Boundary Element Analysis of Crack Problems in Polycrystalline Materials

Galvis, Andres F.; Sollero, Paulo

doi:10.1016/j.mspro.2014.06.311

Cited by 13 publications

(7 citation statements)

References 15 publications

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“…To decrease the computational burden of the simulations, especially in view of the number of samples to be handled in each MC analysis, some authors proposed the use of (grain) boundary element formulations; see e.g. [28,29,30,31], wherein only the grain boundary network has to be discretized to reduce the dimensionality of the problem.…”

Section: Characterization Of the Uncertainties At The Microscalementioning

confidence: 99%

Effect of Imperfections Due to Material Heterogeneity on the Offset of Polysilicon MEMS Structures

Ghisi

Mariani

2019

Sensors

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Monte Carlo analyses on statistical volume elements allow quantifying the effect of polycrystalline morphology, in terms of grain topology and orientation, on the scattering of the elastic properties of polysilicon springs. The results are synthesized through statistical (lognormal) distributions depending on grain size and morphology: such statistical distributions are an accurate and manageable alternative to numerically-burdensome analyses. Together with this quantification of material property uncertainties, the effect of the scattering of the over-etch on the stiffness of the supporting springs can also be accounted for, by subdividing them into domains wherein statistical fluctuations are assumed not to exist. The effectiveness of the proposed stochastic approach is checked with the problem of the quantification of the offset from the designed configuration, due to the residual stresses, for a statically-indeterminate MEMS structure made of heterogeneous (polycrystalline) material.

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Section: Characterization Of the Uncertainties At The Microscalementioning

confidence: 99%

Effect of Imperfections Due to Material Heterogeneity on the Offset of Polysilicon MEMS Structures

Ghisi

Mariani

2019

Sensors

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“…A linear relation for one single grain, namely grain number 10 in Figure 6, can be written as follows Via applying the interface and boundary condition and by using Equation (27) for all the grains in the polycrystalline aggregate, the adaptive system of equations that contains BEM and grain interface equations can be written in a matrix form To get this linear equation, the uniform displacement boundary condition has been applied. In Equation (28), n g represents the number of grains. D contains the matrix H nc in Equation (27) and A the matrix G nc in Equation (27); however, contrary to Equation (27), all these matrices here are defined in local coordinates.…”

Section: The Evaluation Algorithmmentioning

confidence: 99%

“…Crack nucleation and propagation in polycrystalline materials can be studied in cohesive models by different numerical tools such as the BEM or FEM [26,27]. Despite the fact that some of the cohesive laws consider fracture criteria for the first and second mode separately, in [28,29] mixed-mode relations to predict the location of the cohesive zone in polycrystalline are presented.…”

Section: Introductionmentioning

confidence: 99%

Application of the grain boundary formulation and image processing-based algorithm in micro-mechanical analysis of piezoelectric ceramic

Biglar¹,

Trzepieciński²,

Stachowicz

et al. 2017

Mathematics and Mechanics of Solids

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The main subject of this paper is the micro-mechanical analysis of a piezoelectric ceramic. In micro-mechanical analyses, it is very important to have knowledge about the real and natural micro-structure of materials. Therefore, the barium titanate powder was prepared using the solid-state technique, and pellets and beams were manufactured by uniaxial and isostatic pressing. The boundary element method (BEM) is used in order to be combined with three different grain boundary formulations for investigation of micro-mechanics and crack nucleation and evaluation in piezoelectric ceramic. In order to develop a numerical programming algorithm, suitable models of polycrystalline aggregate have to be discretised for the BEM analysis. Hence, original comprehensive algorithms are designed on the basis of image processing methods. Several assumptions are made to model the grain boundary in micro-scale. In the first step, before having any cracks, the traction equilibrium and displacement compatibility are governing equations. When the onset micro-crack starts to initiate, one mixed-mode potential based cohesive law is applied to model grain boundaries and investigate the intergranular crack nucleation and evolution. Upon interface failure, a frictional law is utilised in order to study separation, sliding or sticking between micro-crack surfaces. Several numerical experiments on barium titanate polycrystalline aggregate are presented to show the effectiveness of image processing-based discretisation algorithms and grain boundary formulation in micro-mechanical analysis.

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“…The multi-domain technique has also been used for BE modeling of heat transfer [6] and fluid mechanics [7] problems. The multi-domain methodology seems to be an effective method for bi-materials containing interfacial cracks as well [8,9]. Phan and Mukherjee [10] have implemented the boundary contour method (BCM), which offers a further reduction of the computational cost.…”

Section: Introductionmentioning

confidence: 99%

Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, Under Axisymmetric Singular Loading Sources

Pavlou¹

2017

Int. J. CMEM

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A review of Green's functions for dissimilar or homogeneous elastic space containing penny-shaped or annular interfacial cracks under singular ring-shaped loading sources is presented. The solutions are based on fictitious singular loading sources and superposition of the fundamental solutions of the following two problems: (a) Dissimilar elastic solid without crack under singular source, and (b) Dissimilar elastic solid containing crack under surface tractions. The above Green's functions have the following advantages: (i) No multi-region BE modeling for the dissimilar material is necessary, and (ii) No discretization of the crack surface is necessary. Numerical examples are presented and discussed.

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Boundary Element Analysis of Crack Problems in Polycrystalline Materials

Cited by 13 publications

References 15 publications

Effect of Imperfections Due to Material Heterogeneity on the Offset of Polysilicon MEMS Structures

Effect of Imperfections Due to Material Heterogeneity on the Offset of Polysilicon MEMS Structures

Application of the grain boundary formulation and image processing-based algorithm in micro-mechanical analysis of piezoelectric ceramic

Green’s Functions for Dissimilar or Homogeneous Materials Containing Interfacial Crack, Under Axisymmetric Singular Loading Sources

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