# High-Compression Crash Simulations and Tests of PLA Cubes Fabricated Using Additive Manufacturing FDM with a Scaling Strategy

*Computation*—Computational Engineering)

## Abstract

**:**

## 1. Introduction

^{−1}). The corresponding force–displacement curves displayed a high initial, undesirable peak of force. Chen et al. [16] performed an experimental and numerical investigation of 3D-printed PLA origami tubes printed at 5 mm/min, but, once again, this was conducted under quasi-static uniaxial compression. Quanjin et al. [17] studied the effect of the infill pattern, density, and material type of 3D-printed PLA cubic structures, also under quasi-static loading. They similarly observed an undesirable high peak in force. Yousefi et al. [18] researched additively manufactured, foamed polylactic acid for their potential use as lightweight structures with varying densities by altering deposition temperatures. In their study, they performed tensile and bending tests at a low speed rate of 2 mm/min, demonstrating an improvement in stiffness induced by incorporating sandwich beams with a shell-and-foam core. Strain rates were not reported in this research. Sajadi et al. [19] tested various structures made of PLA, showing a desirable, nearly flat plateau at up to 50% compression and reporting specific energy absorption for each design. Simulations were executed at a very high strain rate of 10

^{10}s

^{−1}using molecular dynamics (MD), while tests were performed at 2 mm/s for a cube of size 50 mm, which led to a low strain rate of 2/50 = 0.04 s

^{−1}. Rahman et al. [19] explored the optimization of FDM manufacturing parameters for assessing the compressive behavior of cubic lattice cores using an experimental approach via the Taguchi method. They used a compression speed of 2 mm/min for a cube with a size of 30 mm, which led to a low strain rate of 0.0667 s

^{−1}. Searching for porous structures tested at high strain rates, we find research for bones. Real bones tested at high strain rates between 10

^{−3}and 10

^{3}s

^{−1}by Qiu et al. [20] showed a large influence of strain rate on Young’s modulus and ultimate stress compared with fresh bone dehydrated and kept in formalin.

- Verify the repeatability of compression force–displacement curves for cubes fabricated using additive manufacturing;
- Verify the scalability of experimental curves to obtain a unique stress–strain curve for all sizes;
- Verify simulations of compression with a unique stress–strain curve and providing a good correlation with experimental results;
- Develop a protocol for assessing dimension mass and velocity for impacts on each cube side;
- Validate explicit simulations with mass scaling to adjust time steps;
- Compare the use of foam materials with conventional plasticity models;
- Validate simulations with large strain rates.

## 2. Materials and Methods

#### 2.1. Fabrication of PLA Cubes

^{3}), as is anticipated for weight.

#### 2.2. Compression Tests of PLA Cubes

^{−1}(ranging from 0.2 mm/s for L = 10 mm up to 0.5 mm/s for L = 25). For all tests, displacement, force, and time were recorded every 0.01 s (100 Hz). Tests were performed at up to 80% compression once the force plateau was reached and all specimens showed a large, undesirable load increase. Therefore, the time required to test the sample was 0.8/0.02 = 40 s, yielding 4000 data points.

_{z}= −0.8 (80% compression), ε

_{x}= ε

_{y}= 0.4, and therefore the area is increased by (1 + 0.4)

^{2}= 1.96, and for the same constant (plateau) force, stress should be reduced by 1/1.96 = 0.51 at 80% compression. As mentioned above, this introduces a large error if the large degree of strain is not calculated accurately.

^{2}and mass and volume by s

^{3}. Using the datasheet for force and displacement, energy was monitored for each specimen up to around 50% deformation to avoid impacts entering the densification zone where a steep slope of force displacement is reached. The expected scaling for energy should be proportional to scaling force and displacement and therefore scaled by s

^{3}. This means that it was necessary to check if we obtained the same energy/mass ratio for all geometries and orientations. Once we selected the amount of energy for impact, we chose the impact mass and velocity. For small specimens, we fixed the average acceleration to be in the range of measurable 50 g and calculated the minimum mass. After the examination of results, it was found that for small specimens, we obtained a mass of 16 kg and velocity of 1.8 m/s, while for a large specimen, these values were 40 kg and 4.5 m/s. For other geometries, mass and velocity were scaled by ratio s, and therefore energy was scaled by ratio s

^{3}. For the maximum ratio s = 2.5, we expected to obtain 2.5 × 50 g = 125 g, which is acceptable for accelerometers before the detailed examination of experiments. Impact time was also estimated as t = v/a assuming constant deceleration. With this, we expected to have impacts of 1.8/(50 × 9.805), approximately 3.6 ms. All these initial numbers are fundamental to acquire accelerometers and signal-monitoring systems of high frequency.

#### 2.3. Simulation of Compression and Impact Tests of PLA Cubes

^{®}Virtual-Performance (previously known as PamCrash) version 2019 software run on an HP Envy Laptop with a 4-core Intel

^{®}Core™ i5-10300H CPU @2.5 GHz. An explicit solution where nodes are constantly updated was used, thus yielding real cross sections and lengths. Therefore, the software uses the true stress and true strain approach.

^{2}), stress (GPa), force (kN), energy (J) and density (kg/mm

^{3}).

^{−1}.

- The first time step was forced to slow down to 0.1 µs, which is the worst-case scenario for small cubes compressed by 90%.
- The second approach utilized a free time step, which changed during compression.
- The third approach involved mass scaling to force the time step to be 5 µs. This entails that if a maximum compression requires a time step of 0.1 µs, density must be multiplied by a factor of (5/0.1)
^{2}= 2500. This is an extreme case of mass scaling where the mass of 1 g of small cubes will result in 2.5 kg, which could derive non-negligible differences in force.

## 3. Results

^{2}), showed a plateau at around 80 MPa. This is because 80 × 625 = 50,000 N = 50 kN was the maximum force allowed by the tensile test machine.

^{3}(1 cm

^{3}= volume of basic cube with L = 10 mm = 1 cm). For 46% compression, it was found that PLA cubes could withstand 21.6 kJ/kg or 25.92 J/cm

^{3}. For 50% compression, it was found that PLA cubes could withstand 25 kJ/kg or 30 J/cm

^{3}.

^{2}/(mg) = 47.8s) with the values from the experimental test and simulation. Errors in the estimation of acceleration from the simulations compared to those from the experiments are also provided.

^{−1}. However, impact tests are not carried out at a constant strain rate. Simulations of this impact allow for the plotting of the engineering strain rate and the true strain rate. The engineering strain rate assumes that the final compression from 4.9 to 5 mm implies a 0.1/10 = 0.01 strain, as the original length of the cube is used. True strain considers the part to be of a real length, calculated as 0.1/5 = 0.02 true strain. Therefore, in large compression, true strain is larger than engineering strain. To calculate explicit finite elements, their updated geometry is used after each time step, providing a true strain rate. Figure 12 shows the strain rate during an impact with a cube for L = 10 mm, m = 16 kg, and v = 1.8 m/s, resulting in 50 J of energy being absorbed.

^{−1}, while compression tests were carried out at a low speed of 0.02 s

^{−1}.

## 4. Discussion

^{3}. Using the findings of this research, the required length size of the cube was estimated to be in the region of 46% deformation, which corresponds to 75 MPa, prior to a steep force increase. This length is also proportional to s. From an experimental point of view, it is possible to calculate drop height, which is proportional to s

^{2}. Finally, it is possible to estimate from the scale factor the expected maximum level of acceleration. This estimation was determined to be 75L

^{2}/(mg) = 47.8s. These values were compared with the maximum values of acceleration from the tests and simulations, yielding a good agreement.

^{2}(49%), while for L = 15, we have a compact area of 144 over 225 mm

^{2}(64%).

^{−1}. For a sample of L = 10 mm to compress 5 mm (strain 0.5) with such a strain rate, we would require a speed of 5 mm × 440 s

^{−1}/ 0.5 strain = 4400 mm/s (22,000 faster than the current set up of 0.2 mm/s) in a time of 5 mm/4400 mm/ms = 0.00113 s. Such a test is impossible to achieve with a controlled acceleration and real compression force measurement as the machine should compensate for inertial forces to move the rigs. Therefore, impact tests are simple approaches for validating high strain rates. However, the strain rate is far from constant, as it starts and ends at zero, achieving a maximum strain rate around the region of interest of maximum acceleration.

## 5. Conclusions

^{3}.

^{−1}, while during the impact tests, the strain rates could reach 440 s

^{−1}, with a variation during the entire impact from the initial zero strain rate value. It is almost impossible to perform an experimental measurement of compression at such a constant strain rate as it would require a speed of 4.4 m/s during a displacement of just 5 mm. Therefore, the design of these impact tests allows the verification of high strain rates.

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Compression testing of cubes of different sizes in different directions for L = 15 and 20 mm.

**Figure 6.**Energy density obtained from experimental compression tests for L = 10, 15, 20, and 25 mm. Energy values at 40%, 46%, and 50% are provided for impact estimation.

**Figure 7.**Force-versus-displacement curves for experimental tests and compression simulations for L = 10, 15, 20, and 25 mm.

**Figure 8.**Stress–strain curve from experiments and compression simulation: (

**a**) full scale and (

**b**) detail for 20–25% strain.

**Figure 9.**Acceleration–time curves obtained from the integration of experiments (Test) and impact simulations (SIM).

**Figure 10.**Acceleration–time curves from the experiment (Test) compared to those from the simulations using different time steps for the worst correlation case for the smallest L, namely, L = 10 mm.

**Figure 11.**Time step used in simulation as a function of simulation time for compression and impact simulation.

**Figure 12.**Engineering strain rate and true strain rate during simulations of impact on PLA specimen.

**Table 1.**Cube size with scale factor ratio “s” compared to L = 10 mm in brackets, fabrication time, theoretical weight, and actual weight.

L [s] (mm) | Time (min) | Theoretical Weight (g) | Actual Weight (g) | Actual Density (kg/m^{3}) |
---|---|---|---|---|

10 [×1.0] | 8 [×1.0] | 1 | 1.241 ± 0.018 or ±1.45% | 1240 |

15 [×1.5] | 25 [×3.1] | 4 | 4.100 ± 0.008 or ±0.20% | 1215 |

20 [×2.0] | 59 [×7.4] | 10 | 9.660 ± 0.036 or ±0.38% | 1207 |

25 [×2.5] | 114 [×14.2] | 19 | 18.820 ± 0.082 or ±0.44% | 1204 |

Input | m (kg) | 16 | 24 [×1.5] | 32 [×2.0] | 40 [×2.5] | 16 × s |

Input | v (m/s) | 1.8 | 2.7 (×1.5) | 3.6 [×2.0] | 4.5 [×2.5] | 1.8 × s |

mv^{2}/2 | E (J) | 25.92 | 87.48 [×1.5^{3}] | 207.3 [×2.0^{3}] | 405 [×2.5^{3}] | 25.92 × s^{3} |

10(E/25.92)^{1/3} | L (mm) | 10 | 15 [×1.5] | 20 [×2.0] | 25 [×2.5] | 10 × s |

v^{2}/(2g) | h (mm) | 165.5 | 372.8 [×1.5^{2}] | 662 [×2.0^{2}] | 1034 [×2.5^{2}] | 165.5 × s^{2} |

Foam 45 | Strain (-) | 0 | 0.032 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 0.99 |

Stress (GPa) | 0 | 0.056 | 0.07 | 0.08 | 0.1 | 0.14 | 0.22 | 0.38 | 2 | |

Plastic 1 | Pl.Strain (-) | 0 | 0.375 | 0.476 | 0.576 | 0.675 | 0.774 | 0.878 | 0.978 | |

Stress (GPa) | 0.056 | 0.042 | 0.043 | 0.044 | 0.051 | 0.058 | 0.071 | 0.091 |

Compression | Impact | |||||
---|---|---|---|---|---|---|

Ts = 0.1 μs | Ts = free | Ts = 5 μs | Ts = 0.1 μs | Ts = free | Ts = 5 μs | |

Mass increase compression (%) | 0% | 0% | 9020% | 0% | 0% | 6280% |

Mass increase impact (%) | 0% | 0% | 0.56% | 0% | 0% | 0.38% |

N.Time Steps | 200,001 | 38,657 | 4001 | 200,001 | 26,621 | 4001 |

CPU (s) | 127 | 26 | 8 | 118 | 19 | 6 |

CPU vs. free (%) | 488% | 100% | 31% | 621% | 100% | 32% |

Input | m (kg) | 16 | 24 (×1.5) | 32 (×2.0) | 40 (×2.5) | 16 × s |

Input | v (m/s) | 1.8 | 2.7 (×1.5) | 3.6 (×2.0) | 4.5 (×2.5) | 1.8 × s |

mv^{2}/2 | E (J) | 25.92 | 87.48 (×1.5^{3}) | 207.3 (×2.0^{3}) | 405 (×2.5^{3}) | 25.92 × s^{3} |

10(E/25.92)^{1/3} | L (mm) | 10 | 15 | 20 | 25 | 10 × s |

v^{2}/(2g) | h (mm) | 165.5 | 372.8 (×1.5^{2}) | 662 (×2.0^{2}) | 1034 (×2.5^{2}) | 165.5 × s^{2} |

75L^{2}/(mg) | a (g) | 47.8 | 71.7 (×1.5) | 95.6 (×2.0) | 119.5 (×2.5) | 47.8 × s |

Test | a (g) | 46 | 69 | 86 | 110 | |

Simulation | a (g) | 45 | 69 | 90 | 115 | |

(sim-test)/test | % | −2.2% | 0% | +4.7% | +4.5% |

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**MDPI and ACS Style**

Garcia-Granada, A.-A.
High-Compression Crash Simulations and Tests of PLA Cubes Fabricated Using Additive Manufacturing FDM with a Scaling Strategy. *Computation* **2024**, *12*, 40.
https://doi.org/10.3390/computation12030040

**AMA Style**

Garcia-Granada A-A.
High-Compression Crash Simulations and Tests of PLA Cubes Fabricated Using Additive Manufacturing FDM with a Scaling Strategy. *Computation*. 2024; 12(3):40.
https://doi.org/10.3390/computation12030040

**Chicago/Turabian Style**

Garcia-Granada, Andres-Amador.
2024. "High-Compression Crash Simulations and Tests of PLA Cubes Fabricated Using Additive Manufacturing FDM with a Scaling Strategy" *Computation* 12, no. 3: 40.
https://doi.org/10.3390/computation12030040