User:Cjcampo/ENES 100/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. The MakerBot Replicator 5th Generation is an alternate 3D printer that could be used.

Conceive
Conception is informally described above. A number of material properties could be important for 3D printed parts: Each of these material properties could depend on one or more of the following variables:
 * Strength
 * Stiffness
 * Hardness
 * Ductility
 * 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.

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. 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.
 * 3-Point Bending Test


 * 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.

Derivation of Engineering Equations
The engineering analysis will start with utilizing engineering mechanics for a simply supported beam with a concentrated load at the mid point. This will establish the Design Loads (Theoretical Loads) for each prism beam tested. All results will be tabulated in excel spreadsheet for manipulation of data for complete analysis. The following is the shear and moment diagram for our simply supported beam with a concentrated load.



The maximum shear value is:

Vmax = R = P/2 and will be measured in lbs.

The maximum moment will be at the midpoint and is:

Mmax = Pl/4 and will be measured in inch x lbs.

The maximum deflection will be at the midpoint and is:

deflection max = Pl^3/48EI

Where:

P = load in lbs

R = Reaction in lbs

V = Shear in lbs

l = span length in inches

M = moment in inch-lbs

E = modulus of elasticity

I = Moment of Inertia

The bending stress fb can be calculated by setting the design moment (theoretical moment) equal to the actual moment and solving for fb. The actual moment is calculated as follows:

Mact = Ixx/y * (fb)

Where:

M = moment in inch-lbs

fb = the bending stress at position y

Ixx = the Moment of Inertia about the x axis (strong axis)

The Moment at yield is at the extreme fiber when the distance y is at it's further distance from the neutral axis. This point will be established as y = c. Moreover, this will provide us the yield stress of the material fy.

M yield = Ixx/c * fy

Setting the deign moment equal to the yield moment and solving for fy will give us the experimental yield stress for each test.

M max = M yield

Mmax = Ixx/c * fy

Solving for fy:

fy = (Mmax * c )/ Ixx

Similarly, The deflection can be set equal to each of the deflections measured.

deflection tested = (Pl^3)/(48EI)

Solving for E:

E = (Pl^3)/ (deflection tested * 48 * Ixx)

The moment of Inertia about the neutral x axis can be calculated and see as follows for our respective prism beams:



Comprehensive and detailed spreadsheets will be complied for all test specimens at all recorded levels. This will allow our team to establish the material properties of all of out tested specimens.

Sample Bending Calculation
Bending Engineering Calculations Green Rectangular - Test 3 - Prism Beam 10% Infill

Givens:

Span = 5.5 in

P = 42.5 lbs

b = .5 in

h= .5 in

c = h/2 = .25 in

MDesign = Pl/4

MDesign = (42.5 lbs * 5.5 in)/4

MDesign = 58.4 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

fy = (Mmax * c )/ Ixx

fy = (58.4 in*lbs * 0.25 in)/ 0.005208 in^4

fy = 2,805 psi = 19.3 Mpa

Sample Deflection Calculation
Deflection Engineering Calculations Green Rectangular - Test 3 - Prism Beam 10% Infill

Givens:

Span = 5.5 in

height (h) = 0.5 in

base (b) = 0.5 in

Ixx = (1/12)*b*h^3

Ixx = (1/12)*(0.5)*(0.5)^3

Ixx = 0.005208 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (22.5 lbs)*(5.5 in)^3 / [(4mm/(25.4mm/in))*48*(0.005208 in^4)]

E = 95,083 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Sample Failure Load Prediciton
Predicted Failure Engineering Calculations for Yellow Triangular Prism Beam with 10% Infill

The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for average PLA material with 10% infill is fy = 3,457 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for the Yellow Triagnualr Prism Beam with 10% Infill.

Given:

Span = 5.5 in

b = .5 in

h= .43 in

c = h/3 = .1433 in

Ixx = 1/36*b*h^3

Ixx = 1/36*.433*.5^2

Ixx = 0.001104 in^4

Mmax = (Ixx/yc)* fy

fy = 3,457 psi (average of all test)

Mmax = (0.005208/4)*3,457 psi

Mmax = 26.6 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

26.6 = Pl/4

P = 26.6*(4)/(5.5)

P = 19.4 lbs

Using the average data base sample fy = 3,457 psi predicts that the green PLA rectangular prism beam (10% infill) with a base of 0.5 inch and height of .43 inch will fail at approximately 19.4 lbs.

The actual failure was 20 lbs.

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.

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 amount of trials ranging from 10 to 20.

The second test performed was the 2-point bending test. The procedure seen below was used to determine PLA's ultimate stress. 

<br \>



Stiffness dependence on PLA color, from most stiff to least stiff
Clear (2.77 GPa) > Luminescent > Blue = Black > Green = Red (2.55 GPa) <br \> 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.

Summary of Results to Date
The following data table summarizes our testing and calculations to date (12-2-14).



 Overall Results 

Overall, the results to date make a lot of sense when compared to each other, published values of PLA material and other popular building materials. The table above summarizes and tabulates the 17 tests performed to date. Moreover, the results gives us working Mechanical Properties of the PLA material in the form of yield stress (fy) and elasticity (E) which allows us to predict the failure load of test before we preform them. This brings the project full circle, allowing us to perform real life Engineering similar to the engineering practiced everyday by structural and mechanical engineers.

When comparing the results to each other, the Red PLA material is the strongest with an average yield stress (fy) of 4,417 psi, followed by the green at 3,934 psi and the yellow at 2,410 psi. When comparing the elasticity (E), the green PLA material is first with an average 102,219 psi closely followed by red with an average value of 94,597 psi and yellow at a distant third with an average value of 73,942 psi. There are factors and variables that skew these results and they will be addressed as well below.

The published yield stress for PLA solid material is 7,300 psi. Our average value tested value for PLA material was 3,510 psi which is a very reasonable number considering we only have 10% infill compared to a solid specimen. The published elasticity value for PLA solid material is 510,000 psi. Our average value tested value for PLA material is 89,012 psi which is a very reasonable number considering we only have 10% infill compared to a solid specimen. All tested specimens to date have been with 10% infill which is significantly lower in strength (fy) and elasticity (E) than solid PLA prism beams. The results validated this and showed that our prism beams with 10% infill make sense. The source for the PLA published data can be found at http://plastics.ulprospector.com/generics/34/c/t/polylactic-acid-pla-properties-processing.

PLA material does very well when comparing its yield strength (fy) to other materials. Even with only a 10% infill the PLA material tests showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum. This is examined in full detail below as the values are plotted against popular building materials. Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. But its weakness is clearly its low E values. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today. This is examined in full detail below as the elasticity (E) values are plotted against popular building materials. The published density value for PLA solid material is 78 lb/ft^3. Our average value tested value for PLA material is 27.7 lb/ft^3 which is a very reasonable number considering we only have 10% infill compared to a solid specimen.

 Variability/Error 

There are several sources of variability in the project to date. The first is PLA color which could affect its mechanical properties and that has been discussed above.

Shape:

Theoretically, the mechanical properties should be the same for each color regardless of shape. This would probably be true if our prism beams were 100% solid PLA material but they are only 10% infill. The 10% infill has a different affect on each shape as the Makerbot manufacturing process results in drastically different densities for the respective shapes. As a result this skews our results and creates some explainable inconsistency's between shapes. As seen from our data, the triangular shapes have the highest density's pushing 40 lb/ft^3. In contrast, the rectangular shapes have the lowest density in the low 20's lb/ft^3. This makes sense as the uniform nature of the rectangular prism is much easier to manufacture with the honey comb infill. Moreover, the percent of infill versus the surface area of the different shapes varies adding to the variably in the comparative densities. The bottom line is that 10% infill is not the same with each shape which is a major source of our variability.

Printer:

Through testing, it is evident that there is a major difference between the densities of the parts produced by the 5th generation printer and the second. So much so that a column on the data table has been added to quickly distinguish which printer produced which part. The only part which was produced by both printers to date was the Green Rectangular Prism with 10% infill. The density of the 5th generation printer is 26.4 lb/ft^3 compared to only 22.6 lb/ft^3 for the 2nd generation 3D printer. This trend between the 2 printers is consistent throughout our data. Moreover, the 2nd generation printer is struggling to produce consistent parts particularly with the yellow PLA material. Unfortunately, with all of the problems the lab had with the printers, our team had to take what we could get. The following pictures show the deficiency of the yellow parts produced by the 2nd generation printer.



Rope Thickness:

Our compiled test data shows that there is also variation between test with the thickness of rope used to support the weight during the testing procedure. The rope thickness has also been added to the data table. I am fearful that the thinner rope is causing another failure mode other than bending on the specimens resulting in lower failure loads (P). In establishing mechanical properties, it is imperative that we induce a bending failure. I recommend that for future tests we only use the bigger rope. Failure modes will be closely monitored and documented so that a true bending failure is the testing goal for all tests.

Repeatably:

I suggest that we complete 2 more trials for prism beam for a total of 3 each and average the values. This will give our team much more accurate results and allow us to isolate odd-ball tests. This will not be possible for any of the red prism beams as the lab is out of red PLA material. Three total trials can be completed for the green PLA material and other colors that are available to produce. The results seem to be reasonable but still I believe there is some experimental error and three trials of each color we be very beneficial. Most importantly, 3 tests will allow our team to isolate the variables described above.

All in all our results make sense. I believe with 3 trials of each we can even improve upon our work to date.

Comparison of Common Material Yield Stresses
The flowing table compares our PLA material yield stress to common materials.



The PLA material does very well when comparing its yield strength to other materials. Even with only a 10% infill the PLA material test showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum. Moreover, the PLA material with only 10% infill has strength values which are roughly half of the 100% solid PLA material.

Comparison of Common Material Modulus of Elasticity's
The flowing table compares our PLA material Elasticity to common materials.



Clearly, the weakness of this PLA material is it's Modulus Of Elasticity (E) when comparing it to other popular construction materials. When comparing to other materials such as wood, aluminum and steel, the E value for PLA material is virtually non-existent. However, when comparing our tested PLA material Elasticity to the published elasticity for 100% solid PAL material it does pretty well with about 15% of the elasticity values.

Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. Buts weakness is clearly its low E numbers. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today.

Comparison of stress/strain to load/deflection curves
The following pictures show some samples of stress vs strain and load vs deflection curves:

This is a good summary showing the stress vs. strain curve for various infills of PLA material. It is important to note that they all take on the same shape as do the curves posted in our wiki pages for our test results. We are looking for a nice linear curve during the elastic region followed by a curve during the plastic, yield and breaking point. Stress is simply force/area. Strain is simply deflection/length. Therefore, the curves for load vs deflection and stress vs strain should be of similar shape for a good test.

This is a great example which shows that Load vs Deflection and stress vs strain are proportional. Once again, it is good practice to plot load vs deflection during a bending test. The major reason is to make sure it takes on the same shape. If there are major discrepancies with the shape of a bending test compared to these curves more than likely something is going wrong in the experiment. All of our load vs deflections test models these curve properly.

Presentation
Link to Presentation