Plasticity spread in mild steel pre-cracked charpy bars

During dynamic service loading, small fatigue cracks are normally seen to emanate from the root of sharp machined stress concentration region. In a recent authors' paper at ICF4, the fracture strength of a charpy type notched beam has been studied in three different engineering materials, when a small fatigue crack emanates from the notch root. Fracture tests on these medium and high strength materials demonstrate the presence of a large size plastic zone near the crack tip [1–6]. To understand the mechanism of fracture for such complex geometry. it is important to know the size and shape of these plastically yielded regions. The present paper is mainly on the experimental measurement of plasticity spread as well as the stress intensity factor (S.I.F.) for such short cracks. Firstly, the S.I.F. is approximately measured by plain transmission photoelasticity on model castolite specimens. Secondly, plastic zones around crack tip are measured for a wide range of notch root radii and crack-length, by using photo-stress PS-3B coating on mild steel pre-cracked charpy type notched specimens. It is observed that for small scale yielding at the crack tip, the plasticity spread is around 60–65° angle to the line of crack-extension. On the contrary, as the gross applied stress approaches the yield strength of the material, the maximum plasticity spreads around 45° angle. Finally, it is noticed that at high stress level, the plastic zone boundary (for short crack) touches the free machined notch surface. These experimental observations explain the nature and degree of non-linearity in a load—C.O.D. diagram during the fracture test of a short cracked-notched specimen. These data are also useful to predict the crack-extension load for an elastic-plastic material.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

Fracture of notched polycarbonate under hydrostatic pressure

The brittle fracture behaviour and plastic deformation of round-notched polycarbonate bars subjected to three-point bending under hydrostatic pressure have been studied. Below a certain critical pressure, the brittle fracture initiated from an internal craze nucleated at the tip of the local plastic zone ahead of the notch rooT. The position of the nucleation of the craze receded from the tip of the notch with increasing applied pressure. When the pressure was increased over a critical value, general yielding occurred by passage of the plastic zone across the notched cross-section, that is, the brittle to ductile transition took place. A qualitative analysis of the stress distribution within the plastic zone explains that the brittle to ductile transition under hydrostatic pressure occurs when the general yield takes place before a critical stress for brittle crack propagation is reached.     

Evaluation and modeling of hydrogen-induced fracture in structural steels

From the macroscopic point of view, the results of hydrogen embrittlement of pearlitic steel strongly depend on compressive residual stresses generated in the vicinity of the crack tip by fatigue precracking of the specimens (the relevant variable is the maximum stress intensity factor during the last stage of fatigue precracking. As far as the kinetic crack growth curve is concerned, the threshold stress intensity value for hydrogen-assisted cracking does not have an intrinsic character but depends on the distribution of compressive residual stresses in the vicinity of the crack tip and, therefore, on the maximum stress intensity factor during the last stage of fatigue precracking. The fractographic analysis of hydrogen embrittlement tests on precracked and notched specimens of high-strength pearlitic steel reveals the existence of a special microscopic mode of fracture associated with hydrogen-induced microdamage: the so-called tearing topography surface or TTS, which can be regarded as the process zone. Hydrostatic stress is the macroscopic variable governing the extension of the TTS zone. It is demonstrated that the distribution of hydrostatic stresses in notched specimens is practically independent of the loading process and the point of maximum hydrostatic stress is a characteristic of the geometry of the problem and never changes its position. The depth of the TTS zone is a function of the electrochemical potential, the maximum fatigue precracking load, and the duration of the test, which reveals its correlation with the process of hydrogen embrittlement. These phenomenological relations can be explained by using a model of stress-assisted diffusion of hydrogen. The role of diffusion as the main mechanism of hydrogen transport in pearlitic steel is demonstrated by comparing the hydrogen-affected region and the plastic zone, which reveals no relationship between them. Hydrostatic stresses play an important role in accelerating the diffusion of hydrogen. The hydrogen-induced fracture of notched specimens of pearlitic steel is a time-dependent phenomenon admitting the kinematic modeling of the process as a function of the strain rate. In this conceptual framework, the local strain rate in the vicinity of the notch tip is the relevant variable controlling the process. For cold-drawn prestressed steel wires, the chemical modeling of the diffusion of hydrogen emphasizes the role of residual stresses generated in smooth wires in the process of manufacturing as well as the role of stresses induced by fatigue loads in precracked wires. In this case, their magnitude depends on the load (maximum stress intensity factor). In notched specimens of austenitic stainless steel, hydrogen damage can be described as multicracking in the area surrounding the notch and failure is induced by plastic instability. In this case, the action of hydrogen can be mechanically simulated as a geometric enlargement of the notch in the form of extended microdamage.     

Effect of martensite transformation on fracture behavior of shape memory alloy NiTi in a notched specimen

In this paper, the finite element calculation of the stress–strain distribution in front of a notch tip were carried out for two materials. One is a shape memory alloy NiTi with the stress-induced martensite transformation, and another is a fully transformed martensite NiTi without the transformation. Based on the results obtained, and combining a model of the fracture process zone, effect of martensite transformation on the fracture behavior of the shape memory alloy NiTi in a notched specimen of plane stress state is comparably analyzed. The results show that the martensite transformation increases the load to produce plastic deformation in the transformed martensite at the notch tip and decreases the maximum normal stress and plastic strain near the notch tip, and tends to suspend the crack nucleation and propagation in the fully transformed martensite in front of the notch tip, and thus increases the fracture load and improves the toughness. A quantitative analysis based on the model of the fracture process zone shows that the martensite transformation in the SMA NiTi causes about 47% increase in the apparent fracture toughness.     

Fatigue life prediction of small notched Ti-6Al-4V specimens using critical distance

This study investigated the method of estimating the fatigue strength of small notched Ti-6Al-4V specimen using the theory of critical distance that employs the stress distribution in the vicinity of the notch root. Circumferential-notched round-bar fatigue tests were conducted to quantify the effects of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius increases the fatigue strength and the greater notch depth decreases the fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the critical distance from notch root. The region from the notch root to the critical distance corresponds to the fatigue fracture process zone for crack initiation. It has been found that a good correlation exists between the critical distance stress and crack initiation life of small notched specimens if the critical distance is calibrated by the two notched fatigue failure curves of different notch root radii. The calibrated critical distances did not vary clearly over a wide range of fatigue failure cycles from medium-cycle low-cycle fatigue regime to high-cycle fatigue regime and have an almost constant value. This critical distance corresponds to the size of crystallographic facet at the fatigue crack initiation site for the wide range of fatigue cycles.     

A methodology for predicting creep/fatigue crack growth rates in Ti 6246

A methodology has been developed which is capable of predicting creep/fatigue crack growth rates at ambient and elevated temperatures in Ti 6246. Predictions are based on finite element analysis and strain-control testing of plain specimens. The prediction of fatigue crack growth rates for a given crack configuration and cyclic plastic zone size is assumed to be consistent with the processes leading to crack initiation in plain specimens. Such an assumption leads to the conclusion that a similar stress–strain profile will lead to similar lives in both the plain specimens and in the cyclic plastic zone ahead of a crack in a notched specimen. Therefore, fatigue crack growth results from the accumulation of damage in the cyclic plastic zone ahead of the crack tip. Once the damage accumulated in this element of material becomes critical, the crack propagates through the damaged region into a new region of virgin material where the process of damage accumulation begins again. The creep/fatigue model is described and assessed with reference to measured fatigue crack growth rate data for Ti 6246 at 20 °C and 500 °C.     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

The kinetics of hydrogen embrittlement: A quantitative diffusion model

Stress assisted diffusion of hydrogen towards the tip of a notch or crack is described by adding a stress-dependent term to Fick's first and second law of diffusion. It is postulated that a critical combination of hydrogen concentration and stress will develop at the edge of the plastic enclave, and that this will produce an incremental crack growing from the edge of the plastic zone towards the notch or crack tip. Crack propagation is treated as a succession of incremental crack bursts. Equations are developed from which the primary and secondary incubation times can be calculated. Approximate solutions are presented for the case of a crack in an infinitely wide flat plate.     

Behavior of a tip of non-propagating fatigue crack during one stress cycle

Measurements and observations were made on the crack closure for the so-called non-propagating crack of notched specimens and for the non-propagating microcrack of unnotched specimens, which were formed in a rotating bending test of annealed carbon steel. Under the condition which produces the non-propagating crack, the ratio of stress range where the crack tip is open, to the full range of the cyclic stress tends gradually to zero with the increase in length of the crack initiated from a notch root.The tip of a non-propagating microcrack on the surface of a plain specimen is also recognized to be closed under the maximum stress level after 10⁷ cycles of the repetitions of the stress slightly below the fatigue limit.From these facts, it can be said that the tip of a so-called non-propagating crack or a non-propagating microcrack is hardly damaged by the repetition of stress which has produced each crack.     

Size effect in fracture of unidirectional composite plates

Fracture of notched, unidirectionally reinforced composite plates with well-bonded ductile matrices is typically preceded by the formation of long, discrete plastic shear zones aligned in the fiber direction. Onset of fracture is associated with a critical tension stress in a certain small process zone ahead of the notch tip; the critical stress is often equal to the tensile strength of the unnotched composite plate. Length of the shear zones can be estimated by plastic limit-analysis, and the local tension stress ahead of the notch found by superposition of the stress caused by remotely applied loads with the stress induced by the shear tractions in the plastic zone, which is shown to be dominated by a logarithmic singularity. In as-fabricated boron-aluminum composites, this fracture mechanism was analyzed and confirmed by numerous experiments (G.J. Dvorak, J. Zarzour and Y. Benveniste, Engineering Fracture Mechanics 42, 501–517, 1992). Since the notch tip field is not described by a stress intensity factor, experimental notched strength data cannot be interpreted in terms of a single material property, such as toughness. An alternative scaling procedure is outlined for prediction of notched strength of wide plates on the basis of data obtained from small size specimens. This revised version was published online in July 2006 with corrections to the Cover Date.     

FATIGUE LIMIT OF BLUNT-NOTCHED COMPONENTS

The position and effective resistance of microstructural barriers and their relation to the fatigue strength of blunt-notched specimens are analysed and modelled for three low-carbon steel microstructures. A relationship for the notch size effect on the basis of the experimental evidence that the fatigue limit (both plain and notched) represents the threshold stress for the propagation of the nucleated microstructurally short cracks, was derived. The derived relationship characterizes the fatigue notch sensitivity by means of the parameter k_td defined as the stress concentration introduced by the notch at a distance d from the notch root surface equal to the distance between microstructural barriers, and was experimentally verified for two notch geometries in three microstructures: ferrite, ferrite–bainite and bainite–martensite.     

Local fracture criterion to describe failure assessment diagrams for a body with a crack/notch

The cohesive zone model and the criterion of average stress in the cohesive zone ahead of the crack/notch tip are used to describe failure assessment diagrams for cracked and notched bodies. The type of loading as well as the elastic stress concentration factor can significantly change the character of the failure assessment diagram.     

A criterion for low-stress brittle fracture of notched specimens based on combined micro- and macro fracture mechanics—1

Based on the combined micro- and macro fracture mechanics, the two requisites necessary for the crack propagation, that is, the energy unstable requisite and the critical local stress requisite, are derived for the low-stress brittle fracture of notched specimens. Thus the fracture criterion was obtained. The criterion is compared with the experimental data, such as on the relationships between the fracture stress or the fracture toughness and the grain size diameter, the crack length, the notch tip radius or the yield stress. The good agreement is obtained.     

Change of fracture mode in Charpy toughness transition temperature range

Abstract

A transition layer of width 5 - 10 μm was found on the boundary between ductile and brittle fracture for Charpy V notch specimens in the transition temperature range of a structural steel having a microstructure of polygonal ferrite -pearlite. The fracture mode in the transition layer was shearing with occasional submicrometre dimples. From tensile tests on notched specimens, the cleavage fracture stress and flow stress by ductile decohesion were determined. Based on the experimental data and the assumption that the volume of metal involved in the plastic deformation during fracture was related to the volume of the dimples, it was deduced that the transition layer width represents the size of the plastic zone immediately before cleavage initiation. The crack opening displacement and the crack tip radius for the change of fracture mode were calculated.     

In situ observation of cyclic fatigue crack propagation of SiC-fiber/SiC composite at room temperature

In situ observation of cyclic fatigue crack propagation of SiC-fiber reinforced SiC composite at room temperature has been carried out by laser microscopy. Both smooth (unnotched) and notched specimens are used for tension-tension cyclic fatigue tests. Cracks initiate at the comers of large pores during loading in smooth specimens. In notched specimens cracks are formed at the interfaces between fibers and matrix that are connected to the notch. The balance between the fiber bridging in the wake of propagating crack tip and the breakage of bridged fibers by the degradation of interfaces maintains a steady cyclic crack propagation. Crack propagation rate gradually decreases with time after the maximum load being applied.     

Fatigue strength of rolled JIS SM50A beams

The fatigue strength of rolled beams with stiffeners welded to the web was examined. The state of residual stress in these beams was varied by different cooling and straightening processes. Parallel series of tests were carried out both on plate specimens with corner-notches, simulating the edge notches in the beam-flange tip, and on fillet welded specimens. These test results were analysed using the fracture mechanics concepts of stable crack growth. A new fracture mechanics model for cracks originating from notches is proposed. This is based on the concept that the cyclic plastic zone size at the root of a notch determines the equivalent size of the notch as a fatigue crack. With this model, the severity of notches as well as their size can be taken into account to describe the initial flaw conditions. With the initial crack size estimated, a theoretical crack-growth equation was derived from the fatigue test data of rolled beams and notched plates. The analysing method together with the derived relationship was applied for the evaluation of the fatigue strength of welded beams and transverse fillet welds. The effect of residual stresses on fatigue behavior of these beams and plate specimens was also estimated by assuming an additional effect of the maximum stress on the theoretical crack-growth equation.     

Fatigue notch sensitivity of steel blunt-notched specimens

The notch sensitivity of three steels with similar plain fatigue limits was analysed and modelled. The analysis was made by using a model previously derived which estimated the fatigue limit of blunt notched components by means of the parameter k_td defined as the stress concentration introduced by the notch at a distance d from the notch root surface equal to the distance between microstructural barriers. The analyses show how the first two or three microstructural barriers define the fatigue limit and the fatigue notch sensitivity of blunt notched specimens.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.