M.M.I. Hammouda

Significance of crack tip plasticity to early notch fatigue crack growth

Abstract This work demonstrates the capability of the extents of both monotonic and cyclic crack tip plasticity in correlating experimental fatigue crack growth (FCG) rates from notches. Experimental results previously published by the authors on early mode I stage II FCG rates from different single edge U-shaped notches in low carbon steel plates were utilised. The plates had different stress concentration factors and had been tested near their fatigue limits at a zero stress ratio and at constant amplitude uniaxial stresses. Eleven tests were numerically simulated with a previously developed in-house two-dimensional cyclic elastic–plastic finite element programme. The cyclic plastic deformation accommodated at the tip of a physical short through-thickness crack artificially advancing from the root of each tested notch was analysed. When the tip of a crack was advancing within the affected zone of the simulated notch, transition behaviour from the notch-affected physical short crack regime to the relatively long crack regime was recognised. The extents of crack tip opening displacements and plastically deformed zones were the subject of that behaviour. Equivalent edge crack lengths were proposed on the assumptions of equal stress intensity factors and monotonic and cyclic crack tip plastically deformed zones. A length parameter devised from the behaviour of short crack tip plasticity showed its capability to correlate early FCG rates from notches. The proposed parameter started its behaviour with a relatively high extent at zero crack length, decreased to a minimum value when the tip of the propagating crack approached the cyclic elastic–plastic boundary before it increased to match the relatively long crack behaviour. Comparison with experimentally observed early FCG in the simulated tests showed an agreement.

Mode II stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates

Abstract The effect of crack surface friction on mode II stress intensity factor (SIF) of a central slant crack in a plate uniformly loaded in uniaxial compression is quantified. A previously developed two-dimensional finite element analysis was utilised after its modification to accommodate the friction between the crack surfaces. The plane strain state was assumed. A new numerical technique was devised to avoid the iteration procedures, which had to be employed due to the existence of frictional forces. The crack inclination angle varied between zero and 75° measured from the horizontal direction. The coefficient of friction of the crack surfaces changed from zero to 1. In case of relatively sliding crack surfaces, mode II SIF existed. As is well known, the resulting mode II SIF decreased with increasing the coefficient of friction of the crack surfaces. Further, mode II SIF increased with increasing crack line inclination angle and then decreased after reaching a maximum value. The angle corresponding to that maximum SIF increased as the coefficient of friction of the crack surfaces increased.

Mode I notch fatigue crack growth behaviour under constant amplitude loading and due to the application of a single tensile overload

Abstract Low carbon steel plates having different single edge U-shaped notches with different geometries were tested near their fatigue limits at different stress ratios and constant amplitude axial stresses. The present work demonstrates experimentally obtained early mode I fatigue crack growth rates from such notches. The experimental fatigue crack growth behaviour clearly showed a minimum rate when the propagating crack reached a length approximately equal to the extent of the notch cyclic plastic zone. Further experiments investigated the effect on the notch fatigue crack growth behaviour of a single tensile overload applied within constant amplitude base load cycles. The tested parameters included the notch geometry, the maximum applied stress and the stress ratio of the base load, the overload ratio and the location of the crack tip at which the overload was applied. In case of an overload cycle applied after having an initiated fatigue crack propagating from the root of a notch, the effects of both overload and stress ratios on the proceeding fatigue crack growth rates were similar to those commonly observed in un-notched plates. When the overload cycle was applied before fatigue testing, more resistance to fatigue crack initiation and propagation was observed. In tests with an overload cycle applied after having a short fatigue crack with its tip located outside the notch root cyclic plastic zone, two minimum rates were observed. One minimum rate was observed if the overload cycle was applied when the initiated crack tip was propagating inside the notch root cyclic plastic zone.

Simulation of mixed mode I/II cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces

Abstract The paper presents a model for near tip-displacements of a short kinked slant crack in a two-dimensional plate subjected to uniaxial cyclic loading. Possible regimes of sticking and sliding contact and separation along the two frictional surfaces of the main crack and the kink were identified. Both stationary and artificially advancing central cracks were analysed with an inhouse finite element package and compared in terms of plastically deformed zones and crack tip relative displacements. An artificial crack tip advance equivalent to one element was allowed along the direction of the assumed kink. Three stress ratios of 0.2, 0 and −1 were assumed. The main crack angle was 45° with a crack length to plate width ratio of 0.3 and the coefficient of friction varied from 0 to 1. The kink angle varied between 60 and −80° measured in a counter-clockwise direction from the main crack line. In the case of a negative stress ratio, extents of both monotonic and cyclic crack tip deformation decreased with increasing the coefficient of friction between the crack surfaces. For positive stress ratios, such an effect was not obvious. The extent of the cyclic crack tip opening displacement appeared as an appropriate candidate to predict the crack initiation angle in the case of mixed mode I/II loading. The present results did not support the use of a maximum effective stress range based on crack tip closure for such prediction. The maximum extent of the crack tip opening displacement corresponded to a kink angle which was nearly the same as that measure obtained from an elastic analysis. The extent of the crack tip sliding displacement at that kink angle was negligible.

Stress intensity factors of a shortly kinked slant central crack with frictional surfaces in uniaxially loaded plates

Abstract An elastic two-dimensional finite element analysis was used to evaluate the modes II and I stress intensity factors of a shortly kinked slant central crack with frictional surfaces in uniaxially loaded plates. Four main crack angles measured from the load direction, i.e. 45, 60, 75, and 85°, with crack length to plate width of 0.1, 0.3, and 0.5 were considered. The coefficients of friction of the crack surfaces were 0, 0.25, 0.5, 0.75 and 1. The kink angle was measured from the main crack line in a counterclockwise direction and varied in increments of 5° between 0 and –120° for the plates loaded in tension and between 0 and +120° for the compressed plates. The ratio of the kink length and the main crack length was 0.0065. The arrangement and the size of the elements around the crack tip were the same for all the meshes generated for the present work. The variation of the computed modes II and I stress intensity factors was dependent on the type of the remotely applied axial load and both main crack and kinking angles. For a fully opened crack, there was a negative kink angle at which mode I stress intensity factor attained a maximum value. That corresponded to approximately zero mode II stress intensity factor. The maximum value of mode I stress intensity factor increased as the main crack angle increased, i.e. the mode I stress intensity factor reached a maximum when the main crack was at 90° to the loading direction. In axially compressed plates, relatively sliding crack surfaces in contact showed opened crack tips only at positive kink angles, which were larger than an angle dependent on the main crack angle. The resulting mode II and mode I stress intensity factors decreased as the coefficient of friction increased. Further, the mode I stress intensity factor increased with the increasing positive kink angle and reached a maximum value before it decreased. On the other hand, the absolute value of the mode II stress intensity factor decreased with the increasing positive kink angle and had a zero value before it increased again. In both types of loading, the measure of the kink angle for the maximum mode I stress intensity factor was independent of the main crack length. The present results showed that the kink angles corresponding to maximum mode I stress intensity factors agreed well with predicted and experimentally observed initial crack growth directions found in the literature.

ELASTIC- PLASTIC ANALYSIS OF NOTCH ROOT STRESS-STRAIN AND DEFORMATION FIELDS UNDER CYCLIC LOADING

Two dimensional elastic-plastic finite element model was used to simulate the stress-strain and the deformation at the root of a notch under both monotonic and cyclic loading. The analysis was performed for the plane stress state and constant amplitude loading of zero stress ratio. Twenty one single edge notches having different depth and radius were studied at different maximum stresses. Relevant kinematic parameters corresponding to loading and unloading phases of a cycle were computed and correlated. Elastic-plastic analyses of the stress concentration factors at the notch root were invoked. The monotonic and cyclic notch root plastically deformed zones are presented

3-D finite element analysis of cyclic deformation at the front of a stationary crack

Publisher Summary This chapter analyzes the deformation behavior and the stress–strain field existing near the front of a stationary crack under cyclic loading to predict the site of fatigue crack initiation. 3D elastic–plastic finite element model is developed to simulate the deformation behavior of a stationary crack under cyclic loading. Relevant kinematic parameters corresponding to loading–unloading–reloading phases of a cycle were computed and correlated. The variation of stresses and strains through the plate thickness was analyzed. The monotonic and cyclic crack tip plastically deformed zones and opening displacements both at the surface and at the midsection of the plate were compared with 2D finite element analyses under plane stress and plane strain conditions. The plastic zone size from the 3D analysis for both the specimen surface and the specimen interior is bounded by its 2D plane stress and plane strain calculations.