GOOSE ` S EGGSHELL STRENGTH AT COMPRESSIVE LOADING

The paper deals with the study of the goose eggs behaviour under compressive loading between two plates using testing device TIRATEST. The influences of the loading orientation as well as the effect of compressive velocity are studied. 226 eggs from Landes geese were chosen for the experiment. Eggs have been loaded between their poles and in the equator plane. Five different compressive velocities (0.0167, 0.167, 0.334, 1.67 and 5 mm.s -1 ) were used. The increase in rupture force with loading rate was observed for loading in all direction (along main axes). Dependence of the rupture force on loading rate was quantifies and described. The highest rupture force was obtained when the eggs were loaded along their axes of symmetry (X-axis). Compression in the equator plane (along the Z-axis) required the least compressive force to break the eggshells. The eggshell strength was described by the rupture force, specific rupture deformation and by the absorbed energy. The rupture force is highly dependent on compression speeds. The dependence of the rupture force on the compression velocity can be described by a power function. The same is valid for the rate dependence of the energy absorbed by the egg up to the fracture. The rate sensitivity of the Goose's eggshells strength is significantly higher than that reported for the hen's eggs


INTRODUCTION
Eggs can be regarded as naturally packaged food.When examining the quality of the packaging, one primarily considers the strength of the eggshell.For table eggs, shells must be strong enough to prevent failure during packing and/or transportation.For hatching eggs, shells have to be thick and strong for preservation of the embryo as well as thin for gas exchange and weak enough to allow the chick to crack the shell when hatching (Narushin and Romanov, 2002).Except common eggs (hens, quails) are also consumed waterfowls eggs producing by small-scale farmers and in Asian countries.
Resulting eggshell strength is influenced by material and structural strength (Bain, 1992).The material strength depends on the association of the mineral and the organic components of the shell.Fraser et al. (1998) mentioned that the organic matrix is considered to play a role in the regulation of various stages of crystal growth (i.e., the deposition of calcium carbonate on organic aggregates), to have the same function as steel in reinforced concrete, or both.Macroscopically is the material strength characterized by the Young`s modulus E, Poisson`s ratio  and namely by the fracture stress.Structural strength, on the other hand, is related to the interaction among the building units and depends on several variables, namely egg dimensions, egg shape, eggshell thickness, and distribution of the shell components.Most techniques that aim at quantifying eggshell strength measure eggs as a whole and thereby make no distinction between these two properties.
The most common technique for the measurement of the shell strength consists in the compression of the egg between two plane plates.This technique has been mostly The aim of this study was to determine the mechanical behaviour of the goose`s eggs under their compression between two plane plate.The main emphasis has been given on the effect of the compression velocity on the parameters describing the eggshell strength, i.e. on the rupture force, eggshell deformation at the rupture, on the energy absorbed during the loading process etc.The study of this effect is limited only to the hen`s eggs.It has been found that the eggshell strength has been significantly depended on the compression rate (Voisey and Hunt 1969; Carter, 1979, Altuntaş andŞekeroğlu, 2008).The investigation of the loading rate on the strength properties of the goose`s eggs should extent our knowledge on this phenomenon.

MATERIAL AND METHODOLOGY
226 eggs (3 days old) from Landes geese were chosen for the experiment.Geese were kept in free-range technology at a commercial breeding farm in the Czech Republic.Eggs were collected from 3 years old geese.
In this paper the analytical description of the eggshell contour curve was also obtained.This description enables to evaluate the radius of the curvature R, egg volume and egg surface.The radii were evaluated at the sharp end, blunt end, and at the maximum width of the egg (equator).No. 1/2014 In order to complete the basic data the values of the eggshell thickness are given in the Table 1.These quantities have been measured at the sharp end of the egg, at the blunt egg and at the maximum of the egg width (at the equator).
The eggs have been compressed between the two plates using testing device TIRATEST 27 025 (TIRA GmbH, DE).The egg sample was placed on the fixed plate and loaded at the compression velocities 0.0167, 0.167, 0.334, 1.67 and 5 mm.s -1 and pressed with a moving plate connected to the load cell until the egg ruptured.Two  Schematic of the egg compression.On the left side the loading along the X-axis is shown.The loading along the Z-axis is displayed on the right part.This orientation is also termed as the loading in the equator plane mutually perpendicular compression axes (X, Z) corresponding to main geometrical axes were usedsee Figure 1.The X-axis represented loading axis along the length dimension and the Z-axis represented the transverse axis covering the width dimension.Two more orientations were considered in case of X-axis.If the egg sharp end is in contact with the moving plate the symbol X s is used.The symbol X b corresponds to the orientation where egg blunt end is in contact with the moving plate.
Response of the egg to compression loading between two parallel plates is characterized by nearly linear increase in the loading force, F, with moving plate displacement p.At the moment of eggshell break the loading force rapidly decreasessee Figure 2.This behaviour was observed in number of researches and described in many; see e. (2) The series of 10 eggs was tested for each orientation.

RESULTS AND DISCUSSION
The experimental records forcedisplacement have been used to the evaluation of the quantities described in the previous charter.The results are summarized the Tables 2 -4, where the basic statistics of the obtained data is presented.
The rupture force increases with the compression velocities as shown in the Figure 3.
For all used orientation of the egg compression the rupture force exhibits its maximum in such loading orientation, when the moving plate is in contact with the sharp end of the egg (X s axis).The experimental data can be fitted by power function: .
The parameters are given in the Table 5. Contrary to the results obtained for the hen`s eggs the goose`s eggs exhibit higher sensitivity of the rupture force to the loading rate.This rate sensitivity can be described by: .
Owing to the values of nsee Table 4 the increase in the loading rate  the rate sensitivity decreases.The same tendency as the rupture force exhibits also absorbed energy E asee Figure 4.These data can be also fitted by the function (3).The parameters of this fitting are presented in the Table 6.
The displacement p m at the egg rupture increases with the compression rate.Its dependence on the orientation of the loading is not the same as for rupture parameters F m and E a see Figure 5.
The egg shape can affect the obtained results.In (ASAE, 2001) method for compression tests of food materials of convex shape is described.According to this theory the loading force should be dependent on the main curvature of the eggshell.If we denote the radii of the curvature at the sharp end as R 1 , at the blunt end as R 2 and at the equator as R 3 than for the loading in the X s , X b and Z-axes we obtain the curvatures k 1 , k 2 , k 3 : Where W is the egg width.
In the Figure 6 the dependence of the rupture force on the eggshell curvature is displayed for the compression velocity 0.0167 mm.s -1 .
The rupture force F m increases with the eggshell curvature k.Experimental data can be fitted by the power function: . c ak F b m

 
(5) The same conclusions have been obtained for all remaining loading velocities.Parameters of the Eq.( 5) are given in the Table 7.
The remaining eggshell strength characteristics also increase with the eggshell curvature.The obtained data can be fitted only by polynoms of order 6 and more.
The effects of the eggshell thickness on rupture parameters were not statistically significant.These characteristics are also independent on the egg shape index SI.This independence may be consequence of a relatively low scatter both of the thickness and SI.
As it has been mentioned in the introduction the rupture force obtained at the compression of the whole egg consists from the material and structural strength.In order to distinguish these two components some numerical simulation of the egg compression should be used.One of the possible approaches has been presented by Trnka et al. ( 2012).
The explanation of the increase in the eggshell strength with the loading rate can be probably explained only in terms of the eggshell microstructure like in the case of many engineering materials (metals, ceramics, polymeric materials etc.).
applied for the study of the mechanical properties of the hen`s eggs (De Ketelaere et al., 2002; Lin et al., 2004; Narushin et al., 2004, Altuntas and Sekeroglu, 2008, Nedomová et al., 2009).There are also some papers on the mechanical behaviour of Japanese quail eggs (Polat et al., 2007), on the strength of the Ostrich`s eggs (Cooper et al., 2009) and many others.The data on the mechanical behaviour of goose`s eggs are very scarce in the literature.

Figure 2
Figure 2 Example of the experimental record of the force during the compression of egg along the Z axis g. De Ketealere et al. (2004) and Lin et al. (2004).Maximum of the loading force is than defined as the rupture force, F m .Specific rupture deformation is defined by the following equation: mm) is the undeformed egg length measured in the direction of the compression axis and p m (mm) is the displacement at the point of rupture of the eggshell(Braga et al., 1999).Energy absorbed (E a ) by an egg at the moment of rupture is defined as: These results are generally similar to those obtained by Altuntaş and Şekeroğlu (2008) and Trnka et al. (2012).

Figure 4
Figure 4 Energy absorbed up to the eggshell fracture

Figure 5 Figure 6
Figure 5 Eggshell displacements at the moment of the eggshell breakage

Table 1
Thickness of the eggshells of the tested eggs

Table 2
Compression in the X s direction

Table 3
Compression in the X b direction Figure 3The influence of the compression velocity on the rupture force

Table 4
Compression in the Z direction