Fracture and energetic strength scaling of soft, brittle, and weakly nonlinear elastomers

An investigation is presented into the fracture and energetic strength scaling of soft and brittle polydimethylsiloxane (PDMS)-based elastomers. Mode I tensile fracture tests on pre-cracked specimens of various sizes are carried out with two PDMS elastomers significantly varying in their stiffness, strength, and toughness. The results are interpreted within the existing framework of the energetic type II Bazant size effect law (SEL). The SEL is found to be applicable to the PDMS elastomers despite their nonlinear stress-strain behavior. This is because the nonlinearity is rather weak, making the strain energy approximately proportional to the square of the nominal stress, similar to linear elastic materials. It is found that at the lab scale, the structural strength of both elastomers scales in a self-similar fashion with specimen size and falls on the large size asymptote of the SEL. Then, the strengths of much smaller specimens are numerically predicted using the cohesive crack model. For both elastomers, these strengths are found to fall squarely on the transitional part of the SEL, implying incomplete self-similarity and a transition to quasi-brittle fracturing. This is due to the increased dominance of the fracture process zone whose size is estimated by various methods. It is shown that if this transition is not accounted for, the structural strength can be over-predicted by 140% or even more for smaller sizes. Thus, for the first time, it is shown that soft elastomers, if weakly nonlinear, exhibit conformance to the energetic type II strength scaling laws.