Sharp Notch Research Articles

Assessing Fatigue Damage in Organic Glass Using Optical Methods

On the basis of fragments of time-averaged speckle images registered with no stopping of cyclic loading, the features of nucleation, onset, and propagation of a crack in the bulk of a transparent prismatic sample with a sharp V-shaped notch have been found. It has been shown that the first signs of fatigue damage occur not at the top of the notch, but at a distance of 400 μm from it in the sample center within an area with a diameter of 200 μm. After the beginning of the development (“onset”) of the crack, the size of the zone of irreversible processes exhibits an increase by an order of magnitude. The distribution of the refractive index and the density around the crack has been studied based on changing speckle images and with the use of ellipsometry. It has been shown that the maximum value of relative change in density being at least 2 × 10–3, is located near the crack. The speckle method can serve a basis for the development of nondestructive testing tools and techniques that make it possible to assess the time preceding crack onset according to the changing rate and the limiting values of the refractive index and material density, as well as according to other parameters affecting the change in the optical paths of waves within small areas about 10 μm in size.

Improving weldability of Al-Si coated press hardened steel using stepped current pulse schedule

Al-Si coated press hardened steel (PHS) were introduced into vehicle body structures for a balance of lightweighting and crashworthiness. However, the weldability of PHS is relatively poor, due to its high carbon equivalent and high strength and is characterized by severe heat affected zone, HAZ softening, and interfacial fracture. The interfacial fracture mode is defined in part by the presence of retained Al-Si coating as a sharp notch at the faying interface following the welding process, which limits the mechanical performance of the joint. To improve the weldability of PHS, a stepped current pulse schedule was proposed for the resistance spot welding (RSW) of 1.5 mm Al-Si coated PHS as a means to effectively promote nugget growth, inhibit expulsion and eliminate the residual Al-Si layer. In this manner the mechanical performance of joints were significantly improved and the desirable button pullout fracture mode was realized.

Development of a laser-based line scan measurement system for the surface characterization of reinforcing steel

Abstract The fatigue behavior of reinforcing bars is mainly influenced by their surface properties. Massive ribs and sharp notches provoke failure in fatigue. For the current research, it was necessary to develop a measurement system in order to allow for the highly precise measurement of the surface of fair sized fatigue specimens. The paper presents the boundary conditions at the beginning of the research project and gives a short overview of the measuring techniques currently used. It presents the development of a laser-based line scan (LLS) measuring system which applies the principle of laser-triangulation. The high accuracy and precision of the system of measurement was quantified in several investigations.

Assessment of the residual life of the high-temperature elements of the turbine rotors through modeling the reduction of the metal continuity

Calculation and experimental estimates of the residual life of steels P2M and EI415 of two strength levels (H and B) are carried out using two methods, the new one and the traditional. The loading was carried out for 300 thousand hours under conditions similar to those in which the metal operates in the zone of blade attachment in the rim of the disk of the first stage of medium-pressure rotors of K-300-240 LMZ and KhTZ turbines. When evaluating the residual life, a gradual decrease in stresses due to creep was taken into account by distinguishing several stages with conditionally constant stresses. According to the new methodology, the residual life was estimated by a change in the metal super-continuity at each stage 47 = ц/п + 1, where u/ is the continuity, n is the crack formation index; whereas in the traditional method the relative damage Р is estimated according to the principle of linear summation of damage (LSP). It is shown that the time dependences P and 47 obey the logarithmic law, while the metal of the fbrgings В (high strength) in all cases had a greater resource compared to the fbrgings H (low strength). For the first time, the process of resource depletion was considered by analyzing the sum of two functions: 47 + P = 1. It is shown that for R2M steel this amount is less than unity; for steel EI415 it is equal to or greater than unity. Proceeding from the literature data on the differences that follows from using LSP rule for a relatively viscous and brittle metal, we suggested that deviations from unity are attributed to the error in estimating the resource according to the LSP principle. Therefore, the result obtained by the new method should be recognized as more accurate. Taking into account the use of samples with a particularly deep sharp notch in which the brittle crack development is guaranteed by the proposed methodology, the new principle of calculating the residual life can be used in determination of the resource for any type of the parts made of the metal subjected to brittle fracture during operation under creep conditions.

On the behaviour of non-propagating cracks in steel and aluminium castings

Casting defects as well as sharp notches can serve as initial points for fatigue cracks under cyclic loading. On the contrary, the cyclic material crack resistance counteracts to crack propagation. Hence, an incipient crack can arrest completely, even though a constant cyclic load is applied. Considering a short propagating crack, the local stress intensity factor, which represents the crack growth driving force, increases due to the crack extension, yet crack arrest may occur. Such an arresting of growing cracks can be traced back to an increase of the materials resistance in terms of crack closure effects. This paper deals with the evaluation of the cyclic short crack behaviour and the assessment of non-propagating cracks for cast aluminium and cast steel in terms of the Frost diagram. At first, single edge notched bending specimens are machined out of both cast materials and investigated in regard to their fracture mechanical short and long crack growth behaviour under varying stress ratios. Moreover, the data is analysed in terms of the short crack resistance (R-curve) and the subsequent long crack growth behaviour. Secondly, detectable surface porosity defects, regarding the aluminium material, and sharp surface notches, as in case of cast steel, are investigated by a linear elastic finite-element simulation to evaluate the local stress concentration factors numerically. Finally, Frost diagrams are set up for both materials and well approved by the detected non-propagating cracks. A final comparison of the investigated fatigue test data points and the Frost diagrams reveals a sound agreement validating the applicability of the presented approach.

Fatigue Precracking Time Estimates for Three-Point Bending Specimens

Specimens containing sharp cracks are needed in certain types of mechanical tests, first and foremost for fracture toughness measurement of materials. Their use, however, is not just limited to this type of test. Another category of experiments deals with characterizing nonlinear vibrations of beams containing breathing cracks. To produce cracked beam specimens, fatigue cracks can be grown ahead of sharp notches under controlled loading. ASTM E399 and ASTM E1820 standards provide guidance on such procedures for preparation of fracture toughness test specimens. However, certain issues which might become important in testing of vibrations of cracked beams, such as the time required for specimen preparation is not addressed in these standards. In this article, both low cycle fatigue methods and linear elastic fracture mechanics methods are used to estimate the number of loading cycles required to have a crack of desired length at the notch tip. Calculation results are compared with experimental ones, and the effects of various factors influencing the required number of loading cycles for a certain crack size are discussed.

An easy and engineering stability criterion of general singular stress concentrators

General singular stress concentrators often occur in engineering components and they represent places prone to crack initiation. Estimation of crack initiation conditions is usually performed by means of stability criteria of generalized fracture mechanics. These stability criteria require knowledge of asymptotic description of the stress state around the general singular stress concentrator. In cases of some concentrators, this analytical-numerical description can be quite difficult and does not belong among straightforward engineering approaches. This paper introduces an easy and engineering way to assess conditions for crack initiation and propagation in general singular stress concentrators using standard numerical approaches. The paper handles well-known criteria of generalized fracture mechanics of sharp and bi-material notches and simplifies them to a practical form usable for engineers. The resulting criterion fits the frame of criteria of finite fracture mechanics and extends their applicability.

Application of digital image correlation method for determination of mixed mode stress intensity factors in sharp notches

In the present study, the applicability of the digital image correlation (DIC) method in deriving the notch stress intensity factors (NSIFs) is examined for sharp V-notched components under mixed mode I/II loading. For this purpose, in the first step, the analytical mixed mode stress and displacement fields around the sharp V-notches and the concept of NSIFs are presented. Then, in the second step, the V-notched diagonally loaded square plate (V-DLSP) specimen is chosen for performing the DIC experiments. Three different notch opening angles with four various combinations of mode I and mode II loadings are considered for the V-DLSP specimens tested. Subsequently, in the third step, the DIC method is employed to determine the experimental displacement fields in the V-DLSP samples. Finally, the displacement fields obtained experimentally from the DIC technique are fitted to the analytical displacement field to derive the NSIFs of sharp V-notches by using a numerical method called the over-deterministic method. Comparing the results obtained from DIC method with those obtained from the finite element (FE) analysis shows the effectiveness of DIC method in determining the stress field around sharp V-notches.

Nelson's notch in the rate-level functions of auditory-nerve fibers might be caused by PIEZO2-mediated reverse-polarity currents in hair cells

Half a century ago, Nelson Kiang and colleagues observed that some spike rate versus stimulus level functions of auditory-nerve-fiber responses to tones are nonmonotonic, exhibiting a sharp notch (“Nelson's notch”) at high stimulus levels. The notch is associated with an abrupt change in the phase of the response by ∼180°. To account for these findings, Kiang proposed a “two-factor cancellation hypothesis” according to which excitation of an auditory-nerve fiber is produced by the sum of two phase-locked factors with opposite phase and with different dependencies on stimulus level, cancelling each other at stimulus levels within the notch. The first factor, which dominates at lower stimulus levels, is likely based on the mechanoelectrical transducer current through mechanoelectrical transducer channels in the tips of the inner-hair-cell stereocilia. The identity of the second factor, which dominates at high stimulus levels, has remained elusive. Here, we hypothesize that the second factor is based on the “anomalous” or “reverse-polarity” currents entering inner hair cells via a second type of mechanosensitive channel, PIEZO2, recently identified in the apical surface of hair cells rather than the tips of their stereocilia.

Notch factor correction using stress triaxiality of plane-stress state in high-cycle fatigue

This research investigates and compares two different factors of notch effects on fatigue life: fatigue strength reduction (Kf) and stress triaxiality. The study includes three notch geometries and focuses on high-cycle fatigue regime under plane-stress state. Also, specimens were designed and cut from sheets made of three different metals. The experimental fatigue life data were taken from NASA official reports. The results demonstrate that the Kf factor poorly incorporates the notch effects for sharp notches and high-strength metals, whereas the stress triaxiality factor, using Abaqus FEA simulation, overcomes these flaws and efficiently incorporates the notch effect in fatigue life models.

The complexity of ECG signal based on multifractal theories and its nonlinear dynamical mechanism

The nonlinear dynamical analysis of biomedical signals has always been the research focus in academic fields. It better uncovers the essential rules in life activities than conventional linear and time-frequency analysis methods. Human body surface electrocardiogram (ECG) signal is non-stationary and frequency-varying by nature, which belongs to a typical nonlinear signal. Therefore, traditional linear analysis methods cannot completely disclose its nonlinear nature. The existing nonlinear dynamic tools, such as correlation dimension (D2), Lyapunov exponent, entropy, detrended fluctuation analysis, multifractal singularity spectrum etc., have already been applied to the studies on heart electrical signals, which proved that this signal has definite chaotic characteristic. The aforementioned nonlinear methods perform better in the analysis of deterministic stochastic signals. In our viewpoints, because all the probabilities in the original data set can be exactly expressed by the corresponding points in the multifractal singularity spectrum f ( α ), the area of the spectrum must comprise the total information of the data. This two-dimensional expression is more accurate than the computation of spectral width Δ α in analyzing the heartbeat signal. With regard to ECG time series, the areas of singularity spectrum should include all the information about the heartbeat dynamics. Considering the irregularity and anisotropy of the heartbeat electrical signal propagation, we investigated the arithmetic mean and dispersing degree of the area calculated from synchronous 12-lead ECG signals obtained from a large number of subjects, who were under different physiological and pathological conditions. The 12-lead ECG records were obtained from 12 sensors positioned on body surfaces, including the limb and chest leads. In addition, the ECG signals were in high frequency section (HFECG), whose frequency components were above 100 Hz (approximately 100 Hz–2 kHz). Some early heart diseases can first be reflected by high-frequency ECG signals, which are often associated with sharp notches and slurs in the time domain. Furthermore, we set sampling frequency of HFECG signal to 1 kHz so that all the components below 500 Hz could be analyzed according to the sampling theorem. Thereafter, by the virtue of the multifractal theory, we investigated the arithmetic mean and dispersing degree computed from singularity spectrum area of synchronous 12-lead ECG signals obtained from different crowds of human subjects. Variance analysis tests revealed all 12-lead ECG signals from above cohorts were statistically identifiable using these two indicators. The experimental results suggest that the arithmetic mean of the area of the 12-lead ECG signals was apparently large for healthy young but small for myocardial infarction (MI) sufferers. Besides, the dispersing degree of the area of the 12-lead ECG signals was obviously small for healthy young but large for MI sufferers. For the other cohorts, such as ischemia sufferers and healthy elderly, these two values were of middle magnitudes. This indicates that with deeper lesions, the fractal-like structure of the heartbeat system is damaged or structurally changed, which may lead to decline in the nonlinear complexity of the system and concomitant increase in the irregularity and anisotropic propagation of ECG signal. In addition, we found that the 12-lead mean value of singularity spectrum area of human ECG signals can reflect the self-discipline control status of human autonomic nerve to some degree. This value gradually decreased with aging. These findings suggest that the self-discipline control of the human autonomic nervous system weakens with aging. The nonlinear complexity of ECG signal then descends and tends to turn from multifractality to monofractality, implying weakened human individual adaptabilities. Our studies on the nonlinear dynamical features of heart electrical signals and ECG variations with age, disease, and human autonomic nerve control, demonstrate theoretical and diagnostic significances.

Prediction of Survivability Time for Express Assessment of Long-Term Performance of Steam Line Metal Parts Made of Steel 10Kh9MFB-Sh

An assessment of the survivability time was performed for the following two parts made of 10Kh9MFB-Sh steel at 600°C and maximum allowable metal stresses: a pipe measuring 630 mm in diameter and having a wall thickness of 25 mm, and a pipe billet produced by electroslag remelting (ESR) technique. The specific feature of the proposed procedure consists in testing samples containing an extra deep and sharp notch. To determine the time to breaking, the notch opening rate was registered at an increased frequency of 0.003 h. It is shown that metal of the billet produced by the ESR technique has an advantage of longer service life in comparison with the hot-worked pipe. A simplified version of the procedure featuring fixed parameters of the breaking conditions is proposed for the base and weld metal.

Effect of small defects on the fatigue strength of martensitic stainless steels

The defect tolerance of three different martensitic stainless steels (17-4PH, X20Cr13 and AISI403) under cyclic loading was investigated. Fatigue tests were performed with specimens containing diverse artificial defects (corrosion pits, single and multiple drilled holes, sharp circumferential notches and pre-cracked holes). The measured cyclic strengths are compared to predictions based on the area parameter model proposed by Murakami and Endo. This model is well applicable to small sharp defects if the threshold condition for crack propagation determines the fatigue limit. The transition size from small to large defects, areatrans, – above which the threshold stress intensity factor range, ΔKth, becomes a constant value – is between 80 and 166 µm for the investigated steels. For larger defects, the threshold for long cracks, ΔKth,lc, serves well to predict the fatigue strength under fully reversed loading, i.e. at a load ratio of R = −1. Comprehensive tests were performed to study the influence of mean stress, and threshold conditions were determined that enable to predict the fatigue limit at different load ratios.A simple equation is introduced to estimate the critical defect size, areacritical, which is the size above which defects become detrimental under cyclic loading. It has been found that areacritical increases with increasing load ratio while areatrans is independent of R. Furthermore, higher values of the threshold stress intensity factor range were determined for large defects (with sizes larger than areatrans) compared to long cracks if the load ratio is higher than R = −1. This could be explained by the plane stress condition at the material surface which is prevalent for surface defects, while the condition for long cracks can be assumed as plane strain.It is further demonstrated that the effect of small defects on the fatigue strength of stainless steels is highly sensitive to the notch root radius, ρ. Small holes with diameters of 100 µm (ρ = 50 µm) or larger are less detrimental for the fatigue strength than defects with high stress concentrations – such as corrosion pits.

On the estimation and modeling of fracture toughness in structural ceramics in a simple way

Fracture toughness testing is based primarily on millimeter-scale macro-notches, but the actual brittle fractures in structural ceramics are often associated with surface scratches, flaws or microcracks of only several dozens of microns. Here, the porous ZrB2, the dense ZrB2-SiC and the reinforced ZrB2-SiC-Graphite ceramics were taken as the experimental targets, and a nanosecond laser notching approach was used to fabricate sharp notches with various depths from 10 μm to 3 mm. The shallow notched fracture toughness value was found to be only 60–80% of the deep notched fracture toughness. Furthermore, the fracture strength and the notch depth followed a linear relationship in double logarithmic coordinates, and the strength value reached the theoretical strength of these three ceramics when extrapolating the notch depth to atomic scale (3 Å). Based on this, a new prediction model of fracture toughness in ceramics was established, which agreed well with the experimental results.

Electro-mechanical singularities of piezoelectric bi-material notches and cracks

The paper aims to carefully investigate an asymptotic in-plane problem of bi-material sharp notches with various geometry and interface cracks in several generally monoclinic piezoelectric bi-materials using the expanded Lekhnitskii-Eshelby-Stroh formalism. A special attention is paid to the change of the asymptotic solution connected with the transition of a very closed notch into an interface crack. Also the influence of arbitrary oriented poling directions upon asymptotic solution is investigated. Four pair-combinations PZT-5H/BaTiO3, PZT-5H/PZT-6B, PZT-5H/PZT-7A and PZT-6B/PZT-7A as representatives of the so-called ε-class of bi-materials and six pair-combinations PZT-4/BaTiO3, PZT-4/PZT-5H, PZT-4/PZT-6B, PZT-4/PZT-7A, PZT-6B/BaTiO3, and PZT-7A/BaTiO3 as representatives of the κ-class of bi-materials are analysed. It is shown that the bi-material classification into ε-class and κ-class introduced by Ou and Wu (2003) for interface cracks cannot be applied to a bi-material notch with a geometry characterized by an arbitrary angle. Ou and Wu bi-material classification also fails for interface cracks if one of the poling angles differs from 90°. The two-state integral derived from Betti’s reciprocal principle for piezoelectric bi-materials is used to evaluate general stress intensity factors (GSIFs) for various piezoelectric bi-materials and notch configurations. The accuracy of GSIFs calculations is tested by comparing the asymptotic solutions with the results obtained by finite element method using a very fine mesh.

Generalized Diagram of the Ultimate Nominal Stresses (Endurance Limit) and the Corresponding Dimensions of the Non-Propagating Fatigue Cracks for Sharp and Blunt Notches

The paper generalizes the original data and the experimental data from the references on the investigation of the mechanisms of initiation and behavior of the non-propagating fatigue cracks in the notches of various shapes and dimensions. The dependence of the ultimate nominal stresses (endurance limit) and their corresponding dimensions of the fatigue cracks on the theoretical stress factor for the notches of various shapes and dimensions is proposed to be schematically presentedin the form of the generalized diagram. The ultimate stresses should be understood as the endurance limits only within the zone of sharp notches provided that their value does not depend on the theoretical stress concentration factor. The limiting dimensions of the non-propagating cracks in the zone of sharp notches should be understood to mean the maximum dimensions of the cracks that are consistent with the ultimate stresses. The generalized diagram indicates the fact that the nominal endurance limit decreases in the zone of blunt notches, while the dimensions of the non-propagating cracks increase with an increase in depth and decrease in the notch radius (with the increase of the theoretical stress concentration factor), whereas they are controlled by the notch depth within the zone of sharp notches. With the increase of the notch depth, the ultimate stresses decrease, while the dimensions of the non-propagating cracks increase. At the constant depth of the notch, the ultimate stresses and dimensions of the non-propagating cracks are independent on the notch radius and value of the theoretical stress concentration factors.

Midbrain sensitivity to spectral cues for sound-source localization: A modeling study

The features of head-related transfer functions (HRTFs) are a key topic in the field of spatial auditory displays. Neural encoding of HRTFs is not well understood; their sharp spectral peaks and notches are not well represented by average rates of relatively widely tuned auditory-nerve (AN) fibers, and phase-locking to the temporal fine structure is not adequate to encode features at high-frequencies. However, low-frequency fluctuations in cochlear responses to wideband stimuli are encoded in time-varying rates of AN fibers across all frequency channels. Here, we focus on modeling the profile of amplitude fluctuations in response to spectral cues across the population of AN channels. The fluctuation profile across AN responses sets up an average-rate profile across inferior colliculus (IC) neurons, which are sensitive to envelope-related low-frequency fluctuations. Both unilateral and bilateral IC model responses indicate that rather than responding to spectral peaks in a given HRTF, IC responses are more sensitive to fluctuations in frequency channels near steep spectral slopes. The influence of the spatial location and stimulus level on model IC responses was examined. Using statistical methods, psychoacoustical thresholds of discrimination of sounds that differ in the source location were estimated and compared to trends in the existing perceptual results. The features of head-related transfer functions (HRTFs) are a key topic in the field of spatial auditory displays. Neural encoding of HRTFs is not well understood; their sharp spectral peaks and notches are not well represented by average rates of relatively widely tuned auditory-nerve (AN) fibers, and phase-locking to the temporal fine structure is not adequate to encode features at high-frequencies. However, low-frequency fluctuations in cochlear responses to wideband stimuli are encoded in time-varying rates of AN fibers across all frequency channels. Here, we focus on modeling the profile of amplitude fluctuations in response to spectral cues across the population of AN channels. The fluctuation profile across AN responses sets up an average-rate profile across inferior colliculus (IC) neurons, which are sensitive to envelope-related low-frequency fluctuations. Both unilateral and bilateral IC model responses indicate that rather than responding to spectral peaks in a given HRTF, IC responses are mor...

A singular element based on dual interpolation BFM for V-shaped notches

• A new singular element based on dual interpolation boundary face method is proposed. • The new element takes into account the variable singularity orders at the notch tip . • Special basis function is introduced to build the shape functions of the proposed element. • The dual interpolation method can provide much higher accuracy than traditional interpolation method. • The numerical results for stress intensity factors obtained by the new element are convergent. A singular element based on dual interpolation boundary face method (DiBFM) is presented for solving V-shaped notch problems in this paper. The stress field around sharp notches is singular, and the singularity orders vary with the notch angle. Thus an element with usual shape functions or traditional singular element cannot lead to high accurate results. To accurately model the distribution of displacement around the notch tip, a new displacement singular element based on DiBFM is proposed. The new element takes into account the variable singularity orders at the notch tip. The dual interpolation method which combines conventional polynomial element interpolation and moving least-squares approximation can provide much higher accuracy than traditional interpolation method. With the proposed singular element based on DiBFM, more accurate displacement results in the vicinity of the notch tip can be evaluated, thus more accurate stress intensity factor (SIF) of the V-shaped notches can be obtained. Numerical examples have demonstrated the validity and accuracy of our method.

A comparison between numerical and approximate methods for rapid calculation of NSIFs

To more rapidly predicting the integrity of components weakened by sharp notches, notch stress intensity factors (NSIFs) are usually evaluated. Many methods have been proposed evaluating NSIFs, ranging from the stress gradient based formulation to methods evaluating strain energy density averaged over a control region. Here, we compare different numerical and approximate methods applied to a square plate with a 45° tilted crack, positioned at the center of the plate. Hence, approximate methods need to FE solutions, obtained from models discretized with fine mesh or, alternatively, with coarse mesh, having to consider the mean value of the local Strain Energy Density (SED) to calculate NSIFs. Furthermore, 2D and 3D numerical simulations have been carried out to investigate the solutions provided by these analytical methods. For this aim, two software based on the Finite Element Method (FEM) and on the Dual Boundary Element Method (DBEM), respectively, have been adopted to solve the proposed study case of the square plate with a 45° tilted crack. These methods can supply accurate predictions of SIFs by means of J-integral calculation. Then, the NSIFs have been calculated at the intersection between the crack front and the free surface of the plate and, to assess the thickness effect on the provided solutions, they have also been calculated at half the thickness along the crack front and for increasing thickness values. Finally, the NSIFs obtained from the analytical and numerical methods have been compared each other to evaluate the level of agreement.

Sea Clutter Cancellation for Passive Radar Sensor Exploiting Multi-Channel Adaptive Filters

Sea clutter suppression in passive radar sensor is a challenging problem because the Doppler frequencies of low-velocity sea-surface targets are typically close to the spectrum of the sea clutter. Conventional approaches based on single-channel high-pass filters are effective for clutter suppression only when the clutter is concentrated in low Doppler region. For sea clutter that has a spread spectrum, however, these approaches have to compromise target signal reception. That is, they either form a narrow notch which does not effectively suppress clutter, or generate a broadened null that simultaneously mitigates low-velocity target signals. Therefore, it is desirable to design a filter that forms a notch broad enough to cover the entire clutter spectrum, with the frequency response rising sharply to a high gain outside the clutter band. Toward this end, in this paper, we develop a generalized multi-channel adaptive filter which, by forming multiple sharp notches over a set of discrete frequencies within the clutter spectrum, achieves effective clutter suppression and target signal preservation. We focus on the fast frequency-domain implementation, and the performance analysis in terms of the frequency response, signal energy loss, and computational complexities is also presented. The effectiveness of the proposed approaches is verified using real-data results.