# Temperature Variability of Poisson’s Ratio and Its Influence on the Complex Modulus Determined by Dynamic Mechanical Analysis

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## Abstract

**:**

## 1. Introduction

_{s}= load/displacement) and the phase lag (δ) [11]. By the association of these variables with the specimen’s geometrical parameters, test configuration (e.g., shear, tensile, cantilever, etc.), and Poisson’s ratio (ν), an algorithm is applied to determine the material complex modulus (E*) [12].

## 2. Methodology

#### 2.1. Materials

^{®}Clever Reinforcement Company 220 epoxy adhesive, Seewen, Switzerland) was used to produce rectangular beams (chemical composition and specimen dimensions in Table 1). These specimens were cured for five days at 20 °C to allow a complete polymerization.

#### 2.2. Tensile Testing

#### 2.3. Dynamic Mechanical Analysis

#### 2.4. Finite Element Analysis

## 3. Results

#### 3.1. Theoretical Modeling

_{s}= F/d).

^{3}w/12) and F is a geometric factor described by Equation (2) [21].

_{s}). More importantly, this formulation considers that it presents a constant value, i.e., it remains stable during the experimental test. In fact, it is known that this is not true, and the value of Poisson’s ratio may change, especially due to temperature-dependent changes in the internal structure of the material.

#### 3.2. Experimental Tensile Testing

#### 3.3. Dynamic Mechanical Analysis

_{s}), and using Equation (1) with a constant value of Poisson’s ratio from the tensile test (ν = 0.27). From this analysis, it may be observed that the increase in temperature was able to promote the changes in the internal structure based on glass transition (T

_{g}) from the severe decrease in stiffness. From the maximum internal friction peak method, it was determined that the average glass transition temperature (T

_{g}) was 78.7 (±1.24) °C. This method implies a deviation relative to other methods (e.g., storage modulus inflection or loss modulus peak); however, it is commonly used in research dynamic mechanical analysis [23].

#### 3.4. Finite Element Analysis

## 4. Discussion—Influence of Poisson’s Ratio

_{g}transition shown by the internal friction peak, there is a consequent extreme dimensional change in width strain due to the increase in Poisson’s ratio.

## 5. Conclusions

- -
- Given that the Poisson’s ratio may change due to external stimulation (e.g., temperature, loading, time, etc.) there is an error associated with the consideration of its value as constant during the DMA test;
- -
- The error is more prominent in situations where Poisson’s ratio increases significantly, and is attributed to shape variations in the specimen, especially in conditions where the final Poisson’s ratio approximates an isochoric (ν ~ 0.5) behavior;
- -
- It is suggested that the evolution of this technology should consider Poisson’s ratio as a variable to eliminate this error in future material characterization.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Representation of the finite element analysis (FEA): (

**a**) boundary conditions, and (

**b**) mesh.

**Figure 3.**Plotting of complex modulus variation as a function of specimen dimensions, stiffness, and Poisson’s ratio variation.

**Figure 7.**Representation of FEA results in terms of width deformation and stress. (

**a**) Deformation; (

**b**) Equivalent Stress.

Chemical Composition | Specimens | |||
---|---|---|---|---|

Component A (Resin) | - (i)
- Bisphenol A
- (ii)
- 1,3-bis(2,3epoxypropoxy)-2,2-dimethylpropane
| Dimension | Value (mm) | SD (mm) |

Thickness | 1.23 | 0.08 | ||

Component B (Hardener) | - (i)
- Poly(oxypropylene)diamine
- (ii)
- Piperazine
- (iii)
- 3,6-diazaoctanethylenediamin
- (iv)
- Triethylenetetramine
| Width | 4.51 | 0.08 |

Length | 30.20 | 0.11 |

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**MDPI and ACS Style**

Carneiro, V.H.; Puga, H.
Temperature Variability of Poisson’s Ratio and Its Influence on the Complex Modulus Determined by Dynamic Mechanical Analysis. *Technologies* **2018**, *6*, 81.
https://doi.org/10.3390/technologies6030081

**AMA Style**

Carneiro VH, Puga H.
Temperature Variability of Poisson’s Ratio and Its Influence on the Complex Modulus Determined by Dynamic Mechanical Analysis. *Technologies*. 2018; 6(3):81.
https://doi.org/10.3390/technologies6030081

**Chicago/Turabian Style**

Carneiro, Vitor H., and Helder Puga.
2018. "Temperature Variability of Poisson’s Ratio and Its Influence on the Complex Modulus Determined by Dynamic Mechanical Analysis" *Technologies* 6, no. 3: 81.
https://doi.org/10.3390/technologies6030081