Finite Element Solutions for Crack-Tip Behavior in Small-Scale Yielding

1976 ◽  
Vol 98 (2) ◽  
pp. 146-151 ◽  
Author(s):  
D. M. Tracey
Keyword(s):  
Finite Element ◽  
Plastic Region ◽  
Crack Tip ◽  
Small Scale ◽  
Element Formulation ◽  
Small Scale Yielding ◽  
Field Problem ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Scale Yielding

The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.

Small Scale Yielding at a Crack Normal to the Interface Between an Elastic and a Yielding Material

1991 ◽  
Vol 239 ◽  
Author(s):  
Ming Y. He ◽  
R. M. McMeeking ◽  
Ning T. Zhang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Brittle Material ◽  
Crack Tip ◽  
Asymptotic Solutions ◽  
Ductile Material ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Element Analysis ◽  
Scale Yielding

ABSTRACTBy using the elastic singular field as a prescribed loading condition, small scale yielding solutions are obtained for a crack normal to the interface between a brittle and a ductile material. Results for both a crack in the brittle material and one in the ductile material are obtained by finite element analysis. The crack tip fields obtained by the finite element analysis are compared with the asymptotic solutions. It is found that near the tip the stress fields approach the asymptotic solutions. If the crack is in the brittle material, the high triaxial stresses are developed near the interface ahead of the crack tip.

scholarly journals Elastic-plastic analysis of crack on bimaterial interface

2005 ◽  
Vol 32 (3) ◽  
pp. 193-207
Author(s):  
Ruzica Nikolic ◽  
Jelena Veljkovic
Keyword(s):  
Phase Angle ◽  
Plastic Material ◽  
Crack Tip ◽  
Bimaterial Interface ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Elastic Plastic ◽  
Singular Form ◽  
Scale Yielding ◽  
New Phase

In this paper are presented solutions for the stress and dis?placement fields for a crack that lies along the interface of an elastic and elastic - plastic material and for a crack between two different elastic - plastic materials. These solutions are obtained using the J2-deformation theory with the power - law strain hardening. In this paper results are described for a small scale yielding at the crack tip. The near tip fields do not have a separable singular form, of the HRR type fields, as in homogeneous media, they do, however bare interesting similarities to certain mixed -mode HRR fields. Under the small scale yielding the elastic fields are specified by a complex stress intensity factor and phase angle loading, while plastic field is characterized by a new phase angle. The size of plastic zone in plane strain and plane stress and displacement fields at the crack tip for the new phase angle are obtained. The crack tip opens smoothly and the crack opening displacement is scaled by the J-integral. The whole analysis is performed by application of the Mathematica symbolic programming routine.

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.

Plastic Stress Intensity Factors for Small Scale Yielding in Antiplane Shear by Caustics

1982 ◽  
Vol 49 (4) ◽  
pp. 754-760 ◽  
Author(s):  
P. S. Theocaris ◽  
C. I. Razem
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Antiplane Shear ◽  
Elastic Behavior ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Scale Yielding ◽  
Plastic Stress

The KIII-stress intensity factor in an edge-cracked plate submitted to antiplane shear may be evaluated by the reflected caustic created around the crack tip, provided that a purely elastic behavior exists at the crack tip [1]. For a work-hardening, elastic-plastic material, when stresses at the vicinity of the crack tip exceed the yield limit of the material, the new shape of caustic differs substantially from the corresponding shape of the elastic solution. In this paper the shape and size of the caustics created at the tip of the crack, when small-scale yielding is established in the vicinity of the crack tip, were studied, based on a closed-form solution introduced by Rice [2]. The plastic stress intensity factor may be evaluated from the dimensions of the plastic caustic. Experimental evidence with cracked plates made of opaque materials, like steel, corroborated the results of the theory.

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