An Analytical Theory for Radial Crack Propagation: Application to Spherical Indentation

Abstract

A simple analytical theory is proposed for estimating the number of radial cracks which will propagate in brittle materials subjected to axisymmetric transverse smface loads. Eirst, an expression is obtained for the stress intensity factor of a traction-free starshaped crack in an infinite elastic membrane subjected to axisymmetric transverse loads. Combining this relation with the critical stress intensity factor criterion for fracture, an implicit expression is obtained which defines the number of cracks as a function of the applied loading, initial fiaw size, and fracture toughness. Based on the form of this expression, we argue that if the initial fiaw size is sufficiently small compared to the length scale associated with the loading, then the number of cracks can be determined approximately in closed-form from the analysis of a traction-free star-shaped crack in a thin body subjected to uniform equibiaxial in-plane tension. In an attempt to validate the theory, comparisons are made with spherical micro-indentation experiments of silicon carbide (Wereszczak and Johanns, 2008, "Spherical Indentation of' SiC," Advances in Ceramic Armor II, Wiley, NY, Chap. 4) and good agreement is obtained for the number of radial cracks as a function of indentation load.

Numerical Simulation of Icebreaking by Underwater-Explosion Bubbles and Compressed-Gas Bubbles Based on the ALE Method

“…In addition, the comparison between the numerical simulation and the experimental results showed that the ice plate used in the numerical simulation was symmetrical and uniform, so the cracks were mostly regular, which was difficult to achieve in the experiment. Therefore, due to the difference between the randomness of the cracks and the inhomogeneous mechanical properties of the ice body, it was more important to focus on the damage pattern of the cracks rather than the specific crack properties in the study, which was previously discussed by Li and Chen; Rabczuk; Seagraves and Radovitzky; and Yuan [40][41][42][43]. This also confirmed the complex mechanical properties of the ice under impact loads.…”

Isotoxal star-shaped polygonal voids and rigid inclusions in nonuniform antiplane shear fields. Part I: Formulation and full-field solution

“…It is for this reason that the closed-form determination of the stress field near a sharp inclusion or void is crucial for the design of ultra-resistant composites. triangular and Vickers pyramidal indenters [7,9,10] and can emerge during drying of colloidal suspensions in capillary tubes [14,18]. Multiple radial crack patterns are generated after low speed impacts 1 on brittle plates [38].…”

Omnidirectionally Stretchable Metal Films with Preformed Radial Nanocracks for Soft Electronics

“…The nanocrack formation is proposed to occur in three steps“bulging,” “initiation,” and “propagation”as revealed by the corresponding images and height profiles (Figure a). The PDMS contains the residual solvent; when thermal evaporation begins ( t Au = 10 nm), the solvent agglomerates and erupts, generating an externally directed force under the Au film so that bulges form in the film . The driving force for the eruption of solvent is assumed to be the evaporation of the internal solvent due to the thermal energy that the deposited atoms transfer to the elastomeric substrate during thermal evaporation.…”

“…The PDMS contains the residual solvent; when thermal evaporation begins (t Au = 10 nm), the solvent agglomerates 37 and erupts, generating an externally directed force under the Au film so that bulges form in the film. 38 The driving force for the eruption of solvent is assumed to be the evaporation of the internal solvent due to the thermal energy that the deposited atoms transfer to the elastomeric substrate during thermal evaporation. This eruption imposes a large tensile stress σ erupt ; when the total applied stress σ th + σ erupt exceeds the critical tensile stress σ tensile of Au, cracking occurs during the subsequent evaporation (t Au = 20 nm) (see the estimation of σ erupt and conditions for the film crack initiation of the film in the Supporting Information; Figures S6 and S7).…”