Mode III Notch Fracture Toughness Assessment for Various Notch Features

In the present paper, two stress-based failure criteria are proposed to predict the notch fracture toughness for three different notch features under pure mode III loading. These criteria are developed based on the two well-known failure concepts of the point-stress and the mean-stress previously used for predicting brittle fracture in notched members under various loading conditions. The validity of the criteria is verified through the comparison of their theoretical predictions with a bulk of test data reported in the open literature on mode III fracture of graphite notched round bars. Very good agreement is shown to exist between the experimental and theoretical results. Moreover, the comparison revealed that the mean-stress criterion is more accurate than the point-stress criterion in predicting mode III brittle fracture of V-notches and semicircular notches.     

Fracture Assessment of Inclined Double Keyhole Notches in Isostatic Graphite

In the present contribution, the static strength of isostatic graphite using keyhole notch specimens under mixed mode loading is investigated. An experimental program was performed and in total, 18 new experimental data are provided. In addition, different loading mode ratios are considered by varying the inclination angle of the notch with respect to the direction of the applied load. The criterion based on the averaged value of the strain energy density over a control volume at the notch edge is applied to assess the static strength of specimens. A sound agreement is found between experimental data and the results obtained from strain energy density criterion.     

Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion

In this work, some recent mixed mode I/II fracture toughness results obtained from Perspex (or polymethylmethacrylate (PMMA)) with four simple cracked specimens subjected to the conventional three-point bend loading are reanalysed based on local energy concept. Although all the mentioned samples have been tested under the same and similar mode mixities, different fracture toughness envelopes were obtained for mixed mode I/II fracture of PMMA. The averaged strain energy density (SED) criterion has been applied in the past for different types of notched specimens (including U, V, O and keyhole notches). It is shown that the mixed mode tensile-in plane shear fracture toughness data obtained from the semicircular and triangular crack type specimens are successfully predicted for sharp cracked PMMA samples using the SED criterion.     

Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I + III loading

Mixed mode I/III behavior of Perspex (polymethyl methacrylate (PMMA)) is studied experimentally and theoretically in this research using a new and simple laboratory test configuration. The specimen is a circular disc containing a sharp V-notch along the diameter that is loaded by the conventional three-point bend fixture. The critical values of notch stress intensity factors (K _I ^V and K _III ^V ) were obtained for the whole combinations of modes I and III simply by changing the notch inclination angle relative to the loading rollers. The value of notch fracture toughness under pure or dominantly tension loads was greater than its corresponding value under mode III or dominantly torsion loads. The experimental results were also predicted very well by employing the local strain energy density (SED) criterion.     

Some recent results on the fatigue strength of notched specimens made of 40CrMoV13.9 steel at room and high temperature

The work summarizes a large bulk of experimental data from specimens made of 40CrMoV13.9 steel. The first part of the paper deals with multiaxial fatigue strength of notched round bars tested under combined tension and torsion loading, both in-phase and out-of-phase. The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. The second part of the paper summarizes data from uniaxial-tension stress-controlled fatigue tests on specimens made of the same steel. Tests are performed varying temperature, from room temperature up to 650°C. Altogether more than 180 new fatigue data are summarised in the present work, corresponding to more than two-years of testing programme. All fatigue data are presented first in terms of nominal stress amplitudes referred to the net area and then re-analysed in terms of the mean value of the strain energy density evaluated over a given, crescent shape volume embracing the stress concentration region. For the specific steel, the radius of the control volume is found to be independent of the loading mode.     

Compressive Brittle Fracture Prediction in Blunt V-Notched PMMA Specimens by Means of the Strain Energy Density Approach

The paper aims to examine the suitability of the strain energy density criterion in predicting the fracture behavior of blunt V-notched specimens under compression load. Recent studies on local stress fields have shown that the strain energy density, averaged over a specific control volume which embraces the notch round border, could be a robust parameter in the brittle fracture assessment of several materials. A set of experimental results recently published in the literature on compressive brittle fracture of V-notched specimens made out of polymethyl methacrylate has here been considered. Finite element analyses have been performed on plane strain condition and experimental data have been summarized by means of the SED criterion. It has been shown that the proposed criterion permits a satisfactory evaluation of the fracture load of polymethyl methacrylate specimens weakened by notches having different opening angles and radii.     

Mixed mode I/II brittle fracture in V-notched Brazilian disk specimens under negative mode I conditions

The well-known round-tip V-notched Brazilian disk specimen is utilized for conducting mixed mode I/II fracture tests on PMMA under negative mode I conditions for different notch angles and various notch radii with the aim to measure experimentally the fracture load and the fracture initiation angle. It is shown by the finite element analysis that although the notch is under negative mode I loading, one side of the notch border still experiences tensile tangential stresses suggesting that fracture would take place from the same side of notch border. Experimental observations also indicated that fracture occurs from the tensile side of the notch border confirming the finite element results. The experimental results are then theoretically estimated by means of two stress-based brittle fracture criteria, namely the round-tip V-notch maximum tangential stress and the mean-stress criteria. It is shown that both criteria provide very good predictions to the experimental results obtained under negative mode I conditions.     

A review on coupled modes in V-notched plates of finite thickness: A generalized approach to the problem

Mode 1, 2 and 3 cannot exist in isolation. One mode provokes the existence of a coupled mode which, in some conditions, can be more dangerous than the generating mode itself. This means that three-dimensional problems are automatically at least dual scale. While for a crack this effect was known to exist for a long period of time, it was largely ignored in theoretical studies of V-shaped notches subjected to in-plane and out-of-plane loading as well as in practical fracture problems associated with such geometries. Only recently, some numerical investigations confirmed that highly localized coupled modes do exist in the close vicinity of the notch tip. The present paper is aimed to briefly review important features of these recently identified singular coupled modes. The most significant results from a comprehensive three-dimensional numerical study are presented here to describe the contribution of these modes into the overall stress state in the close vicinity of the notch tip and discuss the implementation of these new results to the failure and integrity assessment of plate structures with sharp notches.     

Mode I Fracture Analysis of Polymethylmetacrylate Using Modified Energy-Based Models

The paper presents two energy-based approaches to predict the fracture trajectory and the fracture load in components containing a mode I crack. The fracture behavior of polymethylmetacrylate (PMMA) samples was investigated experimentally and theoretically for compact tension and double cantilever beam test specimens. The crack growth trajectories and the values of apparent fracture resistance in these two specimens were considerably different although both were under pure mode I loading. Two energy-based methods, i.e., the strain energy density and the averaged strain energy density criteria were modified to estimate the fracture trajectory and the fracture load in brittle materials respectively by considering the T-stress effects. The difference between the crack trajectories and the fracture resistances of different cracked specimens of the same material (PMMA) was found to be related to the magnitude and the sign of T-stress.     

Transitional failure of hybrid carbon nanotubes under multiaxial loads

Transitional failure envelopes of hybrid single-walled carbon nanotubes functionalized by functional groups and filled with butane molecules under combined tension–torsion are predicted using classical molecular dynamics simulations. The observations reveal that while the tensile failure load decreases with combined torsion, the torsional buckling moment increases with combined tension. As a result, the failure envelopes under combined tension–torsion are definitely different from those under pure tension or torsion. In such combined loading, there is a multitude of failure modes (tensile failure and torsional buckling), and the failure therefore exhibits the feature of transitional failure envelopes. In addition, the functionalization by functional groups decreases both tensile failure load and torsional buckling moment, while filling with butane molecules increases only the torsional buckling moment. Consequently, the transitional failure envelopes of functionalized and filled nanotubes are absolutely different relative to what is predicted for pristine nanotubes.     

On three-dimensional stress analysis of periodic notched plates under tension

By using the finite element method, three-dimensional models of a number of periodic blunt and sharp notches subjected to tension loading are investigated. The aim of this research is to investigate the thickness effect on the location of maximum stress and notch stress intensity factor (NSIF) of corresponding blunt and sharp periodic notches respectively. With this aim, different number of periodic notches as well as different notch opening angles are examined. While for two-dimensional plates weakened by periodic notches some results are available in the literature, this paper first faces the problem of three-dimensional cases. A total of about 100 geometrical configurations are investigated. It is found that, the effect of plate thickness of periodic notched components can be characterized by the relative value with respect to the depth of the notch (H/t). For the blunt periodic notches with relatively higher values of H/t ratio, the value of the maximum tensile stress is located near the free surface. On the contrary for lower values of H/t, it is placed at the middle plane. The same behaviour is observed for sharp periodic notches in terms of notch stress intensity factors.     

Fatigue strength of Al7075 notched plates based on the local SED averaged over a control volume

When pointed V-notches weaken structural components,local stresses are singular and their intensities are expressed in terms of the notch stress intensity factors(NSIFs).These parameters have been widely used for fatigue assessments of welded structures under high cycle fatigue and sharp notches in plates made of brittle materials subjected to static loading.Fine meshes are required to capture the asymptotic stress distributions ahead of the notch tip and evaluate the relevant NSIFs.On the other hand,when the aim is to determine the local Strain Energy Density(SED)averaged in a control volume embracing the point of stress singularity,refined meshes are,not at all,necessary.The SED can be evaluated from nodal displacements and regular coarse meshes provide accurate values for the averaged local SED.In the present contribution,the link between the SED and the NSIFs is discussed by considering some typical welded joints and sharp V-notches.The procedure based on the SED has been also proofed to be useful for determining theoretical stress concentration factors of blunt notches and holes.In the second part of this work an application of the strain energy density to the fatigue assessment of Al7075 notched plates is presented.The experimental data are taken from the recent literature and refer to notched specimens subjected to different shot peening treatments aimed to increase the notch fatigue strength with respect to the parent material.     

Fracture Assessment of Notched Bainitic Functionally Graded Steels under Mixed Mode (I + II) Loading

The averaged value of the strain-energy density over a well-defined volume is one of the powerful criteria to assess the static strength of U- and V-notched specimens. This contribution is the first to investigate the effect of notch parameters (notch radius, notch depth and notch opening angle) for fracture assessment of specimens weakened by blunt V-notches made of bainitic functionally graded steels under mixed mode loading (I + II). A numerical method has been used to evaluate the boundary of the control volume, the mean value of the strain-energy density and the critical fracture load. Different values of the notch radius (0.5, 1.0, 1.5 and 2.0 mm), notch depth (5.5, 6.0 and 6.5 mm), notch opening angle (30°, 60° and 90°) and distance of the applied load from the notch bisector line (5 and 10 mm) have been considered. Moreover, this contribution shows that the mean value of the strain-energy density over the control volume can also be accurately determined from a coarse mesh for functionally graded steels.     

Tensile fracture analysis of V-notches with end holes by means of the local energy

This paper deals with investigating brittle fracture in V-notches with end holes under mode I loading. Thirty-six fracture test results, reported most recently in the literature on a new notched disk-type specimen, namely the Brazilian disk containing central VO-shaped notch made of polymethyl-metacrylate, were theoretically predicted by means of the well-known brittle fracture criterion, namely the strain energy density over a critical control volume which embraces the notch edge. A very good agreement was shown to exist between the experimental and theoretical results.     

A successful combination of the equivalent material concept and the averaged strain energy density criterion for predicting crack initiation from blunt V-notches in ductile aluminum plates under mixed mode loading

Crack initiation from blunt V-notch borders in ductile A16061-T6 plates is investigated experimentally and theoretically under mixed mode I/II loading. Experimental observations with naked eye during loading indicated large plastic deformations around the notch tip at the onset of crack initiation, demonstrating large-scale yielding failure regime for the aluminum plates. To theoretically predict the experimentally obtained value of the maximum load that each plate could sustain, i.e. the load-carrying capacity, without performing elastic-plastic failure analyses, the equivalent material concept (EMC) is combined with a well-known brittle fracture criterion, namely the averaged strain energy density (ASED) criterion. It is shown that the combined EMC-ASED criterion could successfully predict the experimental results for various V-notch angles and radii.     

Ultrasonic guided wave parameters for detection of axial cracks in feeder pipes of PHWR nuclear power plants

The dispersion curves for the feeder pipes in PHWR nuclear power plants were determined. The wave modes used for the detection of notches in the feeder pipe were confirmed as F(m,2) and/or L(0,1) by an analysis of short time Fourier transformation (STFT). The axial notches in the straight pipe were not detectable, but an axial notch in a bent pipe was detected with the mode at the frequency of 500 kHz. Initial F(m,2) and/or L(0,1) modes contains a circumferential displacement and might be converted to certain complicated modes in the bent region, which is sensitive to the axial notch. The circumferential guided wave technique was also applied for quantitative evaluation of the axial notches. The waves generated by a rocking motion of the transducer along the circumferential direction were estimated as the circumferential guided waves after a review of the acquired data and the dispersion curves.     

Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch

Mode conversions of Lamb waves can occur upon encountering damage or defect such as a notch, leading to newly-converted modes apart from wave reflection and transmission. In this paper, the transmission of the fundamental Lamb modes symmetrical S0 and anti-symmetrical A0 with anti-symmetrical notches were investigated in steel plates within the relatively short propagation distance. The group velocity and modal energy of the converted modes were analyzed using simulations and experiments. Two-dimensional finite difference time domain (2D-FDTD) method was employed to calculate the scattering field and extract numerical trends for simulation study and experimental confirmation. Both simulations and experiments revealed that the apparent group velocities of the converted modes in the transmitted signals subject to the notch positions. To describe the mode conversion degree and evaluate the notch severity, wave packets of the originally-transmitted modes and newly-converted modes were separated and corresponding mode energy percentages were analyzed at different notch severities. Frequency-sweeping measurements illustrated that the modal energy percentages varied monotonically over the notch-depth increase with a statistically consistency (R = 1.00, P < 0.0004).     

On the use of hollow tube geometries for resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.     

激光-载荷联合作用下碳纤维／环氧树脂板的断裂阈值研究

 介绍了激光 载荷联合作用下碳纤维/环氧树脂编织复合材料单边缺口板断裂的实验和理论研究。实验测量了断裂阈值曲线,并结合显微观察确定了三种断裂模式：热应力、热减薄和热击穿模式。获得了热应力模式断裂的理论判据,与实验结果基本吻合。该判据建立了断裂临界条件下热－力和几何参数与材料性能参数之间的关系。     

Impact toughness of EK-181 ferritic-martensitic chromium (12%) steel under loading by concentrated bending

The low-temperature fracture of a high-temperature low-activated ferritic-martensitic EK-181 chromium (12%) steel (RUSFER-EK-181: Fe-12Cr-2W-V-Ta-B) is studied using impact and static concentrated bending tests as a function of the specimen dimensions (standard, small), the type of stress concentrator (V-shaped notch, fatigue crack), and the temperature (from −196 to +100°C). The ductile-brittle transition temperature falls in the range from −85 to +35°C. The temperature dependences of stress-intensity factor K _Ic and fracture toughness J _Ic are determined. The severest type of impact toughness tests is represented by tests of V-notched specimens with an additional fatigue crack and two lateral V-shaped notches (three-sided V-shaped notch with a central fatigue crack). The fracture energy of the steel depends on the type of stress concentrator and the specimen dimensions and is determined by the elastic energy and the plastic deformation conditions in the near-surface layers of a specimen, which are controlled by the lateral notches. At the same test temperature, the impact toughness and the fracture toughness are interrelated. Irrespective of the type of specimen (including notches and a fatigue crack), the ferritic-martensitic steel exhibits the same fracture mechanism.