Das rasche Wachstum der additiven Fertigungsindustrie hat aufgrund ihrer erneuerbaren Quellen und vielseitigen Anwendungen Interesse an Polymeren auf Basis von Polymilchsäure (PLA) geweckt. Diese Studie konzentriert sich auf das Torsionsverhalten additiv hergestellter PLA und untersucht die Auswirkungen der Füllungsorientierung auf Torsionskapazität, Schermodul und Schadensindex unter monotonen, zyklischen und umgekehrten zyklischen Belastungen. Die Ergebnisse zeigen, dass Proben mit einem 45 ° -Infill-Orientierungswinkel im Allgemeinen besser abschneiden als Proben mit einer 0 ° / 90 ° -Orientierung. Bemerkenswert ist, dass PLA-zähe Proben im Vergleich zu Standard-PLA höhere Torsionskapazitäten und Umdrehungen aufweisen. Die Studie führt außerdem ein multilineares Idealisierungsmodell ein, um den Trend zur Scherspannungs-Scherdehnung zu vereinfachen, was es für numerische Simulationen wertvoll macht. Insgesamt trägt diese Forschung zu dem begrenzten Wissensschatz über das Drehverhalten additiv hergestellter Polymere bei und unterstreicht die Notwendigkeit weiterer Untersuchungen ihrer anisotropen Eigenschaften und größenabhängigen mechanischen Verhaltensweisen.
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Abstract
Background
Polymers in practical applications often face diverse torsional loads, such as polymeric gears, couplings, scaffolds, etc. Meanwhile, additive manufacturing enables the creation of intricate geometries for specific needs and its application to fabricate various component parts has grown exponentially. Nevertheless, research on cyclic and reversed cyclic torsional loading of additively-manufactured polymers is very limited.
Objective
Mechanical characterization of monotonic, cyclic, and reversed cyclic torsion in polylactic acid (PLA), PLA Premium, and PLA Tough materials.
Methods
Specimens were 3D-printed with a 0° build orientation using an extrusion technique and two infill orientation angles (± 45° and 0°/90°). Specimens were subjected to underwent monotonic, cyclic, and reversed cyclic torsion until failure.
Results
Regardless of material type, ductile fracture governed the behavior under monotonic loading and brittle failure under cyclic and reversed cyclic loadings. Specimens with a ± 45° infill orientation outperformed their 0°/90° counterparts across all materials, with PLA Premium exhibiting superior performance compared to PLA and PLA Tough. Importantly, it was demonstrated that the previously-proposed multilinear idealized shear stress-shear strain curve, developed for monotonic loading of 15 different polymers, also applies to the envelope curves of cyclic and reversed cyclic loading in PLA-based polymers. Thus, it is useful as material model input for numerical simulation purposes.
• One of the first studies, on cyclic, and reversed cyclic torsion of additively-manufactured PLA polymers using the material extrusion method.
• Feasibility of using previously-proposed idealized multi-linear shear stress-shear strain curves for monotonic torsion, and applicable for numerical simulations, was validated for cyclic and reversed cyclic torsional loadings.
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Introduction
The rapid growth of the additive manufacturing industry, which reached a net worth of $23 billion in 2023 according to Tan et al. [1], and is expected to reach $37.2 billion by 2026 [2] has attracted attention from numerous sectors and presents many benefits. Some of these fields, in which additively-manufactured polymers can be used, include biomaterials, metamaterials, automotive engineering, lattice structures, and shape memory polymers [3‐12].
In this context, the polymeric material used in this study, namely polylactic acid (PLA), offers many advantages. PLA is entirely synthesized from renewable sources, including corn, potatoes, potatoes, and beets [13]. The process involves polymerization of the lactide monomer derived from lactic acid (LA) through the fermentation of agricultural products [14]. This method not only results in low carbon dioxide emissions but also brings about substantial energy savings. In comparison to polymers derived from petroleum, PLA production demands 25%–55% less energy, and there are expectations for further reductions in energy consumption in the future [15].
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Although the initial production costs constrained the availability of PLA, the advent of new processing techniques has contributed to increased production volumes, leading to a reduction in PLA prices and a broadening of its applications [16]. PLA is now utilized in diverse fields such as packaging, textiles, and automotive materials [17].
Significant strides in technology have also played a crucial role in securing food and drug administration (FDA) approval for PLA's utilization in biomedical applications. This approval extends to scaffolds, tissue engineering sutures, bone fixators, controlled drug delivery devices, implants, and wound dressings [18].
PLA takes the lead in the emerging bioplastics market. In 2008, the annual consumption was 140,000 tons [16], and by 2011, 25 global companies had established production capacities exceeding 180,000 tons [19]. Within the overall global bioplastics production capacities, approximately 2.11 million metric tons in both 2018 and 2020 [20], PLA represented 10.3% (217,000 tons) in 2018 and 31% (around 676,000 tons) in 2023 [21] which is projected to reach 43.6% (3.24 million tons) in 2028 [21].
PLA's versatility across industries, and regulatory restrictions on synthetic plastics, the global PLA market is forecasted to grow at an annual rate of 15.9% from 2021 to 2030, reaching an estimated value of $4 billion by 2030 [22]. The packaging industry, particularly for food and beverages, held the largest share in both revenue (52.7%) [23] and volume in 2019. Moreover, the biomedical sector is swiftly adopting PLA, and the textile industry is projected to be the most rapidly expanding segment in the forecasted period, driven by the rising demand for PLA filaments and fibers in textiles and nonwovens [22].
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Additively-manufactured PLA can be employed as formwork for structural concrete elements, serving as material for mesh molds. This approach, utilizing plastic reinforcements rather than traditional steel or plywood, presents an appealing ecological perspective [24]. Moreover, PLA proves to be a viable option for the repair or retrofitting of concrete structures [25].
Concerning torsion, the complexity of torsional loads, their co-occurrence with other loads, and the limited research in this regard compared to other mechanical loads have made their characterization rather difficult [26]. Examples of torsional loads in engineering disciplines include polymeric gears in vehicle systems [27], car drive shafts in mechanical engineering [28]; torsional rigidity of wings in aerospace engineering [29], and torsional loads in bones [30] in biomedical engineering where PLA-based components serve as implants. PLA-based composites and scaffolds [31] also undergo torsional loading. Nonetheless, the performance of additively-manufactured polymers in torsion, either monotonic or cyclic, has not been adequately studied, and only a few studies are available in the literature, which will be discussed briefly as follows:
Torres et al. [32] conducted tests on heat-treated (100℃) PLA specimens with a gage length of 50 mm under monotonic torsion (rate: 0.1 rev./min). These specimens were produced through the extrusion process, The chosen parameters included layer thicknesses ranging from 0.1 mm to 0.3 mm in 0.1 mm intervals and infill densities ranging from 20 to 100% in increments of 40%. Treatment durations were set at 0, 5, and 20 min. The maximum mechanical parameters were achieved with a 0.1 mm layer thickness, 100% infill density, and a 20-min heat treatment. The corresponding values for shear modulus and shear stress were determined as 1265 MPa and 62 MPa, respectively. The study highlighted that through heat treatment, the mechanical properties of additively-manufactured components can be comparable to their bulk counterparts. However, there is a significant lack of studies addressing the number of research studies, guidelines, and the effects of heat on additively-manufactured polymers.
Dębski et al. [33] subjected additively-manufactured acrylonitrile butadiene styrene (ABS), high impact polystyrene (HIPS), polyamide (PA), carbon fiber-reinforced PA, and polycarbonate (PC) specimens with infill orientation angles of 0° and 90° to torsion. Results showed that the printing direction played a pivotal role in their torsional strength such that for specimens with layers orthogonal to the axis of rotation, the torsional capacity was minimum whereas for specimens with layers in the direction of rotation axis, torsional capacity was maximum.
Oleksy et al. [34] used PolyJet and material extrusion techniques to 3D print spline connections using ABS polymers. Samples were subjected to torsion subsequently, and results showed 17% higher torque values for the PolyJet additively-manufactured specimens and higher twist angles for material-extrusion-based specimens by two times. Failure patterns were brittle and outside the connection area which are of importance in mechanical machine elements.
Concerning the infill orientation angle, Balderrama-Armendariz et al. [35] subjected ABS additively-manufactured rectangular polymers with infill orientation angles of 0°, 45°, 90°, and ± 45° to torsion. Results showed that for similar specimens, material extrusion printing technique gives similar elastic properties but with less ductility in comparison to injection molding. The infill orientation angle had higher effects than the printing orientation on the mechanical properties. Beattie et al. [36] used the material extrusion technique to 3D print ABS samples in flat, vertical, and 45° edgewise build orientations. Flat and edgewise specimens showed relatively similar strengths with the specimen with the vertical printing orientation exhibiting much poorer performance by approximately 100%. Balderrama-Armendariz et al. [35] and Beattie et al. [36] highlighted that as of 2021, no research exists on the behavior of additively-manufactured polymers subjected to torsion to draw an analogy with their results.
Sadaghian et al. [37] additively manufactured 15 various polymers with two infill orientation angles of ± 45°,0°/90° in a flat build orientation and tested them under monotonic torsion. Except for the flexible materials, all the specimens failed in a brittle manner; in general, specimens with an infill orientation angle of ± 45° outperformed their 0°/90° counterparts.
The study by Budzik et al. [38] aimed to elucidate the impact of internal structure variations in material extrusion additively-manufactured samples (gage length: 50 mm) on tested parameters during unidirectional torsion. Additionally, practical applications of the findings were demonstrated through a spline connection example. The investigated materials included ABS, PLA, hard ABS (HABS), PC/ABS, high-impact polystyrene (UniHIPS), and an unknown composition of soft and strong material (S&S). In summary, samples made from tested materials with internal structure filling ranging from 13 to 65% exhibited similar values for maximal torsional moment and torsion angle at the maximal torsional moment within the scope of one material. The most notable discrepancies in maximal torsional moment and torsion angle were observed in samples with 80% and 99% filling across all tested materials, even when compared to other degrees of internal structure filling. It is noteworthy that for PLA, the maximum torsional capacity was 5358 N.mm for a filling ratio of 99%. The displacement results obtained from the nonlinear analysis in the finite element model of the designed spline connection did not correlate with the displacements recorded after the unidirectional torsion test.
Polymer matrix composites produced through additive manufacturing, consisting of Onyx (a blend of nylon and chopped carbon fiber), and Onyx infused with continuous layers of carbon fiber manufactured in various additive manufacturing build orientations, were subjected to monotonic torsion testing by Fandetti et al. [39]. Each specimen was fabricated with a matrix and fiber layer height of 0.125mm and 100% matrix infill. Findings indicate that specimens manufactured horizontally (X) demonstrated enhanced torsional performance compared to those built vertically (Z). Moreover, the inclusion of continuous carbon fibers led to a general reduction in overall torsional properties. The inferior performance of Onyx-X-CF was linked to issues such as delamination and suboptimal fiber-matrix bonding, highlighting its lower efficacy compared to its non-fiber reinforced counterpart. It is emphasized that literature review on torsional performance of additively-manufactured polymers is very limited and their study was the first one investigating Onyx-based polymers.
Existing literature mainly concern other loading types [40‐44] and shows the scarcity of research on the behavior of additively-manufactured polymers in torsion despite its occurrence solely and/or in combination with other loading types. This study is one of the first attempts to investigate the cyclic, and reversed cyclic torsion of additively-manufactured polymers and contributes to the very limited body of knowledge regarding the torsional behavior of 3D-printed PLA-based polymers. As indicated in the literature, Balderrama-Armendariz et al. [35] and Beattie et al. [36] highlighted that, as of 2021, no research existed on the behavior of additively-manufactured polymers subjected to torsion to compare with their results. The scarcity of research on the torsional behavior of 3D-printed polymers was further emphasized in Ref. [39], published in 2024. Additionally, a report by the National Institute of Standards and Technology (NIST) [45] assessed the applicability of existing standards to polymers and underscored the lack of studies on the torsional behavior of 3D-printed polymers. The report noted that the applicability of standards such as ISO 458–1 [46] for 3D-printed polymers had not been reviewed. This means that if studies do exist in this area, they are so scarce that even repeating the same research is worthwhile to ensure consistency in results and reproducibility of tests.
To this end, PLA, PLA Premium, and PLA Tough materials were additively manufactured in a 0° build orientation using the material extrusion technique with two different infill orientation angles (± 45° and 0°/90°). The parameters of the study included torque-revolution curves, stress–strain curves, shear modulus (\(G\)), dissipated energy (\(E\)), and damage index (\(DI\)) in cyclic and reversed cyclic loadings.
Torsion Fundamentals
It is already known that theories of classic torsion are not applicable to additively-manufactured materials printed layer-by-layer using the material extrusion technique. However, given the absence of a unified methodology, standard, or constitutive models to characterize the behavior of additively-manufactured polymers under torsion, concepts from classic mechanics of materials can offer a rough estimation. According to the fundamentals of classic torsion, the shear strength of a specimen with linear-elastic behavior and a circular cross-section is calculated according to Eq. (1):
$$\tau =G\gamma$$
(1)
where \(G\): the shear modulus, and \(\gamma\): shear strain. It is also a well-established fact that brittle specimens fail in a 45 \(^\circ\) angle relative to the horizon in torsion due to the tensile stresses acting on the critical surface perpendicular to the crack path. Therefore, shear failure is directly correlated with the tensile strength of specimens in brittle materials. Shear strain and shear stress can be obtained based on Eq. (2), and Eq. (3), respectively:
$$\gamma =\frac{r\uptheta }{L}$$
(2)
$$\tau =\frac{Tr}{J}$$
(3)
where \(r\): radius of the cylinder (mm); \(\theta\): angle of revolution (rad.), \(L\): gage length in (mm), \(T\): torsional moment (N.mm), and \(J\): polar moment of inertia (mm4).
Materials and Experimental Procedure
Material extrusion technique was used to additively manufacture specimens in a 0 \(^\circ\) build orientation with two infill orientation angles of \(\pm\) 45 \(^\circ\), and 0 \(^\circ\)/90 \(^\circ\). Definition of infill orientation angle is also given in Fig. 1. It is noteworthy that there are no standards for dimensions of additively-manufactured specimens tested under torsion. The closest standards relate to the temperature-dependent stiffness of plastics [47], and dynamic characteristics of plastics in torsion [48‐50]. Therefore, test specimens were fabricated based on the recommendations for the torsion test of metallic materials under torsion, ISO 18338 [51] as shown in Fig. 2. In total, 36 specimens (Fig. 3) were additively manufactured with 18 specimens for each infill orientation angle (two specimens for each type of loading). The machine used for additive manufacturing of materials was Creality Ender-3 V-2 and the process parameters were based on the information provided by the supplier (Table 1; quantitative chemical and mechanical properties of filaments were unavailable according to the supplier, and the website); just knowing that, the tensile strength of PLA Premium is higher than both PLA Tough and PLA and PLA Tough has a lower tensile strength than PLA but a higher impact resistance than both PLA and PLA Premium.
Fig. 1
Schematic 3D view of infill orientation angles (a) \(\pm\) 45 \(^\circ\) (left), and (b) 0 \(^\circ\)/90 \(^\circ\)
Specifications of materials and process parameters
Materials
Nozzle Diameter (mm)
Nozzle Temperature (\(\boldsymbol{^\circ{\rm C} }\))
Build Platform Temperature (\(\boldsymbol{^\circ{\rm C} }\))
Brand
PLA
0.4
215
65
Porima
PLA Premium
PLA Tough
*Printing speed: 53 mm/s. Layer width: 0.2 mm; Diameter of filaments 1.75 mm; Shell number: 3; Shell width: 0.48 mm
To ensure stability, supports were necessary. These supports were meticulously cut using the Slice Precision Cutter® after the specimens had cooled down, ensuring no damage was inflicted on them. Thereafter, specimens were subjected to torsional loading at a rate of 0.5 rev./min until failure. Torque-revolution curves were obtained from the experiment and their data were used to calculate average stress-average strain values. It is worth noting that based on a previous study by the authors [37], and observations from the monotonic loading of current test specimens (i.e., linear/pseudo linear behavior until the maximum load), displacement-controlled cyclic and reversed cyclic loading protocols were defined according to Fig. 4.
Fig. 4
Loading protocols (a) cyclic, and (b) reversed cyclic
Figure 5 presents the torque-revolution curves of specimens. According to Fig. 5, For PLA, the difference between the average values for specimens with an infill orientation angle of \(\pm\) 45 \(^\circ\) (i.e., 45D-1, 45D-2, 45D-1: a specimen with an infill orientation angle of \(\pm\) 45 \(^\circ\), D: degree, 1: number of the specimen), and those with an infill orientation angle of 0 \(^\circ\)/90 \(^\circ\) is not very noticeable under monotonic loading (8%). The same applies to the specimens tested under cyclic and reversed cyclic loadings. The reason for this issue is that unloading was performed in the plastic range and prior to it, specimens didn’t experience any unloading to dissipate energy. Therefore, their maximum torsional capacities are similar to the case of monotonic loading. What’s more, for a specific infill orientation angle and material, differences between the maximum torsion values under various loadings are insignificant, which is plausible.
Fig. 5
\(T\)-\(\theta\) curves of additively-manufactured PLA under monotonic, cyclic, and reversed cyclic loadings (a) PLA-45D-1, (b) PLA-45D-2, (c) PLA-090D-1, (d) PLA-090D-2
For PLA Premium, average torsional capacities are higher than that of PLA (9% for specimens with an infill orientation angle of \(\pm\) 45 \(^\circ\), and 11% for specimens with an infill orientation angle of 0 \(^\circ\)/90 \(^\circ\)) (see Fig. 6). In most cases, PLA Premium specimens underwent revolutions at least 1.5 times higher than their PLA counterparts when comparing Figs. 5 and 6.
Fig. 6
\(T\)-\(\theta\) curves of additively-manufactured PLA Premium under monotonic, cyclic, and reversed cyclic loadings (a) PLA Premium-45D-1, (b) PLA Premium-45D-2, (c) PLA Premium-090D-1, (d) PLA Premium-090D-2
According to Fig. 7, for PLA Tough, the difference in average torsional capacities between the two infill orientation angles is meaningful and equal to 30%. Similar to PLA Premium, PLA Tough specimens underwent larger revolutions than those of PLA by almost 1.5 times in most cases, and none of the specimens sustained revolutions greater than 30 radians.
Fig. 7
\(T\)-\(\theta\) curves of additively-manufactured PLA Tough under monotonic, cyclic, and reversed cyclic loadings (a) PLA Tough-45D-1, (b) PLA Tough-45D-2, (c) PLA Tough-090D-1, (d) PLA Tough-090D-2
Specimens showed a linear/pseudo-linear trend up to the peak load followed by a sliding of layers which was characterized by a slight decrease in the \(T\)-\(\theta\) curve. Further loading of the specimen was characterized by a relatively stable fluctuation of torsional capacity as the revolutions became larger and separation of printing layers prior to filaments’ fracture. This finding is important because it signifies that the interlayer strength is less than the strength of filament. The underlying reason for the relatively stable fluctuation is that subsequent to debonding of the utmost layers (three shells) that sustained the highest shear stress, inner layers show resistance and do not allow for a sharp decrease in the torsional capacity. During the final stages of loading, specimens underwent large revolutions relative to their capacity, and fracture of filaments was visible in the specimens. In summary, fracture initiated by the failure of three shells which underwent highest strains and affected the failure pattern of the internal parts by somewhat providing an outer boundary. Fracture patterns of specimens are shown in Figs. 8, 9 and 10. Figure 8(f) clearly shows the fracture of the filament which occurred during final stages of loading.
Concerning the stress–strain behavior of test specimens, since Eqs. (2) and (3) were used to convert torque and revolution values to \(\gamma\) and \(\tau\), the same differences between two infill orientation angles are also valid for these curves (Figs. 11–12). Stress values for PLA, as the widely-used additive manufacturing material, vary between 37.42 and 41.45 MPa for the \(\pm\) 45 \(^\circ\) infill orientation angle and 33.35–38.36 MPa for the 0 \(^\circ\)/90 \(^\circ\) infill orientation angle. Strain-hardening behavior is visible in PLA-090D-1&2 under cyclic loading and in some cases (i.e., PLA-090D-1, PLA Tough 090D-1&2 under reversed cyclic loading) progressive inelastic deformation for the more or less same stress value is observed. The trend of monotonic curves indicates a ductile failure, whereas the opposite holds true for the envelope curves of cyclic and reversed cyclic loadings. This observation is intriguing because their trends exhibit a brittle strain-softening manner. This can be justified by the fact that additively-manufactured polymers are non-homogeneous materials, and their performance is affected by both printing parameters and testing methods. What comes to mind is the interlocking mechanism that operates during one direction of loading, causing the layers to twist and stiffen. Loading in the opposite direction unwinds this twist. Through this repetitive procedure, a point is reached where delamination occurs between layers, degrading the torsional performance, rendering poorer performance in subsequent cycles and creating a distinct difference envelope curve of cyclic loadings and monotonic loading. This diminished performance ultimately leads to failure (Fig. 13).
Fig. 11
\(\tau\)-\(\gamma\) and envelope curves of additively-manufactured PLA under monotonic, cyclic, and reversed cyclic loadings (a) PLA-45D-1, (b) PLA-45D-2, (c) PLA-090D-1, (d) PLA-090D-2
For the \(G\) values, defined as the slope of the shear stress–strain upon initial loading, values for PLA between different loading types have an insignificant difference (6%) between the average values for two types of infill orientation angles. Similarly, there is a marginal difference of 7%, and 4% for this parameter under cyclic and reversed cyclic loadings. The changes in \(G\) between the two infill orientation angle types are even less pronounced in PLA Premium in comparison to PLA. For PLA Tough, however, \(G\) variations reach up to 30% for the case of reversed cyclic loading with a minimum of 28% for the cyclic loading case.
Dissipated Energy
According to Table 2, and unlike the trends for \(G\) and \(\tau\) values, the difference between the average dissipated energy (\(E\)) values under monotonic loading for two different infill orientation angles is larger in PLA Tough (26%). Similarly, the differences in \({E}_{1st Peak}\) between two infill orientation angles for PLA and PLA tough specimens are equal to 26%, and 32%, respectively. It should be noted that \({E}_{1st Peak}\) in Table 2 refers to the area under the \(\tau\)-\(\gamma\) curves prior to a notable change in the slope of the curve. \(E\) values in terms of each cycle are given in Fig. 14. As expected, the reversed cyclic condition dissipated larger energy values in comparison to the cyclic loading condition. In all the cases, with an infill orientation angle of \(\pm\) 45 \(^\circ\) have higher \(E\) values than specimens with an infill orientation angle of 0 \(^\circ\)/90 \(^\circ\). At initial stages of loading, when the specimen is relatively intact, the rate of energy dissipation is higher with its peak occurring between 5 and 10th cycles. Specimens that have their peak outside of this range are usually marked by a stable stress range after several subsequent cycles. The difference between maximum \(E\) values between two infill orientation angle types in reversed cyclic loading is much higher than that of the cyclic loading and sometimes exceeds 100%. Overall, PLA Premium shows a superior performance in dissipating energy than PLA and PLA Tough. It is noteworthy that the starting value of counter for the No. of cycles in all the figures is 1, not 0.
Table 2
Summary of experimental results for test specimens
Damage Index (\(DI\)) is a measure of how the modulus of elasticity (or in this case, shear modulus) deteriorates in each cycle. It is considered as the slope of the line connecting the unloading point in each cycle to the point where the descending curve intersects the horizontal axes (where shear stress is zero) relative to the slope of the curve upon initial loading. In other words, \(DI\) is defined according to Eq. (4) as follows:
According to Fig. 15, for a specific cycle No., specimens undergoing reversed cyclic loading have sustained much greater damage than those tested under cyclic loading. On average, for a specific material type, specimens with an infill orientation angle of \(\pm\) 45 \(^\circ\) have endured less damage than that of their 0 \(^\circ\)/90 \(^\circ\) counterpart. Quantitatively speaking, according to Fig. 16, PLA specimens have either failed before reaching the unloading strain of 0.5 or have reached \(DI\) values of at least 0.46 (for PLA-090D-2) under cyclic loading and a minimum \(DI\) of 0.52 for PLA-45D-2 for the same strain value under reversed cyclic loading. Similarly, for PLA Premium specimens, \(DI\) values for the unloading strain of 0.5 vary between 0.33–0.49 for cyclic loading and between 0.61–0.70 for reversed cyclic loading. For PLA Tough the foregoing range is between 0.49–0.65 for cyclic loading and 0.70–0.75 for reversed cyclic loading.
Fig. 15
Damage Index in each cycle (a) PLA, (b) PLA Premium, and (c) PLA Tough
It should be noted that for specimens (mostly PLAs) with significantly lower \(DI\) values than unity, specimens failed in a brittle manner, denoting complete failure such that they could be considered completely damaged from an engineering perspective, and therefore they were not plotted. It is also noteworthy that in cases where the damage value has decreased in relation to the preceding cycle, strain-hardening has occurred and/or minor changes are visible between them that can be attributed to experimental errors. It is also worth noting that based on Fig. 17, no particular trend exists for DI values in terms of the unloading strain when all the three materials are compared as it is highly dependent on the No. of cycle and the type of material.
Fig. 17
Damage Index vs. unloading point strain for different materials (a) cyclic \(\pm\) 45 \(^\circ\), (b) cyclic 0 \(^\circ\)/90 \(^\circ\), (c) reversed cyclic, \(\pm\) 45 \(^\circ\), and (d) reversed cyclic, 0 \(^\circ\)/90 \(^\circ\)
Experimental findings are usually simplified for applicability to numerical simulations or design purposes. Multi-linear idealization is one of the methods used to simplify experimental findings such as the bi-linear simulation of compression and tension in ABS polymers [52], the simulation of fracture in 3D-printed polymers using a bi-linear traction–separation law [53], a trilinear model for the tensile stress–strain curve of high ductility cementitious composite (HDCC) [54], a bilinear model for the tensile stress–strain response of ultra high-performance engineered cementitious composites (UHP-ECCs) [55], and tension softening models for concrete in DIANA software [56]. Additionally, bond-slip models available in the literature [57‐64], multi-linear stress-crack width, and multi-linear stress–strain curves [65] have also been proposed.
Accordingly, herein, the foregoing method was used simplify the shear stress-shear stress trend of additively-manufactured polymers under monotonic, cyclic, and reversed cyclic loading conditions. This method has been previously used by Sadaghian et al. [37] to capture the torsional behavior of additively-manufactured polymers subjected to monotonic torsion only and here, the feasibility and suitability of its application to the envelope curves of cyclic and reversed cyclic torsion are evaluated. Figure 18 shows the proposed multilinear idealization curve. The x and y axes were normalized relative to the maximum shear stress and its equivalent shear strain value to make the findings of this study comparable to those of other researchers. Three assumptions were considered in constructing the multi-linear curve: (1) the same initial \(G\) values with the experimental curves, (2) the area enclosed under the curve is equal to that of the experiment, and (3) the maximum shear stress and its corresponding shear strain values correspond to unity in the curve. The curve in Fig. 18 was established based on experimental observations such that (1) the ascending branch up to parameter “a” denotes the linear branch of the curve; the reason why the pre-peak region was divided into two parts was to better characterize the \(G\) value in the linear branch, (2) after the peak load, a fracture characterized by the debonding of layers and drop of the stress takes place, (3) descending trend in the stress curve, as further loading of the specimen causes further decrease in the stress values but this decrease follows a relatively constant trend as inner layers are intact and provide resistance (region b-c), (4) prior to failure as innermost layers are entangled, a more or less stable fluctuation of shear stress (region c-d) values followed by a sudden drop after point “d” and failure of the specimen in point “e” from an engineering prospective are observed. Region c-d can also be considered as the “residual stress” region. Values of multipliers for monotonic, cyclic and reversed cyclic loadings are given in Tables 3, 4 and 5 in the appendix, respectively.
Fig. 18
Schematic idealized multi-linear shear stress-shear strain curve for torsion
A series of experiments were conducted to characterize the behavior of three additively-manufactured PLA-based polymers in torsion. PLA, PLA Premium, and PLA Tough polymers were additively manufactured using the material extrusion technique in a 0 \(^\circ\) build orientation and were tested under monotonic, cyclic, and reversed cyclic torsional loading until failure. Torque-revolution data were recorded from the experiment, and relevant parameters were calculated based on the experimental findings. The prominent findings of this study are given below:
1-
Overall, average values for specimens with an infill orientation angle of \(\pm\) 45 \(^\circ\) were higher than those of their 0 \(^\circ\)/90 \(^\circ\) counterparts. This superiority was negligible (mostly less than 10%) for PLA in terms of torsional capacity, shear modulus, and irrespective of the loading type, except for dissipated energy values (26%). For PLA Tough, the so-called difference was, however, notable and equal to a minimum of 30% in all the investigated parameters. Additionally, PLA Tough specimens failed at revolution values at least 1.5 times in comparison to PLA.
2-
For the most widely-used additive manufacturing material, PLA, stress values were in the range of 37.42–41.45 MPa for the \(\pm\) 45 \(^\circ\) infill orientation angle, and 33.35–38.36 MPa for the 0 \(^\circ\)/90 \(^\circ\) infill orientation angle. PLA Premium with an infill orientation angle of \(\pm\) 45 \(^\circ\) had a maximum shear stress of 46.30 MPa.
3-
All the specimens irrespective of the loading type failed in a ductile manner under monotonic loading and brittle under cyclic and reversed cyclic loadings. This means that upon the repetitive nature of cyclic loadings, there exists a cycle in which separation of layers takes place rendering poorer performance in its subsequent cycles such that difference between the envelope curves of cyclic loadings and monotonic loading in terms of ductility is significant. Failure was mainly characterized by separation of the outermost layer rather than the filament itself, which shows that the filament strength is higher than the interlayer strength. The stress–strain curve was characterized by a linear/pseudo linear trend up to a peak load.
4-
On average, for a specific material and cycle number, specimens with an infill orientation angle of \(\pm\) 45 \(^\circ\) sustained less damage than their 0 \(^\circ\)/90 \(^\circ\) counterparts. Their difference for a specific material in \(DI\) values was not constant and varies significantly in different cycles. Needless to say, specimens undergoing reversed cyclic loading sustained higher \(DI\) values than those tested under cyclic loading. What’s more, among three additively-manufactured PLA polymers, there is no particular trend for the growth rate of \(DI\) in terms of the unloading strain to choose which material deteriorates faster, as it depends on the unloading strain range and the infill orientation angle.
6-
The previously-proposed normalized multilinear shear stress-shear strain model for 15 different additively-manufactured polymeric materials [37] is also applicable to the monotonic and envelope curves of cyclic and reversed cyclic loadings of PLA-based polymers. This makes it easily usable for numerical simulation purposes.
It is highly emphasized that, given the very limited data regarding the behavior of additively-manufactured polymers under monotonic, cyclic, and reversed cyclic torsion, more studies should be carried out in this regard. Most importantly, based on the literature, additively-manufactured polymers are anisotropic materials, and their mechanical properties are size-dependent [66]. Therefore, there is scope for further research for additively-manufactured polymers with various sizes and geometries in this regard.
Declarations
Competing Interest
The authors have no competing interest to declare.
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Sharma S, Gupta V, Mudgal D (2023) Experimental investigations on polydopamine coated poly lactic acid based biomaterial fabricated using 3D printing for orthopedic applications. Mater Chem Phys 310:128473. https://doi.org/10.1016/j.matchemphys.2023.128473CrossRef
4.
Dadashi A, Azadi M (2023) Experimental bending fatigue data of additive-manufactured PLA biomaterial fabricated by different 3D printing parameters. Progress in Additive Manufacturing 8(2):255–263. https://doi.org/10.1007/s40964-022-00327-1CrossRef
5.
Truszkiewicz E, Thalhamer A, Rossegger M, Vetter M, Meier G, Rossegger E, ... and Berer M (2022) Mechanical behavior of 3D‐printed polymeric metamaterials for lightweight applications. J Appl Polym Sci 139(6):51618. https://doi.org/10.1002/app.51618
6.
Ren L, Wu W, Ren L, Song Z, Liu Q, Li B, ... and Zhou X (2022) 3D Printing of Auxetic Metamaterials with High‐Temperature and Programmable Mechanical Properties. Adv Mater Technol 7(9):2101546. https://doi.org/10.1002/admt.202101546
7.
Salifu S, Desai D, Ogunbiyi O, Mwale K (2022) Recent development in the additive manufacturing of polymer-based composites for automotive structures—A review. Int J Adv Manuf Technol 119(11–12):6877–6891. https://doi.org/10.1007/s00170-021-08569-zCrossRef
8.
Albu SC (2022) Contribution Regarding the Production of PLA Products Through 3D Printing, FDM Technology, Used in the Automotive Industry. In International Conference Interdisciplinarity in Engineering (pp. 197–209). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-031-22375-4_17
9.
Tang C, Liu J, Yang YANG, Liu Y, Jiang S, Hao W (2020) Effect of process parameters on mechanical properties of 3D printed PLA lattice structures. Compos Part C: Open Access 3:100076. https://doi.org/10.1016/j.jcomc.2020.100076CrossRef
10.
Ye G, Bi H, Chen L and Hu Y (2019) Compression and energy absorption performances of 3D printed Polylactic acid lattice core sandwich structures. 3D Printing and Additive Manufacturing 6(6):333–343. https://doi.org/10.1089/3dp.2019.0068
Ahmed J, Hiremath N, Jacob H (2016) Antimicrobial, rheological, and thermal properties of plasticized polylactide films incorporated with essential oils to inhibit Staphylococcus aureus and Campylobacter jejuni. J Food Sci 81(2):E419–E429. https://doi.org/10.1111/1750-3841.13193CrossRef
Agüero Á, Garcia-Sanoguera D, Lascano D, Rojas-Lema S, Ivorra-Martinez J, Fenollar O, Torres-Giner S (2020) Evaluation of different compatibilization strategies to improve the performance of injection-molded green composite pieces made of polylactide reinforced with short flaxseed fibers. Polymers 12(4):821. https://doi.org/10.3390/polym12040821CrossRef
17.
De Silva RT, Pasbakhsh P, Goh KL, Chai SP, Chen J (2014) Synthesis and characterisation of poly (lactic acid)/halloysite bionanocomposite films. J Compos Mater 48(30):3705–3717. https://doi.org/10.1177/0021998313513046CrossRef
18.
Liu H, Chen N, Shan P, Song P, Liu X, Chen J (2019) Toward fully bio-based and supertough PLA blends via in situ formation of cross-linked biopolyamide continuity network. Macromolecules 52(21):8415–8429. https://doi.org/10.1021/acs.macromol.9b01398CrossRef
19.
Carus M (2012) Growth in PLA bioplastics: a production capacity of over 800,000 tonnes expected by 2020. Nova-Institute, Hürth
20.
Bioplastics market data (2018) Global production capacities of bioplastics 2018–2023. European Bioplastics, nova-institute. https://www.european-bioplastics.org. Accessed 4 Jan 2024
21.
Bioplastics market data (2023) BIOPLASTICS MARKET DEVELOPMENT UPDATE 2023. European Bioplastics, nova-institute.https://www.european-bioplastics.org. Accessed 4 Jan 2024
Murad, Y. (2022). Poly-lactic acid and carbon fibers 3D printed bars for seismic retrofitting RC beam-to-column joints subjected to elevated temperature. In Structures (Vol. 43, pp. 1530–1547). Elsevier. https://doi.org/10.1016/j.istruc.2022.07.066
Reitschuster S, Tobie T, Stahl K (2023) Experimental verification of high-performance polymer gears in an electric vehicle powertrain. Forsch Ingenieurwes 87(3):881–890. https://doi.org/10.1007/s10010-023-00682-7CrossRef
Dębski M, Magniszewski M, Bernaczek J, Przeszłowski Ł, Gontarz M and Kiełbicki M (2021) Influence of torsion on the structure of machine elements made of polymeric materials by 3D printing. Polimery 66(5):298–304. https://doi.org/10.14314/polimery.2021.5.3
34.
Oleksy M, Oliwa R, Bulanda K, Budzik G, Przeszłowski Ł, Magniszewski M and Paszkiewicz A (2021) Torsional strength tests of spline connections made of polymer materials (Rapid communication). Polimery 66(1):52–55. https://doi.org/10.14314/polimery.2021.1.7
35.
Balderrama-Armendariz CO, MacDonald E, Espalin D, Cortes-Saenz D, Wicker R, Maldonado-Macias A (2018) Torsion analysis of the anisotropic behavior of FDM technology. Int J Adv Manuf Technol 96:307–317. https://doi.org/10.1007/s00170-018-1602-0CrossRef
36.
Beattie N, Bock N, Anderson T, Edgeworth T, Kloss T, Swanson J (2021) Effects of build orientation on mechanical properties of fused deposition modeling parts. J Mater Eng Perform 30:5059–5065. https://doi.org/10.1007/s11665-021-05624-4CrossRef
37.
Sadaghian H, Khalilzadehtabrizi S, Farzam M, Dehghan S (2022) Behavior of 3D-printed polymers under monotonic torsion–A database of 15 different materials. Addit Manuf 60:103251. https://doi.org/10.1016/j.addma.2022.103251CrossRef
38.
Budzik G, Dziubek T, Przeszłowski ŁP, Sobolewski B, Dębski M, Gontarz ME (2023) Study of unidirectional torsion of samples with different internal structures manufactured in the MEX process. Rapid Prototyp J. https://doi.org/10.1108/RPJ-09-2022-0332CrossRef
39.
Fandetti D, Siddiqui SF and Gordon AP (2024) Torsional Response of 3D Printed Onyx and Onyx-Carbon Fiber Reinforced Composites. In AIAA SCITECH 2024 Forum (p. 1797). Torsional Response of 3D Printed Onyx and Onyx-Carbon Fiber Reinforced Composites. https://doi.org/10.2514/6.2024-1797
Shen Y, Branscomb DJ (2022) A Method to Measure Effective Flexural and Transverse Shear Modulus of Composite Structures with Large Aspect Ratio. Exp Mech 62(6):1051–1056. https://doi.org/10.1007/s11340-022-00845-7CrossRef
42.
Foppiano M, Saluja A, Fayazbakhsh K (2021) The effect of variable nozzle temperature and cross-sectional pattern on interlayer tensile strength of 3D printed ABS specimens. Exp Mech 61:1473–1487. https://doi.org/10.1007/s11340-021-00757-yCrossRef
43.
Rohde S, Cantrell J, Jerez A, Kroese C, Damiani D, Gurnani R, ... and Ifju P (2018) Experimental characterization of the shear properties of 3D–printed ABS and polycarbonate parts. Exp Mech 58:871–884. https://doi.org/10.1007/s11340-017-0343-6
Forster AM (2015) Materials testing standards for additive manufacturing of polymer materials: state of the art and standards applicability. National Institute of Standards and Technology (NIST), U.S. Department of Commerce. NIST Interagency/Internal Report (NISTIR) - 8059
46.
ISO 458–1 (1985) Plastics – Determination of stiffness in torsion of flexible materials – Part 1: General method, ISO/TC 61/SC 2, Ed. Switzerland: International Standards Organization
47.
ASTM D1043 (2016) Standard Test Method for Stiffness Properties of Plastics as a Function of Temperature by Means of a Torsion Test. ASTM International. www.astm.org
48.
ISO 6721–2 (2019) Plastics - Determination of dynamic mechanical properties--Torsion-pendulum method, International Standard Organization (ISO), 3rd Edition, Technical Committee: ISO/TC61/SC5 Physical-chemical properties. www.iso.org
49.
ISO 6721–7 (2019) Plastics - Determination of dynamic mechanical properties--Part 7 Torsional vibration — non-resonance method, International Standard Organization (ISO), 2nd Edition, Technical Committee: ISO/TC61/SC5: Physical-chemical properties. www.iso.org
ISO 18338 (2021) Metallic materials- Torsion test at room temperature, International Standard Organization (ISO), 2nd Edition, Technical Committee: ISO/TC164/SC2: Ductility testing. www.iso.org
52.
Tabacu S, Ducu C (2020) Numerical investigations of 3D printed structures under compressive loads using damage and fracture criterion: Experiments, parameter identification, and validation. Extreme Mech Lett 39:100775. https://doi.org/10.1016/j.eml.2020.100775CrossRef
Gao D, Lv M, Wei D, Pang Y, Tang J (2022) Trilinear tensile stress–strain constitutive model for high ductility cementitious composite with totally recycle fine aggregate. Constr Build Mater 319:126149. https://doi.org/10.1016/j.conbuildmat.2021.126149CrossRef
DIANA FEA BV (2024) DIANA - Finite element analysis user manual (Release 10.9) [Software manual]. DIANA FEA BV
57.
Neubauer U and Rostasy FS (1997) Design aspects of concrete structures strengthened with externally bonded CFRP-plates. In Proceedings of the Seventh International Conference on Structural Faults and Repair, 8 July 1997. Volume 2: Concrete and Composites. ISBN: 0–947644–32–0
58.
Ueda T and Dai JG (2004) New shear bond model for FRP-concrete interface-from modeling to application. In Proceedings of the Second International Conference on FRP Composites in Civil Engineering-CICE (pp. 69–81). ISBN: 90 5809 638 6
Bhosale AB, Lakavath C, Prakash SS (2020) Multi-linear tensile stress-crack width relationships for hybrid fibre reinforced concrete using inverse analysis and digital image correlation. Eng Struct 225:111275. https://doi.org/10.1016/j.engstruct.2020.111275CrossRef
Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.
