Effects of short cracks produced at blunted pre-crack tip on stress and strain distributions

The present work investigates problems: (1) How are the plastic strain and the stress (triaxiality) re-distributed after a short crack initiated, extended and blunted at the pre-crack tip? (2) How do the above changes put a crucial effect on the triggering of the cleavage fracture? Based on the previous observations of configuration changes and fracture surfaces of pre-crack tips, Finite element method (FEM) simulations of a short crack initiated, extended and blunted at a pre-crack tip and calculations of distributions of stress, strain and triaxiality are carried out for 3PB pre-cracked HSLA steel specimens tested at -130^°C. The results reveal that: as long as the fatigue pre-crack is only blunted, in its vicinity a region where the accumulated strain is sufficient to nucleate a crack, and a region where the stress (triaxiality) is sufficient to propagate a crack nucleus are separated by a distance. The nucleated crack cannot be propagated and the cleavage fracture cannot be triggered. While a short crack produced at the fully blunted fatigue pre-crack, the strain retains, the stress (triaxiality) is rebuilt. An initiated and significantly extended and then blunted short crack makes a tip configuration, which on one hand is much sharper than that of the fully blunted original pre-crack tip, on other hand is wide enough to spread its effects into the high stress covered region. This sharpened crack tip configuration re-builds a ‘sharper’ distribution of stress (triaxiality) and makes two regions metioned above closer. Finally the two regions overlap each other and a cleavage crack can be initiated and propagated at a distance ahead of the blunted fatigue pre-crack.     

Stable crack growth in ductile polymers

Growth of a crack in ductile polymers (polyarylate, PTFE, and PU/PMMA blends) was studied. The crack growth was described assuming that local yielding in the crack tip is similar to large-scale shear yielding in rigid-plastic materials. Crack growth was stable, and a wedge shaped crack tip was formed. The crack tip opening displacement and the crack extension in the initial stage of the crack growth were proportional to the square of the strain up to 11% elongation. Dugdale’s equation was modified to describe the magnitude of the crack tip opening. In PA, a yield subzone near the crack tip was observed. This revised version was published online in November 2006 with corrections to the Cover Date.     

ELECTRICAL RESISTANCE VARIATIONS ACROSS A GROWING FATIGUE CRACK AS A FUNCTION OF THE LOAD CYCLE

Greater understanding of fatigue crack growth requires detailed measurements of crack tip plastic flow. A high resolution crack length measurement system based on the electrical potential method has been used to measure the variations in electrical resistance of specimens containing growing fatigue cracks. Crack growth increments caused by individual load cycles could be resolved down to a size of 0.1 μm. The electrical resistance has been found to vary cyclically as a function of the applied load. These variations are consistent with Bowles' observations that the crack initially grows with a very sharp crack tip followed by plastic blunting which is resharpened during unloading. Crack closure effects could be observed in the results generated from tests conducted with stress ratios of 0 and 0.1, but not for a test with a stress ratio of 0.5.     

THE EFFECT OF INTERMEDIATE HEAT TREATMENTS ON OVERLOAD INDUCED RETARDATIONS DURING FATIGUE CRACK GROWTH IN AN Al-ALLOY

Abstract— Crack growth fatigue tests were carried out on 2024-T3 specimens. Constant-amplitude loading was periodically interrupted by 10 overload cycles. Intermediate heat treatments (T4) were applied to remove the residual stress in the crack tip zone and the crack closure wake behind the crack tip. Retardation effects induced by crack closure due to the previous load history were fully erased by the heat treatments. Overload effects were easily introduced again by new overload cycles afterwards. Crack growth rate results and fractographic observations indicate that primary crack tip plastic deformation (in virgin material) is more effective for crack extension than secondary plastic deformation in an existing plastic zone. This conclusion is significant for cycle-by-cycle crack growth prediction models for variable-amplitude loading.     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.     

Interpretation of effects at the static fatigue limit of soda-lime-silicate glass

Crack growth in soda-lime-silicate glass near the static fatigue limit is rationalized by a fracture mechanics model of the crack tip, in which a stressed layer is built up on the crack surface as a consequence of ion exchange at the crack tip. This model extends the one presented earlier by Bunker and Michalske. Ion exchange, between hydronium (H₃O⁺) ions in the solution and sodium (Na⁺) ions in the glass, gives rise to compressive stresses at the tips of cracks in soda-lime-silicate glasses. These compressive stresses are responsible for (1) the occurrence of a fatigue limit in glass, (2) for the fact that crack tips remain sharp at the fatigue limit even though the walls of the crack are corroded by the basic solutions that form as a consequence of ion exchange, (3) for the crack tip bifurcation often observed when cracks are held at the fatigue limit for a while and then restarted at higher loads, and (4) for the fact that a delay time to restart the crack is often observed after the crack is held under load at the static fatigue limit. Most of the predictions are in quantitative agreement with experimental observations on crack growth and crack tip structure for soda-lime-silicate glass. The prediction of the time required to restart the crack is, however, only qualitatively correct, as experimental data report a sharp peak centered at the fatigue limit in the plot of restart time versus hold stress intensity factor, whereas the model gives a broad maximum on such a plot. Clearly, further development of the model will be needed for a better representation of the experimental data.     

A MODEL TO PREDICT THE FATIGUE LIFE OF FIBRE-REINFORCED TITANIUM MATRIX COMPOSITES UNDER CONSTANT AMPLITUDE LOADING

A model based on micro-mechanical concepts has been developed for predicting fatigue crack growth in titanium alloy matrix composites. In terms of the model, the crack system is composed of three zones: the crack, the plastic zone and the fibre. Crack tip plasticity is constrained by the fibres and remains so until certain conditions are met. The condition for crack propagation is that fibre constraint is overcome when the stress at the location of the fibre ahead of the crack tip attains a critical level required for debonding. Crack tip plasticity then increases and the crack is able to propagate round the fibre. The debonding stress is calculated using the shear lag model from values of interfacial shear strength and embedded fibre length published in the literature. If the fibres in the crack wake remain unbroken, friction stresses on the crack flanks are generated, as a result of the matrix sliding along the fibres. The friction stresses (known as the bridging effect) shield the crack tip from the remote stress, reducing the crack growth relative to that of the matrix alone. The bridging stress is calculated by adding together the friction stresses, at each fibre row bridging the crack, which are assumed to be a function of crack opening displacement and sliding distance at each row. The friction stresses at each fibre row will increase as the crack propagates further until a critical level for fibre failure is reached. Fibre failure is modelled through Weibull statistics and published experimental results. Fibre failure will reduce the bridging effect and increase the crack propagation rate. Calculated fatigue lives and crack propagation rates are compared with experimental results for three different materials (32% SCS6/Ti-15-3, 32% and 38% SCS6/Ti-6-4) subjected to mode I fatigue loading. The good agreement shown by these comparisons demonstrates the applicability of the model to predict the fatigue damage in Ti-based MMCs.     

Direct observation of tensile and fatigue cracks

Crack growth in aluminum foil specimens 1 mil thick has been studied under monotonie tension and low cycle fatigue. Crack tip regions were observed during loading by optical microscopy. Following final fracture, the crack path and fracture surface were examined by scanning electron microscopy.

Both tensile and fatigue cracks are typically preceded by a narrow necked region. Voids develop in the neck, crack growth proceeding by their growth and coalescence. As the voids form and grow, the foil necks down to zero thickness along the path of the crack.

Crack growth in both tension and fatigue results from concentrated plastic strain. The plastic flow is heterogeneous to an extent that voids precede the crack. In monotonic tension new voids are continually nucleated in the region of high strain ahead of the growing crack, while in fatigue, the voids result from plastic instabilities under cyclic loading.     

Comparison of static and dynamic fatigue crack growth rates in high-density polyethylene

Static and dynamic fatigue tests have been carried out at 23°C on a single grade of high-density polyethylene, using 6 mm thick, centrally cracked plate specimens. Crack growth rates were determined over a range of frequencies and stress ratios. Analysis of the dynamic data shows that crack growth is related to time under load rather than to number of fatigue cycles. Comparison with static fatigue results shows that unloading accelerates crack propagation, especially if the crack is compressed; these observations are interpreted in terms of crack tip sharpness.     

A crack in a linear-elastic material under mode II loading, revisited

A sharp crack in a two-dimensional infinite linear-elastic material, under pure shear (mode II) loading is re-examined. Several criteria have been proposed for the prediction of the onset and direction of crack extension along a path emanating from the tip of the initial crack. These criteria date back some three decades and are well documented in the literature. All the predictions from the different criteria are close and indicate that the crack extension takes a direction at an angle of ≈ −70° measured counterclockwise from the positive x -axis, in the case of a remotely applied positive shear stress. However, the possibility seems to have been overlooked that the crack extension may initiate not from the crack tip itself, but instead may initiate on the free surface at an infinitesimal distance behind the crack tip. The effect of crack tip plasticity on the relevant stresses in the region of the crack tip is investigated by the application of an elastic–plastic finite element program.     

Closure-free biaxial fatigue crack growth rate and life prediction under various biaxiality ratios in SAE 1045 steel

Biaxial fatigue tests were performed on thin-walled tubular 1045 steel specimens in a test fixture that applied internal and external pressure and axial load. There were two test series, one in which constant amplitude fully reversed strains (CAS) were applied and another in which large periodic compressive overstrain (PCO) cycles causing strains normal to the crack plane were inserted in a constant amplitude history of smaller strain cycles. Ratios of hoop strain to axial strain of λ = ?1, ?0.625, ?ν and +1 were used in each test series. Fatigue crack growth behaviours under CAS and PCO histories were compared, and revealed that the morphology of the fracture surface near the crack tip and the crack growth rate changed dramatically with the application of the compressive overstrains. When the magnitude of the compressive overstrains was increased, the height of the fracture surface irregularities was reduced as the increasing overstrain progressively flattened the fracture surface asperities near the crack tip. The reduced asperity height was accompanied by drastic increases in crack growth rate and decreases in fatigue life. Using a pressurizing device attached to the confocal scanning laser microscope (CSLM), crack opening measurements were obtained. Crack opening measurements showed that the biaxial cracks were fully open at zero internal pressure for block strain histories containing in-phase PCO cycles of yield stress magnitude. Therefore, for the shear-strained samples, there was no crack face interference and the strain intensity range was fully effective. For PCO tests (with biaxial strain ratios of ?0.625 and +1), effective strain intensity data were obtained from tests with positive stress ratios for which cracks did not close. A number of strain intensity parameters derived from well-known fatigue life parameters were used to correlate fatigue crack growth rates for the various strain ratios investigated. Predicted fatigue lifetimes based on a fatigue crack growth rate prediction program using critical shear plane parameters showed good agreement with the experimental fatigue life data.     

FATIGUE AT NOTCHES SUBJECTED TO REVERSED TORSION AND STATIC AXIAL LOADS

Reversed torsion with and without a superimposed end load has been applied to 1% Cr-Mo-V steel specimens containing sharp notches. Crack propagation was monitored by a sensitive d.c. potential drop system that measured crack depths between 25 μm and 0.6 mm from the root of the notch. Stress intensity factors do not satisfactorily correlate all the crack growth data but a strain intensity factor which is a function of material properties and notch plastic zone size shows a significant improvement and provides a single upper bound solution for both ambient and elevated temperatures. This solution permits designers to make safe lifetime assessments. At room temperature cracks initially propagate by mode II along the surface, and mode III radially but at low stresses crack growth is continued by mode I propagation. At higher stresses a transition to mode I cracking is avoided. Elevated temperature causes a brittle layer to form and in this case cracks initially propagate by mode I which then translates to mode III cracking at high stresses. Mode III thresholds are significantly higher than mode I thresholds but a constrained shear strain zone, as found at the root of notches subjected to torsion, permits the initiation and generation of a mode III crack. The application of an axial load enhances the mode III crack propagation rate since this increases the effective crack tip intensification factor.     

Deformation Analysis of Notched Rubber Specimens

Abstract:  The influence of the initial crack tip radius on the strain distribution in the vicinity of the blunted crack tip was determined experimentally by an optical full-field strain analysis method. These experimental results were compared with the calculations of the commercial finite element code ABAQUS 6.4-1. For the simulation a suitable hyperelastic material law was chosen and fitted to experimental data of three different tests (uniaxial tensile, planar tensile, biaxial tensile). Two different elastomer grades (SBR and EPDM) were selected for the experimental work. The utilized optical full-field strain analysis method based on the image correlation technique was found to be an effective tool to determine strains, strain distributions and gradients near to the crack tip for elastomeric materials. Different material behaviour was observed for the two rubber types investigated. While the crack tip was regularly blunted (half circle shape) for EPDM and the strain gradient was low (less steep), the crack tip was sharp (less blunted) with a higher strain gradient for SBR.     

Characteristics of fatigue crack propagation behaviour as identified by hysteresis loop at the crack tip

Fatigue crack propagation tests have been carried out under various load conditions. Hysteresis loops denoting the relationship between load and strain at the crack tip are obtained by using local compliance measurement. Crack growth acceleration, delayed retardation and non‐propagation phenomena are investigated by considering the variation of hysteresis loop expansion and hysteresis loop tail. Based on the physical meaning of hysteresis loops, two types of crack closure are ascertained and the effect of crack closure on fatigue crack propagation is studied. Results show that change of the effective amplitude of the stress intensity factor at the crack tip is the reason that crack propagation rates vary.     

Delamination and fatigue crack growth behavior in Fiber Metal Laminates (Glare) under single overloads

Delamination extension and fatigue crack growth behaviors under single overloads were investigated for GLARE 2-2/1-0.3 with fiber direction of 00/00. The results indicate that the stress intensity factor at the crack tip in metal layer while overload applied, K_tip,ol is a key controlling variable which influences fatigue crack growth and delamination behaviors. When K_tip,ol becomes bigger and exceeds a critical value, an obvious kink in the delamination shape is observed nearby the location of overload applied. Crack growth rate after application of overload could not return to its original level even the crack grows beyond the overload plastic zone. The reduction magnitude of the crack growth rate becomes bigger with the overload ratio (intrinsically K_tip,ol) increasing. These new results for the crack growth behavior have never been reported before, which can be well explained by the delamination extension behavior observed after overload applied.     

Modeling dynamic crack propagation in fiber reinforced composites including frictional effects

Dynamic crack propagation in a unidirectional carbon/epoxy composite is studied through finite element analyses of asymmetric impact (shear loading) of a rod against a rectangular plate. A finite deformation anisotropic visco-plastic model is used to describe the constitutive response of the composite. Crack propagation is simulated by embedding zero thickness interface element along the crack path. An irreversible mixed-mode cohesive law is used to describe the evolution of interface tractions as a function of displacement jumps. Contact and friction behind the crack tip are accounted for in the simulations. The failure of the first interface element at the pre-notch tip models onset of crack extension. Crack propagation is modeled through consecutive failure of interface elements. The dynamic crack propagation phenomenon is studied in terms of crack initiation time, crack speed, mode I and mode II displacement jumps and tractions associated with the failure of interface elements, effective plastic strain at the crack tip and path independent integral J^′. Analyses are carried out at impact velocities of 5, 10, 20, 30 and 40 m/s, assuming the crack wake is frictionless. Moreover, analyses at impact velocities of 30 and 40 m/s are also carried out with a friction coefficient of 0.5, 1, 5 and 10 along the crack surfaces. The analyses show that steady-state intersonic crack propagation in fiber reinforced composite materials occurs when the impact velocity exceeds a given threshold. A steady-state crack speed of 3.9 times the shear wave speed and 83% of the longitudinal wave speed is predicted in the cases in which the impact velocity is above 10 m/s. Detailed discussion is given on the features of sub-sonic and intersonic crack propagation. It is shown that friction effects, behind the crack tip, do not have a significant effect on maximum crack speed; however, they do on characteristics of the shock wave trailing the crack tip. The analyses also show that the contour integral J^′, computed at contours near the crack tip, is indeed path independent and can serve as a parameter for characterizing intersonic crack propagation.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

A unified model of fatigue kinetics based on crack driving force and material resistance

Fatigue in Al-alloys is largely a process of crack growth from pre-existing defects occurring by several different mechanisms, each of which dominates a particular rate-driven segment of fatigue kinetics. These include fatigue void formation through interfacial cracking of secondary particulates, crack extension by brittle micro-fracture (BMF) in near-threshold fatigue, slip driven crack growth in the Paris regime and quasi-static crack extension by the well-known micro-void coalescence (MVC) and the less known fatigue void coalescence (FVC). BMF is mean stress and sequence-sensitive.Mechanism selection for fatigue crack extension in each load cycle occurs on the principle of least resistance to crack driving force represented by ΔK and K_max. Crack extension will switch to a different failure mechanism given reduced resistance to that mechanism by comparison to the current one. Increasing driving force will thus force a switch from BMF to shear and then onto MVC or FVC in that order, over each rising load half-cycle. Higher growth rates will therefore always be associated with a mix of all these mechanisms.     

Experimental evaluation of the effect of residual stress field on crack growth behaviour in C(T) specimen

The effects of the residual stress field resulting from shot peening and the indentation technique were investigated in relation to fatigue crack closure and crack growth behaviour. Compact Specimens of 20NiCrMo2 were used in this investigation. The regions of residual stress field were located behind the fatigue crack tip. Crack closure behaviour was measured with back face strain and crack mouth opening displacement gauges. Crack length was monitored by the compliance and microscopic methods. Residual stress was measured by the incremental hole-drilling method. Subsequently the closure level, propagation rate and resulting crack growth retardation were studied. Crack closure and attendant growth retardation were shown to be dependent on the residual stress field. Residual stresses produced by shot peening and indentation were both compressive. The maximum value of residual stress for both operations were on the surface and at the same intensity. However, the residual stress induced by the indentation technique was deeper. The results showed that the closure effect was stronger in the case of indentation technique.     

Growth of tensile and fatigue cracks in metal foils

The extension of cracks in thin foils of copper, brass, and tantalum has been investigated for both monotonic and cyclic loading using optical microscopy and scanning electron microscopy. Crack growth in both tension and fatigue is found to occur primarily by a void coalescence mechanism, as previously reported for aluminum foils. The particular morphology of void formation exhibited by a given material is determined by its purity level and stacking fault energy, the latter being important as it affects the slip character—varying from planar to wavy—of the metal.Fatigue crack growth without void formation has also been observed in brass and tantalum. The resulting fracture surfaces are flat; a different growth mechanism, attributed to plane strain conditions at the crack tip rather than plane stress, accounts for this mode of propagation.