Mechanical Manifestation of the C-factor

Objectives: In measuring shrinkage stress of resin composites, the specimen constraints transition from those of triaxial at the boundaries to those of near uniaxial at mid-length. A recent theory^[1] shows that magnitude of the shrinkage stress depends on the thickness of the boundary layer under triaxial constraints, which is assumed to be proportional to the disc diameter. This study aims to assess the validity of this theory by measuring the boundary-layer thickness.
Methods: Cylindrical specimens of three resin composites (Filtek^TM One, Z100 and Z250; 3M ESPE), two diameters (4 and 6 mm) and four lengths (2, 3, 5 and 6.5 mm) were bonded to rigid holders fixed at the two ends. Curing was applied from one side of the curved surface using a LED light (Elipar^TM, 3M ESPE) operated at 800 mW/cm² for 40 s. Images (x32) of the specimens before and after curing were obtained with a microscope (MVX10, Olympus) and analyzed using ImageJ (https://imagej.nih.gov/ij) to determine the longitudinal shrinkage profile (Fig. 1a). Boundary layer thickness was determined from the point where shrinkage displacement first reached the value at mid-section.
Results: Shrinkage displacement at mid-section was close to the theoretical value based on published shrinkage-strain data for all the specimens, the ratio between experimental and theoretical values being 1.10±0.09. The boundary-layer thickness was found to be proportional to the specimen diameter only (Fig. 1b), independent of material and specimen length. The proportionality constant was 0.16±0.02, which was approximately 2.8 times that of the effective value indicated by theory.
Conclusions: The boundary-layer thickness of disc specimens used for shrinkage-stress measurement was found to depend on their diameter only. This validates the shrinkage-stress theory recently proposed, even though the effective boundary-layer thickness needed for shrinkage-stress calculation is much smaller than that of the whole boundary layer.