Das Kapitel befasst sich mit der Entwicklung des mechanischen Versagensverhaltens von 3D-gedrucktem Polymerbeton im frühen Alter, einem Material mit überlegenen Eigenschaften, aber höheren Kosten. Es untersucht die zeitabhängige Entwicklung der grünen Festigkeitseigenschaften von frischem Polymerbeton, wie Elastizitätsmodul, Poissons Verhältnis und Versagenskriterien. Die Studie verwendet das Mohr-Coulomb-Modell, um das Versagen des Materials zu beschreiben, und führt über 110 Minuten uniaxiale Druck- und direkte Scherversuche durch. Die Ergebnisse zeigen eine signifikante Zunahme der Druckfestigkeit und des Elastizitätsmoduls im Laufe der Zeit, wobei die Polymergelierung nach 60 Minuten eintritt. Diese Forschung zielt darauf ab, den 3D-Druckprozess für Polymerbeton zu charakterisieren und wertvolle Erkenntnisse für die Entwicklung von Rechenmodellen zu liefern, um die Stabilität von 3D-gedruckten Strukturen zu gewährleisten.
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Abstract
The increasing interest in 3d printing of concrete for infrastructure applications necessitates having a design for this process. Previous research has mostly focused on 3D printable cement-based concrete mixes, with less attention given to 3D printed polymer concrete (PC). PC is a concrete type that uses polymer instead of cement as a binder. It offers improved compressive and tensile strengths, crack resistance and bond strengths, and superior durability than traditional Portland cement concrete, making it an excellent material for 3D printing. This study aims to understand the evolution of the early-age mechanical properties of fresh polymer concrete and its potential failure during printing. Unconfined uniaxial compression and direct shear tests were performed on fresh polymer concrete for the first 110 min after mixing to determine the evolution of mechanical and failure characteristics with time. Such characteristics include compressive strength, modulus of elasticity, cohesive strength, and friction angle. A time-dependent early-age Mohr-Coulomb failure envelope is established to describe the mechanical and failure behavior of 3D printed polymer concrete.
1 Introduction
3D printing is a computer-controlled method of sequentially layering materials to create three-dimensional shapes. This process helps fabricate complex geometries and produce prototypes. The construction industry's gradual shift towards automation has prompted growing research to explore the potential of this technology. 3D concrete printing, in particular, enables architects and builders to produce intricate and asymmetric patterns while minimizing human error leading ways to innovative designs [1, 2].
Concrete made from polymers as a binder, called Polymer Concrete (PC), has been used in various field applications since the 1950s. Such applications include precast architectural façades, underground utilities, wastewater pipes and tanks, manholes, machine foundations, bridge deck overlays, and closures [3]. PC exhibits superior properties such as high tensile and bond strength and outstanding durability [4, 5]. However, its use is often restricted due to its comparatively higher cost [6, 7]. The enhanced characteristics of PC to being impermeable concrete with very high durability [7, 8].
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The unique features of PC and its numerous industrial applications make it a desirable material for 3D printing [9, 10]. However, it is crucial to understand PC's early age rheological, mechanical, and failure characteristics to ensure successful printing and product quality and prevent printing failures. This study examines the time-dependent evolution of fresh polymer concrete's mechanical and failure characteristics, referred to as “green strength” properties, such as modulus of elasticity, Poisson's ratio, and failure criteria. One crucial property of 3D printing is material stability during the printing process [11‐13]. Green strength refers to the ability of fresh concrete to retain its shape and support its weight immediately after compaction or mixing, which results from inter-particle cohesion and friction. The Mohr-Coulomb model represents the green material's failure, a simple and widely used approach to describe the material's strength and deformation properties under different loading conditions [14‐18]. The use of Mohr-Coulomb failure criteria can be supported by the similarly of fresh PC with geomaterials. We aim to characterize the 3D printing process for PC by investigating how its mechanical and failure characteristics change over time. To achieve this, we conducted uniaxial unconfined compression and direct shear tests to measure the mechanical properties of fresh PC. Testing was performed over 110 min to realize the time-dependent evolution of the properties. These observations shall help model and predict the behavior of the 3D printed PC.
2 Materials and Methods
2.1 Materials
PC was produced using Polyester resin cured at room temperature using a Methylene ethyl ketone peroxide hardener. The hardener content was adjusted to achieve a 2-h setting time. High-quality silica sand with a nominal maximum size of 2.36 mm was used as the main aggregate. In addition, a filler combining silica fume, type-F fly ash and fumed silica was used to control material thixotropy. The PC mix design is presented in Table 1. The PC was cured in dry conditions and ambient temperature of 22 ℃ for 7 days of age and showed a mean compressive strength of 59.8 MPa and a mean modulus of elasticity of 7.0 GPa.
Table 1.
PC mix design of 1 cubic meter and 7-day mechanical properties
Material
Weight (kg/m3)
Polymer resin
390
Hardeners
3.0
Aggregate
1537
Fillers (Silica Fume, fumed silica, and fly ash)
162
7-day compressive strength
59.8 MPa
7-day modulus of elasticity
7.0 GPa
2.2 Test Methods
Strength assessment of green PC was executed at different time intervals, including t = 0,30,60,90, and 110 min, with t = 0 being the earliest point after compaction, demolding, placing the sample in the testing arrangement, and initiating the examination, as suggested by previous researchers [15]. The process mentioned above takes around 10 to 15 min. The time span from 0 to 110 min was chosen to match the polymer concrete's setting time and the typical length of the printing process.
For the uniaxial unconfined compression test, as per ASTM D2166-13 [19], a cylinder made of PC material is subjected to axial loading until it fails under compression. The maximum load is divided by the specimen's cross-sectional area to determine the unconfined compressive strength. The cylindrical specimens have a height of 101.6 mm and a diameter of 50.8 mm. Before placing the PC mix in the cylindrical molds, a thin Teflon sheet was laid on both sides, and a lubricant oil spray was used, ensuring the sample's easy removal from the molds. The PC mix was added in three layers, each compacted for 10s on a 30 Hz vibration table to obtain a uniform sample. When the sample was carefully removed from the molds, the Teflon sheet was removed as well. A universal testing machine with a 25.0 kN load capacity and a 1.0 N resolution was used for testing. A steel head with a similar diameter was used to transfer the load to the specimen, while a hardened 3D-printed PC plate was placed beneath the sample to mimic the printing conditions of the layer's bottom in contact with the hardened PC (Fig. 1.a). To replicate the loading rate during printing and avoid the impacts of thixotropic build-up [15], a displacement-controlled test was conducted at a rate of 30 mm/min. At each age, five fresh PC samples were tested. To record the PC specimens’ vertical and lateral deformation during loading, a non-contact digital image correlation measurement system [20] was used.
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The direct shear test, described in ASTM D3080-98 [21], is a method used to investigate the relationship between shear strength and normal stress. The test involves placing a circular disc of material into a shear box mold composed of two steel plates with a 63 mm diameter opening and a specimen height of 36 mm. The plates can slide laterally with respect to each other and are held together with two locking screws to prevent specimen extrusion. Prior to testing, the molds are lightly greased with a lubricant oil spray to minimize side friction. PC was placed in the mold in three layers and compacted for 10 s on a 30 Hz vibration table to ensure homogeneity. The specimen is then tested using the direct shear device equipped with a 450N load cell and data logger (Fig. 1.b). The bottom plate is moved laterally at a constant rate of 10 mm/min while normal vertical stress, σn, is applied using steel weights. Three normal loads of 0N, 10N, and 20N are applied, corresponding to normal loads of 1.1N, 10.9N, and 20.7N, respectively, considering the self weight of PC, on the shear plane located in the middle of the sample. A thin layer of grease is applied to their surface to reduce friction between the plates. Stresses are computed with an updated cross-section due to the considerable deformations during testing. Five specimens are tested at each ages underthree normal load combinations.
Fig. 1.
(a) Test set up for the uniaxial unconfined compression test of fresh PC (b) Direct shear test set up for testing fresh PC.
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The two main parameters that determine the failure of a printed element are strength and stiffness growth over time which are produced by the thixotropic build-up of PC [22‐24]. The Mohr-Coulomb failure criterion was used to describe the shear behavior of green printed PC and can be expressed by Eq. (1):
where \(C\left(t\right)\) is the time-dependent cohesion strength of green PC, \({\sigma }_{n}\) is the normal stress, and \(\phi \left(t\right)\) is the time-dependent friction angle of the fresh PC layer placed against another fresh PC layer. Finally, \({\tau }_{y}\left(t\right)\) is the time-dependent shear strength between two green PC layers.
To understand the evolution of mechanical and fracture characteristics of PC with time, time-temperature measurements of the polymer were made and analyzed using the analysis of temperature derivative (ADT) method [25]. In this method, the polymer resin and hardener were mixed with the same ratio used to produce PC and stirred for one minute in a glass cup. Two thermocouples were prepared with twisted junctions to minimize thermal inertia and directly submerged into the polymer mixture. The thermocouples were positioned near the center, and data were collected every minute.
3 Results and Discussions
Under compressive stresses and from 0 to 30 min, the green PC exhibited a mean compressive strength of 2.1 kPa, gradually increasing to 274 kPa at 110 min. The growth of compressive strength of the fresh polymer concrete up to 110 min is shown in a linear fit in Fig. 2(a). The elastic modulus of green PC starts at 8.1 kPa at t = 0 min and shows linear growth up to 11.6 kPa at t = 30 min, as shown in Fig. 2(b). Subsequently, the elastic modulus increased rapidly and reached 4354.9 kPa at t = 110 min. The polymerization reaction of the polymer in the PC seems to start at 30 min (Fig. 4) and might be responsible for the initiation of an observable elastic modulus and compressive strength after 30 min of placing.
Fig. 2.
a) Time-dependent compressive strength of fresh PC up to 110 min; (b) Time-dependent elastic modulus of fresh PC up to 110 min.
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In shear testing, there was a noticeable linear growth in strength and stiffness during the first 110 min of PC age. The Mohr-Coulomb failure parameters for PC were determined based on direct shear tests, as shown in Fig. 3, Fig. 3 (a) shows that PC cohesion increases slowly and linearly during the first 60 min. A significant change in the rate of cohesion increase was observed after 60 min of the PC age. This might be attributed to polymer gelation (gel transition) at this time. A piecewisefunction (Fig. 3.a) is used to describe the evolution of PC cohesion with time. On the other hand, Fig. 3 (b) shows that the angle of friction of PC seems to be constant at 57 degrees.
Fig. 3.
(a) PC cohesion evolution with time (b) PC internal friction angle of PC of 57° seems constant over time.
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The polymer temperature measurements are presented in Fig. 4. Temperature time derivative was calculated using Origin base functions and curves smoothed using the Savitzky-Golay method. It is apparent that polymer gelation, identified by the peak of the first derivative of the temperature-time curve, takes place at 60 min. This can explain the significant change in the PC cohesion growth rate after 60 min of mixing. This is critical information for the 3D printing process.
Fig. 4.
Thermal analysis of the polymer showing polymer gelling to take place close to 60 min.
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The above investigation showed the time evolution of the mechanical properties of 3D printed PC, including the compressive strength and the axial stiffness. The tests also showed the change in the failure criteria of 3D printed PC, including the cohesion and friction angle with time. Further research is underway to use this data for developing a computational model to simulate the 3D printing process. Such modeling is important to ensure the stability of the 3D printed PC structure.
4 Conclusions
The work presented herein demonstrates the extraction of green strength and failure criteria of fresh PC used for 3D printing. The extracted parameters can be used to develop a computational model that simulates the 3D printing process of PC. The compression strength, the elastic modulus, and the shear strength of fresh PC mix were measured at 0, 30, 60, 90, and 110 min of age. The failure behavior can be described by a time-dependent Mohr-Coulomb failure criterion and linear stress-strain behavior up to failure. The green strength parameters and failure criteria of PC, evolves over time. PC's mean green compressive strength increased from 2.1 kPa at printing time to 274 kPa at 110 min. The mean green elastic modulus increased from 8.1 kPa at time of printing to 4355 kPa at 110 min. PC failure criteria parameters are evidently time-dependent. The PC starts to develop an appreciable strength and stiffness after 30 min of placing due to the start of the polymerization reaction. Furthermore, cohesion showed to have a piecewise function relationship with time with a significant change of slope at 60 min. Temperature analysis of the polymer showed this change coincides with the polymer gelation where the solid polymer formation starts to take place. On the other hand, PC internal friction angle was found to have a constant value of 57 degrees.
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