Stress Relief Evaluation Method for Aluminum Alloy Boxes Based on Gaussian and Cumulative Distribution

LU Hao; ZHU Quanwei; FENG Xiao; GAO Wu

doi:10.3969/j.issn.1674-6457.2026.08.014

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Journal of Netshape Forming Engineering ›› 2026, Vol. 18 ›› Issue (8) : 157-166. DOI: 10.3969/j.issn.1674-6457.2026.08.014

Light Alloy Forming

Stress Relief Evaluation Method for Aluminum Alloy Boxes Based on Gaussian and Cumulative Distribution

LU Hao^1,*, ZHU Quanwei¹, FENG Xiao², GAO Wu²

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Abstract

In response to the lack of consensus within the industry regarding stress relief heat treatment specifications for 5A06 aluminum alloy skin-frame structures, the work aims to systematically evaluate the effectiveness of various processes including natural aging, heat treatment at different temperatures, and vibration aging in eliminating residual stress, to provide a theoretical basis and experimental support for selecting efficient and reliable stress control processes. Non-destructive ultrasonic stress testing technology was employed to measure stresses in panels subjected to different durations of natural aging, low-temperature heat treatment at 130 ℃, high-temperature heat treatment at 310 ℃, and vibration aging. The mean and standard deviations of the residual stress distribution were analyzed with probabilistic statistical methods. An evaluation methodology integrating Gaussian distribution fitting and the Boltzmann cumulative distribution function was proposed to better distinguish the stress relief effects of different processes. After the 130 ℃ heat treatment, residual stress was significantly reduced with improved distribution homogeneity. In contrast, the 310 ℃ treatment resulted in substantial fluctuation in residual stress, indicating that the stress relief effect was not significant. Stresses stabilized after 14 days of natural aging. Vibration aging demonstrated a certain stress homogenization effect. Metallographic analysis revealed that the 130 ℃ treatment had a lesser impact on microstructural changes compared to the 310 ℃ treatment. This work establishes an evaluation method based on probabilistic statistics and cumulative distribution functions to objectively assess the effectiveness of stress relief processes in complex structures. The 130 ℃ low-temperature heat treatment is suitable for stress regulation in this alloy frame structure, whereas the 310 ℃ high-temperature heat treatment is not recommended. The findings provide important theoretical and practical guidance for process optimization in the manufacturing of 5A06 aluminum alloy welded structures.

Key words

5A06 aluminum alloy / heat treatment / residual stress / ultrasonic stress test / probabilistic statistics

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LU Hao, ZHU Quanwei, FENG Xiao, GAO Wu. Stress Relief Evaluation Method for Aluminum Alloy Boxes Based on Gaussian and Cumulative Distribution[J]. Journal of Netshape Forming Engineering. 2026, 18(8): 157-166 https://doi.org/10.3969/j.issn.1674-6457.2026.08.014

References

[1] 刘慧芳, 姜锋, 路丽英, 等. 退火温度对5A06铝合金盐雾腐蚀行为的影响[J]. 轻合金加工技术, 2020, 48(2): 60-65.
LIU H F, JIANG F, LU L Y, et al.Effects of Annealing Temperature on the Salt-Spray Corrosion Behavior of 5A06 Aluminum Alloy[J]. Light Alloy Fabrication Technology, 2020, 48(2): 60-65.
[2] 孙卫国, 徐贺年, 姜文举, 等. 改善5A06-O铝合金板材性能的研究[J]. 轻合金加工技术, 2006, 34(12): 26-28.
SUN W G, XU H N, JIANG W J, et al.Research about Improving Properties of 5A06-O Aluminium Alloy Sheet[J]. Light Alloy Fabrication Technology, 2006, 34(12): 26-28.
[3] CHENG X, YU H P, LYU F, et al.Mechanical Properties and Microstructure Evolution of 5A06 Aluminum Alloy under Two-Step Dynamic Tension[J]. Materials Science and Engineering: A, 2025, 926: 147958.
[4] YAN Z Y, CHEN S J, JIANG F, et al.Effect of Asymmetric Material Flow on the Microstructure and Mechanical Properties of 5A06 Al-Alloy Welded Joint by VPPA Welding[J]. Metals, 2021, 11(1): 120.
[5] YANG Y, LI Y, BI J, et al.Microstructure and Mechanical Properties of 2195/5A06 Dissimilar Joints Made by Resistance Spot Welding[J]. Materials Characterization, 2022, 191: 112147.
[6] YE T, MA J W, JIA Z Y, et al.Microstructure, Mechanical Properties and Low-Temperature Tribological Behavior of Cr/Cr-W/W-DLC/DLC Multilayer Coatings on 5A06 Al Alloy[J]. Journal of Materials Research and Technology, 2022, 18: 810-819.
[7] DU J J, QIAO M K, WANG J, et al.Effect on Microstructure and Mechanical Properties of Friction Stir Welded 5A06 Aluminum Alloy Joints by Deep Cryogenic Treatment[J]. Materials Research Express, 2024, 11(4): 046514.
[8] 王小博, 张旭东, 李昊丞. 去应力退火对焊接结构件残余应力与力学性能的影响与分析[J]. 航天制造技术, 2019(5): 29-32.
WANG X B, ZHANG X D, LI H C.Influence and Analysis of Stress Relief Annealing for a Welded Structure on Residual Stress and Mechanical Properties[J]. Aerospace Manufacturing Technology, 2019(5): 29-32.
[9] 徐双喜, 马甲金, 陈高澎, 等. 挤压成型铝合金薄板焊接接头疲劳强度研究[J]. 武汉理工大学学报(交通科学与工程版), 2025, 49(1): 47-52.
XU S X, MA J J, CHEN G P, et al.Fatigue Assessment of Welded Joints of Extruded Aluminum Alloy Ribbed Sheet[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2025, 49(1): 47-52.
[10] 蔡亮, 陆涓涓, 柯贤朝. PFMEA在导弹发射箱端盖产品关键工序确定中的应用[J]. 中国设备工程, 2024(22): 220-222.
CAI L, LU J J, KE X Z.Application of PFMEA in Determining the Key Process of Missile Launch Box End Cover Products[J]. China Plant Engineering, 2024 (22): 220-222.
[11] 杨鑫宇, 冷子凌, 李伟, 等. 易碎式导弹发射箱盖研究进展[J]. 工程塑料应用, 2022, 50(12): 142-148.
YANG X Y, LENG Z L, LI W, et al.Research Progress of Fragile Missile Launching Box Cover[J]. Engineering Plastics Application, 2022, 50(12): 142-148.
[12] 邹长星, 邓春丽, 袁森. 导弹发射箱发射过程热流固耦合数值模拟[J]. 机械与电子, 2022, 40(7): 22-26.
ZOU C X, DENG C L, YUAN S.Numerical Simulation of Thermal Fluid Solid Coupling of Launch Box[J]. Machinery & Electronics, 2022, 40(7): 22-26.
[13] 蔡建, 詹永富, 罗俊杰. 发射箱复合材料箱体的设计与选材[J]. 四川兵工学报, 2010, 31(8): 36-38.
CAI J, ZHAN Y F, LUO J J.Design and Material Selection of Composite Box for Launching Box[J]. Journal of Sichuan Ordnance, 2010, 31(8): 36-38.
[14] 黄钢, 张清东, 张勃洋, 等. 钢板残余应力检测方法的实验比较[J]. 振动、测试与诊断, 2024, 44(5): 862-870.
HUANG G, ZHANG Q D, ZHANG B Y, et al.Experimental Comparative Study on Detection Methods of Residual Stress of Steel Plate[J]. Journal of Vibration,Measurement & Diagnosis, 2024, 44(5): 862-870.
[15] 李进, 薛润东, 赵仁勇, 等. 基于声弹效应的芳纶增强环氧复合材料残余应力检测技术研究[J]. 电工技术学报, 2023, 38(9): 2519-2527.
LI J, XUE R D, ZHAO R Y, et al.Residual Stress Detection Technology for Aramid Reinforced Epoxy Composites Based on Acoustic-Elastic Effect[J]. Transactions of China Electrotechnical Society, 2023, 38(9): 2519-2527.
[16] 路浩, 邢立伟, 邢敬伟. 超声波法焊接残余应力测量技术[J]. 焊管, 2019, 42(8): 50-55.
LU H, XING L W, XING J W.Ultrasonic Method Measurement of Welding Residual Stress[J]. Welded Pipe and Tube, 2019, 42(8): 50-55.
[17] 侯怀书, 方鑫冲, 张润泽, 等. 薄壁金属直缝圆焊管残余应力超声检测[J]. 制造技术与机床, 2022(2): 126-130.
HOU H S, FANG X C, ZHANG R Z, et al.Ultrasonic Testing of Residual Stress in Welding Area of the Thin-Walled Metal Longitudinal Welded Pipes[J]. Manufacturing Technology & Machine Tool, 2022(2): 126-130.
[18] 杨顺民. 临界折射纵波检测残余应力的关键影响因素研究[D]. 太原: 中北大学, 2019.
YANG S M.Research on Key Influencing Factors for Residual Stresses Measurement with Critically Refracted Longitudinal Waves[D]. Taiyuan: North University of China, 2019.
[19] ZOU D, ZENG X, REN B, et al.Experimental Investigation into Internal Stress Detection of Aluminum Alloy by Phased Array Longitudinal-Wave Ultrasonic Testing[J]. Journal of South China University of Technology (Natural Science Edition), 2023, 51(7): 34-41.
[20] LAI H H, YAN D H, CHANG W J, et al.Effects of Factors from Practical Workpieces on Ultrasonic LCR Method Stress Measurement[J]. Discover Applied Sciences, 2024, 6(7): 335.
[21] LI Y B, LI S S, ZHOU Y J, et al.Research on Method for Measuring Two-Dimensional Stress in Curved Surface Components Using Ultrasonic LCR Waves[C]//2024 18th Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA). Dongguan, China. IEEE, 2025: 405-409.
[22] WANG J X, LI W B, CAI J C, et al.A Novel Stress Measurement Approach for a Metallic Plate Based on Non-Specular Reflection of Bounded Ultrasonic Beams[J]. NDT & E International, 2025, 155: 103436.
[23] LI Z H, GONG Y X, LIU N X, et al.Using Longitudinal Critically Refracted Waves to Detect Absolute Stress of Steel Members Considering the Influence of Temperature[J]. NDT & E International, 2023, 140: 102949.
[24] NIU X C, ZHU L Q, YU Z J, et al.Detection Method of the Neutral Temperature in Continuous Welded Rails Based on Nonlinear Ultrasonic Guided Waves[J]. Nondestructive Testing and Evaluation, 2023, 38(5): 798-826.
[25] MA G B, WANG Q, HONG M C, et al.Preload Detection System Based on Ultrasonic Energy Transmission for Attached Joint Structures[J]. Russian Journal of Nondestructive Testing, 2025, 61(2): 175-185.
[26] LIU Y Z, YAO J F, XU Z J, et al.Improved Ultrasonic Absolute Stress Measurement Based on Optimized Wavelet Transform and Cross-Correlation Algorithm[J]. Measurement, 2025, 246: 116638.