Toughness arising from inherent strength of polymers. (October 2022) - Smith, Travis; Gupta, Chaitanya; Fan, Zehao; Brust, Gregory J.; Vogelsong, Russ; Carr, Caleb; Wang, Shi-Qing
Abstract: This study carries out spatial-resolved optical birefringence observations to quantify, for mode I (tensile opening) loading, the stress intensification at crack tip of brittle and ductile glassy polymers (polymethyl methacrylate—PMMA, polyethylene terephthalate—PET) as well as one type of elastomer: (ethylene propylene diene monomer—EPDM). We measure the stress buildup in a precut specimen by correlating retardation with the corresponding tensile stress. Given the adequate spatial resolution under 10 μ m and natural bluntness of intentional through-cuts, we are able to show that (a) during drawing at different stages up to the onset of fracture in precut PMMA and EPDM, the local stress saturates, namely, ceases to increase as r − 1/2 upon approaching the cut tip (with r reaching r ss in a range of 0.05–0.15 mm), (b) tip stress σ tip, i.e., the tensile stress in the stress saturation zone ( r ≤ r ss ), linearly grows with (operationally defined) stress intensity factor K I until fracture, reaching a level below the breaking stress σ b observed of uncut specimen. Thus, the inherent strength σ F(inh) under plane strain, taken to be the tip stress at fracture is only comparable to σ b . Moreover, a characteristic length P, involved in the observed linearity between K I and σ tip, i.e., in K I = σ tip P 1/2, is found to be comparable to 2 π r ss . Here r ss appears to depend on the tip sharpness, which may be characterized by a radius of curvature ρ tip . Thus, toughness given by the critical stress intensity factor K Ic is determined by the product of σ F(inh) and ρ tip 1/2, and the critical energy release rate G Ic is given by the product of specific work of fracture w F = [ σ F(inh) ] 2 / 2 E and ρ tip .