MODULUS OF ELASTICITY OF RAPESEEDS BY EDOMETRIC AND ACOUSTIC METHODS

Mateusz Stasiak¹, Marek Molenda¹, Józef Horabik^2
1 Department of Physical and Technological Properties of Agricultural Materials, Institute of Agrophysics, Polish Academy of Science, Lublin, Poland
² Institute of Agrophysics, Polish Academy of Sciences, Lublin, Poland

ABSTRACT

Numerous branches of industry deal with granular materials such as pills and powders in the pharmaceutical and food industries or mineral powders in the construction businesses. Efficient handling and processing of large amounts of these materials require understanding of their mechanical behaviour. Process of optimization is based on knowledge of material properties that depends on properties of individual grains, interparticle friction, contact geometry and load history.

Objective of performed project was to determine and compare values of the modulus of elasticity E of rapeseeds, obtained using two methods: uniaxial compression and acoustic testing. Research was carried out for rapeseed beddings of four levels of moisture contents 6, 9, 12 and 15%. Uniaxial compression was used, as proposed by Sawicki [12]. Vertical reference pressure of 100 kPa was applied. With this method E was found to decrease from 9.0 to 6.6 MPa, with an increase in moisture content. Values of E determined using acoustic method, based on measurement of shear wave velocity, were higher then those found in uniaxial compression and decreased from 62 to 3 MPa in a range of hydrostatic pressure. Values of E from acoustic method varied in larger extent with change in moisture content and were dependant on hydrostatic pressure.

Key words: granular material, rapeseed, elasticity, modulus of elasticity, uniaxial compression, shear wave velocity.

INTRODUCTION

Poland, with rapeseeds yield of 1.5 mln tones per year, is one of the leading producers in Europe. As a raw material, rapeseeds is the basic source for food and biofuel oils. It is necessary to handle and process it safety by checking the state of material during the technological process, because of great importance of the product quality for its economical value. Designer of storage systems or processing plants requires knowledge of mechanical properties, which serve as design parameters. Properties of material in bulk depend on properties of individual granules, interparticle friction, contact geometry and load history. Properties are strongly modified by moisture content, which influences the state of the seed coat as well as interior of grains. Design of an efficient technological equipment requires determination of density ρ, angle of internal friction φ, friction coefficient between material and construction material μ, modulus of elasticity E and stress ratio k.

Modulus of elasticity E characterizes elastic deformation of granular beds. Design of equipment for handling and processing of plant granular material requires experimental value of this parameter that depends on pressure [12]. Polish design standard recommends value of E related to pressure in silos that depends on height of the bed [10]. European Standard [2] recommends determination of two values of effective modulus of elasticity. One, denoted E_sl measured during loading of the sample and the second E_su obtained during unloading of the sample. For calculation of values of the two modulus two ratios of change in lateral stress to change in the vertical stress are determined – K_l and K_u for loading and unloading respectively. European Standard [2] recommends determination of E in uniaxial compression test with possibility of measurement of horizontal stress and vertical strain under loads similar to those occurring in the technological process.

Strong influence of moisture content, density and porosity on E of granular materials was observed. Influence of these parameters of sand samples was examined by Liu et al. [8]. The authors reported approximately threefold change in modulus of elasticity, with varying experimental parameters. Value of E is necessary for estimation of silo loads developing with temperature variation [16]. Investigations on agricultural granular materials of Thompson & Ross [16], as well as those of Moya et al. [9], confirmed very strong influence of moisture content and pressure.

Recently, demand of industrial practice has brought about revision of several silo design codes, which included standardization of methods for determination of mechanical properties of granular materials. Standards recommend determination of mechanical properties under load condition, which are similar to the operation loads. Still determinations of some material parameters of granular beddings require standardization of equipment and methods and many laboratories around the world work on their elaboration.

Acoustic methods are widely used in various branches of science and technology. They are commonly applied for detection of internal damages in materials. Ultrasounds are also used for modifications of surface of materials [13]. Application of acoustic methods contributed to great progress in measurements of raw materials properties and products on-line, during the technological process in food industry [1]. In geotechnical applications acoustic methods have shown great advantages, while proved to be convenient and cheap tool in investigation of properties of plant granular material [5]. Application of shear waves in triaxial and uniaxial tests can provide more information about properties of plant granular materials under loads [14].

OBJECTIVE

The objective of performed project was to determine and compare values of modulus of elasticity E of rapeseeds using two methods: uniaxial compression and acoustic testing based on measurement of shear wave velocity.

MATERIAL AND METHODS

Modulus of elasticity E was determined for rapeseeds variety Licosmos at four levels of moisture content: 6, 9, 12 and 15%. Uniaxial compression was used as proposed by Sawicki [11], who distinguished two phases of the unloading in uniaxial compression experiment. The first phase could be used for determination of elastic constants. Figure 1 shows the scheme of the uniaxial compression apparatus that was used in testing [3].

Fig. 1. Uniaxial compression apparatus

The wall of the uniaxial compression tester consisted of two semicircular halves cut along the axis. The halves were connected with four load cells installed in pairs on the two connection lines, restoring cylindrical shape of the apparatus. One half of the wall rested directly upon the base. Bottom and top plates of the apparatus transmitted the vertical load through the load cells. The experimental set made possible for determination of the mean lateral pressure σ_x, mean vertical pressure on the bottom σ_z, and the mean vertical pressure on the top plate σ_z0. Surface of the wall was smooth while the surfaces of the top and bottom plates were rough. The granular material was poured into the test chamber, without vibration or other compacting action. The sample was 80 mm high and 210 mm in diameter. The bedding was loaded to the reference vertical stress σ_z0 of 100 kPa using universal testing machine. During compression, the top plate of the apparatus was moving down with a constant speed of 0.35 mm·min^-1, while the displacement was measured with inductive transducer having accuracy of 0.01 mm. After completing compression unloading took place with the same speed of deformation until the 0 kPa of stress level was reached. Experiments were performed in three replications.

Two phases of the unloading can be distinguished (see fig. 1). During the first phase of unloading (path AB), sample shows linear reaction, which is characteristic for elastic deformation and total vertical deformation ε_z may be expressed as below:

(1)

where ν is Poisson’s ratio. Modulus E was determined using experimental results from linear phase of unloading. The ratio of horizontal stress σ_x to vertical stress σ_z0 was assumed constant (elastic state of stress) and a slope A of a straight line:

(2)

was estimated using linear regression procedure applied to experimental values of stresses. Then, with A estimated, values of Poisson’s ratio ν were calculated as:

(3)

Values of E were estimated using relationship ε_z(σ_z0) (equation 1) with experimental values of ε_z, σ_z0, and ν determined following equation 3.

Linear elastic theory allows calculation of elastic parameters on the basis of measured shear or longitudinal acoustic wave velocities [7]. Initial modulus can be calculated with shear wave velocity V_s and density ρ known as [17]:

         G_max= ρV_s².            (4)

Then modulus of elasticity E of the material can be calculated [4]. Lipiński [6] determined shear wave velocity of Ottawa sand in a range of hydrostatic pressure from 50 to 400 kPa and found it increased from 150 to 300 m·s^-1. Method used by Lipiński [6] was adopted in this project. Experiments were performed for ten levels of hydrostatic pressure in triaxial compression apparatus chamber fitted with piezoelements in top and bottom plates of the apparatus, that made possible generating and recording of acoustic shear waves (fig. 2).

Fig. 2. Equipment for measurement of shear wave velocity in granular material

The elastic properties were determined under load conditions similar to those encountered in industrial storage silos under typical operation regime. The material was poured into the test chamber, without vibration or other compacting action. Maximum normal pressure applied in uniaxial compression test (of 100 kPa) corresponded to pressure produced by approximately 14 m high column of grain. Measurements of shear wave velocity were conducted under hydrostatic pressure ranging from 0 to 90 kPa, that was increased in 10 kPa steps in each experiment. Hydrostatic pressure denoted 0 kPa refers to conditions at the initial state, without additional loading. The sample was cylindrical, 150 mm high and 70 mm in diameter. Measurements were performed at signal frequency of 1 kHz and amplitude of 0.6 V. Vertical deformation of the sample was measured during the experiment with inductive displacement transducer, having accuracy of 0.01 mm. Experiments were performed in three replications.

RESULTS

Uniaxial compression test. Figure 3 shows relationships of vertical stress σ_z0 and total vertical strain ε_z for loading – unloading cycles for rapeseed of four levels of moisture content. First part of the loading curve reflects consolidation of the sample with rearrangement of particles undergoing translation and rotation movements, but without their deformations. Second, steeper part of the curve shows an increase in the plastic and elastic stresses in the sample associated with deformation of particles.

Fig. 3. Experimental data and fitted σz 0(εz) relationships for rapeseed of four levels of moisture content

During this phase of loading deformation takes place mainly in contact areas between grains. Variation in moisture content lead to stiffness changes of particles interior and resulted in large differences between experimental stress – strain relationships.

The modulus of elasticity determined in uniaxial compression test are presented in table 1. Modulus of elasticity of rapeseed ranged from 6.6 MPa for 15% moisture content to 9 MPa for 6% moisture content. Standard deviations of modulus of elasticity were found in the range from ±0.6 MPa to ±0.9 MPa, that confirmed good repeatability of experiments as a result of repeatable internal structure of samples.

Table 1. Moduli of elasticity of rapeseed determined in uniaxial compression test and acoustic testing

Moisture content %	E, MPa u.c.t	E, MPa a.t. (for ph = 90 kPa)	E a.m./E u.c.t
6	9.0 ± 0.6	62 ± 7	9
9	8.7 ± 0.8	58 ± 5	9
12	7.1 ± 0.6	42 ± 5	6
15	6.6 ± 0.9	40 ± 4	6

For a height of bed, corresponding to 100 kPa of normal pressure, Polish Standard [10] recommends applying modulus of elasticity for grain of 20 MPa, thus in good agreement with our result of uniaxial compression. Modulus of elasticity of single grain of rapeseed was examined by Stępniewski [15]. This author assumed that single grain of rapeseed is elastic spherical shell filled with uncompressible liquid and obtained modulus of elasticity equal to 6 MPa for 15% of moisture content, while for 6% of moisture content E was found of 27 MPa. Differences in values of modulus of elasticity of single grain compared to that of bedding of rapeseed result from influence of packing structure and intergranular friction.

Acoustic examination. Mean values of shear wave velocity V_s were found in a range from 50 m·s^-1 to 180 m·s^-1 (Fig. 4). Velocity increased with an increase in pressure p_h and decreased with an increase in seeds moisture content. The highest increase in V_s, with increasing p_h, from 30 to 180 m·s^-1, was found in the case of rapeseeds of 6% moisture content. For seeds of 15% of m. c. wave velocity increased from approximately 50 to 140 m·s^-1. The weakest variation in values of velocity, with an increase in moisture content, was observed for uncompacted samples, marked on graphs as 0 kPa. Maximum change in value of V_s of 40 m·s^-1 was found for 90 kPa of hydrostatic pressure.

Fig. 4. Relationships between hydrostatic pressure ph and shear wave velocity Vs for rapeseed of four levels of moisture content

Mean values of moduli of elasticity calculated based on V_s, density and Poisson’s ratio at four levels of moisture content are presented in figure 5.

Fig. 5. Mean values of moduli of elasticity of rapeseeds of four moisture contents in a range of hydrostatic pressure from 0 to 90 kPa

Moduli of elasticity obtained with acoustic method were found higher than those obtained in uniaxial compression test. This was due to differences in ranges of sample deformation in the two tests that in the case of shear wave velocity estimation was very small (strain in an order of 10^-5) as compared to deformation in uniaxial compression tests (strain of 0.12). Values of E found in uniaxial compression, similarly to those measured with acoustic method, increased with an increase in hydrostatic pressure and decreased with an increase in moisture content. No differences in values of modulus for initial state were observed, while for 90 kPa of hydrostatic pressure difference reached approximately 25 kPa. The highest values of moduli of elasticity, in a range from 10 to 62 kPa, were obtained for rapeseed of 6% of moisture content, while for 15% of m. c. E ranged from 10 to 38 kPa.

Increase in hydrostatic pressure resulted in an increase of shear wave velocity as high as ninefold in connection with an increase in number and stiffness of contacts between seeds during deformation that facilitated wave transmission. Influence of moisture content was found also strong. Increase of moisture content from 6 to 15% resulted in 25% decrease of shear wave velocity. This was a result of weakening of stiffness of contacts between particles and increase of viscosity on the contact surfaces that resulted in stronger damping of propagation of acoustic wave.

Variability of modulus of elasticity was approximately 50 kPa with an increase of hydrostatic pressure up to 90 kPa. Also Moya et al. [9] reported that vertical pressure strongly influenced values of modulus of elasticity. These authors reported that pressure increase from 14.7 to 316 kPa caused increase in E of wheat from 4.45 to 28.8 MPa, while E measured for vertical pressure of 158 kPa during the unloading phase of the same test was found of 64.3 MPa. Considerable influence of deformation velocity on measured parameters was also observed.

CONCLUSIONS

Values of modulus of elasticity E were found increasing with an increase in vertical pressure and decreasing with an increase in moisture content. Values obtained with two methods differed considerably probably as a result of large difference in sample strain that was in an order of 10^-5 in acoustic method and in an order of 10^-1 in uniaxial compression. Using values in calculations of equipment depends on strain rate in designing system.

Values of modulus of elasticity, determined in uniaxial compression test at applied reference pressure of 100 kPa were found in a range from 6.6 MPa to 9 MPa, that was in a reasonable agreement with design standards recommendations [10].

At seeds moisture content of 6% values of E estimated based on measurement of shear wave velocity were found increasing from 11 to 62 MPa with an increase in hydrostatic pressure from 10 to 90 kPa.

Values of E obtained at 90 kPa of hydrostatic pressure decreased from 62 to 40 kPa with moisture content in a range from 6 to 15%.The values of E at p_h = 90 kPa from acoustic method were found maximum approximately 9 times higher than the values obtained in uniaxial compression test at 100 kPa of vertical pressure.

REFERENCES

1. Bijnen F.G.C, van Aalst H., Baillif P.-Y., Blonk J.C.G., Kersten D., Kleinherenbrink F., Lenke R., vander Stappen M.L.M., 2002. In-line structure measurement of food products. Powder Technology 124, 188-194.

2. Eurocode 1. 2003. Basis of design and actions on structures – Part 4: Actions in silos and tanks. European Committee for Standardization. Central Secretariat: rue de Stassart 36, B-1050 Brussels.

3. Horabik J., Molenda M. 2000. Urzadzenie pomiarowe do wyznaczania ilorazu naporu osrodka sypkiego [Device for determination of pressure ratio of granular materials]. Zgłoszenie patentowe nr P-340014. Biuletyn Urzędu Patentowego Nr 22(700), A1(21) 340017 [in Polish].

4. Jastrzębski P., Mutermilch J., Orłowski W., 1985. Wytrzymałosc materiałów [Strength of materials]. Warszawa [in Polish].

5. Kayabalt K., 1996. Soil liquefaction evaluation using shear velocity. Eng. Geology 44, 121-127.

6. Lipiński M.J., 2000. Shear wave velocity for evaluation of state of cohesionless soils. Ann. Warsaw Agric. Univ. Land Reclamation 29, 11-20.

7. Lipiński M.J., 1999. Lab measurement of body wave velocities for determination of geotechnical parameters. Script of paper.

8. Liu J., 1995. Investigation of the stress-strain relationship of sand. J. Terramech. 32(5), 221-230.

9. Moya M., Ayuga F., Guaita M., Aguado P., 2002. Mechanical properties of granular agricultural materials. Transactions of the ASAE, 45(5), 1569-1577.

10. PN-B-03262. 2002. Silosy żelbetowe na materiały sypkie. Obliczenia statyczne, projektowanie, wykonawstwo i eksploatacja [Concrete bins for storing granular materials and silage. Design rules] [in Polish].

11. Sawicki A. 1994. Elasto-plastic interpretation of oedometric test. Arch. Hydro-Eng. Environmental Mech. 41 (1-2), 111-131.

12. Sawicki A., Swidziński W., 1998. Elastic moduli of particulate materials. Powder Technology 96, 24-32.

13. Sen S., Manciu M., Sinkovits R.S., Hurd A.J., 2001. Nonlinear acoustic in granular assemblies. Granular Matter 3, 33-39.

14. Stasiak M., Molenda M., Lipiński M.J., 2002. Możliwosc zastosowania pomiaru prędkosci fal akustycznych do wyznaczania parametrów sprężystosci materiałów sypkich [Possibility of determination of elastic parameters of granular materials based on measurement of shear wave velocity]. Acta Sci. Pol. Technica Agraria 1(2), 89-93 [in Polish].

15. Stępniewski A., 1997. Wpływ wilgotnosci i temperatury na zmiennosc własciwosci mechanicznych nasion rzepaku [Influence of moisture content and temperature on mechanical parameters of rapeseeds]. Praca doktorska, Instytut Agrofizyki PAN, Lublin [in Polish].

16. Thompson S.A., Ross I.J., 1984. Thermal stresses in steel grain bins using the tangent modulus of grain. Transactions of the ASAE (16)3, 165-168.

17. Timoshenko S.P., Goodier J.N., 1970. Theory of elasticity. Tokyo.

 

Accepted for print: 10.10.2006

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Mateusz Stasiak
Department of Physical and Technological Properties
of Agricultural Materials, Institute of Agrophysics,
Polish Academy of Science, Lublin, Poland
Doświadczalna 4,
P.O. Box 201, 20-290 Lublin 27, Poland
Phone: (+48) 81 743 85 58
Fax: (+48) 81 744 50 67
email: mstasiak@ipan.lublin.pl

Marek Molenda
Department of Physical and Technological Properties
of Agricultural Materials, Institute of Agrophysics,
Polish Academy of Science, Lublin, Poland
Doświadczalna 4,
P.O. Box 201, 20-290 Lublin 27, Poland

Józef Horabik
Institute of Agrophysics,
Polish Academy of Sciences, Lublin, Poland
Doświadczalna 4, 20-290 Lubln 27, Poland
phone: (+48 81) 744 50 61
fax (+48 81) 744 50 67

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