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10AGRICULTURAL SCIENCES
PECULIARITIES OF POTATO FLESH SAMPLE DEFORMATION BY UNIAXIAL COMPRESSION
Zhukov V.
D. Sc.,Prof., Chief Researcher Andreev N.
D. Sc., Ac. RAAS, scientific director Lukin N.
D. Sc., director
All-Russian research Institute for starch products - the branch of FSBI "Federal research center of food systems of V.M. Gorbatov" RAS,
Moscow, Russia
Abstract
The uniaxial compression of cylindrical samples of potatoes was investigated. A typical form of a complete stress-strain diagram is an S-shaped curve. The curvature of the diagram became the more, the more flabbiness the potato was. It is noted that the samples were destroyed at an angle of 45 ° to the load axis as a brittle material with a significant deformation of fracture close to 0.3. The material showed non-linear elasticity only up to a stress of 0.1 MPa, after which the deformation became inelastic. In this regard, it was concluded that the use of the term "Young's modulus" to the most significant part of the material deformation in the diagram is inapplicable. It is proposed to consider the ratio of stress to strain of any zone diagram as a modulus of rigidity of materials with cellular structure and denoted by Z. It should be used in the design formulas for the processes and equipment for processing plant and animal raw materials.
Keywords: potato, sample, compression, stress-strain diagram, relaxation, fracture, brittle, rigidity modulus.
INTRODUCTION
Raw of plant and animal origin are supplied for primary processing in the form of hard materials with cellular structure. In the calculation of processes and equipment its mechanical processing stress and strain (relative deformation) parameters should be used similar to those they are defined and entered into the design formulas for structural materials. This applies fully to potatoes, a significant part of which is ground on the production lines of potato starch. The purpose of this study was to refine the relationship between stresses and strain under conditions of uniaxial compression of cylindrical samples cut from potato tubers. Such studies obtain data of the material, i.e. flesh, not form of the tuber. The study of physicomechanical properties of food products with cellular structure (plant and animal products) was the subject of numerous modern publications, including bibliography reviews [1-4]. Young's modulus, Poisson's ratio, stress-strain characteristics under the assumption of elastic deformation up to destruction are determined there. There are publications on changes in the properties of potato tubers or similar properties of other vegetables and fruits, depending on the storage period and temperature [5].
The test is performed using simple physical sample models. As a result graphs are obtained, called diagrams, in stress-strain coordinates (o-e). The diagrams show the points of characteristic qualitative changes in the parameters used for technological equipment design. The most relevant points are the values of ultimate stress (oU), the elastic and inelastic zones, residual strain after destruction (eP), Young's modulus (E) of material for the Hooke's formula o = Ee. Young's modulus reflects a constant coefficient, characterizing only the elastic properties of the material. Therefore, it can
be defined and used only to describe the elastic part of the diagram [6]. It should be noted that both elastic and inelastic strain zones can be linear or nonlinear. Some publications include diagrams of destruction of samples from potato tubers or fruit, which the authors could consider linear up to destruction [1, 5, 7, 8]. This result is due to the fact those the diagrams close to linear, relate to samples of fresh and hard tubers or fruits. Flabby samples of fruits and vegetables from the very beginning of loading show a non-linear S-shaped diagram between stress and strain. For materials with nonlinear elasticity, the Young's modulus is often determined by the linear interpolation of the elastic zone of the diagram.
Diagramms of plant materials indicate the occurrence of residual, i.e. inelastic deformations, starting at low stresses. Therefore, the definition and application of the term "Young's modulus" throughout most of the diagram requires discussion.
MATERIALS AND METHODS
Researches were carried out on a mechanical type installation for testing specimens of various kinds for tension and compression. It provided an opportunity to stop the loading for required period of time, which allowed to consider the loading to be static. Studies of the physico-mechanical properties of potato cultivar "Lorkh" were carried with tubers of varying flabbiness from fresh rigid to flabby. Based on the results of the experiments, we plotted stress-strain diagrams. Our primary experiments with cylindrical samples cut from potato tubers confirmed the presence of relaxation effect [9]. Therefore, further studies were carried out with measurement of stress-strain parameters under intermediating stop-exposure period of 30 seconds. By the end of this period, the stresses decreased by 4-12%, and
then their decline slowed down significantly. Cylindrical samples had a ratio between the length and diameter of the sample equal to l0/ d0=25/14=1.79 and did not lose buckling in the compression tests. Samples of such size ratio had a number of advantages. It increased the deformation of the sample, reduced the unevenness of stresses in the middle part of the sample, where the destruction occurred the most often, and clearly demonstrated the destruction type.
RESULTS AND DISCUSSION
A series of experiments revealed a number of important features. The general form of compression diagrams for hard (fresh) tubers was linear. The stressstrain diagram of flabby tubers becomes S-shaped. This feature is confirmed by other researchers publications [10, 11]. The samples of flabby tubers are intensively deformed in the initial section to up the stress o^0.1 MPa, after which the slope angle of the diagram line increases sharply. The flesh of samples becomes more rigid. Potato samples of any degree of flaccidity were destroyed as a brittle body with formation of a flat surface inclined to the compression line at an angle close to 45 ° (Fig. 1), where the maximum shear stresses are. The residual strain was value about £r^0.3 after total destruction. Such significant residual strain of total destruction of fruit and vegetable samples were also noted by other researchers [1].
Fig.l. A typical photo showing the brittle destruction of a sample cut from a potato tuber.
The next stage of the study was aimed at identifying the strain type (elastic and inelastic) during intermediate full unloading and the next directly after it a new loading. The most obvious occurrence of inelastic strain is the residual strain after subsequent intermediate full unloading of the sample. The number of intermediate unloadings in the sample from one to three. Each subsequent unloading was began with a higher stress. With an increase in the number of unloads, the compression diagram acquires an explicit smaller slope of the line in the stress zone close to the ultimate strength (oU), concluding its general S-shaped form.
Fig.2 shows a characteristic diagram of the longitudinal compression of flabby potato sample with two intermediate unloading to zero and subsequent new loading. The sample showed considerable residual strains of OH and OM at the end the intermediate un-loadings of CH and KM, started with stresses o>0.1 MPa. Residual strains are not detected when unloading at a stress o<0.1 MPa. This indicates elastic nature of the strains at the beginning of the loading.
Oj MPa
oU 0.5
0.4
0.3
0.2
0.1
/_______ j
A 5 P ¿t
7 / k a Jri m JT J] i JT f \ » jr / » N
6 , / y f3 / : / i /
2\ ■-.J; ■■!--# Wft jf * / n / 5 : / '4
B / / 7/ tt
--- / \ i'/J^'7 / ¿aS MZV Jr * ' * y
Fig. 2. A typical compression stress-strain diagram of a potato sample with two intermediate unloadings: o -stress (MPa); e - dimensionless relative deformation (strain), (d/l); l - initial zone of the diagram; 2 and 3 - the curves of the first intermediate unloading (CH) and the subsequent new load (HK); 4 and 5 - curves of the second intermediate unloading (KM) and subsequent new load MP); 6-9 - linearized curves BC, CH, MC and AP; a6-a9 - slope angles of straight lines 6-9; the points marked with letters show characteristic coordinates of the
diagram.
Thus, up to the stress o=0,1 MPa, the elastic strain OB occurs mainly by stretching the sample cells material under increasing pressure of intracellular liquid. After exceeding the stress level 0.1 MPa, intermediate unloading shows presence of residual strain eH and eM, even with rectilinear diagram, like in article [7]. Residual strain after unloading indicate inelastic strain in the sample, while elastic strain continue to grow. Under increase in stresses, the sample first becomes stiffer and the diagram steeply rises (curve BC). Then, the rigidity of the sample begins to decrease, as indicated by the more gentle curve JK and upper slightly sloping curve NP right up to fracture at oU, concluding its general S-shaped form.
The curves of intermediate unloadings CDH and KLM (lines 2 and 4) almost coincide the subsequent loadings HDJ and MLN (sections of lines 3 and 5), which illustrates their elastic character, although nonlinear. Therefore, the tangents of the slope lines 7 and 8 (tga7~ tga8) can formally correspond to definition of Young's modulus, but only for the line zone CK in the diagram. The angles of inclination lines 6 or 9, reflect the influence of not only elastic, but also inelastic component in the full strain. Therefore, the tangents of their angles (tga6 h tga9) cannot be called Young's modulus. They correspond to the name of the stress-strain modulus of rigidity Z, which takes into account both elasticity and inelastic strains. Note that in publications on vegetable and animal raw materials (fruit, vegetables, meat) it is called Young's modulus or Young's conditional modulus. The rigidity module Zi = tgai is a coefficient in the formula oi = Zie. The modulus Z6 = tga6 refers only to the zone BC, Z9=tga9 is the averag for the whole AP diagram. Thus, the strain of a potato tuber sample at compressive stresses below 0.1 MPa occurs as elastic nonlinear of the cellular structure strain. After exceeding this stress, inelastic strains occur and gradually increase to large values. The sample fractures by the type of brittle material.
CONCLUSIONS
Uniaxial compression of samples cut from potato tubers with a ratio of length to diameter of 1.5-2 gives more information about the physic-mechanical properties and the brittle fracture of their flesh.
Potato samples show relaxation properties in the tests. Therefore, it is advisable to conduct study with multiplay periodic short-term stops during loading of the sample.
The sample compression diagram is S-shaped. Hard (fresh) tubers give a diagram close to linear. The flabbier tuber is, the greater is its strain at the initial zone, and the diagram becomes more curved.
Elastic deformations occur in the sample at the initial stage of loading within a stress range below to 0.1 MPa. Inelastic component is added to them at a higher stress. Most of the diagram includes inelastic strain. Therefore, use of the term "Young's modulus" (E), which is an elasticity modulus, is incorrect in the zone of inelastic strain, more correct named the rigidity modulus (Z). For this zone, is the rigidity modulus Z is more
relevant. Due to brittle nature of plant material flesh, the Z modulus is variable for different zones of the diagram, which distinguishes it from ductile materials. The rigidity modulus Zi = tgai, which is the coefficient in the formula ci = Zie, corresponds to those parts of the diagram that include the total (elastic and inelastic) strains. It should be used in the calculation formulas of processes and equipment for processing raw materials of plant origin.
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