Toughness arising from inherent strength of polymers

Fracture Behavior of Polymers in Plastic and Elastomeric States

“…The recent str-POM measurements show 48,49 that (a) stress saturation occurs upon approach to crack tip, as depicted in Figure 2b and (b) σ tip(F) = σ F(inh) is comparable to nominal strength σ b , thus supporting the speculation that plastics are flaw tolerant, contrary to the prevailing viewpoint (Kinloch, 2013).. Ductile plastics are characterized by Young's modulus E, yield stress σ y , and work (density) of fracture w f , i.e., the area under the (engineering) stress vs strain (nominal draw ratio λ = L/L 0 ) curve, equal to w f = ∫ 1 λ f σ engr dλ, which is sometimes termed "toughness" in the non-fracture-mechanics community. There cannot be any confusion between this w f having the dimension of specific energy and toughness G c or K c that also involves a length scale.…”

“…In other words, G c is dictated by the physics at the crack tip. Equation 5 was first derived from str-POM observations, 48 which disclosed the two hidden variables, i.e., material's strength σ F(inh) and a characteristic length that involves the geometric characteristic of the crack tip. The str-POM measurements reveal a zone of finite size where birefringence saturates, implying the cut tip is not infinitely sharp for polymers.…”

“…In other words, σ b ≪ σ tip(F) only if P ≪ a*. In short, through a critical evaluation of past treatments of polymer fracture, recent studies 48,49 have identified and met the pressing needs (a) to estimate inherent strength by experiment, (b) to examine a specific fracture mechanism, (c) to explain why Griffith's fracture criterion (G → G c ) holds true for brittle polymers, i.e., why G c appears to be a material property so that eq 1 holds, and (d) to explore a new understanding of what it means for G c to depend on temperature for rubber. In summary, in the presence of flaws or cracks, fracture behavior indeed requires the concept of toughness K c or G c = (K c ) 2 /E to describe, involving a combination of stress and length.…”

“…For brittle glassy polymers and dry rubbers that are largely linear elastic, LEFM has played a key role in describing fracture behavior of such polymers . We will first review LEFM in Section before extending upon it in Section according to the emergent developments , on the subject.…”

“…On the other hand, linear elastic fracture mechanics (LEFM) rarely employs the concept of σ F(inh) . Recent studies , reported a spatial–temporal resolved polarized optical microscopic ( str- POM) method to estimate σ F(inh) by experiment. They have produced useful insights through identification of a specific fracture mechanism and demonstrated why Griffith’s concept of toughness G c is applicable to characterize the fracture behavior of brittle polymers in the presence of large cracks.…”