Journal of Materials Science

, Volume 53, Issue 14, pp 10071–10094 | Cite as

Multi-scale finite element analysis for tension and ballistic penetration damage characterizations of 2D triaxially braided composite

  • Hongyong Jiang
  • Yiru Ren
  • Songjun Zhang
  • Zhihui Liu
  • Lu Nie


The multi-scale finite element model is presented to analyze tension and ballistic penetration damage characterizations of 2D triaxially braided composite (2DTBC). At the mesoscopic level, the damage of fiber tows is initiated with 3D Hashin criteria, and the damage initiation of pure matrix is predicted by the modified von Mises. The progressive degradation scheme and energy dissipation method are adopted to capture softening behaviors of tow and matrix. The macro-scale damage model is established by maximum-stress criteria and exponential damage evolution. To simulate interface debonding and inter-ply delamination, a triangle traction–separation law is adopted in each scale. Both scale damage models are verified with available experimental results. Based on numerical predictions, the stress–strain responses and damage developments of 2DTBC under axial and transverse tension loading are studied. For ballistic penetration loading, the meso-scale damage mechanisms of 2DTBC are predicted using 1/4 model, 1/2 model, 1-layer model, 2-layer model and 3-layer model. Then, effects of different model and impactor radius on damage modes are analyzed. Additionally, the macro-scale ballistic penetration behaviors of 2DTBC are simulated and compared with experiment. The prediction results for tension and penetration correlate well with experiment results. Both tension and penetration damage characterizations for tow, matrix within tow, pure matrix, interface and inter-ply delamination are revealed. A comparison of penetration damage between meso- and macro-scale presents a similar crack mechanism between two scales.



The authors acknowledge the financial supports from the National Natural Science Foundation of China (No. 11402011). The financial supports from Fundamental Research Funds for the Central Universities (No. 201401390741) are also gratefully acknowledged.

Author’s Contribution

YR helped with the research guidance, technological guidance, quality check of paper and writing level and final decision for submission. HJ contributed to the survey, programming of user material, finite element modeling (preprocessing and post-processing), picture and data processing, damage analysis of meso-scale and macro-scale triaxially braided composite under the tension loading and ballistic impact loading and writing of full text. SZ assisted with the part of work research, dealing of numerical computation error, programming study and numerical result discussion of meso-scale axial tension and transverse tension. ZL involved in numerical result discussion of meso-scale ballistic impact failure. LN contributed to the technological guidance.

Compliance with ethical standards

Conflict of interest

The authors declared no potential conflict of interest with respect to the research, authorship and/or publication of this article.


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Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina
  2. 2.College of Mechanical and Vehicle EngineeringHunan UniversityChangshaChina
  3. 3.China Academy of Launch Vehicle TehcnologyBeijingChina

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