Crack Opening Behavior Research Articles

The influence of applied stress, crack length, and stress intensity factor on crack closure

Experimental and analytical evidence for the influence of applied stress, crack length, and stress intensity factor on crack closure is critically compared and evaluated. Fatigue crack opening behaviors are broadly catalogued into three classes. Class I comprises “near-threshold” behavior, where crack closure levels increase with decreasing stress intensity factor. In class II, the “stable” regime, the crack opening level is independent of the stress intensity factor and crack length but is influenced by the applied stress. Class III is characterized by the loss of elastic constraint accompanying extensive yielding at the crack tip or in the remaining ligament, especially with further crack growth. Here, the crack opening level decreases with increasing crack length until little or no closure occurs. These three different classes of closure behavior are extensively illustrated with both experimental data and the results of numerical closure simulations, particularly original finite element (FE) analyses. No single relationship between crack opening levels and the fundamental fatigue parameters is found to hold universally, due to the wide range of mechanisms which cause or influence closure.

Fatigue crack closure

A loading stage for the scanning electron microscope has been used in conjunction with the stereoimaging technique to study fatigue crack closure for a center notched specimen of an aluminum alloy. The results are compared to similar measurements from single edge notched specimens of the same alloy and other materials. The magnitudes of closure loads were found to be different for these two specimen designs, but the dependence on stress intensity factor ( ΔK) is the same. Comparison of experiments is made with a finite element model simulation of crack opening, a simple model is developed which simulates the observed opening behavior, and a method is given for estimating threshold ΔK from materials parameters and crack opening behavior in the near threshold region.

Crack-tip behaviors of stationary and growing cracks in Al-Fe-X alloys: Part II. Crack opening profile

The crack opening behaviors of monotonically loaded stationary and growing cracks in Al-Fe-X alloys have been examined using the stereoimaging technique. Crack opening displacements (COD’s) have been measured as a function of distance behind the crack tip at different load levels. By comparing with existing asymptotic solutions, the experimental COD results confirm the dominance of the HRR (Hutchinson,[4,6] and Rice and Rosengren[5]) singularity in a stationary crack, the logarithmic singularity in a growing crack, and the transition from the HRR to the logarithmic singularity when a stationary crack extends by a small increment. In addition to the In (r) singularity, experimental evidence suggests the presence of a In2 (r) singularity in plane stress cracks growing into intense shear bands.

Analysis of a pipe elbow with longitudinal through-crack

Elastic-plastic finite element calculations of a 90 degree pipe elbow with straight pipe ends have been carried out. A longitudinal through-crack is located at extrados-position of the elbow. The component is loaded by internal pressure. The FE-models used are generated by means of a coordinate-transformation program from cracked plates generated with usual mesh generators. Besides the evaluation of the structure mechanics behaviour (i.e. plastic zones and stress-distributions) the main point of interest is focussed on the fracture mechanics results like J- integral , crack opening behaviour including some amount of stable crack growth and the calculation of the leakage area.

Fatigue crack growth and microscopic crack opening behaviour under impact fatigue load

The fatigue crack growth rates and crack opening behaviours were observed under impact and non-impact fatigue loads for high strength, low alloy HT-60 steel and austenitic SUS316 stainless steel, which had almost the same ultimate tensile strength of about 600 MPa. Particular attention was paid to the microscopic crack opening behaviour near the crack tip under two load conditions, evaluated using a fine grid method. The results showed no difference between the crack growth rates under impact or non-impact fatigue loads in the case of HT-60 steel, but in the case of SUS316 steel the crack growth rate under impact fatigue was much higher than that under non-impact fatigue. Such a difference between the two steels could be correlated with the microscopic crack opening behaviour under two load conditions; in the case of SUS316 steel, both the effective stress intensity range at the crack tip and the effective crack opening displacement behind the crack tip were larger for the crack formed by impact fatigue load than for the crack formed by non-impact load, whereas in the case of HT-60 steel, the difference between the values under impact and non-impact fatigue loads was significantly smaller.

On the finite element analysis of fatigue crack closure—2. Numerical results

The opening and closing behavior of fatigue cracks is studied with an elastic-plastic finite element model which has been described and evaluated in Part I. Special attention is given to the effects of maximum stress, strain hardening and yield stress. Normalized crack opening stresses decrease with increasing maximum stress and this dependency is stronger for lower stress ratios and lower hardening moduli. Results are interpreted in terms of an interaction between residual deformations and crack opening displacements. The ratio of yield stress to elastic modulus has little effect on crack opening behavior. Data for forward and reversed plastic zone sizes and shapes are presented, demonstrating some dependence on closure. The effects of different constitutive models are investigated, including the influence of mean stress relaxation. Crack closing levels are shown to be lower than crack opening levels, especially at lower stress ratios and higher maximum stresses. Biaxial stresses may also influence the closure behavior of mode I cracks, especially at higher maximum stresses. Opening levels are generally higher for equibiaxial loading and lower for pure shear loading.

人工海水中での６０ｋｇｆ／ｍｍ｀２´級高張力鋼溶接部材の腐食疲労き裂伝ぱ挙動について

The corrosion fatigue crack growth behavior in the butt welded joint of high tensile strength steel has been studied in a synthetic sea water and discussed in relation to the welding residual stress and corrosion deposits.For the base metal, the effect of synthetic sea water on da/dN depended on the stress ratio. At a high stress ratio, a little acceleration of da/dN by the synthetic sea water was observed while at a low stress ratio the da/dN tended to be lower than that in air. For the welded joint, the da/dN was affected by a compressive residual stress in both synthetic sea water and air, and was greater in air than in synthetic sea water. Such a crack growth behavior is related to the crack opening and closure behavior which is influenced by the corrosion deposits and the compressive residual stress.

A method of estimating CTOD for a surface crack through measurement on the crack opening behavior

The conversion method to CTOD from measured clip gauge displacement for a through thickness center cracked specimen and a three point bend CTOD specimen has been already established, for the purpose of obtaining the fracture toughness of the material. However the method for a semielliptical surface flaw has not been established yet because of difficulties of considering the three dimensional effect for the COD.In this paper, we assumed that COD for a surface flaw on the cross sectional plane perpendicular to the plate surface, which is the plane with a single edge crack, can be approximately given by the superposition of CODs for the single edge cracked plane under bending loading and for the center cracked plane under tensile loading, of which the center line corresponds to the plate surface. The bending and the tensile load are determined by the measured mouth COD and crack angle at the surface of the cracked body with a surface flaw.Tensile and bending tests for specimens with various sized semi-elliptical surface notches were carried out to confirm the above idea. In the tests, mouth COD and crack angle were measured by using double clip gauge method and simultaneously, the COD inside the surface notch was also measured by using silicon gum casting method. As a result, the converting method to CTOD at the deepest point of a surface flaw is driven from the measured mouth COD and crack angle at the surface which are obtained by double clip gauge method.The testing result of wide plate estst with a semi-elliptical surface fatigue crack on a multipass welded joint, of which crack tip located at local brittle zone within HAZ, was also analyzed. It was obtained that the critical CTOD for a surface crack of which the tip locates local brittle zone corresponds to the lowest critical CTOD obtained from the three point bend standard CTOD tests of the joint with a through thickness fatigue pre-crack.

Closure effects in delaminated graphite epoxy laminate under compression

Flaws in composite laminates may result in a severe loss of static and dynamic strength. Such flaws may be inherent or gained by misadventure. The extent of this loss can be influenced by several factors including loading, laminate stacking sequence, lamina properties, flaw size and damage type. In this study, the free-edge delamination of a laminated composite under compression loading is investigated. Computational, analytical and experimental tests are performed on a graphite/epoxy laminate AS4/3501-6 containing near surface edge defects and the crack opening behaviour is investigated. The computational analysis consists of a three dimensional finite element model where the plies can be catered for individually and interply delamination modelled. In the experimental investigations, a delamination is simulated by inserting teflon film at appropriate locations during the lay-up process.

Ｓ４５Ｃ焼入焼もどし材の過大過小応力下における微視的疲労き裂伝ぱ

Propagation of microscopic fatigue cracks by periodic overstressing was studied with quenched and tempered 0.45% C steel. Acceleration of crack propagation occured in 0.45% C steel as in the case of 0.15% C steel previously reported, when the crack length was more than 50μm. The lower limit of understress that caused such an acceleration was reduced steeply as the crack length became longer. The acceleration in 0.45% C steel was less than in 0.15% C steel in accordance with the previous result on macroscopic cracks in which the acceleration was less in materials of higher strength. In the cases of short cracks (below 200μm) and long cracks (above 200μm) loaded with low understress, the microscopic fracture surface consisted of small facets, which were supposed to be related to the crystal structure of steel, and cracks observed on the specimen surface propagated intermittently, suggesting that microstructure had a significant effect upon crack propagation under intermittent overstressing. In the case of long cracks loaded with high understress, the microscopic fracture surface consisted of large facets and cracks propagated steadily, indicating that microstructure had less effect. No appreciable difference was observed in crack opening behavior before and after overstressing, and the acceleration of crack propagation was not likely to be related to the crack closure phenomenon.

衝撃荷重下での疲労き裂進展挙動と微視的開口挙動

This paper describes the fatigue crack growth and crack opening behaviors in impact fatigue of two alloy steels; one is a high strength low alloy steel HT-60 and the other is an austenitic stainless steel SUS316. Both of the alloy steels have almost the same ultimate tensile strength of about 600MPa. Major attention was paid to the microscopic crack opening behavior under impact fatigue load measured by means of the fine grating method. The results of the crack growth tests indicated that the crack growth rate in impact fatigue is higher than that in non-impact fatigue for SUS316 alloy steel, but not for HT-60 alloy steel. Such a difference in crack growth behavior between two steels was correlated to the following microscopic crack opening behavior of these steels: In the case of SUS316 alloy steel, both of the effective stress intensity range at a crack tip and the effective crack opening displacement behind the crack tip are larger for the crack propagated under repeated impact load than those for the crack under non-impact load, but in the case of HT-60 alloy steel, the difference in those values measured under impact and non-impact loads is relatively small comparing to the case of SUS316 alloy steel.

疲労き裂の開閉口挙動に及ぼす溶接残留応力の影響に関する研究

Fatigue crack propagation tests were carried out on HT80 steel components on which residual stress fields were induced by electron beam welding, and the influence of residual stress on the fatigue crack opening behavior was investigated. An array of strain gauges attached along the section adjacent and parallel to the section including crack plane was used to examine the variation of stress distribution along the gauges attached section during uploading.In case of notched status, the variation of stress distribution both in welded and unwelded components subjected tensile load showed same aspects regardless the distribution of residual stress. However, in case that fatigue crack propagated, the variation of stress distribution depended on the distribution of residual stress. Based on the above results, it is clarified that residual stress directly affects the fatigue crack opening behavior.

Crack opening behavior near crack tip in impact fatigue

Crack opening behavior near crack tip in impact fatigue

微小格子法による鉄‐ステンレス系層状金属複合板中のき裂開口挙動の観察

A fine-grating technique using laser diffraction was applied to measure the opening distance of fatigue cracks in the two-layered composite plates which were composed of low carbon steel and ferritic or austenitic stainless steel. A common technique of unloading elastic compliance method was also used for the purpose of comparison.It was observed that the crack opening stress near the crack tip determined by the direct observation of the movement of lattice points around the crack tip approximately agreed with that obtained by the unloading elastic compliance method. But the crack opening behavior in the composite plates was quite different from that in the monolithic plates due to the influence of residual stress. An actual stress intensity factor K'max was therefore calculated for the composite plates based on the initial distribution of residual stress, and the crack opening behavior was estimated by using K'max and the crack opening behavior of monolithic plates. The estimated trend showed a good agreement with the observed one for the composite plates composed of low carbon steel and austenitic stainless steel. But, some discrepancy was observed for the composite plates composed of low carbon steel and ferritic stainless steel. This seems to come from a relatively large difference in yield strength between two materials, which may have a large influence especially in the neighborhood of the interface.

衝撃過大荷重による疲労き裂進展の遅延現象について

As one of the on-going studies to investigate the fatigue crack growth characteristics in impact fatigue, the fatigue crack growth behavior resulting from the single application of impact over-load was investigated by using Dual-Phase steel with ultimate tensile strength of about 800MPa as an experimental material. Discussions were made on the retardation of crack growth rate, crack opening behavior after over-loading and fractographical aspect in comparison with the results obtained through the application of single static over-load with peak stress hold time of 3min.The major conclusions obtained are summarized as follows:(1) Retardation of crack growth rate after impact over-loading was not so distinct when compared with the case after static over-loading.(2) The values of crack opening ratio after impact over-loading were higher than after static over-loading.(3) Fractographical observations showed that abrasions were caused on the fractured surfaces after impact over-loading, but not so after static over-loading. The following speculation on the crack tip plastic deformed zone was needed to explain the peculiar crack growth behavior after im- pact over-loading as mentioned above. In comparison with the condition of the plastic zone constructed by static over-load, the size of the zone constructed by impact over-load is smaller, but the strength of this small plastic zone is higher, in other words, the higher density of slip bands is attained under impact over-load.

The prediction of the crack-opening behavior of part-through fatigue cracks under the influence of surface residual stresses

The crack opening behavior of part-through fatigue cracks is modeled using a three-dimensional boundary integral analysis. The predictions show excellent agreement with observed behavior for a corner crack in a Ti-6Al-4V specimen with and without the presence of compressive surface residual stresses. Also, the analysis predicts a lenticular crack opening through-the-thickness when compressive surface stresses are present. The implications of this result for future studies are discussed.

Fracture of ceramics with surface flaws introduced by Knoop indentation

The crack opening behaviour of surface flaws in ceramic materials, produced by Knoop indentation tests, was investigated. The damaged region below the indenter tip was replaced by a wedge. The influence of this wedge is reduced, if tensile stresses are acting at the damaged surface. For alumina the wedging force in moment of fracture was found approximately 50% of its value without additional bending.

Mechanics of fatigue crack propagation by crack-tip plastic blunting

The power relation between the fatigue crack propagation rate da/ dN and the J integral range ΔJ was obtained for OFHC copper, 0.04%C steel and stainless steel (Type 304). The physical meaning of the relation was investigated based on the observation of the crack opening behavior and fractography. The striations, whose spacing was equal to da/ dN , confirm crack-tip blunting as being an operating mechanism for crack growth. da/ dN was expressed as a power function of the crack-tip opening displacement (Δ CTOD), da/ dN = A(Δ CTOD) p , where p was larger than one. The major portion of Δ CTOD contributes to crack growth at high rates, while a considerable fraction of Δ CTOD occurs behind the crack tip at low rates. Δ CTOD is correlated to ΔJ divided by the yield strength σ' Y through the equation, Δ CTOD = B(ΔJ/σ Y′) q , where q is nearly equal to one for 0.04%C steel and is larger than one for copper. The variation of q with material was explained based on the observed distribution of the crack opening displacement. The final equation for fatigue crack growth is given as da/ d N = A · B p(ΔJ/σ Y′) pq. When the shape of the crack tip opening is geometrically similar, both p and q are one. For a general case, both are larger than one, yielding the exponent of the da/ dN-ΔJ relation deviating from 1 up to 2.3.

Elastic-Plastic Analysis of Crack Opening, Stable Growth and Instability Behavior in Flawed 304 SS Piping

Crack initiation, stable growth, instability and crack opening behavior in flawed 304 SS piping has been examined within the framework of the engineering approach developed by Kumar, German and Shih [1]. Crack geometries considered include part-through, complete circumferentially cracked pipe subjected to remote tension, and through-wall flawed pipe in tension and in bending. Effect of flaw type and size, pipe diameter and length, and applied loading on the failure load and mechanism is investigated. Results are employed to assess the net section stress criterion based on plastic collapse. Crack opening area of interest in leak rate evaluations is calculated as a function of applied load or pipe end deflection for stationary as well as growing cracks.

Dynamic Elastic-Plastic Behavior of Circumferential Cracks in a Pipe Subject to Seismic Loading Conditions

An analytical study is performed to investigate the structural stability, and inherent integrity, of a Pressurized Water Reactor primary coolant loop cold leg pipe containing a through-wall circumferential crack. The purpose of this study is to gain a better understanding of the mechanisms and extent of crack opening behavior in a real piping system, and, thus, establish the basis for improved pipe break criteria. Cracks extending one-half the circumference or greater are considered in the pipe. Combined operating pressure plus external seismic loads are applied simultaneously to cause a maximum crack opening effect. A dynamic elastic-plastic analysis is performed to calculate stress intensity factors at the crack tip. The results are compared with experimental fracture toughness data to assess the material’s capability to resist crack extension. A fatigue crack growth study is also performed to determine the range of initial flaw sizes which could grow and extend during normal operation to threaten the integrity of the cold leg pipe.