Fatigue crack growth analysis of a premium rail steel

The fatigue crack growth behavior of a premium rail steel was studied using the Modified Crack Layer (MCL) theory. The rate of energy expended on damage formation and evolution within the active zone was evaluated from the hysteresis energy of unnotched and notched specimens. Due to head hardening of the rail, there is a vertical microstructure gradient inside the rail. In this work, the fatigue test specimens were sliced longitudinally from the head of a new rail near the web which represents the microstructure of the base material. The notch length to sample width ratio (a/w) was 0.1. Fatigue tests were performed on both unnotched and single edge notched (SEN) specimens under tension-tension load control condition at 5 Hz. The maximum fatigue stress was 200 MPa, which is about 40% of the yield strength of the material. The minimum to maximum stress ratio was 0.1. The crack length, number of cycles, and hysteresis loops were recorded during the tests from which the crack speed, the energy release rate, and the hysteresis energy for both notched and unnotched specimens were determined. The rate of energy dissipation on damage formation was evaluated based on the difference between the hysteresis energy for the notched and the unnotched specimens. These data were used in the MCL theory to extract the specific energy of damage, ; a material parameter characteristic of the fatigue crack growth resistance of the rail steel. It was found that the value of is 1300 kJ/m³. Three distinctive stages of crack growth kinetics were observed; crack initiation, stable crack growth and unstable crack growth. Microscopic examination of the active zone revealed damage species in the form of microcracks, inter-granular separation, and plastic deformed material. It is these damages that have led to the crack deceleration in the second stage. The fracture surface was also examined. The initiation region showed drawn-out lamellar pearlite. Ductile tearing and coarse ridges with intensive lamellar formation as well as microcracks were observed in the second region. The formation of these damage species has also contributed to the crack deceleration in the second stage of fatigue crack growth kinetics. The unstable crack growth region displayed cleavage facets initiated from the grain boundaries.     

Low-cycle fatigue strength under step loading of a Si3N4 + SiC nanocomposite at 1350°C

The low-cycle fatigue behaviour of a hot pressed silicon nitride/silicon carbide nanocomposite and a reference monolithic Si₃N₄ have been investigated in 4-point bending at 1350°C in air using stepwise loading. The nanocomposite was prepared using 20% of SiCN amorphous powder as an additive, together with 5% yttria, to crystalline -silicon nitride powder. Two types of specimen have been tested, with and without a sharp notch (notch tip radius 10 m) at applied loads from 50 N with steps of 25 N and from 50 N with steps of 50 N, respectively. Five cycles have been performed at all applied load levels with an amplitude of 50 N for both types of specimen. The deflection of the specimens has been recorded up to specimen failure. The failure load of the unnotched nanocomposite was significantly higher than that of the monolithic material whereas for the notched specimens only a small difference has been found between the failure loads of the monolithic and the composite. Notched specimens of both materials exhibited a similar size of the slow crack growth area at catastrophic fracture, whereas for unnotched specimens the size of the slow crack growth area was significantly larger for the monolithic ceramic. The nanocomposite exhibits higher fatigue strength due to its higher resistance against stress corrosion damage and stress corrosion crack growth.     

Unification of strength scaling between unidirectional,quasi-isotropic,and notched carbon/epoxy laminates

An investigation into size effects and notch sensitivity in quasi-isotropic carbon/epoxy laminates was carried out. The purpose is to draw a complete picture of the strength scaling in unidirectional, quasi-isotropic, and notched carbon/epoxy laminates. A link was established between the strength scaling of the unidirectional and quasi-isotropic laminates. Efforts were made to understand the relationship between unnotched and open-hole strengths. For very small holes, the notched strengths approach the unnotched strength limit. A scaling law based on Weibull statistics was used to predict the unnotched laminate strengths. For very large holes, the same scaling law in conjunction with a detailed 3D ply-by-ply FE analysis with matrix cracks in the 90° plies and delamination cohesive interface elements was used to predict the large notched strengths. A good agreement between the modelling and experimental results was achieved. The effects of 90° matrix cracks on unnotched and notched strengths were also studied.     

Matrix-Dominated Damage in Notched Cross-Ply Composite Laminates: Experimental Observations

The matrix-dominated damage in three highly transparent notched cross-ply laminates with double-edge-semicircular notches were experimentally investigated under a monotonously increasing quasi-static tensile load. A newly designed computer controlled digital camera-video recorder system was successfully used to record the real time damage development due to the enhanced stresses around the notches. The damage states were quantitatively characterised as a function of the nominal strain or stress. It was observed that the notches have significant influences on the formation and propagation of the matrix-dominated subcritical damage. The damage states, which depend on the type of the laminate and the size of the notches, appeared to be highly reproducible. Instead of the conventional longitudinal cracks (splits) and the free-edge delamination in unnotched specimens, notch-induced splits (NISs) and notch-induced delamination (NID) were observed. The notches speed up the transverse damage growth in the areas near the notches, both in density and in length. The ultimate strength of the laminates with different notch size is significantly different, due to the diversities of the final failure mechanisms. The notch size and the laminar thickness are two key parameters determining the mode of the matrix damage and the final failure mechanisms of the laminates.     

The effective surface energy of brittle materials

The effective surface energy of four brittle materials, alumina, poly(methylmethacrylate), glass, and graphite, is calculated from load/deflection curves of notched bars deformed in three-point bending. Two of the methods, which are commonly used in fracture mechanics studies,viz the modified Griffith treatment and the compliance analysis method, are concerned with the effective surface energy at the initiation of fracture, _I . The third method, the work of fracture test, is concerned with the mean effective surface energy over the whole fracture process, _F . The two estimates of _I give consistent values, and there is no systematic variation of _I with notch depth. Values of _F decrease with increasing notch depth as the fracture process becomes more controlled. For alumina _{I F} . For PMMA and glass _I > _F because of a multiplicity of crack sources during fracture initiation. For graphite _I < _F because of subsidiary cracking as fracture proceeds.     

Determination of essential work of necking and tearing from a single tensile test

The energy (or work) characterizing the resistance of a structure to ductile fracture is important for many applications, from structural design to impact protection. Essential work of fracture (EWF) is one such measure traditionally associated with the specific energy, per unit cross sectional area, consumed during ductile fracture in a double edge notched tensile (DENT) specimen. This energy is referred to as essential in order to distinguish it from the non-essential energy consumed on distributed plastic deformation accompanying fracture, but not required for material separation. The present article describes how the essential work of tearing can be determined from a single tensile test on an unnotched specimen. Tensile tests were performed on unnotched dog-bone (DB) tensile specimens carrying large numbers of markers, with continuous measurement of elongation between any two markers using a laser scanning extensometer. From such single test it is then possible to obtain multiple load-elongation curves for a large number of tensile specimens. This data is analyzed by separating contributions to specimen elongation made by distributed (pre-softening) and localized (post-softening) plastic deformation. Essential and non-essential work of necking and tearing is determined for an aluminum alloy subjected to different heat treatments, and results compared with those obtained from conventional DENT tests.     

Strength characterization of yttria-doped sintered silicon nitride

The flexural strength of yttria-doped sintered silicon nitride was evaluated as a function of temperature (20 to 1300 C in air environment), applied stress and time. Two mechanistic regimes were manifest in the temperature dependence of the fracture stress. A temperature-independent region of fast fracture (catastrophic crack extension) existed up to 900 C, in which the mode of crack propagation was primarily transgranular. Above 1000 C, the strength (fracture stress) decreased considerably due to the presence of subcritical or slow crack growth which occurred intergranularly. This material did not show a static oxidation problem in short-term (100 h) tests in the low-temperature regime (600 to 1000 C) as has been observed in other yttria-doped silicon nitrides. Flexural-stress rupture testing in the temperature range 800 to 1200 C in air indicated the material's susceptibility to time-dependent failure, and outlines safe applied stress levels for a given temperature.     

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.     

Fracture toughness and absorbed energy measurements in impact tests on brittle materials

Previous work on impact testing has shown that the energy/unit area (w) normally measured in notched impact tests is dependent on specimen geometry. A fracture mechanical analysis has now been developed to account for the observed dependence ofw on notch size. A correction factor () has been derived to accommodate notch effects and this allows for the calculation of the strain energy release-rateG directly from the measured fracture energies.Tests on PMMA have shown that corrected results are independent of specimen geometry and theG _c for PMMA has been evaluated as 1.04 × 10³ J m^–2. The experimental results show that there is an additional energy term which must be accounted for and this has been interpreted here as being due to kinetic energy losses in the specimens. A conservation of momentum analysis has allowed a realistic correction term to be calculated to include kinetic energy effects and the normalized experimental results show complete consistency between all the geometries used in the test series.It is concluded that the analysis resolves many of the difficulties associated with notched impact testing and provides for the calculation of realistic fracture toughness parameters.     

The role of delamination in failure of fibre-reinforced composites

The mechanisms by which delamination contributes to the failure of fibre-reinforced composites are reviewed. Through-thickness failure owing to interlaminar stresses is considered first, and the effect of delamination in impact and compression after impact. The way in which in-plane failure can occur by delamination and matrix cracks joining up to produce a fracture surface without the need to break fibres is considered next. Examples of quasi-isotropic laminates loaded at different off-axis angles, and with different numbers and thicknesses of ply blocks show large differences in unnotched tensile strength controlled by delamination from the free edge. Similar mechanisms determine the strength of notched specimens and give rise to the hole size effect, whereby tensile strength increases with decreasing hole diameter owing to increased delamination and splitting. Open hole tension and over-height compact tension tests with constant in-plane dimensions show a transition in failure mode with increasing ply block thickness from fibre-dominated fracture to complete delamination. In all these cases, the critical factor controlling strength is the relative propensity to delaminate.     

Effects of sizes of ferrite grains and carbide particles on toughness of notched and precracked specimens of low-alloy steels

Four point bending (4PB) tests of notched specimens and COD tests of precracked specimens were carried out on two steels; one steel was treated into two groups with the same ferrite grain size but different carbide sizes, the other steel with different ferrite grain sizes but similar carbide sizes. The results of the tests show that the toughness measured in notched specimens is mainly determined by the grain sizes, which define the local fracture stress _f; the size of carbide particle plays a minor role. However, on the contrary, in precracked specimens the toughness is sensitive to the carbide sizes, which affect the critical plastic strain _pc for initiating a crack nucleus; the effect of grain size is indistinct. By these inferences the behavioral discrepancy of large grain steel in improvement of crack fracture toughness while reducing the notch toughness is explained.     

Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

The role of microstructure on the fracture toughness and fracture behaviour of rubber-reinforced acrylics

The influence of microstructure on the fracture toughness, unnotched fracture strength, Young's modulus and fracture mechanism of polybutadiene-reinforced poly(methylmethacrylate)s was investigated. The Young's modulus increased with the degree of dispersion of the polybutadiene phase. A core-shell microstructure with fine ( 1 m) rubber particles gave the highest fracture toughness. Cavitation of the polybutadiene phase was the dominant toughening mechanism with the particulate rubber morphologies, although additionally localized plastic yielding was observed on the fracture surface of the material with a core-shell microstructure. The material with a lamellar-type rubber morphology exhibited a high fracture toughness as a result of the rubber phase redirecting the propagating crack to produce a rough fracture surface.     

The effect of fibre length on fracture toughness and notched strength of short carbon fibre/epoxy composites

The effect of radius of curvature on the tensile notched strength of random short carbon fibre/epoxy composites containing 1, 5 and 15 mm length fibres is studied. The strength of all laminates showed a sensitivity to the radius of curvature, with the tensile strength decreasing at smaller radii of curvature. A model is developed to predict notched strength based on assumed evolution and propagation of damage from the tip of the notch. The predictions of the model depend principally on two material properties: the unnotched tensile strength and fracture toughness. Reasonable agreement is achieved between the predicted notched strength and experimental data.     

Effect of stress concentration on strength and ductility of structural materials

This paper gives the investigation results of static strength and tensile ductility of cylindrical specimens with an annular notch of different sharpness made from 35, 80, and ÉI961 steels, and VT3-1 titanium and D16T aluminum alloys. Empirical dependence of relative increase of notched specimens statical strength on the size of the stress concentration factor is determined. A link has been established between the index of locality of plastic strain _l/_B, characterizing the plastic properties of the material and the stress concentration factor K_t·l corresponding to the transition from viscous to quasibrittle fracture.Translated from Problemy Prochnosti, No. 5, pp. 74–78, March, 1991.     

Cohesive crack models for semi-brittle materials derived from localization of damage coupled to plasticity

Based on discontinuous displacement approximation of the continuum and shear band kinematics, two cohesive crack models are derived within the constitutive framework of coupled damage and plasticity. The models employ the Rankine fracture criterion, and the model parameters are determined from a uniaxial tension test (mode I cracking). Bifurcation analysis is used in order to diagnose critical directions along which the crack will gradually develop and propagate. These directions depend on the actual stress state and are kept fixed after fracture has initiated, whereby a fixed crack model is obtained. A discrete crack strategy is employed at the finite element implementation in the sense that interfaces (that represent the cohesive crack) are introduced along inter-element boundaries. This implementation strategy calls for gradual realignment of the mesh as a key feature of the algorithm. Numerical results from the analysis of mixed mode fracture in a notched concrete plate are presented.     

Analysis of the strength and fracture behaviour of unidirectional and angle-ply graphite-aluminium composites

The tensile behaviour of unidirectional and [±]_s angle-ply P100 graphite-reinforced 6061-Al composites was determined as a function of the angle () between the fibre and the applied load. The experimentally determined values of the elastic modulus and tensile strength of the composites are compared with those predicted from classical laminate theory. The measured elastic modulus values agreed with theoretical values, but the strength of the [\+-\gq]_s angle-ply composites was substantially greater than predicted. The discrepancy between experiment and theory is attributed to the stress required to fail the fibre ply/separator foil interface present in the angle-ply composites. The composite failure modes are also documented, and it is shown that the separator foils of the angle-ply composites shift the transition from tensile to shear failure to greater values of\gq relative to the off-axis unidirectional composites.     

Size-strength effects in sapphire and silicon nitride whiskers at 20° C

Tensile tests at 20° C have been carried out on seventy-three sapphire whiskers and on seventeen silicon nitride whiskers. The sapphire whiskers were of 0001, 1¯120, 10¯10, and 10¯11 orientations, while the silicon nitride whiskers were 0001, 11¯20, and 10¯13. Tensile strengths were in the range 45 to 1500 kg/mm², and deformation was found to be purely elastic. The tensile strength data have been analysed and fitted to empirical equations describing the effect of size on strength for different orientations. These empirical equations have been used to deduce possible fracture nucleation mechanisms. It is concluded that, in the case of 0001 sapphire whiskers, fracture nucleation may be due to dislocation pile-ups or interactions, while in the other cases a Griffith flaw mechanism is probably applicable.     

Tensile fracture of centre-notched angle ply (0/±45/0)S and (0/90)2S graphite — epoxy composites

The fracture behaviour of centre-notched (0/± 45/0)_S and (0/90)_2S laminates with increasing notch length has been studied. Two test series have been investigated: specimens of constant width (W=20 mm) and small notch length (2a 12 mm), and specimens with various notch lengths (5 2a 35 mm) and a constant relative notch length (2a/W=0.5). An X-ray technique showed that the damage at the notch tip, which is formed at increasing load, consists mainly of subcracks parallel to the fibres of the constituent layers. The damage zone causes the crack opening displacement (COD) to deviate from the original linearity. TheK _R curve concept has been applied assuming that the COD deviation from linearity is completely the result of original crack extension. This approach fails to describe the notch length effect, because a tangent point between theK _R andK curves was not found and because of a strong dependency of the maximum fracture resistanceK _Rmax on notch length. The fracture behaviour of 20 mm wide specimens could be explained with the point and average stress criteria, based on characteristic lengths which are independent of notch length. At various notch lengths at a constant 2a/W=0.5, however, the characteristic lengths increased with increasing notch length.     

Tensile testing of MEMS materials—recent progress

Tension tests, while standardized for common structural materials, are currently being developed and used for MEMS materials by a small number of researchers. This paper presents recent progress at Hopkins in four areas: Comparison of the tensile test method with different approaches; agreement is found with Young's modulus measurements from membrane tests and with fracture strengths from other tensile tests. Tension-tension fatigue; increased life with decreased applied stress is measured, yielding S-N plots similar to those of metals. Stress versus axial and lateral strain of thick-film silicon carbide; Young's modulus = 420 GPa, Poisson's ratio = 0.21, fracture strength = 0.8 GPa. Polysilicon stress-strain behavior at high temperatures; it deforms inelastically at temperatures above 750°C