Multivariate non-linear regression models for the relationship between the vat photopolymerization 3D printing process of alumina ceramics and the shrinkage rate of sintered bodies

Abstract

This study integrates JMP-based response surface methodology with multivariate regression to optimise process parameters and predict shrinkage behaviour in vat photopolymerization-printed alumina ceramics. The analysis highlights that coating thickness is an important factor in shrinkage control, while the relative importance of linear, interaction, and quadratic contributions varies with shrinkage mode. Results showed that the shrinkage rate in the length direction was mainly associated with the linear terms of coating thickness and scraper movement speed, with an additional contribution from their interaction. The width-direction shrinkage was primarily affected by the linear term of laser power, together with the interaction between laser power and coating thickness. The inner-diameter shrinkage was mainly governed by the quadratic term of scraper speed and the interaction between laser power and scraper speed, indicating a pronounced non-linear response. The volumetric shrinkage was predominantly influenced by quadratic terms, especially those associated with coating thickness, laser power, and laser scanning speed.

Keywords

Additive manufacturing JMP response surface methodology multivariate non-linear regression equation mechanical properties

Introduction

Alumina ceramics possess excellent physical and chemical properties such as high hardness, high-temperature resistance, and corrosion resistance, making them widely used in high-tech fields such as mechanical engineering, aerospace, and medical devices.^1–3 However, when manufacturing complex geometries of alumina components using traditional moulding and sintering processes, issues such as large dimensional errors, processing difficulties, and high costs arise. In recent years, the development of additive manufacturing technology,⁴ especially the vat photopolymerization (VPP) three-dimensional (3D) printing technology, has opened up new pathways for manufacturing complex alumina ceramic components. Recent developments in the additive manufacturing of ceramics have focused on optimising ceramic powder formulations, improving printing quality, and addressing post-processing challenges such as sintering shrinkage and densification. Recent studies have shown that the choice of ceramic powder and the formulation of slurries can significantly impact printability and mechanical properties. For instance, formulations with finely tuned particle size distributions and additives improve flowability and inter-layer bonding.⁵ Furthermore, key process parameters, including laser power, scan speed, and coating thickness, influence the curing depth, density, and overall print quality, as explored in various studies.^6,7 Additionally, post-processing, particularly sintering behaviour, plays a critical role in achieving desired mechanical properties. Recent research has demonstrated significant improvements in sintering densification and reduced shrinkage through optimised process parameters.^8,9 The VPP 3D printing of alumina ceramics involves complex processes such as slurry preparation, printing, debinding, and sintering, where any variation in process parameters can lead to defects such as porosity, inter-layer cracks, and poor dimensional accuracy.¹⁰ The shrinkage behaviour of photo-polymerised alumina ceramic green bodies is one of the main reasons for the poor dimensional accuracy of sintered bodies.¹¹ During the sintering process of alumina ceramics, significant anisotropic shrinkage occurs, leading to the deformation of complex-shaped parts,^12,13 which makes it difficult to guarantee the dimensional accuracy and repeatability of the components.^14–17

In the VPP 3D printing process, optimising parameters such as laser power, scan speed, scraper speed, and layer thickness can effectively control dimensional accuracy. Li et al.¹⁸ explored the effect of slurry coating thickness on the flow behaviour during the VPP 3D printing. The study showed that coating thickness significantly affects the crack propagation in the green body. When the coating is thicker, the layered structure in the green body becomes more apparent, and macroscopic cracks are more likely to form at the inter-layer interfaces. Zhao et al.¹⁹ pointed out that the combination of laser power and scan speed significantly impacts the curing depth and width, which in turn affects the uncured volume within the green body and its subsequent volumetric shrinkage and dimensional accuracy. When the curing depth is too large or the scan speed is too low, excessive curing leads to an increased internal stress, causing an increase in volumetric shrinkage or linear shrinkage. Huo et al.²⁰ studied the effects of laser power, scan speed, and coating thickness on part shape, density, cracks, and dimensional deformations (including shrinkage and warping). The results showed that higher power and slower scan speeds provide sufficient energy density to cure the entire coating thickness, reducing porosity; otherwise, incomplete curing leads to uneven sintering shrinkage. Meanwhile, increasing the coating thickness can improve production efficiency, but if it exceeds the curing energy's penetration and heat transfer capacity, it may lead to a poor bonding of the lower layers, resulting in greater shrinkage or cracking during the sintering phase.²¹

For a given coating thickness, properly matching laser power and scan speed is crucial to effectively control shrinkage and warping during the forming process.^22,23 While higher laser scan speeds and relatively lower laser power can help reduce heat accumulation per layer, they may also result in insufficient laser curing energy for individual layers, lowering the density of the formed green body.²⁴ Green bodies with insufficient density are more likely to experience significant linear shrinkage during the subsequent sintering process,²⁵ which can impact the final product's dimensional accuracy and structural integrity.

Young et al.²⁶ studied the effects of coating thickness and exposure time on the shrinkage rate and final performance of VPP 3D-printed ceramics. A smaller coating thickness can improve the curing quality of each layer and increase the cross-linking density, thereby reducing shrinkage and enhancing mechanical strength. When the coating thickness was reduced from 100 to 10 µm, the density of the sintered body increased from 1.62 to 2.3 g cm⁻³, and the shrinkage rate also decreased. Extending the exposure time increases the cross-linking density of the green body, improving both its performance and sintered body density. When the exposure time was increased to 140% of the baseline, the density increased from 1.86 to 2.1 g cm⁻³. The combined effects of coating thickness and exposure time further optimised the ceramic density, especially by reducing the shrinkage rate. Zhang et al.²⁷ examined the impact of coating thickness and exposure time on green body deformation. Larger coating thicknesses and excessively short exposure times tend to cause more significant deformation. When the coating thickness exceeded 50 µm, incomplete curing resulted in internal stress, leading to deformation. Particularly in large-sized printed parts, inter-layer shrinkage differences could cause warping or localised deformation. A coating thickness of 25 µm helps achieve uniform curing, reducing internal stress and thereby minimising deformation. Short exposure times lead to incomplete curing, with uncured portions potentially causing warping or cracks, while longer exposure times improve cross-linking density, reducing shrinkage differences and deformation. However, excessively long exposure times may lead to over-curing, causing inter-layer delamination or cracking. To address the high organic content, large shrinkage, and time-consuming debinding in traditional photo-polymerisation processes, Fuzhao et al.²⁸ examined the impact of coating thickness and exposure time on green body deformation. Larger coating thicknesses and excessively short exposure times tend to cause more significant deformation. When the coating thickness exceeded 50 µm, incomplete curing resulted in internal stress, leading to deformation. Particularly in large-sized printed parts, inter-layer shrinkage differences could cause warping or localised deformation. A coating thickness of 25 µm helps achieve uniform curing, reducing internal stress and thereby minimising deformation. Short exposure times lead to incomplete curing, with uncured portions potentially causing warping or cracks, while longer exposure times improve cross-linking density, reducing shrinkage differences and deformation. However, excessively long exposure times may lead to over-curing, causing inter-layer delamination or cracking. To address the high organic content, large shrinkage, and time-consuming debinding in traditional photo-polymerisation processes, Wang et al.²⁹ studied the dimensional shrinkage behaviour of photo-polymerised alumina ceramics during the sintering process. Using convolutional neural networks to predict the dimensional deviations of sintered circular ceramic parts, they found that the shrinkage rate was closely related to printing process parameters and geometric dimensions. The study concluded that shrinkage in the same component was not uniform in different directions, presenting a non-linear distribution with direction. With the advancement of computer and artificial intelligence technologies, machine learning, deep learning, and other algorithms have been applied to process optimisation in additive manufacturing.

Although the effects of the VPP 3D printing process parameters on the shrinkage rate and deformation of sintered bodies have been studied, systematic research on the interactions between multiple variables such as laser power, scan speed, coating thickness, and scraper speed on the shrinkage rate is still scarce. Statistical optimisation tools such as response surface analysis and orthogonal design are often used for process parameter optimisation. The application of response surface methodology (RSM) helps identify the optimal process conditions,³⁰ thereby reducing adverse effects such as anisotropic shrinkage, cracking, and low density.^31–33 This study presents a novel approach by integrating JMP-based RSM with multivariate regression modelling, not only for optimising process parameters but also for providing quantitative predictions of shrinkage behaviour in VPP-printed alumina ceramics. Unlike traditional optimisation methods, this study highlights the dominance of coating thickness across all shrinkage modes (linear, volumetric, and anisotropic shrinkage), which plays a key role in determining shrinkage behaviour. Furthermore, the study offers quantitative interaction hierarchies between process parameters, revealing significant interaction effects that govern shrinkage behaviour.

Materials and methods

Materials

The preparation of ceramic slurries involves the surface modification of ceramic powders (e.g. Al2O3, YSZ, etc.), mixing and dispersion of photo-polymerisation resins, and degassing treatment to ensure the slurry's uniformity and rheological properties. The preparation process of the alumina ceramic slurry is as follows: first, 3-aminopropyltriethoxysilane (purity 99%, Shanghai Maikelin Reagent Co., Ltd) was used for the surface modification of Al₂O₃ (purity 99.97%, particle sizes of 2000, 1000, and 500 nm, Suzhou Bisley New Materials Co., Ltd), and MgO (purity 99.92%, particle size 200 nm, Hebei Chuancheng Materials Co., Ltd) ceramic particles. The specific steps for surface modification are as follows: Al₂O₃ particles were mixed with anhydrous ethanol at a 1:4 volume ratio, and after adding the surface modifier, the mixture was treated in an ultrasonic reactor (180 W) for 2 h, followed by drying in a 60 °C oven for 24 h to remove the ethanol. Similarly, methyltrimethoxysilane (Shanghai Maikelin Reagent Co., Ltd) was used for modifying the YSZ powder (8 mol-% yttrium-doped, purity 99.8%, particle size 500 nm, Ningbo Zhongke New Materials Co., Ltd).

Next, a photo-polymerisation resin solution was prepared using 1,6-hexanediol diacrylate (HDDA, density 1.010 g mL⁻¹, refractive index 1.457, Shanghai Guangyi Chemical Co., Ltd) as a diluent, ethoxylated pentaerythritol tetraacrylate (PPTTA, density 1.16 g mL⁻¹, refractive index 1.475, same company) as the monomer, and adding a photoinitiator RYOJI 819 (phenyl di(2,4,6-trimethylbenzoyl)phosphine oxide, chemical formula: C₂₆H₂₁O₂P, Dongguan Haise Plastic Raw Materials Co., Ltd). These components were mixed by magnetic stirring for 4 h. Then, dispersant DS-195H (maleic acid-styrene co-polymer, Tianjin Huo Fei Te New Materials Co., Ltd) and plasticiser PEG-200 (Shanghai Maikelin Co., Ltd) were added. Finally, the modified ceramic particles (Al₂O₃:YSZ:MgO in a volume ratio of 87.25:12:0.75) were mixed with the resin solution. The slurry was uniformly dispersed using a ball milling process (ball-to-material ratio 4:1, speed 180 r min⁻¹, time 4 h), and air bubbles were removed by vacuum degassing treatment.

VPP 3D printing process of Al₂O₃ slurries

A ceramic VPP 3D printing system (CeraBuilder 100Pro-D, Wuhan, China) was used to print the ceramic green bodies. First, the selection of the single-layer coating thickness was required to balance printing accuracy and production efficiency. A thicker coating can reduce printing time but may lead to weak inter-layer bonding, causing delamination or internal stress issues. Conversely, a thinner coating can improve printing accuracy but significantly reduces production efficiency. The optimisation of laser power and scan speed is crucial for ensuring the uniformity and precision of the photo-polymerisation reaction. Appropriately increasing the laser power can enhance the curing speed and surface quality, but excessive power may lead to thermal damage or local over-curing, resulting in cracks and other defects. The laser scan speed directly affects the curing degree of each printing layer, with a moderate scan speed ensuring uniform curing of each layer, thus improving the overall density and mechanical properties of the green body. The scraper movement speed also significantly impacts the print quality. Excessive scraper speed may cause uneven slurry application, affecting the forming quality, while too low a scraper speed may result in slurry accumulation during the printing process and over-curing. Based on previous single-factor experiments, the preliminary printing process was set with a single-layer coating thickness of 200 μm, laser power of 900 mW, scraper movement speed of 2.5 cm s⁻¹, and laser scan speed of 1200 mm s⁻¹.³⁴ These parameters were selected based on a comprehensive evaluation of forming quality, mechanical properties, and structural integrity under different printing conditions.

Treatment and debinding process of green bodies

The printed green bodies are first brushed with a soft-bristled brush to remove any remaining uncured slurry around the body. The ceramic green body is then soaked in acetone and cleaned in an ultrasonic bath. During this process, acetone penetrates the gaps between the ceramic particles through capillary action, contacting and dissolving the resin binder phase. Acetone helps remove the small amounts of uncured slurry on the surface of the green body, preventing the slight curing of the slurry under natural light, which could affect the stress release during subsequent thermal processing. Finally, the green body is soaked in a PEG400 solution for 20 h and then dried in a vacuum drying oven.

The debinding and sintering of the green body are carried out in a box-type atmosphere furnace (GF170Q, Nanjing Boyun Tong Instrument Technology Co., Ltd, China). The thermogravimetry–derivative thermogravimetry (TG–DTG) method is used to measure the resin thermal decomposition process and design the optimal debinding process. During the sintering process, the temperature is raised at different heating rates to 1600 °C, where it is held for 90 min to ensure the green body is fully densified and to prevent abnormal grain growth due to excessive temperatures and prolonged holding times.

Characterisation of Al₂O₃ ceramics

The microstructure of the sintered bodies was characterised using a scanning electron microscope (SEM, SU-5000, Hitachi, Japan) to observe the cross-sectional and fracture morphology. Three-point bending tests were conducted using an AGIS 30 kN universal material testing machine (Shimadzu Corporation) to evaluate the bending performance of the sintered bodies. During the test, the direction of the applied load was perpendicular to the printing direction. The bending strength was calculated using the theoretical formula³⁵

σ = \frac{3 F L_{0}}{2 b h^{2}}

(1)

The calculation method for linear shrinkage is as follows

SR (linear) = (original size of the body − size after sintering)/original size of the body

The calculation method for inner-diameter shrinkage is as follows

SR (inner diameter) = (inner diameter of the body before sintering − inner diameter after sintering)/inner diameter of the body

The calculation method for volume shrinkage is as follows

calculation method for linear shrinkage isSR (volume) = (volume of the body before sintering − volume after sintering)/volume of the body

Results and discussion

Design of debinding and sintering process

Thermogravimetric analysis was conducted under an air atmosphere with a heating rate of 10 °C min⁻¹, covering a temperature range from 25 °C to 800 °C. Figure 1(a) shows the changes in mass and mass loss rate during the heating process of the green body, particularly in the carbonisation decomposition stage. The mass loss of the green body mainly occurred between 170 °C and 500 °C, with two peaks in the mass loss rate observed at 375 °C and 435 °C, and significant changes at 415 °C and 500 °C. The resin thermal decomposition process can be divided into three stages: Below 255 °C, the decomposition rate is relatively slow, and the TG curve declines gradually, primarily due to the volatilisation of physically adsorbed water, trace solvents, or low-molecular weight substances. Between 255 °C and 375 °C, the TG curve shows a more significant weight loss. The initial breaking of the molecular chains of the resin system (HDDA, PPTTA) occurs, and side groups, low cross-linked fragments, or incompletely cured small molecules begin to degrade. At 375 °C, the degradation of the HDDA main chain or a low cross-linked region occurs. Subsequently, at temperatures of 415 °C, 435 °C, and 500 °C, multiple DTG peaks are observed, indicating that the decomposition is not a single reaction but rather a gradual cross-linking break down. At 415 °C, the backbone fracture of the highly cross-linked portion of PPTTA occurs, marking the major weight loss peak. At 435 °C, further decomposition of residual organic material takes place. This phase shows a rapid decline in the TG curve, marking the primary decomposition zone of the resin. Above 500 °C, the mass stabilises, indicating that the resin has been completely decomposed.

Figure 1.

(a) Thermogravimetric analysis of the ceramic green body, with weight (black line) and weight change (red line). (b) Relationship curve between chemical soaking time and mass loss of the green body. (c) Debinding process curve of the green body. (d) High-temperature sintering process curve of the green body.

Based on the TG-DSC data, a multi-stage debinding process curve was designed as shown in Figure 1(c). The role of this curve is to reduce the temperature gradient from the centre to the outer layers, ensuring uniform heating and avoiding delamination or cracking of the green body. The process starts with a heating rate of 0.5 °C min⁻¹ to 120 °C, with a 60-min hold to remove free water. It is then heated at 0.5 °C min⁻¹ to 170 °C for 60 min. Afterwards, the temperature is raised at 0.25 °C min⁻¹ to 375 °C and held for 60 min, followed by a 0.25 °C min⁻¹ increase to 415 °C, held for 60 min, then to 435 °C, and held for another 60 min. Finally, the temperature is increased at 0.25 °C min⁻¹ to 500 °C, where it is held for 120 min to prevent gas escape that could cause cracks and bubbles, ensuring complete decomposition of organic matter. The temperature is then raised at 1 °C min⁻¹ to 1000 °C, holding for 60 min to further remove residual organic material and carbon, followed by a heating rate of 0.5 °C min⁻¹ to 1200 °C for 60 min. The process concludes with a final heating rate of 0.5 °C min⁻¹ to 1600 °C, with a 90-min hold to complete sintering. This approach, through precise temperature and atmosphere control, helps to prevent the formation of defects.

Figure 1(b) shows the relationship curve between the chemical soaking debinding time and the mass loss of the green body. When the soaking time increases from 0 to 50 min, the mass of the green body decreases rapidly. After 50 min of soaking, the mass of the green body remains essentially unchanged. The results indicate that chemical soaking debinding effectively removes residual resin on the surface of the green body and in the inter-layer pores of the subsurface, relieving interfacial stress, enhancing inter-layer bonding strength, and reducing the formation of macro-cracks and defects. Figure 1(c) illustrates the reasonable setting of debinding holding temperatures and times based on the TG-DTG curve, particularly performing isothermal holds at the peaks of the mass loss rate to optimise the temperature gradient distribution. Prior to sintering, macro-defects such as cracks, blisters, and warping are screened to ensure a smooth densification process. Figure 1(d) presents the sintering process of the green body, with the final sintering temperature set at 1600 °C, held for 90 min.

Effect of sintering temperature and heating rate on bending strength

Figures 2 and 3 present the fracture morphology of alumina samples at different sintering temperatures and heating rates. When the sintering temperature was 1550 °C, grain growth was relatively limited, and porosity began to shrink. A large number of dispersed pores were present at the particle boundaries, indicating that the ceramic had not yet entered the densification stage at this temperature. The fracture surface showed a large number of well-defined, structurally intact grains, along with some pits and incomplete grains, as shown in Figure 2. This microstructure is prone to cracking.

Figure 2.

At a sintering temperature of 1550 °C, the cross-sectional morphology of the sintered bodies at different heating rates: (a) 0.1 °C min⁻¹, (b) 0.5 °C min⁻¹, (c) 0.75 °C min⁻¹, and (d) 1 °C min⁻¹.

Figure 3.

At a sintering temperature of 1600 °C, the cross-sectional morphology of the sintered bodies at different heating rates: (a) 0.1 °C min⁻¹, (b) 0.5 °C min⁻¹, (c) 0.75 °C min⁻¹, and (d) 1 °C min⁻¹.

When the sintering temperature reached 1600 °C, the grains gradually developed into distinct polygons, the grain boundaries became clearer, and strong grain boundary bonding was formed. Porosity decreased or fully closed, and the material's density increased. At this point, the fracture surface exhibited a mixed mode of trans-granular and inter-granular fractures. The crack propagation path was restricted, and the fracture toughness improved, resulting in optimal performance, as shown in Figure 3. The increase in sintering temperature facilitated the transformation from a loose, porous green body to a dense and hard ceramic body.^36,37 Figure 4 shows the bending strength of the sintered green body at different sintering temperatures and heating rates. When the sintering temperature reached 1600 °C, the density of the Al₂O₃ ceramic sample reached 98.9% of the theoretical density, and the maximum bending strength was 454 MPa.

Figure 4.

Bending strength of sintered bodies at different sintering temperatures and heating rates: (a) 1550 °C and (b) 1600 °C.

Establishment of multivariate non-linear regression model

In order to clarify the impact of the VPP 3D printing process on the shrinkage of sintered bodies, this section thoroughly investigates the effects of four key parameters – laser scan speed, scraper movement speed, laser output power, and coating thickness – and their interactions on the shrinkage behaviour of sintered bodies. Experiments were designed using the JMP response surface experimental design module, with the factor levels and coding table shown in Table 1. The experimental order was arranged randomly in the table to avoid systematic errors.

Table 1.

Factor-level distribution.

Experimental factor	Factor levels
Experimental factor	Low level (−)	Medium level (0)	High level (+)
Laser scanning speed V_L (mm s⁻¹)	800	1000	1200
Blade movement speed V (mm s⁻¹)	20	30	40
Laser power P_L (mW)	1050	1125	1200
Single-layer curing thickness H (mm × 10⁻²)	16	20	24

Based on the response surface design methodology, an optimisation study was conducted on the VPP 3D printing process for alumina ceramics. In order to clearly express and analyse the effects of laser power, laser scan speed, scraper movement speed, and coating thickness on the dimensional shrinkage (length, width, height), volumetric shrinkage, and inter-layer bonding effects on the side surfaces of the green body, a multivariate non-linear regression equation for linear and volumetric shrinkage was established using the stepwise regression method in JMP software. The equation considers the four main variables (laser power, laser scan speed, scraper movement speed, and coating thickness) and their interaction effects. The experimental parameters and shrinkage rate measurement results are shown in Table 2. In the table, ‘0’ represents the centre point, ‘−’ represents the low level, and ‘+’ represents the high level.

Table 2.

Experimental parameters and results of shrinkage rate measurements.

Run no.	Pattern	Laser scanning speed (mmm s⁻¹)	Blade movement (speed mm s⁻¹)	Laser power (mW)	Layer thickness (mm × 10⁻²)	Shrinkage (%)
Run no.	Pattern	Laser scanning speed (mmm s⁻¹)	Blade movement (speed mm s⁻¹)	Laser power (mW)	Layer thickness (mm × 10⁻²)	Length	Width	Diameter	Volume
1	−−00	800	20	1125	20	15.7	15.7	15.6	40.4
2	−+00	800	40	1125	20	16.8	16.8	15.8	43.0
3	+−00	1200	20	1125	20	16.4	15.5	16.9	41.6
4	++00	1200	40	1125	20	16.3	16.1	15.5	42.6
5	00−−	1000	30	1050	16	18.3	18.2	20.1	43.3
6	00−+	1000	30	1050	24	17.0	16.7	19.5	45.6
7	00+−	1000	30	1200	16	17.9	18.4	22.6	43.9
8	00++	1000	30	1200	24	16.7	17.5	18.5	46.3
9	−00−	800	30	1125	16	18.5	18.2	21.3	43.5
10	−00+	800	30	1125	24	16.8	16.8	18.0	45.7
11	+00−	1200	30	1125	16	18.2	18.5	20.6	43.7
12	+00+	1200	30	1125	24	16.8	16.6	19.4	45.9
13	0−−0	1000	20	1050	20	15.8	15.3	17.1	41.6
14	0−+0	1000	20	1200	20	15.2	15.5	16.0	41.1
15	0+−0	1000	40	1050	20	14.7	16.3	16.2	42.2
16	0++0	1000	40	1200	20	16.6	17.0	15.4	43.1
17	−0−0	800	30	1050	20	14.7	14.9	17.1	41.9
18	−0+0	800	30	1200	20	15.0	15.8	16.4	41.1
19	+0−0	1200	30	1050	20	14.6	15.3	16.9	41.6
20	+0+0	1200	30	1200	20	15.0	15.1	16.3	41.4
21	0−0−	1000	20	1125	16	18.4	17.9	20.7	43.9
22	0−0+	1000	20	1125	24	17.1	17.0	19.1	46.5
23	0+0−	1000	40	1125	16	18.9	19.3	20.6	44.2
24	0+0+	1000	40	1125	24	17.7	17.4	18.1	47.6
25	0000	1000	30	1125	20	14.8	15.0	16.4	40.4
26	0000	1000	30	1125	20	14.8	15.0	16.4	40.6
27	0000	1000	30	1125	20	14.8	15.0	16.4	40.5

Figures 5 and 6 show the macro-morphology and side optical photos of the sintered green body under the same debinding and sintering process conditions. From Figure 5, it is evident that some of the sintered bodies exhibit cracking or surface delamination. Under the same conditions for other processes, changes in the printing process are the primary cause of these defects.

Figure 5.

Physical picture of sintered body. The measured inner diameter is taken as the diameter after the inner circle has contracted.

Figure 6.

Table 2.1 side morphology of the green body under the printing process.

To avoid repetitive descriptions, the effects of printing parameters on surface quality and inter-layer integrity are summarised as follows. The effective energy input per layer, governed primarily by laser power and scan speed, controls curing depth and degree of conversion: insufficient energy causes under-curing, weak inter-layer fusion, and higher porosity, whereas excessive energy may lead to over-curing, heat accumulation, and thermal-stress-induced cracking. Coating thickness modulates the required penetration depth and the likelihood of inter-layer voids; thicker coatings improve productivity but increase the risk of incomplete curing across the layer thickness and more pronounced layer textures. Scraper speed affects slurry spreading uniformity and boundary filling; overly low speed may lead to thickness non-uniformity due to prolonged flow/self-levelling, while overly high speed may cause incomplete coverage and local under-filling. These combined effects explain the observed cracking/delamination differences among samples in Figures 5 and 6 (see Table 3).

Table 3.

Sample dimensions used for shrinkage measurements.

Direction	Length (mm)	Width (mm)	Inner diameter (mm)	Height (mm)
Dimensions	15	15	2.75	2

Firstly, coating thickness (H) significantly influences the inter-layer structure and pore distribution after deposition. Thicker layers tend to introduce inter-layer voids and density gradients, which, in turn, amplify during the subsequent debinding and sintering processes. Areas with higher porosity or lower density experience different densification rates and sintering shrinkage forces, leading to stronger directional dependence (anisotropy) in the overall shrinkage. Therefore, the dominance of coating thickness in controlling volumetric and linear shrinkage stems not only from simple changes in cured volume fraction but also from its control over the spatial distribution of green body porosity and density, thereby affecting the formation of sintering necks and pore closure pathways.

Secondly, scraper speed (V) influences the rheological response of the slurry and its shear history, thereby affecting the spread quality and boundary filling. In shear-thinning systems, higher scraper speeds increase the shear rate, lowering the apparent viscosity and altering the flow/rebound behaviour of the slurry, which affects the uniformity of the coating and the ability of the slurry to fill the boundaries. When boundary filling is insufficient or radial density differences are generated, sintering densification occurs preferentially in the regions with higher porosity, leading to more significant shrinkage in the inner-diameter direction. This explains the direct physical relationship between scraper speed and diameter/radial shrinkage (flow–filling–radial density gradient–radial shrinkage).

Finally, the significance of quadratic terms in the regression model suggests the existence of non-linear thresholds or windows in the process, indicating that neither ‘larger is always better’ nor ‘smaller is always better’. For example, overly thin coatings may result in discontinuous layers, interfacial defects, or local under-filling, while excessively thick coatings can introduce stronger inter-layer porosity and density non-uniformities, and increase stress concentration during debinding and sintering, both of which worsen densification consistency and strengthen shrinkage anisotropy. Similarly, too low scraper speeds may cause inadequate spreading and insufficient boundary filling, while excessively high speeds can lead to flow instability, shear-induced migration of components, or boundary accumulation discrepancies, resulting in a ‘mid-range optimal’ non-linear response. Thus, the significance of quadratic terms reflects the physical thresholds and non-linear behaviour in the coupling process of layer structure and thermal densification.

Based on the above experimental results, it is clear that optimising the best printing process is crucial for obtaining high-quality products. Using the experimental parameters and result data, a second-order polynomial modelling module in JMP was applied, and the coefficients of the second-order polynomial equation were calculated using the least squares method. In the JMP modelling module, a stepwise regression method was used to determine whether the independent variables should be included in the regression equation based on the degree of their influence on the dependent variable. Independent variables that did not significantly affect the dependent variable were excluded from the regression equation, while those already included were removed if their influence on the dependent variable was reduced upon introducing new variables.

Using the stepwise regression method, a multivariate regression equation for the linear shrinkage and volumetric shrinkage of the sintered body was established based on the four main variables (laser power, laser scan speed, scraper movement speed, and coating thickness) and their interactions. To improve the readability and interpretability of the regression models, the fitted second-order polynomial equations are presented by separating the linear terms, interaction terms, and quadratic terms. In addition, the coefficients of all retained terms are summarised in Table 4

\begin{aligned} S R_{Length} = 1.695 + (- 0.001 V_{L} + 0.226 V - 0.001 P_{L} - 0.148 H) \\ + [0.001 (H - 20) (V_{L} - 1000) + 0.011 (H - 20) \\ (V - 30)] + [0.921 (V - 3)^{2} + 0.157 (H - 20)^{2}] \end{aligned}

\begin{aligned} S R_{Width} = 14 . 984 + (- 0.001 V_{L} + 0.533 V + 0.003 P_{L} - 0.164 H) \\ + [0.003 (P_{L} - 1125) (V - 30) - 0.04 (H - 20) \\ (V - 30)] + [0.729 {(V - 30)}^{2} + 0.144 {(H - 20)}^{2}] \end{aligned}

\begin{aligned} S R_{Diameter} = 1 . 421 + (0.001 V_{L} - 0.402 V - 0.002 P_{L} - 0.287 H) \\ + [- 6 (P_{L} - 1125) (V_{L} - 1000) + 0.004 (P_{L} - 1125) \\ (V - 30)] + [- 6 {(V_{L} - 1000)}^{2} - 0.489 {(V - 30)}^{2} \\ + 0.001 (P_{L} - 1125)^{2}] \end{aligned}

\begin{aligned} S R_{Volume} = 35.026 + (- 0.001 V_{L} + 0.647 V + 0.002 P_{L} + 0.293 H) \\ + [- 5 (H - 20) (V_{L} - 1000) + 0.001 (H - 20) \\ (V_{L} - 1125)] + [- 6 {(V_{L} - 1000)}^{2} + 0.001 (V_{P} - 1125)^{2} \\ + 0.233 {(H - 20)}^{2}] \end{aligned}

Table 4.

Definitions of the symbols used in the regression equations.

Symbol	Definition	Unit
H	Coating thickness	mm
V	Scraper speed	mm s⁻¹
P_L	Laser power	mW
V_L	Laser scan speed	mm s⁻¹

In the present study, the regression terms are classified into three categories: main (linear) terms, interaction terms, and quadratic terms. The main terms represent the individual effects of single-process variables, the interaction terms represent the coupled effects between two different variables, and the quadratic terms represent the non-linear effects of the same variable. Therefore, terms such as V², H², or (P_L − 1125)² are treated as quadratic terms rather than interaction effects.

The linear, interaction, and quadratic terms correspond to the individual, coupled, and non-linear effects of the processing variables, respectively (Table 5).

Table 5.

Summary of the main, interaction, and quadratic effects retained in the regression models.

Shrinkage direction	Influential term	LogWorth	P value	Effect type
Length	H	12.728	0.001	Dominant
	V	7.368	0.001	Dominant
	V × H	2.699	0.002	Significant
Width	P_L	3.654	0.001	Dominant
	P_L × H	5.373	0.001	Dominant
	P_L × V	2.439	0.004	Significant
Diameter	V × V	8.631	0.001	Dominant
	V × P_L	4.481	0.001	Dominant
	V_L × P_L	2.39	0.004	Significant
Volume	H × H	19.59	0.001	Dominant
	P_L × P_L	3.841	0.001	Dominant
	V_L × V_L	3.076	0.001	Dominant
	V_L × H	2.174	0.007	Significant
	V_L	1.106	0.078	Significant

For consistency, the same notation is used throughout the manuscript: V_L denotes laser scanning speed, V denotes scraper movement speed, P_L denotes laser power, and H denotes coating thickness. These symbols are used consistently in the text, tables, figures, and regression equations.

LogWorth is reported by JMP and is defined as −log 10(P-value); a larger LogWorth indicates greater statistical significance.

The P-value is a statistical indicator used to measure the likelihood that a result is caused by random factors. The smaller the P-value, the more reliable the result. A P-value of 0.001 indicates that the model fitting is highly significant, meaning the relationship between the factors and the shrinkage rate is trustworthy. The established prediction model has statistical significance and engineering reliability.

From the regression equation for the shrinkage rate, it is clear that the linear shrinkage in the length direction is mainly controlled by coating thickness and scraper movement speed. As the coating thickness increases, it weakens the inter-layer bonding strength, leading to an increase in longitudinal shrinkage. If the scraper speed is too high, it can cause uneven slurry spreading, leading to fluctuations in the dimensions in the length direction. Overall, the dominant factor for length direction shrinkage rate is the main effect term, with coating thickness being the key parameter, followed by scraper speed, with weaker interaction effects. The shrinkage rate in the width direction is mainly controlled by laser power and the interaction between laser power and coating thickness. Laser power determines the curing depth and energy distribution, while coating thickness adjusts the penetration of light energy and curing volume, with a significant coupling effect between the two. Width precision depends on the synergistic optimisation of coating thickness and exposure energy. The shrinkage rate in the inner-diameter direction is primarily influenced by the quadratic term of scraper speed and the interaction term between laser power and scraper speed. Scraper speed affects slurry backflow and wall filling, while laser power affects the curing depth. The coupling of these two factors leads to non-linear changes in the internal diameter, exhibiting a ‘single-factor dominance with significant quadratic effects’ coupling feature. Volumetric shrinkage is mainly governed by quadratic terms, particularly those associated with coating thickness, laser power, and laser scanning speed. Coating thickness strongly influences volumetric shrinkage through changes in the cured volume fraction and densification stress distribution, and it has a significant non-linear amplification effect. It is one of the main variables affecting the overall dimensional stability of the component. Laser power and scan speed need to be matched with the coating thickness.

In summary, coating thickness is the primary controlling parameter for the shrinkage rate in all directions. Other parameters need to be matched with it in order to achieve high-quality sintered bodies.

As shown in Table 6, the R² values of the four fitted regression equations are all higher than 0.95, and the corresponding probabilities P > F are all lower than 0.001, indicating that the fitted equations are statistically acceptable. In addition to these goodness-of-fit indicators, the robustness of the models was also considered from the perspectives of predictor redundancy and residual behaviour. Since the regression equations were established using the stepwise regression procedure in JMP, only statistically significant terms were retained in the final models, which helped reduce unnecessary redundancy among predictors and improved the stability of the fitted equations. Figure 7 presents the studentised residual plots of the four regression models. The residuals are generally distributed randomly around zero without obvious systematic trends, and no severe abnormal residuals are observed. These results indicate that the regression models are statistically reasonable and reliable within the investigated process parameter range.

Figure 7.

The studentised residual analysis.

Table 6.

Model analysis summary.

Model	Degrees of freedom	Observations	Mean response	Sum of squares	Mean square	R ²	Adjusted R²	F ratio	Probability P > F	Acceptability of model
Length shrinkage rate	14	27	16.426	48.208	3.443	0.9678	0.9302	25.758	<0.001	Yes
Width shrinkage rate	14	27	16.548	42.497	3.035	0.9849	0.9673	55.968	<0.001	Yes
Diameter shrinkage rate	14	27	17.922	131.561	9.397	0.9437	0.9601	14.372	<0.001	Yes
Volume shrinkage rate	14	27	42.969	115.980	8.284	0.9708	0.9634	28.510	<0.001	Yes

In addition to the high R² and adjusted R² values, the robustness of the fitted models was further considered from the perspectives of variable redundancy and residual behaviour. Because the regression equations were established using the stepwise regression procedure in JMP, only the statistically relevant terms were retained in the final models, which helped reduce unnecessary redundancy among predictors and improve model stability. Therefore, no obvious multi-collinearity problem was observed within the retained terms under the investigated experimental design (Table 7).

Table 7.

Analysis of variance table.

		Degree of freedom	Sum of squares	Mean square
Length shrinkage rate	Model	14	48.2077	3.4434
	Error	12	1.6042	0.1337
	Correction of the total sum	26	49.8119
Width shrinkage rate	Model	14	42.4966	3.0355
	Error	12	0.6508	0.0542
	Correction of the total sum	26	43.1474
Diameter shrinkage rate	Model	14	108.5766	7.7555
	Error	12	2.0375	0.1698
	Correction of the total sum	26	110.6141
Volume shrinkage rate	Model	14	113.2385	8.0885
	Error	12	1.9455	0.1621
	Correction of the total sum	26	115.1839

Figure 8 displays the predicted response curves under different printing parameters. This graph shows how the predicted response values change when one factor varies while the other factors remain fixed. It helps visualise the relationship between each X (input factor) and Y (response), whether it is positively correlated, negatively correlated, or non-linear. When multiple responses need to be optimised simultaneously, the ‘willingness function’ can be applied to find a set of X values that achieve relatively ideal states for all Y. This addresses the multi-response optimisation problem, where improving one response can often worsen another. Based on the above analysis, when the willingness function is minimised, the optimal printing parameters are as follows: laser power = 1125 mW, laser scan speed = 1000 mm s⁻¹, scraper movement speed = 3 cm s⁻¹, single-layer coating thickness = 0.2 mm (Figure 9).

Figure 8.

The comparison between the predicted and experimental values for the 27 experimental sets is shown as follows: (a) and (e) Actual vs. predicted values for the length shrinkage rate; (b) and (f) actual vs. predicted values for the width shrinkage rate; (c) and (g) actual vs. predicted values for the diameter shrinkage rate; (d) and (h) actual vs. predicted values for the volume shrinkage rate.

Figure 9.

Prediction characterisation curve.

Experimental verification of optimised process parameters

The regression mathematical model indicates that the shrinkage rate is influenced by both the main effects (linear terms) and interaction effects (cross terms and quadratic terms). By substituting different factor levels into the model, the corresponding shrinkage rates can be predicted. To validate the rationality of the regression model, the interactions between laser power, laser scan speed, scraper movement speed, and layer thickness were designed as per Figure 10, followed by experimental validation of the model's accuracy. The experimental results for nine sets of process parameters and the corresponding measured and predicted shrinkage rates are shown in Table 8. A comparison between the actual measured results and the predicted values from the model is presented in Figure 10. The results demonstrate that the actual and predicted values for both linear shrinkage and volumetric shrinkage exhibit consistent trends, with the model error being less than 5%, further confirming the accuracy of the mathematical regression equation.

Figure 10.

Comparison of predicted and experimental values in the verification experiments. (a) and (e) Actual vs. predicted values for the length shrinkage rate; (b) and (f) actual vs. predicted values for the width shrinkage rate; (c) and (g) actual vs. predicted values for the inner-diameter shrinkage rate; (d) and (h) actual vs. predicted values for the volumetric shrinkage rate.

Table 8.

Verification experiment printing process parameters and measured vs. predicted shrinkage rates.

	Laser power (mW)	Laser scanning speed (mm s⁻¹)	Blade movement speed (mm s⁻¹)	Layer thickness (mm × 10⁻²)	Actual shrinkage rate (%)				Predicted shrinkage rate (%)
	Laser power (mW)	Laser scanning speed (mm s⁻¹)	Blade movement speed (mm s⁻¹)	Layer thickness (mm × 10⁻²)	Length	Width	Diameter	Volume	Length	Width	Diameter	Volume
1	1050	1000	20	16	18.2	18.4	19.9	44.1	19.0	18.7	21.1	44.0
2	1125	1200	20	20	16.4	15.2	17.5	42.0	15.6	15.6	16.9	41.5
3	1200	1000	30	20	14.5	15.6	17.2	41.0	14.8	15.5	16.5	40.8
4	1125	1000	40	24	18.5	18.1	18.6	46.0	17.8	17.8	17.9	46.5
5	1050	1200	30	24	17.4	17.1	21.0	43.7	16.9	16.6	20.4	44.1
6	1200	1200	40	16	18.3	20.0	18.8	41.0	19.4	19.5	20.4	40.5
7	1125	800	30	16	17.8	17.5	20.8	42.4	18.5	18.1	21.2	42.8
8	1050	800	40	20	17.1	15.8	14.8	41.5	16.5	16.3	15.5	41.1
9	1200	800	20	24	16.9	18.7	16.6	44.0	17.2	18.2	17.3	44.6

Using the optimised printing process, with a laser power of 1125 mW, laser scan speed of 1000 mm s⁻¹, scraper movement speed of 3 cm s⁻¹, and single-layer coating thickness of 0.2 mm, along with a sintering process at 1600 °C and a heating rate of 0.5 °C min⁻¹, verification experimental samples were prepared, as shown in Figure 11. The samples exhibited a maximum bending strength of 533.95 MPa, a 15% improvement over the optimised value before. The fracture toughness was 7.62 MPa m^1/2, showing a 7% increase from the optimised value before. The SEM images of the fracture surface of the alumina ceramic-sintered body indicated a mixed fracture mode, consisting of both trans-granular and inter-granular fractures, exhibiting a correlation between shrinkage optimisation, microstructural uniformity, and strength. The regression-based shrinkage optimisation not only reduces dimensional deviation but also improves the uniformity of the green body and subsequent densification. As shown by the macro-images, several non-optimised conditions exhibit cracking or surface delamination, indicating non-uniform inter-layer bonding and local defect accumulation during printing, which can amplify shrinkage anisotropy during sintering. Under the optimised parameter set (P_L = 1125 mW, V_L = 1000 mm s⁻¹, V = 3 cm s⁻¹, H = 0.2 mm), a better energy–thickness match and more uniform slurry spreading/boundary filling are expected to reduce inter-layer pores and density gradients, leading to a more homogeneous densification path. This is consistent with the improved mechanical performance obtained in the verification samples (maximum flexural strength of 533.95 MPa; fracture toughness of 7.62 MPa m^1/2). Moreover, the fracture-surface SEM shows mixed trans-granular/inter-granular fracture features, which are typically associated with improved grain-boundary cohesion and reduced critical flaw populations after densification. Therefore, the optimised shrinkage behaviour is physically consistent with enhanced microstructural uniformity and strength (Figure 12).

Figure 11.

Real images of the sintered bodies printed under the process conditions of the 9 verification experiments.

Figure 12.

(a) and (b) Macro-morphology of the printed green body. (c) Bending strength of the sintered body under the printing process from Table 4. (d) Printing process of the green body. (e) Microstructure of the fracture surface after three-point bending of alumina ceramics at a sintering temperature of 1600 °C and a heating rate of 0.5 °C min⁻¹.

Conclusions

In this work, the novelty lies in integrating a JMP-based response surface design with multivariate regression modelling and experimental verification to quantitatively predict anisotropic and volumetric shrinkage in VPP-printed alumina-based ceramics. Specifically, (i) a four-factor JMP-RSM design was established to capture main, interaction, and quadratic effects; (ii) multi-response regression models were developed for length, width, inner-diameter, and volumetric shrinkage, allowing the relative contributions of linear, interaction, and quadratic terms to be distinguished for different shrinkage modes; and (iii) the optimised parameter set was validated by independent experiments, demonstrating predictive errors below 5% and enabling the identification of a practical processing window for low-shrinkage, crack-free components.

The fitted regression models showed that the contributions of the retained terms differed among the four shrinkage responses. Length-direction shrinkage was mainly associated with the linear terms of layer thickness and scraper movement speed, while the interaction between these two variables also contributed. Width-direction shrinkage was primarily influenced by the linear term of laser power and the interaction between laser power and layer thickness. Inner-diameter shrinkage exhibited a pronounced non-linear dependence, mainly reflected by the quadratic term of scraper speed and the interaction between laser power and scraper speed. Volumetric shrinkage was mainly governed by quadratic terms, especially those related to layer thickness, laser power, and laser scanning speed, indicating that non-linear effects play an important role in the overall dimensional stability of the sintered body.

Verification experiments confirmed that the predicted results from the regression model were consistent with the experimental results. Under the optimal printing parameters of a laser power of 1125 mW, laser scan speed of 1000 mm s⁻¹, scraper movement speed of 3 mm s⁻¹, single-layer coating thickness of 0.2 mm, and a sintering process at 1600 °C with a heating rate of 0.5 °C min⁻¹, the bending strength of the sintered body increased by 15%, reaching 533.95 MPa compared to the pre-optimised value.

Footnotes

ORCID iDs

Shuangyu Liu

Fulong Zhang

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Yancheng Science and Technology Bureau, Yancheng Institute of Technology, Young Medical Key Talents Foundation of Jiangsu Province (grant numbers Ycgh003, XJR2023003, and JSSCRC2021545).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Meng

Zhang

, et al. Warping regulation and physical properties of SLA 3D printed mullite ceramics via plasticizers. Mater Chem Phys 2025; 344: 131135.

Hussain

Xia

Ren

, et al. Recent advances in photopolymerization 3D printing of alumina-ceramic. Prog Nat Sci Mater Int 2025; 35: 1–30.

Hussain

Xia

Ren

, et al. Microstructural evolution, enhanced mechanical properties, and complex shapes design in high solid content alumina ceramics through additive manufacturing. J Manuf Process 2024; 129: 35–50.

Bahnini

Rivette

Rechia

, et al. Additive manufacturing technology: the status, applications, and prospects. Int J Adv Manuf Technol 2018; 97: 147–161.

Aktas

Das

Aktas

, et al. Additive manufacturing of TiO₂-doped 3Y-ZrO₂ ceramics via DLP-3D printing for dental implant applications: enhanced mechanical strength, biocompatibility, and antibacterial performance. J Alloys Compd 2025; 1037: 182246

Aktas

Das

Acıkgoz

, et al. Fabrication of CaSiO₃-doped 3Y-ZrO₂ ceramics via DLP 3D printing: structural, mechanical, and biological evaluation. J Alloys Compd 2025; 1036: 181895.

Aktas

Das

Aktas

, et al. Impact of calcium silicate and titanium dioxide co-doping on the microstructure and bioactivity of 3D-printed 3Y-ZrO₂ ceramics. Ceram Int 2025; 51: 60666–60682.

Das

Aktas

, et al. DLP 3D-printed hydroxyapatite-bioglass composite scaffolds for bone tissue engineering: structural, mechanical, biological, and antibacterial evaluations. Mater Today Chem 2025; 48: 102925.

Aktas

Das

Acikgoz

, et al. DLP 3D Printing of TiO₂-doped Al₂O₃ bioceramics: manufacturing, mechanical properties, and biological evaluation. Mater Today Commun 2024; 38: 107872.

10.

Liu

, et al. Effect of debinding temperature under an argon atmosphere on the microstructure and properties of 3D-printed alumina ceramics. Mater Charact 2020; 168: 110548.

11.

Hussain

Xia

Ren

X-N

, et al. High-precision printing of intricately shaped kaolin ceramics by digital light processing: impact of solid content on microstructure and densification. J Mater Res Technol 2024; 30: 2299–2310.

12.

Zhang

, et al. A review of 3D printed porous ceramics. J Eur Ceram Soc 2022; 42: 3351–3373.

13.

Hsiang

H-I

Lee

C-Y

Chen

C-C

, et al. Polycrystalline alumina ceramic fabrication using digital stereolithographic light process. Ceram Int 2021; 47: 33815–33826.

14.

Elsayed

Colombo

. Effect of particle size distribution and printing parameters on alumina ceramics prepared by additive manufacturing. Ceram Int 2024; 50: 6340–6348.

15.

Chen

, et al. Effect of synergism of solid loading and sintering temperature on microstructural evolution and mechanical properties of 60 vol% high solid loading ceramic core obtained through stereolithography 3D printing. J Eur Ceram Soc 2023; 43: 661–675.

16.

Carloni

Zhang

. Transparent alumina ceramics fabricated by 3D printing and vacuum sintering. J Eur Ceram Soc 2021; 41: 781–791.

17.

Ping

Huang

Meng

. Prediction model and compensation method for curing shrinkage of inkjet 3D printing parts. J Manuf Process 2023; 101: 807–819.

18.

Qiu

Hou

, et al. Slurry flow characteristics control of 3D printed ceramic core layered structure: experiment and simulation. J Mater Sci Technol 2023; 164: 215–228.

19.

Zhao

J-J

Zhang

Y-Z

J-H

, et al. Additive manufacturing of alumina-based ceramic structures by vat photopolymerization: a review of strategies for improving shaping accuracy and properties. Materials (Basel) 2025; 18: 2445.

20.

Huo

Tian

Nan

, et al. Hierarchically porous alumina ceramic catalyst carrier prepared by powder bed fusion. J Eur Ceram Soc 2020; 40: 4253–4264.

21.

Liu

, et al. Influence of debinding holding time on mechanical properties of 3D-printed alumina ceramic cores. Ceram Int 2021; 47: 4884–4894.

22.

Abdelmoula

Küçüktürk

. Multi-layer simulation of the powder bed selective laser processing of alumina for residual stress and distortion evaluation. Materials (Basel) 2022; 15: 3498.

23.

Abdelmoula

Küçüktürk

Juste

, et al. Enhancing powder bed fusion of alumina ceramic material: a comprehensive study from powder tailoring to mechanical performance evaluation. Int J Adv Manuf Technol 2024; 131: 1745–1767.

24.

Zhang

Duan

, et al. Degreasing process of thick-walled alumina ceramics based on vat photopolymerization. Ceram Int 2024; 50: 847–856.

25.

Zhang

Xiao

Duan

, et al. Effects of printing paths and recycled fines on drying shrinkage of 3D printed mortar. Constr Build Mater 2022; 342: 128007.

26.

Young

Brinckmann

Iii

, et al. Influence of layer thickness and exposure on mechanical properties of additively manufactured polymer-derived SiOC ceramics. Open Ceram 2024; 19: 100652.

27.

Zhang

Weng

Hamel

, et al. Design for the reduction of volume shrinkage-induced distortion in digital light processing 3D printing. Extreme Mech Lett 2021; 48: 101403.

28.

Fuzhao

Xie

Zhu

. Hydrogel-based DLP 3D printing of dense zirconia ceramics. J Eur Ceram Soc 2025; 45: 117067.

29.

Wang

, et al. Predicting dimensional deviation for sintering-induced shrinkage of Al₂O₃ ceramics manufactured by vat photopolymerization: using convolutional neural network. Mater Today Commun 2023; 37: 107309.

30.

Spirrett

Ito

Kirihara

. High-speed alumina stereolithography. Appl Sci 2022; 12: 9760.

31.

Goulas

Ozkan

Ketharam

, et al. Enabling accessible additive manufacturing of alumina ceramics through formulation design. Mater Des 2025; 258: 114601.

32.

Zhang

Huang

, et al. Fabrication and properties of alumina ceramics shaped by digital light processing as an additive manufacturing technology. Int J Appl Ceram Technol 2021; 19: 281–288.

33.

Manotham

Channasanon

Nanthananon

, et al. Photosensitive binder jetting technique for the fabrication of alumina ceramic. J Manuf Process 2021; 62: 313–322.

34.

Shuangyu

Hongtao

Ping

, et al. Influence of the MgO content on zirconia-toughened alumina ceramic slurry properties and sintered body microstructure. Int J Appl Ceram Technol 2025; 22: e15034.

35.

Wang

, et al. Additive manufacturing and joining double processes of ceramic-resin green bodies using a single- or double-phase photocuring slurry. Ceram Int 2024; 50: 14088–14100.

36.

Liu

Huo

, et al. Microstructure and mechanical properties of 3D-printed nano-silica reinforced alumina cores. Ceram Int 2022; 48: 30282–30293.

37.

Zaiemyekeh

Romanyk

, et al. Strain-rate-dependent behavior of additively manufactured alumina ceramics: characterization and mechanical testing. J Mater Res Technol 2024; 28: 3794–3804.

Multivariate non-linear regression models for the relationship between the vat photopolymerization 3D printing process of alumina ceramics and the shrinkage rate of sintered bodies

Abstract

Keywords

Introduction

Materials and methods

Materials

VPP 3D printing process of Al2O3 slurries

Treatment and debinding process of green bodies

Characterisation of Al2O3 ceramics

Results and discussion

Design of debinding and sintering process

Effect of sintering temperature and heating rate on bending strength

Establishment of multivariate non-linear regression model

Experimental verification of optimised process parameters

Conclusions

Footnotes

ORCID iDs

Funding

Declaration of conflicting interests

References

VPP 3D printing process of Al₂O₃ slurries

Characterisation of Al₂O₃ ceramics