Influence of local factors on composite shrinkage stress development--a finite element analysis

Using finite element analysis (FEA), to determine the nominal shrinkage stress of a composite under different restriction conditions defined by the longitudinal compliance (LC) and C-factor (C) of the testing system, and by the elastic modulus of the bonding substrate (E).

Eight axisymmetric models representing an experimental setup used to determine composite shrinkage stress were simulated. Composite thicknesses of 0.5 mm and 4 mm were tested, defining different C and volumes (C = 6 and vol = 14 mm3 or C = 0.8 and vol = 113 mm3, respectively). The E of the substrate was tested in two levels, 12 GPa and 207 GPa. Two LC values (1 x 10(-6) or 28 x 10(-6) mm/N) were defined for each E value by varying the length of the rods used as bonding substrate (0.3 mm and 9.5 mm for E = 12 GPa; 6.0 mm and 163.9 mm for E = 207 GPa). Materials were considered elastic, homogeneous, and isotropic. Shrinkage was simulated by thermal analogy. Nominal stress (nodal force/cross-sectional area) was calculated for each condition. Results were analyzed using Taguchi's method.

Nominal stress values varied between 1.7 MPa and 30.3 MPa. The main variables were statistically significant (LC: p = 0.0046; C: p = 0.0153; E: p = 0.0155), as well as the LC x E interaction (p = 0.0354). Stress reduction between low and high LC was more pronounced for E = 207 GPa compared to E = 12 GPa. Stress was lower for the high C conditions for both compliance levels.

Not only the C-factor of the testing assembly, but also its LC and the E of the bonding substrate influence stresses generated by composite shrinkage.