Design 3D printing cementitious materials via Fuller Thompson theory and Marson-Percy model
Introduction
3D Printing, also referred to as Additive Manufacturing, is a technology which builds a solid part via a layer-by-layer process [1]. Due to its advantages such as customized production, reduced waste, and diminished lead-time of rapid prototype [2], 3D Printing has attracted much attention from various fields including building and construction [3]. In the last decade, much research has been conducted in the field of 3D Printing for Building and Construction, especially in the development of printing systems such as Mortar Printing [3], [4], [5], FreeFab [6], Contour Crafting [7], [8], [9] and Robotic printing system [10], [11]. While most of the 3D Printing for Building and Construction processes can be classified as 3D Cementitious Materials Printing (3DCMP), little research has been done on how to design materials for 3DCMP [12], [13], [14], especially from the aspect of material design methods for 3DCMP.
Materials used in 3DCMP need to meet certain specific rheological requirements [3], [15]. The most essential steps in 3DCMP are conveying mixed materials to the nozzle via a delivery system and depositing materials to build the solid object in a layer-by-layer manner. In the conveying step, the materials are required to have good pumpability, which indicates how easily material can be conveyed; and in the deposition step, the materials are required to have good buildability, which indicates how well the materials can be stacked stably. Both pumpability and buildability are closely related to the rheology performance of materials, namely static/dynamic yield stress and plastic viscosity. Static yield stress is the minimum shear stress required to initiate the flow and dynamic yield stress is the critical shear stress below which the shear stress is insufficient to maintain the flow. Plastic viscosity is the resistance of a fluid to flow when the fluid is flowing. All these rheological properties are attributed to the inter-particle force [16]. Typically, higher static/dynamic yield stress and plastic viscosity would enhance buildability and hinder pumpability [17] and thus, seeking a balance between buildability and pumpability is critical in material rheology design for 3DCMP.
It is well known that aggregates take up 60–80% of the total volume of cementitious materials, the most commonly used building and construction material worldwide[19]. Rheological properties of cementitious material are highly affected by the gradation of aggregate [18], [19], [20]. Good aggregate gradation contributes to high density and proper rheological properties of materials. Fuller Thompson theory is a classic theory for gradation design. In 1907, W.B Fuller and S.E. Thompson proposed a theory for gradation design based on experimental results [21]. Later, Federal Highway Administration (FHWA) proposed a modified Fuller Thompson equation [22]. Fuller Thompson theory has been widely used in producing high performance concrete [20], [23], designing sustainable concrete with minimum content of cement [24] and optimizing rheology [25].
Rheological performance is significantly affected by the packing fraction of a system as well, which is defined as the ratio of solids to the total volume. Theoretically, materials designed by the continuous gradation can achieve maximum packing fraction, which describes a condition where the void volume reaches minimum for a given system. According to Marson-Percy model [26], the highest packing fraction of materials results in the lowest plastic viscosity.
To fulfill the material rheological property requirements in 3DCMP, Fuller Thompson theory and Marson-Percy model were applied in materials design of 3DCMP. Six different mixtures were prepared with different gradation approaches using five different sands (0.6–1.2 mm, 0.25–0.6 mm, 0.15–0.25 mm, less than 0.15 mm and natural river sand), i.e. mixture A designed by Fuller Thompson theory, mixture B and C designed by uniform-gradations, mixture D and E designed by gap-gradations and mixture F using natural river sand without special gradation design. Rheological tests were carried out to investigate the fresh performance of all mixtures, and printing tests for buildability were conducted among different mixtures via a gantry printer. Density and mechanical performance (compressive and flexural properties) were characterized as well.
It should be noted that the time and temperature effect of rheological/material properties is not considered due to the limited scope of this study. Furthermore, all tests including printing are conducted within 30 min after water addition (21 min after finishing mixing) and under constant lab temperature of 26 °C.
Section snippets
Built-up theory and Bingham model
Perrot et al. established the relation between static yield stress and buildability of 3DCMP [17]. The simplified relation can be expressed as follows:where H (m) and α are the printed height (buildability) and the geometric factor of printed structure respectively; ρ (g/cm3) and g (m/s2) are the density of materials and gravitational constant respectively. τs (Pa) is the static yield stress, which is corresponding to static torque in Fig. 1.
Fig. 1 presents the typical rheological test
Materials
Mixtures in this study consist of Ordinary Portland Cement (OPC, ASTM type I, Grade 42.5), silica fume (SF, undensified, Grade 940, Elkem company), silica sand, fly ash (FA, Class F), natural river sand, water and superplasticizer (SP). Fig. 3 illustrates the particle size distribution of cement, SF and FA, which were analyzed by Mastersizer 2000. Table 1 illustrates the chemical composition of OPC and FA, respectively. Silica sand with four different sizes, i.e., 0.6–1.2 mm, 0.25–0.6 mm,
Mixing procedures
A hobart mixer X200L was used for mixing. Since many factors can affect the rheological properties of cement slurries, such as mixing time, mixing speed and temperature [35], the mixing procedures in this study were fixed to minimize the differences among batches. Firstly, the powder of all solid ingredients was dry mixed for 3 min in stir speed; then water was added, the mixing process continued for 3 min in stir speed followed by 2 min in speed I; and then the SP was added, the mixing process
Rheological analysis
Herein Fig. 10 illustrates the shear stress and shear rate relation from rheological results based on Bingham Plastic model. The raw data of static torque, flow resistance and torque viscosity were shown in Table 3, which were then converted to static/dynamic yield stress and plastic viscosity via Eq. (8) and shown in the same table.
As can be seen from Fig. 10 and Table 3, mixture A has the highest static yield stress and the smallest plastic viscosity, which is very desirable to ensure low
Summary and conclusion
3DCMP requires the material to have low plastic viscosity and high yield stresses to meet the requirements for both pumpability and buildability. Fuller Thompson theory and Marson-Percy model were adopted as a guideline to design construction materials with proper rheological properties for 3DCMP. Six different mixtures (i.e., mixtures A-F) were prepared with various gradation using five different sands (0.6–1.2 mm, 0.25–0.6 mm, 0.15–0.25 mm, less than 0.15 mm and natural river sand). The
Acknowledgement
The authors would like to acknowledge National Research Foundation, Prime Minister's Office, Singapore under its Medium-Sized Centre funding scheme, Singapore Centre for 3D Printing and Sembcorp Design & Construction Pte Ltd for their funding and support in this research project.
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