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Development of a Damage Mechanics Model for Fatigue Life Prediction of 2.5D Woven Composites

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Abstract

A continuum damage model (CDM) is proposed to predict the fatigue life of 2.5D woven composites (2.5DWC) with conformal or voxel meshing. Three independent damage variables of yarn fiber, yarn matrix, and matrix are defined to establish the constitutive relationship of woven composites with damage. The strain energy density, damage driving force, and damage evolution equation of material components are derived in the damage thermodynamics method, and the component correction stress is introduced to eliminate the effect of different meshing methods on fatigue life prediction. The model is implemented in ANSYS with the APDL language to simulate the fatigue failure process of 2.5DWC. The results show that the predicted fatigue life with conformal or voxel meshing differs by only 4.5% and shows agreement with the relevant experimental fatigue life.

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Availability of Data and Material

The datasets used or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\(U_{p}\) :

Displacement in the x, y, and z directions

\({{\varvec{\upvarepsilon}}}_{c}\) ;  \({{\varvec{\upvarepsilon}}}_{c}^{p}\) :

Strain and plastic strain tensors

\(V_{a}\) :

Total volume of the full-cell model

\({\mathbf{S}}_{r}\) :

Flexibility matrix of yarns and matrix

\(E_{r}\) ;  \(G_{r}\) :

Elastic and shear modulus of yarns and matrix

\(\eta_{12}\) ;  \(\eta_{22}\) :

Stiffness correction factors

\(X_{c}\) :

Strength of material components

\(D_{c}\) :

Damage variable of material components

\(F\) :

Dissipation potential function

\(T\) :

Ambient temperature

\(Y_{c}\) :

Damage driving force of material components

\(A_{c}\) ;  \(B_{c}\) ;  \(C_{c}\) :

Unknown parameters of damage evolution equation

\(\sigma_{e,c}\) :

Component correction stress

\({{\varvec{\upxi}}}_{c}\) :

Back strain tensor of material components

\(\gamma_{c}\) :

Damage accumulated plastic strain

\(\Delta L_{q}\) :

Length of the geometric model

\(L_{q}^{A}\) ;  \(L_{q}^{B}\) :

Node coordinates of opposite planes

\(N_{a}\) :

Total number of elements in the full-cell model

\(E_{c}^{D}\) :

Elastic modulus of damaged components

\(\nu_{r}\) :

Poisson’s ratio of yarns and matrix

\(\alpha\) ;  \(\beta\) :

Shear factors

\(V_{f}\) :

Fiber volume fraction

\(\psi\) :

Helmholtz free energy

\(W\) :

Strain energy density

\(\rho\) :

Material density

\({{\varvec{\upsigma}}}_{c}\) :

Stress tensor of material components

\(N_{c}\) :

Fatigue life of material components

\(\phi_{o,c}\) :

Model correction factors

\({{\varvec{\upchi}}}_{c}\) :

Back stress tensor of material components

\(\kappa_{c}\) :

Damage cumulative plastic stress

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Funding

This work was supported by National Science and Technology Major Project (2017-IV-0007–0044) and National Natural Science Foundation of China (52175142).

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Authors and Affiliations

  1. College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Nan Wang, Weidong Wen & Hongjian Zhang

  2. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing, 210016, China

    Nan Wang, Weidong Wen & Hongjian Zhang

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  1. Nan Wang
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Contributions

Nan Wang performed the data analyses and wrote the manuscript. Weidong Wen contributed significantly to analysis and manuscript preparation. Hongjian Zhang helped perform the analysis with constructive discussions.

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Correspondence to Nan Wang.

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Wang, N., Wen, W. & Zhang, H. Development of a Damage Mechanics Model for Fatigue Life Prediction of 2.5D Woven Composites. Appl Compos Mater 30, 185–205 (2023). https://doi.org/10.1007/s10443-022-10079-4

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