Brittle intergranular failure in 2D microstructures: Experiments and computer simulations

Grah, M.; Alzebdeh, Khalid I.; Sheng, Peiyao; Vaudin, Mark D.; Bowman, Keith J.; Ostoja–Starzewski, Martin

doi:10.1016/s1359-6454(96)00044-4

Cited by 69 publications

(24 citation statements)

References 19 publications

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“…This affects mainly layer-wise decrease of the viscosity and an increase of the density and the Young's modulus of the material, in agreement with the common internal subdivision of mantle and crust (Table 1; Gölke and Mechie 1994;Grah et al 1996). We put a quenched noise on the breaking strength of single springs in the system.…”

Section: General Assumptions and Parameterssupporting

confidence: 74%

Faulting of the lithosphere during extension and related rift-flank uplift: a numerical study

Sachau¹,

Koehn²

2010

Int J Earth Sci (Geol Rundsch)

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In this contribution, we present a new model of passive rifting and related rift-flank uplift. The numerical model is based on a lattice spring network coupled with a viscous particle model so that we can simulate visco-elasto-plastic behaviour with dynamic fault development. In our model, we show that rift-flank uplift can be achieved best when extension in the crust is localized and the lower crust is strong so that major rift faults transect the whole crust. Uplift of rift flanks follows a smooth function whereas down-throw in the rift basin takes place in steps. The geometry of the developing faults has also an influence on the uplift; in this case, displacement along major rift faults produces higher flanks than distributed displacement on many faults. Our model also shows that the relative elastic thickness of the crust has only a minor influence on the uplift since fault depth and elastic thickness are not independent. In addition, we show with a second set of simulations and analytically that a strain misfit between the upper and lower boundaries of a stretched crust, which is created by the horizontal extension, leads to an active uplift driven by elastic forces. We compare the numerical simulations, the analytical solution and real surface data from the Albertine rift in the East African Rift System and show that our new model can reproduce realistic features. Our two-layer beam model with strain misfit can also explain why a thick crust in the simulations can have an even higher rift flank than a thin crust even though the thin crust topography has a higher curvature. We discuss the implications of our simulations for real rift systems and for the current theory of rift-flank uplift.

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Section: General Assumptions and Parameterssupporting

confidence: 74%

Faulting of the lithosphere during extension and related rift-flank uplift: a numerical study

Sachau¹,

Koehn²

2010

Int J Earth Sci (Geol Rundsch)

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“…In the models of brittle polycrystalline materials, the fracture properties of the grain boundaries can be characterized by assuming a lower fracture toughness along these boundaries as compared to the grain interiors. Other works (Grah et al 1996;Sukumar et al 2003;Verhoosel and Gutierrez 2009) have proven the validity of this assumption for the study of the intergranular and the transgranular modes of fracture. In the model of grain growth described in Sect.…”

Section: Phase-field Model For Fracture Of Ferroelectric Polycrystalsmentioning

confidence: 85%

Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

Abdollahi

Arias

2012

Int J Fract

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We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing (1) the polycrystalline structure, (2) the location of the cracks, and (3) the ferroelectric domain microstructure. Different polycrystalline microstructures are obtained from computer simulations of grain growth. Then, a phase-field model for fracture in ferroelectric single-crystals is extended to polycrystals by incorporating the differential fracture toughness of the bulk and the grain boundaries, and the different crystal orientations of the grains. Our simulation results show intergranular crack propagation in fine-grain microstructures, while transgranular crack propagation is observed in coarse grains. Crack deflection is shown as the main toughening mechanism in the fine-grain structure. Due to the ferroelectric domain switching mechanism, noticeable fracture toughness enhancement is also obtained for transgranular crack propagation. These observations agree with experiment.

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“…(11) as follows. The fracture properties of the grain boundaries can be characterized by assuming a lower fracture toughness along these boundaries as compared to the grain interiors [35,111,120]. The grain boundaries can be identified through a function ξ of the orientation field variables η i defined as…”

Section: Phase-field Model Of Fracture In Ferroelectric Polycrystalsmentioning

confidence: 99%

Phase-Field Modeling of Fracture in Ferroelectric Materials

Abdollahi

Arias

2014

Arch Computat Methods Eng

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This paper presents a family of phase-field models for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in single and polycrystalline ferroelectric materials. The first objective is to introduce a phase-field model for ferroelectric single crystals. The model naturally couples two existing energetic phasefield approaches for brittle fracture and ferroelectric domain formation and evolution. Simulations show the interactions between the microstructure and the crack under mechanical and electromechanical loadings. Another objective of this paper is to encode different crack face boundary conditions into the phase-field framework since these conditions strongly affect the fracture behavior of ferroelectrics. The smeared imposition of these conditions are discussed and the results are compared with that of sharp crack models to validate the proposed approaches. Simulations show the effects of different conditions and electromechanical loadings on the crack propagation. In a third step, the model is modified by introducing a crack non-interpenetration condition in the variational approach to fracture accounting for the asymmetric behavior in tension and compression. The modified model makes it possible to explain anisotropic crack growth in ferroelectrics under the Vickers indentation loading. This model is also employed for the fracture analysis of multilayer ferroelectric actuators, which shows the potential of the model for future applications. The coupled phase-field model is also extended to polycrystals by introducing realistic polycrystalline microstructures in the model.

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Brittle intergranular failure in 2D microstructures: Experiments and computer simulations

Cited by 69 publications

References 19 publications

Faulting of the lithosphere during extension and related rift-flank uplift: a numerical study

Faulting of the lithosphere during extension and related rift-flank uplift: a numerical study

Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

Phase-Field Modeling of Fracture in Ferroelectric Materials

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