Crack Closure Stress Research Articles

콘크리트의 연속적인 균열성장에 대한 수정 특이-파괴진행대 이론

In this paper, the modified singular fracture process zone (S-FPZ) model is proposed to consider variation of a fracture criterion for continuous crack propagation in concrete. The fracture properties of the proposed fracture model are strain energy release rate at a micro-crack tip and crack closure stress (CCS) versus crack opening displacement (COD) relationship in the FPZ. The proposed model can simulate the estimated fracture energy of experimental results. The analysis results of the experimental data shows that specimen geometry and loading condition did not affect the CCS-COD relation. But the strain energy release rate is a function of not only specimen geometry but also crack extension. Until 25 mm crack extension, the strain energy release rate is a constant minimum value, and then it increased linearly to the maximum value. The maximum fracture criterion occurred at the peak load for an large size specimen. The fracture criterion remains the maximum value after the peak load. The variation of the fracture criterion is caused by micro-cracking and micro-crack localizing. The fracture criterion of strain energy release rate can simply be the size effect of concrete fracture, and it can be used to quantify the micro-tracking and micro-crack localizing behaviors of concrete.

Some improvements in the analysis of fatigue cracks using thermoelasticity

Thermoelastic stress analysis (TSA) has been developed in recent years as a technique for the direct measurement of crack tip stresses in structural components. The technique provides full-field stress maps from the surface of a component subjected to a cyclic load. An improvement in the methodology for monitoring fatigue crack growth and inferring the stress intensity factor from thermoelastic data is presented. The approach is based on a multipoint over-deterministic method (MPODM) [Sanford JR. A general method for determining mix-mode stress intensity factors from isochromatic fringe pattern. Engineering Fracture Mechanics 1979;11:621–33], where experimental data collected from thermoelastic images are fitted to Muskhelishvili’s equations describing the stress field around the crack tip. The fitting algorithm employed is based on the Downhill Simplex Method and includes the crack tip position as a variable to be optimized. Results obtained from artificially generated images and from tests performed using stress relieved and as-welded single edge notched specimens tested at different R-ratios are reported and compared. It is shown that TSA is a sensitive technique for examining the influence of phenomena such as crack closure and residual stresses during fatigue crack growth. Information obtained from the map of phase difference between the forcing signal and the thermal response is presented and discussed. It appears that the phase map may contain information about heat generation at the crack tip due to plastic work and contact of the crack forces.

Spectrum load fatigue—underlying mechanisms and their significance in testing and analysis

The constant amplitude fatigue process is driven by cyclic slip and surface chemistry. These in turn are affected by crack geometry, crack closure and crack-tip stress state, including residual stress. The sensitivity of these factors to spectrum loading determines durability and residual life under service load conditions. Cyclic slip forms the basis for the Rainflow cycle-counting technique and is therefore an integral part of any spectrum load fatigue analysis or test. Assessment of the relative significance of operative mechanisms impacts quality and cost effectiveness of spectrum load tests and also, the reliability of life predictions.

522 マイクロ波二周波数法に及ぼすき裂閉口圧の影響

522 マイクロ波二周波数法に及ぼすき裂閉口圧の影響

微小欠陥材の疲労強度に及ぼすき裂開閉口挙動の影響

It has been recognized that the threshold stress intensity factor range ΔKth of short crack is dependent on many factors. Fatigue tests were performed on materials containing small defects under a wide range of mean stress for three grades of steels with different hardness.Strong dependencies of ΔKth on material hardness, mean stress and defect size were observed. Major tendencies such that softer material had lower ΔKth and smaller defect had lower ΔKth were obtained, which were quite different from those of long cracks. The causes of these effects were investigated based on the crack closure behavior of short crack. The crack closure measurement on a very shallow crack was done. Test results showed that softer material and shorter crack had lower crack closure stresses. It was shown that the threshold effective stress intensity factor range (ΔKeff)th was a unique value for defects deeper than 0.1mm. The crack closure was the major cause of the abovementioned effects of material hardness and mean stress for defects deeper than 0.1mm. On the contrary, (ΔKeff)th significantly decreased compared with that for long cracks when the defect was shallower than 0.1mm. This is another short crack effect which could not be explained only by the crack closure. It was shown that (ΔKeff)th was no more a unique value when the defect depth was shallower than 0.1mm.

Plasticity-induced crack closure under plane-strain conditions in the near-threshold regime

Abstract The change in cyclic plastic deformation at a fatigue crack tip as a function of crack extension and the variation in the crack closure are investigated. The cyclic plastic deformation is modelled by the motion of discrete dislocations. At constant applied crack driving force, the cyclic plastic deformation, that is the cyclic crack-tip-opening displacement, decreases with increasing crack extension. This is caused by an increase in stress intensity factor where the crack closes or, in other words, by a decrease in the local driving force. The crack closure stress intensity reaches a constant level after a crack extension of the order of the size of the plastic zone. Near the threshold of stress intensity this effect, namely plasticity-induced crack closure, is somewhat larger than in the Paris regime.

521 超音波によるき裂閉口圧の計測

A new methodology for evaluating the crack closure stress in fatigue crack surfaces by ultrasonics is proposed. Echo amplitudes of 50 deg. Incidence of shear wave beam against the surface connected back wall cracks in steel specimens are used. In order to account for the exact effect of closure stress on ultrasonic response, the echo amplitude is analyzed based on the artificial application of additional closure stress. The initial closure stress at no load condition is determined by the standard compliance technique. Two empirical relationships among echo amplitude, crack depth and closure stress, are established. Based on these relations, the crack closure stress and crack depth of an unknown crack are determined by inverse analysis of the measured response of the crack. The method demonstrates an excellent capability of quantitative evaluation of crack closing stress as well as crack size.

Effects of whisker content and dimensions on theR-curve behavior of an alumina matrix composite reinforced with silicon carbide whiskers

A study was made of the effects of whisker content and dimensions on theR-curve behavior of an alumina matrix composite reinforced with silicon carbide whiskers. Experiments showed that the risingR-curve behavior is strongly enhanced by the increase in the volume fraction and the size of whiskers. Simulation based on a model of crack face whisker bridgings was made to elucidate the effects on theR-curve of the composite. The validity of the simulation was confirmed by good agreement between the experimental and the calculatedR-curves. In addition to theR-curve, the distribution of crack closure stresses as well as crack tip opening displacements was also calculated, which directly reflects crack face whisker bridging processes in the composite. Then the dependence of whisker content and dimensions on theR-curve was analytically discussed taking the bridging processes into account.

A multiparameter approach to the prediction of fatigue crack growth in metallic materials

A multiparameter approach is proposed for the characterization of fatigue crack growth in metallic materials. The model assesses the combined effects of identifiable multiple variables that can contribute to fatigue crack growth. Mathematical expressions are presented for the determination of fatigue crack growth rates, da/dN, as functions of multiple variables, including stress intensity factor range, ΔK, stress ratio, R, crack closure stress intensity factor, Kcl , the maximum stress intensity factor Kmax , nominal specimen thickness, t, frequency, Ω, and temperature, T. A generalized empirical methodology is proposed for the estimation of fatigue crack growth rates as a function of these variables. The validity of the methodology is then verified by making appropriate comparisons between predicted and measured fatigue crack growth data obtained from experiments on Ti–6Al–4V. The effects of stress ratio and specimen thickness on fatigue crack growth rates are then rationalized by crack closure considerations. The multiparameter model is also shown to provide a good fit to experimental data obtained for HY‐80 steel, Inconel 718 polycrystal and Inconel 718 single crystal. Finally, the implications of the results are discussed for the prediction of fatigue crack growth and fatigue life.

Interactions of fatigue cracks with elastic obstacles

To quantify the growth behaviour of fatigue cracks growing towards microstructural barriers or elastic obstacles, parametric solutions are obtained for crack-tip opening displacement and plasticity-induced crack closure of a mode I fatigue crack growing towards elastic obstacles. Three common bi-material systems are analysed using the finite element method, in which both constituent materials have identical elastic properties but only the phase that contains the crack can deform plastically. It has been found that under monotonic loading the crack-tip opening displacement decreases as the crack-tip approaches the interface boundary, but reaching a non-zero value when the crack-tip terminates at the boundary. For a fatigue crack growing under constant amplitude loading, the crack-closure stress has been found to increase as the crack grows towards the barrier. Based on these results a mechanistic model is proposed to quantify the influence of stress level on the fatigue threshold of microstructurally small fatigue cracks, with predictions being in close agreement with experimental data.

Fatigue crack closure analysis of bridged cracks representing composite repairs

This article presents an analytical and numerical study of the fatigue crack-closure behaviour of a bridged crack representing a crack that has been repaired by a composite patch. It is shown that, provided that the plate stress beneath the patch is less than 40% of the material’s yield stress, the crack-closure stress of a patched crack is approximately equal to that of an unbridged crack under small-scale yielding, depending only on the stress ratio. Furthermore, it is shown that the transient crack-closure behaviour of a patched crack subjected to variable amplitude loading can be determined by analysing an unpatched crack subjected to the same stress intensity factor history. Based on these findings, it is proposed that the fatigue crack closure of a patched crack can be determined by analysing an unpatched centre crack subjected to an adjusted stress, for which an explicit expression is given. Predictions based on the proposed method are shown to correlate very well with experimental results obtained under two aircraft loading spectra.

R‐Curve Behavior and Crack‐Closure Stresses in Barium Titanate and (Mg,Y)‐PSZ Ceramics

R‐curves, process zones, and shielding stresses of barium titanate (BaTiO3) and partially stabilized zirconia (PSZ) have been studied using compact‐tension (CT) specimens. BaTiO3 and PSZ exhibited pronounced R‐curves that rose over similar crack lengths and showed steady‐state toughnesses of 0.7 and 6.4 MPa·m1/2, respectively. Both steady‐state toughnesses were ∼80% larger than the initial fracture toughnesses. Ferroelastic domain switching was the main toughening mechanism in BaTiO3, whereas, in PSZ, transformation toughening was the main toughening mechanism. The crack process zone and crack‐opening‐displacement (COD) profile of each material was studied in detail using atomic force microscopy. Crack‐closure‐stress distributions were extracted from the COD profiles, using weight‐function methods. The resulting stress profiles indicated that compressive residual stresses of 40 MPa in BaTiO3 and 400 MPa in PSZ acted in a limited region behind the crack tip. In the PSZ, crack bridging seemed to be a competing mechanism to transformation toughening.

Fracture process zone modeling of monolithic Al 2O 3

The crack tip displacement fields obtained from moire interferometry were used interactively to drive a finite element (FE) model of double cantilever beam (DCB), alumina specimens subjected to stable crack growth. Through this inverse analysis, the crack-closure stress (CCS) distribution which provided the best fit between the measured and computed crack-opening displacement (COD) along the fracture-process zones (FPZ) trailing the crack tip of two alumina microstructures were determined. The dissipated energy, which was obtained from this FE analysis, at the FPZ was found to be the major energy sink in the larger as well as the smaller grain-size alumina.

Crack closure stresses in fiber reinforced brittle matrix composites

The fracture toughness of an alumina ceramic and a continuous SiC fiber reinforced alumina composite processed by pressureless sintering was studied in situ in a Scanning Electron Microscope (SEM). The applied stress intensity factor was obtained as a function of both applied load and crack extension. Closure stresses across crack surfaces imposed by grain-bridging and fiber-bridging, and hence fracture resistance from bridging were studied by both stress intensity factor and J-integral considerations. Theoretical calculations agree with experimental results. An average fracture resistance of ≈40 J m −2 per fiber and a corresponding toughness of ≈1·6 MPam 1/2 per fiber was obtained for fiber elastic bridging before fiber failure. Fiber-matrix interfacial properties were examined and a technique for evaluating interfacial frictional shear stress was developed.

Residual Stress Measurement by Successive Extension of a Slot: The Crack Compliance Method

This article reviews the technical literature on the determination of a residual stress profile by successive extension of a slot and measurement of the resulting strains or displacements. This technique is known variously in the literature as the crack compliance method, the successive cracking method, the slotting method, and a fracture mechanics based approach. The article briefly summarizes the chronological development of this method and then, to facilitate more detailed review, defines the components that make up the method. The theory section of the article first considers forward method solutions including fracture mechanics, finite element, analytical, and body force methods. Then it examines inverse solutions, including incremental inverses and series expansions. Next, the article reviews all experimental applications of the crack compliance method. Aspects reviewed include the specimen geometry and material, the details of making the slot, the deformation measurement, and the theoretical solutions used to solve for stress. Finally, the article makes a brief qualitative comparison between crack compliance and other residual stress measurement methods. In many situations, the crack compliance method offers several advantages over other methods: improved resolution of residual stress variation with depth; the ability to measure both small and very large parts; measurement of stress intensity factor caused by residual stress; measurement of crack closure stresses; increased sensitivity over other material removal methods; and the ability to measure non-crystalline materials. This review article contains 77 references.

On the finite element simulation of three-dimensional semi-circular fatigue crack growth and closure

The opening and closure behaviour of a three-dimensional semi-circular moving crack has been studied using an elastic–plastic finite element model. For comparison an elastic stationary crack and an elastic–plastic stationary crack have also been studied. Fatigue crack growth has been simulated by the release of crack front nodes on every load cycle. The effects of different node release schemes, the refinement of the finite element mesh and the initial crack length have been studied. Crack closure stress is shown to be similar to crack opening stress under a peak applied stress of 0.7 of the yield stress and an applied stress ratio of R=0. It is observed that the crack closes first on the specimen surface and closes later in the interior of the specimen. It has also been found that even when unloading from peak applied stress to zero applied stress the majority of the interior part of the crack can still be kept open. Detailed stress and plastic strain fields around the crack front are also presented and are discussed briefly.

A NEW MULTIPARAMETER APPROACH TO THE PREDICTION OF FATIGUE CRACK GROWTH

A new multiparameter approach is proposed for the prediction of the combined effects of multiple variables on fatigue crack growth. The method, which is based on multiple linear regression analysis, involves the statistical formulation of mathematical expressions for the crack growth rate, da/dN, as a function of multiple variables, e.g. stress intensity factor range, ΔK, crack closure stress intensity factor, Kcl , and stress ratio, R. A general empirical approach is proposed for the estimation of the fatigue crack growth rate as a function of the above variables. The predictive capability of the empirical approach is then verified by comparing predicted and measured fatigue crack growth and crack growth rate data obtained from tests on a quenched and tempered Q1N (HY80) pressure vessel steel. Error ranges and reliability functions are presented within a probabilistic mechanics framework, and the implications of the results are discussed for the development of generalized fatigue life prediction methods.

Effect of Irreversible Energy Loss on the Fracture Toughness and the Work-of-Fracture of Ceramics Toughened by Crack Face Bridging

The relationship between the fracture toughness and the work-of-fracture of ceramics toughened by crack bridging was discussed using a constant crack closure stress model including irreversible energy loss in the bridging region during crack propagation. The Irwin similarity relationship could not be applied to the bridged crack without modifying stress intensity factor and energy release rate considering the crack closure stress and the energy loss. Moreover, the fracture toughness was not simply related with the work-of-fracture even if the modified Irwin similarity was applied. The fracture toughness was determined as a function of the crack closure stress and the length of the bridging region regardless of the energy loss. On the other hand, the work-of-fracture of bridged crack was increased by the irreversible energy consumption as well as crack closure stress.

Crack growth and closure mechanisms of shear cracks under constant amplitude biaxial straining and periodic compressive overstraining in 1045 steel

Crack growth and roughness induced closure mechanisms of shear cracks under 180° out-of-phase strain histories having constant amplitude straining and periodic compressive overstrains (PCOs) were investigated. The results revealed that shear cracks initially nucleated on a slip band at 45° to the axis of the specimen which coincides with the plane of maximum shear strain. Growth on the shear planes (microcracks) into the specimen surface occupied up to 90–95% of fatigue life during which time the surface length of the microcracks remained nearly constant. Failure then occurred by a rapid linking of microcracks at the end of a test. The opening stress of microcracks was taken to be the applied static stress level at which the crack depth stopped increasing with increasing stress. Observations indicated that as the number of cycles increased the crack depth on the maximum shear plane increased but the crack opening stress did not change appreciably. The crack growth rate in the depth direction on shear planes increased significantly and fatigue strength was reduced by a factor of 1.4 and 1.7 at short and long lives, respectively, when PCOs of near yield point magnitude were applied. Confocal scanning laser microscopy and scanning electron microscopy examinations of fracture surfaces revealed that these PCOs flattened mismatch asperities near the crack tip. The reduction in the height of these irregularities on the fracture surface was accompanied by a reduced crack closure stress and a higher crack growth rate.

CRACK CLOSURE IN SMALL FATIGUE CRACKS—A COMPARISON OF FINITE ELEMENT PREDICTIONS WITH IN‐SITU SCANNING ELECTRON MICROSCOPE MEASUREMENTS

Abstract— A three dimensional, elastic‐plastic, finite element analysis of fatigue crack growth and plasticity‐induced crack closure has been performed for a range of small, semi‐circular cracks. Predicted crack opening displacements have been compared with data obtained from in‐situ SEM measurements for a coarse‐grained aluminium alloy 2024‐T351. The magnitude of fatigue crack closure measured from in‐situ SEM measurements was consistently higher than that predicted from the finite element analysis. It is deduced that the higher closure stresses obtained from in‐situ SEM measurements are due to the contact of asperities on the fatigue crack surfaces. A simple mathematical model is suggested to describe the fatigue crack closure stress caused by the combination of both a plastic wake and asperities on the fatigue crack surfaces. The predicted fatigue crack closure stresses and their dependence on crack size are consistent with experimental measurement.