A polarization modulator unit for a low-frequency telescope in LiteBIRD employs an achromatic half-wave plate (AHWP). It consists of five-layer a-cut sapphire plates, which are stacked based on a Pancharatnam recipe. In this way, the retardance of the AHWP is a half-wave over the bandwidth of 34-161 GHz. The diameter of a single sapphire plate is about 500mm and the thickness is about 5 mm. When a large diameter AHWP is used for a space mission, it is important for the AHWP to survive launch vibration. A preliminary study indicates that the five-layer-stacked HWP has a risk of breakage at the launch unless the 5 layers are glued together and mechanically treated as one disk. In this paper, we report our investigation using a sodium silicate solution which can bond between sapphire plates. This technique has been previously investigated as a candidate cryogenic glue for a mirror material, including sapphire, of the gravitational wave detector, LIGO and KAGRA. We experimentally studied the mechanical strength of the bonded interface for two different surface conditions, polished and unpolished. We demonstrated the tensile and shear strength of above 20MPa for samples with a polished surface, respectively. We also identified that samples glued on a polished surface show higher strength than unpolished ones by a factor of 2 for tensile and 18 for shear strength. We searched for any optical effects, e.g. extra gap or absorption by the bonding interface, by measuring the millimeter-wave transmission spectra in 90-140 GHz. We did not find any optical effect caused by the bonded interface within 2% error in transmittance that is originated from the measurement system.