# MakerBot PLA Material
## Problem

The MakerBot Replicator 2 is a popular 3D printer, available for less than $3000. The printer is capable of printing functional parts from a biodegradable thermoplastic material known as PLA (polylactic acid). The goal of this project is to design and implement a set of tests, in order to experimentally determine the material properties of the PLA material.
* MakerBot Replicator 2
* Three point bending test

## Conceive

Conception is informally described above. A number of material properties could be important for 3D printed parts:
* Strength
* Stiffness
* Hardness
* Ductility
Each of these material properties could depend on one or more of the following variables:
* PLA material color
* Fill direction (orientation on build platform of 3D printer)
* Infill percentage (setting on 3D printer)
* Temperature
* Moisture/Humidity
* Load duration (creep) or repetition (fatigue)
Initially, this project investigates strength and stiffness as functions of material color and fill direction.

## Design

The goal of the design phase is to design a set of test plans for determining PLA material properties.

### Requirements for each test plan

The tests that pass to the implement phase must:
1. be feasible.
2. be economically viable.
3. have reproducible results.
4. be general enough to test multiple variables.
5. not have over 10% error.
6. identify essential material properties in discovering the limitations of PLA.
Material Tests Considered (but not implemented)
Many tests were initially conceived, but many rejected due to their ability to meet all requirements.
1. The Tension Test - a cylindrical test specimen with a smaller central diameter is clamped to a surface. Weight is slowly added and the amount of deformation is measured at each data point. These values are then plotted on a stress/strain diagram and the elastic modulus is found using a graphical method. This test failed the first requirement, it was not a feasible test. The amount of force needed to produce a very small amount of deformation was far too high.
2. The Heating and Cooling Test - a rectangular test specimen is first measured using vernier calipers. The specimen is then subjected to hot temperatures in order to thermally expand. The expanded dimensions are measured, recorded and the coefficient of thermal expansion is calculated. The test is preformed a second time in cold temperatures in order to obtain multiple values to average. This test did not pass into to implement phase due to the lack of importance the group found for CTE. Most printed parts would be operating slightly above or below room temperature causing CTE to not be a necessary factor in determining PLA's limitations.
3. The Sound Test - a small cylindrical test specimen is first used to calculate the density of PLA using the water displacement method. Then a very thin and long cylindrical specimen is laid out with two people at both sides. One person sends a wave through the PLA and the other times how long the disturbance takes to reach them, calculating the wave's velocity. The bulk modulus, also known as the elastic modulus, is then calculated using these experimental values. This test was thrown out due to technical limitations, feasibility, and accuracy. The wave would travel too fast to be accurately recorded and no technology was available to measure the propagating wave's wavelength or frequency to then calculate velocity. :

### Experimental prototypes and testing conducted during design

The first prototype of the 3 point bend test can be seen to the right. The setup consists of two raised triangular blocks supporting the test specimen and a level. A clamp is applied to the center point of the beam and a string is tied to the clamp. Weights are measured with a bathroom scale and tied to string. Deflection of the beam is measured by hand with a small ruler for each weight and recorded. These values were then used to calculate the elastic modulus of each data point and percent error was recorded. The percent error of the wood specimen recorded was around 40%, breaking one of our initial requirements. In order to track the source of error and reduce it a second material was tested, Cpvc pipe. After the second trial percent error was reduced to around 23%. While this value was still outside of our range it was still plausible to improve the experiment and meet requirements with the next design.

### The final test plans

Two test plans were developed, a 3-point bending test and a 2-point bending test. The 3-point test is used to determine the material's stiffness, while the 2-point test is used to determine the material's strength. Both tests require PLA test specimens with dimensions L=220 mm x W=10 mm x H=5 mm.
Below are the finalized experimental procedures to be used for testing. It is our hope they will be able to accurately measure the elastic modulus and ultimate strength of PLA and determine any factors that affect it, such as color, fill direction, and temperature.
* 3-Point Bending Test
When testing this procedure, the data and calculations recorded can be seen in this example: 3 pt Example
The final design of the 3-point bending test, seen to the right, is very similar to our initial prototype. The process was maintained and improved upon significantly reducing sources of error. To begin with, labeled hanging masses were used in the experiment leading to a calculated value of force incorporating very little error. Next, the clamp was removed and simply replaced by a loop at the end of the string, this assures the load will be concentrated at the direct middle of the beam. Lastly, and most importantly, the method of measuring was altered. Before beginning the test, paper is mounted behind the beam and the initial position is marked, this becomes the base line for measuring deflection. Hanging mass is then added and a deflection line is drawn. This is repeated for several data points in order to incorporate an average value. Once all data points are drawn the paper is removed. The distance between the base line and each deflection point is measured with vernier calipers and recorded. After conducting a dry run of this design, the calculated percent error was around 6%, well within our requirements.
* 2-Point Bending Test

### Technical and scientific knowledge

Being that our goal was to design a scientific method in order to calculated the material properties of PLA, formulas were an essential part of our research.
Equation used in the 3-point bending test
This equation relates the applied load and test specimen geometry to the material stiffness.
E = (FL^3)/(4wh^3d)
E = Elastic Modulus, a measure of a material's stiffness
F = Applied Load
L = Distance between the outer supports
w = width of beam
h = height of beam
d = deflection of beam
The applied load, F, was calculated using hanging masses. F = mass(kg)*acceleration due to gravity (9.81 m/s^2) :
Equation used in the 2-point bending test
This equation relates the applied load and test specimen geometry to the material strength.
Equation used in the 2-point bending test:
σult = (FLc)/(12wh^3)
σult = Ultimate Stress, a measure of a material's strength
F = Applies load , calculated as above
L = Distance between the hanging mass and the clamp
c = .5h
w = width of the beam
h = height of the beam :

## Implement
### Goals for implementation performance, cost and quality

1. Tests must be economically feasible. This goal was met, after using many resources from the engineering lab the testing total did not exceed $20.
2. Repeatable results. This goal was met, multiple trials (ranging from 10 to 20) of a single beam were conducted leading to similar results.
3. Accurate test data. This goal was met, all measures were taken to reduce error including many trials and accurate measuring devices.

### Manufacturing the test specimens

The main tool used in the implementation process was the Makerbot Replicator 2. The multiple test specimens used in the 2 point and 3 point bending procedures were first modeled in solid edge. The picture on the left shows the simple rectangular beam with dimensions 220mm x 10mm x 5mm. This model was then uploaded to Makerware where its printing options were modified and then exported to the printable .x3g file. When testing fill direction this model was rotated and contracted to produce a Lxh model and a wxh model, beam fill directions shown to the right.

### Test setup

A variety of tools were required for testing: hanging weight sets (large and small), vernier calipers, rulers, clamps, and materials used to build vertical supports. The only material purchased was the two pine triangular supports, $3.50 each from a local hardware store.
Shown above is the set-up of the 2 point and 3 point testing procedure set-ups. The 2 point procedure, shown in the center, consisted of a very simple set of parts. Once a beam was chosen a hole was drilled into one end at which a string was strung through and tied. A clamp borrowed from the lab was then used to secure the other end in a fixed location. Large weights, also borrowed from the lab, were then used to apply a force to the beam. The basic 3 point procedure, shown on the left, was used for nearly all 3 point trials. Empty bins located in the lab were used to symmetrically suspend the triangular supports which held a beam and a level. Secured to the level was a blank sheet of paper used to mark the beam's initial position and deflection for each mass added. While this simple set-up was ideal for any beam with a lxw or lxh fill direction, the constricted length of a wxh beam and increased amount of needed mass was not supported in this set-up. Instead, two 2x4 wooden beams supported by bins were used to suspend the triangular supports which in turn held a beam and the level. This set-up can be seen pictured to the right.

### Variability and Statistical Analysis

Due to human error and other random factors, experimental values were not always similar. To avoid this error multiple test trials were conducted and averages were taken. These average were then compared by means of statistical analysis in order to determine if differences were statistically significant.
Statistical Analysis
To relate the E-values calculated for the 3 point bending tests two-sample Z-tests were run to compare the average E-values while accounting for standard deviation. To run a two-sample Z-test use either a Ti-83 or Ti-84 calculator.
1. Click stat then edit and enter the average E-values for each test. Place each color's values in a different column.
2. Click stat, right arrow, 1 , 2nd stat, and select a list. Hit enter and a list of value will show up. Record the standard deviation value, which is represented by sigma(calculate the standard deviation for each different color of PLA).
3. Click stat, right arrow twice, 3. On this screen enter in values for sigma 1 and List 1 that correspond to one color (to select a list use 2nd stat). Complete the same process for sigma 2 and List 2 using a different color. Arrow down and make sure Mu1 =/= Mu2, then select calculate.
4. A list of values shows up. Locate the value represented by P. If the P-value is < .05 it can be concluded that the colors have different E-values. If the P-value is > .05 it can not be concluded that the colors have different E-values because they are too similar.
5. Repeat this test 15 time to compare all of the colors and another three times to compare the printing methods. :
Using MATLAB for computing results
Finding E in Matlab
While our tests were not software dependent, Matlab was used in order to help calculate data. Over 110 trials were conducted involving 5 calculations each, these calculations were done using a program written in Matlab which greatly reduced the time that would have been spent solving them manually. :

### Testing and analysis procedures

The first test performed was the 3-point bending test. This procedure was used to determine PLA's modulus of elasticity and to investigate any variable that could affect it. A brief procedure of the 3-point test can be seen below, summarized from the test passed along from the design phase. This brief procedure describing one trial was repeated for the desired number of trials ranging from 10 to 20.
3-Point Test Procedure
3 Point Bending Process (1 Trial):
1. Pick a variable to test, test multiple beams while only changing the wanted variable. Dimensions depend on desired fill direction.
2. Place a mark at least 1 cm from each end of the beam and measure the distance between the two marks, this is the Length(L) measurement.
3. At the center of the beam measure the width(w) and height(h).
4. Place each outer mark on a support and place the string loop and the center mark.
5. Mark the baseline of the beam before any deflection.
6. Add constant increments of mass to the weight hanger while marking each deflection.
7. Measure the deflections of each weight and preform calculations. :
3-Point Test Results
An example of the data found from this procedure can be seen below.
Beam Dimensions: L= .12966 m w= .01004 m h= .00517 m Beam Color: Blue Fill direction: w x h cross sections
Mass (g)Force (N)Deflection (mm)Modulus E (Gpa)
5004.91.952.03
10009.811.892.04
150014.722.712.13
200019.623.712.08
Trial #12345678910
Eavg(GPa)2.072.282.062.162.242.252.282.242.382.16 :
The second test performed was the 2-point bending test. The procedure seen below was used to determine PLA's ultimate stress.
2-Point Test Procedure
1. Retrieve a used beam from previous tests and drill a small hole at one end.
2. Clamp the end with no hole tightly to the workshop table.
3. Tie a coarse string through the hole and place a loop at the end.
4. Slowly add weight, increasing by increments of 200g.
5. After each addition of weight measure the new length from the weight to the fixed end.
6. Continue this process until the beam ultimately breaks.
7. Record the mass and length at the time of breakage and preform calculations. :
2-Point Test Results
ColorMass (kg)Force (N)σ Ultimate (MPa)
Clear3.635.3299.34
Green4.039.24105.98
Glow1.716.6854.10
Black3.433.35105.24
Red3.029.4387.40
Red Beam Test #Mass (kg)Force (N)σ Ultimate (MPa)
Test 15.049.05145.68
Test 24.5544.64132.58
Gold Beam Test #Mass (kg)Force (N)σ Ultimate (MPa)
Test 14.0539.73107.31
Test 24.039.24105.98
Glow Beam test #Mass (kg)Force (N)σ Ultimate (MPa)
Test 12.019.6263.64
Test 22.0520.1165.23
Test 31.8518.1558.87
ColorAverage Mass (kg)Average Force (N)Average σ Ultimate (MPa)
Red4.1841.04121.89
Gold4.0339.49106.65
Glow1.918.6460.46 :

### Summary of results
#### Stiffness dependence on PLA color, from most stiff to least stiff

Clear (2.77 GPa) > Luminescent > Blue = Black > Green = Red (2.55 GPa)
The overall variation between colors is less than 10%.

#### Strength dependence on PLA color, from highest to lowest strength

Black (105 MPa) = Green > Clear > Red (87 MPa) >> Glow (54 MPa) Glow-in-the-dark PLA is an outlier, as the other colors vary by about 20%.

#### Stiffness dependence on PLA color, from most stiff to least stiff

LxW = LxH > WxH Beams are approximately 20% less stiff when printed in the WxH orientation. This corresponds to an upright (vertical) orientation on the build plate when 3D printing.

#### Comparison of PLA strength and stiffness to other common materials

By characterizing the strength and stiffness of PLA, future students will be able to make an educated choice when determining which color and direction to print their project parts. By having an easy to access list students will be able to choose the best combination for their desired effect. For example, if they worry about the strength of the part more than its stiffness a group should print the part in neon green, as it is able to endure the highest amount of stress. On the other hand if a group is printing a part in which the bending of a part would produce failure, they should print this part in clear and with the fill direction opposed to the undesired bending, this would produce a part with the largest modulus of elasticity or the stiffest part.

## Presentation

Link to Presentation