Changing the rheological features of AG-BAG type packaging foil tubes depending on temperature Csatár Attila – Dr. Bellus Zoltán – Dr. Csorba László Hungarian Institute of Agricultural Engineering (MGI) Hungary-2100 Gödöllő, Tessedik S.u.4. Tel: +36-28-511-633 and +36-28-511-649 E-mail:
[email protected],
[email protected],
[email protected] Summary Our goal was to determine the changing of stresses developing in the foils used in foil loading presser machines, depending on the time. We used a viscoelastic model, the PoyntingThomson model during the tests. Our tests were applied between –20 and 45˚C. To determine the displacements and stresses that rise in the foil tube, we have made calculations with the COSMOS/M finite element software package using the analised parameters.
1. INTRODUCTION For preservation and storing of fodder tubular films were generally used in practice in the latest 8-10 years in Hungary. But the examiniations in connection with the method did not study the strength and rheological features of the foil as an individual material. New challenges (high quality end-product, environment protection, new designs, etc.) appear in the Hungarian forage experience accordingt to the EU requirements in the future. This makes inevitable to change the obsolescent technologies in our country, that are operating with many losses and loading the environment. The following data prove the spreading of the new method: Preservation and storing in tubular films started to penetrate in 1997-98 and now we can say that it is used in more than 35 farms. The application was the largest in 2004 when 85-90 000 tonns of sugar-beet chips, around 65 000 tonns of hay silage and about 25 000 tonns of wet corn grit, corn silo, corn cob grit and other agricultural secondary products (cornpeel, marcs, screenings of wet cereals, etc.) has been filled into foil tubes. Considering that about 200 tonns of fodder can be filled in a commonly used (Ø3 m x 60 m) foil tube, we can say that about 850-900 pieces of tubes have been released into commerce.
2. MATERIAL AND METHOD The Poynting-Thomson model The simplest of the linear, rheological models that can describe the creeping and relaxation properties is the Poynting-Thomson model. The differencial equation that describes the connection between the stresses and elongations in uniaxial state is the following: σ + b1σ& = a 0ε + a1ε& , where σ is the stress [MPa], σ& is the time derivative of the stress [MPa/s], ε is the specific elongation [1], ε& is the time derivative of the specific elongation [1/s], and a0,a1,b1 are constant parameters.
Rheological models are generally simulating with systems made of springs and dampings. Within the different rheological models one system can be advantageous for analysing creeping and other for analysing relaxation. Models of the Poynting-Thomson test „Creep” model:
σ+
η3 E1 + E 3
σ& =
E1 ⋅ E 3 E ⋅η ε + 1 3 ε& , E1 + E 3 E1 + E3
„Relaxation” model:
σ+
η2 E2
⋅ σ& = E0 ⋅ ε + η 2 (1 +
E0 )ε& . E2
Relaxation test: We call direct relaxation when we create ε (t = 0) = ε a specific elongation in the t = 0 moment on the specimen and we keep it constant: ε& (t ) = 0. With this circumstances, by solving the differencial equation written above, we get the equation of the relaxation curve:
σ (t ) = ε a ( E 0 + E 2 e
−
E2
η2
t
).
The following figure shows the changing of the specific elongation and specific stress depending on time:
ε εa
t
σ σa σ
R -
The t R =
tR
t
η2
time in the figure is the relaxation time. During this period approx. 60% of the E2 stress decrease occurs. The E0 , E 2 ,η 2 parameters that represent the rheological features of the tested material can be determined with the help of the σ (t ) function that is matched to the points that were set on the tension tester, using the least squares method: n
∆( E0 , E2 ,η 2 ) = ∑{σ i − [ E0ε a + E2ε a ) ⋅ e
−
E2t i
η2
]}2
i =1
where σ i is the measured stress at t i moment and the amount in the brackets is the calculated stress at t i moment. The searched parameters are the solutions of the following equations:
∂∆ = 0, ∂E0
∂∆ = 0, ∂E2
∂∆ = 0, ∂η 2
The tests were processed by using an INSTRON 5581 type test machine completed with an INSTRON 3119 type liquid carbon-dioxide air conditioning system. The tests were applied between –20 and 45˚C. We expanded the foil at a high 500 mm/min speed by 5 mm and then we left the system alone for 2 hours.
INSTRON 5581 type tester and INSTRON 3119 type liquid carbon-dioxide air conditioning system
3. RESULTS We evaluated the results with using the Solver application of the Excel software package. The following chart contains the results of the measurements and calculations. Temperature [°C]
45
40
30
38,38 12,69 19332,85
51,30 13,27 7407,64
57,48 24,95 54116,34
20
10
0
-10
-20
110,70 39,03 47909,45
121,12 37,80 67474,26
119,21 49,62 72213,06
Constants of Modell: E0 E2 h2
MPa MPa MPa*s
92,17 92,98 31,11 40,08 8665,08 22398,50
Parameters of Diff.equation: ao a1 b1
MPa MPa*s s
38,38 51,30 57,48 92,17 92,98 110,70 121,12 119,21 77793,79 36046,24 178788,55 34336,29 74365,77 183805,47 283702,70 245697,68 1523,25 558,26 2169,10 278,52 558,88 1227,61 1785,22 1455,24
Parameters for COSMOS/M: Ex n g tRG
MPa (Poisson ratio) s
51,07 0,24 0,57
64,57 0,24 0,55
82,43 0,24 0,60
123,28 0,24 0,57
133,06 0,24 0,60
149,73 0,24 0,58
158,92 0,24 0,57
168,84 0,24 0,60
1775,31
753,07
2187,72
320,89
565,67
1380,63
2150,90
1499,00
11,50 51,07
14,54 64,57
18,56 82,43
27,77 123,28
29,97 133,06
33,72 149,73
35,79 158,92
38,03 168,84
Secondary calc. K Ea
-
The following figures show the measured and calculated relaxation curves at different temperatures. Relaxation test (-20°C) Stress [MPa]
18 16 14
Measured Stress [MPa]
Calc. Stress [MPa]
12 10 8 6 4 2 Time [s] 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Stress-time diagram of the foil -20°C
Relaxation test (0°C) Stress [MPa]
18 16 14
Measured Stress [MPa]
Calc. Stress [MPa]
12 10 8 6 4 2 Time [s] 0 0
1000
2000
3000
4000
5000
Stress-time diagram of the foil 0°C
6000
7000
8000
Relaxation test (40°C) Stress [MPa]
18 16 14
Measured Stress [MPa]
Calc. Stress [MPa]
12 10 8 6 4 2 Time [s] 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Stress-time diagram of the foil 40°C We have made calculations to determine the displacements and stresses that rise in the foil tube (we have tried to simulate the characteristics of the material in the tube with the characteristics of the sugar beet chip), we have made calculations with the COSMOS/M finite element software package using the analised parameters. We converted the results we got during the matching of the curves to the program to COSMOS/M 2.85 Electronic DocumentationNonlinear Structural Analysis [(NSTA) Structural Research & Analysis Corporation Los Angeles, California 2003]. We considered the mechanical features of the filling constant at all temperatures. EX 1.000000e+005 NUXY 3.000000e-001 GXY 1.000000e+003 DENS 1.500000e+003 This way we ensured the rate of the load, caused by the gravity to be the same at the chosen temperatures. The results of the calculations can be seen on the following figures.
Stress distribution of the foil at -20°C
Stress distribution of the foil at 0°C
Stress distribution of the foil at 45°C
The movements of the top point and the maximum reduced stresses (Huber-Mises-Henky) can be seen in the following chart: °C -20 -10 0 10 20 30 40 45
σ HMH ,max [MPa] 21,4 20,8 20 18 16,8 13,7 11,19 9,57
y max [m] -0,724 -0,725 -0,726 -0,7288 -0,7307 -0,7333 -0,735 -0,7362
Diagrams drawn based on the data of the chart: Sters [MPa]
Stress-Temperature y = -0,1861x + 19,107 R2 = 0,9501
25
20
15
10
5
Temp. [°C] 0 -30
-20
-30
-20
-10
0
10
20
30
40
50
Displacement-Temperature -10
0
10
20
30
40
50 Disp. [m]
-0,722 Temp. [°C]
-0,724 -0,726 -0,728 -0,73 -0,732 -0,734
y = -0,0002x - 0,727 R2 = 0,9854
-0,736 -0,738
LITERATURE
Csatár Attila - Dr. Csorba László: Műanyag csomagoló- és takaró fóliák reólogiai vizsgálata Mezőgazdasági Gépesítési Tanulmányok, Gödöllő, 2004. COSMOS/M 2.85 Electronic Documentation Nonlinear Structural Analysis (NSTA) Structural Research & Analysis Corporation Los Angeles, California 2003 Müller Zoltán: Classification of Rheological Models Composed of Springs and Dashpots. Zeszyty Problemowe Postepow Nauk Rolniczych 1976, z. 168. Müller Zoltán: Mezőgazdasági anyagok mechanikai vizsgálata. Gödöllő, 1988.és 2003. (Jegyzet) Sitkei György: Mezőgazdasági anyagok mechanikája Körmend, 1972. Kézirat
