Showing papers on "Paris' law published in 2011"

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Abstract: This paper extends the theoretical framework presented in the preceding Part I to the lifetime distribution of quasibrittle structures failing at the fracture of one representative volume element under constant amplitude fatigue. The probability distribution of the critical stress amplitude is derived for a given number of cycles and a given minimum-to-maximum stress ratio. The physical mechanism underlying the Paris law for fatigue crack growth is explained under certain plausible assumptions about the damage accumulation in the cyclic fracture process zone at the tip of subcritical crack. This law is then used to relate the probability distribution of critical stress amplitude to the probability distribution of fatigue lifetime. The theory naturally yields a power-law relation for the stress-life curve (S-N curve), which agrees with Basquin's law. Furthermore, the theory indicates that, for quasibrittle structures, the S-N curve must be size dependent. Finally, physical explanation is provided to the experimentally observed systematic deviations of lifetime histograms of various ceramics and bones from the Weibull distribution, and their close fits by the present theory are demonstrated.

Effect of laser shock processing on fatigue crack growth of duplex stainless steel

Abstract: Duplex stainless steels have wide application in different fields like the ship, petrochemical and chemical industries that is due to their high strength and excellent toughness properties as well as their high corrosion resistance. In this work an investigation is performed to evaluate the effect of laser shock processing on some mechanical properties of 2205 duplex stainless steel. Laser shock processing (LSP) or laser shock peening is a new technique for strengthening metals. This process induces a compressive residual stress field which increases fatigue crack initiation life and reduces fatigue crack growth rate. A convergent lens is used to deliver 2.5 J, 8 ns laser pulses by a Q-switched Nd:YAG laser, operating at 10 Hz with infrared (1064 nm) radiation. The pulses are focused to a diameter of 1.5 mm. Effect of pulse density in the residual stress field is evaluated. Residual stress distribution as a function of depth is determined by the contour method. It is observed that the higher the pulse density the greater the compressive residual stress. Pulse densities of 900, 1600 and 2500 pul/cm2 are used. Pre-cracked compact tension specimens were subjected to LSP process and then tested under cyclic loading with R = 0.1. Fatigue crack growth rate is determined and the effect of LSP process parameters is evaluated. In addition fracture toughness is determined in specimens with and without LSP treatment. It is observed that LSP reduces fatigue crack growth and increases fracture toughness if this steel.

Characterisation of foreign object damage (FOD) and early fatigue crack growth in laser shock peened Ti–6Al–4V aerofoil specimens

Abstract: Foreign object damage (FOD) has been identified as one of the primary life limiting factors for fan and compressor blades, with the leading edge of aerofoils particularly susceptible to such damage. In this study, a generic aerofoil specimen of Ti–6Al–4V alloy was used. The specimens were treated by laser shock peening (LSP) to generate compressive residual stresses in the leading edge region prior to impact. FOD was simulated by firing a cubical projectile at the leading edge using a laboratory gas gun at 200 m/s, head-on; and at 250 m/s, at an angle of 45°. The specimens were then subjected to 4-point bend fatigue testing under high cycle (HCF), low cycle (LCF) and combined LCF and HCF loading conditions. Scanning electron microscopy (SEM) was used to characterise the damage features due to FOD. Crack initiation and early crack growth due to FOD and subsequent fatigue growth were examined in detail. The results were compared between the two impact conditions; and with those from samples without LSP treatment as well as those impacted with spherical projectiles. The results seem to suggest that LSP has improved the crack growth resistance post FOD. Delayed onset of crack initiation was observed in LSPed samples compared to those without LSP under similar loading conditions. Damage features depend on the geometry of the projectile, the impact angle as well as the impact velocity.

Cyclic loadings and crystallization of natural rubber: An explanation of fatigue crack propagation reinforcement under a positive loading ratio

Abstract: Natural rubber is known to have excellent fatigue properties. Fatigue crack propagation studies show that, under uniaxial tension loading, fatigue crack growth resistance increases with the loading ratio, even if the peak stress increases. Studies dealing with crack initiation confirm this trend. If strain induced crystallization is believed to play a major role in this reinforcement process, it is not clear yet by which mechanism this reinforcement takes place. Using SEM investigation, it is shown here that the reinforcement process is associated with strong crack branching in the crack tip region. From experimental results it is shown that under particular reinforcing loading condition a cyclic strain hardening process can be observed on the natural rubber which is able to overcome classically observed softening effects. A cumulative strain induced crystallization process is proposed to explain the stress ratio effect on fatigue crack initiation and propagation properties of natural rubber.

Influence of hydrogen and frequency on fatigue crack growth behavior of Cr-Mo steel

Abstract: Fatigue tests on Cr-Mo steel quenched at 860°C and tempered at 580°C were carried out under the frequencies of 0.2, 2, and 20 Hz with specimens containing a small artificial hole. An additional test in which the test frequency was alternately switched between 0.02 and 2 Hz was carried out. Hydrogen charging to the specimens was carried out by an immersion method. The fatigue life of the hydrogen-charged specimens remarkably decreased in comparison with that of the uncharged specimens. The fatigue crack growth rate da/dN increased with decreasing the test frequency f. The acceleration of da/dN saturated at $${\Delta K\,<\,17\,{\rm MPa}\sqrt{m}}$$ for f ≤ 2 Hz. The presence of the upper bound for the fatigue crack growth acceleration was found with respect to the effects of hydrogen and test frequency in a hydrogen environment. The test switching the frequency between 0.02 and 2 Hz resulted the difference in fatigue crack growth morphology which is presumed to be caused by the difference in hydrogen concentration in the vicinity of crack tip. The particular crack morphology under the low test frequency with hydrogen was the localization of the slip around the crack tip and the linearization of the crack growth path. The hydrogen-enhanced striation formation model which was proposed to explain the effect of hydrogen on the fatigue crack growth for an austenitic stainless steel and low carbon steel can be applied also to the quenched and tempered Cr-Mo steel in this study.

STRESS ANALYSIS and FATIGUE of welded structures

Abstract: Fatigue analyses of weldments require detailed knowledge of the stress fields in critical regions. The stress information is subsequently used for finding high local stresses where fatigue cracks may initiate and for calculating stress intensity factors and fatigue crack growth. The method proposed enables the determination of the stress concentration and the stress distribution in the weld toe region using a special shell finite element modelling technique. The procedure consists of a set of rules concerning the development of the finite element mesh necessary to capture the bending and membrane structural stresses. The structural stress data obtained from the shell finite element analysis and relevant stress concentration factors are subsequently used to determine the peak stress and the non-linear through-thickness stress distributions. The peak stress at the weld toe is subsequently used for the determination of fatigue crack initiation life. The stress distribution and the weight function method are used for the determination of stress intensity factors and for the analysis of subsequent fatigue crack growth.

On the Correlation Between Fatigue Striation Spacing and Crack Growth Rate: A Three-Dimensional (3-D) X-ray Synchrotron Tomography Study

Abstract: In situ three-dimensional (3-D) X-ray synchrotron tomography of fatigue crack growth was conducted in a 7075-T6 aluminum alloy. Local measurements of da/dN were possible with the 3-D data sets obtained from tomography. A comparison with fatigue striation spacings obtained from scanning electron microscopy of the fracture surfaces yielded excellent correlation with da/dN obtained from tomography. The X-ray tomography technique can be used to obtain a highly accurate and representative measurements of crack growth locally in the microstructure of the material.

Mode I delamination growth of multidirectional composite laminates under fatigue loading

Abstract: Fatigue delamination growth of multidirectional carbon/bismaleimide composites was investigated to disclose the specific role of ply orientations. Both fatigue crack growth rate and threshold values of strain energy release rate in Mode I were studied by double cantilever beam test. For specimens with rising delamination resistance effect, the fatigue crack growth rate was found to be dependent on normalized interlaminar energy, GI/GIC, rather than GI. The experimental data also show that the fatigue threshold Gth is almost proportional to the corresponding GIC, that is Gth /GIC is constant and hardly affected by the midplane-adjacent fiber orientation. Furthermore, fractographs revealed that the rising delamination resistance is dominantly aroused by fiber bridging and intra-ply fracture.

Grain boundary microstructure and fatigue crack growth in Allvac 718Plus superalloy

Abstract: The correlation between grain boundary microstructure and fatigue crack growth with hold-times was investigated for two conditions of the superalloy Allvac 718Plus; a Standard condition with the recommended distribution of grain boundary phases and a Clean condition with virtually no grain boundary phases. Fatigue testing was performed at 704 degrees C using 10 Hz cyclic load with intermittent hold-times of 100 s at maximum tensile load. Microstructural characterization and fractography were conducted using scanning- and transmission electron microscopy techniques. Auger electron- and X-ray photoelectron spectroscopy techniques were used for oxide analyses on fracture surfaces. It was found that in the Standard condition crack growth is mostly transgranular for 10 Hz loading and intergranular for hold-times, while for the Clean condition crack growth is intergranular in both load modes. The lower hold-time crack growth rates in the Standard condition are attributed to grain boundary delta-phase precipitates. No effect of delta-phase was observed for 10 Hz cyclic loading crack growth rates. Two different types of oxides and oxide colours were found on the fracture surfaces in the Standard condition and could be correlated to the different loading modes. For cyclic loading a bright thin Cr-enriched oxide was dominate and for hold-times a dark and slightly thicker Nb-enriched oxide was dominant These oxide types could be related to the oxidation of delta-phase and the matrix respectively. The influence of delta-phase precipitates on crack propagation is discussed.

Effect of Duplex Aging on the Initiation and Propagation of Fatigue Cracks in the Solute-rich Metastable β Titanium Alloy Ti 38-644

Abstract: Aging of highly β-stabilized titanium alloys commonly leads to the formation of precipitate-free zones being susceptible to fatigue crack initiation. Duplex aging improves the fatigue properties of metastable β titanium alloys by enhancing a homogeneous α phase formation. In this study a duplex-aging cycle was designed for Ti 38-644 (β-C). Depending on the prior processing history heat treatment parameters were adapted on the basis of microstructure studies, hardness measurements and comparative tensile tests. The fatigue limit and fatigue crack growth threshold were determined for duplex-aged β-C. The results indicate that duplex aging promotes a homogeneously precipitated α phase providing excellent values of the fatigue limit. Surface-related fatigue crack initiation was observed. Comparing the fracture surfaces of direct- and duplex-aged β-C a transition of the tensile fracture mode from intergranular to predominantly transgranular was observed accompanied by a gain in ductility at comparable yield strengths. This was assumed to be the reason for the slightly improved fatigue crack growth behavior of duplex-aged as compared to direct-aged β-C. Along the entire heat treatment cycle the microstructure response was evaluated with regard to the particular effects on the fatigue properties. The results indicate clearly that key to success is a completely recrystallized β microstructure and the reasonably controlled aging response.

Fatigue crack growth behavior of the simulated HAZ of 800 MPa grade high-performance steel

Abstract: The present study focuses on the fatigue properties in the weld heat-affected zone (HAZ) of 800 MPa grade high-performance steel, which is commonly used in bridges and buildings. Single- and multi-pass HAZs were simulated by the Gleeble system. Fatigue properties were estimated using a crack propagation test under a 0.3 stress ratio and 0.1 load frequencies. The microstructures and fracture surfaces were analyzed by optical microscopy, scanning electron microscopy, and transmission electron microscopy. The results of the crack propagation test showed that the fatigue crack growth rate of coarse-grained HAZ (CGHAZ) was faster than fine-grained HAZ (FGHAZ), although both regions have identical fully martensite microstructures, because FGHAZ has smaller prior austenite grain and martensite packet sizes, which can act as effective barriers to crack propagation. The fatigue crack growth rate of intercritically reheated CGHAZ (ICCGHAZ) was the fastest among local zones in the HAZ, due to rapid crack initiation and propagation via the massive martensite–austenite (M–A) constituent.