Path-dependent J-integral evaluations around an elliptical hole for large deformation theory

2016 ◽  
Vol 25 (3-4) ◽  
pp. 77-81
Author(s):  
David J. Unger
Keyword(s):  
Work Hardening ◽  
Deformation Theory ◽  
Elliptical Hole ◽  
Exact Expression ◽  
J Integral ◽  
Resistance Curve ◽  
Hardening Material ◽  
Initial Stage ◽  
Path Dependent ◽  
Crack Tip Blunting

AbstractAn exact expression is obtained for a path-dependent J-integral for finite strains of an elliptical hole subject to remote tensile tractions under the Tresca deformation theory for a thin plate composed of non-work hardening material. Possible applications include an analytical resistance curve for the initial stage of crack propagation due to crack tip blunting.

Deformation Versus Modified J-Integral Resistance Curves for Ductile Materials

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Xian-Kui Zhu ◽  
Poh-Sang Lam
Keyword(s):  
Deformation Theory ◽  
Size Dependence ◽  
Fracture Property ◽  
J Integral ◽  
Resistance Curve ◽  
Structural Components ◽  
Ductile Materials ◽  
Size Dependent ◽  
Resistance Curves ◽  
Better Than

The J-integral resistance curve (or J-R curve) is an important fracture property of materials and has gained broad applications in assessing the fracture behavior of structural components. Because the J-integral concept was proposed based on the deformation theory of plasticity, the J-R curve is a deformation-based result. It has been known that the J-R curves of a material depend on specimen size and geometry; therefore, a modified J-integral or Jm was proposed to minimize the size dependence. Extensive experiments have shown that the Jm-R curves might remain size-dependent and could not behave better than the traditional deformation J-R curves. To date, however, it is noticed that the Jm-R curves were still used as “size-independent” results in some fracture mechanics analyses. It is necessary to revisit this topic for further clarification. This paper presents a brief review on the development of deformation and modified J-integral testing, and obtains a simple incremental Jm-integral equation. It is followed by typical experimental results with discussions on the issues of constraint or size dependence of J-R and Jm-R curves for different steels and specimens. Finally, a recommendation is made on properly selecting a resistance curve in the fracture analysis.

Fully Plastic Asymmetric Edge Crack Under Longitudinal Shear

1977 ◽  
Vol 44 (2) ◽  
pp. 255-258
Author(s):  
J. C. Amazigo
Keyword(s):  
Finite Length ◽  
Work Hardening ◽  
Edge Crack ◽  
Longitudinal Shear ◽  
Material Behavior ◽  
J Integral ◽  
Hardening Material ◽  
Stress Strain Relation ◽  
Flow Theories ◽  
Hodograph Transformation

The problem of a semi-infinite work-hardening material with a finite length asymmetric edge crack subjected to uniform remote longitudinal shear is solved exactly by the use of hodograph transformation and the Wiener-Hopf technique. The material behavior is governed by a pure power-hardening stress-strain relation and for monotone loading the results are valid for both deformation and flow theories of plasticity. Numerical values are obtained for the path independent J integral for several values of both the angle of asymmetry and the power-hardening exponent.

J-Integral Analysis of Three-Point Bend Specimen

1989 ◽  
Vol 111 (2) ◽  
pp. 132-137 ◽  
Author(s):  
A. Zahoor
Keyword(s):  
Deformation Theory ◽  
Displacement Curve ◽  
J Integral ◽  
Hardening Material ◽  
Resistance Curves ◽  
Point Bend ◽  
Special Case ◽  
Η Factor ◽  
Uncracked Ligament ◽  
Require Data

A J-integral solution is derived for the three-point bend [SE(B)] specimen. The solution allows analysis for a/W greater than 0.2. The solution is based on an approach that does not require an assumption of net-section yielding in the remaining uncracked ligament. Solutions are presented for both the deformation theory J and modified J. These solutions are suitable for J-resistance curve analysis and require data from only one specimen. Solution for a special case of power law hardening material is presented. Consequences of the separability assumption between load-point displacement and crack length on the resulting J solution are discussed. This work indicates that the plastic η factor from previous solutions is significantly underestimated for a/W less than 0.6. Numerical results show that Jd and JM resistance curves are closer than those obtained from previous solutions. A solution for normalizing the load-displacement curve is also presented.

J-integral studies of crack initiation and crack tip-blunting of phenolphthalein polyether ketone

1994 ◽  
Vol 54 (3) ◽  
pp. 375-383 ◽  
Author(s):  
Yanchun Han ◽  
Yuming Yang ◽  
Binyao Li ◽  
Zhiliu Feng
Keyword(s):  
Crack Initiation ◽  
Crack Tip ◽  
J Integral ◽  
Crack Tip Blunting

Path-Independent Ĵ-Integral Based on Finite Deformation Theory

2013 ◽  
Vol 577-578 ◽  
pp. 189-192
Author(s):  
Zong Min Liu ◽  
Ji Ze Mao ◽  
Hai Yan Song
Keyword(s):  
Finite Deformation ◽  
Deformation Theory ◽  
Theoretical Foundation ◽  
Dynamic Crack Propagation ◽  
Large Strains ◽  
Dynamic Crack ◽  
J Integral ◽  
Base Forces ◽  
Finite Deformation Theory ◽  
Theory Base

For a finite deformation body, there are large strains and displacements on the crack tip. So it is necessary to study-integral based on finite deformation theory. Base forces theory is a new theory for describing finite deformation. In this paper, -integral based on base forces theory are presented. This work provides a new theoretical foundation for studying dynamic crack propagation.

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