Stress Strain Fitting...(former Arrays)

On 5/6/2010 4:26:45 PM, dvmoldovan wrote:
>I'm not going to calibrate
>(no need to since the testing machine is)
___________________________

You can stick with your idea but you won't benefit of the remarks/guidance provided. The problem is lot worse than the mechanical machine. The data that this bloody machine collects is a total nonsense as it does not collect columns of equal length and that bothers the fitting session. The data aren't collected serially vs pressure applied on the sample, it seems to collect in a sort of eye diagram that you have to deploy in an exploitable way for Mathcad.
I have attempted the ascending/descending and got two absolute gorgeous fits that can be qualified in Dirac words: "too beautiful not to be true".

Inspect the data that were removed and conclude they shouldn't have been there in the first place from the collection, which collection you better look for how it works. If you can't exploit the machine and its associated software, then go full manual, i.e: apply pressure and read deformation , all experiments of equal number of elemental tests. After that, make your stress-strain diagram as you wish, but at least you will have raw data that should be fitted just before the stress-strain diagram.

The ascending has 11 data for a perfect fit. Why should you have 196 data for the descending part of the experiment. This puts the project back many threads ago. Wang has about that: 2 dozens of data pairs per experiment. What I don't understand either is why don't you have your stress-strain diagram looking like Wang diagrams ? A damned serious question if your project consists in duplicating the same testing .

jmG

On 5/9/2010 2:38:14 PM, dvmoldovan wrote:
>First, thank you all for your
>time and energy put to my
>rescue. Although your answers
>may sometimes have been not
>what I hoped for (initially),
>you all pointed out several
>flaws in my sheet (and data).
>With you permission I'll start
>over (still based on what has
>been posted here so far).
>Second, let's assume the
>following :
>1. from experiments one has
>gathered data for strains
>(column 1 - microns) and the
>response in stress from the
>material (column 0 - newtons)
>2. there is one function to
>link them together (as
>proposed by Wang)
>
>The question is, how can I
>achieve the best fit between
>experiments and Wang?
>
>I attached my latest work, but
>it doesn't feel right due to
>that inflection point...
>
>Please disregard erratic data,
>discontinuities and others.
>I'm trying to understand the
>principle and the formulas it
>should use before collecting
>any more data...
>
>Kind regards, D.
____________________________

"1. from experiments one has gathered data for strains (column 1 - microns) and the response in stress from the material (column 0 - newtons)"

==> Total non sense: strain is a calculated ratio, dimensionless.

I don't understand negative pressure unless the sensors have inverse polarity or the calibration is zeroed at 2500. But you can see that the project is reversed. So, we are back to square 0, i.e: read the pressure from a dial meter and the deformation from a dial meter too, with much less measurements.



During testing of a material sample, the stress�strain curve is a graphical representation of the relationship between stress, derived from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample, i.e. elongation, compression, or distortion.

In continuum mechanics, stress is a measure of the average force per unit area of a surface within a deformable body on which internal forces act. It is a measure of the intensity of the internal forces acting between particles of a deformable body across imaginary internal surfaces [2]. These internal forces are produced between the particles in the body as a reaction to external forces applied on the body. External forces are either surface forces or body forces. Because the loaded deformable body is assumed as a continuum, these internal forces are distributed continuously within the volume of the material body, i.e., the stress distribution in the body is expressed as a piecewise continuous function of space coordinates and time.

The SI unit for stress is the pascal (symbol Pa), which is equivalent to one newton (force) per square meter (unit area). The unit for stress is the same as that of pressure, which is also a measure of force per unit area.

Strain is the geometrical measure of deformation representing the relative displacement between particles in the material body. It measures how much a given displacement differs locally from a rigid-body displacement.[1] Strain defines the amount of stretch or compression along a material line elements or fibers, the normal strain, and the amount of distortion associated with the sliding of plane layers over each other, the shear strain, within a deforming body.[2] Strain is a dimensionless quantity, which can be expressed as a decimal fraction, a percentage or in parts-per notation. This could be applied by elongation, shortening, or volume changes, or angular distortion.

The Cauchy strain or engineering strain is expressed as the ratio of total deformation to the initial dimension of the material body in which the forces are being applied. The engineering normal strain or engineering extensional strain e of a material line element or fiber axially loaded is expressed as the change in length �L per unit of the original length L of the line element or fibers. The normal strain is positive if the material fibers are stretched or negative if they are compressed. Thus, we have



where is the engineering normal strain, L is the original length of the fiber and is the final length of the fiber.

The engineering shear strain is defined as the change in the angle between two material line elements initially perpendicular to each other in the undeformed or initial configuration

jmG

On 5/9/2010 9:14:16 AM, dvmoldovan wrote:
>Great work! Thanks!
____________________

Don't get discouraged by curve fitting. Over 40 years of that stuff didn't quench my appetite. Build that one by yourself and try the full data set or the two points reduced one. Notice the Minerr is not vectorized,,, Oh ! something new. Now, assume the underlying phenomenon is of that shape, no matter how many zillions of points, you won't get any better fit than the two points one. This example is an "ad absurdum" proof that data set must be collected wisely. It dictates pre-testing to evaluate the shape of the phenomenon, then distribute at best. In term of your project, 1791 points is non sense, simply. Ideally of equal length and not more than needed, strictly raw data from what you apply and what you read.

In that example, an abundant data set can be plotted and the fit governed by " a user two points" for a customized fit based on some known bias from the collection or simply based on a special calibration point, that would then be a "calibrated fit".

jmG