Effect Of Crack Depth Research Articles

On the use of constraint parameter A2 determined from displacement in predicting fracture event

The constraint based fracture mechanics methodology, J– A 2 method, has been used to interpret cleavage fracture recently. In all previous studies, the constraint parameter A 2 was determined by stresses analytically calculated from finite element analyses (FEA). In the current paper, it is first demonstrated that A 2 can be measured during a fracture test using the crack tip opening displacement (CTOD). A single-edge-notched specimen under bending (SENB) is used to compare the A 2 values determined from δ 5 displacement and the stress components. Finally, cleavage fracture toughness values for A533-B reactor pressure vessel (RPV) steel at −40°C obtained from test programs at Oak Ridge National Laboratory (ORNL) and the University of Kansas (KU) are interpreted using the J– A 2 analytical model. Particular emphasis is placed on using the A 2 determined from CTOD to characterize the fracture event. It is demonstrated that the effects of crack depth (shallow vs deep) and specimen size (small vs large) on the fracture toughness from the test programs can be interpreted and predicted using J and the constraint level A 2 measured from the displacement.

EFFECT OF CRACK DEPTH ON THE NATURAL FREQUENCY OF A PRESTRESSED FIXED–FIXED BEAM

The effect of crack depth on the transverse vibrational characteristics of a prestressed fixed–fixed beam is investigated. The natural frequency of the system is obtained by modal analysis. The coupling effect between the crack depth and the axial load on the natural frequency of the system is investigated. Also, experimental work verifies the results of the theoretical analysis. The study shows that there is a significant coupling between the axial load and crack depth, and this coupling effect is directly proportional to the crack depth as well as the axial load. Therefore, the problem of a prestressed cracked beam cannot be treated as a superposition of two separate effects (crack plus axial load) to find the natural frequency of the system.

Ｃ／Ｃ複合材料の破壊機構に及ぼす熱処理温度の影響

There are two major fracture criteria for notched C/C (carbon/carbon) composite materials. One is that the fracture strength is determined by the fracture toughness criterion, and the other is that it is simply decided by the net section stress failure criterion. In the present study, effects of crack depth, specimen size, and the heat treatment temperature on the strength and fracture mechanism of C/C composites were investigated by using double edge cracked plate tension specimen in order to clarify the confusion on the fracture criterion. For the case of carbonized C/C composites (heat-treatment temperature = 1600° C), the notched strength of wider specimens was smaller than the net section stress failure criterion, showing the notch effect. When the ligament length of the notch was shorter than about 8 mm, the fracture strength of notched specimen was well correlated to the net section stress criterion. On the other hand, the notched strength of graphitized C/C composites (heat treatment temperature = 2500 and 3000°C) was well estimated by the net section stress criterion without respect to the ligament length. The strength of smooth specimen for C/C composites was almost the same without respect to the heat-treatment temperature, while the fiber strength decreased by half with increasing the heat-treatment temperature. Thus, the contribution of the fiber strength to composites strength was much higher for the graphitized C/C composites, The change of fracture mechanism in macroscopic and microscopic scale was well correlated to the change of the fracture criterion.

Influence of strength mis-matching on crack driving force and failure assessment curve of weldment

In order to estimate the integrity and safety of welded structures, the mis-matching performance of material properties should be taken into account. This paper has investigated the effects of crack depth and strength mis-matching on the J-integral and the failure assessment curve (FAC) of welded joints by an elasto-plastic finite element method (FEM). The computation results indicate that the mis-matches of yield strength and strain hardening exponent have an obvious effect on the crack driving force and FAC of weldments. For the mis-matching of yield strength the crack driving force of weldments is located between the all-base and all-weld metals. The mismatching of strain hardening exponent has a lesser effect on the crack driving force than mis-matching in yield strength. The computation also shows that it would be conservative to substitute the FAC of weldment by the FAC of all-base or all-weld metals for the case of under-matched weldment but this would be unsafe for the over-matched weldments.

Effects of Crack Depth, Specimen Size, and Out-of-Plane Stress on the Fracture Toughness of Reactor Vessel Steels

Cleavage fracture toughness values for A533-B reactor pressure vessel (RPV) steel at -40°C obtained from test programs at Oak Ridge National Laboratory (ORNL) and University of Kansas (KU) are interpreted using the J-A2 analytical model. The KU test data are from smaller SENB specimens with a/w = 0.1 and 0.5. The ORNL test data are from 1) larger SENB specimens with a/w = 0.1 and 0.5, and 2) a six-point-bend cruciform specimen under either uniaxial or bi-axial loads. The analytical model is based on the critical stress criterion and takes into consideration the constraint effect using the second parameter A2 in addition to the generally accepted loading parameter J. It is demonstrated that the effects of crack depth (shallow versus deep), specimen size (small versus large), and loading type (uniaxial versus biaxial) on the fracture toughness from the test programs can be interpreted and predicted.

Influence of crack depth and strength matching on deformation and plastic zone for welded joint specimen

By using the 2-dimensional elasto-plastic finite element method, the effects of crack depth and strength matching properties of welds on the deformation and plastic zone have been studied for three point bend specimens. The results indicate that, in the loading process of a welded joint specimen, the influence of crack depth and strength matching properties on the deformation parameters such as loading point displacement, crack mouth opening displacement, plastic rotational factor, and development of plastic zone is evident. The boundary between shallow crack and deep crack specimens is also influenced by the strength matching of welded joints. Moreover, the crack depth and strength matching of the welded joints have an important effect on the fracture-resistant capability of the specimens. The fracture-resistant capabilities of shallow crack specimens and overmatched joint specimens are better than those of deep crack specimens and undermatched joint specimens, respectively.

Fully plastic crack-tip fields for plane strain shallow-cracked specimens under pure bending

Detailed finite element (PE) analyses are performed to study the effect of crack depth on crack-tip constraint at full yielding for pure bending of plane strain single-edge-cracked specimens. Analyses are based on small-strain formulations and perfect plasticity. The crack depth a/W ranges from 0.1 to 0.7, and the deformation is applied up to the limiting state of full plasticity where crack-tip stresses reach steady-state limiting values.

On the effects of loading conditions and geometry on time-dependent singular crack tip fields

The amplitudes C( t) of non-steady singular crack tip fields in power law creeping solids are investigated under pure mode I loading and combined mode I and II loading conditions. Approximations to both transient and steady state values of the C( t)-integral for three different specimen geometries and for an intersection geometry representative of a typical power plant component configuration are compared with results obtained from detailed finite element analyses. The effect of crack depth, geometry, creep exponent, and primary (mechanical) loading on the accuracy of C( t) estimates is determined. Finite element solutions for the intersection geometry are used to study the extent of mode mixity under creep conditions in the resulting combined mode I and II crack tip fields. These solutions showed that, within the crack tip region where creep strains dominate, the opening stresses appear more singular than the Hutchinson-Rice-Rosengren (HRR)-type fields, r −1/( n+1) , while the in-plane shear stress component and the equivalent stress are slightly less singular. The solutions also revealed that mode I dominance increases primarily during a very short period immediately after the load is applied, while small scale creep conditions prevail, and does not significantly change thereafter. HRR-type plane strain approximations based on known solutions for mixed mode elastic-plastic cracks under a moderate degree of mode mixity accurately predict axisymmetric finite element solutions.

The Effect of Crack Depth (a) and Crack Depth to Width Ratio (a/W) on the Fracture Toughness of A533-B Steel

Constraint, as related to specimen crack depth (a) or crack depth to specimen width ratio (a/W), can have a significant effect on fracture toughness. In laboratory specimens, both crack depth and the a/W ratio can be varied. However, it is not always possible to model the constraint of a structurally relevant geometry in the laboratory. Nonetheless, an understanding of the role of both crack depth and a/W ratio on the toughness behavior of laboratory specimens will help clarify the role of constraint on fracture toughness and better enable engineers to model the effect of constraint on a flaw in an actual structure. An experimental study of the effect of crack depth and a/W ratio on the fracture toughness of an A533-B steel was conducted and results were compared with large-scale specimens tested at Oak Ridge National Labs (ORNL). Smaller size specimens tested at the University of Kansas (KU) were taken from the actual ends of the specimens tested at ORNL. The specimens tested at both KU and ORNL were square single-edge-notched bend (SENB) specimens with widths ranging from 20.3 to 100.0 mm (0.8 to 4.0 in.), crack depths ranging from 2.0 to 50.0 mm (0.08 to 2.0 in.), and a/W ratios ranging from 0.1 to 0.5. The geometries of the specimens tested at KU were chosen such that comparisons of the toughness of specimens with constant crack depth and varying a/W ratio, as well as comparisons of the toughness of specimens with constant a/W ratio and varying crack depths, could be made. A forthcoming paper, containing finite element analysis results, will compare the analytical basis for the behavior of these various size specimens. The results indicate that both crack depth and a/W ratio affect the fracture toughness of the steel. For deep crack geometries (a/W = 0.5), crack depth has limited effect on the fracture toughness. However, for shallow crack geometries (a/W = 0.1), crack depth has a significant effect on the fracture toughness. For constant crack depth, varying the a/W ratio does affect the fracture toughness. Thus, crack depth and a/W ratio are interdependent with respect to fracture toughness. The findings of this study are significant in helping to understand the role of both crack depth and a/W ratio on fracture toughness and serve as a basis for understanding the effect of constraint on the behavior of actual structures with cracks.

The influence of weld strength mismatch on crack-tip constraint in single edge notch bend specimens

Previous work by Dodds and Anderson provides a framework to quantify finite size and crack depth effects on cleavage fracture toughness when failure occurs at deformation levels where J no longer uniquely describes the state of stresses and strains in the vicinity of the crack tip. Size effects on cleavage fracture are quantified by defining a value termed J SSY: the J to which an infinite body must be loaded to achieve the same likelihood of cleavage fracture as in a finite body. In weld metal fracture toughness testing, mismatch between weld metal and baseplate strength can alter deformation patterns, which complicate size and crack depth effects on cleavage fracture toughness. This study demonstrates that there is virtually no effect of ±20 percent mismatch on J SSYif the distance from the crack tip to the weld/plate interface (L min) exceeds 5 mm. At higher levels of overmatch (50 to 100%), it is no longer possible to parameterize the departure of J SSYfor a weldment from that for a homogeneous SE(B) based on L min alone. Weld geometry significantly influences the accuracy with which J SSYfor a welded SE(B) can be approximated by J SSYfor a homogeneous specimen at these extreme overmatch levels.

Vibration And Stability Of A Rotating Shaft Containing A Transverse Crack

The dynamic response of a rotating shaft containing a transverse crack is investigated. The local flexibility due to the crack is first evaluated from the theory of fracture mechanics. The energy principle in conjunction with the assumed mode method yields the discretized equations of motion; these are time-varying with periodic coefficients due to the "breathing" effect. The steady state responses and the stability criteria are then obtained, and the effects of crack depth, crack location and rotational speed are discussed. The results show that an increase of crack depth magnifies the response amplitude as expected. It is discovered that the crack affects the dynamic response more significantly when it occurs near a place where the bending moment exhibits a larger value. From the FFT analysis of the displacement responses, it is seen that the 1Ω and 2Ω components are excited prominently due to crack. Hence they provide possibly good indices for an on-line crack monitoring system. The stability of a cracked shaft is examined via the Floquet theory, and the results show that, for an undamped shaft, instability occurs as rotation is close to an integer fraction or an integer multiple of the shaft bending frequency when the crack depth reaches half of the radius. However, a small amount of damping is found to raise effectively the unstable region.

Crack-depth effects in the cylindrically guided wave technique for bolt and pump-shaft inspections

The cylindrically guided wave technique (CGWT) has been developed and applied to the inspections of bolt and pump shaft in a nuclear power plant. Using the CGWT, defects were detected after an ultrasonic wave traveled through a long path in a metallic bolt, or shaft. The cylindrically guide wave has been known to be dispersive. This fact is important in the development of the capacity to determine the depth of a crack. A theoretical study was made on wave scattering at the circumferential crack in a long cylinder. The crack tip has an arbitrary radius d, which is less than the cylinder radius a. A time-harmonic incident wave with frequency ω is assumed to impinge on the crack. The scattered field involves several terms and has satisfied the stress-free conditions at the crack surfaces and the cylindrical surface. In this exact three-dimensional formulation, the terms of the displacement at a large distance from the crack were shown as vanishing except for the guided wave terms. The guided waves become predominant in the place where the ultrasonic receivers are usually located. The displacement in the direction of the cylinder axis is written in the form of guided progressive waves. In the process of solution, an integral equation is established. The highest order approximation of the solution is obtained and used in the numerical calculations of the scattered waveforms. The transfer factor of the scattered wave is calculated for a wide range of the frequency spectrum. The scattered waveforms at a distance away from the crack are calculated and presented for various values of the ratio of d to a. Also presented is the variation of the scattered waveform with respect to the distance of travel. The result clearly reveals the effects that the crack depth has on the amplitude and width of the scattered waveforms. It also enhances the capacity of CGWT to determine the depth of a crack.

RESIDUAL STRESS MEASUREMENT FOR A FINITE PLATE UNDER TENSION USING TWO DOUBLE EDGE CRACKS METHOD

Making use of stress distribution in a finite plate with the presence of cracks, residual stress and actual applied stress can be obtained. The finite element technique is used to determine stress intensity factor and stress distribution in a plate having two double edge cracks with different crack depth. Experimental measurement has been carried out in a finite plate subjected to tensile stress. Strain relaxation due to making two double edge cracks is given, residual stress can also be estimated. The effect of crack depth and its location for measuring residual stress is investigated under same tensile loading condition for three different engineering materials. A good agreement between theoretical and experimental determination of stress relaxation is obtained. An engineering chart for obtaining the actual applied stress in a tensile loaded plate is implemented.

A further study about the effect of crack depth and shape on fracture toughness

Fracture toughness tests have been carried out on two different heat-treated steels 60Si2MnA using both through-cracked specimens with different a W ratios and semi-elliptical cracked ones with variable crack size and shape. Effects of crack depth and shape on fracture toughness have been studied. Results show that the material is more resistant to crack growth when the a W ratios are less than 0.1, both shallow through and surface-cracked specimens, give a toughness value which is about 25–30% higher than the deep-cracked ones. But the effect of crack length c and the ratio a c on fracture toughness is negligible. Results also show that the LEFM approach to fracture is not tenable for design stresses where a c is often very small, far less than 2.5( K IC / σ y ) 2.

Effects of crack depth and shape on fracture toughness in a spring steel

An experimental study described in this paper attempts to compare the behaviour of both through-cracked specimens with different a w ratios and surface-cracked test pieces. Results show that the material is more resistant to crack growth when the a w ratios are less than 0.1, both shallow through- and surface-cracked specimens, give a toughness value which is about 25% higher than the deep-cracked ones. But effect of crack shape on fracture toughness is negligible. For a w larger than 0.1, the toughness K lc remains constant. Results also show that the LEFM approach to fracture is not tenable for design stresses where a c is often very small.

Three-dimensional finite element analysis of circumferentially-cracked notched and un-notched cylindrical components

A comprehensive three-dimensional computer-aided finite element study is made in an attempt to calculate the stress intensity factor ( K I ) for a variety of V-notched and un-notched circumferentially-cracked geometries made of mild steel subjected to remote uniform bending moment, M. Throughout the study, the solid modelling facility of SDRC† (GEOMOD) was interactively utilised to create the different cracked geometries. Prior to the analysis, these geometries were transferred to the pre-processor (SUPERTAB) for model creation, mesh definition and model checking. The appropriate remote bending moment and imposed restraints were also applied interactively. In this study, the stress-intensity factor calculations for the different configurations were based upon the resulting displacement field just behind the crack tip. The effect of crack depth, notch-tip radius and included angle of the V-notched specimens upon the stress-intensity factor K I were examined. The work also included the effect of circumferentially cracked un-notched specimens upon K I and comparisons with the earlier solutions of Benthem and Koiter ( Methods of Analysis and Solutions of Crack Problems, pp. 131–178, 1973) and Harris ( J. Basic Engng. 89, 49–54, 1967) were made and the results show good agreement. The finite element study was also extended to evaluate the effect of complete and partial contacts of the cracked surfaces in the compressive side of the specimen upon the resulting stress intensity factor, K I . The current results agree with the general trends of the experimental findings observed earlier by Sawaki, Aoyama and Kawaski ( Int. J. Fracture 26, 43–54, 1984).

Photoelastic determination of mixed-mode stress intensity factors for inclined semi-circular cracks in thin tubes

Metal shims have been used to produce internal and external, semicircular, surface, crack-like flaws in cast, photoelastic models of thin tubes. The effects of crack depth, crack orientation, crack inclination, and crack position (i.e., internal or external) have been determined from the analysis of results from 69 slices taken from 24 ‘crack’ types.It has been shown that by taking eleven terms in the solutions for the crack-tip stress fields, rather than taking only the singular solution, more accurate stress-intensity factors are obtained.