A Two-Parameter Description of the Behaviour of a Process Zone at a Crack Tip: Part I — General Theory

2004 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Process Zone ◽  
Crack Tip ◽  
Relative Displacement ◽  
Small Scale ◽  
Zone Size ◽  
Small Scale Yielding ◽  
Elastic Crack ◽  
Scale Yielding

In quantifying the behaviour of a sharp crack, considerable use has been made of the cohesive process zone description of the non-linear micro-mechanistic processes that are operative in the immediate vicinity of a crack tip. With this description, the non-linearity is modelled so that it is confined to an infinitesimally thin strip, and the analysis is considerably simplified if the description is coupled with the assumption that the stress is uniform within the process zone. When the process zone size is very small compared with the crack size and other dimensions associated with a configuration (the so-called small-scale yielding situation), the crack tip stress intensity factor defines the various parameters associated with the crack: crack tip opening displacement vT, process zone size s, crack opening area A and the effective opening area AD of the process zone. The stress intensity factor relates to the first term in the expansion of the expression for the relative displacement of the faces of an elastic crack, or the expression for the stress ahead of an elastic crack. This paper shows how the various crack parameters vT, s, A and AD are also related to the second term in the expansion of the relative displacement expression, when we relax the assumption that the process zone is very small, i.e. when we proceed beyond the small-scale yielding situation.

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.

A Better Estimation of Plastic Zone Size at the Crack Tip Beyond Irwin's Model

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Y. J. Jia ◽  
M. X. Shi ◽  
Y. Zhao ◽  
B. Liu
Keyword(s):  
Plastic Zone ◽  
Crack Tip ◽  
Plastic Zone Size ◽  
Quantitative Relation ◽  
Small Scale ◽  
Crack Plane ◽  
Zone Size ◽  
Small Scale Yielding ◽  
Scale Yielding ◽  
Remote Stress

Irwin's model on plastic zone at the crack tip is discussed in many fracture mechanics textbooks. However, we found in Irwin's model that the internal resultant force on the crack plane and the one applied in remote field are not strictly balanced. This imbalance leads to the error in the scenario of small scale yielding, and an improper finite plastic zone size (PZS) is predicted when the remote stress approaches the yielding strength. In this paper, an improved model is developed through surrendering some main assumptions used in Irwin's model and an infinite PZS is then predicted as the remote stress goes up close to yielding strength, which implies that this estimation can be applied to situations with large scale yielding. In small scale yielding cases, the new estimation of PZS agrees well with finite element simulation results. In addition, a more accurate quantitative relation between the PZS and the effective stress intensity factor is derived, which might help characterize fracture behaviors in engineering applications.

Estimation of K in Ductile CT and SENB Specimens under LEFM and SSY Regimes by J Integral Method: A Review

2013 ◽  
Vol 275-277 ◽  
pp. 242-246
Author(s):  
Bhimsen Karadin ◽  
Nilesh Satonkar ◽  
Sunil Bhat
Keyword(s):  
Integral Method ◽  
Crack Tip ◽  
Small Scale ◽  
J Integral ◽  
Small Scale Yielding ◽  
Critical Limit ◽  
Ductile Materials ◽  
Ductile Mode ◽  
Scale Yielding ◽  
Material Fracture

Stress intensity factor (K) is the measure of severity of stress at the crack tip. When K exceeds the critical limit (i.e., the material fracture toughness), the crack grows. K is valid in brittle materials (LEFM) and to some extent in ductile materials also provided there is small scale yielding (SSY) at the crack tip. The paper reviews the numerical methodology to obtain KI of ductile, Mode I cracked, CT and SENB test specimens in LEFM and SSY regimes with the help of J integral method. The numerical values are successfully compared with the theoretical values.

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.

A Two-Parameter Description of the Behaviour of a Process Zone at a Crack Tip: Relation Between the Parameters

2005 ◽  
Author(s):  
E. Smith
Keyword(s):  
Process Zone ◽  
Crack Opening ◽  
Crack Tip ◽  
Relative Displacement ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Power Series Expansions ◽  
Elastic Crack ◽  
Crack Tip Opening ◽  
Crack Faces

The relative displacement of the crack faces and the tensile stress ahead of a Mode I elastic crack tip can be expressed, in the immediate vicinity of the tip, by two-term power series expansions, the two terms being associated with the stress intensity factor KI and a dimensionless parameter g0. These parameters feature prominently in cohesive process zone models of a crack tip with regard to the crack tip opening displacement vT, process zone size s, the crack opening area A and the effective opening area AD of the process zone. This paper shows that KI and g0 depend upon each other via a relation which is dependent upon the geometrical configuration but is independent of the configuration’s loading pattern.

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