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

2020 ◽  
Author(s):  
Carsten Broese ◽  
Jan Frischmann ◽  
Charalampos Tsakmakis
Keyword(s):  
Crack Tip ◽  
Gradient Elasticity ◽  
Mode I ◽  
Mode Ii ◽  
Stress And Strain ◽  
Governing Equations ◽  
Crack Tip Fields ◽  
Mode Ii Crack

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.

Nonlinear mode II crack-tip fields for some Hookean materials

1986 ◽  
Vol 6 (3) ◽  
pp. 217-222 ◽  
Author(s):  
C.L. Chow ◽  
C. Ouyang ◽  
X.Q. Lu
Keyword(s):  
Crack Tip ◽  
Mode Ii ◽  
Crack Tip Fields ◽  
Nonlinear Mode ◽  
Mode Ii Crack

The Genesis of Echelon-Mode-I Cracks in the Neighbourhood of a Mode-II-Crack Tip under Uniaxial Compression

2003 ◽  
Vol 251-252 ◽  
pp. 327-332 ◽  
Author(s):  
Akihide Saimoto ◽  
Yoshio Imai ◽  
Toshiyuki Hashida
Keyword(s):  
Uniaxial Compression ◽  
Crack Tip ◽  
Mode I ◽  
Mode Ii ◽  
Mode Ii Crack

Asymptotic Crack-Tip Fields for Perfectly Plastic Solids Under Plane-Stress and Mixed-Mode Loading Conditions

1990 ◽  
Vol 57 (3) ◽  
pp. 635-638 ◽  
Author(s):  
P. Dong ◽  
J. Pan
Keyword(s):  
Plane Stress ◽  
Mixed Mode ◽  
Crack Tip ◽  
Mode I ◽  
Mode Ii ◽  
Crack Tip Field ◽  
Crack Tip Fields ◽  
Perfectly Plastic ◽  
Mixed Mode Crack ◽  
Small Constant

In this paper, we first discuss some of the properties of the crack-tip sectors for perfectly plastic materials under plane-stress conditions. Then starting with the plane-stress mixed-mode crack-tip fields suggested by Shih (1973), we assemble these sectors in a slightly different manner from those in Shih (1973). The missing governing equations needed to completely specify the crack-tip fields for both near mode I and near mode II mixed-mode loadings are derived. The mode I crack-tip field, as the limit of the near mode I cases, differs from Hutchinson’s solution (1968) by the appearance of a small constant stress sector ahead of the crack tip. In addition, the relevance of the solutions of the near mode II cases to some interesting features of the mixed-mode crack-tip fields, as suggested by Budiansky and Rice (1973), is also discussed.

Asymptotic Crack-Tip Fields in Perfectly Plastic Solids Under Mixed Mode II/III Loading Conditions

2006 ◽  
Vol 129 (4) ◽  
pp. 664-669
Author(s):  
J. Pan ◽  
P.-C. Lin
Keyword(s):  
Mixed Mode ◽  
Crack Tip ◽  
Shear Loading ◽  
Mode Ii ◽  
Pure Mode ◽  
Loading Conditions ◽  
Mode Iii ◽  
Plane Shear ◽  
Crack Tip Fields ◽  
Perfectly Plastic

In this paper, governing equations and solutions for asymptotic singular and nonsingular crack-tip sectors in perfectly plastic materials are first summarized under combined in-plane and out-of-plane shear loading conditions. The crack-tip fields under mixed mode II/III loading conditions are then investigated. An assembly of crack-tip sectors is adopted with stress discontinuities along the border of the two constant stress sectors. The solutions of the crack-tip fields under pure mode II, mixed mode II/III, and nearly pure mode III loading conditions are presented. The trends of the angular variations of the mixed mode II/III crack-tip stresses agree with those of the available computational analysis and the asymptotic analysis for low strain hardening materials. The pure mode II crack-tip stresses are similar to those of Hutchinson, and the nearly pure mode III stresses are similar to those of the pure mode III crack-tip field of Rice.

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