An assessment of the crack tip opening displacement criterion for predicting creep crack growth

From a set of finite element (FE) simulations of creep crack growth in compact tension specimens, the critical value of the crack tip opening displacement, CTOD, for creep crack growth has been generated for a Ni-base superalloy (Waspaloy) at 700°C. It was found that the critical value is independent of the initial crack length, amount of previous creep crack growth and the load level. Hence, the CTOD seems likely to be a viable criterion for use in creep crack growth rate analysis. Good agreement was also obtained between the experimental test results and FE predictions of the creep crack growth with time and between the crack growth rate, da/dt, versus the C ^* parameter based on load-line displacement rate.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T_max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.     

Crack tip parameters and elastic-plastic fracture of metals

By using optical displacement-measuring techniques we obtain the crack tip fields in terms of crack tip strain, crack opening angle (COA) and crack tip opening angle (CTOA). Thin plates with different crack configurations made of six elastic-plastic materials with strain hardening exponent ranging from 3 to are studied. We find that the COA resistance curve assumes certain characteristics common to all the materials. The experimental results indicate that the critical value of COA may be used as a fracture toughness parameter for these materials.

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Résumé En utilisant une technique de mesure optique des déplacements, on obtient les champs régnant à l'estrémité d'une entaille, qui s'experiment par la déformation d'extrémité d'entaille, l'angle d'ouverture de la crique (COA et l'angle d'ouverture de la pointe de la crique (CTOA). On étudie des feuillards présentant différentes configurations de fissures et réalisés en six matériaux élasto-plastiques dont les modules d'écrouissage s'échelonnent de 3 à l'infini.On trouve que la courbe de résistance COA suppose certaines caractéristiques communes à tous les matériaux. Les résultats expérimentaux indiquent que la valeur critique du COA peut être utilisée comme paramètre de ténacité à la rupture pour les matériaux étudiés.

     

Simulation of ductile crack growth in thin panels using the crack tip opening angle

The aim of this work is the assessment of the efficiency of the crack tip opening angle (CTOA) with respect to the transferability from one geometry to another, in particular the transferability obtained from Kahn tear tests to M(T) panels. The load-displacement behaviour recorded during a Kahn tear test was reproduced by means of finite element analysis using a variable CTOA as a function of crack length. The CTOA extracted from Kahn tests has then been used to simulate the R-curve of M(T) panels with different widths. Experiments and simulations were run first on a 6013-T6 aluminium alloy and then also on butt, friction stir welded butt joints of the same material.     

Variations of various fracture parameters during the process of subcritical crack growth

The process of subcritical crack growth in a center-cracked specimen made of 2024-T3 aluminum alloy has been analyzed by finite element method. The variations of various fracture parameters in the process of crack growth are presented. A preliminary discussion is made about the general guidances in formulating the governing equation for crack growth.     

The meaning of elastic-plastic fracture criteria during slow crack growth

The J-integral and COD are commonly used to describe resistance to slow, stable crack extensions in ductile materials. Unique relationships between these two parameters are derived for crack growth in the bending configuration, analogous to 449-1. Good agreement is obtained with experiment, particularly if a modified flow stress is employed. Experimental studies of the strains around growing cracks show that the apparent increase in toughness is caused by plastic straining remote from the near-tip region. The postulated geometry independence of the R-curve for flat fracture is examined in the light of these results.

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Résumé On utilise couramment l'intégrale J et le COD pour décrire la résistance à l'extension d'une fissure lente et stable dans des matériaux ductiles. Des relations uniques ont été dérivées entre ces deux paramètres pour une croissance de fissure sous une configuration de flexion, analogue à l'expression 466-1. Un excellent accord a été obtenu avec l'expérience en particulier lorsqu'on utilise une contrainte d'écoulement modifiée. Les études expérimentales des déformations au voisinage de fissures en croissance montrent que l'accroissement apparent de la ténacité causé par une déformation plastique lointaine par rapport aux régions voisines de l'extrémité de la fissure. A la lumière de ces résultats, on examine l'indépendance géométrique supposée de la courbe R.

     

Effect of residual stresses on ductile crack growth resistance

It is well known that residual stresses influence the ductile fracture behaviour. In this paper, a numerical study was performed to assess the effect of residual stresses on ductile crack growth resistance of a typical pipeline steel. A modified boundary layer model was employed for the analysis under plane strain, Mode I loading condition. The residual stress fields were introduced into the finite element model by the eigenstrain method. A sharp crack was embedded in the center of the weld region. The complete Gurson model has been applied to simulate the ductile fracture by microvoid nucleation, growth and coalescence. Results show that tensile residual stresses can significantly reduce the crack growth resistance when the crack growth is small compared with the length scale of the tensile residual stress field. With the crack growth, the effect of residual stresses on the crack growth resistance tends to diminish. The effect of residual stress on ductile crack growth resistance seems independent of the size of geometrically similar welds. When normalized by the weld zone size, the ductile crack growth resistance collapses into one curve, which can be used to assess the structural integrity and evaluate the effect of residual stresses. It has also been found that the effect of residual stresses on crack growth resistance depends on the initial void volume fraction f₀, hardening exponent n and T-stress.     

Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials

This work investigates elastic-plastic crack growth in ceramic/metal functionally graded materials (FGMs). The study employs a phenomenological, cohesive zone model proposed by the authors and simulates crack growth by the gradual degradation of cohesive surfaces ahead of the crack front. The cohesive zone model uses six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) to describe the constitutive response of the material in the cohesive zone. A volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model) describes the elastic-plastic response of the bulk background material. The numerical analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive zone model and the computational scheme to analyze crack growth in a single-edge notch bend, SE(B), specimen made of a TiB/Ti FGM. Cohesive parameters are calibrated using the experimentally measured load versus average crack extension (across the thickness) responses of both Ti metal and TiB/Ti FGM SE(B) specimens. The numerical results show that with the calibrated cohesive gradation parameters for the TiB/Ti system, the load to cause crack extension in the FGM is much smaller than that for the metal. However, the crack initiation load for the TiB/Ti FGM with reduced cohesive gradation parameters (which may be achieved under different manufacturing conditions) could compare to that for the metal. Crack growth responses vary strongly with values of the exponent describing the volume fraction profile for the metal. The investigation also shows significant crack tunneling in the Ti metal SE(B) specimen. For the TiB/Ti FGM system, however, crack tunneling is pronounced only for a metal-rich specimen with relatively smaller cohesive gradation parameter for the metal.     

An elastic-plastic finite element analysis of crack tip fields under biaxial loading conditions

A square plate containing a central crack and subjected to biaxial stresses has been studied by a finite element analysis. An elastic analysis shows that the crack opening displacement and stress of separation ahead of the crack tip are not affected by the mode of biaxial loading and therefore the stress intensity factor adequately describes the crack tip states in an elastic continuum.

An elastic-plastic analysis involving more than localized yielding at the crack tip provides different solutions of crack tip stress fields and crack face displacements for the different modes of biaxial loading.

The equi-biaxial loading mode causes the greatest separation stress but the smallest plastic shear ear and crack displacement. The shear loading system induces the maximum size of shear ear and crack displacement but the smallest value of crack tip separation stress.

     

Influence of crack tip constraint on void growth in ductile FCC single crystals

Effect of constraint (stress triaxiality) on void growth near a notch tip in a FCC single crystal is investigated. Finite element simulations within the modified boundary layer framework are conducted using crystal plasticity constitutive equations and neglecting elastic anisotropy. Displacement boundary conditions based on mode I, elastic, two term K-T field are applied on the outer boundary of a large circular domain. A pre-nucleated void is considered ahead of a stationary notch tip. The interaction between the notch tip and the void is studied under different constraints (T-stress levels) and crystal orientations. It is found that negative T-stress retards the mechanisms of ductile fracture. However, the extent of retardation depends on the crystal orientation. Further, it is found that there exists a particular orientation which delays the ductile fracture processes and hence can potentially improve ductility. This optimal orientation depends on the constraint level.     

On distribution of the plastic strain around the crack tip at the onset of ductile fracture

A very simple model is presented to explain the change in the plastic strain from the crack tip. It is based on a relaxation mechanism by dislocations.

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Zusammenfassung Ein sehr einfaches Modell wird eingebracht zur erklärung der Änderung in der plastischen Verbiegung von der Rißspitze. Es beruht auf einer Relaxationsmechanik durch Versetzungen.

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Résumé Un modèle très simple est présenté pour expliquer le changement dans le gauchissement plastique dès la pointe fente. C'est conformé à un méchanisme de relaxation par dislocations.

     

On the use of the crack tip opening angle parameter to explain the ductile crack growth behavior of miniature compact specimens

Experimental crack resistance curves obtained from miniature compact tension, MC(T), specimens were found to be significantly less tough than those obtained on standard one inch 1T-C(T) specimens. In order to investigate the fundamental reasons behind this unexpected result, local approaches to fracture based on the Rice and Tracey void growth model and the crack tip opening angle (CTOA) concept are used. Local crack growth criteria are identified on test results obtained from 1T-C(T) and are used to predict the MC(T) behavior. Results demonstrate that the CTOA parameter is very effective as it allows transferring results from MC(T) to larger specimens, it is easy to implement in a finite element code, it is mesh size insensitive and can be actually measured although its experimental determination is not straightforward. The β parameter derived from the Rice and Tracey void growth model is unable to explain the experimental results. The possible reasons for the poor performance of the β parameter are discussed.     

Effects of crack depth on elastic-plastic fracture toughness

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.     

An experimental investigation of the effect of specimen type on the crack tip opening displacement and J-integral fracture criteria

The effects of specimen type (precracked tension or bend) on the relationship between the J-integral and the crack tip opening displacement (COD) and on crack initiation values of J and COD were investigated. The material used was a mild steel. COD was measured by infiltrating the crack with a catalytically hardening silicone rubber. The J-integral was measured both by the compliance technique and using analytical formulae. No significant effect of specimen type was noted. Measurements of J from the analytical formulae used agreed well with compliance measurements. Simultaneous J and COD values were also measured on a low alloy steel. The results indicate that the J/G/COD relationships are material dependent, possibly being controlled by the material's work-hardening rate.

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Résumé On a étudié, sur un acier doux, les effets du type d'éprouvette—préfissurée pour essai de traction ou de flexion—sur la relation entre l'intégrale J et le COD, ainsi que sur les valeurs critiques à l'amorçage de J et de COD. On a mesuré le COD en injectant dans la fissure un caoutchouc de silicone à durcissement catalytique. L'intégrale J a été mesurée, de son côté, à la fois par une technique de compliance et par des formules analytiques. On n'a pas noté une influence significative du type d'éprouvette. Les mesures de J émanant des formules analytiques sont en bon accord avec les mesures par compliance. Des mesures simultanées de J et du COD ont également été effectuées sur un acier faiblement allié. Les résultats montrent que les relations entre J, G et le COD dépendent du matériau et qu'elles sont probablement régies per leur module d'écrouissage.

     

Composite crack profile model for CTOD determination III: An experimental application to elastic-plastic crack growth situations

A composite crack profile (CCP) model has been applied for the evaluation of CTOD in the elastic-plastic crack growth situations prevailing in a structural steel. The results have been compared with the ones obtained by conventional method (using plastic hinge model such as Wells etc.) The CTOD-Resistance Curves (δ_R-curves) have also been obtained as a function of specimen thickness, a/w ratio and the loading geometry by using the CCP model. The significance of crack initiation CTOD (δ_i) and the maximum load CTOD (δ_m) has been discussed in relation to various geometrical parameters (i.e. thickness, a/w ratio and loading geometry).