Crack Tip Opening Stress Research Articles

Crack-tip constraint analysis of bending specimens for considering higher order terms in asymptotic solution

In this research, a higher-order asymptotic J-A2-A4 solution was introduced for studying the effect of the bending moment on the crack-tip constraint of a specimen. The solution was applied to TPB and SENB specimens with varying bending moment loads, and compared to other methods such as FEA, HRR solution, J-A2 solution and J-A2-M solution. The results were analyzed and compared with the FEA, J-A2 theory and J-A2-M theory solutions obtained from references. The impact of global bending on the calculation of crack-tip opening stress was also investigated. The findings showed that the J-A2-A4 solution closely matched the FEA numerical results, and better accounted for the influence of global bending compared to the J-A2 method. Therefore, there is no need to modify the J-A2 method by adding a bending moment term, as suggested in the J-A2-M theory.

Analysis of crack closure and wake of plasticity with the distributed dislocation technique

A new method for the analysis of plasticity-induced closure of finite cracks is developed based on the distributed dislocation technique. The method is applied to analyse closure and opening processes for an embedded fatigue crack propagating under constant amplitude cyclic loading. The obtained solution and presented results can serve as a benchmark for numerical procedures utilising the same yield-strip methodology. Comparison with past numerical studies reveals similar trends, though there are some differences in the crack tip opening values, particularly for low and negative R-ratios. The latter may indicate the need for a better approach to the discretisation of the contact, direct and reverse plasticity zones in the numerical procedures which utilise the same methodology. The developed method is general, and it can be adapted to evaluate the crack tip opening stress for other crack geometries and loading conditions.

Crack growth arrester using “gourd-shaped-insert-plate”

In accordance with aging infrastructure systems such as steel bridges, fatigue of metals becomes serious risks. Fatigue crack may lead the structure to catastrophic failure. Countermeasures against fatigue failure are required. “Crack growth arrest and retardation system” using “gourd-shaped-insert-plate” has been developed as a high performance and easy construction method against fatigue crack, by generating fatigue crack closure force and reduce crack tip opening displacement and stress concentration at the fatigue crack tip. Arrester was applied to CT (Compact Tension) specimen and also mockup of steel bridge deck, in order to validate performance of the system. Fatigue crack growth rates of the specimens with arrester were 1/10~1/2 of those without arrester. And apparent threshold stress intensity factor range was increased by about 10~20 MPa√m through using only few gourd-shaped arresters. Also the arrester was applied to the fatigue crack in a mockup of steel bridge deck. Without arrester, fatigue crack growth occurred in accordance with the increase of loading cycles, on the other hand, fatigue crack growth was arrested after installing the arrester in the mockup of steel bridge deck. And to enable quantitative fatigue life assessment in fatigue design, fracture mechanics based-crack closure model with spring elements for the arrester has been verified with good accuracy for fatigue crack growth rate in the tests using CT specimens.

Modeling of creep-fatigue interaction effects on crack growth at elevated temperatures

The well-known load frequency effect on creep-fatigue crack growth is explained by the interactions between fatigue and creep loading and is quantified using the concept of plasticity-induced crack closure. It is shown that the hold time during creep loading affects crack growth rates during subsequent fatigue cycles. Longer hold times lead to lower crack-tip opening stresses and faster crack growth rates during fatigue loading. To model the impact of hold time on crack opening stresses during fatigue loading, a strip-yield model was developed for creep-fatigue crack growth. The strip-yield model computes crack-tip opening stresses, which determine the effective stress intensity factor range and crack growth rate during the fatigue portion of each loading cycle. Maximum stress intensity factor is used to compute the crack growth rate during the creep portion of each cycle. The proposed strip-yield model is used to compute creep-fatigue crack growth rates for several structural materials, i.e., an Astroloy, aluminium alloy 2650 and 316 stainless steel. The model predictions of crack growth rates compare well with published experimental data for these alloys. This model achieves reliable predictions of crack growth rates and life prediction on components subjected to creep-fatigue loading at elevated temperatures by considering loading interaction effects.

Predicting creep-fatigue crack growth rates in Alloy 709 using finite element simulations of plasticity and creep-induced crack closure

This paper reports on a computational study and experimental validation of creep-fatigue crack growth rates at high temperature in two structural materials. The objectives are to develop a methodology to predict creep-fatigue crack growth rates using plasticity-induced crack closure under creep-fatigue loading conditions by characterizing the effect of hold time on crack growth rates during cyclic loading. In this study, the computation of fatigue crack growth rates is based on the crack closure phenomenon. The total crack growth rate during creep-fatigue loading is based on the addition of fatigue crack growth rate during cyclic loading and creep crack growth rate during hold time. The study identifies the effects of frequency and shape of loading cycle on crack-tip opening stresses induced by the combined action of the plasticity-induced crack closure and creep relaxation at the crack tip. Two-dimensional finite element analyses of compact tension specimens are performed to simulate crack growth under cyclic and time-dependent loading conditions. Elastic-plastic-creep material behavior is considered in these simulations. Closure levels are computed for high temperature structural materials such as 9Cr-1Mo steel and Alloy 709. The numerical predictions provide satisfactory agreement with experimental data of creep-fatigue crack growth rates in modified 9Cr-1Mo and Alloy 709 steels at high temperatures.

High-R low growth rate fatigue crack propagation at elevated temperatures

While fatigue cracking is widely considered as the primary cracking mode under cyclic loading conditions, this is not the case for high-R (Kmin/Kmax) low growth rate fatigue crack propagation at elevated temperatures. Creep cracks can sometimes be observed in such situations when the stress intensity factor range ΔK is around the fatigue crack growth threshold stress intensity factor ΔKth. A Time Dependent Failure Assessment Diagram (TDFAD) has been adopted in this study for predicting creep cracking in high-R cyclic loading conditions at elevated temperatures. In addition, attention is also paid to oxide-induced crack closure which is greatly influential at high temperatures. Three power plant steels with different chromium contents, namely 1%Cr, 9%Cr and 18%Cr steels, have been investigated at temperatures between 550°C and 650 °C. The experiments were performed by reducing ΔK continuously to ΔKth. Good accordance has been found between fracture surface observations and the TDFAD approach predictions of creep crack initiation. Apart from creep cracking, high-R ΔKth values have also been found to be influenced by oxide-induced crack closure at elevated temperatures. The enhancement is studied through the relationship between the crack tip opening displacement and stress intensity factor.

Characterization of fracture behavior of human atherosclerotic fibrous caps using a miniature single edge notched tensile test.

One well-established cause of ischemic stroke is atherosclerotic plaque rupture in the carotid artery. Rupture occurs when a tear in the fibrous cap exposes highly thrombogenic material in the lipid core. Though some fibrous cap material properties have been measured, such as ultimate tensile strength and stress-strain responses, there has been very little, if any, data published regarding the fracture behavior of atherosclerotic fibrous caps. This study aims to characterize the qualitative and quantitative fracture behavior of human atherosclerotic plaque tissue obtained from carotid endarterectomy samples using two different metrics. Uniaxial tensile experiments along with miniature single edge notched tensile (MSENT) experiments were performed on strips of isolated fibrous cap. Crack tip opening displacement (CTOD) and stress in the un-cracked segment (UCS) were measured at failure in fibrous cap MSENT specimens subjected to uniaxial tensile loading. Both CTOD and the degree of crack blunting, measured as the radius of curvature of the crack tip, increased as tearing propagated through the tissue. Higher initial stress in the UCS is significantly correlated with higher collagen content and lower macrophage content in the fibrous cap (ρ=0.77, P=0.009; ρ=-0.64, P=0.047; respectively). Trends in the data show that higher CTOD is inversely related to collagen content, though the sample size in this study is insufficient to statistically substantiate this relationship. To the authors' knowledge, this is the pioneering study examining the fracture behavior of fibrous caps and the first use of the CTOD metric in vascular tissue. A tear in the fibrous cap of atherosclerotic plaque can lead to ischemic stroke or myocardial infarction. While there is some information in the literature regarding quantitative measures of fibrous cap failure, there is little information regarding the behavior of the tissue during failure. This study examines the failure behavior of fibrous caps both qualitatively, by examining how and where the tissue fails, and quantitatively, by measuring (a) crack tip opening displacement (CTOD) in vascular tissue for the first time and (b) uniaxial stress in the un-cracked segment (UCS). This study shows that both metrics should be evaluated when assessing plaque vulnerability.

Characterization of near tip stresses for a plane-strain off-center crack in a strength mismatched weld

The past two decades have seen an increasing emphasis on the development of flaw assessment procedures accounting for the state of stress (constraint) near the crack tip. In-service inspections of many nuclear power plants have revealed that cracks are most likely to occur in a weld or in the regions near the weld. In recent work, the authors have proposed a novel three-parameter scheme to characterize the crack tip opening stress, for small-scale yielding, for a crack lying at the center of a strength mismatched weld. The proposed scheme was validated with detailed finite element analyses using the modified boundary layer formulation. In the present work, the previously proposed scheme is extended to an off-center crack lying in the weld region. Apart from analyzing an off-center crack, studies are performed on an interface crack in a weld having finite width. To validate the proposed scheme, modified boundary layer analyses are carried out for a wide range of offset ratio values (ratio of the crack tip-to-weld center distance to the weld half-width), ranging from 0.33 to 0.9, and strength mismatch ratio values (ratio of yield strength of weld to yield strength of base material), ranging from 0.6 to 1.6. Our studies revealed that the proposed analytical scheme works well for all offset ratios and weld mismatch ratios. For an interface crack, crack tip stresses depend mainly on the strength mismatch ratio between the base and weld material. Practically no significant effect is observed of the weld width on the crack tip opening stress of an interfacial crack.

Interaction of welding residual stresses and warm pre-stressing on brittle fracture of a pipe containing an internal semi-elliptical crack

Residual stresses (RS) due to welding process, may change the load bearing capacity of cracked components. These stresses can also affect the benefit of warm pre-stressing (WPS) cycles which are used for improving structure behaviour. RS are obtained from a two-passes welding simulation of a pipe and verified by experiments. A semi-elliptical internal crack at the weld line is considered. Redistribution of RS field after introducing the crack shows a significant tensile RS are remained at the crack tip. Two common WPS cycles, load-cool-fracture (LCF) and load–unload-cool-fracture (LUCF), are applied using the model at room and low temperature subjected to axial loading. Using local approach to fracture shows that welding RS dramatically raise the fracture probability. LCF has more influence on reducing the fracture probability in comparison with LUCF. The interaction of welding RS and WPS cycles still improves the fracture properties, however, welding RS cause to decrease the benefit of WPS. Comparing RS distributions on crack-tip shows that applying WPS cause to release a significant amount of welding RS and therefore, WPS can be very useful for welded structures. The near crack-tip opening stresses at a same fracture load are further studied for all cases.

Characterization of crack tip stresses in plane-strain fracture specimens having weld center crack

Fracture toughness of metals depends strongly on the state of stress near the crack tip. The existing standards (like R-6, SINTAP) are being modified to account for the influence of stress triaxiality in the flaw assessment procedures. These modifications are based on the ability of so-called ‘constraint parameters’ to describe near tip stresses. Crack tip stresses in homogeneous fracture specimens are successfully described in terms of two parameters like J–Q or J–T. For fracture specimens having a weld center crack, strength mismatch ratio between base and weld material and weld width are the additional variables, along with the magnitude of applied loading, type of loading, and geometry of specimen that affect the crack tip stresses. In this work, a novel three-parameter scheme was proposed to estimate the crack tip opening stress accounting for the above-mentioned variables. The first and second parameters represent the crack tip opening stress in a homogeneous fracture specimen under small-scale yielding and are well known. The third parameter accounts for the effect of constraint developed due to weld strength mismatch. It comprises of weld strength mismatch ratio (M, i.e. ratio of yield strength of weld material to that of base material), and a plastic interaction factor (Ip) that scales the size of the plastic zone with the width of the weld material. The plastic interaction factor represents the degree of influence of weld strength mismatch on crack tip constraint for a given mismatch ratio. The proposed scheme was validated with detailed FE analysis using the Modified Boundary Layer formulation.

G031024 デジタル画像相関法を用いた表面き裂開口変位の計測([G031-02]材料力学部門,一般セッション : 非鉄金属の強度と変形(2))

rack opening displacement of the mode I surface crack was measured using digital image correlation. Pulsating tension tests were carried out with the stress ratio R=0.2 and 0.5 using A7075 aluminum alloy. The crack tip opening stress was determined to various crack length based on the crack opening displacement. Crack tip opening stress was the almost same value as the minimum stress when 7M).5. On the other hand, crack tip opening stress was close to the half of the maximum stress when R=0.2. The stress ratio dependence did not disappear, even if the crack propagation rate was arranged with the effective stress intensity factor range. The relationship between the crack propagation rate and crack opening displacement near the crack tip was hardly dependent on the stress ratio.

Effect of constraint induced by crack depth on creep crack-tip stress field in CT specimens

In this paper, the effect of constraint induced by the crack depth on creep crack-tip stress field in compact tension (CT) specimens is examined by finite element analysis, and the effect of creep deformation and damage on the Hutchinson–Rice–Rosengren (HRR) singularity stress field are discussed. The results show the constraint induced by crack depth causes the difference in crack-tip opening stress distributions between the specimens with different crack depth at the same C*. The maximum opening stress appears at a distance from crack tips, and the stress singularity near the crack tips does not exist due to the crack-tip blunting caused by the large creep deformation in the vicinity of the crack tips. The actual stress calculated by the finite element method (FEM) in front of crack tip is significantly lower than that predicted by the HRR field. Based on the reference stress field in the deep crack CT specimen with high constraint, a new constraint parameter R is defined and the constraint effect in the shallow crack specimen is examined at different distances ahead of the crack tip from transient to steady-state creep conditions. During the early stages of creep constraint increases with time, and then approaches a steady state value as time increases. With increasing the distance from crack tips and applied load, the negative R increases and the constraint decreases.

Novel Method for Analyzing Crack Growth in Polymeric Microtensile Specimens by In Situ Atomic Force Microscopy

In this paper a micro tensile test which allows the determination and observation of the crack growth behaviour in thin polymer layers is presented. The setup consists of micromanipulators and piezo actuators for straining the sample while an atomic force microscope (AFM) is used for scanning the crack tip area with high lateral resolution. The stress in the specimen is determined by an optical microscope for observation of the deflection of a force sensing beam. The material under investigation is an amorphous and strongly entangled thermoplastic polyimide which can be patterned photolithographically and is spin cast to form layers of 3 μm thickness. The results show the potential of the setup to measure crack length, crack tip opening and nominal stress. The stress-crack length-diagram then allows to determine different stages during crack growth.

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A3, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A3 decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A3, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.

Domain Switching and Crack Tip Opening Stress Variation in Ferroelectric Ceramics

Evolution of switching zone near a crack tip in ferroelectric ceramics is calculated using the constitutive equations proposed in [1], with an assumption that switching-induced internal fields are minimized by fine domain microstructures and moving charges. A two-dimensional ferroelectric ceramic specimen that has an edge crack and that is poled perpendicular to the crack plane are subjected to external stress and electric fields. Diverse crack tip microstructures are obtained depending on both the history and the ratio of electric and stress loads. It is shown that opposite crack tip opening stresses under the same electric fields are due to opposite distributions of piezoelectric coefficients in the specimens with different crack tip microstructures.

The effect of second principal stress on the fatigue propagation of mode I surface crack in Al 2O 3/Al alloy composites

Using a plate made of A2017-T6 metal matrix composites reinforced with 10 volume % and 20 volume % Al 2O 3 particles and Al alloy possesses the same composition as matrix alloy, the crack propagation rate d a/d N of a mode I surface crack by the simultaneous action of plane bending and cyclic torsion are studied. And the effects of crack tip opening stress σ top, crack opening displacement COD, biaxial stress ratio C (=second principal stress/first principal stress) and the surface roughness of crack section are examined. When stress intensity factor range ΔK is lower than the specific level, d a/d N decreases with the increase of volume fraction of Al 2O 3 in C=0 and C=−0.55. But, d a/d N of Al alloy becomes minimum in C=−1 and the effect of Al 2O 3 particles disappears. σ top rises with the increase of volume fraction of Al 2O 3 particles and the decline of C. On the other hand, COD doesn’t always rise with the decline of C. These phenomena can be explained by the residual compressive stress formed at the surface layer of the specimen by the fatigue test and the surface roughness of crack section.

Effect of Second Principal Stress on Mode I Surface Crack Propagation of Al2O3/Al Alloy Composites.

Using a plate made of A2017-T6 metal matrix composites reinforced with 10 vol. % and 20 vol. % Al2O3 particles, crack propagation rate da/dN of a mode I suface crack by the simultaneous action of plane bending and cyclic torsion is sought. And the effects of crack tip opening stress σtop, crack opening displacement COD and biaxial stress ratio C on da/dN are examined. When ⊿K is lower than the peculiar level, da/dN decreases with the increase of volume fraction of Al2O3 in C=0 and C=-0.55. But da/dN of Al alloy becomes minimum in C=-1 and the effect of Al2O3 particles disappears. σtop increases with Al2O3 particles and the decrease of C. On the other hand, COD not always increases with the decrease of C. These phenomena can be explained by the residual compressive stress formed at the surface layer of the specimen by the fatigue test and the surface roughness of crack section.

The Propagation Behaviour of Mode I Surface Cracks under Biaxial Stresses by the Combination of Plane Bending and Cyclic Torsion

Crack propagation rate of a model surface crack in a plate, the crack tip opening stresses or displacements under various biaxial stress ratios by the simultaneous action of plane bending and cyclic torsion are examined. The aspect ratio of a crack is not affected by the biaxial stress ratio but the relationship between the propagation rate da/dN and the stress intensity factor range ΔK or the effective stress intensity factor range Δ Keff depends on it. This is mainly due to the differences of both CTOD and the scale of the slipped region at the crack tip caused by the difference of biaxial stress ratio.

A Measurement of Fatigue Crack Tip Opening and Closing Points by Means of Strain Interference Method. On Practicality of Strain Interference Method.

The measurement of fatigue crack tip opening stress σop and closing stress σcl occurring in actual equipment is generally very difficult. This is the reason why the range of effective stress intensity factor is not sufficiently applied to the fatigue crack propagation behavior of actual equipment. In this study, the measurement of σop and σcl in large size specimen is carried out by means of the strain interference method and the crack opening and closing points of long crack are successfully measured. Futhermore, σop and σcl in a specimen subjected to a rotating bending stress is measured. From these experimental results, the strain interference method is expected to be applicable to the measurement of σop and σcl in actual equipment.

A Measurement of Fatigue Crack Tip Opening and Closing Points by Means of Strain Interference Method. Accuracy and Comparison with Unloading Elastic Compliance Method.

Fatigue crack tip opening stress σop and closing stress σct can be easily determined with the relationship between the following strain functions f, h and the cyclic stress σ, f=(ey-β)/(ex+α), h=ey+λex, where ey and ex are the strains measured in the vicinity of the crack center (or the crack face), and α, β and λ are constants. With regard to small-size specimens having a center crack or notch, the accuracy of this measurement method is confirmed. If the constants α, β and λ are chosen to proper values, the crack tip opening stress σop and closing stress σot can be judged from the inflection points of the σ-h diagram and σ-f diagram. These stresses coincide with the opening stress σop and the closing stress σct determined by the unloading elastic compliance method.