This paper studies the loading–unloading behaviors of a three-dimensional (3D)-printing built bimaterial structure consisting of an open-cellular plaster frame filled with silicone. The combination of the plaster (ceramic phase) and silicone (elastomer phase) is hypothesized to possess a nonlinearly elastic property and a better ductility. Four-point bending tests with programmed cycles of preceding deformations were conducted. The results show that there exists a linear–nonlinear transition when the bending deflection is around 2 mm in the first cycle bending. As the cycle proceeds, this linear–nonlinear transition is found at the maximum deflection of the previous cycle; meanwhile, the bending stiffness degrades. It is believed that the occurrence of microcracks inside the plaster frame is the mechanism behind the phenomenon. The silicone provides a strong network suppressing the abrupt crack propagation in a brittle material. The effects of the frame structure and plaster–silicone ratio were also compared. A high plaster content and large cell size tend to have a higher stiffness and obvious linear to nonlinear transition while it also has more significant stiffness degradation.
Additive manufacturing (AM) technologies provide the possibility to create almost any kind of complex geometry based on layer-by-layer fabrication [1–3]. The recent development of AM is aiming toward high-precision and high-performance applications, one of which is developing multiple-material 3D printing, also known as composites . AM of composites can be realized by fused deposition modeling (FDM) [5,6], laminated object manufacturing (LOM) , selective laser sintering/melting (SLS/SLM) [8,9], and laser engineered net shape (LENS) . These studies use the preprepared mixtures of the composite materials , such as the mixed powder materials for SLS and the mixed filament for FDM. For example, Chung and Das  studied functionally graded materials by using a commercially available SLS machine. Other techniques manufacture the composites using multiple feeding systems. For example, Wang et al.  used direct laser fabrication (DLF) technique to create Ti-6Al-4V reinforced with TiC. They combined both wire and powder systems for manufacturing. Krishna et al.  presented an experimental study of a functionally graded Co–Cr–Mo coating on Ti-6Al-4V alloy by using LENS with double powder feeder system. The composition gradient was created by exchanging different feed rate of the material powder. Note all existing AM methods for composites are based on material mixtures with different compositions. This paper, in contrast, focuses on AM of the composite using “structural” mixture rather than the material mixture.
Structural mixture here refers to a larger scale of mixing between two or multiple materials, such as reinforced concrete or laminates. The mechanical behaviors of these materials are affected by not only the material composition but also the structure configuration. The produced part, therefore, can be designed structurally for specific needs, such as localized strength or anisotropy property. To distinguish this type of composite from conventional AM composites, the term multimaterial structure is used in this study. The two selected materials here are ceramic and elastomer due to the brittle and hyperelastic natures, respectively, that potentially provide both strength and toughness to the structure.
Conventional materials, such as metals or plastics, usually have a constant modulus of elasticity in the elastic region or when reloaded in the plastic region. Thus, the resilience (i.e., the elastic strain energy absorbed by the material) also remains similar despite the deformation magnitude. The ceramic–elastomer bimaterial structure is anticipated to have varying stiffness and resilience due to the elastic nature of both materials and the stiffness degradation phenomenon. Stiff degradation is a result of microdamages in one of the phases (usually the more brittle one) inside the composites. Gagel et al.  showed that the stiffness degradation occurs on glass-fiber reinforced epoxy material by loading–unloading cycles experiment. Lee and Fenves  reported a model to explain the stiffness degradation of concrete structures. Flores-Johnson et al.  presented a report for degradation of stiffness on crushable foams in uniaxial compression. In general, when the stiffness degradation occurs, the material experiences a longer loading curve in the elastic region while remains a similar maximum strength, which results in increasing resilience. This material is a compromise between the resilience and stiffness.
In this study, the bimaterial structure is made of the plaster as the brittle ceramic phase, and silicone as the elastomer phase. Our prior work  has successfully produced this bimaterial with parametric controls over the composition and structure. While doubted, an elastic–plastic transition was observed in the results. The objective of this paper is to continue the investigation with loading–unloading cycles and interpret the behaviors of this material as well as to determine the effects of composition and structure. For this, the paper is organized as follows: Section 2 first summarizes the preliminary work, including the manufacturing procedures and the single-pass bending results. Section 3 details the experimental design with loading–unloading cycles. Section 4 shows the experimental results, followed by a discussion in Sec. 5. Conclusions and potential future works are presented at the end of the paper.
Summary of Preliminary Work
The bimaterial structures were created with 3D-printed built plaster and silicone resin (PDMS), Sylgard 184 (Dow Corning, Midland, MI). The plaster was built by a commercial powder-based 3D printer, ProJet 160 (3D Systems, Rock Hill, SC). The powder was VisiJet PXL, which contained 80–90% of calcium sulfate hemihydrate (also known as plaster). The bimaterial structure was designed based on an open-cellular unit cubic cell to hold silicone resin, as shown in Fig. 1(a), controlled by two parameters: cell size and solid-to-cell ratio. Cell size defines the length of the cubic cell; the solid-to-cell ratio determines the content of plaster in the part. For example, Figs. 1(b) and 1(c) show the 50% cell with 6.5 and 3.25 mm cell size, which denoted L and S, respectively. The procedures to manufacture the open cell structure are: (1) first print the cell structure with the ProJet 160, (2) dry the parts in the oven to evaporate binder residue, and (3) finally mold the parts with silicone resin along with several degassing cycles. Complete samples are shown in Fig. 2.
In our prior work, a four-point bending test was used to examine the mechanical properties of the bimaterial structures. The test sample size was 128 mm × 13 mm × 6.5 mm with four different composition ratios (25%, 50%, 75%, and 100% of plaster material) along with large (L) and small (S) cells. Typical examples of 50% and 75% structures are shown in Fig. 2. Figure 3 shows the force–deflection curves for the tested samples. The pure plaster (100%), not shown in the figure, ruptured at a deflection of around 3 mm with a nearly linear force–deflection curve. A significant improvement of the bimaterial structures can be seen with regard to its toughness and its total endurable deformation. The bending stiffness and maximum load decrease with a decreasing solid-to-cell ratio, while the toughness increases. These results show that the stiffness and the maximum load are dominated by the amount of the plaster because the plaster possesses a much higher stiffness than silicone resin. On the other hand, for the structures with the same composition ratio, larger unit cell structures tend to have a higher bending stiffness. This could be explained by a greater moment of inertia created by the larger structure. All of these results were confirmed by statistical analysis using a t-test. Moreover, when the amount of the data is sufficient, an empirical rule of mixture can be established.
Of particular interest seen in Fig. 3 is the transition from linear to nonlinear behaviors (marked by Region I and Region II.) This looks similar to the elastic–plastic transition in most materials. However, both plaster and silicone do not have any plastic deformation in their bulk properties. It is hypothesized that this bimaterial structure behaves nonelastically, where the nonlinear transition occurs when the deflection level is around 2 mm. Once the load on the samples becomes zero, the samples should recover to zero deformation. Therefore, in this study, these bimaterial structures are further tested by cyclic loading–unloading experiments via a four-point bending setting. The experimental details are described in the next section.
Experimental Setup and Methods
The four-point bending test setup, as shown in Fig. 4, was used to examine the mechanical behaviors of the bimaterial structures. The testbed was built with a reconfigurable motion stage in the lab, consisting of a servomotor-driven linear actuator (L70, Moog Animatics, Milpitas, CA) and a force dynamometer (Model 9272, Kistler, Winterthur, Switzerland). The loading nose and loading support were manufactured according to ASTM-D7264 standard , with a 5 mm radius, 128 mm support span, and 64 mm loading span. The feed rate for loading–unloading cycling test was set at 12.7 mm/min (0.5 in./min).
In the design of experiment, two different composition ratios were made for testing, including 50% and 75% of plaster material. The results of these different composition ratios were compared to each other and it was decided how the composition of the structures affected their mechanical properties. In these two composition ratios, two different structures were made: 6.5 mm and 3.25 mm long cubic unit cells. The different results from different structures were used to determine the effect of structures on the mechanical properties. Totally, there were four cases for loading–unloading cycling test. Samples are shown in Fig. 2, in which 6.5 mm and 3.25 mm long unit cells are denoted by L and S, respectively.
Four loading–unloading cycles were applied to each sample. The deflection distance for the midspan of the loading nose was 11.18 mm (0.44 in.) for first two cycles. To observe the linear–nonlinear behavior of the samples, the deflection distance was chosen from the preliminary results, which all the samples pass the elastic region in the force–deflection curves. For third and fourth cycles, the deflection distance was 22.35 mm (0.88 in.), which results were used to determine the effect of deflection level on linear–nonlinear behavior.
The results are presented in two sections. One explains the force–deflection curves of these samples with their linear and nonlinear elastic behaviors; the other compares the stiffness among the cases.
Figure 5 shows two repeated test results of all the samples used in this study. The solid line and the dashed line represent two separate test results. The force–deflection curves are almost identical throughout the whole process. This shows a high repeatability of the setup as well as the sample. All of them exhibit similar behavior during the test. For the first cycle, the structure deforms elastically at the beginning of the loading and the elastic region ends when the deflection of the sample is at about 2 mm. This transition point is approximated as it is sometimes unclear on where the point exactly is. This unclarity is understandable as some examples in the cases of 50%S and 50%L show a parabolic curve, which increases the difficultly of identifying exactly where the transition point is. When the deflection exceeds this transition point, the curve turns into a more plateau region, similar to the elastic-to-plastic transition, till the unloading begins. The unloading cycle recovers most of the deflection, but there is a small unrecovered permanent deformation about 2 to 3 mm (point p). The recovery of the most of the deflection indicates that the transition point is a stiffness transition, instead of the yielding point; the material remains elastic beyond this point. For the second loading cycle, the force increases linearly when it reaches the previous unloading point (about 10 mm). The slope of the second loading is lower than the first one. This is an evidence of stiffness degradation. For the unloading part, the second unloading curve is similar to the first unloading curve. The second cycle behaves as to reveal a completely linear elastic deformation with a hysteresis effect, a common phenomenon in polymers.
The third loading cycle follows the linear trend till it reaches the maximum deflection of the previous cycles, and then, the sample again starts to deform nonlinearly. This behavior is almost identical to the first cycle except that the stiffness, unrecovered permanent deformation, and transition points have changed. The unrecovered permanent deformation is about 4 to 5 mm. This is higher than the second cycle, shown as point q in Fig. 5. The fourth cycle is similar to the second cycle, where loading curve shows a linear behavior and unloading curve exhibits slight material hysteresis.
Specifically, in 75%L (Fig. 5(a)), the nonlinear transition is relatively noticeable. The linear region extends straight to the 1.5 mm deflection level and turns into nonlinear deformation before it is unloaded. The maximum load remains around 4.5 N to 5 N as the deflection keeps increasing with the cycles. The second and fourth loadings both show a completely linear curve. In comparison, the transition of 75%S (Fig. 5(b)) is not as clear as that of 75%L. Also, the maximum load of 75%S increases with the increasing deflection over the cycles. No plateau is observed. Therefore, the transition is at a higher force as the cycle proceeds, similar to the strain-hardening effect in the regular stress–strain curve. On the other hand, although the first transition points are not the same, they both land in somewhere between 1.5 mm and 2.5 mm. This implies that the defects (e.g., pores, flaws, cracks) start to take place at this deformation level regardless of the structural configuration. This is particularly true of the 75% structure when it is more dominated by the brittle plaster phase.
The 50% cases have a lower maximum force of each cycle than that of the 75% cases due to the plaster content, which dominates the strength of the structure. In addition, the 50% cases have more obvious “pseudostrain” hardening effect, particularly for 50%S. The maximum force of the nonlinear transition increases significantly with the cycle (deflection). On the other hand, for a fixed plaster content (50% or 75%), the small cell size tends to have more pseudostrain hardening effect. These observations conclude that nonlinear elastic transition behavior and the hardening effect are both affected by the content of plaster and silicone as well as the structure. The repeatability of loading and unloading curves also suggests a stable microstructure inside the material.
Figure 6 shows the comparison of the slope of the force–deflection curve for each cycle of all four cases. This slope in a linear elastic region represents the bending stiffness of the structure. Mathematically, the bending stiffness was calculated using the first 1 mm deflection data from where the force starts to increase. Note there is unrecovered deflection for cycles 2 to 4. The comparison is based on two repeated tests of each case.
For all of the samples, the bending stiffness decreases after each cycle, and all of them show a similar trend for stiffness degradation. From the first cycle to the second cycle, the stiffness of every sample decreases around 50–60%. This is the highest degradation in the whole test. From the second cycle to the third cycle, there is almost no stiffness degradation because no nonlinear deformation occurs in the second cycle. From the third cycle to the fourth cycle, the stiffness significantly decreases again. The amount of degradation is about 30–50%, which is less than the first degradation.
Specifically in each case, for the first cycle, 75%L has the highest stiffness compared to the other cases. 75%S and 50%L have a similar stiffness of the first cycle, which is slightly lower than 75%L but significantly higher than 50%S. After the first cycle, the stiffness of the rest of three cycles becomes similar for 75%L, 75%S, and 50%L cases. This implies that the level of the stiffness degradation of 75%L is higher than 75%S and 50%L. In regard to 50%S case, it shows the lowest stiffness for every cycle compared to all the other cases.
According to the results, different compositions and structures lead to different behaviors during the cycling loads. The discussion is focused on how the nonlinear elastic behavior forms and how the structure affects these behaviors.
The material deforms elastically at the beginning of bending and turns to nonlinear deformation after certain deflection level. Figure 7 illustrates, via diagrams, a hypothesis to explain the phenomenon of the transition from linear to nonlinear elastic behavior. At the beginning of bending, the linear curve is because both materials (plaster and silicone) are elastic. When the deflection level reaches a certain threshold, the deflection of the material creates internal cracks inside the brittle phase. These cracks remain stable and do not propagate abruptly since the surrounding structure is tightly secured by the silicone network (i.e., the orthogonal structure). However, as the cycle proceeds, the larger deflection creates more and more cracks in the structure, which decreases the stiffness of the samples. If the deflection level keeps increasing, the sample will eventually fail because the cracks completely destroy the integrity of the structure. Therefore, when the cracks start to appear in the material, the structure transitions from the linear behavior to the nonlinear behavior. Figure 8 shows the tested sample reloaded from cycle 4 that contains internal cracks in the brittle phase.
Stiffness degradation has been shown qualitatively and quantitatively in Figs. 5 and 6. This stiffness degradation is a result of the microcracks mentioned in the previous discussion. Since the orthogonal structure of silicone can effectively secure the plaster and suppress (or slow down) the crack propagation, the elastic behavior is maintained during repetitive cycles. Although the structure has internally cracked resulting in stiffness degradation, it is not considered failure since the strength does not decrease. Further, the second cycle causes very minimum stiffness degradation (Fig. 6). This provides further evidence in revealing the elastic property. However, as the deformation proceeds to the third cycle, more or larger cracks are produced and thus again, decreases the stiffness. This stiffness degradation phenomenon is expected to reach a threshold where the structure starts to fail.
Specifically in this study, the level of degradation is found dependent on the cell size and composition. According to the results, the stiffness of the large cell structure samples degrades around 60% after the first cycle. However, the small cell samples only degrade 50%. Interestingly, despite large differences in stiffness of the first cycle, the stiffness of all samples tends to be more similar afterward. This could be specific to this combination of materials or the nature of such bimaterial structure. Further investigations with numerical modeling and other materials would need to be conducted in the future.
Modeling of the Bimaterial Structure.
Despite the complex microcrack phenomenon, it is still possible to simulate the behavior of the bimaterial using finite-element analysis (FEA). However, due to the porous nature of the ceramic phase, two issues should be taken into account: the degradation of elastic modulus due to the printed size effect and the infiltration of silicone resin. Our preliminary study in modeling is discussed below.
With printed samples of 100% plaster (solid specimens with no hollow cells), the load–displacement data were obtained from four-point bending experiments. The averaged bending stiffness and the averaged flexural modulus were calculated at 16.13 N/mm and 1611 MPa, respectively. Along with the geometric information, the flexural modulus was used as the elastic modulus in FEA of four-point bending to obtain the load–displacement curve with a slope of 15.35 N/mm. This number agrees well with that of the experiment (16.13 N/mm). To closely match the slope of the experimental load–displacement curve, different elastic modulus values were used in FEA simulations, and the elastic modulus value of 1691 MPa, which is within 5% difference of the flexural modulus, produced the best fit. This demonstrates that with the proper material properties and specimen geometry, FEA can accurately predict the load–displacement response in the experiment.
Experiments and FEA simulations were then carried out for 75%L0, 75%S0, 50%L0, and 50%S0, where the subscripted “0” indicates that the specimens were all plaster with no silicone infiltration into the pores of the cells. The flexural modulus (1611 MPa) was used in all four-point bending simulations. The bending stiffness of all samples obtained from the FEA was then compared to those from the experiments. From Fig. 9, the effect of volume fraction can be clearly observed. For both experiment and FEA simulation, a higher plaster volume fraction (75% versus 50%) resulted in a higher bending stiffness. The cell size on the stiffness of the structure can also be observed. At the same plaster volume fraction, the structures with larger cell size (L versus S) exhibit higher stiffness.
It can also be observed that the difference in stiffness between the experimental results and the FEA predictions increases with decreased plaster volume fraction and decreased cell size. Given that FEA can accurately capture the mechanical response of the structure in four-point bending, the discrepancy indicates that the elastic modulus of the plaster is cell-size dependent. With small cell size, the plaster cell wall is thin, and any microscopic imperfection in the cell wall could have a dominant effect on the continuum scale properties such as the elastic modulus. This is a concern when using a 3D printer to build a complex structure. The resolution of the 3D printer is about 0.41 mm, compared to the smallest feature size of 0.8125 mm in the structure.
As to another issue, it can also be seen that the bending stiffness of every pure plaster is much higher than those in the first cycle of Fig. 6. This indicates that the plaster property was significantly changed under the high-temperature environment for silicone polymerization. The temperature control in the manufacturing process, based on the materials used, is another critical factor for the bimaterial structure.
This study has further tested the mechanical behaviors of the ceramic–elastomer structure under cycling loads. The results showed interesting nonlinear elastic phenomenon and stiffness degradation. The potential application could be for structural components that require high fracture toughness or impact toughness.
The current data have suggested a basic trend for the bimaterial structures under the loading–unloading study. Evolution of microcracks was hypothesized to be the key mechanism behind these phenomena. The continuation of this work will be focused on the FEA development and experimental validation.
The authors would like to acknowledge the material supports from Dow Corning and the experimental assistance from Mozheng Hu. This research is supported by the National Science Foundation Grant No. 1522877.