Effect of incision curvature on measuring fracture energy of soft materials

Abstract

Fracture energy is the property that characterizes how a material resists crack growth. In a standard measurement of fracture energy, an incision is typically introduced into the specimen. It is known that the measured fracture energy may depend on the incision curvature. However, the underlying mechanism of such dependence remains unclear. In this paper, we prepared polyacrylamide/Ca-alginate hydrogel specimens featuring incisions with circular tips of varying diameters. The fracture energy was subsequently measured through a pure shear test. We observed that the fracture energy is proportional to the incision diameter, with a slope comparable to the work of fracture for larger tip diameters. Conversely, for smaller tip diameters, the fracture energy remains independent of the incision diameter and aligns with the intrinsic fracture energy. This transition occurs at an incision diameter comparable to a material-specific scale known as the fractocohesive length. Notably, the fractocohesive length, rather than the inelastic zone scale, successfully explains the dependence of fracture energy measurement on incision curvature. The difference between these two length scales of the material here spans three orders of magnitude. These results will be helpful for establishing standards for measuring fracture energy of soft materials.

Keywords

Fracture energy / incision curvature / fractocohesive length / inelastic zone scale

References

[1] Iwashita T.Effects of notch sharpness and depth on brittle fractures in single-edge notched bend specimens.Eng Fract Mech2016;164:60-73

[2] Wang Y,Suo Z.Polyacrylamide hydrogels. III. Lap shear and peel.J Mech Phys Solids2021;150:104348

[3] Greensmith HW.Rupture of rubber. III. Determination of tear properties.J Polym Sci1955;18:189-200

[4] Rivlin RS.Rupture of rubber. I. Characteristic energy for tearing.J Polym Sci1953;10:291-318

[5] Thomas AG.Rupture of rubber. II. The strain concentration at an incision.J Polym Sci1955;18:177-88

[6] Salazar, A., Patel, Y., Williams, J. G. Influence of crack sharpness on the fracture toughness of epoxy resins. In 13th International Conference on Fracture. Beijing, China, June 16-21, 2013. https://www.gruppofrattura.it/ocs/index.php/ICF/icf13/paper/viewFile/11464/10843. (accessed 2025-09-05).

[7] Moore, D. R., Williams, J., Pavan, A. Fracture mechanics testing methods for polymers, adhesives and composites; Elsevier, 2001. https://shop.elsevier.com/books/fracture-mechanics-testing-methods-for-polymers-adhesives-and-composites/moore/978-0-08-043689-0. (accessed 2025-09-05).

[8] ASTM D5045-14, Standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials, 1999. https://www.astm.org/d5045-14r22.html. (accessed 2025-09-12).

[9] ASTM D6068-10, Standard test method for determining J-R curves of plastics materials, 2002. https://www.astm.org/d6068-10r18.html. (accessed 2025-09-12).

[10] ASTM D624-00, Standard test method for tear strength of conventional vulcanized rubber and thermoplastic elastomers, 2020. https://store.astm.org/d0624-00r20.html. (accessed 2025-09-12).

[11] Chen C,Suo Z.Flaw sensitivity of highly stretchable materials.Extreme Mech Lett2017;10:50-7

[12] Yang C,Suo Z.Polyacrylamide hydrogels. I. Network imperfection.J Mech Phys Solids2019;131:43-55

[13] Zhou Y,Zhao P,Suo Z.Flaw-sensitivity of a tough hydrogel under monotonic and cyclic loads.J Mech Phys Solids2021;153:104483

[14] Liu J,Yin T,Qu S.Polyacrylamide hydrogels. II. elastic dissipater.J Mech Phys Solids2019;133:103737

[15] Fu Y,Qu S.Cavitation/fracture transition of soft materials.J Mech Phys Solids2023;172:105192

[16] Chen X,Yang H.Flaw sensitivity of hydrogels with dynamic covalent bonds.Extreme Mech Lett2024;67:102129

[17] Sun JY,Illeperuma WR.Highly stretchable and tough hydrogels.Nature2012;489:133-6 PMCID:PMC3642868

[18] Shi M,Yin T,Suo Z.Hydrolysis embrittles poly(lactic acid).MRS Bull2023;48:45-55

[19] Irwin GR.Analysis of stresses and strains near the end of a crack traversing a plate.J Appl Mech1957;24:361-4

[20] Begley, J., Landes, J. The J integral as a fracture criterion. In Appeared in Fracture Toughness, proceedings of the 1971 National Symposium on Fracture Mechanics, Part II, University of Illinois, Urbana-Champaign, Illinois, August 31-September 2, 1971. https://trid.trb.org/View/138997. (accessed 2025-09-05).

[21] Landes D.The effect of specimen geometry on J_Ic.Fracture Toughness: Part IICorten, HT; 1972; pp 24-39