project15

Ολοκληρωμένο Αναρτήθηκε Jul 10, 2011 Πληρώθηκε κατά την παράδοση
Ολοκληρωμένο Πληρώθηκε κατά την παράδοση

Stress strain curves provide important information concerning the

material properties of many different types of materials. Stress

strain curves can be generated when a material is stretched while

recording both the force and the displacement of the material.

This project involves the analysis of an experimentally obtained

data set which includes force and displacement information for a

silicone thin film material.

You will be given a data set of which you will be required to process the raw data and then perform

several different numerical analyses as follows:

1. Signal conditioning of data

2. Curve fitting - Stress Strain Powerfit

3. Integration - Strain energy

4. Finite Differences - rate of change of strain energy

## Deliverables

Stress strain curves provide important information concerning the

material properties of many different types of materials. Stress

strain curves can be generated when a material is stretched while

recording both the force and the displacement of the material.

This project involves the analysis of an experimentally obtained

data set which includes force and displacement information for a

silicone thin film material.

You will be given a data set of which you will be required to process the raw data and then perform

several different numerical analyses as follows:

1. Signal conditioning of data

Import data

The data is stored as ASCII, tab delimited text in the following file: StressStrainSi3.txt.

You will need to read this data into MATLAB. Because this is a large data set, and it includes a

header file, the command dlmread can be used to perform this task. This command uses

the following form (use help for more information)

Result=dlmread('filename','\t', first line of numerical data, first column to import)

This command will return a matrix of all of the data, which will then need to be

separated into separate vectors: Vdisp, and Vforce.

Filter noise

Plot the voltage signal of the force data, and observe the noise in the signal. This 60 Hz noise

must be removed before processing the data. This can be done by applying the 60 Hz notch

filter using the provided file: NotchFilter.m . Compare the filtered data with the raw data

to confirm that the filter has removed the noise without altering the data otherwise.

Convert voltage signals to measurements.

The data provided is the raw voltage measurements from a strain gauge force transducer and an

optical displacement sensor. In order to use the data, you must convert the signals from voltage

into force and displacement.

The conversion for each of the measurement devices are given as follows:

Strain gauge: F=[url removed, login to view] +2.4447 SG

Optical transducer: 0.437 0.1 OT

V x e− =

Thin the data set

Under some situations, it is necessary to reduce the number of data points by thinning the data

set. In this case we will do this to increase the stability of the integration and differentiation.

For the set of data provided, this can be done using the colon operator with an increment of

100. The end result should be a data set with 700, rather than 70,000 data points. (One note of

0.4 0.5 0.6 0.7 0.8 0.9 1

2.6

2.8

3

3.2

3.4

3.6

3.8

x 10

4 Stress Strain Curve

Strain

Stress

Sample

Figure 1: Stress strain curve for

Polymer Material

caution: thinning can damage your data and remove or distort high frequency information in

some situations, so this technique should not be used in all applications.)

Crop data set

Once the data is conditioned, you must decide what data to retain from the test. If you plot

Stress vs. Strain for the entire data set, you will see a jumble of curves, however, when the data

for one stretching motion is separated from the rest of the data, a curve similar to that shown in

this figure is created similar to that shown in figure 1. The choice of data can be found by

plotting the filtered stress data and choosing endpoints starting at the largest peak and ending

at the first minimum after that.

2. Curve fitting - Stress Strain Powerfit

The engineering stress, s , and strain, e , are defined as follows:

F

A

s = ,

L

L

e

D

=

Where F is the force, DL is the change in length, 0 0 0

A = t w is the initial cross-sectional area and 0

L is the

original length of the sample. For the given sample, the original dimensions are:

0.1524 ; 0.1016 ; 0.008 o o o

L = m w = m t = m.

The stress-strain curve in the region beyond yielding is often described by the power model:

b s =ae

Use the data prepared in part 1 to curve fit the data to the power model using the linearization method

developed in class. Compare this with a polynomial model (you decide the appropriate order).

Discuss which method is preferable and why. Make sure to use quantitative values such as the

coefficient of determination (r2) in your assessment as well as qualitative assessments such as

comparing the curve fit with the original data.

Please note that you may use cftool to check your work, however, you must perform these operations

using the codes developed in class.

3. Integration - Strain energy

The strain energy U (strain energy describes the amount of potential energy stored in a spring element

when it is stretched) of a material specimen can be written as:

U = s de

Use numerical integration to calculate the strain energy associated with the material using a first and

second order integration for unevenly spaced data (this will be developed based on the ideas of the

trapezoidal, and Simpson's 1/3 rules).

Compare results with those obtained by directly integrating (by hand) the power fit and polynomial

model and by using the MATLAB built-in function trapz.

4. Finite Differences - rate of change of strain energy

Obtain the relation of the rate of change of the strain energy,

U

e

?

?

, as a function of the strain using

finite difference for unevenly spaced data, based on strain energy data obtained using the two different

orders of integration from part 3.

Compare your results of your different values with the original data, s .

Report Requirements

You may work on your project with your group, however, you must turn in individual reports which are

your own unique work.

The key to this project is ORGANIZATION. Your code should be well organized, and the report also must

be clear and concise. The report will be graded based on the rubric provided to confirm that you have

covered the following areas:

Executive Summary or Abstract: In 1-2 paragraphs, summarize the problem and solution methods as

well as briefly stating results and primary conclusions which can be drawn. Should be written after

rests of report is finished. If someone only read the Abstract, they should understand the purpose

and results of your entire project.

Introduction: The introduction should provide a brief description of the science behind the problem

statement. For this I would recommend that you use a source that is able to be referenced such as

one of the many e-books available through the WSU library system. You must properly reference

all sources used.

Solution Method: This section should describe in detail each of the method that are being used. This is

your opportunity to demonstrate that you understand how curve fitting, numerical integration and

finite difference methods work. You must provide should provide a clear, brief description of each

method, referring to your well documented code (which can be presented either in part or whole

and can be contained in an appendix if necessary).

Results: In a well organized way, clearly and concisely display your data. Based on the results of your

calculations and how you will be referring to them in the discussion session you must determine

the best way to display your results. Please describe the results of each section separately in a

clear and concise way.

Discussion: Your discussion section should use the results presented in the previous section to discuss

the different methods used in the project. Here are some questions to help direct your discussion

session (note, you do not need to answer every single question, this is provided to give you a

starting point for discussion) :

What were some of the issues with the original data set, and how were they overcome?

How does the choice of the function used to fit the data affect the resulting fit?

Is is possible to extrapolated data based on the curve fits used?

How can curve fits be used to estimate other values concerning the given data?

Was integrating the curve fit more effective or numerically integrating the data?

What are the strengths and weaknesses of the different finite difference methods?

Conclusion: Use the conclusion to help the reader understand the value of your results. After briefly

summarizing what you found, describe any conclusions which can be drawn from the report,

and/or any ways in which these results could be helpful for problems solving in the future.

References: You must list all of your references. Make sure to cite references where they are used in

the paper as well. Although there are no points allocated for this section, you will not receive full

credit for the report if it is not included.

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