scholarly journals Interface crack problem in layered orthotropic materials under thermo-mechanical loading

2014 ◽  
Vol 51 (25-26) ◽  
pp. 4221-4229 ◽  
Author(s):  
Sheng-Hu Ding ◽  
Yue-Ting Zhou ◽  
Xing Li
Keyword(s):  
Mechanical Loading ◽  
Interface Crack ◽  
Crack Problem ◽  
Orthotropic Materials

Solution for a Semi-Permeable Interface Crack in Elastic Dielectric/Piezoelectric Bimaterials

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Electric Field ◽  
Mechanical Loading ◽  
Interface Crack ◽  
Applied Electric Field ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Silicon Oil ◽  
Elastic Dielectric

A semi-permeable interface crack in infinite elastic dielectric/piezoelectric bimaterials under combined electric and mechanical loading is studied by using the Stroh complex variable theory. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and on the energy release rate (ERR). Thirty five kinds of such bimaterials are considered, which are constructed by five kinds of elastic dielectrics and seven kinds of piezoelectrics, respectively. Numerical results for the interface crack tip singularities are calculated. We demonstrate that, whatever the dielectric phase is much softer or much harder than the piezoelectric phase, the structure of the singular field near the semi-permeable interface crack tip in such bimaterials always consists of the singularity r−1∕2 and a pair of oscillatory singularities r−1∕2±iε. Calculated values of the oscillatory index ε for the 35 kinds of bimaterials are presented in tables, which are always within the range between 0.046 and 0.088. Energy analyses for five kinds of such bimaterials constructed by PZT-4 and the five kinds of elastic dielectrics are studied in more detail under four different cases: (i) the crack is electrically conducting, (ii) the crack gap is filled with air/vacuum, (iii) the crack gap is filled with silicon oil, and (iv) the crack is electrically impermeable. Detailed comparisons on the variable tendencies of the crack tip ERR against the applied electric field are given under some practical electromechanical loading levels. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR. We also conclude that the previous investigations under the impermeable crack model are incorrect since the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack, whereas the previous investigations under the conducting crack model may be accepted in a tolerant way since the results of the ERR show very small discrepancies from those for the semi-permeable crack, especially when the crack gap is filled with silicon oil. In all cases under consideration the curves of the ERR for silicon oil are more likely tending to those for the conducting crack rather than to those for air or vacuum. Finally, we conclude that the variable tendencies of the ERR against the applied electric field have an interesting load-dependent feature when the applied mechanical loading increases. This feature is due to the nonlinear relation between the normal electric displacement component and the applied electromechanical loadings from a quadratic equation.

A Method to Extract Interface Stress Intensity Factors Using Interlayers

2005 ◽  
Author(s):  
Sridhar Santhanam
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Interface Stress ◽  
Mode I ◽  
Universal Relation ◽  
Intensity Factors ◽  
Infinite Blocks

A method is presented here to extract stress intensity factors for interface cracks in plane bimaterial fracture problems. The method relies on considering a companion problem wherein a very thin elastic interlayer is artificially inserted between the two material regions of the original bimaterial problem. The crack in the companion problem is located in the middle of the interlayer with its tip located within the homogeneous interlayer material. When the thickness of the interlayer is small compared with the other length scales of the problem, a universal relation can be established between the actual interface stress intensity factors at the crack tip for the original problem and the mode I and II stress intensity factors associated with the companion problem. The universal relation is determined by formulating and solving a boundary value problem. This universal relation now allows the determination of the stress intensity factors for a generic plane interface crack problem as follows. For a given interface crack problem, the companion problem is formulated and solved using the finite element method. Mode I and II stress intensity factors are obtained using the modified virtual crack closure method. The universal relation is next used to obtain the corresponding interface stress intensity factors for the original interface crack problem. An example problem involving a finite interface crack between two semi-infinite blocks is considered for which analytical solutions exist. It is shown that the method described above provides very acceptable results.

On the Multiscale Finite Element Analysis for Interfacial Fracture in Cu/Low-K Interconnects

2007 ◽  
Author(s):  
Tz-Cheng Chiu ◽  
Huang-Chun Lin
Keyword(s):  
Thin Film ◽  
Fracture Mechanics ◽  
Interface Crack ◽  
Integrated Circuit ◽  
Flip Chip ◽  
Thermal Loading ◽  
Global Analysis ◽  
Crack Problem ◽  
Element Analysis ◽  
Low K

The interface crack problem in integrated circuit devices was considered by using global and local modeling approach. In the global analysis the thin film interconnect was modeled by a homogenized layer with material constants obtained from representative volume element (RVE) analysis. Local analyses were then considered to determine fracture mechanics parameters. It was shown that the multiscale model with RVE approach gives accurate fracture mechanics parameters for an interface crack under either thermal or mechanical loads; while significant error was observed when the thin film layers are ignored in the global analysis. The problem of an interface crack between low-k dielectric and etch-stop thin film in a flip-chip package under thermal loading was also investigated as an application example of the multiscale modeling.

Singularities, interfaces and cracks in dissimilar anisotropic media

1990 ◽  
Vol 427 (1873) ◽  
pp. 331-358 ◽  
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Elastic Anisotropy ◽  
Homogeneous Medium ◽  
Interfacial Crack ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Mode Iii ◽  
Crack Problems

For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.

scholarly journals A molecular-dynamic approach to interface crack problem.

1991 ◽  
Vol 57 (535) ◽  
pp. 678-685 ◽  
Author(s):  
Tadatomo SUGA ◽  
Akira FUNAHASHI ◽  
Yutaka TAKAHASHI
Keyword(s):  
Molecular Dynamic ◽  
Interface Crack ◽  
Crack Problem ◽  
Dynamic Approach
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