# Fracture Statistics for Inorganically-Bound Core Materials

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## Abstract

**:**

## 1. Introduction

#### 1.1. Mechanical De-Coring Properties of Inorganically-Bound Sand

#### 1.2. Weibull Statistics

## 2. Materials and Methods

#### 2.1. Specimen

^{3}.

#### 2.2. Uni-Axial Constant Stress

#### 2.3. Uni-Axial Non-Constant Stress

#### 2.4. Finite Element Model

^{3}) were used for the beam, while the support and load were modeled by analytical rigid bodies with the same dimensions as measured in the universal testing machine. The beam was loaded with the force at a failure probability of 63.2%, corresponding to each load case.

## 3. Results

#### 3.1. Characterisation of the Fracture Behavior

#### 3.2. Probabilistic Distribution of the Strength of Inorganically-Bound Sand Cores

#### 3.3. Volume-Dependence of the Tensile Strength

#### 3.4. Predicting Fracture Stresses for Arbitrary Bending Test Setups

#### 3.5. FEM Simulation of the Four-Point Bending Test Setup

## 4. Discussion

#### 4.1. Model Offset

#### 4.2. Distinguishing between Volume and Surface Failure

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

3PB | 3-point-bending |

4PB | 4-point-bending |

FEM | Finite element method |

SEM | Scanning electron microscope |

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**Figure 3.**Overview of inorganically-bound quartz sand with broken binder bridges (

**a**) and a broken binder bridge with signs of brittle failure (

**b**).

**Figure 5.**Fracture probability for a 3PB and a 4PB (load distance 63 mm) dataset with different effective volumes.

**Figure 10.**The FEM results show the stress in the x-direction of 3PB (top) and 4PB 75.5 mm (bottom), which were used for the calculation of the effective volume.

**Figure 11.**FEM results show the stress in the x-direction of 4PB 75.5 mm with a refined scale (top) and the stress distribution along the lower surface of the bar (bottom).

**Figure 12.**Fracture locations for a 4PB experiment with a 75.5-mm load distance (

**a**) and the broken bending beams (

**b**).

**Figure 13.**Specimen Type A: Prediction of fracture probability from 4PB (75.5 mm) to 3PB based on FEM analysis.

**Figure 14.**Specimen Type A: Prediction of fracture probability from 4PB (28.8 mm) to 3PB based on FEM analysis.

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**MDPI and ACS Style**

Lechner, P.; Stahl, J.; Ettemeyer, F.; Himmel, B.; Tananau-Blumenschein, B.; Volk, W.
Fracture Statistics for Inorganically-Bound Core Materials. *Materials* **2018**, *11*, 2306.
https://doi.org/10.3390/ma11112306

**AMA Style**

Lechner P, Stahl J, Ettemeyer F, Himmel B, Tananau-Blumenschein B, Volk W.
Fracture Statistics for Inorganically-Bound Core Materials. *Materials*. 2018; 11(11):2306.
https://doi.org/10.3390/ma11112306

**Chicago/Turabian Style**

Lechner, Philipp, Jens Stahl, Florian Ettemeyer, Benjamin Himmel, Bianca Tananau-Blumenschein, and Wolfram Volk.
2018. "Fracture Statistics for Inorganically-Bound Core Materials" *Materials* 11, no. 11: 2306.
https://doi.org/10.3390/ma11112306