增材制造钛合金等效弹性张量的细观力学建模与实验研究

doi:10.11900/0412.1961.2023.00451

金属学报

2025, Vol. 61

Issue (9): 1438-1448 DOI: 10.11900/0412.1961.2023.00451

研究论文

本期目录 | 过刊浏览

增材制造钛合金等效弹性张量的细观力学建模与实验研究

谭若涵¹, 宋永锋¹^,², 陈超³, 李丹³, 成庶¹, 李雄兵¹(

)

1 中南大学交通运输工程学院长沙 410075
2 广东工业大学省部共建精密电子制造技术与装备国家重点实验室广州 510006
3 中南大学粉末冶金研究院长沙 410083

Mesomechanical Modeling and Experimental Study of Effective Elastic Tensors in Additively Manufactured Titanium Alloys

TAN Ruohan¹, SONG Yongfeng¹^,², CHEN Chao³, LI Dan³, CHENG Shu¹, LI Xiongbing¹(

)

1 School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China
2 State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment, Guangdong University of Technology, Guangzhou 510006, China
3 Powder Metallurgy Research Institute, Central South University, Changsha 410083, China

引用本文:

谭若涵, 宋永锋, 陈超, 李丹, 成庶, 李雄兵. 增材制造钛合金等效弹性张量的细观力学建模与实验研究[J]. 金属学报, 2025, 61(9): 1438-1448.
Ruohan TAN, Yongfeng SONG, Chao CHEN, Dan LI, Shu CHENG, Xiongbing LI. Mesomechanical Modeling and Experimental Study of Effective Elastic Tensors in Additively Manufactured Titanium Alloys[J]. Acta Metall Sin, 2025, 61(9): 1438-1448.

全文: PDF(2522 KB) HTML

摘要:

孔隙和织构均为增材制造(AM)多晶体金属的重要特征，但已有的细观力学模型无法研究2者的耦合作用对材料力学性能的影响机理。因此，本工作构建了双相金属材料的改进Mori-Tanaka (modified Mori-Tanaka，MMT)模型，在此基础上预测AM Ti-6Al-4V合金的等效弹性张量，进而探究AM 多晶体材料的微观结构对材料宏观力学性能的影响规律。本模型结合了传统MT模型和微分法，可综合分析各向异性多晶体织构和孔隙2个耦合因素与宏观力学性能的内在联系。通过有损和无损实验，研究了2种孔隙率和织构的AM Ti-6Al-4V试块的相变行为、晶粒取向分布函数、孔隙率和孔隙形貌特征。为验证理论预测的准确性，采用稀疏法与所建立模型进行对比分析；同时进行拉伸实验和超声实验，基于MMT模型得到的Young's模量与拉伸实验结果的平均绝对百分比误差(MAPE)分别为0.87%和2.51%，基于MMT模型得到的等效弹性刚度张量( $C e f f$ )与超声实验结果的MAPE分别为9.47%和4.45%。可见，实验结果从力学和无损检测2个角度验证了MMT模型的有效性，为研究AM 多晶体材料的微观结构对宏观力学性能的作用机理提供了一种有效的细观力学分析方法。

关键词 ：等效弹性张量, 增材制造, 钛合金, 各向异性, 改进MT模型, 孔隙, 织构

Abstract：

Additively manufactured (AM) Ti-6Al-4V alloys are known for their lightweight and superior mechanical properties and are increasingly being favored in the aerospace, energy, and biomedical industries. Among the available AM technologies, selective laser melting (SLM) stands out for its ability to fabricate complex-shaped Ti-6Al-4V efficiently and economically through near-net-shape manufacturing. Despite their advantages, SLM-produced parts often suffer from mechanical anisotropy and contain microdefects such as pores, cracks, and residual stresses, restricting their wider application. Addressing these issues requires a thorough understanding of the effects of texture and porosity on the mechanical properties of AM materials, which is necessary for developing components that comply with strict industry standards. Previous research has predominantly focused on studying the impact of texture or porosity on material properties, overlooking the interplay between these two critical factors. This work introduces an advanced modified Mori-Tanaka (MMT) model that simultaneously considers both texture and porosity in dual-phase AM Ti-6Al-4V alloys. This model enhances the traditional Mori-Tanaka approach by integrating it with the differential method, facilitating a nuanced analysis of how texture and porosity jointly influence the mechanical behavior of polycrystals. For model development, phase transitions and grain orientations are characterized using EBSD, whereas the 3D Gaussian distribution function describes the texture distribution within the polycrystal. Micro/nano computed tomography (CT) plays a pivotal role in determining the volume fraction and morphology of pores, providing crucial data for the model. These parameters were incorporated into the mesomechanical model to analyze the effective elastic stiffness tensor and Young's modulus, quantifying their collective impact on the alloy's mechanical properties. To validate the model, tensile and ultrasonic tests are conducted for two samples with different porosities and textures and compared their outcomes to evaluate the material's mechanical behavior, which exhibits characteristics of transverse isotropy. The comparison highlights the MMT model's superior precision, especially at higher porosity levels, with mean absolute percentage errors (MAPE) between Young's modulus obtained from the MMT model and the tensile test for two samples were 0.87% and 2.51%, respectively. Similarly, the MAPE between the effective elastic stiffness tensor derived from the MMT model and the ultrasonic test were 9.47% and 4.45%, respectively. These findings underscore the model's effectiveness in predicting material properties and its potential as a robust tool for exploring the interactions between microstructural elements and macroscopic mechanical properties of AM polycrystalline materials.

Key words： effective elastic tensor additive manufacturing titanium alloy anisotropy modified MT model porosity texture

收稿日期: 2023-11-14

ZTFLH:

TB301

基金资助:湖南省科技创新领军人才项目(2023RC1015);湖南省自然科学基金项目(2023JJ60159)

通讯作者: 李雄兵，lixb213@csu.edu.cn，主要从事无损检测与评价的研究

Corresponding author: LI Xiongbing, professor, Tel: 15084761518, E-mail: lixb213@csu.edu.cn

作者简介: 谭若涵，女，1993年生，博士

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https://www.ams.org.cn/CN/10.11900/0412.1961.2023.00451 或 https://www.ams.org.cn/CN/Y2025/V61/I9/1438

图1 增材制造(AM) Ti-6Al-4V合金(MMT)模型的流程图

表1 Ti-6Al-4V合金的单晶弹性常数(c(r))[19] (GPa)

表2 AM Ti-6Al-4V试块的EBSD分析结果

图2 AM Ti-6Al-4V试块中晶粒的微观结构及取向分布

图3 AM Ti-6Al-4V试块Euler角(θ)的概率密度分布图

图4 AM Ti-6Al-4V试块的孔隙重构

图5 AM Ti-6Al-4V试块孔隙体积和球度的概率密度分布图

表3 AM Ti-6Al-4V试块在不同方向的最大载荷和Young's模量

Sample	$C 11 e f f$	$C 22 e f f$	$C 33 e f f$	$C 44 e f f$	$C 55 e f f$	$C 66 e f f$
A	142.7 ± 1.0	143.4 ± 0.2	137.4 ± 0.4	44.1 ± 0.7	44.6 ± 0.4	43.2 ± 0.4
B	169.4 ± 0.7	168.6 ± 0.7	171.6 ± 0.1	47.1 ± 2.2	46.8 ± 2.1	45.2 ± 1.2

表4 超声实验测得AM Ti-6Al-4V试块的等效弹性刚度张量( Ceff) (GPa)

图6 MMT模型得到的AM Ti-6Al-4V试块的 Ceff

图7 MMT模型与稀疏法得到的AM Ti-6Al-4V试块的 Ceff

表5 基于MMT模型和稀疏法以及拉伸实验测得的AM Ti-6Al-4V试块不同方向的Young's模量及其平均绝对百分比误差(MAPE)和均等系数(EC)

Sample	Indicator	$C 11 e f f$ GPa	$C 22 e f f$ GPa	$C 33 e f f$ GPa	$C 44 e f f$ GPa	$C 55 e f f$ GPa	$C 66 e f f$ GPa	MAPE %	EC %
A	V-MMT	152.60	163.09	157.36	48.42	40.50	44.06	9.47	94.35
A	Ultrasonic	143.68	143.23	136.92	44.11	44.98	43.18
B	V-MMT	165.65	175.67	170.34	51.25	43.31	46.97	4.45	98.49
B	Ultrasonic	169.43	169.60	171.60	47.09	46.79	45.21

表6 基于MMT模型和超声实验获得的AM Ti-6Al-4V试块 Ceff及其MAPE和EC

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