# Mecanica Del Medio Continuo - Ejercicios

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First MIT Conference on Computational
Fluid and Solid Mechanics, Massachusetts Institute of Technology
Cambridge, Massachusetts, USA. June 12-15, 2001.
Nonlinear finite element modeling of surface cracks in a nuclear pressure pipe
F. Labbea and J.R. Donosob
a
Mechanical Engineering Department and bMaterials Science Department.
Casilla 110-V,Valparaíso, CHILE
flabbe@usm.cl
Abstract
Surface cracks are often encountered in power plants component and have been recognized as a
major origin of potential catastrophic failure for such components. Failure assessment of cracks in
nuclear pressure pipes has been done currently by a one-parameter fracture mechanics approach.
The J-integral is the one-parameter used, and has been proved to beuseful to predict ductile crack
initiation. However, when shallow surface cracks and/or a fully plastic condition develops around
the crack, the J-integral alone does not describe completely the crack tip stress field and a second
parameter is necessary to consider. In addition, defects like surface cracks produces a very
complex stress field at the close vicinity of the crack tip due tothree-dimensional effects, highly
nonlinear large deformations, microestructural fracture process, etc. Hence, a detailed nonlinear
three-dimensional stress analysis needs to be done.
In this paper, a nonlinear finite element modeling of the three-dimensional elastic-plastic stress
field around a crack tip in a pipe, is used to evaluate a second fracture mechanics parameter Q. The
pipe is subjectedto a pressure loading and the Q parameter measures the degree of triaxiality
around the crack tip.
The crack is modeled as a three-dimensional semi-elliptic inner surface flaw in the axial
direction. The depth-to-length ratio of the elliptic crack is a/2c = 0.1, and the depth-to-thickness
ratios analyzed are from shallow crack (a/t = 0.125) to a deep crack (a/t = 0.75). The finite elementpipe model is sufficiently long to avoid end effects upon loading. Due to load and geometry
symmetry, only one fourth of the complete pipe needs to be considered, with appropriate boundary
conditions imposed on the planes of symmetry. The material, an A 516 Gr. 70 steel used in the
nuclear industry, is modeled with a flow theory of plasticity.
In order to obtain an accurate and completethree-dimensional crack tip stress fields, a highdensity finite elements mesh with three-dimensional quadratic isoparametric 20-node brick was
located around the crack-tip zone. A finite deformation theory was used to account for the highly
nonlinear behavior around the crack tip. The complete pipe finite element model contains 11,262
twenty-node quadratic bricks. Numerical results are presented for thecrack-tip stress field and Q
Keywords: Computational fracture mechanics; Two-parameter fracture mechanics; Surface cracks;
Nonlinear finite element modeling; Pressure pipe; Simulation Modeling Applications.

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1. Introduction
Surface cracks are often encountered in power plants component and have been recognized as amajor origin of potential catastrophic failure for such components. To prevent these failures,
fracture mechanics methodologies are normally applied to evaluate the structural integrity of
pressure pipe and vessels.
The application of conventional fracture mechanics techniques relies on the notion that a single
parameter, such as the J-integral, uniquely characterizes the resistance of amaterial to fracture,
Landes [1] and Rice [2]. The J-integral is a measure of the intensity of the stress and deformation
fields on the singular crack-tip solution for a nonlinear material obtained by Hutchinson[3] and
Rice and Rosengren [4] is referred as the HRR singularity field. There is general agreement that
the applicability of this one-parameter J-approach is limited to a high constraint...