1 edition of **Application of the J-integral and the modified J-integral to cases of large crack extension** found in the catalog.

Application of the J-integral and the modified J-integral to cases of large crack extension

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Published
**1989** by Division of Engineering, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission in Washington, DC .

Written in English

- Steel -- Fracture -- Mathematical models.,
- R-curves.,
- Fracture mechanics.

**Edition Notes**

Statement | prepared by J.A. Joyce ... [et al.]. |

Contributions | Joyce, J. A. 1945-, U.S. Nuclear Regulatory Commission. Office of Nuclear Regulatory Research. Division of Engineering., United States Naval Academy., David Taylor Research Center. |

The Physical Object | |
---|---|

Pagination | ix, 34 p. : |

Number of Pages | 34 |

ID Numbers | |

Open Library | OL15293718M |

extension analysis. Each crack-path increment is first predicted by the maximum principal stress criterion and then corrected to account for the discreteness of the analysis. For each increment of the crack extension. the dual boundary element method is applied to perform a stress analysis of the structure and the J-integral technique is. Fig. 1: Counter J-Integral [16]. The J-Integral around a crack tip is frequently expressed in a more general form as lim k iijjk i u J wn n d ε x σ →∞ Γ ⎛⎞∂ =− Γ⎜⎟ ⎝⎠∂ ∫ 3 Where Ji is the component of the J-integral for crack opening in the xi direction and ε is a small region around the crack tip. This integral is File Size: KB.

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Get this from a library. Application of the J-integral and the modified J-integral to cases of large crack extension. [J A Joyce; U.S. Nuclear Regulatory Commission. Office of Nuclear Regulatory Research.

Division of Engineering.; United States Naval Academy.; David Taylor Research Center.;]. The J-integral is widely accepted as a measure of elastic-plastic fracture toughness of engineering en size and geometry dependence were first noted in fracture toughness measurements using the ASTM E calculation of the deformation J-integral (J d) by McCabe and Landes [1] in The modified J-integral (J m) was introduced by Ernst [2] to attempt to minimize or eliminate Cited by: 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 J Cited by: 5. The J-integral is widely accepted as a measure of elastic-plastic fracture toughness of engineering alloys. Specimen size and geometry dependence were first noted in fracture toughness measurements using the ASTM-E standard calculation of the deformation J-integral (J/sub d/) in Cited by: Application of the J-integral and the modified J-integral to cases of large crack extension.

Technical Report Joyce, J standard calculation of the deformation J-integral (J/sub d/) in The modified J-integral (J/sub m/) was introduced to attempt to minimize or eliminate size and geometry dependence when crack growth was appreciable. Crack extension due to one nonproportional load cycle, step 8 above, is computed using the approach developed in Spievak et al.

().As previously mentioned, a modified Paris model that accounts for crack closure effects is used. A crack is assumed to advance when its maximum SIF is large enough to overcome closure and is larger than the maximum SIF of the previous load step.

The application of an atomistic J-inte gral to a ductile crack 11 for the largest system, that: (a) there is relaxation after emission, (b) the stress ﬁeld in between the crack tip and the.

modified J-integral to cases of large crack extension, ASTM STPp, Wilson A.D. and Donald J.K., Evaluating steel toughness using various elastic-plastic. The J-integral is widely accepted as a fracture mechanics parameter for both linear and nonlinear material is related to the energy release associated with crack growth and is a measure of the intensity of deformation at a notch or crack tip, especially for nonlinear materials.

where is the strain energy density, is the traction vector, is an arbitrary contour around the tip of the crack, n is the unit vector normal to ;, and u are the stress, strain, and displacement field, respectively. Rice, J.

R.,showed that the J integral is a path-independent line integral and it represents the strain energy release rate of nonlinear elastic materials. A modified line-plasticity model, involving concept of structured nonlinear zone coupled with the final stretch criterion governing the crack propagation, is used to show the effects of material strain-hardening and the redistribution of strain caused by an advancing quasi-static crack, on the essential parameters pertinent to a mathematical description of elasto-plastic fracture process Cited by: The paper presents the results of a theoretical investigation whose objective has been to see whether there are advantages to be gained from using the modified J-integral in procedures for estimating the critical crack length for CANDU pressure typical operation conditions, and with irradiated tubes having critical crack lengths over a wide range, it is shown that the slope of the Author: E.

Smith. J-Integral Near a Stationary Crack in an Elastic-Plastic Material 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 J 2-ﬂow plasticity.

Small-scale Cited by: Elastic and elastic-plastic fracture mechanics solutions are modified to predict the behaviour of short cracks. An effective crack length, l 0 is introduced into the solutions for both the linear elastic stress intensity factor and the J integral.

Crack growth results for short cracks, in both elastic and plastic strain fields of unnotched specimens, when interpreted in terms of the modified Cited by: The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material.

The theoretical concept of J-integral was developed in by G. Cherepanov and independently in by James R. Rice, who showed that an energetic contour path integral (called J) was independent of the path around a crack.

happen, is a small region compared to the specimen size, and is at the crack tip • Therefore – Linear elastic stress analysis describes the fracture process with accuracy Mode I Mode II Mode III (opening) (sliding) (shearing) Fracture Mechanics –NLFM J-Integral 2File Size: 2MB.

deformation, stress, and the J-integral in 3D for a bi-modular three point bend cracked specimen as shown in Fig. The properties of nuclear grade graphite material incorporated in this study has been referred from graphite design hand book [14].

The evaluation of J-integral for 3D is a tedious task even for a unimodular case due to. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.

In modern materials science, fracture mechanics is an important tool used to improve the. as a unique way of experimentally measuring the J-Integral. The crack driving force will usually be determined numerically and as such the J-Integral method is the best method.

Codes The most popular codes, in terms of fracture parameters, can be delineated into two groups; J-Integral - EPRI, R6, PD and ETMFile Size: 29KB. J Integral Continued Z d u M @ u d = w d y T s d a S x J J represents the rate of change of net potential energy with respect to crack advance (per unit thickness of crack front) for a non-linear elastic solid.

J also can be thought of as the energy ﬂow into the crack tip. Thus, J is a measure of the singularityFile Size: KB. Test results from J Ic studies are analyzed by a resistance curve technique.

J values from bend type specimens containing a deep precrack are plotted as a function of crack extension measured from the specimen fracture surface. Using these plots a technique is suggested for establishing a J Ic measurement point. Data from an A steel are presented for describing this method of J Ic by: A mathematical expression; a line or surface integral that encloses the crack front from one crack surface to the other, used to characterize the fracture toughness of a material having appreciable plasticity before fracture.

The J-integral eliminates the need to describe the behaviour of the material near the crack tip by considering the local stress-strain field around the crack front; Jk is. This paper is an extension of our previous works to examine whether the failure criterion can be applied to examine the feasibility of miniaturized Charpy type SE(B) specimens, that is, (1) whether the criterion could predict the occurrence of cleavage fracture accompanied by negligibly small stable crack extension (hereinafter denoted as fracture) and (2) whether is identical to that observed Cited by: 4.

The micro-cracks would occurr with the deformation in the composite materials. It would be expanded to the macro-crack in bonding surface and eventually leads to the overall damage of the structure. The initial defects will be inevitably involved in the production of the laminated composite structures.

They also lead to delamination crack propagation and structural : Dong Zhao, Yang Zhao, Xiang Rong Fu, Wen Jie Wang.

The J integral is a third method of determining toughness and is based on the amount of energy required to propagate a crack. Both CTOD and J can be measured on the same specimen by using two clip gauges, one to measure CTOD, the other to measure J.

crack (i.e., conventional MPM), ν(p,i) = 1 if the line crosses a crack and the particle is above the crack, or ν(p,i) = 2 if the line crosses the crack and the particle is below the crack. The concept of “above” or “below” the crack is relative to a coordi-nate system with the crack tip at the origin and the.

J -integral The J –integral is a very effective way of calculating the energy associated with the singularity.

• Numerical stable. • Independent of material (can be plasticity). • Easily programmed in a finite element context.

• Basically postprocessing of a Finite Element model with the crack modelled. 12File Size: KB. Computation of a path independent contour integration but it yields directly the independent values of the opening mode and shear mode stress intensity factors. The calculations are not sensitive to the choice of contour.

To the J-integral calculation, the present scheme calculates separately the factors KI and KII. A simple method to determine the SIFs for the three-dimensional crack is Cited by: 1. Linear elastic fracture mechanics A large ﬁeld of fracture mechanics uses concepts and theories in which linear elastic material behavior is an essential assumption.

This is the case for Linear Elastic Fracture Mechanics (LEFM). Prediction of crack growth can File Size: 1MB. Methods for Evaluation of the J-Integral and the Modified J-Integral.

Shiro KUBO 1) 1) Faculty of Engineering, Osaka University Released /01/15 received /10/22 Full Text PDF Preview. Full Text PDF [K] Abstracts References() Cited-By(2) Full Text PDF [K].

G-based crack extension resistance I. an integration constant JJ-integral J. critical J-integral at fracture instability J. plane strain fracture toughness characterized by J-integral J.

elastic component of J-integral J. crack initiation toughness characterized by J-integral J. plastic component of J-integral J. maxCited by: J-INTEGRAL CALCULATION WITH MARC • central crack in thin plate • mode I loading • crack length a m plate width W m plate height H m plate thickness B m loading σ Pa Young’s modulus E GPa Poisson’s ratio ν.

into the consideration in the J-integral analysis [8]. Therefore, J-integral is exclusively used to study the component made of ductile materials or any component experienced large plastic deformation.

In addition, the calculation of J-integral using FEA required special skills and it is also an exhausted. The J-integral is calculated by a virtual crack extension method, modified for thermal-elastic-plastic crack problems.

It is shown that the effect of thermal/residual stresses is negligibly small when fully plastic conditions are achieved. The experimental procedure for determining the crack-extension resistance (R-curve or J-R curve) of a material requires the measurement of crack extension (Δa; Δa = a (i) – a 0) that occurs during loading of a pre-cracked specimen.

In the case of sub-millimetre sized samples this is a very difficult by: The analysis of crack problems through fracture mechanics has been applied to the study of materials such as glass, metals and ceramics because relatively simple fracture criteria describe the failure of these materials.

The increased attention paid to experimental rock fracture mechanics has led to major contributions to the solving of. View J INTEGRAL_1 from MAE at North Carolina State University. 1 J INTEGRAL including a crack tip The path o c c, the crack tip singularity is excluded.

2 For k = 1, W n1 ij n j ui,1 d 0 W n1. The fracture behaviour of polymers is strongly affected by the addition of rigid particles. Several features of the particles have a decisive influence on the values of the fracture toughness: shape and size, chemical nature, surface nature, concentration by volume, and orientation.

Among those of thermoplastic matrix, polypropylene (PP) composites are the most industrially employed for many Cited by: As both parameters, averaged local SED and J ‐integral, describe crack initiation at pointed or blunt notches, the relation between the two is shortly reviewed in this article.

It is not possible to review the great variety of J ‐integral concepts related to analysis and application. The exposition below is subdivided in a pointed notch Cited by: This paper introduces an enriched Boundary Element Method in which functions are introduced that are known to model singularities or discontinuities from a priori knowledge of the solution space.

Additional fundamental solutions are introduced to solve for the additional unknowns created by enrichment and a numerical integration routine is outlined for the evaluation of strongly singular and.

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.Crack J-integral Path-independent integral Chemo-mechanics abstract In this study, we first demonstrate that the J-integral in classical linear elasticity becomes path-dependent when the solid is subjected to combined electrical, chemical and mechanical loadings.

We .The software has a number of advanced features not available in other crack growth software and these can be used to perform crack growth simulation in residual stress fields, apply pressure directly to the crack face for leak-before-burst type analysis, and investigate crack closure using sophisticated crack surface contact algorithms.