scholarly journals Oscillatory Singularity Behaviors Near Interface Crack Tip for Mode II of Orthotropic Bimaterial

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiaomei Yang ◽  
Weiyang Yang ◽  
Junlin Li ◽  
Xuexia Zhang
Keyword(s):  
Interface Crack ◽  
Linear Independence ◽  
Linear Equations ◽  
Crack Tip ◽  
Analytic Solutions ◽  
Mode Ii ◽  
Crack Tip Field ◽  
Fracture Behaviors ◽  
Stress Functions ◽  
Singularity Exponent

The fracture behaviors near the interface crack tip for mode II of orthotropic bimaterial are discussed. The oscillatory singularity fields are researched. The stress functions are chosen which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions and linear independence, the system of twelve nonhomogeneous linear equations is derived. According to the condition for the system of nonhomogeneous linear equations which has a solution, the singularity exponent is determined. Total coefficients are found by means of successive elimination of the unknowns. The theoretical formulae of stress intensity factors and analytic solutions of stress field near the interface crack tip are obtained. The crack tip field is shown by figures.

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.

Crack-tip field on mode II interface crack of double dissimilar orthotropic composite materials

2009 ◽  
Vol 30 (12) ◽  
pp. 1489-1504 ◽  
Author(s):  
Xue-xia Zhang ◽  
Xiao-chao Cui ◽  
Wei-yang Yang ◽  
Jun-lin Li
Keyword(s):  
Composite Materials ◽  
Interface Crack ◽  
Crack Tip ◽  
Mode Ii ◽  
Crack Tip Field ◽  
Orthotropic Composite

The Elastic-Viscoplastic Field Near Mode II Dynamic Propagating Crack-Tip of Interface in Double Dissimilar Materials

2010 ◽  
Vol 97-101 ◽  
pp. 625-628
Author(s):  
Wen Yan Liang ◽  
Zhen Qing Wang ◽  
Hong Qing Lv
Keyword(s):  
Interface Crack ◽  
Crack Tip ◽  
Dissimilar Materials ◽  
Viscosity Coefficient ◽  
Mode Ii ◽  
Crack Tip Field ◽  
Displacement Potential ◽  
Viscosity Effect ◽  
Dynamic Propagating ◽  
Propagating Crack

The existence of viscosity effect at the interface of double dissimilar materials has an important impact to the distribution of interface crack-tip field and the properties variety of the interface itself. The singular is considered in crack-tip, and the elastic-viscoplastic governing equations of double dissimilar materials at quasi-static propagating interface crack-tip field are established. The displacement potential function and boundary condition of interface crack-tip are introduced, and the numerical analysis of rigid-elastic viscoplastic interface for mode II are worked out. The stress-strain fields are obtained at the crack-tip and the variations of solutions are discussed according to each parameter. The numerical results show that the viscosity effect is a main factor of interface propagating crack-tip field, and the interface crack-tip is a viscoplastic field that is governed by viscosity coefficient、Mach number and singular factor.

Stress Singularities near Interface Crack Tip for Mode II of Orthotropic Bi-Material

2014 ◽  
Vol 1004-1005 ◽  
pp. 473-478
Author(s):  
Mu Yang Li ◽  
Jun Lin Li ◽  
Xiu Feng Xie
Keyword(s):  
Composite Material ◽  
Interface Crack ◽  
Crack Tip ◽  
Mode Ii ◽  
Stress Singularities ◽  
Intensity Factors ◽  
Complex Singularity ◽  
Singularity Exponents ◽  
Analytic Expressions ◽  
Stress Functions

Using the method of composite material complex and constructing new stress functions with complex singularity exponents, the problem of singularities near interface crack tip for mode II of orthotropic bi-material is studied. Boundary value problems of generalized bi-harmonic equations can be solved with the help of boundary conditions, then four kinds of stress singularities are deduced, respectively, such as the constant singularity at λ=-1/2, the non-constant singularity at λ=-1/2+ε , the constant oscillation singularity at λ=-1/2+iε, and non-constant oscillation singularity at λ=-1/2+c+iε. For each case, the analytic expressions for stress intensity factors near the central-penetrated interface crack tip for mode II of orthotropic bi-material are obtained.

The Steady-State Growing Crack-Tip Field Characteristics of Mode I Elastic-Viscoplastic/Rigid Interface Cracks

2010 ◽  
Vol 452-453 ◽  
pp. 113-116
Author(s):  
Wen Yan Liang ◽  
Zhen Qing Wang ◽  
Hong Qing Lv
Keyword(s):  
Interface Crack ◽  
Crack Tip ◽  
Dissimilar Materials ◽  
Viscosity Coefficient ◽  
Mode I ◽  
Crack Tip Field ◽  
Displacement Potential ◽  
Viscosity Effect ◽  
Singularity Exponent ◽  
Rigid Interface

The existence of viscosity effect at the interface of double dissimilar materials has an important impact to the distribution of interface crack-tip field and the properties variety of the interface itself. The singularity and viscosity are considered in crack-tip, and the elastic-viscoplastic governing equations of double dissimilar materials at interface crack-tip field are established. The displacement potential function and boundary condition of interface crack-tip are introduced, and the numerical analysis of elstic-viscoplastic/rigid interface for mode I are worked out. The stress-strain fields are obtained at the crack-tip and the variation rules of solutions are discussed according to each parameter. 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.

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.

Crack-Tip Field of a Supersonic Bimaterial Interface Crack

2002 ◽  
Vol 69 (5) ◽  
pp. 693-696 ◽  
Author(s):  
J. Wu
Keyword(s):  
Interface Crack ◽  
Crack Tip ◽  
Bimaterial Interface ◽  
Crack Tip Field ◽  
Asymptotic Field ◽  
Homogeneous Materials ◽  
Supersonic Regime ◽  
Bimaterial Interface Crack

The sextic approach was used to investigate the asymptotic field of a bimaterial interface crack in the entire supersonic regime and extended to include the combination of isotropic and homogeneous materials, where the sextic method had been considered difficult. Application to typical systems was demonstrated.

Study on Stress and Strain Field of Mode II Quasi-Static Growing Crack in Pressure-Sensitive Dilatant Material

2009 ◽  
Vol 417-418 ◽  
pp. 665-668
Author(s):  
Yong Yang ◽  
Ning Li ◽  
Li Qiang Tang
Keyword(s):  
Poisson Ratio ◽  
Crack Tip ◽  
Asymptotic Solutions ◽  
Mode Ii ◽  
Stress And Strain ◽  
Viscous Effect ◽  
Crack Tip Field ◽  
Pressure Sensitive ◽  
Stress Mode ◽  
Growing Crack

A mechanical model of the pressure-sensitive dilatant material is established in order to investigate the viscous effect in quasi-static growing crack-tip field. The constitutive equations on the pressure-sensitive dilatant material are deducted. Through asymptotic analysis, it is shown that in the stable creep growing stage, the elastic-deformation and the visco-deformation are equally dominant in the near-tip field, as . The asymptotic solutions of separative variable in the crack-tip field of plane stress mode II quasi-static are aslo obtained. According to numerical calculation, the curves of stress, strain and displacement in terms of various parameters are given. The asymptotic solutions of quasi-static growing crack-tip field gained here can conveniently degenerate the incompressible case, when the Poisson ratio , named as HR field. The conclusions can provide the references for further studying the dynamic growing crack-tip field in the pressure-sensitive dilatant material.

A Crack in an Electrode Layer between Two Dissimilar Piezoelectric Materials

2007 ◽  
Vol 353-358 ◽  
pp. 231-234
Author(s):  
Hyeon Gyu Beom ◽  
Y.H. Kim ◽  
C.K. Yoon ◽  
Chong Du Cho
Keyword(s):  
Closed Form ◽  
Interface Crack ◽  
Analytic Functions ◽  
Piezoelectric Materials ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Crack Tip Field ◽  
Electrode Layer ◽  
Finite Crack ◽  
Electromechanical Loading

A crack on the conductive interface between two dissimilar piezoelectric ceramics under electromechanical loading is investigated. The closed form of the singular crack tip fields for the interface crack is derived here using an analysis based on analytic functions. It is shown that the interfacial crack-tip field consists of a pair of oscillatory singularities. A closed form of the solution for a finite crack on the conductive interface between dissimilar piezoelectric media is also derived.

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