Ductile fracture of a pipe with a rectangular three-dimensional defect

A model is constructed to describe the ductile fracture of a pipe with a rectangular three-dimensional defect. Upper and lower bounds are obtained for the burst pressure. The first is calculated for a rectangular crack, while the second is calculated for an axisymmetric three-dimensional defect. It is shown that if the half-width of the defect b₀ is equal to 2(Rt_n)^1/2 — where R is the radius of the pipe and t_n is the net thickness of the pipe wall—then the defect can be regarded as axisymmetric. Calculated values of burst pressure are compared with literature data from full-scale tests of pipes. The results can be used to analyze actual defects in pipelines (pitting, etc.), as well as in conducting full- scale tests of pipes and pressure vessels.Translated from Problemy Prochnosti, No. 9, pp. 55–66, September, 1995.     

Simulation of the limit state of thin-walled pipes with repeating axial defects

The existing standards for simulation of multiple defects are, as a rule, created for the analysis of brittle strength of cracked bodies. At the same time, it seems much more important to be able to determine the ultimate load of ductile fracture P_LL. We propose a general analytic procedure for the evaluation of P_LL for pipes with two equal surface defects (cracks or concentrators) or through cracks. Analysis of the accumulated data shows that the generally accepted rules for simulation of defects are nonconservative and may lead to qualitative errors. Scientific and Engineering Center of Materials-Science Support of the Production and Certification of Equipment of Nuclear Power Plants at the Institute for Problems of Strength of the National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 172 – 180, March – April, 1998.     

Description of two-dimensional spallation in pure copper

A new ductile dynamic failure model, based on a porous element consisting of a single spherical void of radius a in a sphere of radius b subject to internal pressure P_g and external stress _r = – P + ( – 1) P_g is developed in the present work. Work-hardening behavior, rate-dependent contribution and inertial effects are taken into account in the model. Stress controlling mechanism is adopted while considering the contribution of void nucleation to rate of porosity . The mathematical model presented here is incorporated in a hydrodynamic two-dimensional finite-difference computer code, to simulate two-dimensional spallation of pure copper. Comparison of numerical calculation with experimental results shows that the model described the process of spall experiment successfully. The future improvements of the model are discussed.     

An Equation of State for High-Temperature Superconductor

In the present paper the expression of cohesive energy and the bulk modulus as a function of volume are formulated for high-T _c copper oxide superconductors. The model employed consists of long-range electrostatic Coulomb interaction and short-range overlap repulsion. The short-range overlap potential is considered in the Born–Landé inverse power form. The model parameters of the Born–Landé model are calculated from the equilibrium condition and data of bulk modulus at room temperature. The computed values of pressure derivatives of bulk modulus at P=0 and the values of bulk modulus are found to be in very close agreement with experimental values for high-T _c copper oxide and their nonsuperconducting parent compounds. It is also found that the quantity U/U(V ₀) of these compounds increases with increasing hydrostistic pressure.     

Some observations on the assessment of short,sharp cracks at the roots of blunt notches,and their effect on brittle fracture

The paper is concerned with effects of short, sharp quench cracks at the roots of blunt notches on cleavage fracture in a coarse-grained martensitic microstructure. At test temperatures between –196 and –140°C, such cracks control cleavage fracture. The values of local stress intensities calculated by loading such short cracks with the stress field ahead of the blunt notch are closely similar to the values of K _IC measured in long-crack fracture toughness tests. At the test temperature of –100°C, such sharp cracks are blunted out (by ductile crack growth) and appear to play no part in the subsequent failure mechanism, which is now better characterised by values of the local cleavage fracture stress _F ^* , below the notch. At the test temperature of –120°C, a transition region is seen with a large observed scatter in faulure load.In a fine-grained martensitic microstructure tested in the ST-L orientation brittle plates of manganese sulphide inclusions have been shown to promote cleavage fracture at –196°C.

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Résumé Le mémoire est relatif aux effets de fissures de trempe courtes et aiguës dans le found d'entailles arrondies sur la rupture par clivage dans une microstructure martensitique à gross grains. Aux températures d'essai de –196°C et de –140°C, de telles fissures déterminent la rupture par clivage. Les valeurs de concentration locale de la contrainte, calculées en sollicitant ces fissures avec un champ de tension appliqué sur l'entaille arrondie, sont très similaires aux valeurs de K _IC mesurées lors d'essais de ténacité à la rupture sur des fissures longues. A une température de –100°C, les fissures aiguës s'émoussent lors de leur croissance ductile, et n'apparaissent pas jouer un rôle dans le mécanisme de rupture ultérieure, lequel est à présent mieux caractérisé par les valeurs de la tension locale de rupture par clivage _F ^* , au droit de l'entaille.A la température de –120°C, apparaît une zone de transition, avec une grande dispersion de la charge de rupture.Dans une microstructure martensitique à grains fins soumise à essai dans le sens ST-L, des plaquettes fragiles d'inclusion de Sulphure de Manganèse favorisent une rupture par clivage à –196°C.

     

Speed of sound,isochoric heat capacity,and coefficients of adiabatic and isothermal expansion in methyl alcohol at atmospheric pressure

The frequency-pulse method is used to measure the speed of sound in ethyl and methyl alcohols at atmospheric pressure over the temperature range 293–351°K. Values of isochoric heat capacity and coefficients of adiabatic and isothermal expansion of methyl alcohol at atmospheric pressure are calculated for the pressure range 175.47–337.85°K.Notation T temperature - v specific volume - W velocity of sound - C_V, C_P isochoric and isobaric heat - _S, _T adibatic and isothermal contraction coefficients - coefficient of thermal expansion Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 92–98, January, 1982.     

Liquid helium at negative pressures: Nucleation of bubbles and anomalous phonon dispersion

We calculate the rate at which bubbles nucleate in⁴He when the liquid is at negative pressure. Previous calculations have predicted that at low temperatures (T0.3 K) the nucleation rate remains low until a pressure of roughly –15 bar is reached. We show that this result is incorrect, and that at a critical pressure P_c (–9 bar) the liquid becomes macroscopically unstable. We have made a calculation of the nucleation rate allowing for this effect. It is shown that the effect of quantum nucleation is small and probably hard to observe experimentally. Finally, we demonstrate that one can understand the pressure dependence of the phonon dispersion relation by a simple model. This model uses a parameter which also enters into the nucleation calculation.     

Prediction of the Inversion Curve and the Maximum Value of μJ–T for Some Refrigerants

In the present work, the thermodynamic states of the inversion curve have been obtained using only p–v–T data. We have also shown a linear relationship between compressibility factor and pressure for each branch of the inversion curve. These lines can be used to find the maximum inversion pressure, P _in ^M . Finally, we have predicted the temperature at which the Joule–Thomson coefficient, _J–T, has its maximum value for each isobar, by using the specific heat capacity, isobaric expansivity, or compressibility factor.     

Use of a Ring DWTT Specimen for Determination of Steel NDT from Pipe of Diameter Less than DN500

It has become recognized that the drop weight tearing test (DWTT) energy better represents the ductile fracture resistance of pipe steels since it utilizes a specimen that has the full thickness of the pipe and has a fracture path long enough to reach steady-state fracture resistance. However, the API 5L code does not require it for pipe sizes less than DN500. The aim of this paper is to propose a DWTT specific to small diameter pipes based on a new specimen, the ring drop weight tearing test (RDWTT) specimen; to evaluate the transition temperature T _{t, DWTT} and nil ductility temperature of the pipe steel API 5L X65; to introduce the transition temperature T _{t, DWTT} in the transition temperature material master curve of the API 5L X65 steel; and to compare the prediction of the crack ductile extension in a pipe based on the RDWTT’s energy and crack tip opening angle in the case of the steel API 5L X65.     

Mixed Mode Stress Intensity Factor Determination of Multiple Cracks in Hollow Circular Pipe

Failure of pressure vessels and piping due to high temperature applications occurs due to the formation of fatigue cracks caused by cyclic load. It is well known that, the consequences of collapses of pipes causing enormous disruption of daily life. Thus there is a need to design and manufacture the pipes with precision and care. The major cause of crack nucleation in pipes is due to corrosion and internal fluid pressure. The crack-tip stresses are determined using stress intensity factor (SIF). In the present work an attempt has been made to determine the SIF for multiple cracks in a circular pipe subjected to internal fluid pressure. Two surface cracks of same size were introduced at the inner wall of the tube. The crack depth ratio (a/t) ranging between 0.1 and 0.5 and crack aspect ratio (a/c) of 0.6 and 1.0 was considered. Internal fluid pressure of 100 MPa was applied at the inner surface of the pipe and the corresponding SIF was measured. SIF values were calculated with consideration of mode-II and mode-III fracture in order to predict the exact SIF. As available SIF solutions of cracked pipes are limited to mode-I fracture, present work presents the influence of additional influence of mode-II and mode-III fracture. It is observed that, as crack depth ratio increases, SIF also increases considerably for semi-circular cracks. Higher SIF values were observed at the crack surface region [S/S ₀ = ±1] compared to crack middle [S/S ₀ = 0] region. A crossover in SIF was noted at a crack depth ratio of 0.3. At higher crack depths, SIF values decrease at the crack surface region due to additional influence of mode-II and mode-III fracture. In contrast to semi-circular cracks, SIF values are higher at the crack surface region for semi-elliptic cracks irrespective of the crack depths.     

Fabrication and mechanical properties of silicon carbide–silicon nitride nanocomposites

A powder mixture of ultrafine –SiC–35 wt% –Si₃N₄ containing 6 wt% Al₂O₃ and 4 wt% Y₂O₃ as sintering additives were liquid–phase sintered at 1800°C for 30 min by hot–pressing. The hot–pressed composites were subsequently annealed at 1920°C under nitrogen–gas–pressure to enhance grain growth. The average grain–size of the sintered bodies were ranged from 96 to 251 nm for SiC and from 202 to 407 nm for Si₃N₄, which were much finer than those of ordinary sintered SiC–Si₃N₄ composites. Both strength and fracture toughness of fine–grained SiC–Si₃N₄ composites increased with increasing grain size. Such results suggested that a small amount of grain growth in the fine–grained region (250 nm for SiC and 400 nm for Si₃N₄) was beneficial for mechanical properties of the composites. The room–temperature flexural strength and fracture toughness of the 8–h annealed composites were 698 MPa and 4.7 MPa · m^1/2, respectively.     

Superconductivity, Upper Critical Field and Anomalous Normal State in CePd2Si2 Near the Quantum Critical Point

We report resistivity measurements performed on a high quality single crystal of CePd₂Si₂ under hydrostatic pressure. At ambient pressure the de Haas–van Alphen effect has been also studied. Two different frequencies with weak angular dependence were detected with magnetic field lying in the basal plane, while another frequency was found with magnetic field parallel to the tetragonal c axis. Near the critical pressure, P_c27 kbar, where the antiferromagnetic transition vanishes, the normal state resistivity does not follow the usual Fermi-liquid (FL) behavior and is described by a T^1.3 law, while just below P_c, the resistivity shows clearly separated spin wave and electron–electron contributions. At P_c, the FL form of (T) is not restored even at magnetic field up to 6T. The first appearance of superconductivity is observed at P=19 kbar, and the critical temperature increases with pressure up to 27 kbar. The analysis of the upper critical field at P_c shows that the superconducting state is well described by a weak coupling, clean limit model with a slightly anisotropic orbital limit and a strongly anisotropic paramagnetic one.     

Application of the essential work of fracture method in ranking the performance in service of high-density polyethylene resins employed in pressure pipes

High-density polyethylene resins have increasingly been used in the production of pipes for water- and gas-pressurized distribution systems and are expected to remain in service for several years, but they eventually fail prematurely by creep fracture. Usual standard methods used to rank resins in terms of their resistance to fracture are expensive and non-practical for quality control purposes, justifying the search for alternative methods. Essential work of fracture (EWF) method provides a relatively simple procedure to characterize the fracture behavior of ductile polymers, such as polyethylene resins. In the present work, six resins were analyzed using the EWF methodology. The results show that the plastic work dissipation factor, βw _p , is the most reliable parameter to evaluate the performance. Attention must be given to specimen preparation that might result in excessive dispersion in the results, especially for the essential work of fracture w _e .     

Substantiation of two-criterial,failureestimation diagram for pressure vessels and pipelines with axial through cracks

A form of diagram for failure estimation is tested on the basis of results of full-scale experiments on the failure of pressure vessels and pipelines with axial through cracks. Use of the two-criterial approach to predict the failure of structural components containing a crack in the brittle, mixed, and ductile regions of failure is substantiated. For example, the brittle failure of cylindrical bodies with through cracks is monitored by criteria of linear fracture mechanics, and ductile failure by the criterion established when the load attains its limiting value (P=P_l ^d).Translated from Problemy Prochnosti, No. 11, pp. 34–45, November, 1992.     

Load and directional effects on microhardness and estimation of toughness and brittleness for flux-grown LaBO3 crystals

Results of microhardness measurements on (100) and (110) planes of flux-grown LaBO₃ crystals, in the applied load range of 10–100g, are presented. The microhardness was found to decrease with increasing load in a non-linear manner. By applying Hays and Kendall's law, the materials resistance pressure and other constants of the equation could be calculated. Hardness anisotropy, showing periodic variation of H _v with the maxima and minima repeating at every 15° change in orientation of the indentor, is described and discussed. H _max/H_min are estimated as 1.14 and 1.06 for (100) and (110) planes, respectively. The fracture toughness values, K _c, determined from measurements of crack lengths, are estimated to be 1.6, 1.7 MN m^–3/2 (for (100) planes) and 1.2, 1.5 MN m^–3/2 (for (110) planes) at 90 and 100g loads, respectively. The brittleness index, B _i, is estimated as 4.6, 4.0 m^–1/2 (for (100) planes) 6.0, 4.6 m^–1/2 (for (110) planes) at 90 and 100g, loads respectively.     

Fracture Resistance of Residually-Stressed Ceramic Laminated Structures

We have studied the effect of residual stresses on fracture resistance and crack arrest behavior of asymmetric ceramic laminated Si ₃ N ₄/Si ₃ N ₄–TiN structures. Using the compliance method, we assessed the technique of R-curve construction for laminar composites. For laminar structures with layers varying by their elastic characteristics we developed an analytical method for calculation of fracture resistance – crack length dependence. The method applicability is verified by calculation of stress intensity factors for laminar specimens with an edge crack. The calculated results are compared to the experimental data.     

The mechanical behaviour of high-impact polystyrene under pressure

High-impact polystyrene [HIPS], a two-phase polymeric system, has been investigated studying the pressure dependence of stress-elongation behaviour in tension over the range from atmospheric pressure to 4 kbar at room temperature and constant strain-rate. A comparative study of polystyrene [PS] was also undertaken. HIPS sealed from the environment exhibited ductile behaviour at all pressures. Surprisingly, specimens exposed to silicone oil environment exhibited two transitions as the applied hydrostatic pressure was raised: a ductile-to-brittle followed by a brittle-to-ductile transition. Stress-whitening was suppressed at relatively low pressures. The dilational requirement for profuse crazing was restrained by the combined effect of fluid under pressure resulting in the suppression of the energy absorption mechanism.Analysis of the stress-elongation curves for sealed specimens indicated that the pressure dependency of craze-initiation stress differs from that of shear band initiation stress. The brittle-to-ductile transition occurred when the initiation stresses of both processes became equal. The principal stress for craze initiation showed almost no pressure dependency, suggesting that crazes initiate when the principal stress level of the tensile specimen reaches a critical value irrespective of the applied hydrostatic pressure. A value for the proposed triaxial tension around the rubber particles was determined from the experimental results and found to be in good agreement with a calculated value. A general mechanics argument was used to explain the existence of the ductile-to-brittle and the brittle-to-ductile transition in HIPS, and also to predict the pressure dependencies of brittle-fracture stress and craze-initiation stress for sealed and non-sealed specimens.Nomenclature P hydrostatic pressure, here taken as always positive - BD brittle-to-ductile transition - CS craze-to-shear band transition - _T observed tensile stress - ¹ the first principal stress - _f ^s fracture stress for sealed specimens - _f ^ns fracture stress for non-sealed specimens - _y yield stress - _f fracture stress - _ci craze initiation stress     

Energy absorption and ductile failure in metal sheets under lateral indentation by a sphere

This paper is concerned with the mechanics of lateral indentation of a rigid sphere into a thin, ductile metal plate. The paper presents a study including experiments, analytical theories and finite element calculations. The focus is on the prediction plate failure and on the energy absorption up to this point. Load–displacement curves from experiments are presented for various plate geometries (circular, square, rectangular), indentor radii and locations of loading on the plate. The experiments show that the penetration to ductile fracture and the energy absorption is sensitive to both plate geometry, loading position and indentor geometry. The plate fails by localised necking followed closely by material fracture. Analytical theories are derived for the load–displacement behaviour of a plastic membrane up to failure. The point of plate failure is determined by a global stability criterion taking into account both the change of geometric and material stiffness during the indentation process. For the cases of axis-symmetric loading very good agreement between measured and theoretical load–displacement curves up to — and including — the point of initial plate failure is found. Curve fitting to the theoretical solutions produced the following expressions for the penetration and absorbed energy up to plate failure: where C₀ and n are the strength coefficient and the hardening exponent in the material power law, t₀ is the initial plate thickness, R_b is the indentor radius and R is the plate radius. The tests were also modelled by the use of a commercially available finite element program. It is shown that the applied finite element method can accurately predict the response up to necking and fracture initiation for both symmetric and non-symmetric loading.     

Tait's Equation of State for Liquid Mixtures

The methods of statistical theory of liquid state are used to validate the well-known Tait's equation of state for liquid mixtures. An expression is derived which relates the coefficients A and B of Tait's equation of state to the parameters of steepness of repulsion forces m and to the thermodynamic properties of the system. P–V–T–x measurements for a water-acetone system are performed to check the theoretical results. The method of molecular dynamics is used to calculate the parameters of steepness of repulsion forces of a water-acetone mixture at different temperatures and concentrations. It is demonstrated that m in the treated ranges of temperature and pressure assumes a constant value of 15. The theoretically obtained coefficient A coincides with the experimentally obtained value within the experimental error, and the coefficient B describes qualitatively correctly the temperature and concentration dependences obtained as a result of P–V–T–x measurements.