# Influence of Test Specimen Geometry on Probability of Failure of Composites Based on Weibull Weakest Link Theory

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## Abstract

**:**

## 1. Introduction

## 2. Motivation

## 3. The Weibull Model for the Probability of Failure

#### 3.1. Test Specimens

- Straight-sided specimen, based on standard ISO 527-5:2009 [21]; thickness $t=2\mathrm{mm}$, cross-sectional area $A=30{\mathrm{mm}}^{2}$, tested volume $V=4800{\mathrm{mm}}^{3}$.
- Straight-sided specimen, based on standard ISO 527-5:2009 [21]; thickness $t=5\mathrm{mm}$, cross-sectional area $A=75{\mathrm{mm}}^{2}$, tested volume $V=12,000{\mathrm{mm}}^{3}$.
- Non-straight-sided specimen, butterfly-shaped, designed at DTU Wind Energy [14]; thickness $t=2\mathrm{mm}$, cross-sectional area $A$ in the range $30\u201355{\mathrm{mm}}^{2}$, tested constant stress volume $V=1800{\mathrm{mm}}^{3}$, tested non-constant stress volume $V=9800{\mathrm{mm}}^{3}$.

#### 3.2. Comparison between Constant Stress Specimens

#### 3.3. Comparison between Constant vs. Non-Constant Stress Specimens

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Stress–strain curves of straight-sided (black curves) and butterfly (red curves) test specimens. The crosses (+) at the end of the curves represent standard deviations of failure stress and strain to failure. The inset shows pictures of the test specimens before and after the test.

**Figure 2.**Geometry and dimensions of analyzed test specimens: (I) straight-sided, $t=2\mathrm{mm}$; (II) straight-sided, $t=5\mathrm{mm}$; (III) non-straight-sided, butterfly-shaped, $t=2\mathrm{mm}$. For all three test specimens, the width in the gauge section is $15\mathrm{mm}$. Arrows indicate the two comparisons of the stress ratio for the same probability of failure made in the present study. The analyzed part of the specimens is the non-hatched part between the grips.

**Figure 3.**The ratio of stress for the same probability of failure as a function of the Weibull modulus. Shown are the two analyzed comparisons between test Specimens I and II (blue curve) and test Specimens I and III (red curve).

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**MDPI and ACS Style**

Kumar, R.; Madsen, B.; Lilholt, H.; Mikkelsen, L.P.
Influence of Test Specimen Geometry on Probability of Failure of Composites Based on Weibull Weakest Link Theory. *Materials* **2022**, *15*, 3911.
https://doi.org/10.3390/ma15113911

**AMA Style**

Kumar R, Madsen B, Lilholt H, Mikkelsen LP.
Influence of Test Specimen Geometry on Probability of Failure of Composites Based on Weibull Weakest Link Theory. *Materials*. 2022; 15(11):3911.
https://doi.org/10.3390/ma15113911

**Chicago/Turabian Style**

Kumar, Rajnish, Bo Madsen, Hans Lilholt, and Lars P. Mikkelsen.
2022. "Influence of Test Specimen Geometry on Probability of Failure of Composites Based on Weibull Weakest Link Theory" *Materials* 15, no. 11: 3911.
https://doi.org/10.3390/ma15113911