A study of dynamic caustics around running interface crack tip

1999 ◽  
Vol 15 (2) ◽  
pp. 182-192 ◽  
Author(s):  
Xiong Chunyang ◽  
Yao Xuefeng ◽  
Fang Jing
Keyword(s):  
Interface Crack ◽  
Crack Tip ◽  
Dynamic Caustics

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.

Stress Field of Semi-Infinite Interface Crack Tip of Double Dissimilar Orthotropic Composite Materials

2010 ◽  
Vol 97-101 ◽  
pp. 1223-1226
Author(s):  
Jun Lin Li ◽  
Shao Qin Zhang
Keyword(s):  
Composite Material ◽  
Composite Materials ◽  
Interface Crack ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Stress Fields ◽  
Displacement Fields ◽  
Orthotropic Composite ◽  
Stress Functions ◽  
Secular Equations

The problem of orthotropic composite materials semi-infinite interfacial crack was studied, by constructing new stress functions and employing the method of composite material complex. In the case that the secular equations’ discriminates the and theoretical solutions to the stress fields and the displacement fields near semi-infinite interface crack tip without oscillation and inter-embedding between the interfaces of the crack are obtained, a comparison with finite element example was done to verify the correction of theoretical solution.

Fracture Analysis near Interface Crack Tip for Mode I of Orthotropic Bi-Materials

2012 ◽  
Vol 490-495 ◽  
pp. 3242-3252
Author(s):  
An Qiang Dong ◽  
Wei Yang Yang ◽  
Jun Lin Li
Keyword(s):  
Interface Crack ◽  
Linear Equations ◽  
Complex Function ◽  
Stress Singularity ◽  
Crack Tip ◽  
Analytic Solutions ◽  
Mode I ◽  
Biharmonic Equations ◽  
Singularity Exponents ◽  
Orthotropic Composites

The mechanical behaviors near interface crack tip for mode I of double dissimilar orthotropic composites are studied. By translating governing equations into generalized biharmonic equations, the stress functions containing two stress singularity exponents are found with the help of a complex function method. Based on the boundary conditions, two systems of non-homogeneous linear equations are obtained. Through solving these systems two real stress singularity exponents are determined under appropriate condition of bimaterial engineering parameters. By the uniqueness theorem of limit,both the theoretical formulae of stress intensity factors and analytic solutions of stress field and displacement field near interface crack tip are deduced.

Elastic-Viscoplastic Field at the Mixed-Mode Crack-Tip under Compression and Shear

2011 ◽  
Vol 488-489 ◽  
pp. 452-455
Author(s):  
Wen Yan Liang ◽  
Zhen Qing Wang ◽  
Fang Liu
Keyword(s):  
Interface Crack ◽  
Mixed Mode ◽  
Crack Tip ◽  
Viscosity Coefficient ◽  
Crack Tip Field ◽  
Displacement Potential ◽  
Dynamic Propagation ◽  
Singularity Exponent ◽  
Crack Interface ◽  
Main Factor

In the present paper, the mechanical model of dynamic propagation interface crack of the compression-shear mixed mode is proposed by using the elastic-viscoplastic constitutive model. Then the governing equations of propagation crack interface at crack tip are given. The numerical analysis is accomplished for the interface crack of compression-shear mixed mode by introducing a displacement potential function and some boundary conditions at interface crack tip. The distributed regularities of stress-strain fields of interface crack tip are discussed with several special parameters. The numerical results show that the viscosity effect is a main factor of interface propagating at crack-tip field, and the interface crack-tip is a viscoplastic field that is governed by viscosity coefficient、Mach number and singularity exponent.

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