Estimating Warpage of Selective Laser Sintering Parts Using Thermomechanical Analysis

The plastics used in Selective Laser Sintering (SLS) have a higher thermal expansion when compared with other materials. Therefore, it is important to know how the dimensions of an SLS part change at different temperatures during the build and during use. The higher the thermal expansion coefficient, the more prone are the parts to warpage or curling and the build-up of residual stresses. Learn more!

Selective Laser Sintering (SLS) is one of the most used Additive Manufacturing technologies to produce structural plastic parts. The plastics used in SLS have a higher thermal expansion when compared with other materials such as metals or ceramics. Therefore, it is important to know how the dimensions of an SLS part change at different temperatures during the build and during use. The higher the thermal expansion coefficient, often referred to as α or CTE, the more prone are the parts to warpage or curling and the build-up of residual stresses.

This is the case because the higher the thermal expansion coefficient, the larger is the effect of even the smallest temperature differences in the process. The thermal expansion or rather shrinkage during the process depends on the thermal shrinkage of the material and – in the case of semi-crystalline materials often used in SLS – the shrinkage due to crystallization. The amount of crystallization shrinkage depends on the polymer structure itself, but also the cooling temperatures. Looking at the SLS process, temperature gradients are inevitable and cooling rates are small.

Why the recoating process is responsible for creating curling

The most important factor for warpage – also called curling – is the recoating process. When a new layer of powder is applied, it is taken from the reservoirs on the sides. The powder there has to be kept colder (between 80 – 100°C for PA12) to keep it from agglomerating and caking together. Then, this colder powder is deposited on top of the molten material (for PA12 above 186°C) and the surrounding solid powder that is preheated to around 168°C. This results in a heat exchange in the different regions. Even so the IR heaters on top of the build envelope are working to heat the new layer up to 168°C as fast as possible, some cooling and reheating will occur, which introduces local transient temperature states.

This happens throughout the build, but is most pronounced when the first few layers are build. When the first layer is being melted, it is supported by a cooler bottom layer. During coating, colder powder is also deposited on the top, which rapidly cools this layer and likely initiates crystallization. When the newly deposited material is hit by the laser and melted, a steep temperature gradient between the first and second layer exists, which leads to compressive stresses at the top and tensile stresses on the bottom. This stress imbalance results in the upward curling of the layer. Curling means that the thin build sticks out of the powder bed at the corners and can be displaced or even ripped up by the next coating motion. This would be a failed print and typically needs to be aborted.

Understanding the curling effect

The degree to which the layer curls out of the plane, δ, depends on the temperature gradient, ΔT (between top and bottom), the length of the part, L, its thickness, d, as well as the thermal expansion coefficient α following this relationship shown in Figure 1:

Schematic Curling Effect
Figure 1: Schematic of the curling effect with relevant parameters

This shows that for the same layer (or part) geometry, a high thermal gradient, ΔT, leads to more pronounced curling (high δ) if the coefficient of thermal expansion (α) is high as well. It is also obvious that the longer the part (large L) or to a lesser degree the thinner the part (small d), the higher is δ. Once more layers are stacked on top of each other, the thermal gradient is smaller and curling will only be a problem in thin sections of the part.

How to determine the coefficient of thermal expansion

To determine the CTE of a material a dilatometer or in the case of polymers, more typically a Thermomechanical Analyzer (TMA) is used. This measurement is typically performed on solid polymer samples that are being heated to temperatures close to melting. Although it should represent the reversal of the thermal and crystallization shrinkage happening during the process, it is not a direct measure of it and is not capable of capturing the full melting process.

For this study, dogbone specimens with 4.5 mm thickness were printed at the Institute of Polymer Technology (LKT) at the University Erlangen-Nuremberg with PA12 powder using standard parameters of 0.4 J/mm³. Then, samples of 10 mm x 5 mm x 4.5 mm were prepared and analyzed at NETZSCH Analyzing & Testing Since the thermal expansion of unfilled PA12 is considered isotropic, the samples were only extracted in one build orientation (X-direction):

TMA Sample
Figure 2: Location of the TMA sample and its orientation in the global build coordinate system

The measurements were performed with a NETZSCH TMA 402 F1 Hyperion® equipped with a steel furnace. Following an initial cooling step, the temperature was increased at 5 K/min from -15…170°C, which corresponds to the temperature of the build envelope. The thermal expansion coefficient was calculated using the mean CTE analysis (m. CTE), which computes the slope between two data points using a reference temperature Tref of 20°C. Following DIN 51054-1 the mean is given as

where Tref is the reference temperature (typically around 20 to 25°C for measurements that start below 0°) and L0 is the length at room temperature.

All measurement conditions are summarized in the following table:

Table 1: Measurement conditions

Sample holderExpansion, made of  SiO2
Sample load50 mN
Gas flow rate50 ml/min
Temperature range-15…170°C at a heating rate of 5 K/min

Estimating curling for different temperature gradients

The measurement results are depicted in Figure 3. The glass transition Tg is located at 36°C (extrapolated onset), which is in good agreement with literature values for PA12. The mean CTE was calculated below and above the Tg. However, it was observed that above 130°C, the slope changes again and therefore, an additional CTE value in the temperature range of the process was analyzed between 150…170°C.

TMA Measurement SLS Sample
Figure 3: Measured length change of the sample and detection of the Tg as well as of the CTEs below and above the Tg

Using the measured CTE(150…170°C) of 323 x 10-6 K-1 in an exemplary analysis, the difference between a 1 and 5 K temperature deviation can be visualized using constant dimensions for L (50 mm) and d (1 mm):

Using these assumptions, it can be seen that the degree to which the layer curls out of the plane, δ, can be significant even for small temperature gradients. Especially, the curling up by 0.1 mm can be enough for the roller to bump into and drag the previous build layers with it.

About Institute of Polymer Technology (LKT)

The Institute of Polymer Technology is an academic research institute at the Friedrich-Alexander University of Erlangen-Nuremberg. It is one of the leaders in Additive Manufacturing research; particularly SLS. Other main research areas include Lightweight Design and FRP, Materials and Processing, Joining Technology and Tribology. In addition to these research focuses, the institute is also working on cross-disciplinary topics such as Filler Material ­Compounding, Simulation of Processing and Applications, Radiation Cross-linked Thermoplastics, Gentle Processing and many more.

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