scholarly journals Fracture Assessment of U-notches under Mode I Loading by means of Critical Value of the J-integral

2011 ◽  
Vol 10 ◽  
pp. 807-812 ◽  
Author(s):  
Ehsan Barati ◽  
Filippo Berto
Keyword(s):  
Critical Value ◽  
Mode I ◽  
J Integral ◽  
Mode I Loading ◽  
Fracture Assessment

A comparison between rapid expressions for evaluation of the critical J-integral in plates with U-notches under mode I loading

2011 ◽  
Vol 46 (8) ◽  
pp. 852-865 ◽  
Author(s):  
E Barati ◽  
F Berto
Keyword(s):  
Loading Condition ◽  
Control Volume ◽  
Notch Root ◽  
Critical Value ◽  
Fracture Load ◽  
Mode I ◽  
J Integral ◽  
Root Radius ◽  
Notch Root Radius ◽  
Mode I Loading

In this paper, some practical linear-elastic equations for evaluation of the critical value of the J-integral in plates with U-notches under mode I loading are presented and applied to brittle and quasi-brittle materials. The relationship between the J-integral and strain energy averaged over a well-defined control volume, depending on the static properties of the material, is applied, with the aim of obtaining the final expressions. It is found that these three proposed equations provide the same results, with any differences being negligible. By using one of these equations, one can evaluate Jcr and then predict the critical fracture load by means of the Jcr criterion. The results have shown that the critical value of the J-integral ( Jcr) is a function of the ratio of the material control radius to the notch-root radius ( Rc/ρ), the ratio of specimen width to notch depth ( w/ a), the notch acuity ( a/ρ), and the loading condition (tensile or bending loadings) in U-notches under mode I loading. However, the effect of the loading condition, a/ρ and w/ a ratios may be negligible. Therefore only the Rc/ρ ratio (i.e. the material properties and the notch-root radius of the specimen) affects Jcr.

Shape Sensitivity Analysis of Linear-Elastic Cracked Structures Under Mode-I Loading

2002 ◽  
Vol 124 (4) ◽  
pp. 476-482 ◽  
Author(s):  
Guofeng Chen ◽  
Sharif Rahman ◽  
Young Ho Park
Keyword(s):  
Sensitivity Analysis ◽  
Finite Difference Methods ◽  
Mode I ◽  
J Integral ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Material Derivative ◽  
Linear Elastic ◽  
Mode I Loading ◽  
Element Method

A new method is presented for shape sensitivity analysis of a crack in a homogeneous, isotropic, and linear-elastic body subject to mode-I loading conditions. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of any approximate numerical techniques, such as the finite element method, boundary element method, or others. Since the J-integral is represented by domain integration, only the first-order sensitivity of displacement field is needed. Two numerical examples are presented to illustrate the proposed method. The results show that the maximum difference in calculating the sensitivity of J-integral by the proposed method and reference solutions by analytical or finite-difference methods is less than three percent.

Acoustoelastic Determination of Forces on a Crack in Mixed-Mode Loading

1983 ◽  
Vol 50 (2) ◽  
pp. 379-382 ◽  
Author(s):  
R. B. King ◽  
G. Herrmann
Keyword(s):  
Nondestructive Evaluation ◽  
Mixed Mode ◽  
Experimental Results ◽  
Mode I ◽  
J Integral ◽  
Mixed Mode Loading ◽  
Central Crack ◽  
Ultrasonic Measurements ◽  
Mode I Loading

A technique previously presented [1] for the nondestructive evaluation of the J integral in cracked samples from ultrasonic measurements of stress, and successfully tested on specimens under mode I loading, is extended here to mixed-mode loading. Experimental results are presented for both the J and L integrals in a specimen with a slanted central crack loaded in tension, which agree well with theoretical values.

On the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
Dorinamaria Carka ◽  
Chad M. Landis
Keyword(s):  
Finite Element ◽  
Plastic Zone ◽  
Boundary Conditions ◽  
Path Dependence ◽  
Crack Tip ◽  
Mode I ◽  
Far Field ◽  
J Integral ◽  
Mode I Loading ◽  
Poisson's Ratios

The path-dependence of the J-integral is investigated numerically via the finite-element method, for a range of loadings, Poisson’s ratios, and hardening exponents within the context of J2-flow plasticity. Small-scale yielding assumptions are employed using Dirichlet-to-Neumann map boundary conditions on a circular boundary that encloses the plastic zone. This construct allows for a dense finite-element mesh within the plastic zone and accurate far-field boundary conditions. Details of the crack tip field that have been computed previously by others, including the existence of an elastic sector in mode I loading, are confirmed. The somewhat unexpected result is that J for a contour approaching zero radius around the crack tip is approximately 18% lower than the far-field value for mode I loading for Poisson’s ratios characteristic of metals. In contrast, practically no path-dependence is found for mode II. The applications of T- or S-stress, whether applied proportionally with the K-field or prior to K, have only a modest effect on the path-dependence.

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