A note on evaluating the fracture energy of thin ceramic layers by cleavage

A new method is suggested aimed at evaluating _IC , the mode I fracture energy of thin brittle layers. The fracture energy is obtained by cleaving a ceramic layer sandwiched between two metallic layers, joined by brazing. The driving force for the cleavage is the mismatch between the thermal expansion coefficients of the ceramic and the metallic layers. The fracture energy is calculated from the strain energy released in the cleaved sandwiched structure. Based on this method, the fracture energy of the ceramic layer can be evaluated if the cleavage temperature is known, either by visual inspection or instrumentation. The method is effective for thin ceramic layers, for the determination of the fracture energy of cleavage planes of single crystal brittle solids (provided the cleavage plane is within the plane of the specimen), and for the interfacial fracture energy of ceramic/ceramic or ceramic/metal joints. In order to verify and calibrate the test method, polycrystalline alumina thin plates were joined by brazing with Ti-6Al-4V alloy using Wesgo Cusil ABA alloy. The appropriate selection of materials and geometry, and some difficulties arising from this method are discussed.     

Strength Assessment for Butt Joints of Steel 50 by the Fracture Toughness Criteria

We propose an experimental-theoretical engineering procedure for assessing the strength of butt-welded joints using the force (K_Ic) and strain (_c) criteria of the brittle and quasibrittle fracture mechanics, respectively. For this purpose, beam specimens with square and bevel welds and an initial edge crack or notch in the weld metal are tested under three-point bending. The parameter K_Imax controlling fracture of a bent beam with an inclined (Mode I + Mode II) crack is assessed taking into account the values of the stress intensity factors K_I and K_II, and the crack inclination angle ^*. We also studied the plastic zone at the crack tip and the crack propagation kinetics depending on the weld geometry and the V-notch tip radius for butt-welded joints. The data obtained allow one to rate such joints by their strength according to the fracture toughness criteria K_Ic and _c.     

Investigation of the Fracture of Brittle Bodies Due to Their Contact Interaction with Rigid Dies

We propose a theoretical and experimental procedure for determining fracture conditions of brittle bodies subjected to the action of rigid dies of various shapes. Similarly to the fracture mechanics approach, we specify the stress intensity factors K₁ and K₂ in the vicinity of the die base, which determine the conditions of crack initiation, as well as values of the angle between cracks and the specimen base. It is established that upon the specimen compression by the die, the angle of the inclination of the fracture surface to the specimen base plane remains practically unchanged , which agrees fairly well with the theoretical data obtained. Body fragments have been revealed after pressing dies of different types into specimens: in a shape close to a circular cone for a round die, in a shape close to a quadrangular pyramid for a square die, and in a shape close to a triangular prism for a rectangular die.     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities

Crack extension paths are often irregular, producing rough fracture surfaces which have a fractal geometry. In this paper, crack tip motion along a fractal crack trace is analysed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. The ratio of the dynamic stress intensity factor to the applied stress intensity factor K(L(D, t), V)/K(L(t), 0), is a function of apparent crack velocity V_o, microstructure parameter d/a (grain size/crack increment step length), fractal dimension D, and fractal kinking angle of crack extension path . For fractal crack propagation, the apparent (or measured) crack velocity V_o, cannot approach the Rayleigh wave speed Cr. Why V_o is significantly lower than Cr in dynamic fracture experiments can be explained by the effects of fractal crack propagation. The dynamic stress intensity factor and apparent crack velocity are strongly affected by the microstructure parameter (d/a), fractal dimension D, and fractal kinking angle of crack extension path . This is in good agreement with experimental findings.     

Fatigue striation in a wide range of crack propagation rates up to 70 μm/cycle in a ductile structural steel

The relationship between striation spacing and fatigue crack propagation rate up to 70 m/cycle was investigated for a ductile structural steel, qualified as JIS SM58Q. A modified compact-type specimen 400 mm wide and a centre-cracked specimen 200 mm wide were tested at a stress ratio, R, of 0 and 0.8. The fracture surface of the specimen was examined in detail under a scanning electron microscope. The crack propagation rate was expressed by a power function of the range of stress intensity factor from 0.1 to 70 m/cycle for R=0 and to 0.5 m/cycle for R=0.8. The striation spacing coincided with the fatigue crack propagation rate over the range 0.1 to 70 m/cycle. The profile of striation was found to be a ridge and valley type, and the ridges on one fracture surface coincided with those on the matching surface. It is suggested that the striation is formed by a plastic blunting mechanism.     

Slow-crack propagations through bimaterial interfaces studied by scanning electron microscopy

The scanning electron microscope (SEM) is used for the study of slow crack propagation through a bimaterial interface. This work is concerned with the variation of crack velocity, the variation of crack tip opening angle (CTOA) and the stress intensity factor (K) at the crack tip, and the investigation of crack arrest phenomena at the bimaterial interface. It was observed that the crack accelerates to a maximum velocity as the crack tip approaches the interface and then decreases rapidly to a minimum value at the interface. The interface acts as a decelerator to crack propagation. The position and the value of the maximum velocity depends on the mechanical properties of two phases and specimen configuration. The crack propagates at a constant CTOA until it arrests at the interface. During the crack-arrest time the CTOA increases rapidly to a limiting value. Then the crack passes across the interface and propagates in the next phase with almost the same CTOA as the initial crack in phase I. The stress intensity factor,K, increases to a maximum value near the bimaterial interface.     

Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model

This study explores applications of three-parameter Weibull stress models to predict cleavage fracture behavior in ferritic structural steels tested in the transition region. The work emphasizes the role of the threshold parameters (_th and _{w – min}) in cleavage fracture predictions of a surface crack specimen loaded predominantly in tension for an A515-70 pressure vessel steel. A recently proposed procedure based upon a toughness scaling methodology using a modified Weibull stress (^* _w) extends the calibration scheme for the Weibull modulus, m, to include the threshold parameters. The methodology is applied to calibrate the Weibull stress parameter for the tested material and then to predict the toughness distribution for the surface crack specimen. While the functional relationship between ^* _w and m suggests a strong effect of the threshold stress, _th, on the calibrated m-parameter, the results show a remarkably weak dependence of fracture predictions on _th as does the dependence of fracture predictions on _w–min for this specimen.     

Temperature field in a plate containing a system of heat sources

The temperature field is determined in a circular plate with a system of thin extrinsic heat sources.Notation T temperature in the plate with the inclusions - r polar radius - polar angle - time - (r,) coefficient of thermal conductivity - (r,) heat transfer coefficient - C(r,) volume heat capacity - W(r,, ) specific intensity of the heat sources - half thickness of the plate - (x) Dirac's delta function - ¯T finite Fourier cosine transform of the temperature - p parameter for this transformation - T Laplace transform of the temperature - s its parameter - Iv(x) Bessel function with imaginary argument of order - K _v (x) the MacDonald function of order - and dimensionless temperature - Po Pomerantz number - Bi Biot number - Fo Fourier's number - dimensionless polar radius - b₁ ^* dimensionless radius of the circle on which the inclusions are placed - R^* dimensionless radius of the plate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 495–502, March, 1981.     

Coupled double-diffusive thermocapillary instability: Linear and nonlinear analysis

The onset of Marangoni instability of the quiescent equilibrium in a binary liquid layer open to the atmosphere at its nondeformable interface in the no-gravity environment and subjected to the simultaneous presence of the normal temperature gradient and of the tangential temperature and solute concentration gradients is studied. The no-flow equilibrium is possible for specially chosen values of the imposed tangential gradients only. Linear stability analysis shows that the instability is longwave for very small values of the parameter that specifies the ratio between the tangential and normal temperature gradients. For higher values of the instability is shortwave. It is found in the latter case that the instability is always oscillatory for nonzero and for any value of the inverse Lewis number L^-1 1. Weakly nonlinear analysis in the regime of small is carried out to derive the nonlinear evolution equation describing a wave propagation along the layer. The primary bifurcation from the equilibrium state is found to be supercritical for very small values of and becomes subcritical thereafter.     

Extrudate distortion studies of polystyrene using an extrusion rheometer

Uncorrected and corrected logarithmic flow-curves for a general purpose polystyrene (MW=261000 and MW/MN=4.4) obtained using a Davenport Extrusion Rheometer are shown for the range 160 to 200° C. The uncorrected flow curves show a change in slope, but at the lower extrusion temperatures this change occurs after the appearance of distorted extrudates. The onset of extrudate distortion obtained from observation does not coincide with the change in slope of the graph. The corrected logarithmic flow curves show no change in slope. Values of and _c from both sets of graphs show that is inversely proportional to _c, and for the higher melt temperatures the corrected _c values increase with temperature. The high value of critical wall stress at 160° C is attributed to the increase in melt elasticity with decreasing temperature being a greater effect than the decrease in elasticity due to a decrease in .     

Optimum notch configurations for the chevron-notched four-point bend specimens

The failure sequence following crack formation in a chevron-notched four-point bend specimen is examined in a parametric study using the Bluhm slice synthesis model. Premature failure resulting from crack formation forces which exceed those required to propagate a crack beyond is examined together with the critical crack length and critical crack front length. An energy based approach is used to establish factors which forecast the tendency of such premature failure due to crack formation for any selected chevron-notched geometry. A comparative study reveals that, for constant values of ₁ and ₀, the dimensionless beam compliance and stress intensity factor are essentially independent of specimen width and thickness. The chevron tip position ₀ has its primary effect on the force required to initiate a sharp crack. Small values for ₀ maximize the stable region length, however, the premature failure tendency is also high for smaller ₀ values. Improvements in premature failure resistance can be realized for larger values of ₀ with only a minor reduction in the stable region length. The stable region length is also maximized for larger chevron base positions, ₁, but the chance for premature failure is also raised. Smaller base positions improve the premature failure resistance with only minor decreases in the stable region length. Chevron geometries having a good balance of premature failure resistance, stable region length, and crack front length are 0.20 ₀0.03 and 0.70₁0.80NASA Resident Research Associate at Lewis Research Center.     

Interfacial stress state present in a “thin-slice” fibre push-out test

An analysis of the stress distributions along the fibre-matrix interface in a thin-slice fibre push-out test is presented for selected test geometries. For the small specimen thicknesses often required to displace large-diameter fibres with high interfacial shear strengths, finite element analysis indicates that large bending stresses may be present. The magnitude of these stresses and their spatial distribution can be very sensitive to the test configuration. For certain test geometries, the specimen configuration itself may alter the interfacial failure process from one which initiates due to a maximum in shear stress near the top surface adjacent to the indentor, to one which involves mixed mode crack growth up from the bottom surface and/or yielding within the matrix near the interface.     

Torsional boundary layer effects in shells of revolution undergoing large axisymmetric deformation

Numerical and asymptotic solutions are developed to the equations governing large torsional, axisymmetric deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.List of symbols Latin symbols a General dependent variable - a ^(mn) Terms of the asymptotic expansion of a(x) - b Characteristic length - c Scalar curvature components in the normal direction - c , c , , c Cosine of , respectively - C Material constant with units of a Young's modulus - e _i Deformed local orthonormal basis associated with (, s, n)(x ₁, x ₂, x ₃) coordinates - Undeformed cylindrical coordinate basis - Intermediate coordinate basis - g Shear correction factor - H Horizontal stress resultants - l ₁ Strain invariant - k Scalar curvature components - L Undeformed cylinder length - M Moment resultants - M _r, M , M _z Moment resultant components in the basis - N Membrane stress resultants - p Internal pressure - p _H, p _v Horizontal and vertical surface loads, respectively - p _i Thickness-averaged surface tractions - Q Transverse shear stress resultants - , r Radial coordinate prior to, after deformation - R Undeformed cylinder radius - , s Meridional coordinate prior to, after deformation - s , s _x, , s Sine of , respectively - , S Reference surface prior to, after deformation - S ₁, S ₂ Shear stress resultants parallel to the reference surface - S ₃ Average transverse normal stress resultant - t Undformed shell thickness - T Axial torque - V Vertical stress resultants - w Two-dimensional strain-energy density function - w _n Terms in expansion for w - W Three-dimensional strain-energy density function - x Undeformed axial coordinate in cylinder - , z Axial coordinate prior to, after deformation     

Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Summary Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.Melt-spinning, polymer and glass industries and the cooling of extruded metallic plates are practical applications of this problem.Results for skin-friction and heat-transfer coefficients are given. Larger acceleration is accompanied by larger skin-friction and heat-transfer coefficients. Rapid cooling of the sheet is accompanied by a larger Nusselt number.Nomenclature sheet width - c dimensionless constant - c _f local skin friction coefficient - F dimensionless transformed stream function - G dimensionless transformed temperature - local heat transfer coefficient - fluid thermal conductivity - length of deformation zone - m exponent of surface speed variation - q exponent of surface temperature variation - T dimensionless temperature - sheet surface temperature - solidification temperature - ambient temperature - sheet thickness - u velocity component along the sheet - u _s sheet surface velocity - wind up velocity - v velocity component normal to the sheet - x dimensionless coordinate along the sheet - y dimensionless coordinate normal to the sheet - Nu Nusselt number, - Pr Prandtl number, - Re Reynolds number, - =Re^–0.5 - dimensionless similarity coordinate - dynamic viscosity - kinematic viscosity - fluid mass density - sheet mass density - wall shear stress - dimensionless stream function With 3 Figures     

Measurement of mixed-mode fracture parameters near cracks in homogeneous and bimaterial beams

An investigation of deformation fields and evaluation of fracture parameters near mixed-mode cracks in homogeneous and bimaterial specimens under elastostatic conditions is undertaken. A modified edge notched flexural geometry is proposed for testing bimaterial interface fracture toughness. The ability of the specimen in providing a fairly wide range of mode mixities is demonstrated through direct optical measurements and a simple flexural analysis. A full field optical shearing interferometry called Coherent Gradient Sensing (CGS) is used to map crack tip deformations in real time. Experimental measurements and predictions based on beam theory are found to be in good agreement. Also, for a large stiffness mismatch bimaterial system, the interface crack initiation toughness is evaluated as a function of the crack tip mode mixity.     

Creep crack growth in brittle materials

During steady state crack growth by diffusive cavitation at grain boundaries, crack tip fields are relaxed due to the presence of a cavitation zone. In the present analysis, analytic solutions for the actual crack tip stress fields and the crack velocity in the presence of cavitation zone consisting of continuously distributed cavities ahead of the crack tip are derived using the smeared volume concept. Results indicate that the r ^–1/2 singularity is now attenuated to r ^{–1/2 +} (0<<1/2) singularity. The singularity attenuation parameter is a function of the crack velocity and material parameters. The crack growth rate is related to the mode I stress intensity factor K by K ² at relatively high load, K ⁿ at intermediate load, and approaches zero at small load near K _th. Meanwhile, the cavitation zone extends further into the material due to the stress relaxation at the crack tip and the subsequent stress redistribution. Such relaxation effects become very distinct at low crack velocity and low applied load. Key words: Creep crack growth, brittle material, diffusive cavity growth, sintering stress, crack tip stress field.     

Non-linear response of internal friction to tensile strain rate and frequency during plastic deformation of high-purity aluminium

The internal friction of high-purity aluminium during the process of plastic deformation was measured by a middle torsion pendulum on a modified tensile testing machine. The effects of tensile strain rate, , in the range of 0.73×10^–6 to 50×10^–6s^–1, and frequency of internal friction measurement, f, in the range of 0.38 to 2.6 Hz were studied. The results showed a non-linear dependence of internal friction, Q ^–1, on and f ^–1 or on (=2 f). The interrelationship between internal friction during the process of plastic deformation and dislocation motion, and the effect of non-linearity on the dynamic behaviour of dislocations are discussed.     

Crack growth and residual stress in Al-Li metal matrix composites under far-field cyclic compression

The growth of cracks under far-field cyclic compressive loading in aluminium-lithium (Al-Li) alloys reinforced with SiC particulates is investigated in notched compact tension specimens (CT). When cracks were initiated from the root of the notch, progressive deceleration occurred with the initial crack growth being largest. After crack arrest, analysis indicated that the initial residual stress diminished as the crack became non-propagating and at arrest the crack faces appeared to be open. When the crack closure loads were determined, it was shown that not all the stress amplitude produced crack growth and opening. This effect of crack closure was enhanced for small stress fields when the effective stress intensity dropped to the fatigue threshold of the alloy. For large residual stress fields the effective stress intensity range was well above the threshold and the initial crack growth rates were largest in the alloy containing the reinforcement particles. A residual strain model was used to determine the residual stress introduced in the root of the notch from the first compressive preload. It is shown that the fatigue crack growth was confined to a region of tensile stress within the residual stress field and the initial crack propagation rates were enhanced by the presence of the reinforcement. A dependence of the stress magnitude on growth rates was also established — the greater the residual stress at the root of the notch the larger the growth rates. The reinforcement had an additional amplification effect in terms of tensile distance from the notch. The effective stress intensity range, K, was investigated using compliance measurements and a model is introduced which explains the underlying features and mechanism of accelerated growth in both alloys, taking into account the reinforcement phase, plastic zone-size dependence and the residual stress field of the MMC.