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.

Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part II—Structure of Small-Scale Yielding Fields

1989 ◽  
Vol 56 (4) ◽  
pp. 763-779 ◽  
Author(s):  
C. F. Shih ◽  
R. J. Asaro
Keyword(s):  
Plastic Zone ◽  
Crack Tip ◽  
Mathematical Structure ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Crack Face ◽  
Crack Tip Fields ◽  
Bimaterial Interfaces ◽  
Scale Yielding ◽  
Crack Face Contact

In Part I we found that although the near tip fields of cracks on bimaterial interfaces do not have a separable form of the HRR type, they appear to be nearly separable in an annular zone within the plastic zone. Furthermore, the fields bear strong similarities to mixed mode HRR fields for homogeneous medium. Based on our numerical results, we have been able to identify a clear mathematical structure. We found that the small-scale yielding crack tip fields are members of a family parameterized by a near tip phase angle ξ, and that the fields nearly scale with the value of the J-integral. In Part II, the original derivation of the mathematical structure of the small-scale yielding fields is elaborated upon. The issue of crack face contact is addressed and the phenomenology is described in terms of the phase parameter ξ. Crack tip plastic deformation results in an open crack for a range of ξ which is nearly symmetric about the state corresponding to pure remote tension. Plane-strain plastic zones and crack tip fields for the complete range of ξ are presented. Over distances comparable to the size of the dominant plastic zone, the stress levels that can be achieved are limited by the yield stress of the weaker (lower yield strength) material. On the other hand, the stresses well within the plastic zone are governed by the strain-hardening behavior of the more plastically compliant (lower strain-hardening) material. We observe that the extent of the annular zone where the fields are nearly separable (i.e., of the HRR form) is dependent on the remote load combinations and the material combination. When the tractions on the interface are predominantly tensile, there are no indications of crack face contact over any length scale of physical relevance. Instead, the crack tip opens smoothly and crack tip fields as well as the crack opening displacement are scaled by the J-integral. The paper concludes with a discussion on the range of load combinations which could be applied to two fracture test specimen geometries to obtain valid fracture toughness data.

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.

Analytical Prediction Model for Fatigue Crack Propagation Rate under Tension-Compression Loading

2013 ◽  
Vol 842 ◽  
pp. 455-461
Author(s):  
Yu Sha ◽  
Shi Gang Bai ◽  
Ya Hui Wang
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Plastic Zone ◽  
Crack Propagation ◽  
Compressive Stress ◽  
Fatigue Crack Propagation ◽  
Crack Tip ◽  
Plastic Zone Size ◽  
Zone Size ◽  
Compression Loading

Elastic–plastic finite element analyses have been performed to study the compressive stress effect on fatigue crack growth under applied tension–compression loading. The near crack tip stress, crack tip opening displacement and crack tip plastic zone size were obtained for a kinematic hardening material. The results have shown that the near crack tip local stress, displacement and reverse plastic zone size are controlled by the maximum stress intensity factors Kmax and the applied compressive stress σmaxcom under tension–compression. Based on the finite element analysis results, a fatigue crack propagation model using Kmax and σmaxcom as a parameters under tension–compression loading has been developed.The models under tension–compression loading agreed well with experimental observations.

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