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Numerical comprehensive optimization and evaluation on ballistic behavior of ceramic/FRP composites based on AHP model

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Abstract

Multi-layer ceramic/fiber reinforced polymer (FRP) composite, especially Al2O3/carbon-aramid hybrid FRP composite, is a common ceramic composite armor system (CCAS) in the protection field. Aiming at selecting an optimal configuration from several schemes with different discrete structural parameters, including the thickness ratio of carbon fiber (CF) to aramid fiber (AF), the prepreg’s number of layers (PNL) of CF and AF, etc., a two-step comprehensive optimization and evaluation method is proposed based on the parametrical study of the ballistic behavior and improved analytical hierarchy process (AHP) conducted by finite element analysis (FEA) and Python programming, respectively. The results demonstrate the effectiveness of this two-step methodology despite the influence of these discrete factors on the ballistic behavior is intricate. Besides, when the PNL is less, the configuration with the PNL of CF is 8, the thickness ratio of CF to AF is 3:7 and the PNL of AF is 14 is the desirable design scheme with the highest comprehensive ballistic behavior.

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Abbreviations

t 0, t C, t A :

Thickness of cohesive layer, CF and AF

σ ⋆ :

Normalized equivalent von Mises stress

σ ⋆i , σ ⋆f :

Equivalent intact and fracture stress

A, B, C, M, N :

Material constants for ceramic

P ⋆ , T ⋆ :

Normalized actual pressure and tensile pressure

\(\dot{\varepsilon}\) :

Temperature or Celsius temperature scale

μ :

Compressive volumetric strain

K 1, K 2, K 3 :

Material constants for EOS

P, ΔP :

Pressure and its increment

D :

Damage variable for ceramic

D 1, D 2 :

Damage coefficients for ceramic

\(\Delta\overline{\varepsilon}^{\text{pl}}\) :

Increment of equivalent plastic strain

\(\overline{\varepsilon}_{f}^{\text{pl}}(P)\) :

Fracture equivalent plastic strain

β :

Bulking factor

HEL :

Hugoniot elastic limit

P HEL :

Pressure at HEL

ρ :

Density

E :

Elastic modulus

G :

Shear modulus

ν :

Poisson’s ratio

X, Y, Z :

Longitudinal, transverse and normal strength

S :

Shear strength

t :

Nominal stress vector

K :

Stiffness vector

δ :

Displacement vector

G C :

Fracture energy

σ b :

Tensile strength for cohesive layer

σ s :

Tensile yield strength for cohesive layer

ε f :

Tensile failure strain for cohesive layer

v 0, v r :

Initial impact velocity and residual velocity

v bl :

Ballistic limit velocity

F d :

Delamination factor

F da :

Adjusted delamination factor

R max :

Maximum radius of delamination area

R nom :

Nominal radius of bullet hole

A del :

Cumulative peripheral delamination area

A max, A nom :

Areas belonging to Rmax and Rnom

A :

PCM of criteria in criterion layer

B (k) :

PCM of alternatives for criterion k

α, β (k) :

Non-normalized column weight vector

w (A) :

Weight vector of PCM A

\(\boldsymbol{w}^{(B^{(k)})}\) :

Weight vectors of PCM B(k)

CR :

Consistency ration

RI :

Random consistency index

CI :

Consistency index

λ max(A):

Maximum eigenvalue of PCM A

W :

Comprehensive grade vector

W′:

Modified comprehensive grade vector

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Acknowledgments

The work was supported by the National Natural Science Foundation of China (Grant No. 12072095), Science Foundation of National Key Laboratory of Science and Technology on Advanced Composites in Special Environments (Grant No. 6142905232205) and College Student Entrepreneurship Assistance Program of Heilongjiang Province (Grant No. 14233).

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Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin, 150001, P.R. China

    Shibao Wu, Zhonghai Xu, Chunxing Hu, Ruoyu Li, Rongguo Wang & Xiaodong He

  2. Shenzhen STRONG Advanced Materials Research Institute Co., Ltd, Shenzhen, 518000, P.R. China

    Xiaodong He

Authors
  1. Shibao Wu
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  2. Zhonghai Xu
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  3. Chunxing Hu
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  4. Ruoyu Li
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  5. Rongguo Wang
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  6. Xiaodong He
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Correspondence to Zhonghai Xu or Xiaodong He.

Additional information

Zhonghai Xu received Ph.D. degree in Jilin University, Jilin, China, in 2008. Now he is a Professor and Ph.D. supervisor in Center for Composite Materials and Structures, School of Astronautics, Harbin Institute of Technology. He is mainly engaged in the research of composite structure feature sensitivity analysis, advanced composite structure design, damage failure analysis and evaluation.

Xiaodong He received Ph.D. degree in Harbin Institute of Technology, Harbin, China. Now he is a Professor, Ph.D. supervisor and Cheung Kong Scholar Distinguished Professor in Center for Composite Materials and Structures, School of Astronautics, Harbin Institute of Technology. He is mainly engaged in the research of lightweight structures and composites, thermal protection structures and materials.

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Wu, S., Xu, Z., Hu, C. et al. Numerical comprehensive optimization and evaluation on ballistic behavior of ceramic/FRP composites based on AHP model. J Mech Sci Technol 38, 2397–2410 (2024). https://doi.org/10.1007/s12206-024-0418-0

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  • DOI: https://doi.org/10.1007/s12206-024-0418-0

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