Stable Crack Extension Research Articles

Application of ductile fracture assessment methods for the assessment of pressure vessels from high strength steels (HSS)

The economical and safe design of pressure vessels requires, besides others, also a detailed knowledge of the vessel failure behaviour in the case of existing imperfections or cracks. The behaviour of a cracked component under a given loading situation depends on material toughness. For ferritic steels, the material toughness is varying with temperature. At low temperature dominantly brittle fracture behaviour is observed, at high temperature the failure mode is dominantly ductile fracture. The transition between these two extremes is floating. In the case of existing or postulated cracks, the safety analysis has to be performed using fracture mechanics methods. In the lower shelf of toughness, K Ic as of ASTM E 399 is the characterising value for crack initiation and immediate unstable crack extension (cleavage). In the upper shelf level the characterising value is the ‘actual crack initiation toughness’ J i acc. to ISO 12135, characterising the onset of slow stable crack extension. For the transition regime in ASTM E 1921 the instability values K Jc are defined, characterising cleavage failure after more or less extended ductile crack growth. The safety analysis of a component operated in the upper shelf of the material toughness, has to consider initiation as well as stable crack extension following initiation. The inclusion of any crack extension into this consideration needs to consider the influence of the constraint in front of a crack tip, leading to multiaxial stress conditions and decreasing the material crack resistance significantly. Thus, the exclusion of crack initiation needs to be proven in a first step of each safety analysis. Assessing the component in a uniform way over the relevant temperature range is possible by using initiation characteristics, which also have the advantage of transferability. A change of criterion considering initiation at the lower shelf, instability in the transition range and again initiation in the upper shelf can be avoided. Depending on the aim of the analysis, the fracture mechanics safety analysis procedures can be used to determine the critical load, the critical crack size or the required material characteristic.

The effect of Goldbonder on the adhesion between porcelain and pure titanium.

The present study examines the effect of a Goldbonder on the adhesion between titanium and porcelain as measured by the strain energy release rate (G) associated with the interfacial fracture of porcelain and titanium. The influence of surface treatment of titanium prior to Goldbonder application was also examined. The porcelain side of the specimens was notched to the interface with a thin diamond saw, and then a pre-crack was made at the metal-porcelain interface by a special jig. The samples were subjected to a four-point bending test resulting in stable crack extension from which G was calculated. Both the cracked cross-section of interface and peeled fracture surface were examined with scanning electron microscope (SEM). The mean G values were 81.57 +/- 10.34, 46.01 +/- 14.83, and 15.98 +/- 1.76 J m(-2) for the sandblasted surface with the Goldbonder, polished surface with the Goldbonder, and sandblasted surface with the Pastebonder, respectively. The G values revealed significant differences (P < 0.01) between Goldbonder and Pastebonder, and between the sandblasted and polished surfaces with Goldbonder. The SEM photographs and elemental analysis showed that Goldbonder developed both chemical and mechanical bonding to titanium and porcelain.

Fracture mechanics testing on specimens with low constraint––standardisation activities within ISO and ASTM

Fracture mechanics tests are traditionally designed to measure material resistance to stable or unstable crack extension using specimens that are highly constrained to plastic deformation. For a variety of reasons, structural members may be made of thin gage-materials with inherently low constraint to plastic deformation. There is currently little guidance for measuring crack extension resistance under such conditions. The international standards organisations ISO and ASTM are responding to that need, and this paper describes one aspect of their current activity. Two procedures are being developed; one based on the δ 5 crack opening displacement parameter, the other on the constant value of the crack tip opening angle, ψ c. The measurement of δ 5 is well established and relatively simple, whereas ψ c is more difficult to determine experimentally. Evaluations of ψ c from finite-element analyses are currently the most accurate approach, since measurements can only be made on the exterior surfaces similar to δ 5. Questions naturally arise regarding the correspondence of surface indication with full-thickness response in the laboratory experience. Both measures of crack extension resistance are suitable for structural assessment. The δ 5 concept is applied by means of crack driving force formulae from existing assessment procedures and hence relatively easy to use. On the other hand, the CTOA concept is potentially more accurate and can be applied to cases of multiple cracks and complex structures. But its structural application requires numerical methods, which have been successful in predicting the failure of large-scale cracked structural components.

A threshold stress intensity factor at the onset of stable crack extension of Knoop indentation cracks

Observation of the stable growth of indentation cracks in controlled bending tests is an attractive tool to study the R-curve behaviour of ceramic materials. In some crack growth experiments deviations from the ideal behaviour were observed––i.e. the cracks did not grow immediately upon application of the external load, but only after a certain applied stress is exceeded. The existence of such a threshold stress intensity for the onset of stable crack growth can be described by a disbalance of the residual stress intensity at the indentation crack tip and the fracture toughness after completion of the indentation cycle. A fracture mechanical description of this phenomenon is presented. The consequences which arise for the evaluation of crack growth data are explained by means of measured crack extension curves of Knoop indentation cracks in silicon nitride.

Bruchmechanisches Bewerten dünnwandiger Strukturen - Analytische Simulation des stabilen Rissfortschritts in dünnwandigen Strukturen mittels SINTAP

rials and loaded in tension, bending, and biaxial tension. Based on the data obtained an analytical thin wall option is proposed which makes use of the basic equations of SINTAP but specifying the general CTOD term by the CTOD-δ 5 parameter. This parameter is also proposed in recent ASTM and ISO draft standards for testing low constraint specimens. In accordance to these, thin wall is defined for a crack length or ligament length to thickness ratio equal to or larger than four. The option is demonstrated to be a suitable tool for estimating the load carrying capacity as well as the stable crack extension behaviour. Whereas the predictions showed some conservatism for sheets thicker than about 5 mm they were best estimates for very thin sheets of 1.6, 2.5 and 3 mm thickness.

Numerical simulation of crack extension in aluminium welds

Experimental and numerical investigations on stable crack extension of aluminium-laser beam welds (6XXX-series) are presented. Experiments are carried out on C(T)-specimens. Initial cracks are assumed in the base material and in the fusion zone. Local mechanical quantities are determined by micro-flat tensile specimen, taken from the weld nugget, the heat affected zone and the base material. Finite element calculations together with an evolution strategy are used in order to determine parameters of the Gurson–Tvergaard–Needleman model (GTN-model) used for the simulations. Crack propagation in the base material as well as in the undermatched fusion zone is described in terms of fracture resistance curves. It is found that the GTN-model is able to simulate ductile crack growth in the base material and the fusion zone using non-standard model parameters.

Application of the European flaw assessment procedure SINTAP to thin wall structures: Analytical assessment levels

The recently developed European flaw assessment procedure SINTAP has been applied to 29 thin sheets made of five different materials and loaded in tension, bending and biaxial tension. Based on these data the analytical SINTAP assessment levels are evaluated with respect of their ability to predict the failure loads as well as stable crack extension behaviour.

Simulation of cup–cone fracture using the cohesive model

The cohesive model is used for the prediction of the crack path during stable crack extension in ductile materials. The problem of crack-path deviation is investigated by means of simulation of crack propagation in a round tensile bar. The respective phenomenon is known as cup–cone fracture. It is shown that the model is able to predict the failure mechanism, which consists of normal fracture in the center and combined normal/shear fracture in the so-called “shear lips” at the specimen’s rim. The damage evolution and crack path predicted by the model are presented. The effect of the normal and shear failure parameters on the crack-deflection point and several aspects of the finite element mesh are discussed.

콘크리트의 파괴저항에 대한 균열속도의 영향

Tests of concrete CLWL-DCB specimens had been conducted with displacement-controlled dynamic loading. The crack velocities for 381mm crack extension were 0.80 mm/sec ~ 215m/sec. The external work and the kinetic and strain energies were derived from the measured external load and load-point displacement. The fracture resistance of a running crack was calculated from the fitted curves of the fracture energy required for the tests. The standard error of the fracture energy was less than 3.2%. The increasing rate of the fracture resistance for 28 mm initial crack extension or micro-cracking was relatively small, and then the slope of the fracture resistance increased to the maximum value at 90∼145 mm crack extension depending on crack velocity. The maximum fracture resistance remained for 185 mm crack extension, and then the faster crack velocity showed the faster decreasing rate of the maximum fracture resistance. The maximum fracture resistance increased proportionally to the logarithm of the crack velocity from 142 N/m to 217 N/m when the crack velocity was faster than 0.273 m/sec. The maximum fracture resistance of the fastest tests was similar to the average fracture energy density of 215 N/m. To measure the fracture resistance of concrete, the stable crack extension should be larger than 90∼145 mm depending on crack velocity.

Studies on the relationship between acoustic emission characteristics and fractu re toughness of materials

The corelation between acoustic emission characteristics and their fracture toughness has been investigated in this paper based on the study of high-strength al uminum alloy cracking process by using advanced acoustic emission experiment sys tem and smooth tensile specimens as well as DCB specimens with premade cracks. E xperimental results showed that the specimens emitted strong signals with an amp litude above 35 dB when a stable crack extension started at K1C. Stro nger and more complicated acoustic emission signals were found during unstable crack extension, and the cumulative energy of acoustic emission events were found to b e linearly related with the macroscopic fracture energy.

Thermal shock resistance of yttria-stabilized zirconia with Palmqvist indentation cracks

Thermal shock behaviour of two tetragonal zirconia polycrystals stabilised with 2.5% molar yttria and with different fracture toughness have been investigated by analysing stable crack extension of indentation Palmqvist cracks in the quench indentation test. It is shown that the ratio between the thermal stress intensity factor and the fracture toughness can be easily obtained by measuring the stable crack extension. It is shown that deviations from the expected maximum stable crack extension during thermal shock can be accounted for by subcritical crack growth and by a reduction in the level of residual stresses. For small indentation loads, R-curve effects become important and must be considered to explain the experimental results.

Computational simulation on deformation behavior of CT specimens of TRIP steel under mode I loading for evaluation of fracture toughness

Past experimental studies have revealed that TRIP steel possesses favorable fracture toughness because of strain-induced martensitic transformation during large plastic deformation. However, problems associated with the mechanism of high fracture toughness are still unclear. The prediction and control of the deformation and transformation behaviors of TRIP steel near the crack tip are indispensable for obtaining the required fracture toughness. Here, the deformation behaviors of CT specimens of TRIP steel are simulated by FEM under mode I loading at various temperatures for the cases of stationary cracks and stable crack extensions. In the case of a stable crack extension, the nodal release technique and concept of pull-back force are introduced. The fracture toughnesses for TRIP steel and an austenitic material without martensitic transformation are also calculated by path integrals such as J and T∗ integrals. The mechanism of high fracture toughness due to strain-induced martensitic transformation for the case of stationary crack is discussed by comparing the computational results for TRIP steel with those for austenitic material. Then, the mechanism of strain-induced martensitic transformation toughening for TRIP steel due to crack extension is investigated.

Interlaminar Fracture Toughness of a Graphite/Epoxy Multidirectional Composite1

In this paper, an experimental investigation on interlaminar fracture behavior and fracture toughness of a graphite/epoxy multidirectional composite laminate is presented using end-notched flexure specimens. The 0/θ interfaces are considered. The interlaminar fracture toughness is obtained and compared using three data reduction methods, i.e., the area method, classical laminated plate theory, and finite element analysis. Results show that the toughness value depends on the data reduction method used. Two different crack-length-to-span ratios are chosen to study how the stable or unstable crack extension influences the toughness measurement. It is observed that the toughness obtained from the tests of stable crack extension is appreciably higher than that from the tests of unstable crack extension. It is also seen that friction resulting from contact of crack surfaces greatly affects the measured toughness in the case of stable crack extension. In addition, effects of the specimen geometry and fiber orientation on the interlaminar fracture toughness are also evaluated. [S0094-4289(00)02804-8]

Crack stability and strength variability in alumina ceramics with rising toughness-curve behavior

Aluminas with four distinct microstructures have been fabricated to investigate the influence of grain size and grain morphology on strength variability. The four microstructures comprise two grain size scales and are characterized as either “equiaxed” with a narrow size distribution or “elongate” with a higher aspect ratio and a broader size distribution. Indentation-strength tests indicate that only the coarse-grain, elongate microstructure exhibits a strong rising toughness-curve ( T-curve or R-curve). Furthermore, in situ measurements demonstrate that the coarse-grain, elongate microstructure is the only one that displays significant stable crack extension from annealed indentation flaws free of contact-induced residual stress. Strength tests on polished specimens indicate that the highest mean strength is achieved in the fine-grain, equiaxed material with little or no T-curve. The lowest strength variability, however, is exhibited by the coarse-grain, elongate alumina and is rationalized in terms of the strong rising T-curve and its associated influence on crack stability. The study suggests that maximum reliability is achieved when the T-curve is sufficiently strong to stabilize the propagation of natural flaws en route to failure.

Effects of rubber content and temperature on unstable fracture behavior in ABS materials with different particle sizes

The fracture behavior of ABS materials with a particle diameter of 110 nm and of 330 nm was studied using instrumented Charpy impact tests. The effects of rubber content and temperature on fracture behavior, deformation mode, stable crack extension, plastic zone size, J-integral value, and crack opening displacement were investigated. In the case of a particle size of 110 nm, the material was found to break in a brittle manner, and the dominant crack mechanism was unstable crack propagation. Fracture toughness increases with increasing rubber content. In the case of a particle size of 330 nm, brittle-to-tough transition was observed. The J-integral value first increases with rubber content, then levels off after the rubber content is greater than 16 wt %. The J-integral value of a particle diameter of 330 nm was found to be much greater than that of 110 nm. The J-integral value of both series first increased with increasing temperature until reaching the maximum value, after which it decreased with further increasing temperature. The conclusion is that a particle diameter of 330 nm is more efficient than that of 110 nm in toughening, but for both series the effectiveness of rubber modification decreases with increasing temperatures higher than 40 degreesC because of intrinsic craze formation in the SAN matrix at temperatures near the glass transition of SAN. (C) 2000 John Wiley & Sons, Inc.

Flaw Stability in Mild Steel Tanks in the Upper-Shelf Ductile Range—Part I: Mechanical Properties

Mechanical properties of 1950’s vintage, A285 Grade B carbon steels have been compiled for elastic-plastic fracture mechanics analysis of storage tanks (Lam and Sindelar, 2000). The properties are from standard Charpy V-notch (CVN), 0.4T planform compact tension (C(T)), and tensile (T) specimens machined from archival steel from large water piping. The piping and storage tanks were constructed in the 1950s from semi-killed, hot-rolled carbon steel plate specified as A285 Grade B. Evaluation of potential aging mechanisms at both service conditions shows no loss in fracture resistance of the steel in either case. Site and literature data show that the A285, Grade B steel, at and above approximately 70°F (21°C), is in the upper transition to upper shelf region for absorbed energy and is not subject to cleavage cracking or a brittle fracture mode. Furthermore, the tank sidewalls are 1/2 or 5/8-in. (12.7 or 15.875 mm) thick, and therefore, the J-resistance JR curve that characterizes material resistance to stable crack extension under elastic-plastic deformation best defines the material fracture toughness. The JR, curves for several heats of A285, Grade B steel tested at 40°F (4.4°C), a temperature near the average ductile-to-brittle (DBTT) transition temperature (CVN at 15 ft-lb or 20.3 J), are presented. This data is applicable to evaluate flaw stability of the storage tanks that are operated above 70°F (21°C) since, even at 40°F (4.4°C), crack advance is observed to proceed by ductile tearing. [S0094-9930(00)00402-9]

Fracture toughness ( KIc) of a dental porcelain determined by fractographic analysis

Objectives: Fractographic analysis of indentation cracks is performed following flexure testing as part of the ASTM (1999) standard for fracture toughness, K Ic, determination in advanced ceramics. This method depends on the conduciveness of the material towards fractographic interpretation. The purpose of this study was to evaluate the use of fractography in fracture toughness methods with a feldspathic dental porcelain, in which K Ic was measured fractographically as well as numerically using two controlled-flaw beam bending techniques. Methods: The following methods for K Ic determination were applied to a dental porcelain containing a leucite volume fraction of 15–20%: (1) surface crack in flexure (SCF) (dependent upon fractographic analysis); and (2) indentation strength (IS) at indentation loads of 9.8 and 19.6 N (applying both standard numeric calculations and fractographic analysis). The testing environments were (1) ambient air (IS and SCF) and (2) flowing dry nitrogen (SCF). Results: No significant differences were found between numeric and fractographic K Ic values for the IS technique at both indentation loads (9.8 and 19.6 N) in ambient air, although K Ic values were sensitive to indentation load. Due to the presence of residual stresses, stable crack extension was observed fractographically in all IS specimens, as evidenced by differences between initial ( a initial) and critical ( a critical) crack dimensions. For the SCF method, there was a significant difference in toughness between specimens tested in air versus dry nitrogen, however no fractographic evidence for chemically assisted slow crack growth (SCG) was observed. Significance: The SCF method as described by the ASTM standard was applicable to the feldspathic porcelain and produced very comparable results with the numeric toughness calculations of the IS procedure. However, fractographic analysis of the surface crack was somewhat difficult for this glassy ceramic compared with polycrystalline ceramics. Knowledge about stable crack extension or slow crack growth and its fractographic appearance is essential when estimating the toughness from examination of flaw dimensions on fractured surfaces since large calculation errors may occur if these effects are not taken into account.

Low alloy steel piping test for fracture criteria of leak before break

A total of seven pipe fracture tests were performed to provide the data for establishing fracture criteria of leak before break for the low alloy steel pipe, which is expected to be applied to reactor coolant piping and feedwater piping in advanced PWRs in Japan. Test pipes were 6-inch and 8-inch diameter pipes made of SFVQ1A or STPA24 low alloy steel. A circumferential through-wall crack was introduced at the center of a pipe, and four-point bending load was applied without internal pressure. Stable crack extensions were observed in all of the experiments. The net-section criteria (NSC), R6 method option 2 and option 3 were used to estimate the maximum applied load. The predicted values by three kinds of evaluation methods were compared with the experimental loads. Most of the predicted maximum loads agreed well with the experimental maximum loads within 20% difference. The NSC gave the most accurate prediction but also gave unconservative results in some test cases. The predicted maximum loads by R6 option 2 were conservative in all of the test cases. From the viewpoint of conservativeness R6 method can be used for evaluation of the low alloy steel pipe fracture. Therefore, the leak before break (LBB) concept could be applied to the protective design standard against pipe break for the material.

Three Point Bending Tests with Abrupt Change of Loading Velocity for Brittle Materials.

In this research, the behaviour of crack-rate sensitive brittle materials in three point bending tests with an abrupt change of loading velocity was studied. The experiments using crack stabilizer and the numerical simulations taking account of crack-rate effect on fracture toughness were performed for two types of tests, i.e. incremental (or decremental) and relaxation tests. After a change of loading velocity from V0 to V1, a transition range on the load-deflection curve was observed. In the relaxation tests, the load decreases gradually with time. However, the stable crack extension still continued even after the loading velocity equalled zero. These results observed in incremental and relaxation tests were well simulated by the numerical simulations. It was also found that these tests were quite useful to determine the crack-rate sensitivity parameter of the test materials.

Effect of Precrack “Halos” on Fracture Toughness Determined by the Surface Crack in Flexure Method

The surface crack in flexure method, which is used to determine the fracture toughness of dense ceramics, necessitates the measurement of precrack sizes by fractographic examination. Stable crack extension may occur from flaws under ambient, room‐temperature conditions, even in the relatively short time under load during fast fracture strength or fracture toughness testing. In this article, fractographic techniques are used to characterize evidence of stable crack extension, a “halo,” around Knoop indentation surface cracks. Optical examination of the fracture surfaces of a high‐purity Al2O3, an AlN, a glass‐ceramic, and a MgF2 reveal the presence of a halo around the periphery of each precrack. The halo in the AlN is merely an optical effect due to crack reorientation, whereas the halo in the MgF2 is due to indentation‐induced residual stresses initiating crack growth. However, for the Al2O3 and the glass‐ceramic, environmentally assisted slow crack growth is the cause of the halo. In the latter two materials, this stable crack extension must be included as part of the critical crack size to determine the appropriate fracture toughness.