Quasi-static straight and oscillatory crack propagation in ferroelectric ceramics due to moving electric field: experiments and theory

Niefanger, R.; Pham, V.-B.; Schneider, Gerold A.; Bahr, H.‐A.; Balke, Herbert; Bahr, U.

doi:10.1016/j.actamat.2003.08.034

Cited by 8 publications

(4 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the transition from straight to oscillating crack (the onset of global directional instability) cannot be determined with a local consideration, which often has been done in literature by Marder (1994), Adda-Bedia and Pomeau (1995), Deegan et al (2003), Bouchbinder et al (2003). Only with a global analysis (for example, Niefanger et al 2004) in which the whole crack path (crack tip in all phases) is considered, this transition can be determined correctly ).…”

Section: The Solutions By Cotterell and Rice (1980) And Sumi Et Al (mentioning

confidence: 97%

Crack paths and the problem of global directional stability

Pham

Bahr

et al. 2006

Int J Fract

Self Cite

View full text Add to dashboard Cite

Crack paths of original Griffith crack and edge crack under biaxial remote mode-I loading after different local disturbances are calculated by using integro-differential equations of first-order perturbation and numerical simulation with FEM respectively.Considering the asymptotic behaviour for large crack lengths the problem of global directional stability is reinvestigated extending the work by Melin. For the Griffith crack, correct power functions for the asymptotic path with one or both crack tips growing have been determined. The wellknown critical stress biaxiality ratio R c = 1 for the global directional stability has been obtained independently whether the crack is disturbed by local imperfections in geometry or in loading. For an edge crack the calculated critical stress biaxiality ratio for the global directional stability R c = 0.616, also irrespective of the local disturbances, corresponds to a positive T-stress and is considerably smaller than the value R > 0.95 estimated by Melin (2002). In general, cracks need not propagate asymptotically in the direction perpendicular to the largest principal stress (without crack). This is found to be due to the effect of the boundaries.Considering the initial crack growth exclusively, it is shown that the solution for crack path prediction in series expansion form as derived by Cotterell and Rice (1980) for traction-free crack faces (after correction of a misprint) is exact in the two first terms in all cases. Thus, for small crack growth the Cotterell and Rice solution is universal with respect to all loading and geometrical situations.

show abstract

Section: The Solutions By Cotterell and Rice (1980) And Sumi Et Al (mentioning

confidence: 97%

Crack paths and the problem of global directional stability

Pham

Bahr

et al. 2006

Int J Fract

Self Cite

View full text Add to dashboard Cite

show abstract

“…They derived expressions for crack spacing and propagation rate from a stability analysis of the stationary solution. Furthermore, wavy cracks have been described from a glass strip pulled from a hot oven into a cold bath Addabedia and Pomeau (1995), Bouchbinder et al (2003), Menouillard and Belytschko (2011) from thermally loaded single crystals of silicon (Deegan et al 2003) and from ferroelectric ceramics exposed to a moving electric field (Niefanger et al 2004). Addabedia and Pomeau (1995) and Bouchbinder et al (2003) performed stability analyses and Menouillard and Belytschko (2011) employed local symmetry criteria and numerical simulation for analysing the path of a single oscillating crack, where temperature was treated as a background field unrelated to the crack.…”

Section: Crack Spacing and Overall Dissipation Ratementioning

confidence: 99%

Evolution of chemically induced cracks in alkali feldspar: thermodynamic analysis

et al. 2022

View full text Add to dashboard Cite

A system of edge cracks was applied to polished (010) surfaces of K-rich gem-quality alkali feldspar by diffusion-mediated cation exchange between oriented feldspar plates and a Na-rich NaCl–KCl salt melt. The cation exchange produced a Na-rich layer at and beneath the specimen surface, and the associated strongly anisotropic lattice contraction lead to a tensile stress state at the specimen surface, which induced fracturing. Cation exchange along the newly formed crack flanks produced Na-enriched diffusion halos around the cracks, and the associated lattice contraction and tensile stress state caused continuous crack growth. The cracks nucleated with non-uniform spacing on the sample surface and quickly attained nearly uniform spacing below the surface by systematic turning along their early propagation paths. In places, conspicuous wavy cracks oscillating several times before attaining their final position between the neighboring cracks were produced. It is shown that the evolution of irregularly spaced towards regularly spaced cracks including the systematic turning and wavyness along the early propagation paths maximizes the rate of free energy dissipation in every evolutionary stage of the system. Maximization of the dissipation rate is suggested as a criterion for selection of the most probable evolution path for a system undergoing chemically induced diffusion mediated fracturing in an anisotropic homogeneous brittle material.

show abstract

“…The second group of experiments have reported crack initiation and propagation from insulating notches, under electric fields applied perpendicularly to the notch. [20,21,22,23,24,25,26,27,28,29,30]. However, theoretical approaches show that electric fields, perpendicular to an insulating crack, decrease the total energy release rate, i.e.…”

Section: Introductionmentioning

confidence: 99%