The critical tensile stress criterion for cleavage

An elastic-plastic analysis was used to accurately measure the microscopic cleavage strength _inff ^sup* of notched bars of high nitrogen steel in bending. It was found that _inff ^sup* increases as the root radius of the notch decreases. For > 0.010, the variation of _inff ^sup* with , and the difference between _ingff ^sup* and the cleavage fracture strength of a plane tensile specimen, _f, may result from a statistical effect, due to differences in the volume of highly stressed material in the plastic zone. For < .010, the primary reason for the apparent increase in _inff ^sup* with decreasing , is the steep stress gradient at the notch tip, which forces the critical plastic zone size to extend further to insure that unstable microcraek propagation can occur. Both the statistical and stress gradient effects have been quantitatively evaluated and found to be in good agreement with the experimental data.

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Zusammenfassung Man benutzte eine elastisch-plastische Analyse, um die miktoskopische Spaltungssärke _inff ^sup* von eingekerbten Stahlbarren mit hohem Stickstoffgehalt im Krümmen sorgfältig zu messen. Man stellte fest, dass _inff ^sup* sich vergrösserte während der Wurzelradius der Kerbe sick verringerte. Da > 0.010 ist, ist die Variation von _inff ^sup* mit der Spaitungsfrakturstärke einer planaren Spannungsprobe, _f durch einen statistischen Effekt und durch Unterschiede in dem Volumen von stark angespanntem Material in der plastischen Zone verursacht. Da > 0.010 ist, ist der ursprüngliche Grund für die augenscheinliche Zunahme in _f mit verringertem , der tiefe Anspannungsgradiente an der Kerbenspitze, durch welche sich die kritische, plastische Zonengrösse weiter ausdehnen muss, um die labile Mikrorissausbreitung zu sichern. Die statistischen und Anspannungsgradienteffekte wurden quantitative ausgewertet und man fand gute Übereinstimmung mit den experimentellen werten.

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Résumé Une analyse élastoplastique a été utilisée pour la mesure précise de la résistance microscopique du clivage _inff ^sup* de barreaux entaillées d'acier à haute teneur en azote et soumis à flexion.On a trouvé que _inff ^sup* s'accroit lorsque diminue le rayon d'arrondi à la racine de fentaille. Lorsque est supérieur à 0,25 mm, la variation de _inff ^sup* en fonction de est due à un effet statistique du aux différences de volume de matière soumis, dans la zone de déformation plastique, à des contraintes; élevées. Il en est également de même l'écart entre _inff ^sup* et la contrainte de rupture par clivage dune éprouvette de traction sans entaille.Lorsque est inférieur à 0,25 mm, la raison principale de l'accroissement de _inff ^sup* avec des valeurs de décroissantes réside dans l'existence d'un gradient aigu des contraintes à la pointe de la fissure. Un tel gradient force à s'accrcître lesdimensions de la zone critique de deformation plastique, pour que puisse se produire une propagation instable dune microfissure.On a pu évaluer quantitativement ces effets statistiques d'une part et de gradients de contraintes d'autre part, et l'on s'est trouvé en accord satisfaisant avec les données expérimenetales.

     

Distributions of stress and plastic strain in notched tensile bars

The paper deals with a classical problem in fracture mechanics, namely the determination of stresses and plastic strains at the minimum cross-section of a notched tensile specimen. Ideas of Hill and Bridgman are combined to develop a new approximate method for solving this problem. The main aim of the paper is to introduce a damage variable in the analysis without any complicated numerical procedure. The material model proposed by Lemaitre is used to predict the evolution of the damage variable. However, any other model resulting in the incompressibility condition may be adopted with no difficulties. This revised version was published online in July 2006 with corrections to the Cover Date.     

The master curve and the constitutive equation for creep deformation and fracture for Cr-Mo-V steel throughout smooth,notched and precracked specimens

It has been shown experimentally that the master curve for creep deformation versus the ratio of time to fracture time, can be obtained for smooth, notched and precracked specimens of Cr-Mo-V steel, a high-temperature ductile material. A simple unified constitutive equation, i.e. a master curve equation, has been proposed. It is suggested that there is some correlation between the creep deformation fracture curve and the creep damage size master curve. Although the range of the applicability of methodology might be rather limited, the development of this concept is needed for improved long-term creep lives and for other creep ductile materials.     

A notched coupon approach for tensile testing of braided composites

A notched coupon geometry was evaluated as a method for tensile testing of 2D triaxial braid composites. Edge initiated shear failure has been observed in transverse tension tests using straight-sided coupons based on ASTM D3039. The notched coupon was designed to reduce the effects of edge initiated failure and produce the desired tensile failure. A limited set of tests were performed with partial pressurization of tubes to determine the transverse tensile strength in the absence of edge initiated failure. The transverse strength measured with the notched coupons was considerably higher than the straight-sided coupons, comparable to the tube results, and closer to the maximum possible strength based on maximum fiber strain. Further investigations of the effects of the observed biaxial stress state and stress concentrations in the notched geometry are needed.     

Fatigue-creep and plastic collapse of notched bars

The paper describes a study of the application of a new assessment method, based on the linear matching method (LMM), to the creep fatigue of notched bars of Udimet 720Li at 650 °C. This high strength nickel based alloy is taken as typical of alloys used in high temperature gas turbine applications. The primary purpose of the study is to see whether it is possible to predict the failure modes for such alloys in terms of standard materials data by the evaluation of a sequence of simplified calculations corresponding to the steady state cyclic stress history. These calculations involve the evaluation of limit load, shakedown limit and ratchet limit for perfect plasticity, rapid cycle creep solutions and the evaluation of an elastic follow‐up factor. Within the limitations of the tests, the correlation between predicted failure mode and observed mode is very good and the calculations clearly show up the differences between the two types of notched bars discussed. This implies that LM methods are well suited to the evaluation of failure modes in materials of this type.     

A flow criterion for oriented polyethylene in tensile deformation

Tensile test specimens were cut from high density polyethylene that had been fully cold drawn. The angle between the tensile axis and the draw direction was varied from 30 to 80° and the specimens were deformed at temperatures between 0 and 120° C. Deformation beyond yield occurred without any work hardening and could be described in terms of a flow criterion. The parameters of the flow criterion were found to be slightly dependent upon the initial orientation angle, but highly temperature sensitive.     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

Elastic impact loading of notched beams and bars

Four types of impact specimen, Charpy, Izod, Slender Cantilever and Double Notched Bar, are studied using the technique of dynamic photoelasticity. The growth of fringes with time in low modulus photoelastic material is analysed for each speciment and it is concluded that the stress wave behaviour of the Cantilever geometries and Double Notched Bar offer advantages over the traditional Charpy specimen.

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Résumé On étudie quatre types d'éprouvettes de résilience — Charpy V, Izod, Cantilever mince et Barreau à double entaille — en utilisant une technique de photoélasticité dynamique.On analyse pour chaque type d'éprouvette la croissance en fonction du temps de franges, en utilisant un matériau photoélastique à bas module, et on conclut que les géométries Cantilever et Barreau doublement entaillé présentent certains avantages sur l'éprouvette traditionnelle Charpy, quant au comportement vis-à-vis de l'onde de contrainte.

     

A statistical model for cleavage fracture in notched specimens of C–Mn steel

A statistical model for cleavage fracture in notched specimens of C-Mn steel has been proposed. This model is based on a recently suggested physical model. This statistical model satisfactorily describes the distributions of the cumulative failure probability and failure probability density of 36 notched specimens fractured at various loads at test temperature of −196 °C. The minimum notch toughness has also been discussed.     

A notched cross weld tensile testing method for determining true stress-strain curves for weldments

Cross weld tensile testing is widely used in the industry to qualify welds. In these conventional testing fracture load is measured and the location of fracture (weld metal, base metal or heat affected zone) is evaluated. Because the load-elongation curve depends on the location of fracture and the initial gauge length, it cannot be utilized in the failure assessment of weldments. Failure assessment of weldments requires input of true stress-strain behaviour for each material zone. In this paper, a notched cross weld tensile testing method is proposed for determining the true stress-strain curve for each material zone of a weldment. In the proposed method, cylindrical cross weld tensile specimens, with a notch located either in the weld metal, base metal or possibly heat affected zone are applied. Due to the notch, plastic deformation is forced to develop in the notched region. A load versus diameter reduction curve is recorded. It has been shown that the true strain at maximum load is independent of the notch geometry. Furthermore, the materials true stress-strain curve can be determined from the recorded load versus diameter reduction curve of a notched cross weld tensile specimen by dividing a geometry-factor G, which is approximated by a quadratic function of the specimen diameter to notch radius ratio and a linear function of the true strain at the maximum load. It is found that G is independent of the material zone length when the homogenous material length is larger or equal to the minimum diameter.     

The prediction of R-curves and notched tensile strength for composite laminates

A new model is proposed to explain the cracking and fracture of notched composite laminates. It is based on the energy absorption associated with the micromechanisms of fracture. Crack-growth resistance curves (R-curves) are predicted for a wide range of laminate constructions and materials, and the corresponding notched strengths deduced. Both R-curve and notched strength predictions are in good agreement with published data. The effect of improved fibre-matrix bonding on laminate notched strength is investigated in a case-study, and is successfully predicted using the model.     

Fracture of geometrically scaled,notched three-point-bend bars of high strength steel

The purpose of the experimental work reported in this paper was to provide data that may serve for the development of scaling rules for ductile fracture initiation at blunt notches. Fracture experiments were performed with three sizes of geometrically scaled notched bend specimens of high strength low hardening HY-130 steel using carefully scaled fixturing. Fracture initiation, defined as the appearance of the first sub-millimeter crack with a tensile opening, was reliably detected, using acoustic emission and direct visual inspection with a microscope. Comparison of the normalized load versus load-point displacement curves revealed a significant scale effect on the condition for fracture initiation, with large specimens fracturing at smaller normalized displacement than smaller specimens. The normalized displacement at fracture does not decrease in direct proportion to specimen size. Metallographic cross-sections of the specimens and fractographic observations revealed that at the microscale, fracture initiates by shear localization followed by nucleation and growth of voids under shear and tension in the localization zone. This mechanism profoundly modifies the stress and strain gradients at the notch root so that microstructural length scales become fracture controlling parameters. Both changes are probably responsible for the observed scaling behavior.     

Fully plastic analyses for notched bars and plates using finite element limit analysis

In the present work, fully plastic analyses for notched bars and (plane strain) plates in tension are performed, via finite element (FE) limit analysis based on non-hardening plasticity, from which plastic limit loads and stress fields are determined. Relevant geometric parameters are systematically varied to cover all possible ranges of the notch depth and radius. For the limit loads, it is found that the FE solutions for the notched plate agree well with the existing solution. For the notched bar, however, the FE solutions are found to be significantly different from known solutions, and accordingly the new approximation is given. Regarding fully plastic stress fields, it is found that, for the notched plate, the maximum hydrostatic (mean normal) stress overall occurs in the center of the specimen, which strongly depends on the relative notch depth and the notch radius-to-depth ratio. On the other hand, for the notched bar, the maximum hydrostatic stress can occur in between the center of the specimen and the notch tip. The maximum hydrostatic stress for a given notch depth can occur not for the cracked case, but for the notched case with a certain radius. This is true for both bars and plates. For a given notch radius, on the other hand, the maximum hydrostatic stress increases monotonically with the decreasing notch radius.     

Analysis of creep rupture in a notched tensile bar

For circumferentially notched, round tensile bars the creep rupture behaviour is analysed, based on constitutive relations that account for the nucleation and growth of grain boundary cavities in polycrystalline metals at high temperatures. Both diffusive cavity growth and growth by dislocation creep of the surrounding grains is incorporated in the model, and in some cases free grain boundary sliding is assumed. Failure by cavity coalescence is predicted at small overall strains in the range where cavity growth is constrained by the rate of dislocation creep of the grains, whereas outside this range large occur prior to failure.In the analyses for notched specimens, where the stress fields are strongly non-uniform, first failure occurs at the notch tip, and subsequently a macroscopic crack grows into the material. Various combinations of material parameters are considered, and in most cases the crack is found to grow in the plane of the notch. The results are related to earlier experimental and computational investigations of creep rupture in notched bars.     

A size effect law for notched tensile strength of woven carbon/epoxy laminates

Specimen-size effect and notch-size effect on the tensile strength of woven fabric carbon/epoxy laminates are evaluated and modeled. For two different layups of [(0/90)₁₂] and [(±45)₂/(0/90)₅]_S, respectively, static tension tests were performed on two-dimensional geometrically similar unnotched and double-edge notched specimens scaled to three different sizes. Experimental results demonstrate that the notched strength of the woven CFRP laminates depend on the size of specimen as well as the size of notch. The ratio of notched strength to unnotched strength decreases as the length of notch increases, regardless of the size of specimen. For a given size of notch, the notch strength ratio becomes larger with decreasing size of specimen. A notch-size effect law is derived by means of the Neuber interpolation method. A specimen-size effect is embedded into the notch sensitivity parameter involved by the notch-size effect law to establish a size effect law that can cope with these two kinds of size effect. The engineering size effect law proposed can adequately describe the specimen-size effect as well as notch-size effect on the tensile strength of the woven CFRP laminates. It is also demonstrated that the size effect law allows determining the size independent fracture toughness on the basis of notched strengths of small specimens that fail in a quasi-brittle manner.