Small-Scale Yielding Analysis of Mixed Mode Plane-Strain Crack Problems

2009 ◽  
pp. 187-187-24 ◽  
Author(s):  
CF Shih
Keyword(s):  
Plane Strain ◽  
Mixed Mode ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Crack Problems ◽  
Scale Yielding ◽  
Plane Strain Crack

Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I—Small Scale Yielding

1988 ◽  
Vol 55 (2) ◽  
pp. 299-316 ◽  
Author(s):  
C. F. Shih ◽  
R. J. Asaro
Keyword(s):  
Phase Angle ◽  
Mixed Mode ◽  
Numerical Solutions ◽  
Crack Tip ◽  
Small Scale ◽  
Plastic Behavior ◽  
Small Scale Yielding ◽  
Elastic Plastic ◽  
Crack Problems ◽  
Scale Yielding

Full-field numerical solutions for a crack which lies along the interface of an elastic-plastic medium and a rigid substrate are presented. The solutions are obtained using a small strain version of the J2-deformation theory with power-law strain hardening. In the present article, results for loading causing only small scale yielding at the crack tip are described; in subsequent articles the mathematical structure of the crack-tip fields under small scale yielding and results for contained yielding and fully plastic behavior will be presented. We find that although the near-tip fields do not appear to have a separable singular form, of the HRR-type fields as in homogeneous media, they do, however, bear interesting similarities to certain mixed-mode HRR fields. Under small scale yielding, where the remote elastic fields are specified by a complex stress-concentration vector Q = |Q|eiφ with φ being the phase angle between the two in-plane stress modes, we find that the plastic fields are members of a family parameterized by a new phase angle ξ, ≡ φ + εln(QQ/σ02L), and the fields nearly scale with the well-defined energy release rate as evaluated by the J-integral. Here σ0 is the reference yield stress and L is the total crack length (or a relevant length of the crack geometry). Numerical procedures appropriate for solving a general class of interface crack problems are also presented. A description of a numerical method for extracting the mixed mode stress intensities for cracks at interfaces and in homogeneous isotropic or anisotropic media, is included.

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