Non-propagating Cracks Research Articles

Analysis of Crack Nonpropagation Behavior during Fatigue Crack Growth

Fatigue crack propagation tests are carried out under two types of block loading amplitude using a high-precision local compliance measurement.Relationship between the shape change of hysteresis loops and the nonpropagating crack is studied.Based on relationships of compliance change,crack opening/closure phenomena and elastic-plastic behavior near the crack tip in a loading cycle,the mechanism of crack nonpropagation is investigated.It is shown that the profile of nonpropagating crack tip may be cuspate or obtuse at the maximum load.Crack nonpropagation means that there is no tension plastic zone and no compressive plastic zone generated at the crack tip.The loads FRCPG and FRPG are defined according to the residual tension deformation layer in a load cycle,and the equivalence waveforms of crack propagation induced by the crack tip plastic zone at the maximum and minimum loads can be known and used for counting random load waveforms,thus providing a theoretical basis for forecasting the residual life of engineering structure.

Increasing Behavior of Strength for Fatigue Fracture of Austenitic Stainless Steel during Fatigue Tests at Elevated Temperature

In order to clarify notch effect on fatigue strength of an austenitic stainless steel, rotating bending fatigue tests were carried out for smooth and notched specimens at 573K. Clear endurance limits were recognized and the fatigue strength did not decrease continuously with increasing stress concentration factor Kt, notwithstanding any non-propagating crack was not recognized at notch roots for specimens endured at 108 stress cycles. According to hardness tests, an area of notch root hardened during fatigue test by dynamic strain aging. The hardening behavior occurred remarkably with increasing Kt. Effects of Kt and the hardening behavior on fatigue strength canceled each other, and then fatigue strength became insensitive to Kt. Fatigue strength σSIT obtained by stress increment fatigue tests became higher than the ordinary fatigue strength for each specimen of Kt, that is, the coaxing effect was recognized clearly. This result indicated that the strength for fatigue fracture increased gradually during fatigue test. σSIT had a peak value at Kt of 2.0 and it decreased with increasing Kt sensitively. The increasing behavior of strength for fatigue fracture depended on Kt and fatigue fracture was controlled by circumstances of hardened material and stress amplitude considering Kt.

The Ability of Current Models for Fatigue Life Prediction of Shot Peened Components

It is well known that shot peening has a marked benefit on fatigue life for the majority of applications. This effect is attributed mainly due to the compressive residual stress state at the component’s surface due to shot peening. The present paper evaluates the ability of several fatigue life prediction models, commonly used for general analyses, to predict the behaviour of components with compressive residual stress due to shot peening. Advanced elastic-plastic finite element analyses were carried out in order to obtain stress, strain, strain energy and fracture mechanics parameters for cracks within a compressive residual stress field. With these results several total fatigue life prediction models (including critical distance methods) and fracture mechanics based models were applied in order to predict fatigue life. Fatigue life predictions were compared with several experimental fatigue tests carried out on specimens, representative of a critical region of a compressor disc in a gas turbine aero engine. The results obtained showed that total fatigue life methods, even if combined with critical distance methods, give conservative results when shot peening is considered. Fatigue life was successfully predicted using the method proposed by Cameron and Smith, by adding initiation life to crack propagation life. This last method was also successfully applied for the prediction of non-propagating cracks that were observed during the experimental tests.

Fatigue failure assessment under stress gradients using small crack fatigue concepts

The present work describes a microstructurally-based methodology to assess fatigue limits in specimens under stress/strain gradients by using a single concept of modelling the growth of a small crack driven (or retarded) by a rapidly changing stress field and interacting with the microstructural barriers (e.g. grain boundaries) of the material. This description is based in what is called Microstructural Fracture Mechanics, which extend techniques successfully employed to long cracks in LEFM to cracks whose length is comparable to the size of the microstructure of the material. The methodology is successfully applied to notched components. The classical limits for crack initiation and crack propagation up to failure in notched components are clearly identified and predicted. The appearance of non-propagating cracks and their expected lengths are also estimated. Finally, a practical extension of this methodology to analyse the fatigue failure under stress/strain gradients and stress ratio variations with depth typically generated in fretting-fatigue problems is also presented.

Instability during cohesive zone growth

Tensile microcracking of quasi-brittle materials is studied by means of micromechanics, based on (i) an elasto-damaging cohesive zone model accounting for cohesive softening and (ii) a dilute distribution of non-interacting microcracks of uniform orientation and size. Considering virgin microcracks (initially without cohesive zones), macroscopic tensile load increase results in growth of cohesive zones ahead of stationary (non-propagating) cracks and, subsequently, in crack propagation which, notably, will be encountered before the cohesive zones are fully developed i.e. onset of instable cohesive zone growth will be encountered at a load level (i) at which tractions are still transmitted across the inner edges of the cohesive zones and (ii) at which the separation at the inner edges of the cohesive zones is smaller than its critical value. Focusing on onset of instable cohesive zone growth, the chosen approach allows for accessing quantities characterizing the stability limit (e.g., the intensity of the macroscopic loading and the opening at the inner edges of the cohesive zones), without raising the need for non-linear Finite Element analyses. It is shown that the tensile macrostrength of materials containing virgin microcracks is larger than the one related to cracks with already initially fully developed cohesive zones, and related strength differences are quantified for a wide class of cohesive softening behavior. The proposed model is validated by comparing model predictions with an exact solution (available for the special case of constant cohesive tractions) and with results from reliable Finite Element analyses. The paper will be of interest for engineers involved in testing and/or in modeling of quasi-brittle media including cementitious materials and rock.

Estimating the Effects of Microscopic Stress Concentrations on the Fatigue Endurance of Thin-walled High Strength Steel

The effects of microscopic surface stress concentrations on the fatigue endurance of thin-walled high strength steel were systematically estimated by numerical analysis and plane-bending fatigue tests with Schenck-type specimens, using the commercially available static implicit method FEA software I-DEAS ver. 11 for the stress distribution calculations. The microscopic stress concentration factor αi, from notch depth t=50 μm and notch root radius ρ=6 μm microscopic surface ridges, monotonously increased with increases in the roughness ridge direction, θ, from 1 to 7 in the bending mode. A fitted curve was developed for deriving the calculated stress concentration, αθ, from the superposition of the principal stresses. In the twisting mode, αi varied from about 4 to 7. The θ dependency of αi was smaller than that in bending mode. The empirical rule that the specimen collection direction has a lesser effect in twisting mode fatigue was supported by the αi value. It is reported that the fatigue notch factor β increased linearly with increases in the macroscopic stress concentration factor αa of up to 3. On the other hand, β slowly increased with increases in αi until it exceeded about 2. This marked difference might be due to differences between their respective stress gradients, which was well described by Nisitani and Endo by using a parameter ρ. A plane-bending fatigue test was performed with an artificial surface micro-groove of θ=0, 90° using 590 MPa class strength circumferentially flattened electric resistance welded tube. The θ=0° micro-groove had little effect on the fatigue endurance in bending. On the other hand, the fatigue cracks of all the θ=90° specimens initiated at the basilar part of the micro-groove without any nonpropagating cracks. The fatigue notch factor β seems to be determined by only αi independent of ρ in the microscopic stress concentration field.

Shear Mode Growth and Threshold of Small Fatigue Cracks in SUJ2 Bearing Steel

The shear mode propagation and threshold behaviors of small, semi-elliptical fatigue cracks were investigated in the JIS-SUJ2 bearing steel. Fully-reversed torsional loading was combined with a static axial compressive load to obtain crack growth in the longitudinal direction of cylindrical specimens. Non-propagating cracks smaller than ≅1mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens, and (ii) by using smooth specimens in constant stress amplitude tests. The Mode II and Mode III threshold stress intensity factor ranges, ΔKIIth and ΔKIIIth, were estimated from the shapes and dimensions of non-propagating cracks. The threshold values decreased with a decrease in crack size, and there was no significant difference between ΔKIIth and ΔKIIIth. Wear on the crack faces was inferred by a powder and also by changes in microstructure in the wake of a crack. The ΔKIIth in the absence of interference of crack faces was estimated to be approximately 13MPa·m1/2 for a 1mm long crack.

Fatigue Crack Initiation in Alloy 718 at Elevated Temperature

In order to investigate the mechanism of fatigue crack initiation in Alloy 718 at elevated temperature, rotating bending fatigue tests were carried out at room temperature and 500℃ for the alloy with different grain sizes of 18 and 88μm. Fatigue strength in the long life region decreased markedly with increase in grain size at both temperatures. Non-propagating cracks of one or two grain sizes were observed in both fine and coarse grained specimens under stress levels near a horizontal line in each S-N curve, though the S-N curve of fine grained specimens showed a duplex one at 500℃. All of fractures occurred from surface in the life range up to 108cycles except for those originated from the subsurface of fine grained specimens at 500℃ beyond∼107cycles. Cracks nucleated from not only slip bands but also annealing twin boundaries, irrespective of grain size and fracture type. The frequency for twin boundary cracking increased with increases in grain size and temperature and with decrease in stress.

Fatigue notch sensitivity and the notch size effect

It has long been known that the fatigue notch factor K F, given by σ w0/ σ w, where σ w0 is smooth specimen fatigue strength ( R = −1) and σ w is the fatigue strength of a notch-containing specimen, is less than the theoretical stress concentration factor, K T. Empirical rules have been proposed by Peterson and by Kuhn and Hardrath for the estimation of K F which involve the notch radius and a material constant. El Haddad, Topper and Smith provided one means for understanding the factors determining K F. The present paper provides an alternative approach based upon a consideration of the development of fatigue crack closure. The effect of crack closure on the formation of non-propagating cracks is also discussed.

Crack Size Dependency of Shear-Mode Fatigue Crack Threshold in Bearing Steel

Semi-elliptical shear-mode fatigue cracks were promoted in the axial direction of round specimens of SAE52100 bearing steel by fully-reversed cyclic torsion tests under a static axial compressive stress. Non-propagating cracks smaller than 1 mm were obtained in two ways; (i) stress amplitude decreasing tests of notched specimens, or (ii) constant stress amplitude tests of smooth specimens. The threshold stress intensity factor ranges, (KIIth and (KIIIth, showed a crack size dependency.

Fatigue Property of Shot-peened Spring Steel with an Artificial Pit

The fatigue property of shot-peened specimens with a semispherical artificial pit of varied diameter was investigated. Shot peening (SP) and stress shot peening (SSP) were administered to the specimens, followed by etching hole diameter of 0.2, 0.4, and 0.8 mm. After that, bending fatigue tests were carried out on the specimens. The fatigue strength of the SP specimen was improved substantially because of the compressive residual stress generated on the surface, furthermore, the SSP specimen shows a higher fatigue strength due to the formation of greater compressive residual stress than SP.A@In the case of shot-peened specimens and stress shot peened specimens, the specimen having an artificial pit with d=0.2mm fractured from outside the artificial pit. Therefore, d=0.2mm diameter artificial pit was acceptable in the case of SP or SSP specimen. Multiple non-propagating cracks were observed in a peened specimen after fatigue testing. It is considered that the reason why the artificial pit is acceptable is the stress intensity factor range, which is reduced by compressive residual stress by SP or SSP, becomes smaller than the threshold stress intensity factor range compared to the fatigue limit stress of un-shot peened material.

Peculiarity of Notch Effect on High Cycle Fatigue Strength of a Stainless Steel SUS316NG at 300°C

Rotating bending fatigue tests were carried out for notched specimens of a SUS316NG austenitic stainless steel at 300°C. Nevertheless any non-propagating crack was not recognized at the root of the notch for specimens endured at 108 stress cycles, the fatigue strength at 108 cycles did not decrease continuously with increasing the stress concentration factor. An area of the root of notch hardened during fatigue test at 300°C by dynamic strain aging. The hardening behavior became remarkably with increasing the stress concentration factor. Effects of the stress concentration factor and hardening behavior on the fatigue strength cancel each other, and then dependency of the fatigue strength on the stress concentration factor becomes insensitive.

Fatigue Failure under Varying Loading within Fatigue Limit Diagram

Although fatigue limit diagram is defined in principle for constant stress amplitude condition, it is often considered that fatigue failure would not occur even in varying loading if applied stresses were kept within the fatigue limit diagram. However, it was shown in the case of small-notched specimen and fretting fatigue that fatigue failure occurred in some special case of variable amplitude loading condition even when all stress amplitudes were kept within the fatigue limit diagram. The cause of this phenomenon was examined using two-step and repeated two-step stress patterns in which the first step stress was with zero mean stress and the second step stress had a high mean stress. A non-propagating crack was formed by the first step stress. This crack functioned as a pre-crack for the second step stress with high mean stress. Consequently, fatigue failure occurred even when all stress amplitudes were kept within the fatigue limit diagram. It was an unexpected fracture caused by the interference effect of non-propagating crack and mean stress change.

ANN-Based Crack Identification in Rotor System with Multi-Crack in Shaft

Rotating machinery, such as steam turbo, compressor, and aeroengine etc., are widely used in many industrial fields. Among the important rotor faults, the fatigue crack fault, which can lead to catastrophic failure and cause injuries and severe damage to machinery if undetected in its early stages, is most difficult to detect efficiently with traditional methods. In the paper, based on the truth of the change of the mode shapes of the cracked structure, a new method by combining accurate finite element model of rotor with multi-crack in shaft and artificial neural network (ANN) is proposed to identify the location and depth of cracks in rotating machinery. First, based on fracture mechanics and the energy principle of Paris, the accurate FE model of the rotor system considering several localized on-edge non-propagating open cracks with different depth, is built to produce the specific mode shapes. Then a set of different mode shapes of a rotor system with localized cracks in several different positions and depths, which will be treated as the input of the designed ANN model, can be obtained by repeating the above step. At last, with several selected crack cases, the errors between the results obtained by using the trained ANN model and FEM ones are compared and illustrated. Meanwhile, the influences of crack in the different position on the identification success are analyzed. The method is validated on the test-rig and proved to have good effectiveness in identification process.

Effect of High Tensile Pre-Strain on the Torsional Fatigue Properties of a Structural Steel

This study is developed to investigate the effect of monotonic plastic deformation on the torsional fatigue properties of a structural steel. Five different kinds of tensile pre-strain, 2%, 5%, 8%, 12% and 22%, were applied to the specimens, respectively. And the maximum pre-strain value is near to the necking strain of the test material. The effects of tensile pre-strain on surface hardness, fatigue crack initiation and propagation behaviors, and the behavior of non-propagating cracks. The main results obtained are: The fatigue limits are 145, 160,175, 200 and 215MPa for specimens with tensile pre-strain of 2% 5%, 8%, 12% and 22%, which are improved to 104%, 114%, 125%, 143% and 153% of the fatigue limit for non-pre-strained specimens, respectively. The torsional fatigue limit increases with the tensile pre-strain increasing, until the pre-strain value being near to the necking strain ratio. However, the fatigue limit increase becomes more slowly for high tensile pre-strained specimens than the lower ones. The fatigue cracks of the tensile pre-strained specimens initiated earlier than that of the non-pre-strained specimens, and the propagation is also accelerated, but there is no effect on the fatigue crack initiation point and the branch point. Non-propagating crack length becomes shorter with increasing of tensile pre-strain until the value near the necking strain, and the quantity of non-propagating crack increases at the same time.

Coaxing Effect in Stainless Steels and High-Strength Steels

The effects of prestrain and strength level on the coaxing behavior were studied in austenitic stainless steels and high strength steels, respectively. The materials used were austenitic stainless steels, SUS304 and SUS316, and high strength steels, SCM435, SNCM439 and SUJ2. Stress incremental fatigue tests were performed using cantilever-type rotating bending fatigue testing machines. It was found that the steels except for SUJ2 showed a marked coaxing effect. Non-propagating cracks were not detected in all the steels examined. Based on hardness test, X-ray diffraction measurement and EBSD analysis, it was indicated that the coaxing effect occurred due to work hardening and strain-induced martensite transformation in austenitic stainless steels and to strain-aging in high strength steels.

Formulation of cracked beam element for analysis of fractured skeletal structures

In this paper, a cracked element is developed incorporating a non-propagating edge crack into a structural beam member. The additional flexibility that the crack generates is evaluated using strain energy density factors given by linear fracture mechanics. Based on this flexibility the stiffness matrix of the cracked beam element is deduced. The governing equations of the element can be treated as in the usual way of finite element procedures. In this formulation, the crack depth and location are considered as independent global design parameters. Thus, this element is appropriate for static and dynamic analysis of skeletal structures with crack-like damages. The convergence, accuracy and computational efficiency of the presented element are validated through comparisons with experimental and numerical results available from the literature.

Fatigue strength of small-notched specimens under variable amplitude loading within the fatigue limit diagram

Although the fatigue limit diagram is defined in principle for constant stress amplitude, it is often considered that fatigue failure would not occur, even in varying loading, if applied stresses were kept within the fatigue limit diagram. However, it was shown in the case of small-notched specimens that fatigue failure occurred in some special cases of variable amplitude loading, even when all stress amplitudes were kept within the fatigue limit diagram. The cause of this phenomenon was examined using two-step stress and repeated two-step stress patterns in which the first step stress was chosen to be equal to the fatigue limit with zero mean stress and a mean stress was superposed on the second step stress. A non-propagating crack was formed by the first step stress. This crack functioned as a pre-crack for the second step stress with high mean stress. Consequently, fatigue failure occurred even when all stress amplitudes were kept within the fatigue limit diagram. It was an unexpected fracture caused by the interference effect of a non-propagating crack and a mean stress change.

Short fatigue crack growth in aluminium alloy 6082-T6

Fatigue crack growth tests on 6082-T6 aluminium specimens have been carried out. The single edge notched tension specimens had a spark eroded 0.2 mm deep starter notch. In order to measure the crack growth, a special direct current potential drop method was used. The experiments were carried out at four different stress ratios. The crack growth data validate the long crack growth data given in Eurocode 9 [CEN. ENV 1999-2: Eurocode 9: Design of aluminium structures. Part 2: Structures susceptible to fatigue. European Committee for Standardisation, 1998.] and some indication of accelerated crack growth for short cracks was found. An effective stress intensity factor, which is a generalisation of an approach proposed by El Haddad et al. [El Haddad MH, Topper TH, Smith KN. Prediction of nonpropagating cracks. Eng Fract Mech 1979; 11:573–84], has been applied to correct for short crack growth behaviour. It has been shown that the potential drop technique can be successfully used to measure crack growth in aluminium specimens. The mean stress dependence was found to be less pronounced than for the 7075-T6 and 2024-T3 aluminium alloys.

Non-propagating cracks and high-cycle fatigue failures in sharply notched specimens under in-phase Mode I and II loading

Sharply notched specimens were tested under in-phase Mode I and II loading to study the non-propagating crack behaviour in the presence of complex stress states. The material employed in the present investigation was a commercial low carbon steel. Non-propagating cracks were generated under different ratios between Mode I and Mode II stress components. The direct inspection of the cracked samples showed that the early stage of the crack propagation was mixed Mode governed (Stage 1-like process), whereas the subsequent propagation was seen to be mainly Mode I dominated (Stage 2-like process). Moreover, it was observed that non-propagating crack length tended to increase as the Mode II contribution to fatigue damage increased. In any case, independently of the degree of multiaxiality, their average length was of the order of 2 L, where L was the material characteristic length calculated according to the theory of critical distances. Finally, the detected crack paths were used to form some hypotheses on the reason why two methods previously formulated by the authors are successful in predicting the multiaxial high-cycle fatigue strength, even though they make quite different assumptions on the physical mechanisms damaging metallic materials in the high-cycle fatigue regime.