- Email: [email protected]
Some Viscoelastic Properties of Sugar Beet- and Carrot Roots
3rd IFAC/CIGR Workshop on Control Applications in Post-Harvest and Processing Technology, October 3-5, 2001, Tokyo, Japan
SOME VISCOELASTlC PROPERTIES OF SUGAR BEET- AND CARROT ROOTS
K. A. Golacki
Department o/Technical Sciences, University 0/Agriculture in Lub/in Doswiadczalna 50a, 20280 Lublin, Poland
Abstract: The aim of the work was the new attempt to estimation of the amount of inner micro damages in plant materials during deformation on the base of viscoelastic characteristics. The procedure requires two values of energy: the really one absorbed by the sample and the other which is calculated on the base of the rheological model. The difference between two energy values might be an indicator of the degree of sample damage. The experiments were carried out in quasi-static and impact loading conditions. Copyright CJ 2000 IFAC Keywords: Energy of deformation, viscoelasticity, micro damages
1. INTRODUCTION Plant materials with high level of water content including sugar beet- and carrot roots are especially exposed to damage during harvesting and cleaning processes, clamp building, transport and factory intake. Then roots are subjected to impacts and compression, which may cause different kinds of damage such as root breakage, bruising, splitting and surface abrasion. Recent studies have indicated that existing harvesting technology allows a decrease of the level of damage. However, the increase of requirements of roots cleanliness at consecutive stages of handling process contributes towards production of new damage. In spite of usually distinguished damage defmed on the base of their depth and shape, there are many internal damage. Even small amount of energy applied by the sample can be enough to cause tissue degradation and production of enzymatic reaction which is followed by sucrose losses and decay process. In order to better understanding bruising susceptibility the viscoelastic reaction of the roots on various kinds of mechanical loading was determined in this paper. To obtain viscoelastic properties plant material was subjected to
- 223-
preliminary deformation. This process was followed by the stress relaxation process, which characterises partly damaged material different from the material in its early stage. Therefore, parameters obtained in the results of stress relaxation tests were different depending the course of deformation and the amount of inner micro damage. In this paper it was assumed that generalised Maxwell model describes well the stress relaxation behaviour after preliminary deformation (Sitkey, 1986). On the base of experimental force-time curve it was easy to calculate both energy absorbed by the sample and parameters of the rheological model. Knowing the values of parameters of that model and strain history we could calculate energy required for deformation of the model in the conditions similar to those in the experiment. In this way we could obtain two values of the same energy: one really absorbed by the sample in the experiment and the other which was calculated for the model. The comparison of both energy values could give the answer to the question: how many inner micro damage appear in the material as a result of various loading conditions?
2. MATERIALS AND METHODS Experiments were carried out on sugar beet roots of the Korab variety and carrot roots of the Perfekcja variety. Roots were picked in October and underwent compression and stress relaxation test between two and five days after picking. In the same time carrot roots underwent impact test.
2. I.Compresion and stress relaxation test. The carrot root samples used in this test were cylindrical with the same diameter and length of 26 mm. That value of diameter allowed keeping the natural proportion of two basic tissues in carrot root: cortex and core. Samples were compressed axially between two parallel plates using Instron device. Five various rate of initial defonnation from the range 8.33·10-~ m/s to 3.33.10-3 were used. On reaching the strain 0.08 mm/mm (Le. defonnation equal 2.08 mm) the compression was stopped. The force response with tine was recorded for a period of 120 sec. Sugar beet roots samples used in compression and stress relaxation test were cylindrical as well with the same diameter and length of 20 mm. The test was designed to detennine the influence of initial defonnation rate on the course of stress relaxation functions of two types of samples cut from the same root and axially compressed. One specimen was free to expand in the radial direction while the other one was constrained - compressed in a special rigid chamber (Hughes and Segerlind, 1972). Three values of rate of defonnation 3.33·10-4 m/s, 1.66.10-3 m/s and 3.33.10-3 m/s were used. The initial strain value was established at the level of 0.16 mm/mm (Le. defonnation equal 3.2 mm). Stress relaxation measurements were made on the same devices and in the same condition like in the case of carrot roots. Initial strain caused stress equals relatively about 30% of failure stress for both kinds of roots.
2.3. Theoretical description.
The method described by Chen and Fridley (1972) and Mohsenin (1970) was used for the theoretical description of phenomenon of stress relaxation in cylindrically shaped plant material. Maxwell body was used as a mechanical model of carrot root samples. In this model the rate of preliminary assigned defonnation was taken into account. Therefore presented model took the stress relaxation into consideration, which occurred during the time of preliminary defonnation. The obtained experimental curves were approximated numerically by means of exponential equation (1): 3
F(t) = LA;e-a;l,
(I)
;=1
where: F(t) - reaction force of a sample during stress relaxation experiment, Ai, u; - coefficients. The reaction force of cylindrically shaped Maxwell body compressed axially at the fixed rate could be described as Chen and Fridley (1972):
F(t) =
S r l~ fr{m ial!j -tj_dc,je 3
~
-5.(/.-l j ) } 'I,
e
~(I-l.) 'I,
(2)
where: S - sample cross-sectional area, I - sample length, a - rate of defonnation, tm - time of defonnation. Parameters E j and 11; could be calculated after comparing two fonnulas (I) and (2). The next step was the calculation of energy required for the hypothetical defonnation of the sample model in the same conditions like those in the experiment. The energy absorbed by the sample model during compression or impact could be expressed as: A",
ec =
'",
fF(l)dl = fF{t) a dt
(3)
o 0 where: 'A. - defonnation ('A. = a t), 'A.... - maximum defonnation ('A.... = a tm).
2.2. Impact and stress relaxation test.
To expand the range of rate of initial defonnation carrot roots underwent impact test. In this kind of test the same samples (diameter and length equal 26 mm) were impacted at four rates: 0.5 m/s, 1.0 m/s, 1.5 m/s and 2.0 m/s. A special impact device (Golacki, et aI., 1999) that can limit the maximum defonnation of each sample was used. On reaching the defonnation equal 2.08 mm impact was stopped and force response with time was recorded a on data logger for 120 sec.
By putting the equation (2) into equation (3) we received the final fonnula for expression of the energy absorbed by the sample model. Energy ec could be calculated numerically. The energy absorbed by the sample in the experiment (ea) was calculated on the base of the area situated under reaction-force curve within the growth of defonnation.
3. RESULTS AND DISCUSSION As a result of the experiments the force-time curves for carrot roots samples pressed and impacted axially were obtained. Similar curves were obtained for
- 224-
240r--~-~~_~~
~ ~ ,g c .2 U ~
230 220 210 200
o
0,30
o
o o
o
0
o
190 '0 180 § 170 .~ 160 )( ~
_ _~ ~_ _---'
0,26
5:
o
8
g
° 0,22
Gl
>. ~
0,18
c
0,14
•
Gl
w
234
5
6
7
8
9
0
10
2
c:
o
~
'0
7
9
8
10
r---~--~-~~----'
o o
0,78
constrained unconstrained
5.:
800
0,72
_------------1---
o Gl
t~ _____________
iiIII
6
5
Fig. 3. The effect of deformation rate on energy absorbed by the carrot root sample (ea) and energy calculated for the sample model (et). Description of numbers of deformation rate see fig. 1. 0,84
'-.... ....
4
3
Number of deformation rate
1200
~
• •
0,10
Fig. 1. The effect of deformation rate on maximum of reaction force for carrot roots during preliminary deformation. Identification the numbers of deformation rate: I - 8.33 10's m/s, 2 - 3.33 10-4 m/s, 3 - 8.33 10,4 m/s, 4 - 1.66 10-3 m/s, 5 - 3.33 10.3 m/s, 6 - 0.5 m/s, 7 - 1.0 m/s, 8 - 1.5 m/s, 9 - 2.0 m/so
.E
• • • I
0
150L......~~~~~_~~ _ _~_ _......J
o
~ B
···i··. . ··i...i ~ I • • ....,
..
o
8
s
0 []
Gl
Number of deformation rate
z
"n.... e. ...... ec
.. 0,66
I
Gl
0,60
400
0,54 '--_ _
E
~
__
~
__
~
_
___l
::J
E
.~
::::!:
o
0,000
0,000 0,001
0,002
0,003
0,001
Fig. 2. The effect of deformation rate on maximum of reaction force for constrained and unconstrained samples of sugar beet root during preliminary deformation.
0,004
Fig. 4. The effect of deformation rate on energy absorbed by the unconstrained sugar beet samples (ea) and energy calculated for the sample model (et). 0,32 0
0,28
sugar beet samples pressed as a constrained and unconstrained. Fig. 1 shows the influence of the rate of deformation on maximum force value necessary for 8% deformation of the sample. In quasi-static loading conditions (numbers of deformation rate from 1 to 5) the maximum force value increased with the increase of the deformation rate. In the case of impact loading (numbers of deformation rate from 6 to 9) the maximum force showed a large scatter of values. The tendency to increase of maximum reaction force for constrained and unconstrained sugar beet samples with increase of deformation rate presented fig. 2. This results showed that tested materials behaved like typical viscoelastic body within the quasi static range of loading.
0,003
Rate of deformation [m/s]
0,004
Rate of deformation [m/s)
0,002
0,24 2-
0,20
0
..
Gl
0,16
Gl
0,12 0,08 0,04 0,000
u.... ~ ea
0
~
•• --0--_
0
0
[]
~
. o
0,001
~
------------ --.
• 0,002
0,003
0,004
Rate of deformation [m/s)
Fig. 5. The effect of deformation rate on energy absorbed by the constrained sugar beet samples (ea) and energy calculated for the sample model (et). Fig. 3, 4 and 5 showed the influence of the deformation rate on the values of the two energies: absorbed by the sample and calculated for the model. et values were lover in comparison with adequate
- 225-
values of e.. It means that for deformation of all kinds of the samples more energy is needed than for hypothetical deformation of the model under identical conditions like those in the experiment. In spite of the existence of the difference of e. and eo we could not confirm the inadequacy of the carrot and sugar beet root model. The model identified the sample on the base of the stress relaxation course after the load application. Thus except for the deformation of viscoelastic nature micro damage and other phenomena of plastic nature could appear in this samples. The difference of two energy values e. eo increased with the increase of deformation speed in quasi-static and impact loading conditions. Therefore it seemed to be a proof that the number of internal micro damage in carrot root tissue increases at the higher speed of deformation. It was interesting to observe the tendency of decrease in the energy value calculated for the model (eo) at the highest of the used deformation speeds (fig. 3). It was caused by the decreased values of coefficients Ei and T]i., which were used in calculation of eo (formula 2 and 3). These coefficients represented elasticity and viscosity decrease after the application of deformation at higher speed. It might be suspected that there was a certain border of deformation speed and crossing it could result in the rapid increase of the number of micro damage in the tested material. In quasi-static conditions the fluid flow in the tissue material meets the increase of resistance and therefore some cell walls might break as a result of increased tension. In impact conditions the time is too short for the fluid flow and the material behaves rather like an elastic body. The lack of time for the fluid flow in the material causes damage, which appear earlier in the course of deformation. That might be confIrmed by the fact of increased subtraction e. - eo when compared with objectively absorbed energy e. - indicator P (fig. 6 and 7).
50
;?
P = (ea - ec)/ea
e....
30
B
20
0
0 0
8
0,3
-B
0,2
B
a.
...0
...... unconstrained
B
'6 E 0,1
'u..
constrained
•
.....·······..·········..··i··
0,0 0
6e-4 0,001 0,002 0,002 0,003 0,004 Rate of deformation (mls]
Fig. 7. The effect of deformation rate on indicator P for constrained and unconstrained sugar beat samples. The full verification of all the results of presented investigation is difficult at this point. The efficient quantitative method of the evaluation of the degree of damage of plant tissue with high water content is not known. Some information on the subject might be obtained by the analysis of the deformed tissue with the electronic microscope (Konstankiewicz, et al., 1997), (Rodriguez, et aI., 1990). It seems that this method is not suitable in the case of this work as it is rather qualitative not quantitative method. The use of the method of chemical analysis might be efficacious to estimate the number of micro damages in plant material.
4. CONCLUSION It was found that the difference between two energy
values might be an indicator of the degree of plant materials damage. Results of investigation for carrot roots showed that might be a certain rate of deformation limit exceeding of which results in rapid increase of the numbers of micro damages in tested material.
0
ACKNOWLEDGMENTS
0
0
0
.9
'6 E
~
e
40
a....
0,4
This work has been partly supported by Polish Committee of Scientific Research under grant 5P06 F006/19
0
10 0
REFERENCES 0
2
3
4
5
6
7
8
9
10
Number of deformation rate
Fig. 6. The effect of deformation rate on indicator P for carrot root samples. Description of numbers of deformation rate - see fig. 1.
Chen, P., R.B. Fridley (1972). Analytical method for determining viscoelastic constants of agricultural products. Transaction of the ASAE, 15(6), 11031106. Golacki, K., Z. Stropek and A. Grabos (1999). Test relaksacji napr~zen w materiale biologicznym w warunkach obcil\.zenia dynamicznego - realizacja techniczna Intynieria Rolnicza, 2, 55-61 (in Polish).
- 226-
Hughes, H., L.J. Segerlind (1972) A rapid mechanical method for determining Poisson's ratio in biological materials. ASAE Paper No. 72-310, ASAE, St. Joseph, MI 49085. Konstankiewicz, K., A. Kr61, B. Stoczkowska (1997). Microscopic methods for the investigations of plant tissue. 6th Int. Conference of Agrophysics, Book of Abstracts 2, 251-252. Mohsenin, N. N. (1970). Physical properties ofplant and animal materials. Gordon and Breach Science Publishers, Vol. I. New York.
Murrase, H., G. E. Merva, L. I. Segerlind (1979). Failure mode of vegetative tissue. ASAE Paper No. 79-3064. Rodriguez, L. M., M. Ruiz, M. R. De Felipe (1990). Differences in the structural responses of "GranySmith" apples under mechanical impact and compression. Journal of Texture Studies, 21, 155164. Sitkey, G. (1986). Mechanics of agricultural materials. Akademia Kiado, Budapest.
- 227-
SOME VISCOELASTlC PROPERTIES OF SUGAR BEET- AND CARROT ROOTS
K. A. Golacki
Department o/Technical Sciences, University 0/Agriculture in Lub/in Doswiadczalna 50a, 20280 Lublin, Poland
Abstract: The aim of the work was the new attempt to estimation of the amount of inner micro damages in plant materials during deformation on the base of viscoelastic characteristics. The procedure requires two values of energy: the really one absorbed by the sample and the other which is calculated on the base of the rheological model. The difference between two energy values might be an indicator of the degree of sample damage. The experiments were carried out in quasi-static and impact loading conditions. Copyright CJ 2000 IFAC Keywords: Energy of deformation, viscoelasticity, micro damages
1. INTRODUCTION Plant materials with high level of water content including sugar beet- and carrot roots are especially exposed to damage during harvesting and cleaning processes, clamp building, transport and factory intake. Then roots are subjected to impacts and compression, which may cause different kinds of damage such as root breakage, bruising, splitting and surface abrasion. Recent studies have indicated that existing harvesting technology allows a decrease of the level of damage. However, the increase of requirements of roots cleanliness at consecutive stages of handling process contributes towards production of new damage. In spite of usually distinguished damage defmed on the base of their depth and shape, there are many internal damage. Even small amount of energy applied by the sample can be enough to cause tissue degradation and production of enzymatic reaction which is followed by sucrose losses and decay process. In order to better understanding bruising susceptibility the viscoelastic reaction of the roots on various kinds of mechanical loading was determined in this paper. To obtain viscoelastic properties plant material was subjected to
- 223-
preliminary deformation. This process was followed by the stress relaxation process, which characterises partly damaged material different from the material in its early stage. Therefore, parameters obtained in the results of stress relaxation tests were different depending the course of deformation and the amount of inner micro damage. In this paper it was assumed that generalised Maxwell model describes well the stress relaxation behaviour after preliminary deformation (Sitkey, 1986). On the base of experimental force-time curve it was easy to calculate both energy absorbed by the sample and parameters of the rheological model. Knowing the values of parameters of that model and strain history we could calculate energy required for deformation of the model in the conditions similar to those in the experiment. In this way we could obtain two values of the same energy: one really absorbed by the sample in the experiment and the other which was calculated for the model. The comparison of both energy values could give the answer to the question: how many inner micro damage appear in the material as a result of various loading conditions?
2. MATERIALS AND METHODS Experiments were carried out on sugar beet roots of the Korab variety and carrot roots of the Perfekcja variety. Roots were picked in October and underwent compression and stress relaxation test between two and five days after picking. In the same time carrot roots underwent impact test.
2. I.Compresion and stress relaxation test. The carrot root samples used in this test were cylindrical with the same diameter and length of 26 mm. That value of diameter allowed keeping the natural proportion of two basic tissues in carrot root: cortex and core. Samples were compressed axially between two parallel plates using Instron device. Five various rate of initial defonnation from the range 8.33·10-~ m/s to 3.33.10-3 were used. On reaching the strain 0.08 mm/mm (Le. defonnation equal 2.08 mm) the compression was stopped. The force response with tine was recorded for a period of 120 sec. Sugar beet roots samples used in compression and stress relaxation test were cylindrical as well with the same diameter and length of 20 mm. The test was designed to detennine the influence of initial defonnation rate on the course of stress relaxation functions of two types of samples cut from the same root and axially compressed. One specimen was free to expand in the radial direction while the other one was constrained - compressed in a special rigid chamber (Hughes and Segerlind, 1972). Three values of rate of defonnation 3.33·10-4 m/s, 1.66.10-3 m/s and 3.33.10-3 m/s were used. The initial strain value was established at the level of 0.16 mm/mm (Le. defonnation equal 3.2 mm). Stress relaxation measurements were made on the same devices and in the same condition like in the case of carrot roots. Initial strain caused stress equals relatively about 30% of failure stress for both kinds of roots.
2.3. Theoretical description.
The method described by Chen and Fridley (1972) and Mohsenin (1970) was used for the theoretical description of phenomenon of stress relaxation in cylindrically shaped plant material. Maxwell body was used as a mechanical model of carrot root samples. In this model the rate of preliminary assigned defonnation was taken into account. Therefore presented model took the stress relaxation into consideration, which occurred during the time of preliminary defonnation. The obtained experimental curves were approximated numerically by means of exponential equation (1): 3
F(t) = LA;e-a;l,
(I)
;=1
where: F(t) - reaction force of a sample during stress relaxation experiment, Ai, u; - coefficients. The reaction force of cylindrically shaped Maxwell body compressed axially at the fixed rate could be described as Chen and Fridley (1972):
F(t) =
S r l~ fr{m ial!j -tj_dc,je 3
~
-5.(/.-l j ) } 'I,
e
~(I-l.) 'I,
(2)
where: S - sample cross-sectional area, I - sample length, a - rate of defonnation, tm - time of defonnation. Parameters E j and 11; could be calculated after comparing two fonnulas (I) and (2). The next step was the calculation of energy required for the hypothetical defonnation of the sample model in the same conditions like those in the experiment. The energy absorbed by the sample model during compression or impact could be expressed as: A",
ec =
'",
fF(l)dl = fF{t) a dt
(3)
o 0 where: 'A. - defonnation ('A. = a t), 'A.... - maximum defonnation ('A.... = a tm).
2.2. Impact and stress relaxation test.
To expand the range of rate of initial defonnation carrot roots underwent impact test. In this kind of test the same samples (diameter and length equal 26 mm) were impacted at four rates: 0.5 m/s, 1.0 m/s, 1.5 m/s and 2.0 m/s. A special impact device (Golacki, et aI., 1999) that can limit the maximum defonnation of each sample was used. On reaching the defonnation equal 2.08 mm impact was stopped and force response with time was recorded a on data logger for 120 sec.
By putting the equation (2) into equation (3) we received the final fonnula for expression of the energy absorbed by the sample model. Energy ec could be calculated numerically. The energy absorbed by the sample in the experiment (ea) was calculated on the base of the area situated under reaction-force curve within the growth of defonnation.
3. RESULTS AND DISCUSSION As a result of the experiments the force-time curves for carrot roots samples pressed and impacted axially were obtained. Similar curves were obtained for
- 224-
240r--~-~~_~~
~ ~ ,g c .2 U ~
230 220 210 200
o
0,30
o
o o
o
0
o
190 '0 180 § 170 .~ 160 )( ~
_ _~ ~_ _---'
0,26
5:
o
8
g
° 0,22
Gl
>. ~
0,18
c
0,14
•
Gl
w
234
5
6
7
8
9
0
10
2
c:
o
~
'0
7
9
8
10
r---~--~-~~----'
o o
0,78
constrained unconstrained
5.:
800
0,72
_------------1---
o Gl
t~ _____________
iiIII
6
5
Fig. 3. The effect of deformation rate on energy absorbed by the carrot root sample (ea) and energy calculated for the sample model (et). Description of numbers of deformation rate see fig. 1. 0,84
'-.... ....
4
3
Number of deformation rate
1200
~
• •
0,10
Fig. 1. The effect of deformation rate on maximum of reaction force for carrot roots during preliminary deformation. Identification the numbers of deformation rate: I - 8.33 10's m/s, 2 - 3.33 10-4 m/s, 3 - 8.33 10,4 m/s, 4 - 1.66 10-3 m/s, 5 - 3.33 10.3 m/s, 6 - 0.5 m/s, 7 - 1.0 m/s, 8 - 1.5 m/s, 9 - 2.0 m/so
.E
• • • I
0
150L......~~~~~_~~ _ _~_ _......J
o
~ B
···i··. . ··i...i ~ I • • ....,
..
o
8
s
0 []
Gl
Number of deformation rate
z
"n.... e. ...... ec
.. 0,66
I
Gl
0,60
400
0,54 '--_ _
E
~
__
~
__
~
_
___l
::J
E
.~
::::!:
o
0,000
0,000 0,001
0,002
0,003
0,001
Fig. 2. The effect of deformation rate on maximum of reaction force for constrained and unconstrained samples of sugar beet root during preliminary deformation.
0,004
Fig. 4. The effect of deformation rate on energy absorbed by the unconstrained sugar beet samples (ea) and energy calculated for the sample model (et). 0,32 0
0,28
sugar beet samples pressed as a constrained and unconstrained. Fig. 1 shows the influence of the rate of deformation on maximum force value necessary for 8% deformation of the sample. In quasi-static loading conditions (numbers of deformation rate from 1 to 5) the maximum force value increased with the increase of the deformation rate. In the case of impact loading (numbers of deformation rate from 6 to 9) the maximum force showed a large scatter of values. The tendency to increase of maximum reaction force for constrained and unconstrained sugar beet samples with increase of deformation rate presented fig. 2. This results showed that tested materials behaved like typical viscoelastic body within the quasi static range of loading.
0,003
Rate of deformation [m/s]
0,004
Rate of deformation [m/s)
0,002
0,24 2-
0,20
0
..
Gl
0,16
Gl
0,12 0,08 0,04 0,000
u.... ~ ea
0
~
•• --0--_
0
0
[]
~
. o
0,001
~
------------ --.
• 0,002
0,003
0,004
Rate of deformation [m/s)
Fig. 5. The effect of deformation rate on energy absorbed by the constrained sugar beet samples (ea) and energy calculated for the sample model (et). Fig. 3, 4 and 5 showed the influence of the deformation rate on the values of the two energies: absorbed by the sample and calculated for the model. et values were lover in comparison with adequate
- 225-
values of e.. It means that for deformation of all kinds of the samples more energy is needed than for hypothetical deformation of the model under identical conditions like those in the experiment. In spite of the existence of the difference of e. and eo we could not confirm the inadequacy of the carrot and sugar beet root model. The model identified the sample on the base of the stress relaxation course after the load application. Thus except for the deformation of viscoelastic nature micro damage and other phenomena of plastic nature could appear in this samples. The difference of two energy values e. eo increased with the increase of deformation speed in quasi-static and impact loading conditions. Therefore it seemed to be a proof that the number of internal micro damage in carrot root tissue increases at the higher speed of deformation. It was interesting to observe the tendency of decrease in the energy value calculated for the model (eo) at the highest of the used deformation speeds (fig. 3). It was caused by the decreased values of coefficients Ei and T]i., which were used in calculation of eo (formula 2 and 3). These coefficients represented elasticity and viscosity decrease after the application of deformation at higher speed. It might be suspected that there was a certain border of deformation speed and crossing it could result in the rapid increase of the number of micro damage in the tested material. In quasi-static conditions the fluid flow in the tissue material meets the increase of resistance and therefore some cell walls might break as a result of increased tension. In impact conditions the time is too short for the fluid flow and the material behaves rather like an elastic body. The lack of time for the fluid flow in the material causes damage, which appear earlier in the course of deformation. That might be confIrmed by the fact of increased subtraction e. - eo when compared with objectively absorbed energy e. - indicator P (fig. 6 and 7).
50
;?
P = (ea - ec)/ea
e....
30
B
20
0
0 0
8
0,3
-B
0,2
B
a.
...0
...... unconstrained
B
'6 E 0,1
'u..
constrained
•
.....·······..·········..··i··
0,0 0
6e-4 0,001 0,002 0,002 0,003 0,004 Rate of deformation (mls]
Fig. 7. The effect of deformation rate on indicator P for constrained and unconstrained sugar beat samples. The full verification of all the results of presented investigation is difficult at this point. The efficient quantitative method of the evaluation of the degree of damage of plant tissue with high water content is not known. Some information on the subject might be obtained by the analysis of the deformed tissue with the electronic microscope (Konstankiewicz, et al., 1997), (Rodriguez, et aI., 1990). It seems that this method is not suitable in the case of this work as it is rather qualitative not quantitative method. The use of the method of chemical analysis might be efficacious to estimate the number of micro damages in plant material.
4. CONCLUSION It was found that the difference between two energy
values might be an indicator of the degree of plant materials damage. Results of investigation for carrot roots showed that might be a certain rate of deformation limit exceeding of which results in rapid increase of the numbers of micro damages in tested material.
0
ACKNOWLEDGMENTS
0
0
0
.9
'6 E
~
e
40
a....
0,4
This work has been partly supported by Polish Committee of Scientific Research under grant 5P06 F006/19
0
10 0
REFERENCES 0
2
3
4
5
6
7
8
9
10
Number of deformation rate
Fig. 6. The effect of deformation rate on indicator P for carrot root samples. Description of numbers of deformation rate - see fig. 1.
Chen, P., R.B. Fridley (1972). Analytical method for determining viscoelastic constants of agricultural products. Transaction of the ASAE, 15(6), 11031106. Golacki, K., Z. Stropek and A. Grabos (1999). Test relaksacji napr~zen w materiale biologicznym w warunkach obcil\.zenia dynamicznego - realizacja techniczna Intynieria Rolnicza, 2, 55-61 (in Polish).
- 226-
Hughes, H., L.J. Segerlind (1972) A rapid mechanical method for determining Poisson's ratio in biological materials. ASAE Paper No. 72-310, ASAE, St. Joseph, MI 49085. Konstankiewicz, K., A. Kr61, B. Stoczkowska (1997). Microscopic methods for the investigations of plant tissue. 6th Int. Conference of Agrophysics, Book of Abstracts 2, 251-252. Mohsenin, N. N. (1970). Physical properties ofplant and animal materials. Gordon and Breach Science Publishers, Vol. I. New York.
Murrase, H., G. E. Merva, L. I. Segerlind (1979). Failure mode of vegetative tissue. ASAE Paper No. 79-3064. Rodriguez, L. M., M. Ruiz, M. R. De Felipe (1990). Differences in the structural responses of "GranySmith" apples under mechanical impact and compression. Journal of Texture Studies, 21, 155164. Sitkey, G. (1986). Mechanics of agricultural materials. Akademia Kiado, Budapest.
- 227-