The equivalence of K Ic and J Ic fracture-toughness measurements in Ni−Cr−Mo steels

Several series of fracture-toughness measurements were made in 4340 type steels, using both the standardK _Ic test method and theJ _Ic test method described by Landes and Begley.K _Ic results andJ _Ic results converted toK _Ic units are nearly identical for a given steel over a range of specimen size. The fracture toughness of steels produced by vacuum-degassing, remelt, and airmelt processes are compared over a range of yield stress. SimplifiedJ _Ic test procedures are suggested for use with Ni?Cr?Mo steels within certain ranges of yield stress and specimen geometry.     

A system of modified epoxies for dynamic photoelastic studies of fracture

In order to develop a moderately tough transparent polymer, a three-component modified epoxy was investigated. The polymer system included an epichlorohydrin/bisphenol A epoxy, a polyoxypropyleneamine curing agent and a curing accelerator. Twelve different compositions were prepared and evaluated in a series of static and dynamic tests to determine the material properties important in photoelastic studies of fracture. Static tests showed that the critical strain-energy release rate could be varied from 1.4 to 4.1 lb/in. by changing the constituents in the blending of the epoxy. These results forG _Ic indicate that the modified epoxies are considerably tougher than Homalite 100 (G _Ic =0.33 lb/in.) which is commonly employed as a model material in dynamic photoelastic studies. Dynamic photoelastic tests were conducted with half-plane models in order to determine the dilatational- and distortional-wave velocities,c ₁ andc ₂, as well as dynamic values of the modulus of elasticityE and Poisson's ratio ν at loading times of the order of 10^?5 s. These results indicated that the dynamic modulus of some of the modified epoxies was significantly higher than the static modulus indicating that these polymers are rate sensitive. One of the epoxy materials, Blend No. 3 withG _Ic =2.65 lb/in. (464J/m²), was calibrated dynamically. The material fringe value changed nearly linearly as a logarithmic function of time with an increase of about 100 percent as the loading time decreased from 10⁴ to 10^?4 s. This large variation inf _σ implies that the calibration constant must be adjusted when interpreting dynamic fringe patterns. Two of the epoxy compositions were also characterized in a number of fracture experiments involving crack propagation at velocities ranging from arrest conditions to terminal velocity where branching initiates. Dynamic isochromatic-fringe loops were photographed with a Cranz-Schardin multiple-spark camera. The fringe loops were analyzed to give the instantaneous stress-intensity factorK as a function of crack velocity å. The å vs.K curves appear to be invertedL shapes; however, there appears to be a double branch on the vertical part of theL. Also a slightly higherK is required for accelerating cracks and a lowerK for decelerating cracks. Further investigation is required to identify the basic mechanism involved in this fracture behavior.     

K Ic and J-resistance-curve measurements on Nevada tuff

Linear-elastic fracture mechanics and J-integral test methods were used to determine the static fracture behavior of a porous volcanic tuff. Notched and prefatigued specimens of two different sizes were tested in three-point bending. The fracture toughness (K _Ic ) and theJ-resistance (J vs. crack growth) curve for each specimen was determined. The results indicate that there is good agreement between the fracture parameters determined by the two methods; however, there is some dependence of the results on specimen size. Possible reasons for this specimen-size dependence are discussed.     

Dynamic mechanical and fracture properties of an infiltrated TiC-1080 steel cermet

The dynamic mechanical and fracture properties of a TiC porous network infiltrated with1080 steel are reported. Following infiltration, the cermet is subjected to various heat treatments that affect essentially the steel matrix. Dynamic compression tests show that the heat treatments increase the fracture strength of the cermet. The quasi-static fracture toughness (K_Ic) is also increased by the heat treatments. The dynamic (initiation) fracture toughness (K_Id) is substantially higher (by about a factor of 3) than its static counterpart. Failure mechanisms consist mainly of cleavage of the TiC and matrix grains, along with minor interfacial decohesion. However, dynamic loading induces substantial damage around the crack tip, consisting essentially of cleavage of TiC grains. Microcrak toughnening is believed to be responsible for the high dynamic toughness of the material. The critical microstructural fracture event is thus identified as the spreading of TiC cleavage microcracks into the neighboring steel grains.     

Fracture Characterization of Steels by Means of the Small Punch Test

A hot rolled API X-70 steel plate and its heat-affected zone (the region with the maximum hardness and lowest toughness of the welded joint made using this steel) were employed to obtain the material’s room temperature elasto-plastic fracture toughness, J_Ic, by means of small punch tests (SPTs) using both conventional un-notched samples and longitudinally-notched SPT specimens. In the latter case, the notches were manufactured by micromachining different notch depth-to-thickness ratios (a/t?=?0.3 and 0.4). The representative toughness parameter used with the conventional SPT tests was the maximum strain measured directly in the failed region, while in the case of the notched samples, the consumed energy until the initiation of a crack from the tip of the notch was considered the most useful parameter of choice. The onset of crack initiation was determined directly from the load-displacement plot of each test with the aid of scanning electron microscope observations performed on different samples over which interrupted tests had been conducted. These tests were interrupted at different percentages of the maximum registered load. A simple correlation between the energy consumed until the initiation of crack growth in the notched SPT sample and the critical J value obtained using standard tests (J-R curves) was determined, defining an easy and promising way to derive fracture toughness from miniature SPT tests.     

Initiation and arrest of cracks on two pipeline steels at low temperature

Dynamic fracture toughness at initiationK _1d and fracture toughness at arrestK _1a were measured on two pipeline steel grades. Dynamic fracture toughness was measured at a very high loading rate with the help of split Hopkinson pressure bars. The values ofK _1d andK _1a are compared. The purpose of this work is to examine the possibilities of using dynamic fracture toughness at crack initiation as a lower bound of crack arrest toughness. This work has practical applications because crack arrest tests are difficult to perform, give scattered results and are costly and time consuming. This procedure shows that it is possible to economize and rationalize using intelligent technology.     

Considerations for instrumentation of typical dynamic tests

Three tests recently performed at U. S. Steel's Research Laboratory are used as examples to describe the general application of tape-recorder instrumentation to testing under dynamic-loading conditions. Along with the general discussion of the test instrumentation, the need for suitable equipment and data analysis to prevent erroneous conclusions is also discussed. The three test examples used are (1) the analysis of a long-running ductile fracture, (2) dynamicK _Ic tests, and (3) the dynamic analysis of a 90-ft derrick. Major dynamic-instrumentation problems associated with these studies include those of electrically generated noise, cable cross talk, excessive lead lengths, and crack-speed measurements, as well as problems associated with the interpretation of dynamic results. In each case, the general problem is discussed and the solution explained. Of particular significance are the development of a circuit to measure the velocity of rapid long-running fractures and the development of techniques for eliminating induced noise in timing circuits. A crack-opening-displacement transducer is suggested for measuring the dynamicK _Ic , instead of the usual instrumented loading tup.     

J resistance curves in aluminum SEN specimens using Moiré interferometry

TheU _y -displacement field obtained by white-light moiré interferometry were used to estimate the approximate far- and near-fieldJ-integral values associated with the subcritical crack growths in fatigue precracked 7075-T6 and blunt notched and fatigue precracked 2024-0 and 5052-H32 aluminum, single-edged notch (SEN) specimens. The initial phases of theJ-resistance curves for the somewhat brittle 7075-T6 and the two ductile 2024-0 and 5052-H32 aluminum SEN specimens are presented. Paper was presented at the 1987 SEM Spring Conference on Experimental Mechanics held in Houston, TX on June 14–19.     

Loading rate spectra for fracture initiation in metals

In the first part of the paper a review of experimental results is presented on the effects of loading rate of the fracture initiation toughness of structural alloys. Recent progress in new experimental techniques enables for measuring the fracture initiation properties over ten orders of magnitude in , where loading rate for plane strain fracture toughness. The range covered in experiments is

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.Experimental results for aluminum and titanium alloys, as well as for some steels are discussed. Those results are shown as loading rate spectra where the fracture toughness K_Ic is plotted versus log at constant temperature. The patterns of the loading rate spectra demonstrate a negative role of the strain rate sensitivity in the process of fracture initiation, at least within a certain ranges of the loading rate .In the second part an attempt is presented to model the observed phenomena. Consequently, a new model has been proposed which combines an semi-empirical correlation between the critical fracture stress σ_F, yield stress σ_y from one side and a simple thermally activated potential of plastic flow from the other. It has been demonstrated that this simple approach can predict properly a fundamental changes in the loading rate spectra for steels.     

Characterization of crack-tip strain singularity in brittle-microcracking materials by means of the photoelastic-coating method

The strain fields ahead of crack tips in rock, mortar, and graphite were measured using a photoelastic coating method. A transparent ferroelectric ceramic was used as a coating material to observe the photoelastic fringe pattern. A coating plate of 110–150 μm thick was placed on single-edge-notch specimens, and photoelasticity experiments were conducted in three-point bending under a polarizing microscope. The results show that the principal-strain difference ahead of the crack tip is given by $$\Delta \in = \Delta \in _o [(J/\sigma _{ult} )/r]^m $$ whereσ _ult is the ultimate tensile strength,r is the distance from the crack tip, and9? _o andm are material constants. Based on this observation, the use of theJ _Ic concept in determining the fracture toughness of brittle-microcracking materials is discussed.     

Influence of temperature on a carbon–fibre epoxy composite subjected to static and fatigue loading under mode-I delamination

In this paper, interlaminar crack initiation and propagation under mode-I with static and fatigue loading of a composite material are experimentally assessed for different test temperatures. The material under study is made of a 3501-6 epoxy matrix reinforced with AS4 unidirectional carbon fibres, with a symmetric laminate configuration [0°]_16/S. In the experimental programme, DCB specimens were tested under static and fatigue loading. Based on the results obtained from static tests, fatigue tests were programmed to analyse the mode-I fatigue behaviour, so the necessary number of cycles was calculated for initiation and propagation of the crack at the different temperatures. G–N curves were determined under fatigue loading, N being the number of cycles at which delamination begins for a given energy release rate. G_ICmax–a, a–N and da/dN–a curves were also determined for different G_cr rates (90%, 85%, 75%, etc.) and different test temperatures: 90 °C, 50 °C, 20 °C, 0 °C, ?30 °C and ?60 °C.     

Revisit to the determination of stress-intensity factors and J-integrals using the caustics method

Applications of the optical (shadow) method of reflective caustics to measurement of the stress-intensity factor andJ integral in various specimens are investigated. The necessary experimental requirements to help determine accurate stress-intensity factor andJ integral are described. The ratios ofr _o (radius of initial curve)/r _p (plastic-zone size) andr _o/t(thickness of specimen) are found to be very important experimental parameters to obtain meaningful stress and/or strain intensities surrounding crack tips. The appropriate ranges to determine accurate values of stress-intensity factor andJ integral for polycarbonate (compact tension) and aluminum (c-shaped tension) specimens are presented. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

An improved experimental method for the determination of the critical stress intensity factor KIc of brittle materials

The critical stress intensity factor K_Ic is determined by a simple and accurate method, using small test specimens and a simple procedure in this paper.Single edge V-notched tension specimens made of PMMA are subjected to a load which is slowly increased until the crack begins to move from the notch tip. During the crack propagation event shadow patterns at the tip of the crack are recorded in a video recorder. Under these loading conditions, the creating real crack propagate slowly until the crack propagation velocity take an abrupt increase and the entire fracture of the specimen takes place. The stress intensity factor which correspond to the transition from the slow to fast crack speed, is the critical stress intensity factor K_Ic and it can be the fracture toughness of the material.The results are accurate and in good agreement with those values of K_Ic which are calculated by approximate theoretical expressions.The purpose of this paper is to introduce an improved, simple and accurate experimental method for the determination of fracture toughness of brittle materials.     

Heat transfer and pressure drop in fluidized bed cooling tower

Experimental investigation has been carried out on a counter flow three-phase fluidized bed cooling tower (FBCT) with different static bed heights. The efficient static bd height for the present tower is found to be between 11 cm and 13 cm. The pressure drop observed is in the order of 0.6 mm of water column per cm of static bed height within the range of parameters investigated.

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Wärmeübergang und Druckverlust in einem Fließbett-Kühlturm

Zusammenfassung An einem Fließbett-Kühlturm unterschiedlicher Statischer Betthöhen, der von einem in drei Phasen vorliegenden Fluid im Gegenstrom beaufschlagt wird, wurde eine experimentelle Untersuchung durchgeführt. Die wirksamen statischen Betthöhen ergaben sich bei diesem Turm zu 11 und 13 cm, der gemessene Druckverlust lag bei etwa 0,6 mm Wassersäule je Zentimeter statischer Betthöhe und zwar im gesamten Variationsbereich der Versuchsparameter.

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Nomenclature p pressure drop across the bed in mm of water column - L liquid flow rate, kg/hr - G gas flow rate, kg/hr - V static bed height – m - T ₁ cold water temperature, °C - T ₂ hot water temperature, °C - i _i specific enthalpy of saturated air, kJ/kg - i _g specific enthalpy of the bulk of the air locally, kJ/kg - K mass transfer coefficient, kg/m² – hr - a cooling area per unit volume, m²/m³     

On ductile fracture initiation toughness: Effects of void volume fraction,void shape and void distribution

This paper studies the effects of the initial relative void spacing, void pattern, void shape and void volume fraction on ductile fracture toughness using three-dimensional, small scale yielding models, where voids are assumed to pre-exist in the material and are explicitly modeled using refined finite elements. Results of this study can be used to explain the observed fracture toughness anisotropy in industrial alloys. Our analyses suggest that simplified models containing a single row of voids ahead of the crack tip is sufficient when the initial void volume fraction remains small. When the initial void volume fraction becomes large, these simplified models can predict the fracture initiation toughness (J_Ic) with adequate accuracy but cannot predict the correct J–R curve because they over-predict the interaction among growing voids on the plane of crack propagation. Consequently, finite element models containing multiple rows of voids should be used when the material has large initial void volume fraction.     

Residual fracture energy of cement paste, mortar and concrete subject to high temperature

Quantifying high temperature damage is an issue that can hardly be dealt with experimentally because of the complexity of the loading control, of temperature and of moisture. The experimental investigation was carried out. The measurement of the mechanical characteristics (fracture energy, tensile strength, elastic modulus and thermal damage parameter) of five cementitious materials, cement paste, mortar, ordinary concrete and two HPC concretes were performed by three-point bending tests after heating/cooling cycles at 120, 250 and 400 °C. The tests showed that the cementitious materials behave almost identical when the fracture energy G_f is considered as a function of maximum temperature. The thermal damage due to heating from 120 to 400 °C increases the fracture energy by 50% with the reference tests at room temperature. A more tortuous crack surface is one reasonable explanation for the significant increase in G_f. It is demonstrated that the temperature exposure makes all cementitious materials tested significantly more ductile and less resistant.     

Influence on fiber inclination and interfacial conditions on fracture in composite materials

Dynamic photoelasticity has been used to study the effect of the fiber-matrix interface and fiber orientation on dynamic crack growth in fiber composites. Two types of fiber-matrix interfaces are considered: well bonded and partly debonded. The fiber-matrix interface is characterized by conducting fiber pullout tests. Partly debonded fibers aligned with the loading direction, result in higher fiber debonded lengths, lower dynamic stress-intensity factorK _ID and lower fracture surface roughness compared to well bonded fibers. Orientation of brittle fibers, with respect to the loading direction, impairs their ability to lowerK _ID , while oriented ductile fibers produce no significant change inK _ID . Misalignment of fibers from the loading direction reduces the fiber debonded length due to kinding of the fiber at the crack face.     

Fracture mechanics applications of absorbed specific fracture energy: Notch and unnotched specimens

The Absorbed Specific Fracture Energy (ASFE)^* is an energy criterion that may be applied to evaluate the embrittlement and fracture properties of low and medium strength structural materials. Some new results are presented to illustrate the application of ASFE, and relating them to the other fracture criteria such as J_1c and K_1c. A comparison of results is made for static and dynamic loading, and the influence of neutron irradiation.     

A new ductile fracture theory and its applications

This investigation discusses further the extent to which a new damage theory recently proposed by the author can serve as a unified theory to characterize various ductile failure problems. A general damage integral and corresponding criterion for ductile fracture are presented. A new parameter for ductile fracture is emphasized, which is experimentally verified as a material constant independent of stress state, has clear physical meaning, and can easily be determined. The applicability of this theory to evaluation of the ductility of welds and engineering materials under various conditions is examined. Also, it is used to predict the effect of residual stress on failure of welds, to predict sheetforming limits, and to correlate the variability of elasto-plastic fracture toughness valuesJ _1c and δ _c with different specimen geometries. A new constraint correction method is proposed, and constraint corrected new toughness parameterJ _dc and δ _dc are recommended. Experiments have shown that the toughness variation with different specimen geometries can effectively be removed by use of the method. The general applicability of the theory to characterization of various ductile failures provides a new design tool for engineering components or structures.     

Multiple specimen J-integral testing at intermediate rates

The effect of experimental technique on the measurement of elastic-plastic fracture toughness has been investigated. Multiple-specimenJ-integral measurements have been performed at an intermediate loading rate. One set of measurements was conducted completely under computer/servohydraulic control, while another set was performed with a fixture that mechanically limits the maximum displacement and load. For the single condition tested, a minimal effect was measured on the initiation fracture toughness. An increased effect was seen on the measured crack-growth-resistance (J-R) curve as the amount of crack growth increased. The consequences of such testing methods in terms of general (intermediate loading rate) testing will be discussed.