# Strain Measurements within Fibre Boards. Part II: Strain Concentrations at the Crack Tip of MDF Specimens Tested by the Wedge Splitting Method

^{1}

^{2}

^{3}

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## Abstract

**:**

^{2}and the critical stress intensity factor was 0.11 ± 0.02 MPa.

## 1. Introduction

**Figure 1.**Wedge splitting test setup for the core layer testing of medium density fiber board (MDF). Specimen is reinforced by steel plates glued to the face layers of MDF.

_{IC}. This is a parameter used in linear elastic fracture mechanics (LEFM). Prerequisites of LEFM are linear elastic material properties and a self-similar crack growth–properties which are only approximately satisfied for MDF since fibre bridging and micro cracking takes place [10]. Moreover, the formation of micro cracks and fibre bridging around the crack tip makes crack length measurement almost impossible [8].

_{f}is described as the total fracture energy normalized by the broken area and describes an average crack resistance for the analysed material and specimen size [10].

^{3}were used. According to Müller et al., [13], ESPI measurements are a suitable tool for the validation of numerical material analysis by means of FE modelling. For a comparison with data from the literature, the stress intensity factor and the specific fracture energy were calculated. The results gained are used to analyse the appropriateness of the calculated models and to determine the applicability of the adopted wedge splitting experiment for the analysis of the core layer in wood based panels.

## 2. Experimental Section

#### 2.1. Specific Fracture Energy

_{f}is a material characteristic and characterizes the specimen’s resistance to crack growth. G

_{f}was calculated by dividing the integral of the load displacement curve by the fracture surface area (see Equation 1).

#### 2.2. Stress Intensity Factor

_{IC}, a FE simulation was performed to describe the basic mechanisms of fracture. In this calculation, the special case of the sandwich construction of the specimen, consisting of wood based panel and metal, was taken into account. The calculations were carried out with the commercial FE program ABAQUS®. The specimen was simulated as a two dimensional plane strain model. Isotropic and linear material properties were assumed. The crack tip was simulated with 36 collapsed 8-node biquadratic plane strain elements with mid-side nodes placed at ¼ of the distance along the element side to create quarter-point elements representing $1/\sqrt{r}$ stress singularity [25,26]. The ABAQUS® routine for the fracture toughness K

_{I}was used to compute the critical values. The whole model consisted of 754 elements. Several simulations with varying moduli of elasticity (Poisson ratio was fixed to 0.1) were performed in order reproduce the experimental initial slope and determine the modulus of elasticity representing the experiment. Found the modulus of elasticity, the fracture toughness was calculated by the ABAQUS® routine with the maximum load from experimental load displacement curves.

#### 2.3. Speckle Measurement

**Figure 2.**Schematic drawing of the Michelson interferometer (

**a**) and electronic speckle pattern interferometry (ESPI) optics set-up for wedge splitting in-plane measurements (

**b**).

## 3. Results and Discussion

^{3}. The specific fracture energy was calculated from the load displacement curves and the stress intensity factors were calculated using a FE simulation. To validate the FE simulation and to analyze crack length, ESPI measurements were performed.

#### 3.1. Specific Fracture Energy

_{f}were performed with nine specimens and yielded a mean value of 45.2 J/m

^{2}± 14.4 J/m

^{2}. Matsumoto and Nairn [10] found values of 48.4 J/m

^{2}for the initiation toughness G

_{C}of MDF for the same loading direction but a mean density of 737 kg/m

^{3}and 48.2 J/m

^{2}for specimens with a density of 609 kg/m

^{3}. Both kinds of materials had the same thickness of 19 mm. Using the values from the crack resistance curve (R-curve) provided by Matsumoto and Nairn [10], the specific fracture energy can be compared to the wedge splitting experiments with (L − a) = 90 mm as follows:

_{f}extrapolated from the data of Matsumoto and Nairn are approx. 30% higher than current experimental results.

**Table 1.**Initiation toughness G

_{C}, slope of rising R-curve from Matsumoto and Nairn (1) [10] and specific fracture energy G

_{f}predicted according to Equation 2 for a ligament length of 90 mm (2).

Panel | G_{C}^{1} (J/m^{2}) | Slope^{1} (J/m^{3}) | G_{f}^{2} (J/m^{2}) |
---|---|---|---|

609 kg/m^{3} (19 mm) | 48,2 | 296 | 61,52 |

737 kg/m^{3} (19 mm) | 48,4 | 303 | 62,04 |

#### 3.2. Stress Intensity Factor

_{IC}= 0.111 ± 0.015 Mpam

^{0.5}. Only a few experiments analyzing the fracture toughness of MDF were found in the literature. Niemz et al., [23,24] used CT specimens according to ASTM 399 to analyze the stress intensity factor. The specimens were oriented parallel to the board plane and yielded K

_{IC}values of 1.81 ± 0.33 MPam

^{0.5}(CV 18.2%) for a density of 710 kg/m

^{3}(20 °C/65% RH) and numbers in a range of 0.36 ± 0.03 MPam

^{0.5}(8.3% CV) to 1.29 ± 0.06 MPam

^{0.5}(CV 4.7%) with a density of 500 kg/m

^{3}, depending on the equilibrium moisture content, which varied from 21.4% to 3.5%. The differences between our data and the data from Niemz et al., [23,24] can be traced back to the fact that the specimens were tested perpendicularly to experiments presented here and that these literature values reflect a combination of face layer and core layer. Matsumoto and Nairn [32] used modified CT specimens for testing the middle layer of MDF. They provided experimental results for the initiation toughness G

_{c}and the modulus of elasticity E from simulations of 19 mm thick MDF boards. To compare their results with the results presented here, the well-known equation from linear elastic fracture mechanics was used:

_{IC}= 0.111 ± 0.015 Mpam

^{0.5}. The labeling “MDF 38” and “MDF 46” reflects the density of the specimens in 38 lbs/ft

^{3}and 46 lbs/ft

^{3}.

**Table 2.**Initiation toughness, modulus of elasticity and Poisson’s ratio from [32]; K

_{IC}calculated according to Equation 2.

Density, (kg/m^{3}) | G_{c}, (J/m^{2}) | E, (MPa) | ν, (-) | K_{IC}, (MPam^{0.5}) | |
---|---|---|---|---|---|

MDF 38 | 609 | 59 | 90 | 0.33 | 0.077 |

MDF 46 | 737 | 48 | 200 | 0.33 | 0.104 |

#### 3.3. ESPI Measurement

**Figure 3.**(

**a**) measured in-plane horizontal strain distribution ε

_{xx}(µm/mm); (

**b**) measured vertical strain profile ε

_{yy}; and (

**c**) shear strain profile.

_{xx}were examined along the horizontal and vertical lines shown in Figure 4. Profile lines shown in Figure 5 and Figure 6 were used to determine the size of the fracture process zone.

**Figure 4.**Contour graph of ε

_{xx}(µm/mm) showing the intersection lines were the horizontal and vertical profiles were extracted.

_{ib}= 0.51 ± 0.19 MPa [31] to calculate the critical strain at failure. The calculation of corresponding strain yielded

**Figure 5.**Vertical profile lines of e

_{xx}in crack growth direction from ESPI measurements and from simulation. Dashed horizontal line shows critical strain at failure onset. Fracture process zone length can be determined within 5 to 10 mm.

**Figure 6.**Horizontal profile lines of e

_{xx}experimental and simulated. Dashed line represent strain at yielding providing a process zone with of 2.4 mm (acc. to method 1), whereas solid horizontal line touches the first maxima at left and right side of the center peak leading to a process zone width of 6.3 mm (acc. to method 2).

Specimen | Process zone length in crack forward direction from vertical profiles in (mm); Method 1 | Process zone width in (mm) from horizontal profiles; Method 1 | Process zone width in (mm) from horizontal profiles; Method 2 |
---|---|---|---|

1 (KS 3) | 7.66 | 2.44 | 6.23 |

2 (KS 7) | 5.47 | 2.75 | 6.58 |

3 (KS 12) | 5.83 | 2.57 | 6.12 |

_{y}in [33]).

_{pw}is approximately 1.25 times the process zone in forward direction [33]; for a Poisson ratio of 0.1, it gives r

_{pw}= 6.3 mm. This value is close to the second method of experimental evaluation. It might be concluded from the process zone size and shape, comparing the ESPI results with the FE simulation (see Figure 5 and Figure 6), that the material behaves isotropically within the range of measurement. This conclusion is supported by the well-known correlation between the modulus of elasticity and the density. The density profile shown in part one of this series [31] is approx. constant within ±10 mm from center; therefore the isotropic FE-simulation might describe the material and setup correctly within the measurement plane and region. Nevertheless, there might be a different modulus of elasticity in the direction of depth.

## 4. Conclusions

## Acknowledgments

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**MDPI and ACS Style**

Sinn, G.; Müller, U.; Konnerth, J.; Rathke, J.
Strain Measurements within Fibre Boards. Part II: Strain Concentrations at the Crack Tip of MDF Specimens Tested by the Wedge Splitting Method. *Materials* **2012**, *5*, 1495-1507.
https://doi.org/10.3390/ma5081495

**AMA Style**

Sinn G, Müller U, Konnerth J, Rathke J.
Strain Measurements within Fibre Boards. Part II: Strain Concentrations at the Crack Tip of MDF Specimens Tested by the Wedge Splitting Method. *Materials*. 2012; 5(8):1495-1507.
https://doi.org/10.3390/ma5081495

**Chicago/Turabian Style**

Sinn, Gerhard, Ulrich Müller, Johannes Konnerth, and Jörn Rathke.
2012. "Strain Measurements within Fibre Boards. Part II: Strain Concentrations at the Crack Tip of MDF Specimens Tested by the Wedge Splitting Method" *Materials* 5, no. 8: 1495-1507.
https://doi.org/10.3390/ma5081495