The polarization modulator unit for the low-frequency telescope in LiteBIRD employs an achromatic half-wave plate (AHWP). It consists of five layers of a-cut sapphire plate, which are stacked based on a Pancharatnam recipe. In this way, the retardance of the AHWP is a half-wave over a bandwidth of 34 to 161 GHz. The diameter of a single sapphire plate is about 500 mm and the thickness is 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 five layers are glued together and mechanically treated as one disk. We report our investigation using a sodium silicate solution that can bond the sapphire plates. This technique has been previously investigated as a candidate of cryogenic bonding for a mirror material, including sapphire, of the gravitational wave experiments: LIGO, VIRGO, and KAGRA. We experimentally studied the mechanical strength of the bonded interface for two different surface conditions: polished and unpolished. We demonstrated that the tensile and shear strength >20  MPa for samples with a polished surface. This satisfied the requirement of 5.5 MPa derived from the mechanical simulation assuming a launch load of 30 G. We identified that samples glued on a polished surface exhibit higher strength than unpolished ones by a factor of 2 for tensile and 18 for shear strength. We measured the millimeter-wave transmittance between 90 and 140 GHz using sapphire plates with a diameter of 50 mm before and after bonding. We did not find any optical effects caused by the bonded interface within 2% error in transmittance, which originates from the measurement system.