Why cutting is easier than tearing elastomers

Abstract

Tearing tough soft solids such as rubbers, leather or meat is much harder than cutting them with a sharp blade. To understand why, we use samples labeled with mechanically sensitive fluorophores to investigate cutting and fracture behavior in PDMS elastomers and quantify the extent of bond scission resulting from cutting pre-stretched samples. Our findings reveal that stretch-induced cracks produce significant deformation, bond scission and blunting near the crack tip, requiring more energy to propagate. In contrast, using blades reduces the amount of stretching and blunting required for crack propagation, resulting in a lower fracture energy. The measured linear correlation between fracture energy and the areal density of broken chains clarifies the relationship between pre-stretching, blunting, and molecular damage. These multi-scale insights demonstrate the key differences between fracture and cutting mechanics of soft materials, allowing to optimize engineering applications, such as rubber and food processing, energy-efficient recycling, biomedical and surgical devices, protective equipment and sports gear.

Fig. 1. Schematic representation of the pure-shear cutting and damage mapping.

a Sketch of the pure-shear cutting and stretching experiment. b Sketch of the PDMS network at the molecular scale with unbroken mechanophores represented as blue stars and activated mechanophores as yellow stars. This damage occurs in the blunted crack tip zone during the combined stretching/cutting process. c Sketch of the post-mortem PDMS cutting sample.

Fig. 2. Results of the pure-shear cutting experiments.

a Force-displacement curves during the cutting process for different stretch ratios λ. b Variation of the plateau force f (blue) and the blunting radius r_b (red) as a function of stretch ratio λ. The error bars correspond to the standard deviation. c The crack extension energy obtained by Eq. (4) is represented as a function of the stretch ratio, as well as the two separate contributions to the strain energy release rate from cutting Eq. (2) and stretching Eq. (3). The results can be divided into three distinct regions: Region I: out-of-plane deformation and frictional contact, Region II: clean cutting in steady-state, and Region III: pure fracture without the blade. d Left: The crack opening profile for different stretch ratios (scale bar: 1 mm). Right: Parabolic fitting of the crack opening profile to estimate the blunting radius r_b (R²₁ = 0.9484, R²₂ = 0.9688). NB: the crack tip region at a lower scale than the blunting radius was excluded from the parabolic fit since it is affected by non-linear terms.

Fig. 3. Postmortem mapping of damage by bond scission.

a Mechanophores (DACL) based on π-extended anthracene-maleimide adducts yield π-extended anthracene moieties upon force-induced cycloreversion. b The mechanophores are incorporated into the PDMS chains by substituting a given fraction of the crosslinks. c After cutting the pure shear samples at a given value of pre-stretch λ, fluorescence microscopy was performed near the fracture surfaces (red square) and represented in (d), the size bar corresponds to 100 μm in all damage maps: the PDMS sample is on the left of the bright fracture surface where damage is concentrated. e Comparison of the damage maps for two different pre-stretch λ of 1.2 (i) and 1.45 (ii) with the corresponding average depth profile of bond damage φ_y.

Fig. 4. Changes in the damage distribution.

a The damage zone depth d and (b) the dimensionless damage surface density $\overline{\mathrm{\Sigma }}$ in the cutting edge as a function of the applied stretch ratio λ. The error bars for each data point represent the standard deviation of the fluctuations over several hundred independent depth profiles acquired on at least three different samples.

Fig. 5. Interpretation of the damage mechanisms.

a The relationship between the cutting/fracture energy and the surface density of broken bonds. b The relationship between the blunting radius r_b and damage zone depth d. c Photos of the cutting and tearing process (scale bar: 1 mm) and the sketch of the damage mechanism: the contribution of the cutting blade allows the propagation of the fracture for a lower applied stretch and a reduced radius of blunting of the tip. The reduction of the volume where large strains are experienced in front of the crack tip results in the reduction of the number of chains broken per unit fracture surface area and, thus, of the crack extension energy.