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Solid Mechanics project · IIT Hyderabad
How much will it sag?
A 3D-printed PLA beam under a constant load keeps bending with time. We measured that creep on a real beam for 24 hours, fit a model to the first 6 hours, and checked whether it predicts the rest.
Main result
Could 6 hours of data predict the later sag?
Predicted
Measured
Prediction error
Predicted compared with measured
Free length
Clamp edge to load point
Stress at the clamp
Starting stiffness
Creep readings
Core idea: Creeping observed as a function of time.
Experiment setup
Beam configuration
Use your measured averages. Beam age is the time from printing to the start of the creep run. Earlier test loads don't reset it. Thickness error counts three times in E, because I depends on t³.
Workflow
Project progress
Sources of error
What can spoil a creep test
- Tape carrying the load. Its slow slip looks exactly like creep.
- Moving the camera, or bumping the clamp or table.
- Retightening the clamp during the run.
- A fan or direct sun. Log the temperature at every reading.
- Equal time gaps. Space readings closer together early on.
Simulation
3D beam lab
Tip deflection
Extra sag since 10 s
Apparent E now
9 short lessons, then a quiz
How creep works
From what bending does to a beam, down to what PLA's molecules do under a load that never changes. No background needed. Each lesson takes about a minute.
Short tests · about 10 s per load
Step 1: E and kθ
With the clamp fixed, each load hangs from a thread loop at several distances a from the clamp edge. Deflection is measured at the load point, 10 s after the load settles.
Readings
Load tests
| Load distance a (mm) | Mass (g) | Deflection δ (mm) | C = δ/P (mm/N) | Remove |
|---|
Results
Stiffness
Effective E
—
Effective clamp stiffness kθ
—
From one photo, kθ = P L / θ₀. Compare it with the value above.
Straight-line test
C / a² against a
Constant load
Creep readings
Tip deflection from each photo, measured from the unloaded photo. Time is since the load went on. Write it as 10 s, 5 min or 1.5 h; a bare number means hours.
From your error workbook
Measurement errors
Copy the three standard uncertainties from the Click Error, Scale Error and Camera Error sheets. Error bars then show ±2 × the combined error, about a 95 % range: U = 2√(click² + (scale % × δ)² + camera²).
Reading schedule
Tip deflection
| Time | Tip δ (mm) | Temp (°C) | Note | Remove |
|---|
Live plot
Deflection over time
Live plot
Room temperature
Calibrate, then test
Fit and predict
The fit only sees readings up to the cutoff. Later readings test it, so a good result means the model predicted data it had never seen.
Model comparison
Three models, same readings
| Model | Fitted numbers | Fit error (rms) | Mean error, unseen readings | Error at last reading |
|---|
Result
Measured and predicted deflection
Predictions
Later deflection
| Time | Predicted | Reading noise | Measured | Error |
|---|
“Reading noise” is only the spread from photo error. Temperature and model error add to it.
Keep it honest
Frozen prediction
From all readings under load
Which stage of creep did we reach?
Creep rate is how fast the tip is sinking. Each point is the average rate over a window that doubles in time, such as 1 h to 2 h. Falling rate means primary creep, a steady rate means secondary creep, and a rising rate is the sign of tertiary creep, which ends in failure.
Design result
E is not one number
Eapp(t) = P L³ / (3 I δ(t)). It uses the tip deflection, so it includes clamp rotation.
Using the result
Design tools
Estimate the sag of another cantilever with the same cross-section and print settings. Since δ ∝ P L³, the measured curve scales to the new length and load.
Result
Sag over time
New part
Your cantilever
First reading (10 s)
—
Reaches allowed sag
—
Stress at the clamp
—
Reliable up to
—
3× the longest reading
Design chart
Which E should a designer use?
| Load held for | E to use | Sag compared with 10 s | Basis |
|---|
Beat the model
Guess the sag
You see how far the beam bent in the first moments. Guess how far it had sunk after 24 hours under the same load. Then see how you did against the model.
Real beam beside the model
Photos vs model
Drag through the readings. The photo, the 3D model and the curve all move together.
Photo
Real beam
No photo for this reading
Simulation
Model at the same moment
Measured tip
—
Model
—
Difference
—
Room temperature
—
Result
Where this moment sits on the curve
Matching
Which photo belongs to which reading?
Photos are matched in filename order. Check each one and correct any that are wrong.
| Photo | File | Reading | Remove |
|---|
About this project
CreepLab
A student project on how a 3D-printed PLA beam keeps sagging under a constant load, and whether a short test can predict that sag.
What we did
We printed a 220 × 20 × 4 mm PLA beam at 60% infill and clamped it as a cantilever. Short load tests gave its effective stiffness E and the clamp's rotational stiffness kθ.
We then hung a constant load of about 100 g and photographed the tip: repeatedly up to 6 hours, then at 12, 18 and 24 hours. The beam was then unclamped.
Three creep models were fitted to the first 6 hours only. The later readings test those fits, so this is a hold-out test: they already existed when the fit was made, but the fit never used them.
Limits of these results
- The results come from one test on one beam, so they don't describe all printed PLA.
- The ageing rate μ is taken from published PLA data, because one beam can't measure it.
- The beam carried some test loads before the creep run.
- The test ran in a normal room, not a temperature-controlled chamber.
- The 3D lab and molecular animations are explanatory simulations, not measurements.
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Project details
References
Fischbach & Weinberg (2023), source of the published PLA creep and ageing values. arXiv:2302.11240
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