Mechanical and Thermal Characterization of Phase-Change Material and High-Density Polyethylene Functional Composites for Thermal Energy Storage

Phase-change materials (PCMs) for thermal energy storage or thermal management applications are of significant interest because they absorb large amounts of heat at a nearly constant temperature when changing phase from a solid to a liquid. Two types of PCMs, inorganic (e.g., water and salt hydrates) and organic (e.g., paraffin waxes, fatty acids, and plant-based materials), are primarily used for thermal energy storage systems in various applications [1] such as thermal comfort [2–5], load shifting and peak shaving [6–9], thermal management of photovoltaics [10–15], solar still desalination [16,17], concentrated solar power [18–21], and cold-storage/delivery for perishable products [22–25]. Organic PCMs are the main focus of this study because they are chemically stable, melt congruently, and are mostly non-toxic/non-corrosive [26], unlike their inorganic counter-parts [27–29]. Furthermore, they can be shape stabilized with certain polymers, such as high-density polyethylene (HDPE), which can have many applications for advanced manufacturing.

Since the PCM cycles between solid and liquid phases, encapsulation or containment of the PCM is necessary. Inorganic PCMs are particularly difficult to contain since they have variable water content and are hydrophilic [27]. Organic PCMs, such as paraffins, are usually compatible with metal containers; nonetheless, they contain hydrocarbons, which makes sealing them with certain plastics difficult as the PCM can leak through the material structure. However, specific polymers such as HDPE, low-density polyethylene (LDPE), polypropylene (PP), polyethylene (PE), and others have supporting matrices that can be used to trap and shape stabilize the PCM [30,31]. The polymer used needs a higher melting point because, when shape stabilized and heated, the PCM remains contained within the polymer matrix. HDPE, in particular, has been found to be compatible with many different types of organic PCMs. In 1997, Inaba and Tu [32] were the first to shape stabilize PCM (pentacosane C₂₅H₅₂) in HDPE. PCM can be shape stabilized using the common methods of high-temperature mixing, polymer extrusion, or casting [33,34].

The miscibility, thermal properties, and leakage issues of PCM combined with different polymers, such as HDPE, LDPE, and linear low-density polyethylene (LLDPE), were explored by Chen and Wolcott [35,36]. The combination of 70$%$ PCM with 30$%$ HDPE showed the least amount of leakage when compared to the alternative polymers. Blends with different polyethylenes [37–42] and different paraffin waxes [43–49] have had extensive investigations of their thermal and structural properties. Additionally, additives in HDPE and PCM composites have been researched as well [50–62]. HDPE is used in the present study since it is compatible with many types of organic PCMs, based on prior literature illustrated above.

The influence of PCM content in HDPE, LDPE, and LLDPE on the thermal and tensile properties was studied by Molefi et al. [40], who used a melt-press process and determined that as PCM increased, the tensile strength and thermal stability decreased. Chalkia et al. [63], using casting to manufacture their shape-stabilized composites, explored the mechanical properties of organic PCMs combined with HDPE and PP under high temperatures over a 40-day period and found that the introduction of PCM decreased the mechanical properties significantly. The mechanical strength of the HDPE was decreased immediately after the incorporation of PCM but was remarkably restored after 28 days due to achieved uniformity from the molecular dispersion of PCM. A plasticization effect was observed by Mu et al. [49] after they developed a shape-stabilized paraffin and HDPE blend for PCMs, using a twin-screw extrusion and compression-molding process, with high and low melting points. Different modes of deformation (tension, flexural, compression) decreased as they increased PCM. Similarly, Krupa et al. [64] observed plasticization that led to a decrease in thermal and mechanical properties when microencapsulated paraffin wax was blended with HDPE and hot-pressed. These studies are supportive of the current research and the present paper expands on additional tests to see the impacts on hardness, effective latent heat of fusion, and thermal conductivity.

The injection-molded mechanical and thermal properties in the present work have been explored to develop a comparable foundation for future 3D-printed PCM/HDPE composites using fused filament fabrication (FFF). Since being patented in 1989 [65], FFF has seen significant advancements needed to produce polymer-encapsulated thermal energy storage systems that enable enhanced heat transfer with intricate geometrical features—the eventual application of the PCM/HDPE composite material studied here. Polymer heat exchangers for these types of applications are advantageous because they are light, corrosion resistant, and inexpensive. Low thermal conductivity of polymers can be mitigated by decreasing the wall thickness [7,66,67], which is easily done using FFF, without the need for high-thermal-conductivity fillers [68–70]. Alternative manufacturing techniques, such as injection molding, cannot achieve the high surface-area-to-volume ratios needed for improved heat transfer. However, the injection-molded composites examined in this study will provide a baseline for comparison when investigating the properties of the eventual 3D-printed materials.

The thermal properties and composition of extruded PCM/HDPE composite filament were investigated for the purpose of FFF in previous work by the present authors [71,72]. In more recent work, the extruded PCM/HDPE composite filament was 3D printed using FFF, and the thermal properties were further explored [73,74]. To combine PCM and HDPE, high-temperature mixing was used and followed by a pelletizing and extrusion process. Through this process, a functional composite filament with a 1.75-mm diameter and thermal energy storage capability was developed. The effective latent heat of fusion of the filament, which corresponds to the thermal energy storage capacity of the composite, and thermal conductivity of the composite were measured.

In the current study, HDPE was used to shape stabilize organic PCM that changes phase at 42 $∘$C using an injection molder. The mechanical characteristics, such as tensile strength, modulus of elasticity, and hardness, along with thermal characteristics, such as latent heat of fusion, phase-change temperature, and thermal conductivity, are the main focus. The microstructures of the HDPE and the composite after tensile-test failure were performed and visualized as well.

PureTemp 42 (PCM42) was supplied from PureTemp (Minneapolis, MN), HDPE pellets from INEOS Olefins, and Polymers (League City, TX) were supplied. The thermal and mechanical properties provided by the manufacturers of the PCM42 [75] and HDPE [76] are provided in Table 1. In the table, T_sl is the phase-change temperature, h_sl is the latent heat of fusion, ρ is the density, k is the thermal conductivity, TS is the tensile strength, and E is the modulus of elasticity.

Ideally, since the PCM percentage directly correlates to the thermal energy storage capacity, the amount of PCM in the composite should be maximized; however, the structural integrity (i.e., flexibility) of the filament for 3D printing can be diminished by adding too much PCM. If too much PCM is in the mixture, the filament becomes too brittle. The PCM42/HDPE composites were created by pre-melting and mixing the materials to form specific mass ratios. The mass content of the PCM42 in the mixture was varied between 20% and 50%, in increments of 10%. It was determined that the maximum amount of PCM content that can be added to the HDPE while still producing viable filament for printing is approximately 50%. A differential scanning calorimeter (DSC) was used to estimate the amount of PCM loss due to the manufacturing process by examining the latent heats of fusion and melt temperatures of both the PCM42 and the HDPE in each functional composite (discussed in Sec. 5.4). Due to variable losses across multiple mixtures, and for consistency, each ratio will be referred to as its original intended mixture, as listed in Table 2.

After mixing, each PCM42/HDPE composite ratio was pelletized using a shredder (SHR3D IT, 3devo, Utrecht, The Netherlands) and extruded into composite filament (keeping a consistent 1.75-mm diameter) using a filament extruder (Next 1.0, 3devo, Utrecht, The Netherlands). The composites were extruded in this manner to mimic the process the material would undergo for 3D printing as completed in the previous study [73]. Instead of printing the composite, it was shredded again and injection molded into the necessary shapes to obtain baseline values for eventual comparison to their 3D-printed counter-parts.

Custom machine molds and a plastic injection-molding machine (Pim-Shooter Model 150A, LNS Technologies, Scotts Valley, CA) were used to fabricate specimens for tensile, hardness, and thermal conductivity testing. For each specimen, a machine mold was fabricated to meet ASTM D638 [77] (tensile test) and ASTM D2240 [78] (hardness test) standards, which are discussed in the next sections. Using the tensile testing mold as an example, Fig. 1 shows the features incorporated into each mold. The runner is the point where the material is injected, which leads the molten flow into the mold through the gate, which is placed away from any point of testing and the interface between the gate. The tensile test specimen is 1.27 mm × 0.76 mm. The gate was strategically placed since excess material must be removed at that location after injection molding, and avoidance of interference/inaccuracies during the testing process was prioritized. The test coupon cavity dictates the shape of the specimen as it is the internal feature to be filled. The vent was placed on the opposite side of the flow for each mold to allow air to escape throughout the process and had a height of 0.0254 mm.

The temperature of the injection-molding machine was set based on the mixture (see Table 3), because as PCM was added to the composite, the melt temperature of the composite material decreased. The necessary mold was selected and set in an oven at 120 $∘$C for a minimum of 5 min. Once the material was melted and the mold was warm enough, the mold runner was lined up with the molding-machine tip. The manual lever on the injection molder was used to inject the material until the mold was visibly filled. After injection, the mold was cooled at room temperature (22 $∘$C) until the part was effectively solidified (or settled) before removal. Cooling the mold was necessary to prevent warping and damage to the part, which can occur when the part is prematurely removed from the mold without adequate time to cool. Once removed, the specimens were cleaned and visually inspected. Figure 2 depicts the injection-molded specimens for the tensile, hardness, and thermal conductivity tests. The dimensions met respective ASTM standards and final samples were measured with a caliper to ensure standards were met within tolerances specified in the ASTM standard.

The tensile properties of the PCM42/HDPE composite ratios were measured with an electromechanical test machine (Criterion Electromechanical Test System Model CA43.504, MTS, Eden Prairie, MN) with a 50 kN load cell and a displacement rate of 0.833 mm/s. Testing was completed following the ASTM D638 standard [77] at two different temperatures, above and below the melt temperature of the PCM at 45 $∘$C (20% relative humidity) and room temperature (22 $∘$C, 56% relative humidity), respectively. These temperatures were selected in order to observe the effects of both the solid and liquid (when melted) PCM on the thermal and mechanical properties of the composite.

The specimens were injection-molded to meet the Type IV tensile bar dimensions and specifications as defined by the ASTM D638 standard [77]. For five specimens, each end was mounted in the grips of the test machine and the force was recorded while the specimen was monotonically loaded in tension with the load cell.

Microstructure visualization of the samples was conducted using a scanning electron microscope (SEM, Quanta 650, ThermoFisher Scientific, Hillsboro, OR) to characterize the cross-sectional topography post-tensile testing. The SEM was operated using an accelerating voltage of 15 kV and a vacuum pressure ranging between 1.6 and 3.37 × 10⁻⁶ Torr. To improve conductivity and prevent surface charging, the samples were coated in gold (Sputter Coater 108, Cressington Scientific Instruments, Watford, UK).

The indentation hardness of the PCM42/HDPE composites were investigated per ASTM D2240 [78]. A Shore D durometer (durometer 53-762-102-0, Fowler, Canton, MA) was used to press an indentation head into the material until the flat bottom of the device was resting on the surface of the material. As specified in the standard, a flat 50.8 mm × 50.8 mm square with 6.35 mm thickness was tested at five different locations, as shown in Fig. 3, at room temperature for pure HDPE and for each PCM42/HDPE ratio. Each measurement was taken at least 12.7 mm (0.5 in.) from the edge or another measurement. ASTM D2240 [78] does not provide a testing standard for non-standard conditions, such as elevated temperature.

A DSC (DSC 3 STARe, Mettler Toledo, Columbus, OH) was used to obtain the phase-change temperatures and latent heats of fusion of the samples. The latent heat of fusion can be used to determine the effective amount of PCM in each tensile-test specimen. Samples, masses between 14 and 18 mg (measured using an analytical balance (XS105DU, Mettler Toledo, Columbus, OH)), were placed in 40 μL aluminum crucibles before being held isothermally at 10 $∘$C for 15 min, then heated from 10 $∘$C to 200 $∘$C at a heating rate of 2 $∘$C/min. Samples were then held isothermally at 200 $∘$C for 15 min and then cooled at −2 $∘$C/min until reaching a temperature of 10 $∘$C. Heatflow and temperature were recorded every 1 s, and the heating/cooling cycles were repeated at least three times to ensure repeatability and good contact between the sample and the bottom of the crucible.

An example heat flow versus temperature graph provided by the DSC is shown in Fig. 4. In the figure, the first and second peaks represent the phase change of PCM42 and HDPE in the sample, respectively. The latent heat of fusion is defined as the integral of the heatflow with respect to time during the phase change. The onset and endset temperatures are defined as the intersections between the tangents of the leading and trailing edges of the peak and the baseline.

To ensure even material distribution within the injection-molded parts, samples from eight different locations, defined in Fig. 5, on a random tensile-test specimen from each injection-molding lot was examined. It was found that there was a less than 1% variance in latent heats of fusion for the eight sampling locations for all lot samples tested. The consistent results allowed for further DSC measurements to be completed by testing one location per test specimen.

Thermal conductivity measurements were completed using a thermal constants analyzer (Transient Plane Source (TPS) 2500S, Hot Disk, Gothenburg, Sweden) with power of 50 mW and a sampling time of 10 s. A 4-mm-diameter sensor (C7577, Hot Disk, Gothenburg, Sweden) was secured between two 25-mm-diameter injection-molded samples with a thickness of 4 mm, as shown in Fig. 6. The sensor is made up of a resistive heater that allows for simultaneous temperature monitoring. The temperature response of the sensor while a constant heat flux is applied is used to determine the thermal conductivity of the sample set.

The tensile strength and modulus of elasticity were found for five samples of each ratio at room temperature and heated to 45 $∘$C. The average values, along with the corresponding standard deviations, are found in Table 4 and visually represented in Figs. 7 and 8. The tensile strength and modulus of elasticity for pure HDPE are 11.0% and 4.9% lower, respectively, than the values provided by the manufacturer (Table 1). When comparing pure HDPE to Sample D (the composite with the highest amount of PCM), both the tensile strength and modulus of elasticity decrease by 45.3% and 13.7%, respectively, at room temperature and decrease by 68.1% and 85.3%, respectively, when heated to 45 $∘$C. The larger decreases in tensile strength and modulus of elasticity in the heated case are due to the PCM being in a liquid state, which results in the PCM42/HDPE composite essentially becoming HDPE porous media with liquid PCM as the interstitial fluid. At least when the PCM is in the solid state, it can contribute to the structural strength of the composite.

Figure 9 has been prepared to show example stress-strain curves at room temperature for each sample. The HDPE and Samples A and B exhibit ductile failure, and Samples C and D show brittle failure with limited ductile deformation. At room temperature, as the PCM content increases, the average tensile strength decreases by 45.3% from pure HDPE to Sample D (Fig. 7). The decrease in tensile strength seen here aligns with other studies which have presented similar trends [40,79]. The average modulus of elasticity for the room-temperature results initially decreases by 21.4% from pure HDPE to Sample A and then increases 8.9% from Sample A to D (Fig. 8). However, it should be noted that although the average modulus of elasticity from Sample A to D increases, the standard deviation error bars overlap significantly; therefore, the increasing trend may not be statistically significant.

At room temperature, several of the samples (HDPE and Samples A and B), due to their ductility, exhibited neck propagation. Neck propagation is a phenomenon where a localized neck is formed in the material during failure, which then begins to elongate and steadily lengthen until the neck reaches the edges of the sample. This behavior is unique to certain metals and polymers with restrictions on deformation rate and material structure and has been studied extensively for HDPE [80–84]. The addition of PCM appears to alter the neck propagation effect significantly. Adding a small amount of PCM to HDPE (as seen in Samples A and B) decreases the tensile strength and subsequently decreases the stress during neck propagation, which remains constant throughout. Note, the loading condition during the necking remains identical throughout all samples, implying the neck is smaller in cross section for Samples A and B than pure HDPE at the point of failure. Mass conservation indicates that the material is allowed to stretch farther before the necking reaches the end of the sample, which is observed in Samples A and B. The end result is an increase in elongation, as the PCM42/HDPE composite is able to deform significantly farther than without the addition of PCM to the pure HDPE. However, with the further addition of more PCM (as seen in Samples C and D), the samples fall outside of the conditions required for significant neck propagation to exist. Subsequently, Samples C and D fail rapidly after a short localized necking, with Sample D failing at a lower stress due to the increased PCM content, exhibiting brittle-like behavior.

Figure 10, which displays representative stress-strain curves, shows that all of the samples exhibit ductile failure when heated to 45 $∘$C. Furthermore, both the tensile strength and modulus of elasticity decrease as the content of the PCM increases, as shown in Figs. 7 and 8. Comparing pure HDPE to Sample D, the tensile strength and modulus of elasticity decrease by 68.1% and 85.3%, respectively. The decrease in both tensile strength and modulus of elasticity is associated with the increase of PCM and is more noticeable than room temperature due to the liquid state of the PCM. Pure HDPE and Samples A, B, and C did not break before the tensile machine met the limits set by the heated-chamber size, while Sample D did fracture within the limits. The higher the content of PCM, the more porous the HDPE becomes when the test specimen is heated higher than the PCM phase-change temperature, which results in liquid PCM filling the HDPE matrix causing the sample to become less durable mechanically.

Microstructures, known as fibrils (string-like sections) and crazes (spherical voids) can sometimes be used to determine the degree of ductility a specimen experiences at the time of failure. Polymers typically do not exhibit brittle failure characteristics comparable to what occurs in metal, unless certain environmental conditions are met. Failures that have a planar layer deformation of less than 1 μm can be categorized as a brittle failure on a microscopic level [85]. An example of this can be seen in Fig. 11, which illustrates the brittle failure of a heated HDPE tensile specimen that was frozen and shattered using liquid nitrogen after it failed to fracture within the size limits of the heated chamber. This specimen shows clear signs of transverse fracture propagation, known as brittle fracture bands, and is the only specimen out of all of the samples that exhibits this behavior (due to the frozen fracturing and not the tensile test). In comparison, Fig. 12 shows an HDPE specimen that failed under room temperature conditions. The specimen exhibits clear signs of ductile failure in the form of crazes and fibrils.

Sample D, shown in Fig. 13, is of special interest since it is the sample with the highest ratio of PCM. While in the heated chamber, the PCM within the HDPE matrix is in a liquid state, causing the specimen to experience a decrease in resistance to deformation. The lowered resistance results in the formation of long fibrils that dominate the fracture area, as shown in Fig. 13(a). Under room temperature conditions, shown in Fig. 13(b), although the stress-strain curve for Sample D showed brittle-like behavior (Fig. 9), the microstructures show evidence of ductile failure, confirming the discussions in Sec. 5.1.1.

For each hardness specimen, measurements were taken at five different locations (Fig. 3) at room temperature and averaged. The average hardness and standard deviation results are presented in Table 5. The information is also displayed in Fig. 14 as a bar graph for comparison purposes; the error bars representing the standard deviation. The hardness value for pure HDPE is 9.4% lower than the value provided by the manufacturer (Table 1). Based upon the results, it can be seen that the hardness decreases as PCM is added. Similar hardness trends were seen by Ehid and Fleischer [86] when adding HDPE to pure paraffin wax. The hardness of Sample D is only 17.9% less than the value for pure HDPE. The incremental changes in hardness correspond to the addition of PCM. The hardness decreases by 6.2% between pure HDPE and Sample A, and another decrease of 6.2% occurs between Samples A and B. A smaller decrease of 5.9% between Samples B and C is observed, but there is only a 0.8% decrease between Samples C and D. Similar to the phenomenon mentioned in Sec. 5.1.1, at room temperature, the composite exhibits different mechanical behavior for samples with higher PCM content. When the PCM percentage is high enough in the composite, the decrease in hardness begins to plateau; however, the difference between the values is not statistically different due to the overlapping error bars. Further ratios with higher amounts of PCM need to be tested to confirm the continuation of this trend.

Upon completion of the tensile testing for each ratio, a single corner sample was taken from six randomly selected tensile-test specimens, three from room-temperature tests and three from heated tests. It was observed that, in general, the heated chamber from the mechanical testing had no discernible influence on the values obtained. Therefore, all measurements for each ratio (combined room temperature and heated) were averaged. The average phase-change temperature ranges (T_peak, T_onset, and T_endset are defined in Fig. 4) and latent heats of fusion (h_sl), along with corresponding standard deviations, are shown in Table 6. Figure 4 represents a typical heat flow versus temperature curve for the PCM42/HDPE composite. The first peak represents the latent heat of the phase change of the PCM, and the second peak represents the phase change of the HDPE. In the table, the effective latent heat due to the PCM42 changing phase is presented under the PCM column, and the effective latent heat due to the HDPE changing phase is presented under the HDPE column. As a baseline, values for pure PCM42 and pure HDPE are also shown.

As a way to determine the effective amount of PCM42 in each composite sample, the ratio of the effective latent heat of fusion of the PCM42/HDPE composite and the latent heat of fusion of the pure PCM42 was calculated. Based on the results from Table 6, Sample A had an effective PCM percentage of 9.2%, Sample B had 13.4%, Sample C had 23.7%, and Sample D had 28.6%. When comparing these values with the original intended ratios (Fig. 2), there was significant loss in PCM during the processing steps, as the percent PCM42 achievable here was considerably less then previous studies [72,73]. However, the manufacturing process in the prior studies [72,73], which included filament extrusion and FFF, was different than in the present study. Furthermore, in Refs. [72,73], besides the fact that the HDPE blend was slightly different, the latent heat of fusion of the filament was measured after one extrusion, and the latent heat of fusion was measured after two extrusions (filament making and injection molding) in the present study. Although material loss during fabrication significantly factors into the reduced ratios, other chemical interactions due to mixing may also play a role. It also appears that approximately 28.6% PCM42 is the upper limit with this set of materials and processing steps, since an increase in 10% PCM42 from Samples C to D only increased the final ratio by 4.9%.

The composite mixture also causes the PCM42 melting temperature to decrease. For the lowest ratio (Sample D), the peak melting temperature drops approximately 4 $∘$C to 38.9 $∘$C. This effect is diminished as the PCM42 ratio increases, with the peak melting temperature only dropping 3 $∘$C to 40.3 $∘$C in Sample D. The peak melting temperature of the HDPE is also influenced, being reduced the most with higher PCM42 ratios. In Sample D, the peak melting temperature of the HDPE is about 7 $∘$C lower than the pure material. The peak melting temperature is reduced by only 3.4 $∘$C in Sample A, which has the lowest PCM42 ratio.

The average thermal conductivity and standard deviation of the pure HDPE and each sample can be seen in Table 7 and Fig. 15. For each material blend, three different thermal conductivity specimens were measured six times each. The trend is similar to the hardness results. As the PCM content increases, there is a slight reduction in thermal conductivity. The value decreases slightly with the increase in the PCM ratio, which is expected since the thermal conductivity of the PCM (measured to be 0.276 W/(m · K) [73]) is much lower than HDPE.

A shape-stabilized PCM42/HDPE composite was fabricated using an injection-molding process, and the initial mass content of PCM in the mixture varied between 20% and 50%. Through DSC testing, it was determined the effective thermal storage capability was considerably less than the expected value due to the loss of PCM in the composite after the manufacturing process. With increased PCM content, the thermal conductivity, hardness, and tensile properties decreased, and during tensile testing, several samples exhibited a significant change in neck propagation due to the presence of PCM. After tensile testing, the microstructures of the PCM42/HDPE composite material were investigated utilizing SEM. Ductile failures were observed for pure HDPE at room temperature and for the PCM42/HDPE composite at room temperature and when heated.

The results are useful in relation to manufacturing purposes since the ability to shape stabilize different amounts of PCM in a polymer can be used to potentially transform the fabrication of thermal energy storage and management systems. Thermal cycling for long-term stability and leakage issues need to be investigated further. However, HDPE and PCM have been proven to be compatible, and epoxy coatings applied to the outside of the fabricated parts to seal may be used to mitigate leakage issues [87,88]. Injection molding of these composites has laid a baseline foundation of mechanical and thermal characteristics for comparison to specimens produced by additive manufacturing, such as FFF.

Support from the National Science Foundation (NSF) is acknowledged under Grant No. MRI-1337742 for the purchase of the SEM. M.A.M. acknowledges support through the NSF Graduate Research Fellowship Program under Grant No. DGE-2041850. This research was performed under an appointment to the Building Technologies Office (BTO) IBUILD- Graduate Research Fellowship administered by the Oak Ridge Institute for Science and Education (ORISE) and managed by Oak Ridge National Laboratory (ORNL) for the U.S. Department of Energy (DOE). ORISE is managed by Oak Ridge Associated Universities (ORAU). All opinions expressed in this paper are the author’s and do not necessarily reflect the policies and views of DOE, EERE, BTO, ORISE, ORAU, or ORNL.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

k =

thermal conductivity (W/(m · K))

E =

modulus of elasticity (N/mm²)

T =

temperature (⁠$∘$C)

h_sl =

latent heat of fusion (kJ/kg)

T_sl =

phase-change temperature (⁠$∘$C)

TS =

tensile strength (N/mm²)

$ε$ =

engineering strain (N/mm²)

ρ =

density (kg/m³)

σ =

engineering stress (N/mm²)