# Deformation and Failure Behavior of Wooden Sandwich Composites with Taiji Honeycomb Core under a Three-Point Bending Test

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Experiments

#### 2.1. Composite Design

#### 2.2. Specimen Fabrication

^{2}. After that, a compression load of 0.1 MPa was applied on those sandwich beams and kept for 4 h to form strong internal strength of composite. To minimize the size effect of the honeycomb structure, all specimens were cut to the width of 58 mm (Figure 2d–f).

#### 2.3. Test Methods

## 3. Result and Discuss

#### 3.1. Failure Process of Sandwich Beam (Experimental Results)

#### 3.2. Failure Load Prediction of Sandwich Beam

#### 3.2.1. Shear Failure

#### 3.2.2. Indentation

#### 3.2.3. Face Yield

#### 3.3. Mechanical Prediction of Taiji Honeycomb Core

#### 3.3.1. Compression Buckling Stress

#### 3.3.2. Shear Buckling Stress

#### 3.3.3. Compression Modulus

#### 3.4. Analytical Comparison between Taiji Honeycomb and Traditional Hexagonal One

#### 3.5. Comparison between Experiment and Analytical Solution

#### 3.6. The Parametric Effect on Failure Load

#### 3.7. Failure Map of Sandwich Beam with Taiji Honeycomb Core

_{c}+ h

_{f})/L for horizontal axis and h

_{f}/L for vertical axis; thus, all possible beam geometries are graphed for a given material combination. In this study, the experiments concentrate on a wooden sandwich composite with a paper honeycomb core and various geometrical parameters. Those material properties have been characterized (Table 1 and Table 2). It should be noted that the core properties are ${\sigma}_{cr}={\sigma}_{tc}=0.22\text{}\mathrm{MPa}$ (Equation (9)) and ${\tau}_{cs}={\tau}_{ts}=0.25\text{}\mathrm{MPa}$ (Equation (12)),$\text{}{E}_{cz}={E}_{tc}=19.5\text{}\mathrm{MPa}$ (Equation (13)), that are fixed to the average values without considering the side effect or core thickness.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The idealized structure of honeycomb core: (

**a**) Traditional hexagonal honeycomb, (

**b**) Taiji honeycomb.

**Figure 3.**Typical load-displacement curve of core shear failure of wooden sandwich beam with Taiji honeycomb core (A3B2C2): (

**a**): Unloaded; (

**b**) buckling of inclined cell wall; (

**c**) buckling of whole cell wall; (

**d**) post-buckling stage.

**Figure 4.**Photographs and strain distribution of core shear failure process of wooden sandwich beam with Taiji honeycomb core:

**a1**for photograph,

**a2**for ${\u03f5}_{x}$,

**a3**for ${\gamma}_{xy}$ and

**a4**for ${\epsilon}_{y}$ under unloaded condition;

**b1**for photograph,

**b2**for ${\u03f5}_{x}$,

**b3**for ${\gamma}_{xy}$ and

**b4**for ${\epsilon}_{y}$ under buckling of inclined cell wall;

**c1**for photograph,

**c2**for ${\u03f5}_{x}$,

**c3**for ${\gamma}_{xy}$ and

**c4**for ${\epsilon}_{y}$ under buckling of whole cell wall;

**d1**for photograph,

**d2**for ${\u03f5}_{x}$,

**d3**for ${\gamma}_{xy}$ and

**d4**for ${\epsilon}_{y}$ under post-buckling stage.

**Figure 5.**Typical load-displacement curve of indentation process of wooden sandwich beam with Taiji honeycomb core (A1B3C3): (

**a**) unloaded; (

**b**) initiation of indentation; (

**c**) showing condition after indentation.

**Figure 6.**Photographs and strain distribution of the indentation process of the wooden sandwich beam with Taiji honeycomb core:

**a1**for photograph,

**a2**for ${\u03f5}_{x}$,

**a3**for ${\gamma}_{xy}$ and

**a4**for ${\epsilon}_{y}$ under unloaded condition;

**b1**for photograph,

**b2**for ${\u03f5}_{x}$,

**b3**for ${\gamma}_{xy}$ and

**b4**for ${\epsilon}_{y}$ under initiation of indentation;

**c1**for photograph,

**c2**for ${\u03f5}_{x}$,

**c3**for ${\gamma}_{xy}$ and

**c4**for ${\epsilon}_{y}$ after indentation.

**Figure 8.**The effect of core thickness on failure load under a three-point bending test: (

**a**) Sandwich beam with 3.175 mm MDF face under span of 76.2 mm; (

**b**) sandwich beam with 3.175 mm MDF face under span of 228.6; (

**c**) sandwich beam with 3.175 MDF face under span of 381 mm.

**Figure 9.**The effect of face sheets type on failure load of sandwich beam under three-point bending.

**Figure 10.**The effect of span distance on failure load under three-point bending: (

**a**) Sandwich beam with 3.175 mm MDF face and 15.875 mm core; (

**b**) sandwich beam with 3.175 mm MDF face and 25.4 mm core; (

**c**) sandwich beam with 3.175 mm MDF face and 34.925 mm core.

**Figure 11.**Failure map based on construction parameters: (

**a**) sandwich beam with 3.175 mm MDF surface, (

**b**) sandwich beam with 3.175 mm PLY surface, (

**c**) sandwich beam with 6.35 mm PLY surface.

**Table 1.**Properties of the medium density fiber board (MDF) and plywood (PLY) used in the outer layers (skins).

Material | Thickness (mm) | Density (Kg/m^{3}) | Moisture Content (%) | Bending Strength (MPa) | Bending Modulus (MPa) |
---|---|---|---|---|---|

MDF | 3.175 | 869.0 | 5.4 | 28.9 | 5399.9 |

PLY | 3.175 | 683.6 | 5.6 | 88.2 | 20,578.0 |

PLY | 6.35 | 672.5 | 5.4 | 64.2 | 13,598.7 |

Material | Thickness (mm) | Moisture Content (%) | Tensile Strength (MPa) | Tensile Modulus (MPa) |
---|---|---|---|---|

Kraft paper | 0.1778 | 5.4 | 13.2 | 453.0 |

Group | Code | Surface Sheet (A) | Core Thickness (B, mm) | Span Distance (D, mm) |
---|---|---|---|---|

1 | A1B1C1 | 3.175 mm MDF | 15.875 | 76.2 |

2 | A1B2C1 | 3.175 mm MDF | 25.4 | 76.2 |

3 | A1B3C1 | 3.175 mm MDF | 34.925 | 76.2 |

4 | A1B1C2 | 3.175 mm MDF | 15.875 | 228.6 |

5 | A1B2C2 | 3.175 mm MDF | 25.4 | 228.6 |

6 | A1B3C2 | 3.175 mm MDF | 34.925 | 228.6 |

7 | A2B2C2 | 3.175 mm PLY | 25.4 | 228.6 |

8 | A3B2C2 | 6.35 mm PLY | 25.4 | 228.6 |

9 | A1B1C3 | 3.175 mm MDF | 15.875 | 381 |

10 | A1B2C3 | 3.175 mm MDF | 25.4 | 381 |

11 | A1B3C3 | 3.175 mm MDF | 34.925 | 381 |

Group | Code | Surface Sheet (A) | Core Thickness (B, mm) | Span Distance (D, mm) | Fail Mode | Test Results (N) | Standard Deviation | CSS (N) | ES (N) | PSBS (N) | PSBS-R (N) | ESBS (N) | ESBS-R (N) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | A1B1C1 | 3.175 mm MDF | 15.875 | 76.2 | Indentation | 647.9 | 170.1 | ﹨ | 409.4 | 1125.4 | 893.1 | 420.1 | 629.7 |

2 | A1B2C1 | 3.175 mm MDF | 25.4 | 76.2 | Indentation | 721.2 | 178.3 | ﹨ | 541.1 | 1186.4 | 941.6 | 438.3 | 657.3 |

3 | A1B3C1 | 3.175 mm MDF | 34.925 | 76.2 | Indentation | 789.0 | 83.4 | ﹨ | 591.0 | 1344.8 | 1067.1 | 482.8 | 724.5 |

4 | A1B1C2 | 3.175 mm MDF | 15.875 | 228.6 | Indentation | 587.8 | 77.7 | ﹨ | 473.5 | 762.3 | 605.2 | 384.0 | 576.3 |

5 | A1B2C2 | 3.175 mm MDF | 25.4 | 228.6 | Indentation | 682.9 | 101.8 | ﹨ | 522.9 | 880.2 | 712.0 | 429.9 | 644.8 |

6 | A1B3C2 | 3.175 mm MDF | 34.925 | 228.6 | Indentation | 670.7 | 78.5 | ﹨ | 588.3 | 1007.9 | 801.0 | 468.1 | 702.2 |

7 | A2B2C2 | 3.175 mm PLY | 25.4 | 228.6 | Indentation/Core shear | 739.6 | 90.3 | 939.8 | 687.5 | 1258.0 | 998.6 | 555.8 | 833.5 |

8 | A3B2C2 | 6.35 mm PLY | 25.4 | 228.6 | Core shear | 1314.1 | 206.4 | 1037.3 | ﹨ | ﹨ | ﹨ | ﹨ | ﹨ |

9 | A1B1C3 | 3.175 mm MDF | 15.875 | 381 | Indentation with face yield | 567.5 | 63.0 | ﹨ | 482.4 | 705.8 | 560.3 | 392.0 | 587.8 |

10 | A1B2C3 | 3.175 mm MDF | 25.4 | 381 | Indentation | 674.6 | 141.7 | ﹨ | 553.1 | 815.2 | 647.0 | 439.7 | 659.5 |

11 | A1B3C3 | 3.175 mm MDF | 34.925 | 381 | Indentation | 756.9 | 81.7 | ﹨ | 585.6 | 870.9 | 691.1 | 463.2 | 694.6 |

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## Share and Cite

**MDPI and ACS Style**

Hao, J.; Wu, X.; Oporto, G.; Wang, J.; Dahle, G.; Nan, N.
Deformation and Failure Behavior of Wooden Sandwich Composites with Taiji Honeycomb Core under a Three-Point Bending Test. *Materials* **2018**, *11*, 2325.
https://doi.org/10.3390/ma11112325

**AMA Style**

Hao J, Wu X, Oporto G, Wang J, Dahle G, Nan N.
Deformation and Failure Behavior of Wooden Sandwich Composites with Taiji Honeycomb Core under a Three-Point Bending Test. *Materials*. 2018; 11(11):2325.
https://doi.org/10.3390/ma11112325

**Chicago/Turabian Style**

Hao, Jingxin, Xinfeng Wu, Gloria Oporto, Jingxin Wang, Gregory Dahle, and Nan Nan.
2018. "Deformation and Failure Behavior of Wooden Sandwich Composites with Taiji Honeycomb Core under a Three-Point Bending Test" *Materials* 11, no. 11: 2325.
https://doi.org/10.3390/ma11112325