Fracture of Soft Foam Solids: Interplay of Visco- and Plasto-elasticity

Abstract

Fracture mechanical properties of a very soft solidified foam of polyethylene with Young's modulus about 1 MPa are studied by changing stretching velocity in a wide range, by using sheets of the material in order to suppress finite-size effects. Unexpectedly, we find that the fracture can be described well by linear elastic fracture mechanics for a given fracture rate in the wide range. This allows a direct determination of velocity-dependent fracture energy of the soft foam. As a result, we find that the fracture energy is composed of a static plastoelastic component and another dynamic viscoelastic component, elucidating a simple physical interpretation of each component and giving guiding principles useful for practical applications to reinforce industrial polymer materials. Furthermore, we introduce a finite stress criterion for fracture that is similar in spirit to the cohesive zone model and, using our data, demonstrate that this stress criterion is consistent with the Griffith's energy balance. I n nature and in daily life, there is a variety of cellular structures or foam solids, ranging from familiar ones, such as cork, balsa, bread, coral, and apples, 1 to exotic remarkable ones, such as the stereom of echinoderms, 2 the skeleton of a certain sponge, 3 and the frustules of diatoms. 4 Cellular solids are generally lightweight smart materials like spider webs 5,6 and support our life, for example, daily by their insulating or shock-absorbing features. Active studies on foam solids to date have revealed, e.g., (1) simple fracture mechanical properties that are well-understood as a function of the volume fraction of solid ϕ 7−9 and (2) advantages of the porous structure for reinforcement. 10,11 However, experimental studies are limited to hard cellular solids with Young's modulus E larger than 3000 MPa, such as poly(methyl acrylate) (PMA), rigid polyurethane (PU), and cellular glass. In addition, any velocity dependences of fracture properties of foam solids have never been discussed in a systematic way, while such an issue has received considerable attention for adhesive interface, 12−14 flexible laminates, 15 viscoelastic solids, 16,17 and weakly cross-linked gels. 18,19 Recently, a very soft polyethylene foam with E around 1 MPa has been studied, and scaling laws different from those for hard porous materials were established. 20 Here, we study the fracture energy of similar soft foams with changing fracture rate in a wide range to surprisingly find that linear elastic fracture mechanics 21,22 works well for a fixed velocity in the wide range. The velocity-dependent fracture energy is shown to be composed of a static plastoelastic component and another dynamic viscoelastic component, with the latter scaling linearly with the rate. The velocity dependence originates from that of a yield stress that is introduced through the opening distance at crack tips ( Figure 1). Furthermore, we demonstrate that the Griffith criterion can be regarded as a stress criterion: we find with our data that the Griffith's ene...

Visco- and plastoelastic fracture of nanoporous polymer sheets

“…Since we have established the same reasoning for Eq. (3) in Ref [26]. for soft foam sheets of polyethylene, the present result suggests a certain degree of universality of Eq.…”

“…were measured with a hand-made setup, which was used in our previous study [26]. This Fracture mechanical measurements are performed with the same setup but with introducing a macroscopic line crack with a sharp knife at the center of the sample (see Fig.…”

Initial rigid response and softening transition of highly stretchable kirigami sheet materials

“…The material of sheet samples is Kent paper (high quality paper with fine texture mainly used for drafting) of thickness h ( h ≃ 0.2–0.3 mm), whose Young’s modulus E is measured to be in the range E ≃ 2.45–3.27 GPa (with the standard deviations less than ≃5%). We measured force as a function of extension by a force gauge (FGP-0.2, NIDEC-Shimpo) mounted on an automatic slider system (EZSM6D040, Oriental Motor) as in the previous studies on fracture 17 18 19 . The extension speed is fixed to a slow speed (0.5 mm/s) to remove dynamic effects.…”

Crack propagation in porous polymer sheets with different pore sizes

“…[10] In the case of a polyethylene foam sheet whose typical foam size is of millimeter-scale, it was found that the flow of polymer happens only on the scale of foam at the crack tip. [16] The structural size-effect is also verified with numerical simulations; it has been shown that, by changing the mesh size of a network model for elastic sheets, the failure stress of a sheet with a crack can be tuned. [17] For crack propagation, in a numerical simulation [18] and a theoretical model, [12] it is confirmed that mesh size affects crack velocities.…”

“…However, the direct measurement for matrix materials is impossible as explained above while these matrix properties are reflected in bulk viscoelastic measurements to some extent, which is similar for the three samples. In addition, the most important length scale at crack tips is the pore size; for example, the crack opening distance, the size of yielding zone near the crack tips, [28] the size of the region in which viscous flow occurs, [16] and the radius of curvature at a crack tip are all governed by the pore size. These are the reasons we consider the pore size should be physically most important for considering crack propagation in the present porous polymers.…”