Void growth by grain-boundary diffusion in fine grained materials

Cocks, A.C.F.; Searle, Andrew

doi:10.1016/0167-6636(91)90024-t

Cited by 26 publications

(26 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The detailed structure of all these matrices is given by Cocks [ 1 ] and Cocks and Searle [2]. Once the degrees of freedom are determined from (8) the detailed stress distribution along any grain boundary facet can be obtained from (1) and (2). This distribution can be written in the following form…”

Section: Governing Equations and Methods Of Analysismentioning

confidence: 99%

“…where the matrix [D] is given by Cocks and Searle [2], [u] is the matrix of degrees of freedom associated with a given element, Fig. 3, and tr + and 0"-are the stresses normal to the boundary (the Lagrange multipliers) at each end of the facet.…”

Section: Governing Equations and Methods Of Analysismentioning

confidence: 99%

“…Cocks [1] and Cocks and Searle [2] have demonstrated how the above system of equations can be used to analyse the growth of voids and facet sized cracks in fine grained materials. Recently the authors [10] have developed a computer package, NAD-GB (Numerical Analysis of Diffusion along Grain Boundaries), which has powerful pre-and post processors, allowing problems with large numbers of degrees of freedom to be formulated (such as that represented by Fig.…”

Section: Governing Equations and Methods Of Analysismentioning

confidence: 99%

See 2 more Smart Citations

The effect of grain-size on the stress and velocity fields ahead of a crack in a material which deforms by Coble creep

Pan

Cocks

1993

Int J Fract

View full text Add to dashboard Cite

The stress and velocity fields ahead of a grain-boundary crack in a material which deforms by Coble creep are investigated for a series of grain sizes using the numerical analysis technique established by Cocks I-1-3]. The numerical results are compared with the linear viscous fields obtained by the boundary element method and the finite element method. It is demonstrated that a detailed knowledge of the micromechanical processes of material transport and deformation are required to determine the stress and displacement fields for the grains which immediately surround the crack tip. But the response of the surrounding material can be adequately described from a conventional linear viscous analysis of the problem.

show abstract

Section: Governing Equations and Methods Of Analysismentioning

confidence: 99%

Section: Governing Equations and Methods Of Analysismentioning

confidence: 99%

Section: Governing Equations and Methods Of Analysismentioning

confidence: 99%

See 1 more Smart Citation

The effect of grain-size on the stress and velocity fields ahead of a crack in a material which deforms by Coble creep

Pan

Cocks

1993

Int J Fract

View full text Add to dashboard Cite

show abstract

“…Cook et al 25 , 26 have demonstrated a finiteelement-type analysis of the grain-boundary diffusion process, and have developed a numerical calculation method to obtain the void growth (or atomic flux) whose driving force is the stress gradient. We analyzed and verified the void growth by using the above-mentioned technique in the fundamental analysis.…”

Section: Fundamental Analysis Calculation Model and Calculation Condimentioning

confidence: 99%

Void Growth Behavior in ULSI Cu Interconnections by Grain-Boundary Diffusion Simulation

Onishi

Mizuno

Yoshikawa

et al. 2010

Journal of Elec Materi

View full text Add to dashboard Cite

The behavior of void growth in ultra-large-scale integration Cu interconnections has been investigated by grain-boundary diffusion simulation to confirm the effectiveness of the high-pressure reflow process for suppressing stressinduced voiding. Void growth was simulated by combining stress analysis and atomic flux analysis. The former was calculated by the finite-element method (FEM), and the latter was calculated by an unusual FEM in which grain boundaries were defined as elements. From the results of void growth analysis, we found that voids tend to disappear during the isochronal annealing step and that the void shrinkage rate can be increased by two to three times by applying pressure of 150 MPa compared with normal-pressure annealing. From the simulation results, it can be conjectured that the high-pressure reflow process is effective for eliminating voids in via holes of Cu interconnections.

show abstract

“…In porous components where large macropores and small micropores both exist, the different interactions of the inclusions and the matrix will further complicate the situation. Considerable efforts have been made to understand the sintering of porous ceramic materials [1][2][3][4][5][6][7][8][9][10][11]. However, very few published models study the situation of a macroporous body where large and small pores coexist [12,13].…”

Section: Introductionmentioning

confidence: 99%

Densification modeling studies on porous Al2O3 component

Lü

2010

Powder Metall Met Ceram

View full text Add to dashboard Cite

A model for sintering of porous ceramic material is applied to study the densification behavior of a porous Al 2 O 3 system that contains pores of different sizes. In the model, a sintering potential associated with the shrinkage of large macropores is considered separately from that of small pores. The predictions from the model are found to be in good agreement with the experimental data. The results show that consideration of the shrinkage of large macropores, which is traditionally assumed to be very stable, provides a more accurate prediction results for the densification of a multi-porous body.

show abstract

Void growth by grain-boundary diffusion in fine grained materials

Cited by 26 publications

References 7 publications

The effect of grain-size on the stress and velocity fields ahead of a crack in a material which deforms by Coble creep

The effect of grain-size on the stress and velocity fields ahead of a crack in a material which deforms by Coble creep

Void Growth Behavior in ULSI Cu Interconnections by Grain-Boundary Diffusion Simulation

Densification modeling studies on porous Al2O3 component

Contact Info

Product

Resources

About