigue & Fracture of Engineering Materials & Structures, 2022, 45(8):2174-2186.

[91] 吴圣川, 胡雅楠, 康国政. 材料疲劳损伤行为的先进光源表征技术[M]. 北京: 科学出版社, 2018.

[92] WU S C, HU Y N, KANG G Z. Characterization of material fatigue damage via advanced light source tomography[M]. Beijing: Science Press, 2018.

[93] QIAN W, QIN H, RACK A, et al. Ultrahigh-tempera-ture fatigue origin of SiC/SiC composites [PP/OL]. SSRN[2026-01-14]. http://dx.doi.org/10.2139/ssrn.5706325.

[94] BAO J G, WU Z K, WU S C, et al. Hot dwell-fatigue behaviour of additively manufactured AlSi10Mg alloy: relaxation,cyclic softening and fracture mechanisms[J]. International Journal of Fatigue, 2021, 151:106408.

[95] 曲选辉, 张国庆, 章林. 粉末冶金技术在航空发动机中的应用[J]. 航空材料学报, 2014, 34(1):1-10.

[96] QU X H, ZHANG G Q, ZHANG L. Applications of powder metallurgy technologies in aero-engines[J]. Journal of Aeronautical Materials, 2014, 34(1):1-10.

[97] 田世藩, 张国庆, 李周, 等. 先进航空发动机涡轮盘合金及涡轮盘制造[J]. 航空材料学报, 2003, 23(增刊 1):233-238.

[98] TIAN S F, ZHANG G Q, LI Z, et al. The disk superal-loys and disk manufacturing technologies for advanced aero engine[J]. Journal of Aeronautical Materials, 2003, 23(Suppl 1):233-238.

[99] 张国庆, 张义文, 郑亮, 等. 航空发动机用粉末高温合金及制备技术研究进展[J]. 金属学报, 2019, 55(9):1133-1144.

[100] ZHANG G Q, ZHANG Y W, ZHENG L, et al. Research progress in powder metallurgy superalloys and manufac-turing technologies for aero-engine application[J]. Acta Metallurgica Sinica, 2019, 55(9):1133-1144.

[101] 王习术, 刘安, 许巍, 等. FGHxx 系列合金疲劳损伤行为表征、评价与展望[J]. 固体力学学报, 2022, 43(4):369-385.

[102] WANG X S, LIU A, XU W, et al. Characterization, evaluation and perspective for fatigue damage behaviors of FGHxx-series nickel-based P/M superalloys[J]. Chi-nese Journal of Solid Mechanics, 2022, 43(4):369-385.

[103] 刘佳宾, 刘新灵, 李振. 粉末高温合金夹杂物引起疲劳裂纹萌生微观机理研究现状[J]. 材料导报, 2021, 35(增刊 2):385-390.

[104] LIU J B, LIU X L, LI Z. Research status of micro-mech-anism of fatigue crack initiation caused by inclusions in powder superalloy[J]. Materials Reports, 2021, 35(Suppl 2):385-390.

[105] LIU A, ZHANG Y T, WANG X S, et al. Evaluation of the influences of the stress ratio,temperatures,and local microstructure on small fatigue crack propagation behavior of the FGH96 superalloy[J]. International Journal of Fatigue, 2023, 171:107573.

[106] LIU A, LIANG Z, WANG X S, et al. Investigation of fatigue small crack propagation behavior in superalloy FGH96 under different stress ratios[J]. Journal of Mate-rials Engineering and Performance, 2023, 32(12) : 5554-5565.

[107] 徐宇飞, 胡殿印, 毛建兴, 等. 考虑应力比及温度影响的粉末高温合金短裂纹扩展模型研究[J]. 推进技术, 2023, 44(5):232-239.

[108] XU Y F, HU D Y, MAO J X, et al. Powder superalloy short crack growth model considering effects of stress ratio and temperature[J]. Journal of Propulsion Technol-ogy, 2023, 44(5):232-239.

[109] HU D Y, WANG T, MA Q H, et al. Effect of inclusions on low cycle fatigue lifetime in a powder metallurgy nickel-based superalloy FGH96[J]. International Jour-nal of Fatigue, 2019, 118:237-248.

[110] ZHONG B, WANG Y R, WEI D S, et al. Multiaxial fatigue life prediction for powder metallurgy superalloy FGH96 based on stress gradient effect[J]. International Journal of Fatigue, 2018, 109:26-36.

[111] WANG Y R, WANG X C, ZHONG B, et al. Estimation of fatigue parameters in total strain life equation for powder metallurgy superalloy FGH96 and other metal-lic materials[J]. International Journal of Fatigue, 2019, 122:116-124.

[112] LIANG Z, LIU A, WANG X S, et al. Experimental and modeling study on small fatigue crack initiation and propagation behavior of Inconel 617[J]. International Journal of Fatigue, 2022, 164:107158.

[113] WANG L, FENG S Z, WANG Y G, et al. Porosity defects in additively manufactured metal materials: for-mation mechanisms,impact on performance and regula-tion[J]. International Materials Reviews, 2025: 09506 608251371459.

[114] GABBETT C, DOOLAN L, SYNNATSCHKE K, et al. Quantitative analysis of printed nanostructured net-works using high-resolution 3D FIB-SEM nanotomogra-phy[J]. Nature Communications, 2024, 15:278.

[115] MURPHY-LEONARD A D, et al. Characterization of microstruc-ture in additively manufactured 316L using automated serial sectioning[J]. Current Opinion in Solid State and Materials Science, 2020, 24(3):100819.

[116] ROTTMANN P F, POLONSKY A T, FRANCIS T, et al. TriBeam tomography and microstructure evolution in additively manufactured Alnico magnets[J]. Materials Today, 2021, 49:23-34.

[117] JIAO Z H, XU R D, YU H C, et al. Evaluation on ten-sile and fatigue crack growth performances of Ti6Al4V alloy produced by selective laser melting[J]. Procedia Structural Integrity, 2017, 7:124-132.

[118] 武亮亮, 焦泽辉, 于慧臣. 激光选区熔化 TC4 合金小裂纹扩展行为[J]. 材料工程, 2023, 51(6):83-92.

[119] WU L L, JIAO Z H, YU H C. Small crack growth behavior in selective laser melted TC4 alloy[J]. Journal of Materials Engineering, 2023, 51(6):83-92.

[120] XU Z W, LIU A, WANG X S. The influence of build-ing direction on the fatigue crack propagation behavior of Ti6Al4V alloy produced by selective laser melting[J]. Materials Science and Engineering: A, 2019, 767:138409.

[121] XU Z W, LIU A, WANG X S, et al. Fatigue limit pre-diction model and fatigue crack growth mechanism for selective laser melting Ti6Al4V samples with inherent defects[J]. International Journal of Fatigue, 2021, 143: 106008.

[122] XU Z W, LIU A, WANG X S. Fatigue performance and crack propagation behavior of selective laser melted AlSi10Mg in 0° 15° 45° and 90° building directions[J]. Materials Science and Engineering: A, 2021, 812:141141.

[123] XU Z W, LIU A, WANG X S. Influence of macrozones on the fatigue cracking behavior and fracture mecha-nisms of rolled Ti-6Al-4V alloy[J]. Materials Science and Engineering:A, 2021, 824:141824.

[124] XU Z W, LIU A, WANG X S. Fatigue performance dif-ferences between rolled and selective laser melted Ti6Al4V alloys[J]. Materials Characterization, 2022, 189:111963.

[125] QU Z, ZHANG Z J, LIU R, et al. High fatigue resis-tance in a titanium alloy via near-void-free 3D printing[J]. Nature, 2024, 626(8001):999-1004.

[126] QU Z, ZHANG Z J, LIU R, et al. Naturally high fatigue performance of a 3D printing titanium alloy across all stress ratios[J]. Science Advances, 2025, 11(34):0937.

[127] WU Z K, WU S C, KRUZIC J J, et al. Critical damage events of 3D printed AlSi10Mg alloy via in situ syn-chrotron X-ray tomography[J]. Acta Materialia, 2025, 282:120464.

[128] WANG L, FENG S Z, WANG Y G, et al. The effect of porosity on the fatigue crack growth behavior of selec-tive laser melted TA15 titanium alloy[J]. Engineering Failure Analysis, 2025, 170:109305.

[129] EL HADDAD M H, TOPPER T H, SMITH K N. Pre-diction of non propagating cracks[J]. Engineering Frac-ture Mechanics, 1979, 11(3):573-584.

[130] 吴学仁, 刘建中. 基于小裂纹理论的航空材料疲劳全寿命预测[J]. 航空学报, 2006, 27(2):219-226.

[131] WU X R, LIU J Z. Total fatigue life prediction for aero-nautical materials by using small-crack theory[J]. Acta Aeronautica et Astronautica Sinica, 2006, 27(2) : 219-226.

[132] 张丽, 吴学仁. 基于小裂纹理论的 GH4169 高温合金的疲劳全寿命预测[J]. 航空材料学报, 2014, 34(6): 75-83.

[133] ZHANG L, WU X R. Fatigue-life prediction method based on small-crack theory in GH4169 superalloy[J]. Journal of Aeronautical Materials, 2014, 34(6):75-83.

[134] JIN S Z, SUN J Y, YUAN H. Anisotropic cyclic plastic-ity modeling for additively manufactured nickel-based superalloys[J]. Fatigue & Fracture of Engineering Mate-rials & Structures, 2022, 45(8):2371-2387.

[135] JIN S Z, PEI C H, YUAN H, et al. Multi-axial fatigue life assessment of additively manufactured nickel-based superalloys[J]. International Journal of Fatigue, 2022, 163:107049.

[136] JIN S Z, YUAN H. Determination of equivalent crack length for voids in metallic alloys based on continuum damage mechanics modeling[J]. Engineering Fracture Mechanics, 2024, 310:110437.