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

doi:10.11900/0412.1961.2023.00451

Acta Metall Sin

2025, Vol. 61

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

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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

Cite this article:

TAN Ruohan, SONG Yongfeng, CHEN Chao, LI Dan, CHENG Shu, LI Xiongbing. Mesomechanical Modeling and Experimental Study of Effective Elastic Tensors in Additively Manufactured Titanium Alloys. Acta Metall Sin, 2025, 61(9): 1438-1448.

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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

Received: 14 November 2023

ZTFLH:

TB301

Fund: Hunan Provincial Science and Technology Innovation Leading Talent Project(2023RC1015);Natural Science Foundation of Hunan Province(2023JJ60159)

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

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	TAN Ruohan
	SONG Yongfeng
	CHEN Chao
	LI Dan
	CHENG Shu
	LI Xiongbing

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https://www.ams.org.cn/EN/10.11900/0412.1961.2023.00451 OR https://www.ams.org.cn/EN/Y2025/V61/I9/1438

Fig.1 Flowchart of modified Mori-Tanaka (MMT) model in additively manufactured (AM) Ti-6Al-4V alloy (w is any initial plane layer, C^eff is effective elastic stiffness tensor, $C i j e f f$ is the component of C^eff, γ is Young's modulus. Samples A and B are manufactured with different printing parameters)

Table 1 Single crystal elastic constant (c(r)) of Ti-6Al-4V alloy^[19]

Table 2 EBSD analysis results of AM Ti-6Al-4V samples

Fig.2 Inverse pole figures (IPFs) paralleling to axis Z (a1, b1), IPFs of reconstructed phase β (a2, b2), orientation distribution function (ODF) maps of phase β (a3, b3), and ODF maps of phase α (a4, b4) of AM Ti-6Al-4V sample A (a1-a4) and sample B (b1-b4) (θ—Euler angle)

Fig.3 Probability density distribution map of θ in AM Ti-6Al-4V sample

Fig.4 Pore reconfigurations of AM Ti-6Al-4V sample A (a) and sample B (b)

Fig.5 Probability density distribution maps of pore volume (a) and sphericity (b) in AM Ti-6Al-4V samples (Inset in Fig.5a shows the locally enlarged map)

Table 3 Maximum load (P_max) and γ of AM Ti-6Al-4V samples in different directions

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

Table 4 C^eff of AM Ti-6Al-4V samples measured by ultrasonic test

Fig.6 $C 11 e f f$ (a), $C 55 e f f$ (b), $C 13 e f f$ (c), and $C 23 e f f$ (d) of AM Ti-6Al-4V samples obtained by MMT model (Insets show the locally enlarged curves. n—iteration number)

Fig.7 $C 22 e f f$ of AM Ti-6Al-4V samples obtained by MMT model and sparse method (SM) (Inset shows the locally enlarged curves)

Table 5 γ in different directions of AM Ti-6Al-4V alloy by MMT model, SM, and tensile test, along with its average absolute percentage error (MAPE) and equalization coefficient (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

Table 6

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

, and

C 66 e f f

of AM Ti-6Al-4V alloy by MMT method and ultrasonic test, along with its MAPE and EC

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