Influence of nanometre-sized notch and water on the fracture behaviour of single crystal silicon microelements

The influence of a notch and a water environment on the quasi‐static and fatigue fracture behaviour was investigated in single crystal silicon microelements. The tests were conducted in smooth and notched microcantilever beam samples. Smooth specimens were prepared by micromachining (photo‐etching) of (110) silicon wafers. For some specimens, a nanometre‐sized notch was machined 100 μm away from the sample root by using a focused ion beam system. A machining condition was optimized, and the V‐shaped notch was successfully introduced. The radius of curvature of the notch, measured by an atomic force microscope (AFM), decreased with an increase in notch depth, and ranged from about 20 to 100 nm. Single‐crystal Si microelements deformed elastically until final failure, which was of a brittle nature. The maximum fracture strength of a smooth microcantilever specimen reached about 7.7 GPa, which was higher than that obtained in millimetre‐sized single crystal Si samples. However, the fracture strength decreased with an increase in notch depth, even though the notch depth was of the order of a nanometre. This means that a nanometre deep notch, which is often regarded as surface roughness in ordinary‐sized mechanical components, caused a decrease in the fracture strength of Si microelements. The fracture initiated at the notch, and then the {111} crack propagated in the direction normal to the sample surface. Fatigue tests were also conducted in laboratory air and in pure water at a stress cycle frequency of 0.1 Hz and a stress ratio of 0.1. In laboratory air, no fatigue damage was observed even though the surface was nanoscopically examined by an AFM. However, when the fatigue tests were conducted in pure water, the fatigue lives in water were decreased. Crack formation on the {111} plane was promoted by a synergistic effect of the dynamic loading and the water environment. Atomic force microscopy was capable of imaging the nanoscopic cracks, which caused failure in water.     

Mode I Fracture Toughness of CNT‐Reinforced PMMA

The influence of carbon nanotube (CNT) concentration on the fracture toughness of poly(methyl methacrylate) (PMMA) was examined on single‐edge V‐notched‐beam (SEVNB) specimens. Six groups of SEVNB specimens containing 0.5, 1, 2, 4, 8.5 wt% of CNTs and neat PMMA as a reference were tested. First, a notch was introduced into the specimens by a specially made disk whose edge is V‐shaped with a 30^° angle and a 30 μm tip width. As suggested by an American Society for Testing and Materials Standard for polymers, induction of a natural crack was attempted, without success. Therefore, fracture toughness values were determined with the ‘sharp’ machined notch by means of a calibration formula. These were compared to values obtained using a stress concentration factor and found to differ by less than 3%. The latter calculation takes into account the geometry of the notch. Results showed a decrease in the fracture toughness values with an increase in the CNT concentration. For specimens in which a natural crack was attempted, referred to as a razor‐cut notch, a significant increase in the apparent fracture toughness was observed, as a result of the induced damage.     

Fatigue of casting flaws at a notch root under an SAE service load history

Smooth and notched specimens of a 319 cast aluminium alloy were fatigue tested under a Society of Automotive Engineers service load history in the as-cast and hipped conditions. The hipping process, which includes subjecting the cast material to a high pressure at high temperature and then slowly cooling down to eliminate internal flaws, decreased the flaw size and improved the fatigue life of cast Al 319 smooth specimens. A 0.6-mm-diameter hole was drilled at the notch root of notched specimens to simulate a natural flaw at the notch root. Specimens with two different notch sizes were tested. Circular edge notches reduced the fatigue strength and a 0.6-mm-diameter drilled hole at the notch root resulted in a further reduction.
The fatigue lives of smooth specimens, notched specimens and notched specimens with a flaw at the notch root subjected to the service load history were predicted using the strain-life approach, an effective strain-life approach and a strain-based intensity factor crack growth model. In crack growth modelling of the fatigue life of smooth cast aluminium specimens the flaw was modelled as a circular edge notch having the same diameter as the flaw. However, in the case of a flaw at a notch root the flaw was modelled as a three-dimensional cavity subjected to the notch stress field and the crack length was predicted in the longitudinal and transverse directions of the specimen cross-section. The strain-life approach was unconservative for all specimen geometries studied. The effective strain-life approach gave good predictions for smooth and blunt notched specimens but gave very conservative predictions for the specimens with flaws in the notch roots. The crack growth calculations gave accurate predictions for all the specimen geometries.     

NOTCHED FATIGUE BEHAVIOUR OF TWO COLD ROLLED STEELS

Abstract— A SAE1010 plain carbon steel and a SAE945X HSLA steel were cold rolled to various thickness reductions. Centre notched specimens were tested under stress control at a stress ratio of—1. The effect of loading direction on the fatigue strength was examined. The notched specimen fatigue strength was only slightly increased by cold rolling, since two opposing factors: the smooth specimen fatigue strength and the notch sensitivity, were increased by cold rolling. The notched specimen fatigue strength in the transverse direction was approximately the same as that in the longitudinal direction. An empirical equation and equations derived from fracture mechanics and Neuber's rule were applied to predict the fatigue notch factor for the sharp and blunt notch geometries examined. A reasonable agreement between the predictions and the experimental results was observed for the sharp notches. For the blunt notches, the predicted fatigue notch factors were conservative.     

Fatigue life behaviour of TiAlN and TiAlN/CrN coated notched P20 steel specimens

The performance of single layer TiAlN and multilayered TiAlN/CrN physical vapour deposition coatings deposited on AISI P20 steel substrate in affecting overall fatigue resistance of notched specimens was assessed and compared with the performance of the uncoated counterparts. V‐shaped circumferential notches on cylindrical specimens were adopted for fatigue tests. Surface coating characteristics such as hardness, elastic modulus and microstrains were measured and found to be different and often larger than those of the steel substrate. Unlike the un‐notched (smooth) coated specimens, which are known to exhibit large improvements in fatigue life in the high cycle fatigue regime, considerable reductions in fatigue life of the coated notched samples were observed. This was understood to be because of the coating's brittleness, which induces at the notch tip early and frequent fatigue crack initiations, especially in the case of multiple layered coatings. Scanning electron microscope images showed more crack initiation sites in both the coated specimens compared with the uncoated specimen. Also, presence of dimples on the surface confirmed dimple rupture mechanism in the ductile steel substrate in the coated and uncoated specimens.     

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 toughness measurement of thin-film silicon

The fracture toughness of single‐crystal silicon thin films oriented to (100) and (110) was investigated by tensile testing under both 〈100〉 and 〈110〉 loading conditions. The specimen was fabricated from a p‐type Czochralski (CZ)‐grown wafer and passed through a thermal process during the fabrication of the test device. The measured fracture toughness is dependent on the loading direction in the tensile test and independent of the specimen surface orientation. The test results were 1.94 MPa√m in the 〈100〉 direction and 1.17 MPa√m in the 〈110〉. In these tests, no longitudinal size effect on the fracture stress or fracture toughness was observed. The SEM photographs obtained from the fracture specimens after the tensile test show that the crack initiated from the notch tip and propagated straight in the across‐the‐width direction on the (110) or (111) cleavage plane.     

Numerical prediction of notch bluntness effect on fracture resistance of SM490A carbon steel

The present work investigates the notch radius effect on fracture resistance using the finite element (FE) damage analysis based on the multiaxial fracture strain model. The damage model was determined from experimental data of notched bar tensile and fracture toughness test data using a sharp‐cracked compact tension specimen. Then, the FE damage analysis was applied to simulate fracture resistance tests of SM490A carbon steel specimens with different notch radii. Comparison of simulated results with experimental data showed good agreement. Further simulation was then performed to see effects of the specimen size, thickness, and side groove on J‐R curves for different notch radii. It was found that effects of the specimen size and thickness became more pronounced for the larger notch radius. Furthermore, it was found that without side groove, tearing modulus for notched specimens was similar to that for cracked specimens, regardless of the notch radius.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

The fatigue strength of centrifugally cast spheroidal graphite iron pipe

The fatigue strength of centrifugally cast spheroidal graphite (SG) iron pipe was investigated. A parallel series of tests were carried out both on plain plate specimens which were extracted from an iron pipe, and on notched iron specimens. These results were compared with results for rolled steel beams, which were made from a steel with a tensile strength similar to the SG iron [1]. It was found that the strengths at a life of $\text{2 × 10}{}^6$ cycles differed only by 20% between the SG iron pipe and the rolled steel beam, whereas those of plain plate specimens of the two materials differed by 38%. The fatigue failure in the SG iron pipe initiated from the inherent gas pores existing in the inner surface of the pipe, while the fracture in the rolled steel beams originated from external notch defects. Thus, the steel beam appeared more sensitive to the external notches than the SG iron pipe, when the notch size was smaller than 1 mm. However, it was revealed from the fatigue tests on notched plates that, as the notch became severer, the fatigue strength of SG iron became more affected by the notches than did that of the steel. A fracture mechanics analysis indicated that this was because the fatigue crack growth rate for SG iron was three times as high as that for steel.     

Influence of notch severity on thermomechanical fatigue life of a directionally solidified Ni‐base superalloy

The aim of this work is to understand the influence of notches under thermomechanical fatigue (TMF) in a directionally solidified Ni‐base superalloy. Experiments were performed utilizing linear out‐of‐phase and in‐phase TMF loadings on longitudinally oriented smooth and cylindrically notched specimens. Several notch severities were considered with elastic stress concentrations ranging from 1.3 to 3.0. The local response of the notched specimens was determined using the finite element method with a transversely isotropic viscoplastic constitutive model. Comparing the analysis to experiments, the locations observed for crack nucleation in the notch, which are offset from the notch root in directionally solidified alloys, are consistent with the maximum von Mises stress. Various local and nonlocal methods are evaluated to understand the life trends under out‐of‐phase TMF. The results show that a nonlocal invariant area‐averaging method is the best approach for collapsing the TMF lives of specimens with different notch severities.     

Shear fracture tests of concrete

Symmetrically notched beam specimens of concrete and mortar, loaded near the notches by concentrated forces that produce a concentrated shear force zone, are tested to failure. The cracks do not propagate from the notches in the direction normal to the maximum principal stress but in a direction in which shear stresses dominate. Thus, the failure is due essentially to shear fracture (Mode II). The crack propagation direction seems to be governed by maximum energy release rate. Tests of geometrically similar specimens yield maximum loads which agree with the recently established size effect law for blunt fracture, previously verified for tensile fracture (Mode I). This further implies that the energy required for crack growth increases with the crack extension from the notch. The R-curve that describes this increase is determined from the size effect. The size effect also yields the shear fracture energy, which is found to be about 25-times larger than that for Mode I and to agree with the value predicted by the crack band model. The fracture specimen is simple to use but not perfect for shear fracture because the deformation has a symmetric component with a non zero normal stress across the crack plane. Nevertheless, these disturbing effects appear to be unimportant. The results are of interest for certain types of structures subjected to blast, impact, earthquake, and concentrated loads.     

A size effect law for notched tensile strength of woven carbon/epoxy laminates

Specimen-size effect and notch-size effect on the tensile strength of woven fabric carbon/epoxy laminates are evaluated and modeled. For two different layups of [(0/90)₁₂] and [(±45)₂/(0/90)₅]_S, respectively, static tension tests were performed on two-dimensional geometrically similar unnotched and double-edge notched specimens scaled to three different sizes. Experimental results demonstrate that the notched strength of the woven CFRP laminates depend on the size of specimen as well as the size of notch. The ratio of notched strength to unnotched strength decreases as the length of notch increases, regardless of the size of specimen. For a given size of notch, the notch strength ratio becomes larger with decreasing size of specimen. A notch-size effect law is derived by means of the Neuber interpolation method. A specimen-size effect is embedded into the notch sensitivity parameter involved by the notch-size effect law to establish a size effect law that can cope with these two kinds of size effect. The engineering size effect law proposed can adequately describe the specimen-size effect as well as notch-size effect on the tensile strength of the woven CFRP laminates. It is also demonstrated that the size effect law allows determining the size independent fracture toughness on the basis of notched strengths of small specimens that fail in a quasi-brittle manner.     

Advances in the mechanism of cleavage fracture of low alloy steel at low temperature. Part I: Critical event

The critical event of cleavage is variable for different types of specimens made of the same steel. In notched specimens (Charpy V or 4 PB) over a wide temperature range as low as -196°C, the critical event is the propagation of a ferrite grain-sized crack (30-40μm). In precracked specimens at a moderately low temperature (around -110°C) it is the propagation of a second phase particle-sized crack (< 10μm). At ever lower temperatures (-150°C - -196°C) the cleavage fracture is nucleation-controlled. No matter whether a notched specimen or a precracked specimen is used, as long as a fibrous crack has been initiated and propagated in it, the critical event is the propagation of a ferrite grain-sized crack and the fracture behavior can be handled as in a specimen with an acute notch. The difference of ‘σ ’values measured in a notched specimen and a precracked specimen is caused by a change of the critical event in these two specimens. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thickness effect on crack tip deformation at fracture

The crack tip deformation at the onset of surface crack growth for four single edge cracked specimens having four different thicknesses were studied. The specimens were made of the ductile and tough HY-80 steel. The thickness contraction in the crack tip region and the tensile strain in the direction of load were measured. The crack tip necking-in acts like a notch. The depths, the root radii, and the angle changes of the necking-in notches were measured. The results indicated that the near tip strain can be used as a fracture criterion of ductile and tough materials. It was also found that the fracture strengths of the cracked specimens can be correlated with the tensile ductilities measured with Clausing specimens.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

Failure assessment on central-sharp notched carbon/epoxy laminates

Fracture models to predict the strength of laminated composites having sharp notches demand the un-notched strength and the critical damage size ahead of the notch. The critical damage size, in general, depends on the material, geometry of the specimen and size of the sharp notch. The extraordinary success of a fracture model lies in its ability to combine a theoretical framework with experimentally measured quantities. Modifications are made in one of the stress-fracture criteria known as the point stress criterion for accurate prediction of notched tensile strength of composite laminates containing sharp notches. To examine the adequacy of these modifications, fracture data of central-sharp notched carbon/epoxy composite laminates with various lay-ups are considered. The notched strength estimates are found to be close to the test results. The modified point stress criterion is very simple and accurate in predicting the notched tensile strength of laminated composites.     

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.     

A Finite Fracture Mechanics approach to the asymptotic behaviour of U‐notched structures

A Finite Fracture Mechanics (FFM) criterion is formalized to predict the critical failure loads of brittle U‐notched specimens, subjected to mode I loading. The criterion, recently applied to V‐notched structures, requires the contemporaneous fulfilment of stress requirements and energy conditions for fracture to propagate: the stress field ahead of the notch tip and the stress intensity factor related to a crack stemming from the root are involved. Both the apparent fracture toughness and the critical crack advancement result to be structural parameters. For sufficiently slender notches, the root radius becomes the only relevant geometric dimension. The consistency of the approach is proved by the comparison with experimental data available in the Literature.