Creep crack growth in joints of a thermoplastic

An investigation of creep crack growth in butt heat fusion joints in a high density polyethylene (HDPE) is performed to quantify their life expectancy. Three point bend specimens containing a centrally located notched joint are used in creep crack growth tests at ambient and elevated temperatures. A quasi-nonlinear viscoelastic fracture mechanics model is used to deduce the crack growth histories from the measured load-point displacement histories. The initiation time for crack growth and the rate of crack growth are correlated with the stress intensity factor for combinations of initial crack lengths, applied loads and test temperatures. The elevated temperature data are shifted bidirectionally, utilizing shift functions derived from stress relaxation tests, to develop master curves for the initiation time and rate of crack growth. These master curves are used to predict the life of a girth joint containing an initial circumferential surface crack extending through 10 percent of the thickness of a pressurized pipe.     

A damage model for creep crack growth

A model is developed for damage produced by the growth of isolated grain boundary cavities under power law creep. This damage model is combined with the small scale yielding stress and strain fields to predict the damage ahead of a stationary and a steadily propagating crack tip in an elastic-power law creeping material. A failure criterion, based upon the damage ahead of the crack tip attaining a critical value, is invoked. This criterion leads to predictions for the incubation time prior to initiation of crack growth and for the relationship between the remote stress intensity factor and the steady state crack speed. Results are presented for both elastic-primary and -secondary creep crack growth. In either case, there exists a minimum stress intensity factor below which steady state crack growth is not possible. Comparisons of the predictions of this model with others for steady state crack propagation in elastic-secondary creeping materials are also made.

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Résumé On développe un modèle décrivant le dommage produit par la croissance de cavités isolées aux frontières des grains sous l'effet d'un fluage selon une loi parabolique. Ce modèle d'endommagement est combiné aux champs de contrainte et de déformation conduisant à une plastification à petite échelle, en vue de prédire le dommage qui se produit en avant de l'extrémité d'une fissure stationaire et en propagation lente, dans un matériau soumis à fluage selon une loi élastique. On invoque un critère de rupture basé sur la valeur critique atteinte par le dommage en avant de l'extrémité de la fisure. Ce critère conduit à prédire le temps d'incubation avant amorçage de la croissance d'une fissure, ainsi que la relation entre le facteur d'intensité des contraintes appliquées à une certaine distance et la vitesse de croissance stable de la fissure.On présente les résultats dans les cas de croissance d'une fissure de fluage au stade secondaire. Dans les deux cas, il existe un facteur d'intensité de contrainte minimum en dessous duquel une croissance stable de la fissure n'est pas possible. On procède également à des comparaisons des prédictions données par ce modèle avec d'autres, pour la propagation en état stable d'une fissure dans des matériaux soumis à fluage secondaire élastique.

     

An accelerated method for establishing the long term performance of polyethylene gas pipe materials

It was demonstrated in a previous investigation that both horizontal and vertical shifting is required to produce master curves for the relaxation moduli from elevated temperature data for polyethylene gas pipe materials. In this study, the shift functions obtained from these stress relaxation tests are applied to an assortment of elevated temperature time-dependent failure data for a variety of medium and high density polyethylenes. In all cases the data are successfully shifted to produce coherent master curves within the intrinsic scatter of the original data sets. The implication is that these horizontal and vertical shift functions are, for all practical purposes, universal for polyethylene gas pipe materials. This finding provides the basis for interpreting elevated temperature test data for polyethylene pipe materials so that a substantial savings in cost and time may be achieved in assessing the performance, structural integrity, and life expectancy of piping systems made from these materials.     

Modeling of dynamic crack propagation: II. Validation of two-dimensional analysis

The problem of fast fracture and crack arrest in rectangular fracture specimens under plane strain conditions is investigated within the confines of linear elastic fracture mechanics. A development consistent with the energy-balance criterion for fracture is obtained by first expressing the strain and kinetic energies in their finite-difference forms. These forms are used in Lagrange's equations and in the definition of the energy release rate to obtain the governing field equations. This development is subsequently used to make predictions that are compared with their measured counterparts. Agreement of predicted and observed compliances of SEN, CT, and DCB specimens is found to be very good. A direct comparison of predicted and measured results is made for a rapid fracture and crack arrest in an Araldite B DCB specimen. The predicted crack growth, crack-time history, and variations of the dynamic stress intensity factor and crack speed with crack length during propagation agree remarkably well with the experimental data.

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Résumé On étudie à l'aide de la mécanique de la rupture linéaire et élastique le problème de la fissure rapide et de l'arrêt de fissuration dans des éprouvettes de rupture rectangulaires soumises à des conditions d'état plan de déformation. Un développement compatible avec le critère d'équilibre de l'énergie pour la rupture est obtenu en exprimant d'abord les déformations et les énergies cynétiques sous des formes de différences finies. Ces formes sont utilisées dans les équations de Lagrange et dans la définition de la vitesse de relaxation d'énergie, afin d'obtenir des équations de champ. Ce développement est ensuite utilisé pour faire des prédictions qui sont comparées avec les mesures expérimentales. Un accord entre les compliances prédites et observées dans le cas d'éprouvettes SEN, CT et DCB, apparait comme particulièrement satisfaisant. Une comparaison directe des résultats prédits et mesurés est effectuée dans le cas d'une rupture rapide et dans le cas d'un arrêt de fissure dans une éprouvette DCB en Araldite B. La vitesse prédite pour la croissance de la fissure, le déroulement de la fissuration, et les variations dans le facteur d'intensité de contraintes dynamiques et dans la vitesse de fissuration en fonction de la longueur de la fissure au cours de la propagation sont en remarquable accord avec les données expérimentales.

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Part I will be published in the next issue.     

A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior

Many polymeric materials, including structural adhesives, exhibit anonlinear viscoelastic response. The nonlinear theory of Knauss and Emri(Polym. Engrg. Sci. 27, 1987, 87–100) is based on the Doolittle conceptthat the free volume controls the mobility of polymer molecules and,thus, the inherent time scale of the material. It then follows thatfactors such as temperature and moisture, which change the free volume,will influence the time scale. Furthermore, stress-induced dilatationwill also affect the free volume and, hence, the time scale. However,during this investigation, dilatational effects alone were found to beinsufficient for describing the response of near pure shear tests of abisphenol A epoxy with amido amine hardener. Thus, the free volumeapproach presented here has been modified to include distortionaleffects in the inherent time scale of the material. The same was foundto be true for a urethane adhesive.The small strain viscoelastic responses of the two materials havebeen determined from master curves of uniaxial and bulk creep testing atvarious temperatures. The nonlinear free volume model, modified toinclude distortional effects in the reduced time, was incorporated inthe ABAQUS finite element code via a user-defined material subroutine.For the epoxy, validation of the modified theory (a strain-basedformulation of free volume) has been achieved through good agreementbetween the computational and experimental results of butterfly-shapedArcan specimens subjected to loadings ranging from near pure shear toshear with various amounts of superposed tension and compression. Inaddition to predicting the response under a variety of multiaxial stressstates, the modified free volume theory also accurately predicts theformation and growth of shear banding, or regions of highly localizeddeformation, which have been found to occur upon continued loading ofthe epoxy. The urethane did not appear to exhibit any localizeddeformation over the range of temperatures at which it was tested.As a result, a stress-based modified free volume approach was requiredto model its multiaxial and temperature-dependent behavior. Althoughfree volume was the unifying parameter for the two materials, the needfor a stress-based and strain-based formulation of the free volume forthe urethane and epoxy, respectively, could not be reconciled at thistime.     

Viscoelastic material characterization and modeling for polyethylene

An extensive set of stress relaxation and constant strain rate tests for characterizing the mechanical responses of a medium density polyethylene and a high density polyethylene that are commonly used in natural gas distribution piping is described and analyzed. The development of coherent master curves for the relaxation modulus, maximum stress, and the time-to-failure for pressurized pipes through a combination of both horizontal and vertical shifting is presented. The relaxation data are used to develop a nonlinear Viscoelastic material model. The model is assessed by making comparisons of the predicted stress-strain response with the measured response in the constant strain rate tests.     

Creep crack growth in an elastic-creeping material Part II: mode I

The quasi-static growth of a crack in an elastic-creeping material under mode I loading is investigated. The creep strain rate of the material is assumed to be governed by a power law involving the stress and creep strain. The major emphasis of this investigation is on elastic-primary creep response. The asymptotic crack tip fields for a quasi-statically extending crack under conditions of plane strain and plane stress are developed. The asymptotic fields are unambiguously determined in terms of the instantaneous crack speed and material parameters and are independent of the prior crack history, specimen geometry, and loading. A plane strain finite element analysis is performed to determine the complete stress and strain fields. These fields are compared with the asymptotic ones to establish the zone of dominance of the crack tip fields. The zone of dominance can be a very small fraction of the size of the creep zone attending the crack up.

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Résumé On étudie la croissance quasi-statique d'une fissure dans un matériau sujet à fluage élastique sous une sollicitation de Mode I. On suppose que la vitesse de déformation en fluage du matériau est régie par une loi parabolique comportant la contrainte et la déformation. L'accent est surtout mis sur la réponse au fluage élastique primaire.On établit les configurations asymptotiques règnant à l'extrémité de la fissure, dans le cas d'une fissure quasi-statique en extension sour état plan de dilatation ou sous état plan de tension. Ces champs sont déterminés sans ambiguïté par la vitesse instantanée de la fissuration et par les paramétres du matériau; ils sont indépendants de l'histoire primitive de la fissure, de la géométrie de l'éprouvette et de la sollicitation. On effectue une analyse par éléments finis en déformations planes pour déterminer complètement les champs de contrainte et de dilatation, que l'on compare aux champs asymptotiques aux fins d'établir la zone de prédominance des champs à l'extrémité de la fissure. Cette zone peut être une fraction très petite de la taille de la zone où s'effectue un fluage au voisinage de l'extrémité de la fissure.

     

Modeling of dynamic crack propagation: I. validation of one-dimensional analysis

The formulation of the problem of a rapidly propagating crack in a double cantilever beam specimen is re-examined using Reissner's variational principle. The governing equations are first solved to obtain the static compliance which is in good agreement with measured values. The equations of motion in conjunction with the energy balance criterion for a running crack are solved using a finite difference method. Predicted crack growth versus time, crack speed versus crack length and dynamic stress intensity factor versus crack length are all found to be in very good agreement with their measured counterparts for a polymer.

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Résumé On réexamine la formulation du problème d'une fissure se propageant rapidement dans une éprouvette en poutre double cantilever en utilisant le principe variationnel de Reissner. Les équations de base sont en premier lieu résolue en vue d'obtenir une compliance statique en bon agrément avec les valeurs mesurées. Les équations de mouvement en relation avec un critère d'équilibre énergétique dans le cas d'une fissure en mouvement sont résolues en utilisant une méthode par différences finies. On trouve que la croissance prédite de la fissure en fonction du temps, la vitesse de propagation en fonction de la longueur de fissure et le factuer d'intensité des contraintes en fonction de la longueur de la fissure sont en excellent agrément avec les valeurs correspondantes mesurées dans le cas d'un polymère.

     

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.