Effect of size and location of spherical pores on transverse rupture strength of WC-Co cemented carbides

The effect of the size and location of spherical pores on the transverse rupture strength of WC-10Co cemented carbides was investigated. Based on the observations of fractographies of the transverse rupture test specimens, it was found that the cracks in WC-10Co cemented carbides initiate from the spherical closed pores near the surface, not from the open pores at the surface. The relationship between the transverse rupture strength and the size and location of the spherical pores was analyzed considering the stress field near the spherical shaped pores. In this analysis, for one spherical pore, a critical location exists within the specimen where the transverse rupture strength is minimized, but not on the surface of the specimen. By considering the various sizes and locations of pores, a map showing the transverse rupture strength according to the location and size of pores was obtained.     

Grain size effect on wear resistance of WC-Co cemented carbides under different tribological conditions

The grain-size dependence of wear resistance of WC-Co cemented carbides(with mean WC grain sizes of 2.2 μm,1.6 μm,0.8 μm and 0.4 μm,respectively) was investigated under different tribological conditions.The results showed that the grain size had opposite effects on wear resistance of the cemented carbides in dry sliding wear and microabrasion tests.In the former condition,with decrease of WC grain size hence the increase of hardness,plastic deformation,fracture,fragmentation and oxidation were all mitigated,leading to a drastic decrease in the wear rate.In the latter condition,pull-out of WC grains after Co removal dominated the wear,so that the hardness of cemented carbide was not a core factor.As a result,the wear resistance of the cemented carbide generally showed a decreasing trend with decrease of the grain size,except for a slight increase in the ultrafine-grained cemented carbide.Single-pass scratching of the cemented carbides under various loads indicated the same failure mechanism as that in the sliding wear tests.Furthermore,the reasons for severe surface oxidation of the coarse-grained cemented carbides were disclosed.     

Influence of bimaterial interface on kinking behaviour of a crack growth emanating from notch

The mechanism of crack deviation by an interface modifies considerably the behaviour of bimaterials fracture. Their fracture resistance is highly affected by the difference of the elastic properties of the bonded materials. In this work, the finite element method is applied to analyze the behaviour of a crack emanating from semicircular notch root growing in interface ceramic/metal composites and perpendicularly to this interface. The obtained results showed that the crack grew to interface from harder material, its energy decreased at the approach of the interface, in this case was retarded; an inverse phenomenon occurs if the crack is propagated towards a lower strength material and its energy increases, it has tendency to accelerate. The effects of geometry on the crack deflection near the interface are also discussed.     

Influence of disbond on notch crack behaviour in single bonded lap joints

The behaviour of the adhesive bonded joints due to the imposed eccentric loading generates a very complex distribution of the stress in the structure. Good adhesion between substrate and adhesive ensures a successful and lasting assembly. In this study the finite element method is used to analyze the behaviour of a bonded lap joint of dissimilar materials. The effects of the mechanical properties of the joints on the shear stress variation with and without presence of a circular notch are investigated. The results show that the maximum shear stresses are located at a distance of about 18% that of the lap length whatever the type of material used. In addition, the stress intensity factor is amplified by the presence of the negative effect of disband whose increase is linearly proportional to the square of the stress intensity factor. It reached its maximum value for a crack length equal to two-fifths of the notch radius.     

Investigation of failure criteria for a sharp notch

In this study, a method of evaluating the static strength of a V-shaped notch based on the singular stress field at the notch tip is studied. The singular stress fields is defined by two parameters, and , which correspond to the intensities of symmetric stress field and the skew-symmetric field, respectively. Four kinds of fracture criteria are considered; two of them are based on the tensile strength σ _B and the other two are based on the fracture toughness K _IC . The usefulness of the criteria is investigated through the experimental results carried out on plane specimens of acrylic resin having a sharp notch for various notch configurations such as the opening angle, the inclined angle and the notch depth. It is shown that the criteria using stress intensity factor and the energy release rate not sensitive to the length of the virtual crack .     

Influence of notch root radius on ductile rupture fracture toughness evaluation with Charpy-V type specimens

The blunt notch fracture toughness of four types of carbon-manganese steel (ASTM A516 grade 70) has been determined by J-integral tests on Charpy-V type samples with different values of notch root radius, ρ. J-ρ plots, determined using specimens with a notch depth to width ratio, a/w, equal to 0.5, have shown the existence of a limiting ρ value (ρ_eff) below which applied J-intergral values at fracture initiation are constant. These ρ_eff values have been seen to depend only on second-phase particle distribution and not on their volume fraction or on the steel ferritic grain size. The procedure for deriving J-integral values at the onset of stable crack growth from J resistance curves in the case of notches has also been discussed. Experiments with Charpy specimens with a/w = 0.2 do not allow the derivation of meaningful J-ρ plots. In all cases, a ductile fracture criterion based on the constancy of the notch tip strain at rupture initiation has been proved when ρ >ρ_eff.     

Numerical analysis of the notch effect and the behaviour of notch crack in adhesively bonded composite laminates

In this study the finite element method is used to analyse the notch effect and the behaviour of notch cracks in adhesively composite laminate under tension by computing respectively the stress concentration factor at the notch tip which characterize the notch strength and the stress intensity factor at the crack tip which characterize the resistance to the crack propagation. The effects of the adhesive properties and fiber orientation on the variation of both stress concentration and stress intensity factors are highlighted. The obtained results show that the notch strength is reduced in the layer of the laminate of which the fiber orientation is in the applied load direction; the resistance to the crack propagation is also reduced in this type of layer. The stress intensity factor at the tip of notch crack exhibits an asymptotic behaviour as the crack length increases.     

Rate and microstructure influence on the fracture behavior of cemented carbides WC-Co and WC-Ni

Tungsten carbide has both industrial and military applications, from high strength end mill dies and geological drilling, to kinetic energy penetrators. In these extreme environments, an understanding of the dynamic fracture properties and the potential influence of grade microstructure is necessary. The present work investigates fracture behavior of cobalt and nickel cemented tungsten carbide with varying grain size and binder content. Notched hardmetal WC-Co and WC-Ni samples are impacted under mode-I (opening) fracture conditions, and the dynamic stress intensity factor is determined from digital image correlation using ultra high-speed imaging, and compared with quasi-static values. In both grain size and binder content variants examined, the dynamic fracture toughness increased from the quasi-static by a factor of 1.51–2.44. In addition, a 7% increase in cobalt binder content (while maintaining nominally identical average grain size) resulted in a 20% increase in quasi-static fracture toughness, from 8.62 to 10.38 MPa\(\sqrt{\text {m}}\); while the same binder increase resulted in a 34% decrease in critical SIF from 21.07 to 15.72 MPa\(\sqrt{\text {m}}\). The 6% nickel binder WC was found to have a 4.5% higher quasi-static fracture toughness than the 6% cobalt binder WC of the same grain size, but a statistically insignificant difference under dynamic loading. Overall, there is a 28% increase in the quasi-static fracture toughness of tungsten carbide samples with an increase of average grain size from 1 to 3 \(\upmu \)m, and under dynamic loading the larger grain WC shows a nominally identical increase in fracture toughness. These findings are discussed within the theory of classical dynamic fracture mechanics, the implications of the experimental configurations pursued, and the microstructural features are examined using fractography.     

Influence of carbides morphology on fracture toughness of cast steel G200CrMoNi4-3-3

We analyze the influence of small modification of chemical composition of G200CrMoNi4-3-3 cast steel on the morphology of carbides and on material crack resistance. Using the Termo-Calc software the volume fraction of carbide phase was determined and the results correlated with microstructure observations. Crack resistance of cast steel was determined using SENB specimens and finding critical values of stress intensity factor K_Q. Metallographic and fractographic observations of fracture surfaces allowed identifying the mechanism of cracking. __________ Translated from Problemy Prochnosti, No. 1, pp. 137–140, January–February, 2008.     

Stress intensity factors for cracked T-sections and dynamic behaviour of T-beams

This paper presents an extension of a simple and convenient method proposed by Kienzler and Herrmann [An elementary theory of defective beams. Acta Mech 1986;62:37-46] to estimate the stress intensity factors of cracked beams and bars. This method is based on an elementary beam theory estimation of the strain energy release as the crack is widened into a fracture band. As an extension, the power of the simple beam theory analysis is demonstrated by application to cracked T-beams subjected to a bending moment, shear forces and a torsion. Moreover, the present work addresses the coupled bending-torsional vibration of cracked T-beams within the context of the dynamic stiffness matrix method of analysing structures.     

Fracture toughness evaluation of a H.S.L.A. steel

The fracture toughness, J_Ic of a 3.5 Ni-Cr-Mo-V steel has been measured using the ASTM method. The results have been used to predict the stress intensity factor, K_Ic from the relationship between linear elastic and elastic-plastic fracture parameters. These predicted values were compared with K_Ic values obtained from empirical equations based on valid K_Ic tests, involving the Charpy upper shelf energy. It was found that the ASTM method for measuring J_Ic led to conservative estimates of K_Ic.     

The effect of binder thickness and residual stresses on the fracture toughness of cemented carbides

Much of the data on WC-Co cermets show that the fracture toughness,K _Ic, increases with increasing tungsten carbide grain size at fixed volume fraction of the cobalt binder phase. It is shown that the origin of this effect can be explained on the basis of the plane stress fracture of constrained cobalt phase and the periodic internal stresses arising due to differential thermal contraction of the two phases. Quantitative models have been derived which take these two effects into account. The effect of macroscopic residual stresses, such as those generated by milling WC-Co drilling inserts, on the apparent toughness has also been analysed. It is shown that for the chevron-notched type specimen the macroscopic residual stress affects not only the maximum load but also the length of the crack at which the maximum occurs. A graphical method is presented which permits the evaluation of the true K_Ic.     

Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor

In this paper we investigate the stress intensity factors (SIFs) of multiple penny-shaped cracks in an elastic solid cylinder under mode I (axial tension) loading. The cracks are located symmetrically and in parallel to one another in the isotropic cylinder. The fractal-like finite element method (FFEM) is employed to study the interaction of multiple cracks and to demonstrate the efficiency of the FFEM for multiple crack problems. The results show that the SIF values of the inner cracks, which are denoted as crack number 1,2,3,…,(n+1)/2 of a stack of n parallel cracks, are lower than the SIF values of a single crack by between 16% and 48%. Also, the outermost crack, that is the crack closest to the boundaries of a multiple cracked body, has the highest SIF values and is, therefore, likely to fail first.     

Stress intensity factor computation using the method of fundamental solutions

In this paper, we study the application of the method of fundamental solutions to the computation of stress intensity factors in linear elastic fracture mechanics. The displacements are approximated by linear combinations of the fundamental solutions of the Cauchy–Navier equations of elasticity and the leading terms for the displacement near the crack tip. The applicability of two formulations of the method is demonstrated on two mode I crack problems, where it is shown that accurate approximations for the stress intensity factors can be obtained with relatively few degrees of freedom. Parts of this work were undertaken while the first author was a Visiting Professor in the Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401, U.S.A.     

A quantitative evaluation of fatigue crack shielding forces using photoelasticity

The mechanisms controlling the phenomenon of plasticity-induced shielding during fatigue are investigated and quantified by fitting a recently developed model to photoelastic data. The model derives from the Muskhelishvili approach and includes additional terms to describe the effect of plasticity on the elastic stress field around the crack tip. The photoelastic technique used a polycarbonate CT specimen containing a naturally propagating fatigue crack from which full-field data was obtained digitally using the phase-stepping method. The model was fitted to approximately 1000 data values for the isochromatic fringe order around the crack tip and generated values for the stress intensity factor and T-stress plus an interfacial shear stress intensity factor and a retardation intensity factor which together characterize the influence of plasticity on crack growth.     

Influence of the fracture softening behaviour of wood on load-COD curve and R-curve

A cohesive crack model is used to analyse failure of wood in mode I along the grain. Several configurations of the gradual fracture softening behaviour of an interface, meshed with joint-elements located on the potential crack path, are investigated. Different constitutive laws, obtained from a single normalized polynomial function, are tested in order to estimate the influence of parameters such as, the tensile strength, the fracture energy or the ultimate opening of the interface, on the macroscopic response of a fracture specimen. Numerical results are compared with experimental data obtained on DCB specimen. We argue that the fracture energy related to the constitutive law must correspond to the plateau value of the R-curve. Moreover, this study reveals that the peak load of a load-COD (Crack Opening Displacement) curve is strongly affected by the slope of the softening behaviour. Finally, we present a review of the influence of each parameter describing the softening function on: (1) the load-COD curve and (2) the corresponding R-curve.     

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.     

Analysis of fracture behaviour of the cement mantle of reconstructed acetabulum

In this study, the finite element method was used to analyse the crack behaviour in the cement of a reconstructed acetabulum by computing the stress intensity factors at the crack tip. Three loading cases were examined (Fig. 6). These cases present the different human body postures. Both positions and orientations of crack effect on the SIF variation were analysed. When valuating the crack position effect, one notices no risk of crack propagation under the load type 1; however, under the load type 2 and the load type 3 this risk is more important. Load type 3 is the most dangerous loading condition. When computing crack orientation, one noted that the risk of crack propagation is higher when the crack inclination is 20° and 100°.     

Comments on the evaluation of the stress intensity factor for a general re-entrant corner in anisotropic bi-materials

This paper illustrates an efficient contour integral procedure to obtain stress intensity factors in combination of the asymptotic analysis with finite element analysis. Note that this set-up is very general: the material can be anisotropic elastic, and the specimen can be built as a bi-material system, notches of arbitrary opening angle can be analyzed (γ = 0 → crack, γ = 180° → free edge).The purpose of this technical note is to comment on three issues in the notch mechanics: the interpretation of the eigenvalue equation, the definition of stress intensity factors, and the effect of the outer contour location on H-integral evaluations.