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.

scholarly journals Mixed-mode crack tip fields in a polycrystalline aluminum alloy

2019 ◽  
Vol 300 ◽  
pp. 11004 ◽  
Author(s):  
Marcel Wicke ◽  
Angelika Brueckner-Foit
Keyword(s):  
Mixed Mode ◽  
Crack Tip ◽  
Strain Partitioning ◽  
Crack Tip Field ◽  
Polycrystalline Aluminum ◽  
Digital Twin ◽  
Crack Tip Fields ◽  
Mixed Mode Crack ◽  
Threshold Regime ◽  
Near Threshold

Carefully performed experiments with long cracks in the near-threshold regime have shown that the crack tip field of these cracks significantly deviate from the expected mode-I butterfly-shaped ones and resemble strongly to mixed-mode crack tip fields. A simulation study using a crystal plasticity (CP) approach has been utilized in order to understand this phenomenon. To this end, a digital twin of an aluminum sample fatigued in the near-threshold regime was generated with the help of electron backscatter diffraction (EBSD) and X-ray tomography. Once set-up, the digital twin was loaded in uniaxial tension using the fast spectral solver implemented in the Düsseldorf Advanced Material Simulation Kit (DAMASK). The versatility of this experimental-computational approach for studying the strain partitioning at the crack tip is demonstrated in this work.

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.

Asymptotic Crack-Tip Fields in Perfectly Plastic Solids Under Combined In-Plane and Out-of-Plane Shear Loading Conditions

2005 ◽  
Author(s):  
J. Pan
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 non-singular 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.

Mixed Mode I/III Crack-Tip Fields for Perfectly Plastic Mises Materials

2007 ◽  
Author(s):  
J. Pan
Keyword(s):  
Mixed Mode ◽  
Crack Tip ◽  
Shear Loading ◽  
Mode I ◽  
Pure Mode ◽  
Loading Conditions ◽  
Plane Shear ◽  
Tensile Stresses ◽  
Crack Tip Fields ◽  
Perfectly Plastic

In this paper, governing equations and solutions for asymptotic singular and non-singular crack-tip sectors in perfectly plastic Mises materials are first reviewed under combined in-plane and out-of-plane shear loading conditions. The crack-tip fields under mixed mode I/III loading conditions are then investigated. One assembly of four crack-tip plastic sectors is adopted with stress discontinuities along the border of two constant stress sectors. The solutions of the crack-tip fields under pure mode I and mixed mode I/III loading conditions are presented. The crack-tip fields under pure mode I and mixed mode I/III loading conditions give fully-plastic solutions with various hydrostatic tensile stresses ahead of the crack tip. The characteristics of the mode I limits of fully plastic crack-tip fields with different hydrostatic tensile stresses ahead of the crack tip agree well the past computational results under pure mode I with different constraint conditions.

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