Crack-Tip Strain Field in Supershear Crack of Elastomers

Mai, Thanh-Tam; Okuno, Kenichiro; Tsunoda, Katsuhiko; Urayama, Kenji

doi:10.1021/acsmacrolett.0c00213

Cited by 28 publications

(45 citation statements)

References 49 publications

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“…The paper has found novel local solutions to mode I and mode II fracture in isotropic linear elasticity that describe supersonic and intersonic crack propagation showing remarkable similarities to experimental and computational models previously reported in the literature (Gao et al 2001;Rosakis 2002;Abraham et al 2002;Guo et al 2003;Buehler et al 2003;Hao et al 2004;Petersan et al 2004;Willmott and Field 2006;Radi and Loret 2008;Bizzarri et al 2010;Schubnel et al 2011;Barras et al 2018;Yue et al 2019;Mai et al 2020). Despite these results, no theoretical predictions describing Mach cone solutions had been reported in the literature before.…”

Section: Discussionsupporting

confidence: 73%

“…However, recent results both experimental and computational have shown crack propagation at significantly higher speeds both in the intersonic range and even beyond the speed of sound (Rosakis et al 1999;Needleman 1999;Abraham and Gao 2000;Huang and Gao 2001;Gao et al 2001;Rosakis 2002;Abraham et al 2002;Guo et al 2003;Buehler et al 2003;Hao et al 2004). Moreover, some of the published results exhibit features akin to shock waves of supersonic flow where solution discontinuities are seen to emerge from the crack tip as it travels along the material (Petersan et al 2004;Willmott and Field 2006;Radi and Loret 2008;Bizzarri et al 2010;Schubnel et al 2011;Barras et al 2018;Yue et al 2019;Mai et al 2020). No analytical models have been reported that predict such behaviour in linear elasticity.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Bonet

Gil

2021

Int J Fract

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This paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

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Section: Discussionsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Bonet

Gil

2021

Int J Fract

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“…Fracture mechanics theory shows that the deformation field around the crack tip is usually much larger than in the bulk far from the crack due to the presence of a singularity in both stress and strain (31)(32)(33)(34). To observe the stress distribution around the crack tip during the fatigue test, the birefringence (circular polarization) was monitored during cyclic loading.…”

Section: Fatigue Fracture Behaviorsmentioning

confidence: 99%

Effect of mesoscale phase contrast on fatigue-delaying behavior of self-healing hydrogels

Cui

Kurokawa

et al. 2021

Sci. Adv.

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We investigate the fatigue resistance of chemically cross-linked polyampholyte hydrogels with a hierarchical structure due to phase separation and find that the details of the structure, as characterized by SAXS, control the mechanisms of crack propagation. When gels exhibit a strong phase contrast and a low cross-linking level, the stress singularity around the crack tip is gradually eliminated with increasing fatigue cycles and this suppresses crack growth, beneficial for high fatigue resistance. On the contrary, the stress concentration persists in weakly phase-separated gels, resulting in low fatigue resistance. A material parameter, λtran, is identified, correlated to the onset of non-affine deformation of the mesophase structure in a hydrogel without crack, which governs the slow-to-fast transition in fatigue crack growth. The detailed role played by the mesoscale structure on fatigue resistance provides design principles for developing self-healing, tough, and fatigue-resistant soft materials.

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“…In this section, the velocity and strain fields will be examined for the presence of discontinuities that were mentioned earlier. Transonic cracks in elastomers in mode-I have been reported as well in Petersan et al (2004), Chen et al (2011), Mai et al (2020. However, those studies do not report any discontinuities in strain or velocity fields.…”

Section: Additional Observations On the 40 MM Specimenmentioning

confidence: 97%

The role played by viscoelasticity in the bulk material during the propagation of a dynamic crack in elastomers

2021

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Investigation of dynamic fracture of elastomers can still be considered to be a relatively open area. When a sheet of elastomer is stretched in a tensile machine and a crack is introduced, the crack propagates at a speed that depends on the initial stretch level. There are instances where this speed is noted to exceed the shear wave speed based on the elastic modulus under high imposed stretches. Such cracks are called transonic cracks. It was usually hypothesized that either the hyperelastic or viscoelastic stiffening of the bulk material raises the wave speeds resulting in crack speeds entering the transonic regime. This article revisits the experiments performed on Polyurethane elastomers in Corre et al. (Int J Fract 224(1):83-100, 2020) to study the implications of both these hypotheses. Crack propagation has not been explicitly modeled, but the crack speeds are implicitly imposed on the geometry using the boundary conditions extracted from the experimental data. It has been determined that the viscoelasticity in the bulk is needed to describe and understand the transonic cracks in polyurethane elastomer. The inclu-

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Crack-Tip Strain Field in Supershear Crack of Elastomers

Cited by 28 publications

References 49 publications

Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Effect of mesoscale phase contrast on fatigue-delaying behavior of self-healing hydrogels

The role played by viscoelasticity in the bulk material during the propagation of a dynamic crack in elastomers

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