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An integrated computational framework for simulating the failure response of carbon fiber reinforced polymer composites

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Abstract

A new computational framework is introduced for the automated finite element (FE) modeling of fiber reinforced composites and simulating their micromechanical behavior. The proposed methodology relies on a new microstructure reconstruction algorithm that implements the centroidal Voronoi tessellation (CVT) to generate an initial uniform distribution of fibers with desired volume fraction and size distribution in a repeating unit cell of the composite. The genetic algorithm (GA) is then employed to optimize locations of fibers such that they replicate the target spatial arrangement. We also use a non-iterative mesh generation algorithm, named conforming to interface structured adaptive mesh refinement (CISAMR), to create FE models of the CFRPC. The CVT–GA–CISAMR framework is then employed to investigate the appropriate size of the composite’s representative volume element. We also study the strength and failure mechanisms in the CFRPC subject to varying uniaxial and mixed-mode loadings.

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Abbreviations

\(\varOmega \) :

Macroscopic open domain of a CFRPC panel

\(\varGamma \) :

Macroscopic domain boundary of a CFRPC panel

\(\mathbf n _{\text {M}}\) :

Outward unit vector normal to \(\partial \varOmega \)

\(\varGamma _\mathbf{u }\) :

Dirichlet boundary conditions region

\(\varGamma _\mathbf{t }\) :

Neumann boundary conditions region

\(\varTheta \) :

Microscopic open domain of a repeating unit cell (RUC) of the CFRPC

\(\varLambda \) :

Microscopic domain boundary of an RUC of the composite

\(\mathbf n _{\text {m}}\) :

Outward unit vector normal to \(\varLambda \)

\(\mathbf u _{\text {M}}\) :

Displacement field a the macro scale

\(\mathbf u _{\text {m}}\) :

Displacement field a the micro scale

\(\xi \) :

Ratio of the microscopic to macroscopic length scales

\(\mathbb {C}\) :

Elasticity tensor

\({\varvec{\sigma }}_{\text {M}}\) :

Macroscopic stress tensor

\({\varvec{\varepsilon }}_{\text {M}}\) :

Macroscopic strain tensor

\({\varvec{\sigma }}_{\text {m}}\) :

Microscopic stress tensor

\({\varvec{\varepsilon }}_{\text {m}}\) :

Microscopic strain tensor

\(\varPhi _{\text {M}}\) :

Macroscopic free energy density

\(\varPhi _{\text {m}}\) :

Microscopic free energy density

\(\omega \) :

Damage variable

\(\chi ^t\) :

Internal state variable tracking the magnitude of damage

\(\varPhi ^{\text {in}}_{\text {m}}\) :

Energy threshold associated with the initiation of damage

\(p_1, p_2\) :

Scalar parameters determining the shape of the damage surface

\(\dot{\kappa }\) :

Damage consistency parameter

\(\delta \) :

Effective opening displacement along cohesive interface

\(\beta \) :

Mode mixity parameter

\(\delta _{n}\) :

Normal displacement of the cohesive interface

\(\delta _{s}\) :

Sliding displacement of the cohesive interface

\(\varPhi _c\) :

Cohesive free energy

\(\sigma _{c}\) :

Maximum cohesive normal traction

\(\delta _{c}\) :

Characteristic opening displacement

t :

Effective traction

\(\delta _{max}\) :

Maximum effective opening displacement

\(t_{max}\) :

Maximum effective traction

\(\zeta _c\) :

Cohesive viscous regularization parameter

\(f_{\text {sd}}(r)\) :

Fibers radii r distribution function

\(N_{\text {sd}}\) :

Mean value of the probability distribution of r

\(S_{\text {sd}}\) :

Standard deviation of the probability distribution of r

\(f_\text {nn}(r)\) :

Nearest neighbor distance function

\(f_\text {rd}(r)\) :

Radial distribution function

\(N_{\text {nn}}\) :

Mean value of the probability distribution of nearest neighbor distances

\(S_{\text {nn}}\) :

Standard deviation of probability distribution of nearest neighbor distances

\(\rho \) :

Average number of fibers in a unit area

N :

Total number of fibers

\(n_i(r)\) :

Number of fiber centroids located in an annulus with radius r and thickness dr

\(V_f\) :

Target volume fraction

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Acknowledgements

This work has been supported the Air Force Office of Scientific Research (AFOSR) under grant number FA9550-17-1-0350 and also in part by the Ohio State University Simulation Innovation and Modeling Center (SIMCenter) through support from Honda R&D Americas, Inc.. The authors also acknowledge the allocation of computing time from the Ohio Supercomputer Center (OSC).

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Authors and Affiliations

  1. Department of Integrated Systems Engineering, The Ohio State University, 1971 Neil Avenue, Columbus, OH, 43210, USA

    Hossein Ahmadian

  2. Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH, 43210, USA

    Bowen Liang & Soheil Soghrati

  3. Department of Materials Science and Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH, 43210, USA

    Soheil Soghrati

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  1. Hossein Ahmadian
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Correspondence to Soheil Soghrati.

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Ahmadian, H., Liang, B. & Soghrati, S. An integrated computational framework for simulating the failure response of carbon fiber reinforced polymer composites. Comput Mech 60, 1033–1055 (2017). https://doi.org/10.1007/s00466-017-1457-5

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