Effect of size on plasticity and fracture toughness

The effect of thickness and width of CT specimens on the plastic zone size has been investigated. The investigation also examines the applicability of the various approaches to fracture toughness measurements such as ASTM E399 K_Ic, J_Ic, R-curve and a new procedure of K_Ic determination proposed recently, to a steel which has medium strength and which undergoes pop-in type unstable crack extension during the toughness testing. The results show that in CT specimens with a constant aspect ratio prepared from a given material and loaded to a given stress intensity factor, the plastic zone size decreases, as the specimen width increases; on the other hand, the thickness has only a comparatively small effect on the plastic zone size. The new procedure of K_Ic determination is verified with experiments on specimens with width to thickness ratio of about 50 and it gives a size independent K_Ic value in specimens whose thickness is 4.5 times less than that required by ASTM E399. The new procedure gives a meaningful value of K_Ic in a situation where all other methods such as ASTM E399 K_Ic, J_Ic and R-curve approach are observed to be inapplicable.     

Ein einfaches Verfahren zur Bestimmung gültiger Bruchzähigkeitswerte von Hartmetallen

A Simple Method of Determining Valid Fracture Toughness Data of Cemented Carbides From a comparison of published data it follows that a valid determination of the fracture toughness of cemented carbides depends on the use of samples containing sharp cracks. It is shown that using the technique of controlled fracture experiments sharp cracks of a given length can be introduced easily and reproducibly into bend specimens. A new evaluation method permits the fracture toughness to be calculated without knowing the crack length if the compliance of the pre-cracked specimen is measured. The K_Ic values determined in this way are characterized by a very small scatter and agree well with data from the literature which were obtained from specimens of similar composition. A comparison of the flaw size calculated from K_Ic and the bend strength to the failure size detected in fractographic studies shows very good agreement.     

Ermittlung des Bruchwiderstands an Oxidkeramik und Hartmetallen mit verschiedenen Methoden

Fracture Toughness Determination of Alumina and Cemented Carbide with Different Testing Methods Fracture toughness of a sintered alumina and two tungsten carbidecobalt materials was determined using four-point-bend specimens with straight through and chevron notches and with the short rod specimen. With the specimens with a straight through notch a lower K_Ic was measured for Al₂O₃ and a higher for WC-Co compared to the chevron-notched specimens. This behavior was explained by the different shapes of the crack growth resistance curves and the different critical notch radii. For Al₂O₃ a steeply rising crack growth resistance curve was measured in a controlled fracture test, for WC-Co a flatter curve was obtained. The effect of the shape of the crack growth resistance curve and of notch width on the evaluated toughness is discussed.     

Bruchmechanische Charakterisierung des Vergütungsstahls 30 CrNiMo 8 nach verschiedenen Anlaßbehandlungen

Fracture Mechanics Characterisation of the Q & T Steel 30 CrNiMo 8 after Different Heat Treatments The investigations show that the fracture toughness K_Ic of the Q & T steel 30 CrNiMo 8 for large structural members is more sensitive to a change of the tempering treatment than the Charpy energy A_v. For tempering temperatures between 200 and 250°C the fracture toughness K_Ic shows maximum values with K_Ic ? 87 MN/m^3/2, R_m = 1800 MN/m² and R_p0,2 = 1400 MN/m² at room temperature. With these values this steel may be an inexpensive alternative to the maraging steels, for example to 18 Ni 300 (X 2 NiCoMo 18 9 5) with K_Ic = 76 MN/m^3/2 at R_m = 2100 MN/m² and R_p0.2 = 2000 MN/m² (aged 4 h 480°C). Elastic-plastic fracture toughness values K_Ji were determined at onset of stable crack growth with specimens that fail after more or less large plastic deformations because the thickness of specimen is too small or test temperature and tempering temperature, respectively are too high. These values are essentially independent of specimen size, if some minimum size conditions are fulfilled, and they are in agreement with the linear elastic fracture toughness K_Ic. But the test of more especially large linear elastic failing specimens may clarify the uncertainty whether this procedure delivers conservative results in all cases.     

Study on ASTM E399 and ASTM E1921 standards

Costs of ASTM E399 and ASTM E1921 tests, which were developed to determine the fracture toughness (K_Ic) and the ductile–brittle transition temperature of ferritic steels, respectively, are considered high and the procedures are also very complicated. In this study, a method, which is more cost‐effective and easier to carry out, is proposed.     

Fracture Toughness Determination for Aluminium Alloy 2011-T6 using Tensile Notched Round Bar (NRB) Test Pieces

While the use of notched round bar (NRB) test pieces to determine planestrain fracture toughness K _Ic is not novel, relatively few authors have so far attempted this. This letter serves to report a series of such tests conducted on Al 2011-T6, a high mechanical strength, free-machining aluminium alloy. A total of 9 specimens was used, comprising 3 specimens each of 3 different notch root radii, ρ. No fatigue precracking was carried out. A graph of apparent fracture toughness K _ρ versus ρ / D was extrapolated to zero, corresponding to a fatigue pre-cracked configuration. The resulting K _Ic for this alloy tested using the NRB specimens was thus found to be 27.9 MPa√m. This is a valid K _Ic value, as there is only a 6.8% difference between it and the median value (26.0 MPa√m) determined previously from 67 tests using the existing ASTM E399 standard. A new geometric correlation based on ρ, D and d is proposed to linearly extrapolate K _ρ values, measured on NRB specimens with arbitrary geometries (but assuming plane-strain conditions hold), back to a single value of K _Ic.     

Evaluation of the ISO <Emphasis Type="Italic">J</Emphasis> initiation procedure using the EURO fracture toughness data set

The multiple specimen J _0.2/BL initiation fracture toughness test procedure from the ISO standard, ISO 12135:2002, is evaluated using the EURO fracture toughness data set. This standard is also compared with the ASTM standard, ASTM E 1820, multiple specimen J _Ic procedure. The EURO round robin data set was generated to evaluate the transition fracture toughness methods for steels. However, many of the tests resulted in ductile fracture behavior giving final J versus ductile crack extension points. This is the information that is measured in a multiple specimen J initiation fracture toughness test. The data set has more than 300 individual points of J versus crack extension with four different specimen sizes. It may be the largest data set of that type produced for one material. Therefore, its use to determine J initiation values can provide an important evaluation of the standard procedures. The results showed that a J _0.2/BL value could be determined from the ISO standard for three of the four specimen sizes, the smallest size did not meet the specimen size requirement on J. The construction line slopes in this method are very steep compared with the ASTM construction line slopes. This resulted in low J initiation values, about a factor of two lower than the one from the ASTM method. Of the various criteria imposed to determine a valid J _0.2/BL value, the one limiting the maximum J value was the most questionable. It had an effect of eliminating small specimen data that was identical to acceptable large specimen data.     

A new method for determining the fracture toughness of main pipeline steels

One of the fundamental aims of fracture mechanics is to define fracture toughness K_IC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large‐sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.     

Compliance calibration of a family of short rod and short bar fracture toughness specimens

A family of short rod and short bar specimen geometries is defined for which the calibrations of all members of the family are equivalent. The family includes most of the short rod and short bar specimens now being used to test metallic materials. Experimental compliance vs crack length measurements were made for calibration purposes on members of the family and on specimens which purposely differed from the family in certain respects. The resulting calibrations are presented in a form which is readily usable in analyzing short rod/short bar fracture toughness tests.The calibrations of this study are used to correlate with previously published short rod calibrations. Very good agreement among compliance-derived calibrations was found, but the currently-used calibration based on comparison testing against ASTM E399 K_Ic tests was found to be several percent lower than the compliance-based calibrations. Probable reasons for such a discrepancy are discussed, and recommendations are made concerning which calibration to use.     

Der Mischbruch im Zugversuch

Mixed fracture in the tension test If a tensile test specimen does not break before by cleavage, voids are nucleated at second-phase particles and inclusions during plastic deformation. At the center of the necked region these voids coalesce by internal necking or shearing of the material between them forming a fibrous crack which expands radially. In a temperature range which is dependent on the material cleavage fracture is initiated by the fibrous crack, resulting in a mixed fracture. If no cleavage fracture is initiated a completely fibrous fracture is formed. Mixed fracture surfaces consist of a cleavage fracture zone surrounding the central fibrous fracture zone and the tensile specimen behaves like a fracture mechanics specimen. Fracture toughness can be calculated by equations for tensile specimens with a central penny shaped crack. A comparison of fracture toughness values obtained by the use of unnotched tensile specimens and of fracture mechanics specimens show good agreement inbetween the temperature range of valid K_lc values according to standards of linear-elastic fracture mechanics.     

Mode-I fracture toughness testing of thick section FRP composites using the ESE(T) specimen

Experimental and numerical analyses are performed to determine the translayer mode-I fracture toughness of a thick-section fiber reinforced polymeric composite using the eccentrically loaded, single-edge-notch tension, ESE(T) specimen. Finite element analyses using the virtual crack closure technique were performed to assess the effect of material orthotropy on the mode-I stress intensity factors in the ESE(T) specimen. The stress intensity factors for the proposed ESE(T) geometry, are calculated as a function of the material orthotropic parameters. The formula is validated for a class of thick composite materials. The thick composite tested in this study is a pultruded composite material that consists of roving and continuous filament mat layers with E-glass fiber and polyester matrix materials. Data reduction from the fracture tests was performed using two methods based on existing metallic and composite ASTM [ASTM E 1922, Standard Test Method for Translaminar Fracture Toughness of Laminated Polymer Matrix Composites, Annual Book of ASTM Standards, 1997; ASTM E 399, Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials, Annual Book of ASTM Standards, 1997] fracture testing standards. Criteria for assessing test validity and for determining the critical load used in calculating the fracture toughness were examined. Crack growth measurements were performed to determine the amount of stable crack growth before reaching critical load. The load versus notch mouth opening displacement, for different crack length to width ratios is affected by material orthotropy, nonlinearity, and stable crack propagation. The mode-I translayer fracture toughness and response during crack growth is reported for ESE(T) specimen with roving layers oriented both, transverse and parallel to the loading direction.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

The use of small specimen strength ratio for measuring fracture toughness

The specimen strength ratio ($\text{R}{}_{\mathrm{s}}$), determined from small specimen tests was correlated with plane strain fracture toughness ($\text{K}{}_{\mathrm{Ic}}$) values for many heats of A533B-1 steel. A variety of loading rate and specimen size results suggest that $\text{K}{}_{\mathrm{Ic}}$ can be predicted from the small specimen strength ratio up to values of $\text{R}{}_{\mathrm{s}}$ near 2.0. Also, conservative estimates of cleavage-initiated, elastic-plastic fracture toughness can extend beyond $\text{R}{}_{\mathrm{s}}$ values of 2.0. The ASTM E399 size criterion appears to be too restrictive for the class of steel studied, and a more appropriate requirement would reduce the ASTM criterion by a factor of four.     

Fracture toughness evaluation of a H.S.L.A. steel

The fracture toughness, J_Ic of a 3.5 Ni-Cr-Mo-V steel has been measured using the ASTM method. The results have been used to predict the stress intensity factor, K_Ic from the relationship between linear elastic and elastic-plastic fracture parameters. These predicted values were compared with K_Ic values obtained from empirical equations based on valid K_Ic tests, involving the Charpy upper shelf energy. It was found that the ASTM method for measuring J_Ic led to conservative estimates of K_Ic.     

A direct estimate of JIc from the load versus load-line displacement record

The purpose of this study is to examine the current standard fracture toughness test procedure to determine if there could be an easier method to get a J_Ic value from the test record. The current method for determining J_Ic involves a detailed computational and construction procedure. The objective in this study is to simplify the analysis for the determination of J_Ic. The results of this study show that the load and displacement record for a fracture toughness test can be used to directly estimate a J_Q value, a provisional value for fracture toughness, J_Ic. The J value taken at the maximum load point can be used along with an adjustment factor to estimate a J_Q value. This J_Q estimate is close to the one obtained from the construction procedure of ASTM Standard E 1820. When a unit‐sized specimen is tested, that is, a specimen with a width of 50 mm and a thickness of 25 mm the maximum load point provides a direct estimate of J_Q. Other sizes require a size adjustment factor, which is simply a square root relationship between the width of the test specimen and a unit width. The proposed new method of estimating J_Q is simple in concept and requires a minimum number of calculations. It appears to produce values of J_Q which are comparable to those obtained from the ASTM E1820 construction procedure and may produce less scatter.     

Fracture toughness of austempered chilled ductile iron

Abstract

The structure and properties of ductile iron are highly dependent on the solidification mechanism, and chills are used to promote directional solidification to obtain sound castings. A series of fracture toughness experiments was carried out, involving austempered chilled ductile iron containing 3·42%C, 1·8%Si, and other alloying elements. By using copper chills of different thicknesses, the fracture toughness with varying chill rate was examined. Fracture toughness tests were carried out using three point bend specimens, each with a chevron notch, according to ASTM Standard E399 : 1990. It was found that the fracture toughness of austempered chilled ductile iron is highly dependent on the location in the casting from where the test specimens are taken and also on the nickel and molybdenum contents of the material. Chill thickness, however, also affects the fracture toughness of the material.     

Effects of specimen thickness on fracture toughness of an aluminum alloy

J-integral resistance curves for three specimen thicknesses and valid (according to ASTM Method E 399) K _Icvalues at 76 K are reported for aluminum alloy 2219. The J-integral values were independent of thickness at small crack extensions, but at substantial crack extensions the values for the thin specimens were larger than those for the thick specimens. The measured J _Icvalues were less than those calculated from the measured K _Icvalues. The reason for this discrepancy was that crack extension occurred before the K _Icmeasurement point was reached.

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Résumé On fournit les courbes de résistance experimée par l'intégrale le J pour trois épaisseurs d'éprouvettes et les valeurs valides de K _Ic(suivant la méthode ASTM.E.399) à 76 K pour un alliage d'aluminium 2219.Les valeurs de l'intégrale J sont indépendantes de l'épaisseur dans le cas de petites extensions de fissure, mais on observe qu'elles sont plus élevées pour des faibles épaisseurs que pour des épaisseurs plus fortes, lorsque l'extension de la fissure devient importante.Les valeurs de J _Icmesurées sont plus basses que celles calculées à partir de mesures de K _Ic. Cette différence résulte de ce que l'extension de la fissure se produit avant que ne soit atteint le point de mesure de K _Ic.

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This research was partially supported by the Advanced Research Projects Agency of the US Department of Defense; it is a contribution of NBS, not subject to copyright.

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NRC-NBS Postdoctoral Research Associate, 1974–1975.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

Application of the method of caustics to the centre-cracked diametral compression test specimen

Normalized Mode I stress intensity factors,N ₁(a/R), for symmetrical radial cracks in diametral compression test specimens were experimentally evaluated using disc specimens of polymethyl methacrylate and the method of caustics. The method of caustics was first employed with precracked three-point bend specimens to assess the optical constant for the test material. This material property and the diameters of the caustics as a function of the applied load at different relative crack lengths (a/R) yielded the non-dimensional stress intensity factors using equations presented by Theocaris. These experimental values agreed closely with the theoretical solutions reported in the literature. Disc specimens of a polycrystalline alumina were also tested in diametral compression at temperatures up to 1000° C and the measured fracture toughness values were compared to those measured with chevron-notched bend specimens. It is shown that the centre-cracked diametral compression specimens give very reproducible fracture toughness measurements, and the specimen and the test technique can be usefully employed to assess the fracture toughness of structural ceramics at both ambient and elevated temperatures.     

Evaluation of the fracture toughness properties of polytetrafluoroethylene

Polytetrafluoroethylene (PTFE) (Dupont Tradename Teflon) is a common polymer with many structural applications including sheet, gaskets, bearing pads, piston rings and diaphragms. The interest here developed because this polymer is being considered as the major component of a newly proposed `reactive' material with a possible application as a projectile to replace common inertial projectiles. Little mechanical property data is available on this material since it is commonly used only as a coating material with the dominant properties being its low friction coefficient and high application temperature. Previous work (Joyce, 2003) on commercially available sheet PTFE material has demonstrated the applicability of the normalization method of ASTM E1820 (1999), the elastic-plastic fracture toughness standard to develop fracture toughness properties of this material over a range of test temperatures and loading rates. Additional work on the aluminum filled `reactive' derivative of the basic PTFE polymer (Joyce and Joyce, 2004) has also recently been completed. In this work, standard ASTM E1820 fracture toughness specimens machined from sintered pucks of PTFE were tested at four test temperatures and at a range of test rates to determine the J _Ic and J resistance curve characteristics of the PTFE material. The major results are that while crack extension is difficult at standard laboratory loading rates at ambient (21 °C) temperature or above, for temperatures slightly below ambient or for elevated loading rates, a rapid degradation of fracture resistance occurs and cracking occurs in a ductile or even nearly brittle manner.