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A multi-phase-field model for fiber-reinforced composite laminates based on puck failure theory

Pavan Kumar Asur Vijaya Kumar, Rafael Fleischhacker, Aamir Dean, Heinz E Pettermann

Abstract

This article proposes a multi-phase-field model using the Puck failure theory to predict the failure in fiber-reinforced composites (FRCs) laminates. Specifically, this work proposes a two-dimensional multi-field model in conjunction with a mesh overlay method to compute in-plane damage in the FRCs laminates with various ply orientations. The formulation considers the two independent phase-field variables to trigger fiber and inter-fiber-dominated failure separately, thereby accessing the interrelation between the damage. Furthermore, the model considers two characteristic length scales and two structural tensors to describe the damage modes accurately. Each ply in the laminate is represented using a separate mesh and is combined using the mesh overlay method. Four benchmark examples are utilized to demonstrate the predictive capability of the proposed model. Specifically, coupon tests in tensile and compressive loading, open-hole tension, compact tension, and double-edged notched tension examples are presented along with the comparison with the experimental results from the literature. Furthermore, results regarding cross-ply laminates and isotropic laminates show the model's ability to mimic the experimental results both qualitatively and quantitatively.

A multi-phase-field model for fiber-reinforced composite laminates based on puck failure theory

Abstract

This article proposes a multi-phase-field model using the Puck failure theory to predict the failure in fiber-reinforced composites (FRCs) laminates. Specifically, this work proposes a two-dimensional multi-field model in conjunction with a mesh overlay method to compute in-plane damage in the FRCs laminates with various ply orientations. The formulation considers the two independent phase-field variables to trigger fiber and inter-fiber-dominated failure separately, thereby accessing the interrelation between the damage. Furthermore, the model considers two characteristic length scales and two structural tensors to describe the damage modes accurately. Each ply in the laminate is represented using a separate mesh and is combined using the mesh overlay method. Four benchmark examples are utilized to demonstrate the predictive capability of the proposed model. Specifically, coupon tests in tensile and compressive loading, open-hole tension, compact tension, and double-edged notched tension examples are presented along with the comparison with the experimental results from the literature. Furthermore, results regarding cross-ply laminates and isotropic laminates show the model's ability to mimic the experimental results both qualitatively and quantitatively.
Paper Structure (20 sections, 50 equations, 22 figures, 9 tables)

This paper contains 20 sections, 50 equations, 22 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Variational Formulation
  3. PUCK Failure Criteria
  4. Fiber Failure
  5. Matrix Failure
  6. Thermodynamic Consistency and Driving Force
  7. Finite Element Implementation: Compact UEL
  8. Numerical Examples
  9. Coupon Tests
  10. Open Hole Tension
  11. Open Hole Tension- $[0^\circ_4/90^\circ_4]_s$
  12. Open Hole Tension- $[45^\circ_4/-45^\circ_4]_s$
  13. Compact Tension
  14. Double Notched Tension
  15. Cross-Ply Laminate $[0/90]_s$
  16. ...and 5 more sections

Figures (22)

  • Figure 1: Geometrical description of the body under consideration.
  • Figure 2: Geometric description of the mesh overlay method.
  • Figure 3: a) Geometric description of the Coupon test along with the dimensions and boundary conditions (in tension), b) force vs. displacement curves corresponding to the compressive cases, and c) force vs. displacement curves corresponding to the tensile tests.
  • Figure 4: Matrix crack pattern of the coupons for the compressive cases a) C-75, b) C-60, and c) C-45 as well as well as for the tensile tests d) T-75 and e) T-45.
  • Figure 5: Geometric description of open hole tension test along with the Boundary conditions, fiber orientation. The indicated symmetry plane (dash-dotted line) is used only for the $[0^\circ_4/90^\circ_4]_s$ layup.
  • ...and 17 more figures