Square Root Of Crack Length Research Articles

A simple fracture mechanics estimation of the fatigue endurance of welded joints

The use of fracture mechanics based methodologies to assess the influence of defects on welded components has become increasingly important for industrial applications and design, in the last decades. However, there are still objections against these approaches due to their complexity and the consequent need of qualified personnel with certain level of knowledge of fracture mechanics. Therefore, development of simplified methods to evaluate severity of defects can be valuable for practical purposes. In the present work, a manageable expression is proposed to calculate the applied stress intensity factor for crack growth, which is proportional to the square root of crack length and the stress concentration factor at the location of the crack in the un-cracked body. The latter was obtained with numerical simulation of transversely loaded butt, T and cruciform joints. By means of the resistance curve method that accounts for short crack behaviour, these results can be compared with threshold for crack propagation to estimate the fatigue resistance of welded joints. Besides, a simple expression was derived to estimate the fatigue endurance, which can be used to understand and analyse in a simplified manner the influence of the main geometrical and mechanical parameters, like weld geometry, residual stresses and size of defects, among others. Estimations were compared with experimental results from literature for different weld configurations, and they proved to be conservative. Methodology is valid for toe cracks in as-welded joints.

Propagation of surface initiated rolling contact fatigue cracks in bearing steel

Surface initiated rolling contact fatigue, leading to a surface failure known as pitting, is a life limiting failure mode in many modern machine elements, particularly rolling element bearings. Most research on rolling contact fatigue considers total life to pitting. Instead, this work studies the growth of rolling contact fatigue cracks before they develop into surface pits in an attempt to better understand crack propagation mechanisms. A triple-contact disc machine was used to perform pitting experiments on bearing steel samples under closely controlled contact conditions in mixed lubrication regime. Crack growth across the specimen surface was monitored and crack propagation rates extracted. The morphology of the generated cracks was observed by preparing sections of cracked specimens at the end of the test. It was found that crack initiation occurred very early in total life, which was attributed to high asperity stresses due to mixed lubrication regime. Total life to pitting was dominated by crack propagation. Results provide direct evidence of two distinct stages of crack growth in rolling contact fatigue: stage 1, within which cracks grow at a slow and relatively steady rate, consumed most of the total life; and stage 2, reached at a critical crack length, within which the propagation rate rapidly increases. Contact pressure and crack size were shown to be the main parameters controlling the propagation rate. Results show that crack propagation under rolling contact fatigue follows similar trends to those known to occur in classical fatigue. A log-log plot of measured crack growth rates against the product of maximum contact pressure and the square root of crack length, a parameter describing the applied stress intensity, produces a straight line for stage 2 propagation. This provides the first evidence that growth of hereby-identified stage 2 rolling contact fatigue cracks can be described by a Paris-type power law, where the rate of crack growth across the surface is proportional to the contact pressure raised to a power of approximately 7.5.

Indentation Fracture Studies of a BaTiO3 Thin Film on a Silicon Substrate

AbstractIt has been experimentally and theoretically found that the critical applied stress intensity factor for indentation cracking also depends linearly on the reciprocal of the square root of crack length when the indentation fracture technique is used to measure residual stresses in thin films.

On the Crack Length and the Low Temperature Brittleness of a Carbon Steel Subjected to Corrosion Fatigue

The lengths of the cracks formed by the corrosion fatigue in saline are studied on the smooth specimens or a carbon steel, and the effect or corrosion fatigue on the low temperature brittleness is discussed. The cracks occur at the early stage of the fatigue life and the cyclic rates of their propagation dl/dN depend on the true stress σck repeated at the root of the crack, where k represents the notch effect of corrosion pits increasing with time. The transition temperature Tr°C of the specimens having the cracks caused by corrosion fatigue and the rate or its change with cycle ΔTr/ΔN rise with increasins of cyclic ratio. It also rises according to the increase of square root of crack length l1/2, having no relation to the nominal stress σc of the corrosion fatigue.

On the Crack Length and the Low Temperature Brittleness of a Carbon Steel Subjected to Corrosion Fatigue

The lengths of the cracks formed by the corrosion fatigue in saline are studied on the smooth specimens of a carbon steel, and the effect of corrosion fatigue on the low temperature brittleness is discussed. The cracks occur at early stage of the fatigue life and the cyclic rates of their propagation dl/dN depend on the actual stress σck repeated at the root of the crack, where k represents the notch effect of corrosion pits increasing with time. The transition temperature Tr °C. of the specimens having the cracks caused by corrosion fatigue and the rate of its change with cycle ΔTr/ΔN rise with increasing of cyclic ratio. It also rises according to the increase of square root of crack length l1/2, having no relation to the nominal stress σc of the corrosion fatigue.

Relationship of Surface Structure of Glass to Residual Laminar Stresses

The force necessary to detach a glass test block from a sample of tempered glass to which it is glued is shown to be linearly related to the stress in the tempered glass. Fine microscopic glue lines left on the tempered glass after detachment of the test block are suggested as Griffith cracks by comparison of the glue lines with the pattern made visible by treatment of tempered samples with sodium vapor. A linear relationship between the square root of the total crack length on a sample and the stress in the glass is demonstrated. The linear relationship between the square root of the crack length and stress is derived theoretically.