Eindhoven University of Technology - TU/eEindhoven University of Technology Department of Mechanical...
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Eindhoven University of Technology Department of Mechanical Engineering Mechanical Properties of Pre-Deformed Steel Samples Manufactured with a Discrete Die. Subject specialist: MSc. S. H. A. Boers Student: H. W. Slootbeek 0497782
Transcript of Eindhoven University of Technology - TU/eEindhoven University of Technology Department of Mechanical...
Eindhoven University of Technology
Department of Mechanical Engineering
Mechanical Properties of Pre-Deformed Steel Samples Manufactured with a Discrete Die.
Subject specialist: MSc. S. H. A. Boers Student: H. W. Slootbeek 0497782
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Content 1. Introduction on the discrete die and experiments..............................................3
2. The tensile test experiments .............................................................................4
2.1 The scoured and pre-deformed samples.....................................................4
2.2 Solved pre-deformed samples.....................................................................6
2.3 Solved not pre-deformed samples...............................................................7
3. Models for processing data...............................................................................8
3.1 Forces and displacements from the tensile device......................................8
3.2 Lengths computed with the optical microscope...........................................8
3.3 Strains computed with Aramis .....................................................................9
3.4 Computations of stresses..........................................................................10
4. Results............................................................................................................13
4.1 The scoured and pre-deformed samples...................................................13
4.2 Solved pre-deformed samples...................................................................14
4.3 Solved not pre-deformed samples.............................................................18
5. Discussion ......................................................................................................19
6. Conclusion ......................................................................................................20
References .........................................................................................................21
Appendices .........................................................................................................22
Scoured and pre-deformed samples ...............................................................22
Solved and pre-deformed samples..................................................................26
Final group of samples ....................................................................................29
MATLAB® file excel.m .....................................................................................30
MATLAB® file pixel.m ......................................................................................31
MATLAB® file aramis.m...................................................................................33
MATLAB® file sample.m ..................................................................................34
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1. Introduction on the discrete die and experiments Thin sheet metal is used for many products such as licence plates, the outer body shell of vehicles and food or beverage cans. Because these products are produced in vast amounts, it is efficient to design an exclusive mould for these components, which makes production, fast and accurate. However, the outer skin of an exclusive jetfighter for example, consists of many slightly different round parts. Thus designing a specific mould for each component is extremely expensive and time-consuming process, because only a few jetfighters are built. Therefore, an adjustable large-scale discrete mould has been developed to fabricate the elements of the outer shell. The adjustable discrete mould consists of a matrix of square elements, which are individually positioned by small electrical motors [1]. Consequently, the mould can be used for much more components and at lower costs. For manufacturing small metal sheet products a higher resolution is required and recently an alternative discrete mould is designed which can be used for the production of small products [2]. This mould has a working volume in the range of cubic millimetres, instead of cubic metres for the mould of a jetfighter. The mould of the small parts consists of a matrix with one millimetre in diameter cylindrical rods, which are positioned by pressing a computer numerically controlled (CNC) metal block against the rods. After the positioning, a pair of clamps at the side will fix the rods and the mould can be used for manufacturing products. During the test period of the mould a reasonable number of products has been broken as a consequence of too large deformation. Further research has shown that the used sheet material is anisotropic due to the rolling in the fabrication process [3]. In order to predict the failure of the material during manufacturing, a strain-path dependent material model will be used. Validation of the model will be done with the small-scale discrete die. The final goal is to determine a set of intermediate die shapes in order to produce a product with an optimal strain distribution at the end of the manufacturing process. At this moment it would be interesting to determine some material parameters in the deformed state. The tensile strength is an important material property, and plays a key role in the model. Nevertheless, the material parameters such as yield strength and Young’s modulus are also important but are, due to practical constraints, hard to determine and lay beyond the scope of this report. Therefore, this report will examine the tensile strength of pre-deformed 0.2 mm thick steel sheets. This report is divided into six parts. Section two of this report deals with the preparations and procedure of the experiments. Section three describes a model for processing data and Section four shows the results of the experiments. Section 5 points out how the experiments are interpreted. In Section six some conclusions are drawn from the experimental results.
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2. The tensile test experiments Samples with a parabolic bump are manufactured from circular discs of 60 millimetres in diameter, which are prepared out of 0.2 mm thick steel, with a thin PET layer on both sides. The PET layer is scoured away for some samples, while for other samples the PET layer is solved in a chemical solution. Furthermore some samples are pre-deformed while others are not deformed in order to have a reference. Due to the different preparations of the samples for the experiments, this section is divided into three subsections parallel to the three different sample preparations.
• The scoured and pre-deformed samples.
• Solved and pre-deformed samples.
• Solved and not pre-deformed samples.
2.1 The scoured and pre-deformed samples
2.1.1 PET layer removal
Before the PET layer is removed, the rolling direction of the disc is determined and marked with an arrow parallel to the rolling direction. Then sandpaper is used to scour away one half of the PET layer, because afterwards it will be impossible to obtain the rolling direction. Scratches on the disc due to scouring will conceal the rolling direction. After one half of the disc has been scoured an arrow is drawn on the metal in extension of the remaining arrow on the PET layer. Thereafter the other half of the PET layer is scoured away and again arrow is drawn on the metal in extension of the remaining arrow in the metal. Finally, the PET on the other side of the disc is scoured away and after measuring the thickness t0 of the disc, the disc is prepared for pre-deformation.
2.1.2 Determine sample orientation
When the samples are prepared out of the discs, a parameter α is introduced. α determines the angle between the rolling direction and the axial direction of the sample and the tensile direction a
r
during the tensile test. Figure 1. Furthermore a parameter β is introduced which defines the angle between longitudinal angle of the sample and the longitudinal of the pre-deformed bump. The values of α and β are kept zero for the first series of samples.
2.1.3 Disc deformation
Once the orientation of the samples is known, the discs are positioned under the mould and pre-deformed. The pre-
Figure 1 red is rolling direction, blue is sample length and green is bump length
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deformation causes the material to elongate bi-axially in the plane of the disc. Moreover, the elongation in direction is larger than in direction at the centre of the disc [2]. It has also been found that the largest strains are in the centre of the bump and hence the largest thickness reduction is in this point. Here the thickness t is measured, because thickness is an important parameter for determination of the cross section area.
2.1.4 Sample preparation
After the disc has been completely finished a tensile test bar is made out of the disc by electrical discharge machining. (EDM) Figure 2. However, as the disc is round, accurate positioning is rather difficult which is shown in Figure 2. Here the rolling direction arrow on the disc is also shown and it is not parallel to the length of the sample as it should be. After the samples have been prepared from the discs, they are pressed between two smooth squared bars in order to flatten them. It should be checked whether the flattening of the samples gives rise to non-negligible deformations. To complete the sample preparation a second EDM operation has been done to remove any cracks on the edges of the dam, due to flattening of the sample.
2.1.5 Sample testing set-up
Tensile tests have been done with a 500 N load cell mounted in a small tensile test device. Because the thickness of the pre-deformed samples is not homogeneous due to the pre-deformation, the displacement measurement of the tensile device could not be used to determine the strains in the sample. Therefore a few scratches are made on the sample as a reference point. Then the sample is clamped in a tensile device and together they are positioned under an optical microscope. Finally a camera is set on top of the microscope to make pictures of the tensile test at a constant frequency.
2.1.6 Tensile sample testing
During the test, the tensile device applies a constant rate of drawing on the sample in order to break it. After the test, the strains between the reference scratches are determined from the pictures by hand. In combination with the data from the tensile device, stresses in the material are computed by using the force and cross-section at any given moment.
Figure 2 sample out of electrical discharge machined disc.
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2.2 Solved pre-deformed samples
2.2.1 PET layer removal
In the second group of discs, the PET layer is chemically removed by hanging the discs in a solution of 1-methyle-2-pyrolidion at a temperature of 90 degrees Celsius for ten minutes. [4] Then a rolling direction arrow is drawn on the disc and the thickness of the disc is measured.
2.2.2 Sample orientation
In this series the values of α and β are 0, 45 or 90 degrees. There has been tried to have three samples for each combination of α and β but due to unforeseen constrains there are only 9 results for β is equal to zero and varying α and two results for α is equal to β is equal to 45 respectively 90 degrees.
2.2.3 Sample preparation
Nonetheless after the discs have been deformed as described in Section 2.1.3, the thickness in the centre of the disc with the largest deformation is measured. A small notch and holes have been made to fix the disc during the EDM process to prevent the discs to rotate. Figure 3. Finally, the samples are prepared from the discs with an EDM process likewise as described in Section 2.1.4.
2.2.4 Solving sample test problems
The strains are very hard to determine from pictures of the first series because of two reasons. First the contrast of the images is low and second the sample gets out of focus. In order to solve the first problem there is chosen for determining the strains with Aramis. Aramis is a tool that uses the digital image correlation (DIC) technique and Aramis determines the in-plane strain in hundreds of points on the sample. The second problem occurred because the sample is not completely flat at the beginning of the tensile test. Therefore a 30 N pre-load is applied such that the sample remains in focus during the tensile test.
2.2.5 Sample testing
The Aramis software requires a set of digital images of which the gray scale value distributions are compared in order to determine strains. A contrast is artificially applied on the samples with black and white paint. Figure 3. After the sample preparation they are examined in a tensile test and a set of pictures is made with Aramis. Then the strains are determined in about 60 points in the thinnest part of the sample. Figure 3. In combination with the data
Figure 3 samples with notch on the left and holes on both sides.
Figure 3 prepared sample for digital image correlation.
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from the tensile device, stresses in the material are computed by using the force and cross-section at any given moment.
2.3 Solved not pre-deformed samples.
2.3.1 Differences with the previous series
The final group of samples is prepared likewise as discussed in Section 2.2. Only these samples are not pre-deformed which implies that β is not determined. Here has also been tried to have three samples for each α but due to unforeseen constrains there are only two results for α equals zero respectively ninety degrees. Nevertheless, these samples are examined exactly the same way as the previous ones.
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3. Models for processing data After the tests have been done, four data models are written, whereby the test data is processed. These data models are in the appendices, while the most important calculations are explained in the following four subsections.
• Forces and displacements from the tensile device (Excel)
• Lengths computed with the optical microscope (Pixel)
• Strains computed with Aramis (Aramis)
• Computations of stresses (Sample)
3.1 Forces and displacements from the tensile device
The data from the experiment on the tensile device is saved and exported to an EXCEL® file. This file contains the applied displacement ∆L, force F and relative time t of the test. The data is arranged in columns in the EXCEL® file and copied to a matrix EXCEL in a MATLAB®.
∆
∆
∆
=
ppp
iii
n
LFt
LFt
LFt
EXCELMMM
000
(1)
In this formula index n is the number of the sample and the other index i is from zero to p. p is the last measurement of the test and the sample is also broken here. In conclusion at the end of the test Fp equals zero.
3.2 Lengths computed with the optical microscope
As mentioned in previous section, it is not sufficient to use the data from the tensile tester because the thickness of the samples is not homogeneous. Therefore pictures are made with a camera set on top of the microscope. With these pictures the lengths in the sample are determined. Counting the number of pixels and using a conversion factor, determines the distance L between two reference points. The distances between the references and the width of the sample are put in a matrix A in MATLAB®.
=
mxmxmxmy
ixixixiy
xxxy
n
LLLL
LLLL
LLLL
A
,,,,
,,,,
1,1,1,1,
321
321
321
MMMM (2)
In here the index x or y stands for the length respectively the width of the sample. The sub-index stands for the distance between two reference points in length. In addition, the summation of all distances in length at one time step is the length
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between the two outer reference points. Furthermore the index i, is from 1 to m, where m is the final picture or time step at which the sample is broken. Furthermore some extra data is attached to this file. The first value is the thickness t→Lz,1 measured after pre-deformation. The second value is the column xf of A wherein fracture occurs between the reference points.
=
000
0001,
f
z
nx
LN (3)
=
n
n
nN
APIXEL (4)
3.3 Strains computed with Aramis
The strains for each point k are automatically determined and saved in a text file. But as the data is only needed from a small part of the sample, the text files from each photo can only be exported. These text files contain data of every point in the sample at a certain time step. Fortunately these points, which contain the data, are labelled with coordinates. Therefore, it is sufficient to call the coordinates xi in the length of the sample.
( )fcolumn xxxxnx ~~~~~
321= (5)
The tilde on top of a parameter stands for a column, which size is equal to the number of samples. By these parameters the technical stain or engineering strain percentage e% is derived and averaged for each photo, whereupon the strain is converted to the logarithmic strain ε.
+
=∑
= 1100
ln 1
%,
k
ek
i
i
ε (6)
=
fff xyxxx
iyixi
yx
photo
photo
photo
ARAMIS
,,
,,
1,1,1
εε
εε
εε
MMM (7)
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3.4 Computations of stresses
A main file with a calling sequence for all three files is set up in order to process the data from the previous MATLAB® files. In this file the tensile strength TS is computed and various graphs are drawn. To come to these results the files are called as follows:
• The excel file with the forces
• The pixel or aramis file with the lengths respectively strains
3.4.1 The excel file with the forces
First the excel file is called and the rate of drawing vn is computed.
1020
1020
tt
LLvn
−
∆−∆= (8)
The speed is not computed at the start, because of start up errors. After the speed is computed then, dependent on the sample, pixel or aramis is called.
3.4.2 The strains on the samples
3.4.2.1 Converting lengths to strains If the sample is examined with the optical microscope the displacements L first need to be converted to logarithmic strains ε.
=
1
~
ln~
L
Lε (9)
3.4.2.3 Adding boundary conditions Alternatively, if the sample is examined with aremis the thickness Lz,1 due to pre-deformation has to be given in. Furthermore the time between two photos is not constant for these samples and is given in, whereas the time between photos made with the optical microscope is constant and set on one second. In addition this is also the case for the orientation of the samples, which is constant for the first series of samples but not for the other samples.
( )T
zLtndata 1,
~~~~~ ∆= βα (10)
3.4.2.4 Dealing with pre-load Once all these parameters are known the only problem, which has to be solved is the pre-load, of 30 Newton F30 that is applied in order to flatten the sample. Yet this problem cannot be solved because the photos are not linked with the enforced loads. Combining the time column of the tensile device and the time step of the photos makes the connection between both. The effect of relating these time variables makes it possible to relate a force to a displacement or a stress to a strain.
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The consequence of this makes it possible to solve the problem of pre-loading, which caused an error in the strain ∆εara. The strain is not zero at the first photo and therefore a correction is made. The created pre-strain is linear interpolated to make sure that the force equals zero and the strain also equals zero.
EA
Fara
0
30=∆ε (11)
In equation 11 the correction strain is calculated and there is assumed that the Young’s modulus equals 210 GPa despite of the pre-deformation [5]. Furthermore is assumed that the cross section surface A0 , defined as Lz,1 times Ly,1, remains constant during preloading because the stress is reasonable smaller than the yield strength Y [6]. 3.4.2.5 Dealing with flattening The first samples are not pre-loaded and these samples flatten first before they are fully loaded. The result of this flattening is a higher value for the strain ∆εerr
and is corrected likewise as explained in the previous section.
EA
Ferr
erropt
0
−∆=∆ εε YA
Ferr <<0
(12)
3.4.2.6 Thickness reduction Once the strains have been corrected the thickness reduction is determined. There is assumed that the volume of the material will not change during deformation, because the deformation quickly becomes plastic. So the change thickness is calculated by subtracting the strain in the width from the strain in the length of the sample.
0=++=∆
zyxV
Vεεε (13)
3.4.3 Computation of the tensile strength
Then the cross section area for each moment is determined and in combination with the applied force, the stress is computed.
)exp(0, zzyzy LLLLA ε== (14)
As the maximum value for the stress equals the tensile strength so in the end the tensile strength is determined.
A
FTS == maxσ (15)
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In order to complete the computations correctly the mean and standard deviation of the TS are also calculated [7].
n
x
x
n
i
i∑== 1 (16)
( )
1
1
2
−
−
=∑
=
n
xx
s
n
i
i
(17)
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4. Results After the main model is made as described in the previous section, it is run and the results of this model is pointed out in this section. These results are divided into the three kinds of samples that have been made. Hence this section is split in the following sub-sections
• The scoured and pre-deformed samples.
• Solved and pre-deformed samples.
• Solved and not pre-deformed samples.
4.1 The scoured and pre-deformed samples
The first group of samples is not deformed under different angles as mentioned earlier, although the rate of drawing is different for some samples. Moreover the first group is cut to make them fit in the tensile tester. Unfortunately some samples are cut too small whereby the width y of the samples becomes approximately as wide as the centre of the tensile test bar. Table 1. The too large reduction in the width can have a primary effect on the outcome and also the speed can have some influence.
No. α [o]
β [o]
v [µm/s]
t0
[µm] t
[µm] y1
[mm] y2
[mm] TS
[MPa] 01►1 0 0 X X X X X X
02►2 0 0 X 215 158 X X X
03►3 0 0 20 216 149 X X X
04►3 0 0 1 217 159 X X X
05 0 0 10 220 159 8,8 9.2 392
06 0 0 10 222 159 4,2 7.6 378
07 0 0 10 221 149 9,6 9.6 405
08►2 0 0 X 214 159 X X X
09 0 0 10 220 162 9.0 9.2 386
10 0 0 10 222 161 9.0 8.9 383
11 0 0 10 216 163 9.3 8.7 379
12►2 0 0 X 213 160 X X X
13►3 0 0 20 211 159 X X X
14 0 0 10 217 158 8.2 9.0 390
15►4 0 0 X 217 X X X X
16 0 0 10 224 166 8.1 9.2 382
17 0 0 10 214 164 5.6 8.8 386
18►5 0 0 -10 217 164 X X X
19 0 0 20 217 162 8.6 8.9 388
20►3 0 0 20 216 152 X X X
Table 1 properties of the scoured pre-deformed samples. ►1 Test sample. ►3. Tensile test without photos. ►2 Samples used for other purposes. ►4, 5 Error in preparation or test.
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Figure four shows a lower fracture strain at a much lower rate of drawing. However, this is only one measurement and in contradiction to theories in fracture mechanics [8]. Therefore more research is needed to investigate the influence of the rate of drawing. Furthermore the spread for higher drawing rates is more or less the same and seems not to be important. On the other hand the width after cutting, y is significant and increases the fracture strain, which is logical. Though, this is only one measurement and it is an error and thus not important at all.
4.2 Solved pre-deformed samples
The properties of the second group of samples are in table 2. However there are just a few results, because of technical problems. The samples with footnote 3 are computed in more ore less the same way as the others, nonetheless the computations are done over all the calculated points in Aramis. There might be expected that this will lead to a more accurate solution, but as the cross section area is not constant it does not lead to a more precise measurement.
Figure 4 Force versus displacement curves of the scoured pre-deformed samples. Purple, black, blue and red stand speeds of for –10, 1, 10 and 20 µm/s respectively.
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No. α [o]
β [o]
v [µm/s]
t0 [µm]
t [µm]
TS [Mpa]
No. α [o]
β [o]
v [µm/s]
t0 [µm]
t [µm]
TS [Mpa]
21 0 0 5 214 161 394 35 45 0 5 215 168 387 22 0 0 5 214 161 393 36►3 45 90 5 216 170 366 23 0 0 5 214 165 388 37►3 45 90 5 215 171 365 24 45 45 5 213 176 367 38►3 45 90 5 215 161 374 25 45 45 5 215 160 389 39►3 0 90 5 218 170 372
26►1 45 45 5 219 162 X 40►3 0 90 5 214 169 376 27 90 90 5 216 169 371 41►3 0 90 5 211 169 376
28►3 90 90 5 217 163 376 42►3 90 45 20 215 172 379 29►3 90 90 5 217 162 384 43►1 90 45 5 214 170 X 30►3 0 45 5 216 169 375 44►3 90 45 5 216 176 367 31►2 0 45 5 216 169 X 45 90 0 5 216 180 372 32►1 0 45 10 215 169 X 46 90 0 5 216 174 380 33 45 0 5 218 174 371 47 90 0 5 216 178 379 34 45 0 5 214 171 371
Figure 5 Stress versus strain curves of the solved pre-deformed samples and an angle β equals zero. The green spot is the maximum force on the tensile tester and the blue,
purple and red curves are tests at an angle α of 0, 45 or 90 degrees respectively
Table 2 properties of the solved pre-deformed samples. ►1 Step measurement. ►3 Previous measurement
►2 Measurement incomplete.
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4.2.1 Samples with varying α
Figure five shows the stress versus strain curves of the solved pre-deformed samples and the colour blue, purple and red of the lines stand for an α of 0, 45 and 90 degree respectively. It should be noted that, since β equals zero, the differences in the result can be caused by the different angle α. Accordingly, the orientation of the disc primarily influences the stress-strain relation of the sample. Besides, the tensile strength is also significant influenced by the orientation of the disc, which can also be concluded from tables three and four. Whereupon the tensile strength in the rolling direction increases due to rolling, moreover rolling also causes the original material to stretch in the
perpendicular direction. Consequently this explains the slighter increase in the perpendicular rolling direction and the lower tensile strength under α equal 45 degrees. Finally the fracture strain also seems to change, dependent on the orientation, but as the spread is reasonable large more data is needed to state this firmly.
Table 3 bump parallel to length of the sample.
Table 4 average values.
No. TS [MPa]
α β
21-23 392 0 0 33-35 375 45 0 45-47 377 90 0
No. TS [MPa]
α β
21 394 0 0 22 393 0 0 23 388 0 0 33 367 45 0 34 371 45 0 35 387 45 0 45 372 90 0 46 380 90 0 47 379 90 0
Figure 6 Stress versus strain curves of the solved pre-deformed samples. The green spot is the maximum force on the tensile tester and the blue, purple and red curves are tests at an angle α equals β of 0, 45 or 90 degrees respectively
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4.2.2 Samples with equally varying α and β
For some samples the bump is kept parallel to the rolling direction while the samples are made out of the discs under different angles, thus α equals β. So differences in the results are first and foremost subscribed to variances in pre-deformation. The stress versus strain curves from some of these samples are drawn in Figure six and the colours of the curves stand for the same angles as in Figure five. Now there can be concluded that the most significant change lies in the tensile strength. Here the tensile strength has decreased as α increased that is to say the tensile strength decreases as the pre-strain increases, which is in accordance with previous studies [9].
No. α [o]
v [µm/s]
t0 [µm]
t [µm]
TS [Mpa]
48 0 20 217 X 301 49►1 0 20 217 X X 50►3 0 20 216 X 307 51►3 45 20 217 X 294 52►2 45 20 218 X X 53►3 45 20 216 X 285 54►2 90 20 215 X X 55►3 90 20 216 X 299 56 90 20 216 X 307
Figure 7 Stress versus strain curves of the solved not pre-deformed samples. The green spot is the maximum force on the tensile tester and the blue and red curves
are tests at an angle α of 0 or 90 degrees respectively.
Table 5 properties of the solved not pre-deformed samples. ►1 Step measurement. ►2 Measurement incomplete. ►3 Previous measurement
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4.3 Solved not pre-deformed samples
The properties of the not pre-deformed samples are set in table 5. Here similar conditions must be applied as in the previous group. Although the error made by averaging the strains in all the points might seem small in the pre-deformed samples, in this final group it is much more significant. From Figure seven not much can be concluded there can only be confirmed that the initial material is stretched in the rolling direction and at right angles to the rolling direction. The initial spreads due to aging and the differences in fracture strain in association with previous measurements are not significant enough to draw any conclusions.
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5. Discussion In the following paragraphs some comments and recommendations will be discussed concerning the sample preparation and tensile test results. Four important issues on this topic can be researched in order to clearly understand the association between tensile strength and pre-deformation. These four topics are:
• Thickness reduction due to PET removal.
• Heat built-up due to EDM.
• Stress built-up due to EDM.
• Induced strains due to flattening.
• Deviations due to initiation of the devices. First of all, the removal of the PET layer in both methods brought to light two questions. The first question is to what extend the discs can be scoured in order to remove the PET layer, without damaging the metal. The other question is, if the chemical solution will etch away part of the metal disc. Secondly, the EDM operation might have influenced the samples, whereby the properties of the material have changed, due to heat built-up in the EDM discharge zone. This can be tested by making samples with different dam widths but has also not been done. Third, is also related to the EDM operation, which is the roughness of the edges. The roughness might initiate a crack due to stress built-up, whereby the sample breaks prematurely. The deviations in tensile strength due to stress built up are probably larger than the effects due to heat built-up but need to be investigated first. Then there is the flattening of the sample, which certainly induces extra stresses and strains. It is tried to make the samples width as small as possible to minimize this effect and it is believed that the stresses and strains due to the pre-deformation are significantly higher than the stresses and strains that are introduced during the flattening. Moreover it will be fairly difficult to make them negligible small. Finally there are the computational errors but these can be significantly reduced by good calibration and correct use of the equipment. There is only one problem at the start of the experiment. For the experiment, two instruments must be initiated at the same time, which is rather difficult. Accordingly, an error is made which smaller than one percent for the pre-deformed samples and a few percent for the not pre-deformed samples.
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6. Conclusion These experiments show that the tensile strength of the pre-deformed steel is dependent on the rolling direction of the 0.2 mm thick steel sheets. This is shown in both pre-deformed samples and not pre-deformed samples. In addition the amount pre-deformation also influences the tensile strength and decreases as the pre-deformation increases and is analogous to the formed hypothesis in the introduction. Although there are several discussion points, the results are satisfying. However these points should be taken into account in new experiments and more accurate measurements are preferable. By doing so the uncertainties can be reduced and more accurate values can be used in the model, which is currently designed.
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References [1] U.M Papaziean, ‘Tools of change’. Mechanical Engineering, volume 124,
No 2 p. 52 February 2002. [2] S. H. A. Boers, ‘Optimum path and discrete 3D forming’, Eindhoven
University of Technology, 2004. [3] J. J. Backx, ‘Faalgedrag bij de vervorming van plaatstaal en de voordelen
welke discrete matrijzen hierin kunnen bieden.”Eindhoven University of Technology, 2004.
[4] http://www.cdc.gov/niosh/ipcsndut/ndut0513.html on August 25, 2005 [5] S. Kalpakjian, ‘manufacturing and technology’, Prentice Hall, inc. 2001 [6] M. P. Groover, ‘Fundamentals of Modern Manufacturing’, J. Wiley & Sons,
inc. 1996 [7] D. C. Montgomery. ‘Applied Statistics and Probability for Engineers’, J.
Wiley & Sons, inc. 1999 [8] P.J.G. Schreurs, ‘Fracture Mechanics’, Eindhoven University of
Technology Lecture Notes. [9] S. Bouvier, ‘Modelling of anisotropic work-hardening behaviour of metallic
materials subjected to strain-path changes’, Computational Materials Science Volume 32, Issues 3-4 , March 2005, Pages 301-315
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Appendices
Scoured and pre-deformed samples
Goal
The goal of the experiment is to determine the tensile strength of a pre-deformed disc. A tensile test bar sample is cut from a pre-deformed disc. Afterwards the sample is tested in a tensile device.
Experiment requisites
- Magnetic block with on and of switch
- Discs ∅60 mm. - Protection sheet - Sandpaper (P180) - Sandpaper (P80) - Black waterproof marker - Hand screw - 2 metal smooth bars - Teflon - Cutting block - Protractor - Calliper gauge - Screw gauge - Pan and paper - Scratch pin - Tensile tester with a 500N load
cell - Optic microscope with camera.
PET-layer removal
By using the waterproof marker at first, the rolling direction is marked on the disc with an arrow drawn. Figure b1. Then the disc is fixed on a magnetic block with a protection sheet in between, Figure b2, whereupon one half of the disc is scoured with the coarse sandpaper. The other half of the arrow remains visible, because after scouring the rolling direction is not visible. When the shiny metal appears the fine sandpaper is used. After the entire PET on one half of the disc has been removed an arrow is drawn on the metal in extension of the previous arrow. Likewise the other half of the disc is scoured and finally the other side of the disc.
Figure b1 disc with arrow in rolling direction
Figure b2 disc on magnet with protection sheet in between
23
Pre-deforming and measuring of the disc
After the disc has been scoured the thickness of the disc is firstly measured with the screw gauge at ten different points and averaged. Secondly, the diameter of the disc is measured with a calliper gauge whereupon the disc is pre-deformed. Thirdly, the disc is put under the press at the right angle pre-deformed at a pressure of 1,8 MPa. Figures b3 to b5. Then the disc, with the formed elliptic bump, is removed from the press. Figure b6. Finally the thickness in the top of the bump, where the strains are the largest, Figure 7, is measured.
Figure b3 the parts are stacked up each other from top to bottom and then from left to right.
Figure b4 the mould with the disc and from top to bottom are the mould, brown rubber, disc, black rubber and mould form. Around stands a mould holder
Figure b5 press with the mould in between
Figure b6 Pre-deformed disc Figure b7 Strains in the pre-deformed disc
24
Producing the tensile test bar samples
Once the disc has been deformed and measured, a sketch is made of the sample at first. Second, the first form of the sample is drawn in blue. Figure b8. Third the disc and sketch are brought to the EDM-machine, where the sample is made out of the disc. Then the sample is pressed and flattened between two smooth metal bars by using a hand screw. To assure that the sample will not
deform unnecessarily, the sample is flattened from the outside in. Figure b9. After a sketch is made in red for the next EDM process the sample is finally processed to remove small cracks on the edges due to flattening. Figure b8.
Preparations of the samples
As soon as the sample is processed for the second time some preparations must be done before the sample is tested. First the sample is adjusted to the correct length and width on a cutting block. Secondly the dam of the sample is marked black and finally every few millimetres some reference scratches are carefully applied, Figure b10, where after the sample is ready to be tested.
Adjustments of tensile device
First a 500N load cell is installed on the tensile device. Second the sample is clamped in the tensile tester, after which the screws are equally tightened. Figure b11. Third the rate of drawing is tuned on 10 µm/s and the frequency is tuned on 10 1/s. In the end the time, displacement and force on the load cell will be saved in a matrix. Figure b12.
Adjustments optical microscope
Once the sample is clamped into the tensile device, both are placed under the microscope. Figure b13. Next the microscope is focused on at least two scratches in the middle of the sample. Finally the camera is positioned on top of the microscope and set on a delay of one photo every second.
Figure b8 blue sketch first form; red sketch second form.
Figure b9 First both left and right
sides are flattened then the centre.
Figure b10 Reference marks on sample
Figure b11 sample in tester, whole set up is placed under microscope
25
The tensile test
Now everything is ready to do the experiments. First the camera is turned on, thus it makes pictures before t0, which will be deleted at the end whereupon the tensile device is started. Both are turned off after the sample is broken. After the test is finished the data and photos are saved. Once all com-ponents are removed and the devices are reset a new experi-ment can be done.
Figure b12 computer, which collects and
saves data from tester.
Figure b13 optical microscope under which the tester is positioned. The blue block on top of the microscope is the camera that makes photos
during the experiment
26
Solved and pre-deformed samples
Goal
The goal of this experiment is also to determine the tensile strength of a pre-deformed disc. A tensile test bar sample with a specific orientation is made out of a pre-deformed disc and afterwards the sample is tested in a tensile device.
Experiment requisites
- Discs ∅60 mm. - Black waterproof marker - Hand screw - 2 metal smooth rods - Teflon - Plate shears - Protractor - Calliper gauge - Screw gauge - Pen and paper - Glass rod - Tensile tester with a 500N load cell - Black and white paint sprayer - Paper clips - Beaker 1000ml - Stirring magnet - Heater - Thermometer - Stand - Clamp - 1-Methyle-2-Pyrolidon solution - Tissue - Acetone
- Steel bits ∅3, ∅10 - Drill set up - Drill mould - Gloves
Solving the PET layer
In this experiment the PET-layer is solved in a chemical solution. The 1-Methyle-2-Pyrolidon solution is poured into a beaker and set on a heater in a fume-cupboard. The solution is heated to 90 oC, however, the temperature must be held constant, because above 96 oC there is a reasonable risk of explosion. Therefore the temperature is coupled to the heater to make sure the experiment will be safe. While the solution is heating up, the paper clips are just attached to the discs. Then the glass rod is threaded through the paperclips and the discs are hung in the solution. After a while the PET-layer starts to slide off the discs
27
and the discs are taken out of the solution. Then the remaining PET is peeled off the discs and the discs are cleaned with tissues immersed in acetone.
Marking the rolling direction
After the PET has been removed the rolling direction is marked with two dots on the top and the bottom of the disc. Furthermore the angle of the bump to the rolling directions is marked, where after the discs are deformed just like the first group of samples.
Producing the tensile test bar samples
To prevent the discs from rotating during the EDM process marks are made in the discs. First a one-millimetre notch is cut out of the disc’s edge on the sample’s axis. Figure b14 Then disc is put in the drill mould with notch and both notches are positioned to the same spot. Figures b15 and b16. Thereafter the holes are drilled through the mould
in the disc whereupon burrs are trimmed off with the larger bit. Finally the disc is ready to be processed in order to obtain samples, which is done likewise as the first series.
Preparations of the samples
First, the sample is cut to fit in the tensile device. Second a contrast is artificially applied on the sample with black and white paint. Figure b17. Third the sample is fixed into the tensile device similar as the first series. Then the rate of drawing is set on 5 µm/s and the frequency on 2 1/s, while the other settings remain the same.
Figure b15 drill moulds wherein between the discs are positioned. The notch of the disc is positioned to the notch of the mould.
Figure b16 both drill moulds
fixed on each other
Figure b17 contrast on sample with the area used for
calculations.
Figure b14. Sample with notch and holes made on
the sample’s axis.
28
Adjustment of Aramis camera
Now the whole set up is positioned under the Aramis cameras. Then the image exposure is adjusted because over exposed and cannot participate in the measurement. Finally the cameras are set on a delay of one second and the other settings are likewise as the first series.
The tensile test
Similar as the first group the camera is started first, after which the tensile tester is turned on. Once the sample is broken the data is saved, however, the camera data is saved somewhat different. After the experiment has been done, a small area is selected around the crack. In this area the strains are computed in a grid with points separated 0.15 mm and an overlap of 50 µm. Once the strains have been computed it is filtered in order to remove extremes. Then an area of points, over the width of the sample and three points long, is selected, which is used to compute the tensile strength of the material. Once the strains in these points are computed and archived the next sample can be tested.
29
Final group of samples
These samples are likewise made and tested as the previous group, nonetheless there are some differences. First of all these samples are not pre-deformed and therefore they are not flattened. Because the samples are not pre-deformed they are thicker than the previous ones and thus the tuning of the devices is somewhat different. The tensile tester is tuned on a rate of drawing of 20 µm/s and the delay of the Aramis camera on 2.5 seconds. The other settings remain the same as the previous series.
30
MATLAB® file excel.m function S = excel(n)
% Input of the results from the excel chart S = [time(s) load(N)
% elongation(Gmm)] These results are measured by the computer, which
% is connected to the tensile bar. This file will find the right excel
% results with a sample. If no excel chart is available an empty matrix
% S is returned and you will be notified.
% sample 3
if n==3
S = [0 0 0
0.11 2 1
0.2 1.5 3
0.31 3 5
0.41 3.4 6
0.52 6 9
0.61 8.6 11
0.7 10.5 12
0.81 11.2 15
0.91 14.9 16 % 10th element for calculation of speed
1.01 17.7 19
1.11 19.4 20
1.2 22.5 22
1.31 24.9 24
1.41 27 25
1.51 31 28
1.61 34.4 29
1.7 36.4 31
1.81 41.7 33
1.91 44.7 35 % 20th element for calculation of speed
2.02 47.9 37
2.11 50.6 38
....
....
17.7 84.3 320 ] ;
% sample 4
elseif n==4
S = [0 0.3 0
....
....
% Sample 56
elseif n==56
....
....
else
disp('No results of sample found')
S = [];
end
31
MATLAB® file pixel.m function AA = pixel(n)
% Here are given the number of pixels between 2 reference points in the
% sample for different time steps. This file finds the right pixel
% result with the samples. If there are no pixel results found an empty
% matrix AA is returned and you will be notified. The first samples
% are measured by hand and the others are measured by a computer. For
% the first samples the steps, at which strain, localization, shear
% and fracture occur, are given. The column at which the crack occurs
% is also given. The thinnest thickness is also given, but for all the
% samples. For the other samples the orientation to the rolling
% direction is given. In which the first number is the angle of the
% longitude the bump and the second of the sample.
% sample 5
% An = [Y X1 (X2 (X3))]. X2 X3 are only included if they gave a
% reference point in all the steps. L is the total length and can by
% calculated as follow: L = X1 + X2 + X3. Y is the width of the sample.
if n==5
A = [ 941-197 482-59 1169-482; % pix(el) measurements
941-197 482-59 1169-482;
941-197 482-59 1169-482;
940-197 482-58 1170-482; % strain
940-197 481-57 1170-481;
940-197 481-57 1171-481;
940-197 480-56 1172-480;
939-197 480-55 1173-480; % localization
939-198 480-54 1175-480;
938-199 479-53 1177-479;
937-200 478-51 1179-478;
934-201 475-48 1182-475; % shear
931-202 472-45 1186-472;
929-204 469-42 1189-469;
926-206 466-39 1192-466;
923-207 462-35 1196-462;
918-210 458-31 1200-458] ; % fatal crack
nloc = 8; % localization
nshear = 12; % shear
nfrac = 17; % fatal crack
loz = 159e-6; % thickness of the sample in the top
xf = 3; % interval column of A where fracture occurs
% sample 6
elseif n==6
....
....
nloc = 8;
nshear = 9;
nfrac = 13;
loz = 162e-6;
xf = 2;
32
else
disp('No pixel results of sample found')
A = [];
end
% Putting all the results together in one matrix.
% N = [# 0 (0 (0))]
if prod(size(A)) ~= 0
N = [ loz zeros(1,size(A,2)-1);
xf zeros(1,size(A,2)-1)];
AA = [c*A;N];
else
AA = A;
end
33
MATLAB® file aramis.m function AA = aramis(n)
% Accurate data from aramis. This file calls the points in a small part
% of the sample and calculates the average logarithmic strains in a
% stage in x and y direction.
% xcolumn = [ n x1 x2 x3 xf]
xcolumn = [21 104 105 106 67; % recalculated samples
22 113 114 115 63;
23 103 104 105 72;
24 99 100 101 70;
25 87 88 89 64;
27 114 115 116 81;
33 112 113 114 72;
34 71 72 73 78;
35 75 76 77 86;
45 86 87 88 76;
46 114 115 116 75;
47 98 99 100 73;
48 100 101 102 75;
56 95 96 97 78];
sn = (xcolumn(:,1) - n);
ddsn = det(diag(sn));
if ddsn == 0 % Check of sample is recalculated
nn = find(xcolumn(:,1) == n);
sampel = [0 0 0];
for photo = 1:xcolumn(nn,5)
[x exproc eyproc] = textread(sprintf('%d/%dnew-Stage-0%d.txt',n,n…
…,photo), '%f %*f %*f %*f %*f %*f %*f %*f %f %f', 'headerlines', 10);
x1x = find(x == xcolumn(nn,2));
x2x = find(x == xcolumn(nn,3));
x3x = find(x == xcolumn(nn,4));
xexz = [exproc(x1x);exproc(x2x);exproc(x3x)]/100;
xeyz = [eyproc(x1x);eyproc(x2x);eyproc(x3x)]/100;
xex = xexz(find(xexz)); % engineering strain without zero elements
xey = xeyz(find(xeyz));
if (prod(size(xex))*prod(size(xey)))~=0
Gexs = log(mean(xex)+1); % Logaritmic strain
Geys = log(mean(xey)+1); % Ge = ln(Gl) = ln(e+1)
end
sampel = [sampel; photo Gexs Geys];
end
AA = sampel;
else
disp('No pixel results of sample found')
AA = [];
end
34
MATLAB® file sample.m function sample
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SAMPLES %
% %
% This file returns the results of one or more samples. You must %
% follow the commands on the screen and the rest will be done %
% automatically. This file will call pixel.m, excel.m and aramis.m %
% for data and should therefore be in the same work folder as %
% sample.m. %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all % Clear all data in Matlab
close all % Close all figures in Matlab
clc % Clear command screen
n = input('Give sample number(s) between 1 and 56. ');
disp(' ') % Layout
disp('Answer the following questions with 1 for yes, or 0 for no. ')
disp(' ')
graph(1) = input('Would you like to see the samples with…
… photo moments? ');
disp(' ')
graph(2) = input('would you like to see the samples sorted…
… out on orientation? ');
disp(' ')
graph(3) = input('Would you like to see the samples sorted…
… out deformation speed? ');
disp(' ')
graph(4) = input('Would you like to see a stress strain…
… curve of each sample? ');
disp(' ')
TS = []; % For the individual values of TS from n
N = []; % For the numbers of n
alpha = []; % For the individual angle orientation of the sample
beta = []; % For the individual angle orientation of the bump
result = []; % N, E and TS in one matrix
v = zeros(size(n)); % velocity is needed for sorting out the results
for k = 1:length(n) % Calculating all samples one by one
disp(' ') % Layout
disp(' ')
disp(' ')
disp(n(k))
disp('=================================================')
S = excel(n(k)); % Calling the right results of F(n), t(n), dL(n)
if prod(size(S)) ~= 0 % Checking if there are results of the sample
% Dividing the matrix in different columns.
t = S(:,1); % t(ime) in seconds
F = S(:,2); % F(orce) in Newtons
dL = S(:,3)*1e-6; % dL displacement in meters
35
% Calculating the speed of clamps in m/s. v(k) = 0 => L/t. There is
% started after 10 steps so startup errors are left out
v(k) = (dL(20) - dL(10))/(t(20) - t(10));
% As the matrices in pixel.m are not of a similar structure they need
% to be sorted out.
% Series 1 of 2
if n(k) <= 20
AA = pixel(n(k)); % Calling the right results of X, Y and parameters
Alpha = 0; % Orientation of the sample in the mold
Beta = 0;
if prod(size(AA)) ~= 0 % Checking if there are results of the sample
A = AA(1:size(AA,1)-2,:);% Remove parameters from the pixel results
% Removing photo's before t=0 by checking if row(i+1) - row(i) = 0
i = 1;
while sum(abs(A(i+1,2:size(A,2))'-A(i,2:size(A,2))')) == 0
i = i + 1;
end
% Making time column for photo moments. Timestep(tt) determines how
% many time steps are needed in excel.m before a new picture is
% made in pixel .m
tt = t(size(t,1))/(size(A,1)-i);
ast = [0:tt:t(size(t,1))]'; % Time column corresponding with
% photo's
% and excel.m
% Making force column for photo moments and finding the time step
% closest to the photo moment.
asf = []; % Force column corresponding with photo's and excel.m
j = 1;
for as = 1:length(ast)
while abs(ast(as)-t(j)) >= 0.055*(t(20)-t(10))
j=j+1;
end
asf = [asf;F(j)];
end
fmax = find(asf==max(asf));
% Finding the Length in x direction of pixel.m
Lyx = A(i:size(A,1),:); % Calculating the length in meters in x,
% y direction
Lx = Lyx(:,AA( size(AA,1)));
Ly = Lyx(:,1);
% Correction for flattening of the sample
rc = []; % Rate coefficient of each step
for rcn = 2:size(Lx,1)
if Lx(rcn) - Lx(rcn-1) == 0
rc = [rc;0]; % Take zero for divide by zero
else
rc = [rc; (asf(rcn) - asf(rcn-1)) / (Lx(rcn) - Lx(rcn-1))];
end
end
rcmax = find(rc==max(rc)); % Steepest rate
Lx1 = Lx(rcmax) - asf(rcmax)/max(rc); % Length correction
36
Ly1 = 3e-3;
asf = [ 0 ; asf(rcmax:size(asf,1) ,1) ];
ast = [ 0 ; ast(rcmax:size(ast,1) ,1) ];
Lx = [ Lx1 ; Lx(rcmax:size(Lx ,1) ,1) ];
Ly = [ Ly1 ; Ly(rcmax:size(Ly ,1) ,1) ];
% Determining L(t=0) in z direction
Lz1 = AA( size(AA,1)-1 ,1);
% Determining elongations, strains and stresses
Glx = Lx/Lx1; % G(reek)l (lambda) elongation
Gly = Ly/Ly1;
Gex = log(Glx); % (epsilon) strain (logarithmic)
Gey = log(Gly);
Gez = -Gex-Gey;
Glz = exp(Gez);
Lz = Glz*Lz1;
Area= Ly.*Lz;
Gsx = asf./Area; % (sigma) Gs = F/A natural stress in Pascal
TSn = max(Gsx); % Tensile Strength in Pascal
% printing results for sample
fprintf('%s\n','TS [MPa]')
fprintf(' %3d\n',round(TSn/1e6))
% putting the results of each sample together
TS = [TS; TSn ];
N = [N ; n(k)];
alpha = [alpha ; Alpha];
beta = [beta ; Beta];
result = [N TS];
rres = [N round(TS/1e6) alpha beta];
end
% Plotting the results
else
% Series 2 of 2
% Accurate measurement
AA = aramis(n(k));% Calling the right results of X, Y and parameters
if prod(size(AA)) ~= 0 % Checking if there are results of the sample
% data = [nr alpha beta delay Lz1]'
data = [ 21 22 23 24 25 27 28 29 30 33 34 35 36 37 38
0 0 0 45 45 90 90 90 0 45 45 45 45 45 45
0 0 0 45 45 90 90 90 45 0 0 0 90 90 90
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
161 161 165 176 160 169 163 162 169 174 171 168 170 171 161
39 40 41 42 44 45 46 47 48 50 51 53 55 56;
0 0 0 90 90 90 90 90 0 0 45 45 90 90;
90 90 90 45 45 0 0 0 99 99 99 99 99 99;
1 1 1 1 1 1 1 1 2.5 5 2.5 2.5 2.5 2.5;
170 169 169 172 176 180 174 178 217 216 217 216 216 216];
nn = find(data(1,:) == n(k));
Alpha = data(2,nn);
37
Beta = data(3,nn);
dt = data(4,nn);
% Removing photo's before t=0
stage0 = AA(size(AA,1),1) - dt*fix(max(t));
if stage0 < 0
disp('Stage measurment fails after fatal crack growth')
photo = AA;
else
AA(:,1) = AA(:,1) - stage0;
photo = AA(stage0+1:size(AA,1),:);
end
% Making force column for photo moments and finding the time step
% closest to the photo moment.
photofour = [];
j = 1;
jmax = size(t,1);
for as = 1:size(photo,1)
while ( abs( dt*photo(as,1) - t(j) ) > 0.1 ) & ( j<jmax )
j=j+1;
end
photofour = [photofour;F(j)];
end
photo(:,4) = photofour;
photo(:,1) = dt*photo(:,1);
fmax = find(photofour==max(photofour));
% Finding elastic part in x direction. Plastic strains seems to
% start at some places around 120 newton.
ne = 1;
while (photo(ne,4) < 120) & (n(k)<48)
ne = ne + 1;
end
% Calculating surfase area estimation at t=0 in m*m
Ly1 = 3e-3; % L0 in y direction
Lz1 = data(5,nn)*1e-6;
Lyest = Ly1*exp(photo(:,3)); % L = L0*exp(Ge)
Lzest = Lz1*exp( -(photo(:,2)+photo(:,3)) ); %Gez + Gey + Gex = 0
Aest = Lyest.*Lzest;
% Calculating initial strains and total strains due to start at
% F(t=0) = 30 N
F0 = photo(1,4);
Gex0 = F0/Aest(1)/210e9; % G(reek) e(psilon) in x-direction at t=0
GGex = [0 ; photo(:,2) + Gex0];
GG = 40;
z = 0;
while z~=1
GG = GG + 1;
z = (GG + 1 == size(GGex,1)) | ((GGex(GG+1) - GGex(GG)) < 0);
end
Gex = GGex(1:GG);
Gey0 = -0.3*Gex0;
GGey = [0 ; photo(:,3) + Gey0];
Gey = GGey(1:GG);
Gez0 = -Gex0-Gey0;
38
Gez = -Gey -Gex; %Gez + Gey + Gex = 0
% Calculating lengths in y and z direction, stress and strength
Ly = Ly1*exp(Gey);
Lz = Lz1*exp(Gez);
A = Ly.*Lz;
Gsx = [photo(1:GG,4)]./A; % (sigma) Gs = F/A natural stress in
% Pascal
TSn = max(Gsx); % Tensile Strength in Pascal
% printing results for sample
fprintf('%s\n','TS [MPa]')
fprintf(' %3d\n',round(TSn/1e6))
% putting the results of each sample together
TS = [TS; TSn ];
N = [N ; n(k)];
alpha = [alpha ; Alpha];
beta = [beta ; Beta];
result = [N TS];
rres = [N round(TS/1e6) alpha beta];
end
% Plotting the results
% All samples in an individual graph, with photo moments
end
% Samples sorted out on orientation to the rolling direction
% Samples sorted out by velocity
% Stress strain curves of the samples
end
disp('-------------------------------------------------')
end
if prod(size(result))~=0
% Printing all values in a matrix form
disp(' ')
disp(' ')
disp(' ')
disp('All values')
disp('==============================================================')
fprintf('%s\n','Sample TS [MPa] alpha beta')
disp('==============================================================')
fprintf(' %3d %3d %3d %3d\n',rres')
% Calculating mean value (gem) and standard deviation
if prod(size(result)) ~= 0 % Check if something can be calculated
for nM = 1:size(result,2)-1 % Calculating the mean of E, TS and Y
gem(nM) = sum(result(:,nM+1))/size(result,1);
if size(result,1) > 1 % Check if standard deviation can be
% calculated
s(nM) = sqrt(sum((result(:,nM+1)-gem(nM)).^2)/(size(result,1)-1));
end
end
39
% Printing mean values and standard deviation
if size(result,1) <= 1 % Return the results of a single calculated
% sample
disp(' ')
disp(' ')
disp(' ')
disp('Results')
disp('==========================================================')
fprintf('%s\n','TS [MPa]')
fprintf(' %3d\n',round(gem(1)/1e6))
else % Return the mean and standard deviation of the samples
disp(' ')
disp(' ')
disp(' ')
disp('Mean results and standard deviation')
disp('==========================================================')
fprintf('%s\n','TS [MPa]')
fprintf('%3d +- %2d\n',round(gem(1)/1e6), round(s(1)/1e6))
end
disp('----------------------------------------------------------')
end
end
