Determination of elasticity modulus and Poisson ratio of two onion varieties under different loading conditions

Abstract

Introduction: Poisson ratio and modulus of elasticity are two fundamental properties of elastic and viscoelastic solids that use in solving all contact problems, including the calculation of stress, the contact surfaces and elastic deformation (Mohsenin, 1986; Gentle and Halsall, 1982). There are many published literature on Poisson ratio and elasticity modulus of fruit and vegetables. Shitanda et al. (2002) calculated Poisson ratio of rice by considering Boussinesq’s theory. They showed that the Poisson ratio is greater for shorter varieties. In another study, researchers used the instrumented bending beam to measure the lateral expansion of red beans. They were considered Poisson ratio as the ratio of transverse strain to the longitudinal strain (regardless of the geometry of the sample) and were calculated modulus of elasticity with Hertz theory for convex bodies (Kiani Deh Kiani et al., 2009). Cakir et al. (2002) was determined the Poisson ratio and elastic modulus of some onion varieties. They used a simple formula to determine the transverse strain that developed by Sitkei (1986) for prism-shaped rod, regardless of the geometry of the product. Reviewed scientific literature shows that these parameters have not been studied according to the geometric shape of onions and was not used by a more accurate method, such as image processing to determine these parameters. The objective of this study was to evaluate the mechanical properties of two varieties of onions. Poisson ratio was determined with image processing. Considering shape of the onions and deformation value, and using Hertz’s theory with Poisson ratio, modulus of elasticity was calculated. The effects of loading directions (polar or equatorial), deformation value (5, 10 and 15 mm), loading speed (15 or 25 mm min-1) and onion varieties (Red and Yellow) on the modulus of elasticity and apparent Poisson’s ratio were examined. Materials and Methods: The onions harvested in autumn, 20 days before conducting the tests. Onion samples kept at room temperature (21oC). Onions of each cultivar were randomly selected. Diameters of onion were measured with a digital vernier caliper. In each run, eight onions were randomly selected and the loading test and photography were done together and the average values reported. All mechanical tests were performed using a Universal Testing Machine (UTM) (Model H5KS, Tinius Olsen Company) between two rigid plates. The loading was made with two constant speeds of 15 and 25 mm min-1. Deformation values were 5, 10 and 15 mm. The onions were loaded either axially or laterally until rupture point and photography were done together. The initial and current onion diameters along the y and x axes obtained by using image processing and the strains were calculated. Having axially and laterally strains of the onions, the apparent Poisson's ratio was calculated using equation presented by Figura and Teixeira 2007; Kiani Deh Kiani et al., 2009; Pallottino et al., 2011; Kabas and Ozmerzi 2008; Gladyszewska and Ciupak 2009. A factorial experiment based on a completely randomized design with 8 replications was applied. The significant differences of means were compared by using the Duncan’s multiple range test at 5% significant level. SPSS 20.0 software was used for data analysis. Results and Discussion: According to the analysis of variance (Table 2), the effects of speed and displacement of loading was significant in 5% probability levels. In addition, interaction effect varieties × directions × speed along Y, varieties × directions, varieties × speed and directions × speed along X was significant in 1, 1, 5 and 5% probability levels, respectively. The average of the apparent Poisson ratio for Yellow onion was less than that obtained for the Red onion, because Red onions have softer texture than Yellow onions. Apparent Poisson ratio was obtained as 0.2623 to 0.4485 and 0.2423 to 0.4179 for Yellow and Red onions, respectively. With increasing deformation, apparent Poisson ratio increased. Modulus of elasticity along X and Y According to the analysis of variance (Table 2), the effects of speed and displacement of loading and directions × speed was significant in 1% probability levels. The average of the modulus of elasticity for Red onion was less than that obtained for the Yellow onion because Yellow onion has tougher and more powerful texture than Red onion. Modulus of elasticity were obtained as 2.032 to 5.449 and 1.829 to 5.311 MPa for Yellow and Red onions, respectively. The modulus of elasticity for lateral loading was less than that obtained for the axial loading. With increasing deformation, the modulus of elasticity decreased. The modulus of elasticity for lateral loading in loading speed 25 mm min-1 was less than that obtained for loading speed 15 mm min-1. Conclusions: The results were summarized as below: Loading speed, deformation value and their interaction effect were significant in different confidence levels for apparent Poisson's ratio and modulus of elasticity. The compression force of Yellow onion was more than Red onion. Thus, it can be concluded that Yellow onions have more strength against the forces and loading. The modulus of elasticity for lateral loading was less than that obtained for the axial loading. It is better to be considered for packaging of onions. The modulus of elasticity for lateral loading in loading speed 25 mm min-1 was less than that obtained for loading speed 15 mm min-1. With increasing deformation, the modulus of elasticity and apparent Poisson’s ratio decreased and increased, respectively.

Keywords

• elasticity modulus
• hertz’s theory
• image processing
• onion
• poisson ratio