Asymptotic solutions of mode I steady growth crack in materials under creep conditions

2015 ◽  
Vol 28 (5) ◽  
pp. 578-591 ◽  
Author(s):  
Qinghua Meng ◽  
Zhenqing Wang
Keyword(s):  
Asymptotic Solutions ◽  
Mode I ◽  
Steady Growth ◽  
Growth Crack

Maximal Crack Tip Shielding by Microcracking

1989 ◽  
Vol 56 (2) ◽  
pp. 279-283 ◽  
Author(s):  
M. Ortiz ◽  
A. E. Giannakopoulos
Keyword(s):  
Crack Tip ◽  
Asymptotic Solutions ◽  
Shielding Effect ◽  
Mode I ◽  
Anisotropic Damage ◽  
Maximum Tension ◽  
Damage Models ◽  
Singular Field ◽  
Crack Tip Shielding

It is shown here that the shielding effect of a distribution of microcracks, i.e., the extent to which they alleviate the severity of a near-tip singular field, is maximized when the microcracks develop normal to the direction of maximum tension. In passing, we derive mode I asymptotic solutions for a class of anisotropic damage models.

Study on Quasi-Static Growing Crack Field in Visco-Elastic Compressible Material

2011 ◽  
Vol 488-489 ◽  
pp. 694-697
Author(s):  
Yong Yang ◽  
Guo Hui Wu ◽  
Li Qiang Tang
Keyword(s):  
Poisson Ratio ◽  
Crack Tip ◽  
Asymptotic Solutions ◽  
Stress Fields ◽  
Mode I ◽  
Mode Ii ◽  
Compressible Material ◽  
Displacement Fields ◽  
Crack Tip Field ◽  
Growing Crack

A mechanical model of the visco-elastic compressible material is established in order to investigate the viscous effect in quasi-static growing crack-tip field. The constitutive equations on the visco-elastic compressible 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 r-1/(n-1). The asymptotic solutions of separative variable in the crack-tip field are aslo obtained. According to numerical calculation, the curves of stress, stain and displacement are given. The results indicate that the near-tip fields are mainly governed by the creep exponent ; the stress fields of mode I and mode II is slightly affected by the elastic compressible deformation; the strain and displacement fields of mode I are deeply affected by the elastic compressible deformation. However, the strain and displacement fields of mode II are less affected by the elastic compressible deformation. The asymptotic solutions of dynamic 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 compressible material.

Dynamic Growing Crack Tip Field in Visco-Elastic Compressible Material

2008 ◽  
Vol 385-387 ◽  
pp. 101-104
Author(s):  
Yong Yang ◽  
Li Qiang Tang ◽  
Yong Wang ◽  
Chen Feng
Keyword(s):  
Poisson Ratio ◽  
Crack Tip ◽  
Asymptotic Solutions ◽  
Stress Fields ◽  
Mode I ◽  
Mode Ii ◽  
Compressible Material ◽  
Displacement Fields ◽  
Crack Tip Field ◽  
Growing Crack

A mechanical model of the visco-elastic compressible material is established in order to investigate the viscous effect in dynamic growing crack-tip field. The constitutive equations on the visco-elastic compressible 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 1 ( 1) n r− − . The asymptotic solutions of separative variable in the crack-tip field are aslo obtained. According to numerical calculation, the curves of stress, stain and displacement are given. The results indicate that the near-tip fields are mainly governed by the creep exponent n and Mach number M ; the stress fields of mode I and mode II is slightly affected by the elastic compressible deformation; the strain and displacement fields of mode I are deeply affected by the elastic compressible deformation. However, the strain and displacement fields of mode II are less affected by the elastic compressible deformation. The asymptotic solutions of dynamic growing crack-tip field gained here can conveniently degenerate the incompressible case, when the Poisson ratio 0.5 ν→ , named as HR field. The conclusions can provide the references for further studying the dynamic growing crack-tip field in compressible material.

scholarly journals Mode-I and Mode-II Crack Tip Fields in Implicit Gradient Elasticity Based on Laplacians of Stress and Strain. Part II: Asymptotic Solutions

2020 ◽  
Author(s):  
Carsten Broese ◽  
Jan Frischmann ◽  
Charalampos Tsakmakis
Keyword(s):  
Gradient Elasticity ◽  
Asymptotic Solutions ◽  
Mode I ◽  
Mode Ii ◽  
Stress And Strain ◽  
Classical Elasticity ◽  
Crack Problems ◽  
Mode Ii Crack ◽  
Model Equations ◽  
Mode Ii Loading

We develop asymptotic solutions for near-tip fields of Mode-I and Mode-II crack problems and for model responses reflected by implicit gradient elasticity. Especially, a model of gradient elasticity is considered, which is based on Laplacians of stress and strain and turns out to be derivable as a particular case of micromorphic (microstrain) elasticity. While the governing model equations of the crack problems are developed in Part I, the present paper addresses analytical solutions for near-tip fields by using asymptotic expansions of Williams’ type. It is shown that for the assumptions made in Part I, the model does not eliminiate the well-known singularities of classical elasticity. This is in contrast to conclusions made elsewhere, which rely upon different assumptions. However, there are significant differences in comparison to classical elasticity, which are discussed in the paper. For instance, in the case of Mode-II loading conditions, the leading terms of the asymptotic solution for the components of the double stress exhibit the remarkable property that they include two stress intensity factors.

Study on Mode I Quasi-Static Growing Crack Field in the Pressure-Sensitive Dilatant Material

2010 ◽  
Vol 452-453 ◽  
pp. 205-208
Author(s):  
Yong Yang ◽  
Guo Hui Wu ◽  
Li Qiang Tang ◽  
Ning Li
Keyword(s):  
Mechanical Model ◽  
Poisson Ratio ◽  
Crack Tip ◽  
Asymptotic Solutions ◽  
Mode I ◽  
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 mode I 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 I 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.

Sign in / Sign up

Export Citation Format

Share Document