On the estimation of the elastoplastic work needed to initiate crack tearing (original) (raw)
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Calculation of T – Stress on 3D Specimens with Crack
Procedia Engineering, 2012
The stress intensity factor (SIF) and T-stress are important parameters when estimating the residual life in structures with cracks. In this study, the finite element method was used to calculate the SIF and T-stress. High order elements were employed at the crack tip to represent displacement behavior. Computation of crack characteristics (K factor and T-stress) in three dimensional specimens is presented. The stress intensity factor is determined by processing of the displacements around the crack tip. Different methods have been used for calculating the T-stress. Crack characteristics, as a function of distance from the crack tip across the specimen's thickness, is given here.
Recent finite element studies in plasticity and fracture mechanics
Computer Methods in Applied Mechanics and Engineering, 1979
The paper reviews recent work on fundamentals of elastic-plastic finite-element analysis and its applications to the mechanics of crack opening and growth in ductile solids. The presentation begins with a precise formu~tion of incremental equilibrium equations and their finite-element forms in a marines valid for deformations of arbitrary magnitude. Special features of computational procedures are outlined for accuracy in view of the near-incompressibility of elastic-plastic response. Applications to crack mechanics include the analysis of large plastic deformations at a progressively opening crack tip, the determination of J integral values and of limitations to I characterizations of the intensity of the crack tip field, and the determination of crack tip fields in stable crack growth.
Effects of crack depth on elastic-plastic fracture toughness
International Journal of Fracture, 1991
Short crack test specimens (a/W ~ 0.50) are frequently employed when conventional deep crack specimens are either inappropriate or impossible to obtain, for example, in testing of particular microstructures in weldments and in-service structures containing shallow surface flaws, Values of elastic plastic fracture toughness, here characterized by the crack tip opening displacement (CTOD), are presented for square (cross-section) three-point bend specimens with a/W ratios of 0.15 and 0.50 throughout the lower-shelf and lower-transition regions. Three dimensional, finite-element analyses are employed to correlate the measured load and crack mouth opening displacement (CMOD) values to the corresponding CTOD values, thus eliminating a major source of experimental difficulty in previous studies of shallow crack specimens. In the lower-transition region, where extensive plasticity (but no ductile crack growth) precedes brittle fracture, critical CTOD values for short crack specimens are significantly larger (factor of 2-3) than the CTOD values for deep crack specimens at identical temperatures. Short crack specimens are shown to exhibit increased toughness at the initiation of ductile tearing and decreased brittle-to-ductile transition temperatures. Numerical analyses for the two a/W ratios reveal large differences in stress fields ahead of the crack tip at identical CTOD levels which verify the experimentally observed differences in critical CTOD values. Correlations of the predicted stresses with measured critical CTOD values demonstrate the limitations of single-parameter fracture mechanics (as currently developed) to characterize the response.
Crack paths and the linear elastic analysis of cracked bodies.PDF
The linear elastic analysis of cracked bodies is a Twentieth Century development, with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. Linear elastic fracture mechanics (LEFM) developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth. The first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969. Finite element analysis had a significant influence on the development of LEFM. Corner point singularities were investigated in the late 1970s. It was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors difficult and their validity questionable. In 1998 it was shown that the assumption that crack growth is in mode I leads to geometric constraints on permissible fatigue crack paths. Current open questions are. The need for a new field parameter, probably a singularity, to describe the stresses at surfaces. How best to allow for the influence of corner point singularities in three dimensional numerical predictions of fatigue crack paths. Adequate description of fatigue crack path stability.
Stress intensity factors (SIF), the fulcrum for linear elastic fracture mechanics (LEFM) predictions, quantify LE stress fields around crack tips, except very near the tips, in which they predict singular stresses. Hence, SIF-based analysis cannot describe stresses exactly at the cracked piece critical point. However, real materials are neither linear nor elastic at high stresses. Thus all loaded cracked pieces must have a nonlinear plastic zone (pz) close to their crack tips. If this (pz) size is small in relation to the piece dimensions, the stress field remains predominantly LE, hence controlled by the SIF. In such cases, the SIF can then be used to estimate the (pz) size by locating up to where the material yields in front of the crack tip. This means that LEFM predictions can be self-validated by the (pz) size estimated from a LE stress field. In other words, if (pz) is small, SIF can be used to describe crack effects. Therefore, the precise estimation of (pz) is a problem of major practical importance for crack analysis and structural integrity evaluations.The first classical (pz) estimates proposed by Irwin and by Dugdale are based only on the SIF value, but it has long been recognized their precision is quite limited to very low nominal stresses. Improved estimates have been proposed considering the T-stress, the name given by Irwin for the Williams series constant or zero order term. However, neither the SIF nor the T-stress can reproduce LE stress fields which obey all boundary conditions in cracked components. In particular, they cannot reproduce the nominal stress far from the crack tip. It is quite surprising that such a fact has not been well treated in the literature so far, since it has a major influence on the LE predicted (pz) size and shape. Indeed, using the correct LE stress field in the Griffith plate, generated by its complete Westergaard stress function (which of course not only reproduces the nominal stress that loads it, but is also confirmed by the Inglis plate solution when its elliptical notch root is supposed equal to half the crack tip opening displacement), it is showed that the nominal stress to yielding strength ratio has a major influence on the (pz) size and shape. This first part of this two-paper work presents the complete LE stress field solution for the Griffith plate, and compares the (pz) estimates generated from it with the classical and the T-stress corrected (pz) estimates, demonstrating the importance of using correct stress fields to evaluate LEFM limitations.
On the variation in crack-opening stresses at different locations in a three-dimensional body
Crack propagation and closure behavior of thin, and thick middle crack tension specimens under constant amplitude loading were investigated using a three dimensional elastic plastic finite element analysis of fatigue crack propagation and closure. In the thin specimens the crack front closed first on the exterior (free) surface and closed last in the interior during the unloading portion of cyclic loading; a load reduced displacement technique was used to determine crack opening stresses at specified locations in the plate from the displacements calculated after the seven cycle. All the locations were on the plate external surface and were located near the crack tip, behind the crack tip, at the centerline of the crack. With this technique, the opening stresses at the specified points were found to be 0.52, 0.42, and 0.39 times the maximum applied stress.