BLOQUE X: LA EUROPA DEL BARROCO
PRESENTACIÓN DE LA UNIDAD 5 Título
2.3.1. Tensile testing
Tensile testing of PDMS blends was carried out using the Instron 3366, a bench-top, computer controlled dual column tensometer or universal testing machine (Instron, UK). The maximum load capacity was 10 kN and the maximum test speed was 500 mm/min. The 6 different types of PDMS used as described in Table 2 (Section 2.1.3) were tested using this instrument and 3 samples were tested for each PDMS blend (n=3). The PDMS samples were cut into rectangles of 80 mm in length and 25 mm in width with a gage length of 30 mm. The thickness of the PDMS blends had previously been measured and they ranged between 600 – 800 µm. The test speed or extension rate was set to 254 mm/min. The samples were tested using ultimate tensile strength (UTS) until failure of the PDMS samples or when they broke. The extension rate was chosen based on the crosshead velocity used in the literature previously as part of several experiments to characterise the bulk mechanical properties of PDMS (Johnston et al., 2014).
Tensile testing carried out by Johnston et al was performed to the American Society for Testing and Materials (ASTM) International standards and also used a universal testing machine. The ASTM method for tensile testing is the standard used to compare mechanical properties of different materials and is suitable for most materials. However, some materials such as elastomers can exhibit elastic behaviour even at high strain levels (Johnston et al., 2014). The same test speed was used in tensile tests carried out on PDMS blends. The data obtained from the experiments included load, extension, tensile strain and tensile stress. Figure 8 shows a typical load/extension curve obtained from tensile testing of PDMS samples.
56
Figure 5 – Representative load extension curve for PDMS 184. Tensile testing was carried out on all samples to their ultimate tensile strength (UTS) or failure of the PDMS sample.
The UTS of the PDMS sample or the failure point was measured as well as the engineering stress and strain for these experiments. The Young’s modulus was calculated from the engineering stress strain curves obtained from the tensile testing data. The Instron 3366 software calculated the tensile strain (mm/mm) by dividing the extension (mm) by the gage length of the PDMS (30 mm). From the stress strain curve, Young’s modulus can be calculated from the linear portion of the curve (Liu et al., 2009). A representative engineering stress strain curve is shown in Figure 9. This showed the data obtained from tensile testing of PDMS 184 and the data range plotted on the graph was limited to 0.3 strain. By limiting the data to this strain level, a linear fit equation could be used (Excel) to obtain the stress and strain values and calculate the Young’s modulus, as in the literature it has been shown that at lower levels of strain below 40 %, the elastic linear region can be used for calculations of Young’s modulus (Kim, Kim and Jeong, 2011; Johnston et al., 2014; Lee et al., 2016). The area of the slope used for deriving the engineering stress and strain to be used in Young’s modulus calculations has been highlighted in Figure 9 on the representative curve.
0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 Load ( N ) Extension (mm)
Load extension curve for PDMS 184
ultimate tensile strength (UTS)57 The stress and strain values were used from the linear part of the graph as shown in Figure 9 in order to calculate the Young’s modulus using the following equation:
𝐸 =
𝜎𝜀 Equation 2 – Young’s modulus (Beer, 2012)
In the Young’s modulus equation, E is Young’s modulus,
𝜎
is the engineering stress and𝜀
is the engineering strain. Equation 2 is derived from Hooke’s law which describes the linear relationship between stress and strain in relatively small material deformations (Beer, 2012).
Figure 6 – An engineering stress strain curve for PDMS 184 showing a representative linear fit with data rate limited to 0.3 strain. y = 0.2653x + 0.0005 R² = 0.9965 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Ten si le str e ss (M Pa) Tensile Strain
58
2.3.2. Electronic speckle pattern interferometry (ESPI)
Another method of mechanical testing was carried out using a laser interferometry technique, using a rig and method designed by Abby Wilson as detailed in her PhD thesis titled “An Investigation into the use of Laser Speckle Interferometry for the Analysis of Corneal Biomechanics” written by Abby Wilson© (Wilson, 2017). ESPI is a technique that generates displacement in the sample and gives a value of maximum displacement. The experiments were also conducted by Abby Wilson and the raw data was processed by Abby Wilson to obtain the maximum deflection data. ESPI has been used for several years in the engineering industry to quantify the mechanical properties of materials, detect structural differences within the material and predict failure models (Zhang et al., 1998; Wilson, Marshall and Tyrer, 2016).
Laser interferometry is also a useful tool for quantifying the mechanical properties of soft biological tissue such as the cornea as it is a non-destructive real time method and can be adjusted to physiological pressures as it is highly sensitive (Wilson, Marshall and Tyrer, 2016). In addition to this, the mechanical response to loading in terms of the displacement can be measured across a whole surface enabling an improved understanding of the mechanical responses of certain biological tissues (Wilson, Marshall and Tyrer, 2016). Hence why ESPI was used on the PDMS blends and this allowed a much more sensitive and appropriate technique to be used that considered the material properties and elastic characteristics of the PDMS and also the thickness of the sample (Wilson, 2017).
For the work carried out in this thesis, the maximum displacement values were then used as shown in Equations 3 – 6 (Roark and Young, 1989);
Firstly hydrostatic pressure was used within the rig (rig design and methodology by Abby Wilson), where 𝝆 was the density of fluid in this case water, g was gravity and ∆𝒉 was the height change from the baseline.
59 Assumptions were made about the PDMS sample and it was assumed to behave as a circular flat plate with uniform load and a fixed boundary. For this calculation, the maximum stress and deflection for a loaded flat plate were used as shown in Equations 4 and 5. Where σm is the maximum stress (N/m2), p is the uniform surface pressure on the plate (N/m2), r is the radius of the circular plate (m), Ym is the maximum deflection, D is flexural rigidity (E.t3/12(1-v2)), E is Young’s modulus of elasticity (N/m2) and t is plate thickness (m).
𝜎
𝑚=
3𝑝𝑟24𝑡2 Equation 4 - At edges of the plate
𝑌
𝑚=
𝑝𝑟464 𝐷
=
0.171𝑝𝑟4
𝐸.𝑡3 Equation 5 - At the centre of the plate
Therefore to find E the equation became;
𝐸 =
0.171.𝑝𝑟4𝑌𝑚.𝑡3 Equation 6 - Young’s modulus using maximum deflection.
The pressure (p) used was 7.35 Pa and the thicknesses (m) of the PDMS samples used for ESPI were measured using the Talysurf CLI 2000 (Taylor Hobson®, UK). The average thicknesses used are detailed in Table 3 below. The radius (r) used was 6.5625 mm or 6.56 x 10-3 m and the maximum
deflection was obtained from experiments and data processing carried out by Abby Wilson, given in millimetres (Table 4, Chapter 3, Section 3.2.2.2). All units were converted to metres for calculations and the results are discussed in Chapter 3 Section 3.2.2.2.
60
Table 3 – Thickness measurements of PDMS blends used in ESPI Young’s modulus calculations converted to metres for use in calculations (average values, n=3, ±SD).
PDMS Average Thickness (µm) Average Thickness (m)
184 839.81±227 8.3981 x 10-4
10:1 756.16±247 7.5616 x 10-4
5:1 683.18±163 6.8318 x 10-4
1:1 789.04±251 7.8904 x 10-4