A comparative study of dynamic, ductile fracture initiation in two specimen configurations

In this work a single edge notched plate (SEN(T)) subjected to a tensile stress pulse is analysed, using a 2D plane strain dynamic finite element procedure. The interaction of the notch with a pre-nucleated hole ahead of it is examined. The background material is modelled by the Gurson constitutive law and ductile failure by microvoid coalescence in the ligament connecting the notch and the hole is simulated. Both rate independent and rate dependent material behaviour is considered. The notch tip region is subjected to a range of loading rates J by varying the peak value and the rise time of the applied stress pulse. The results obtained from these simulations are compared with a three point bend (TPB) specimen subjected to impact loading analysed in an earlier work [3]. The variation of J at fracture initiation, J _c, with average loading rate J is obtained from the finite element simulations. It is found that the functional relationship between J _c and J is fairly independent of the specimen geometry and is only dependent on material behaviour.     

Constraint Loss under Dynamic Loading in Rate Independent Plastic Solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J ₂ flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J–Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K _dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K _dc for .     

Determination of large deformation and fracture behaviour of starch gels from conventional and wire cutting experiments

Large deformation and fracture properties of two types of starch gels were investigated through uniaxial compression, single edge-notched bend (SENB) and wire cutting experiments. Tests were performed at various loading rates and for various starch/powder concentrations (%w/w). It was found that starch gels exhibit rate independent stress–strain behaviour but show rate-dependent fracture behaviour, i.e. stress–strain curves at three loading rates are similar but fracture stress and fracture strain increase with increasing strain rate. This is rather unusual and interesting behaviour. SENB and wire cutting experiments also revealed rate-dependent fracture behaviour and that the true fracture toughness (G _c) values increase with loading/cutting speeds and starch powder concentration. In addition, the G _c values from wire cutting and SENB tests were in reasonable agreement. The wire cutting process was also studied numerically using finite element techniques. A non-linear elastic constitutive relationship based on Ogden was used to model the starch gels and a frictionless condition was assumed at the wire–starch gel contact interface. A fracture criterion based on maximum principal strain was assumed for the prediction of the steady state cutting force.     

Critical currents in cylindrical,superconducting granular aluminum films

Critical currents in cylindrical granular Al thin films of different thicknesses and electron mean free paths have been measured as a function of temperature. Experimental values of critical current tiI_c in all specimens are less than the theoretical pair-breaking current. The observed temperature dependence of I _c is in agreement with the theoretical one near the critical temperature, but not at lower temperatures. Effects of the manner in which the current terminals are attached to the specimen and of a deliberately applied weak spot on I _c have been investigated. The dependence of I _c on the rise time and the width of the pulse current has been studied.     

A fracture mechanics analysis of the effect of rubber content on rubber-modified polystyrene

Consideration is given to achieving test conditons in which linear elastic fracture mechanics may be employed to measure toughness in these rather ductile materials. This is achieved by testing wide specimens (100 mm) and these are employed to measureK _c over a wide range of temperatures for materials with several rubber levels. It is shown that bothK _c and the yield stress are determined by the extent of crazing and that, at the low rates used here, the full crazing capacity of the polystyrene is utilized by the addition of about 1% of rubber.     

Dynamic fracture behaviour of Fe78Si9B13 metallic glass ribbon under laser shock loading

The fracture behaviour of Fe₇₈Si₉B₁₃ metallic glass under laser shock loading was investigated. Morphologies of the fracture surface and laser irradiated surface were characterized using scanning electron microscope. The results show that the fracture surface consists of sliding region and final fracture region with crack propagation. Liquid droplets and melted belts are scattered on the fracture surface as the notable features compared with fracture surface morphology under quasistatic loading, indicating the significant temperature increase in shear bands during dynamic loading. The primary and secondary shear bands are distributed on the specimen surface resulting from the simultaneous operation of multiple shear bands at high strain rates. Ripples with the characteristic spacing of about 1 µm are generated on the laser irradiated surface because of the interaction of laser pulse with solid surface.     

Fracture mechanics of short glass fibre-reinforced nylon composite

The fracture behaviour of injection-moulded short glass fibre-reinforced, thermoplastic nylon 6.6 plaques has been studied under static loading using compact tension specimens and under impact loading using single-edge notched charpy specimens. The influences of specimen position as taken from the plaque mouldings, notch direction, notch sharpness and the rate of testing on the fracture toughness of this composite system were investigated. Results indicated that the fracture toughness is highest for the cracks perpendicular to the mould fill direction and is lowest for cracks parallel to the mould fill direction. A single fracture parameter, K _c, seems to be inadequate for fracture toughness characterization. Evaluation of the fracture toughness as a function of notch sharpness indicated that for notches perpendicular to the mould fill direction the fracture toughness is not affected by the sharpness of the initial notch. However, for cracks in the mould fill direction, sharpness of the initial notch had a significant effect upon the measured value of the fracture toughness. Results also indicated, that the fracture toughness is rate insensitive over the crosshead speed ranging from 0.5–50 mm min^–1. Finally, the specimen position, as taken from plaque mouldings, had no significant effect on the measured value of the fracture toughness.     

Fracture toughness and crack-growth measurements in GRP

Critical crack tip stress intensity factor (K _c) measurements were made for polyester resin reinforced with glass chopped strand mat (CSM) and woven roving fabric (WRF). Specimen thickness and initial crack length were varied for centre notched (CN) 100 mm wide specimens. Some specimens were saturated by immersion in water under pressure. K _c was negligibly affected by specimen thickness and it was concluded that plane strain conditions are not achieved in laminates of normal thickness. Scatter can be reduced by adjusting results to a standard glass content and K _c varies continuously with crack length. The CSM experiments were extended to 915 mm wide specimens which failed at very low nett section stresses but there may be a region in which K _c is roughly constant relative to crack length. In WRF specimens, however, it is the nett section stress which is constant at a value substantially below the UTS. Fatigue crack-growth studies were carried out on CN specimens. The Paris law adequately describes crack growth in CSM specimens at low rates of growth but Forman's law is better at high rates of growth. Neither law is valid for WRF material when dry but the behaviour changes after saturation with water. The crack-growth resistance of both materials is severely reduced by saturation with water.     

High yield four-point bend thin film adhesion testing techniques

Novel four-point bend specimen geometries are proposed for improved test yield over standard four-point bend specimens when measuring high-strength and ultra-thin film structures. The fracture energies of both a Cu/SiN dielectric diffusion barrier interface and a high-k/metal gate (HfO₂/Pt–Ti metal bilayer) interface are reported. Four novel specimen types were evaluated and result in significantly increased test yield as compared to the standard four-point bend specimens. The modified four-point bend specimens were fabricated by altering the crystallographic orientation, width, and thickness of the beams which make up the specimen. The mechanics of the four-point bend test are discussed for each different specimen type. The increased test yield is explained in terms of the stresses which develop in the specimen during testing, the phase angle of loading experienced for each specimen type, and the anisotropic fracture properties of single crystal silicon.     

Fracture behaviour of glass-fibre mat-reinforced structural nylon RIM composites studied by microscopic and acoustic emission techniques

The fracture and failure behaviour of continuous glass-fibre mat-reinforced nylon block copolymer were studied at monotonic increased loading at different temperatures (T=–40 to 80 °C and deformation rates (v=1 and 1000 mm min^–1). The fracture toughness,K _c, was determined on compact tension specimens of different size in order to elucidate size effects.K _c increased with increasing glass-fibre mat content and with deformation rate, whereas increasing temperature resulted in lowerK _c values.K _c was unaffected by the free ligament width of the compact tension specimens used. The failure manner was studied by acoustic emission and microscopic techniques (transmitted light and scanning electron microscopy). Simultaneous monitoring of the failure mode by acoustic emission and transmitted light microscopy allowed the failure sequence to be deduced and led to a reliable discrimination between the observed failure events based on their acoustic emission signal characteristics (e.g. amplitude, energy). For this composite with a very ductile thermoplastic matrix the following failure steps were concluded: (a) fibre debonding due to crack-tip blunting, (b) network-type deformation of the glass-fibre mat with concomitant fibre debonding and voiding of the matrix, (c) formation of kinked strands with crack opening due to matrix yielding, (d) fracture of the bent filaments within the strands followed by pull-out processes (fibre-fibre, fibre-matrix). The development of the damage zone was also assessed by acoustic emission via localization of the related events. It was established that the damage zone reaches its maximum dimension at the maximum load and only its shape changes along the crack-growth direction upon further loading.     

Effect of fibre surface treatment on yielding and fracture behaviour of glass fibre-polypropylene composite

Two parallel studies of the mechanical properties of composites based on modified polypropylene is presented. The fillers used were either uncoated-glassy fibres or glassy fibres coated with aluminium. The tensile properties and fracture behaviour are investigated as a function of filler content over a range of temperatures and strain rates. The measured elastic modulus, tensile strength, and fracture parameters, G _c and K _c, showed dependencies on filler content. The observed enhancement is found to be remarkable in the case of composites containing uncoated surface treated glass fibres. The tensile yield stress of all the composites prepared showed strain rate and temperature dependence. Stress activation volume and activation energy of single-activated yielding processes are determined. The observed fracture morphology could explain the reinforcement behaviour of the measured mechanical properties.On sabbatical leave from the Physics Department of the University of Jordan, Amman, Jordan     

Instrumented impact testing of polyethersulphone

The impact behaviour of polyethersulphone has been studied using a specially constructed instrumented impact testing machine. This machine is of the pendulum type and the samples are fractured in three-point bend loading. It is shown that accurate force/deformation curves can be obtained, in spite of complications due to flexural vibrations of the test sample. Measurements were made on both sharp-notched and blunt-notched specimens over a range of crack lengths. It was found that the sharp-notched samples could be analysed in terms of fracture toughness, G _C, whereas the blunt-notched samples corresponded to a constant critical stress at the root of the notch. The importance of multiple crazes at the crack tip in bluntnotched specimens is emphasized. It is also shown that ageing reduces the fracture toughness, while on the other hand, the critical stress observed in blunt-notched specimens, which has been associated with the craze initiation stress, is not affected by ageing.     

Effect of temperature and superimposed dynamic and static stresses on mechanical properties of epoxy-bonded joints

Adhesive joints are subjected during their service life to different combinations of dynamic and static stresses. While the behaviour of the adhesives in relatively simple states of stress is well characterized, their response to superimposed stresses of different types acting in different directions has scarcely been investigated. In the study presented in this paper, single lap joints made with different formulations of epoxy adhesives were subjected to combined shear creep stresses and torsional oscillations applied simultaneously and along perpendicular axes of the specimen. The main conclusion based on the results of this investigation is that such a simple combination of stresses affects considerably the mechanical behaviour of the joint. A significant increase of the shear strength of the joint was recorded for specimens subjected to superimposed stresses at temperatures lower than the T _g of the adhesive. Application of similar combinations of stresses at temperatures close to or higher than the T _g led to a decrease of the shear strength of the joint. The fracture morphology of the joints made with the investigated epoxy resins was qualitatively correlated with changes induced by the superimposed loading in the T _g of the adhesive. The fatigue fracture surface of adhesives is characterized by striations and furrows, similar to bulk specimens that failed in the same fashion.     

Modelling the softening within the fracture process zone associated with the fissuring mode of crack growth in Zr-2.5Nb CANDU pressure tube material

The fissuring mode of fracture in CANDU pressure tube material, and in particular Stage 1 crack growth (essentially flat J _R curve) as observed in some irradiated compact toughness specimens has been investigated. Models are presented of the fracture process zone associated with a crack that tunnels at the specimen mid-section, which extends preliminary work reported earlier. Various types of process zone behaviour are analysed, and based on an appropriate value for J _c, the J value associated with the cumulative mode of crack propagation in irradiated material, together with an estimate of the tensile stress at the leading edge of the process zone, the known failure mechanism (formation, growth and coalescence of voids) of the ligaments between the fissures is shown to be reasonably consistent with the experimental measurements of the fissure spacing and fissure length.     

Viscoelasticity of ceramics at high temperatures

The dependence of the fracture toughness, K _IC, on the loading rate has been calculated. On the basis of linear elastic fracture mechanics (LEFM) a strong dependence of the fracture toughness on the loading rate is obtained if subcritical crack growth is taken into account. If the subcritical crack growth parameters n and B are sufficiently small, which correspond to a high velocity of crack extension, the fracture toughness should decrease at lower loading rates. This behaviour is similar to the well-known decrease of bending strength. The experimental results for alumina containing glassy phase as a model material, however, show a maximum in a certain regime of loading rates. A model is established, which combines LEFM and the viscoelasticity, and leads to a maximum of K _IC at a certain loading rate dependent on the viscosity of the glassy phase.     

Effects of strain rate and matrix structure on transition of toughness of spheroidal graphite cast irons

Abstract

ensile, three point bend J _c, and Charpy V-notch impact tests were carried out at various loading speeds and temperatures on ferritic, pearlitic–ferritic, and pearlitic spheroidal graphite cast irons. The 0·2% proof stress increased monotonically with decreasing temperature. Similar behaviour was observed for tensile strength, but the temperature range over which it occurred was limited. Both 0·2% proof stress and tensile strength were increased slightly by increasing the crosshead speed. The energy for fracture per unit volume in tensile tests was evaluated as the mean of the tensile strength plus proof stress multiplied by elongation. This energy reveals the ductile–brittle transition behaviour in the same manner as J _c value or Charpy impact energy. An increase of loading speed shifted the transition curve of the energy for fracture to higher temperature, leaving the upper shelf value unchanged. An increase of pearlite volume fraction in the matrix also shifted the curves to higher temperature, decreased the upper shelf value, and reduced the slope of the transition curve. The transition temperatures of the energy for fractureJ _c value, and Charpy impact energy were found to be linearly related to the logarithm of strain rate.

MST/1343     

Modelling the fracture behaviour of adhesively-bonded joints as a function of test rate

Tapered-double cantilever-beam joints were manufactured from aluminium-alloy substrates bonded together using a single-part, rubber-toughened, epoxy adhesive. The mode I fracture behaviour of the joints was investigated as a function of loading rate by conducting a series of tests at crosshead speeds ranging from 3.33 × 10⁻⁶ m/s to 13.5 m/s. Unstable (i.e. stick–slip crack) growth behaviour was observed at test rates between 0.1 m/s and 6 m/s, whilst stable crack growth occurred at both lower and higher rates of loading. The adhesive fracture energy, G_Ic, was estimated analytically, and the experiments were simulated numerically employing an implicit finite-volume method together with a cohesive-zone model. Good agreement was achieved between the numerical predictions, analytical results and the experimental observations over the entire range of loading rates investigated. The numerical simulations were able very readily to predict the stable crack growth which was observed, at both the slowest and highest rates of loading. However, the unstable crack propagation that was observed could only be predicted accurately when a particular rate-dependent cohesive-zone model was used. This crack-velocity dependency of G_Ic was also supported by the predictions of an adiabatic thermal-heating model.     

The effect of specimen size on the fracture energy and softening function of concrete

This paper examines the effect of specimen size on the fracture energy of concrete, G_F, as measured using the three-point bending test on pre-notched beams prescribed by RILEM TC-50 [1]. The concept of partial fracture energy is introduced and used to explain the observed size effect. The opening displacement at the top of the notch in the test specimen at the end of the test, ω, is affected by the size of the specimen, which in turn affects the measured value of the concrete fracture energy. In theory, when the specimen is large enough to allow the fracture process zone to develop fully,w _f will reach its critical value,w _c , and the effect of specimen size onG _F will be eliminated. The experimental results included here show that in reality the size of the specimen does affect the measurement ofG _F , even when the size is such that the fracture process zone develops fully. This may be due to local plastic deformation in the area around the loading point, which is particularly significant in larger specimens. It may also be due to differences in the influence of the boundary conditions of the test for different specimen sizes. In addition, a procedure is outlined for the determination of the softening function for concrete based on the fracture energy measured in RILEM tests, in which the specimens are small enough to ensure that the energy measured is actually due to fracture and not plastic deformation.     

Fracture mechanics behaviour of austenitic compacted graphite cast iron

The fracture mechanics behaviour of high-nickel austenitic compacted graphite cast iron was studied and the effects of graphite morphology, alloying elements and specimen thickness on the mechanical properties, plane stress fracture toughness, and fatigue crack growth rate were evaluated. It was found that the graphite morphology, i.e. the percentage of compacted graphite present, was the major determinant of all properties of the materials investigated. The irons with a greater amount of compacted graphite (the balance was nodular graphite in austenitic matrix) resulted in lower tensile strength, yield strength, elongation and K _c fracture toughness but higher crack-growth index values (poorer crack-growth resistance). For 25 mm thick specimens, K _c values of the austenitic compacted graphite cast irons in this study were in the range of 58–64 MPa m^1/2. This is higher than ferritic/pearlitic ductile iron of 43–53 Mpa m^1/2, and is compatible to Ni-resist austenitic ductile iron of 64.1 Mpa m^1/2. The addition of cobalt not only contributed to slightly higher values of mechanical properties, but also higher plane stress fracture toughness and better crack growth resistance. Optical microscopy, scanning electron microscopy and X-ray diffraction techniques were applied to correlate the microstructural features to the properties attained.     

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values J _c ) for shallow crack specimens are significantly larger (factor of 2–3) than the J _c )-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate J _c )-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.