Study of influence of notch root radius on fracture behaviour of extra deep drawn steel sheets

Fracture tests are carried out on extra deep drawn steel CT specimens containing notches with different values of notch root radius (ρ= 0.07–0.75 mm). Experimental findings clearly show a critical notch root radius (ρ_c) below which the fracture toughness remains independent of ρ and above which it varies linearly with ρ. The 3D finite element analysis shows that the location of maximum stress level causing crack initiation is in the vicinity of notch tip. The maximum stress level is independent of ρ; however, its location is shifted away from notch tip along unbroken ligament length with increase in ρ.     

DYNAMIC FATIGUE AND COMPUTER SIMULATION OF THE BEHAVIOUR OF Y2O3-ZrO2 CERAMICS

Abstract— There is a critical stress rate K _c for each of the three ZrO₂ ceramics tested. Fracture is controlled by the materials polycrystal fracture toughness, K ^c_p, if the stress rate is less than K _c. Otherwise, fracture is controlled by the single crystal fracture toughness, K ^c_s. The crack growth parameters determined by dynamic fatigue experiments can only represent macrocrack growth behaviour although the fracture of specimens in experiments originates from small surface flaws.     

THE SIZE OF PLASTIC ZONES AND FATIGUE CRACK GROWTH BEHAVIOUR OF THREE FORMS OF A Ti–6Al–2.5Mo–1.5Cr ALLOY

The effect of microstructure on the fatigue properties of Ti–6Al–2.5Mo–1.5Cr alloy was investigated. The experimental results for both the fatigue crack initiation and propagation behaviour, as well as the dynamic fracture toughness ( K _Id ) showed clearly that a lamellar microstructure is superior to two other structures. It was found that, as in the case of steels, the initiation and subsequent growth of cracks in the titanium specimens with a sharp notch may also occur on loading levels below the threshold values of the K factor (Δ K _th ) determined for long fatigue cracks. In addition, measurements by interferential-contrast of the plastic zone size on the surface of specimens revealed that the different rate of crack growth at identical values of Δ K in individual structural states can roughly be correlated with the size of the plastic zone. A general relationship between the fatigue crack growth rate and plastic zone size, the modulus of elasticity and the role of crack tip shielding is discussed.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.     

EFFECTS OF CRACK LENGTH, NOTCH ROOT RADIUS AND GRAIN SIZE ON FRACTURE TOUGHNESS OF FINE CERAMICS

Generally, fracture toughness and fracture stress of ceramics depend on crack length, notch root radius and grain size. These three parameters are most important when assessing the integrity of structural ceramic members and developing high-performance ceramics. A new failure criterion called the process zone size failure criterion, has been proposed based on the existence of a crack-tip process zone. Using this criterion, it is shown that theoretical values are in good agreement with many test results quoted from many papers. It is concluded that this failure criterion is useful when evaluating crack length and notch root radius problems. The effect of grain size on both the fracture toughness and on the toughening mechanism is also considered.     

ELASTIC-PLASTIC FRACTURE MECHANICS FOR INITIATION AND PROPAGATION OF NOTCH FATIGUE CRACKS

Abstract Initiation and propagation are considered to be controlled by the extent of total plastic shear deformation φ. Crack initiation and crack propagation occur when φ, exceeds a critical threshold value which can be equated to threshold conditions determined from linear elastic fracture mechanics analyses. When a crack is in a plastically deformed zone φ_t=φ _p +φ _e . where φ _p is the component of φ _t due to notch bulk plasticity and φ _e , is the component of φ _t due to a linear elastic fracture mechanics (LEFM) analysis of the crack tip plasticity field.
When cracks initiate at notch roots φ _t > φ_th. As the crack propagates in the notch plastic zone the rate of decrease of v _p will be different from the rate of increase of φ _e and it is possible for φ _t to decrease to a level below φ_th thereby creating a non-propagating crack.     

PROBABILISTIC ASPECTS OF CLEAVAGE CRACK INITIATION SITES AND FRACTURE TOUGHNESS

Abstract— Fracture toughness tests were performed in the ductile-brittle transition temperature range using 110 specimens of the three-point bend and CT types. Probabilistic characteristics of fracture toughness and cleavage crack initiation sites were analysed in detail, together with the fibrous crack shape, from which the plane strain region in the specimen was deduced. The criterion for obtaining plane strain at the mid plane of the specimen was established as: B ≤ 0.004{ K _c( J )/σ _y }²+ 0.01. The thickness effect of cleavage fracture toughness for the specimen satisfying this equation is mainly caused by the statistical distribution of the weakest points ahead of the crack front (the Weibull volume effect).     

A MODEL OF FATIGUE CRACK GROWTH AFTER AN OVERLOAD IN D16T Al-ALLOY SUBJECTED TO BIAXIAL CYCLIC LOADS AT VARIOUS R-RATIOS

Abstract— Fatigue crack growth after a biaxial overload has been investigated. The crack retardation parameters, N _D, and, a _D, do not have monotonous dependencies on the biaxial stress ratio, λ, because the shear stress, τ_III, acting in the perpendicular direction of the specimen face, influenced the values of these parameters.
It has been found that the plastic zone size parameters, r _ab, and Δ, do not increase monotonously with increasing λ ratio. The plastic zone size in the crack growth direction, r _ho= a _D13, was calculated on the basis of newly proposed relations.
Crack growth after an overload was simulated on the basis of the equivalent mode I stress intensity factor, IC_C, invoking a unified kinetic diagram and calculated crack increments, a _D13 and a _D=Δ_c, where Δ_c is the maximum value of the calculated size of plastic zone. The experimental data for crack growth after an overload had good agreement with the calculated data.     

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.     

ESTIMATING INITIATION TIMES OF SECONDARY FATIGUE CRACKS IN DAMAGE TOLERANCE ANALYSIS

Abstract— Fatigue cracking of complex structure often involves several interacting cracks developing in a sequence of crack growth, arrest and reinitiation. A "combined" method of damage tolerance analysis is presented which employs fracture mechanics concepts to calculate crack growth and fatigue data from notched coupons with the appropriate notch radius for the crack initiation phase. The notched coupon data, plotted as peak elastic notch stress vs cycles to crack initiation, are shown to be applicable even when limited yielding occurs at the notch root. For several practical reasons it is recommended to select the initial crack size, a _i, for the crack growth phase to be as large as possible, but in accord with two selection criteria. First, a _i, must be within a notch-root region wherein the elastic stress distributions near a variety of notches are virtually identical. Secondly, a _i must be small enough not to significantly influence the stress distributions for other cracks. The Combined Method is illustrated by means of an example involving fatigue crack growth along a widthwise row of holes in 305 mm wide test panels.     

Effects of notch geometry on the local cleavage fracture stress σf

An elastic–plastic finite element method (FEM) is used to analyse the stress and strain distributions ahead of notches with various depths and flank angles in four-point bending (4PB) specimens of a C–Mn steel. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ _f is measured. By increasing the notch depth and notch flank angle from 2.25 to 8.25 mm and 10 to 90°, respectively, the distributions of high stress and strain at the moment of fracture show considerable variations. However, the value of σ _f stays relatively constant. The critical fracture event is thus shown to be identical, i.e. the propagation of a ferrite grain-sized crack into the neighbouring matrix. It is concluded that σ _f is mainly determined by the length of the critical microcrack, while the notch geometry and its associated stress volume have little effect on the value of σ _f . The cleavage site ahead of a notch is determined by the stress distributions and the positions of the weakest grains.     

THE RELATION BETWEEN STRESS INTENSITY FACTOR AND ENERGY RELEASE RATE IN THE PRESENCE OF R-CURVE BEHAVIOUR

Abstract— Failure of ceramic materials occurs when the stress intensity factor of the most serious crack in a component reaches a critical value K_I,_C, the fracture toughness of the material. In case of ideal brittle materials the fracture toughness is independent of the crack extension and, consequently, identical with the stress intensity factor K_I,_Onecessary for the onset of stable crack growth. It is a well-known fact that failure of several ceramics is influenced by an increasing crack-growth resistance curve. The effect of increasing crack resistance has consequences on many properties of ceramic materials. In this report the authors discuss some aspects of R -curve behaviour as represented by stress intensity factors or energies.     

Notch fracture toughness of high-strength Al alloys

In this study, the notch fracture toughness (NFT) of high-strength Al alloys was examined by a non-standardized procedure. The NFT is defined as the critical notch stress-intensity factor (NSIF) K_ρ,c, which is determined by using several methods of analysis and computing. A set of specimens with different notch root radii made from overaged 7xxx alloy forging was selected. The influence of the notch radius on the fracture toughness of the material was considered. It was found that the notch radius strongly affects the fracture behavior of forged 7xxx alloy in overaged condition. The notch fracture toughness was higher than the fracture toughness of a cracked specimen and increased linearly with notch radius. The critical notch radius was related to the spacing of intermetallic (IM) particles which promote an intergranular or transgranular fracture mechanism according to their size. It appeared that ductile transgranular fracture generated by the formation of dimples around dispersoids and matrix precipitates was predominant which indicates that intense strains are limited to a much smaller zone than the coarse IM particles spacing. This double mechanism is also operate for crack propagation of ductile fatigue. The nature and morphology of IM particles exert significant effects on the rate of fatigue crack growth and fracture toughness properties.     

CYCLIC LOADING AND FRACTURE TOUGHNESS OF STEELS

Abstract— The paper considers the effect of cyclic loading and loading rate upon fracture toughness characteristics of steels at room and low temperatures. It is shown that fracture toughness of a low-alloy ferrite-pearlite steel with 0·1% C (steel 1) and for 15G2AFDps steel of the same class (steel 2) are 2 to 2·5 times lower under cyclic loading (50 and 0·5 Hz) and dynamic loading (= 1·5 × 10⁶MPa √m s⁻¹) than under static loading (= 0·6 to 9 MPa √m s⁻¹). For quenched and low-tempered 45 steel at 293 K and for armco-iron at 77 K fracture toughness characteristics do not depend on the loading condition. Macro- and micro-fractographic investigations revealed a correlation between the plastic zone size and the length of brittle fracture areas which are formed in steels 1 and 2, and in armco-iron during unstable propagation of the fatigue crack. Dependence of the decrease of the critical stress intensity factor under cyclic loading on the number of load cycles are obtained for repeating ( R = 0) and alternating bending ( R =−1) of specimens with a crack. A model for the transition from stable to unstable crack propagation is proposed involving crack velocity in the zone ahead of the crack tip damaged by cyclic plastic deformation. A new approach is suggested to the classification of materials on the basis of the sensitivity of fracture toughness characteristics to cyclic conditions of loading.     

Validity requirements of circumferentially notched tensile specimens for the determination of the interfacial fracture toughness of coatings

A simple method was developed for evaluating the interfacial fracture toughness of coatings on substrates using circumferentially notched tensile (CNT) specimens. Mild steel cylindrical substrates of 0°, 15°, 30°, 45° and 60° notch angles with electroplated nickel were tensile tested. A well defined pre-crack was introduced at the interface for the quantitative evaluation of adhesion. In situ acoustic signals and scanning electron microscope were used to analyze the crack initiation and propagation. Finite element analyses were used to evaluate the critical interface energy release rate. The size of the plastic zone was determined for different notch angles to validate application of the linear elastic approach in determining the interfacial fracture toughness. The validity requirements have been proposed for this specimen, considering the yield strength of the coating and substrate, pre-crack position, notch angle and plastic zone size. The obtained interfacial fracture toughness values using CNT specimens was found to be very close to the values obtained by others using standard specimens.     

Brittle failures from U- and V-notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite-size volumes

A large bulk of static test results carried out on notched specimens are presented in a unified way by using the mean value of the strain energy density (SED) over a given finite-size volume surrounding the highly stressed regions. In plane problems, when cracks or pointed V-notches are considered, the volume becomes a circle or a circular sector, respectively, with R _C being the radius. R _C depends on the fracture toughness of the material, the ultimate tensile strength and the Poisson's ratio. When the notch is blunt, the control area assumes a crescent shape and R _C is its width as measured along the notch bisector.
About 900 experimental data, taken from recent literature, are involved in the local SED-based synthesis. They have been obtained from (a) U- and V-notched specimens made of different materials tested under mode I loading; (b) U- and V-notched specimens made of polymethyl-metacrylate (PMMA) and an acrylic resin, respectively, tested in mixed, I + II, mode; (c) U-notched specimens made of ceramics materials tested under mode I.
The local SED values are normalized to the critical SED values (as determined from unnotched specimens) and plotted as a function of the R / R _C ratio. A scatter band is obtained whose mean value does not depend on R / R _C, whereas the ratio between the upper and the lower limits are found to be about equal to 1.6. The strong variability of the non-dimensional radius R / R _C (ranging here from about zero to around 1000) makes stringent the check of the approach based on the mean value of the local SED on a material-dependent control volume.     

ELEVATED TEMPERATURE FRACTURE OF PARTICULATE-REINFORCED ALUMINUM PART I: FRACTURE TOUGHNESS

Abstract—The plane-strain initiation and growth fracture toughnesses of powder-metallurgy-processed, SiC particulate-reinforced 2009 plate were measured at temperatures from 25°C to 316°C. Initiation toughness from electrical potential monitoring ( K _JICi) is 18 MPa°m at 25°C, and is nearly constant to 220°C before decreasing sharply to 6 MPa°m at 316°C. Growth toughness, given by the tearing modulus ( T _R), is less than 3 from 25°C to 125°C, and increases dramatically above 200°C. The magnitude and temperature dependence of initiation toughness depend on detection of the critical fracture event. Standard measures of toughness K _IC and K _JIC exceed K _JICi and increase to a plateau with increasing temperature. The fracture mode for the composite is microvoid nucleation, growth and coalescence at all temperatures. Void nucleation is associated with SiC; such particles both crack and create stress and plastic strain concentrations that rupture the interface or adjacent matrix, particularly at corners. Matrix plasticity and cavitation increase with increasing temperature. Void growth is regular at all temperatures, but limited by adjacent SiC particles. Both K _JICi and T _R are governed by the temperature-dependent crack-tip plastic stress and strain fields, and the intrinsic damage resistance of the composite microstructure.     

A note on Orowan mechanism below the root of an yielding crack like notch in a strain-hardening metal

Based on Orowan's historic model, a local fracture initiation criterion is proposed for high strength strain-hardening metals. A crack like notch geometry is studied in the following Von Mises yielding materials: (a) an ideally plastic-elastic solid, and (b) a power law strain-hardening metal. Orowan mechanism is seen to be dominant below the root region of an yielding crack like notch, just before the onset of fracture. Close to the elastic-plastic interface, Orowan's Kink-band forms inside the plastic region, when a mismatch Kink-stress (in radial component only) reaches a critical value in this particular region. It is extremely important to note that, this narrow Kink-band zone, where the micro-cracks are likely to nucleate, lies at a distance approx. $\text{3}\text{4}\text{s}$, where s is the size of the plastic zone on the crack extension plane under a plane strain deformation. A reverse slip mechanism operates in this region in addition to the presence of a pure hydrostatic tension, just before the release of this critical Kink-stress. Due to this stress history, a large inhomogeneous strain-localization occurs in a narrow band, which could then interact with the free notch surface before the onset of final instability. Thus, at the onset of crack extension, (satisfying Griffith-Irwin criterion of fracture), the stress intensification at the notch tip root is directly proportional to the strength of this critical strain-localization and inversely proportional to the plastic zone size on the crack extension plane. Hence, it is concluded that: Orowan's mechanism and McClintock's criteria for critical strain-localizations should play the most important roles for predicting the local fracture behaviour of metals.