# Characterization and Numerical Modelling of Through-Thickness Metallic-Pin-Reinforced Fibre/Thermoplastic Composites under Bending Loading

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Material Specification

^{®}TPP 60745) supplied by Saint Gobain-Vetrotex. It is a 2/2-twill weave offering an area density of 745 g/m² with a fibre volume fraction of 35% after consolidation. The specimens for bending tests were cutting from the 10 layers of fabric material and stacked in 0°/90° orientation. The stack of layers was then vacuumed and consolidated in an autoclave at a temperature above the melting temperature of the polypropylene (more than 200 °C) under a pressure of 5 bar. Afterwards, the specimens are cut by water jet. The specimen has a length of 120 mm, a width of 12 mm and a thickness of 5 mm. The material structure of the GF/PP material before and after the consolidation is shown in Figure 1.

#### 2.2. Specimen Configuration

_{10}CrNi

_{18}stainless steel, has a total length of 20 mm and a diameter of 0.99 mm. The pins were inserted perpendicular to the top surface of the specimen resulting in a maximum deviation of about 10° resulting from inhomogeneities in the composite material. After insertion, the pins are shorter to length with regard to the specimen thickness of 5 mm. Softened polymer material which is pressed out of the pin area at the beginning and at the end of the insertion process is finally removed. In this study, four reinforcement configurations (A–D) are in focus, which exhibit a pin density from 0.05 (A) to 0.59 (B) up to 1.18% (C and D) in the overall specimen section (Figure 2).

#### 2.3. Experimental Setup and Measurement Techniques

## 3. Experimental Results

#### 3.1. Force-Displacement Curves

#### 3.2. Failure Pattern

## 4. Numerical Analysis

#### 4.1. Finite Element Model

#### 4.2. Material Modelling

_{dij t/c}for each loading direction (i,j = 1, 2, 3), with t denoting tension and c compression. The damage surface in stress space using a variable function H is described by the following condition by means of nominal stresses σ

_{i}and τ

_{ij}:

_{it/c,fail}and γ

_{ij,fail}were used:

_{i,del}and γ

_{ij,del}is reached and the element is finally deleted. The required material parameters result from previous experimental works by means of basic characterization tests under tensile, compression and shear loading [3,38,39,40]. For simplification, the layup of the specimens with consistent hybrid yarns in both reinforcement direction, the balanced textile architecture and the symmetric lay-up result in a bidirectional layer with almost same in-plane engineering constants. Via the experimental determined parameters and corresponding stress-strain-relationship, the material input parameter for the CZM model were determined by single-element-tests. The engineering constants (Young’s moduli E

_{i}, shear moduli G

_{ij}and Poisson’s ratios v

_{ij}), onset of damage in terms of strengths R

_{dij t/c}, and failure strains ε

_{it/c,fail}and γ

_{ij,fail}for the GF/PP composite material for each loading direction (i,j = 1, 2, 3) are listed in Table 2.

_{d}for compression and R

_{s}for shear loading) for the post-failure behaviour was carried out based on specimens with a single pin reinforcement (configuration A) in regard to its failure pattern and force-displacement behaviour. The final parameters for element deletion are listed in Table 3. The relevance of these non-physical parameter for the global failure pattern accompanied by the global structural response is shown in Figure 7. Especially, the element deletion in the contact area below the stamps was addressed here.

#### 4.3. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Specimen configuration: (

**A**) 0.05% pin density; (

**B**) 0.59% pin density; (

**C**) regular pattern with 1.18% pin density; (

**D**) zigzag pattern with 1.18% pin density.

**Figure 4.**Comparison of experimental force-displacement curves: (

**a**) entire results; (

**b**) detailed elastic domain; (

**c**) detailed damage and failure domain.

**Figure 5.**Characteristic damage and failure pattern for each configuration: (

**A**) 0.05% pin density; (

**B**) 0.59% pin density; (

**C**) regular pattern with 1.18% pin density; (

**D**) zigzag pattern with 1.18% pin density.

**Figure 8.**Comparison of experimental and numerical force-displacement curves: (

**a**) entire results; (

**b**) detailed elastic domain; (

**c**) detailed damage and failure domain.

$\mathbf{Initial}\mathbf{Stiffness}\mathit{M}$ (N/mm) | $\mathbf{Cohesive}\mathbf{Strength}\mathit{t}$ (MPa) | $\mathbf{Critical}\mathbf{Strain}\mathbf{Energy}\mathbf{Release}\mathbf{Rate}\mathit{G}$ (N/mm) |
---|---|---|

${M}_{nn}$ 74,670 | ${t}_{n}^{0}$ 12.6 | ${G}_{IC}$ 2.5 |

${M}_{ss}$ 26,670 | ${t}_{s}^{0}$ 92.0 | ${G}_{IIC}$ 3.5 |

${M}_{tt}$ 26,670 | ${t}_{t}^{0}$ 92.0 | ${G}_{IIIC}$ 3.5 |

**Table 2.**Engineering constants, onset of damage in terms of strengths and failure strains for glass-polypropylene (GF/PP) composite material.

Material Parameter | Unit | Value |
---|---|---|

E_{1} | (GPa) | 14.9 |

E_{2} | (GPa) | 14.9 |

E_{3} | (GPa) | 1.50 |

ν_{12} | (-) | 0.08 |

ν_{13} | (-) | 0.17 |

ν_{23} | (-) | 0.17 |

G_{12} | (MPa) | 7500 |

G_{13} | (MPa) | 1050 |

G_{23} | (MPa) | 1050 |

R_{d}_{1t} | (MPa) | 60 |

R_{d}_{1c} | (MPa) | 35 |

R_{d}_{2t} | (MPa) | 60 |

R_{d}_{2c} | (MPa) | 35 |

R_{d}_{3t} | (MPa) | 12.4 |

R_{d}_{3c} | (MPa) | 477 |

R_{d}_{12} | (MPa) | 25 |

R_{d}_{13} | (MPa) | 9 |

R_{d}_{23} | (MPa) | 9 |

ε_{1t, fail} | (-) | 0.1 |

ε_{1c, fail} | (-) | 0.03 |

ε_{2t, fail} | (-) | 0.1 |

ε_{2c, fail} | (-) | 0.03 |

ε_{3t, fail} | (-) | 0.2 |

ε_{3c, fail} | (-) | 0.08 |

γ_{12, fail} | (-) | 0.016 |

γ_{13, fail} | (-) | 0.014 |

γ_{23, fail} | (-) | 0.014 |

**Table 3.**Element eroding strains and scale factor for minimum stress limit after stress maximum for GF/PP composite material.

Material Parameter | Unit | Value |
---|---|---|

ε_{1, del} | (-) | 3.0 |

ε_{2, del} | (-) | 3.0 |

γ_{12, del} | (-) | 0.15 |

R_{c} | (MPa) | 0.5 |

R_{s} | (MPa) | 1.0 |

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**MDPI and ACS Style**

Böhm, H.; Zhang, H.; Gröger, B.; Hornig, A.; Gude, M.
Characterization and Numerical Modelling of Through-Thickness Metallic-Pin-Reinforced Fibre/Thermoplastic Composites under Bending Loading. *J. Compos. Sci.* **2020**, *4*, 188.
https://doi.org/10.3390/jcs4040188

**AMA Style**

Böhm H, Zhang H, Gröger B, Hornig A, Gude M.
Characterization and Numerical Modelling of Through-Thickness Metallic-Pin-Reinforced Fibre/Thermoplastic Composites under Bending Loading. *Journal of Composites Science*. 2020; 4(4):188.
https://doi.org/10.3390/jcs4040188

**Chicago/Turabian Style**

Böhm, Holger, Hailun Zhang, Benjamin Gröger, Andreas Hornig, and Maik Gude.
2020. "Characterization and Numerical Modelling of Through-Thickness Metallic-Pin-Reinforced Fibre/Thermoplastic Composites under Bending Loading" *Journal of Composites Science* 4, no. 4: 188.
https://doi.org/10.3390/jcs4040188