Influence of test parameters on the measurement of the essential work of fracture of zinc sheets

The Essential Work of Fracture (EWF) concept is used to characterize the fracture of thin plates of a zinc alloy. The consistency and applicability of the EWF approach are discussed. The successive stages of the fracture process were studied: the evolution of the shape of the crack tip was observed with a scanning electron microscope, the shape of the plastic zone and the evolution of necking in the ligament ahead of the crack tip were measured using a laser profilometer and the onset of cracking in the ligament was detected by means of a TV camera coupled with acoustic emission recording. The influence of both test parameters and material parameters on the Essential Work of Fracture (W _e ) and on the CTOD (_c) are elucidated. The effects of specimen geometry, deformation rate, texture and grain size are especially investigated. The main advantages and drawbacks of the EWF method are highlighted.     

Evaluation of the economic effects of Brite-Euram programmes on the European industry

This article deals with an evaluation performed by BETA group about the economic effects of EU R & D programmes (Brite, Euram and Brite-Euram I) on the European industry. The approach used is based on an original methodology designed by BETA, which aims at evaluating those effects at a micro level (i.e. the participants to the programmes) by means of direct interviews of 176 partners involved in 50 projects. The definition of these economic effects is firstly described, as well as the different steps of the evaluation work. Then the overall results of the study are presented, showing the importance of both direct and indirect observed effects in monetary terms. Finally, some more detailed results highlight the positive impact of some aspects of the organization structure set up for the analyzed R & D projects on the amount of observed effects: i) the participation of a university lab; ii) the participation of at least one partner involved in a fundamental research work; iii) the diversity of research tasks over a scale ranging from fundamental research to industrialization work; iv) the combination of user-type and producer-type of activity in one given organisation (integration effect) or in one given project (consortia effect), etc...     

The mechanism of brittle fracture in notched impact tests on polycarbonate

The impact testing of notched polycarbonate bars that are thick enough to yield in plane strain has been investigated. Shear bands occur in the plastic zone that resemble the slip line field for yielding from a circular notch. Eventually, an internal craze nucleates at the tip of the plastic zone, where the stresses are highest, and a crack forms in the thickest part of the craze. Above –15 C the stress for the craze to nucleate is a nearly constant multiple of the yield stress. It is shown that previous observations that annealing polycarbonate causes a ductile to brittle transition is a consequence of testing bars of thickness less than 5 mm.     

Plane-stress essential work of ductile fracture for polycarbonate

The effect of specimen geometry, specimen size and the specimen orientation on the essential work of fracture for polycarbonate is investigated. Two different test geometries, namely the single-edge notched tension and double-edge notched tension specimens, are used to evaluate the essential work of fracture for crack propagation. It is shown that the specific essential work of fracture for crack propagation,w _e is independent of the test piece geometries and the size of the test piece. It seems that for a given sheet thickness,w _e is a fundamental material property being independent of the specimen geometry and size. The value ofw _e does change with the orientation of the initial notch with respect to the melt flow direction. The straight-line relationships between the total specific work of fracture,w _f, and ligament length,L, breaks down when the ligament length to specimen thickness ratio is less than about three, because the fracture data fall in the plane stress-plane strain transition region. A plane strain specific essential work of fracture,w _le|, was obtained by extrapolating the best regression line of the data to a zero ligament. For the initial notch in the melt flow direction, values forw _e andw _le, were approximately 28 and 3 kJ m^–2, respectively. The specific essential work of initiation,w _le was about 4.3 kJ m^–2 ·J _R curves (J-a curves) were also obtained and it is shown that the intercept and the slope of theJ _r curve, i.e.J _C and dJ/da, are related tow _e and the slope of thew _f versus ligament plot.     

Comparison of various methods of measuring kic on small precracked bend specimens that fracture after general yield

An experimental investigation into the measurement of fracture toughness on small precracked bend specimens after general yield is described. Six parameters are compared on the basis of their accuracy and utility in predicting $\text{K}$_Ic. The parameters are: (i) the on-load crack tip opening displacement, COD, (ii) the lateral (notch root, crack tip) contraction, NRC, (iii) the angle of bend, (iv) the stretch zone, (v) the $\text{J}$ integral, and (vi) the equivalent energy. The materials used were. for the most part, A533B and 4340 steels.     

The role of ultimate elongation in the determination of valid ligament range of essential work of fracture tests

In this study, the feasibility of a previously proposed ultimate elongation-based criterion of essential work of fracture (EWF) method was reconsidered for several materials. Suitable ductility level (DL) ranges for the EWF testing of polymers were discussed, too. It was shown that there is a relationship between the DL terms and the experimentally estimated crack opening displacement values. Based on Coterell’s estimate of the size of the fracture process zone a lower ligament limit of EWF concept was also presented. This lower bound should be considered for thin samples where the original thickness-dependent criteria seemed to be not severe enough.     

Underpinning of a simple blunt flaw fracture initiation relation

With the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture as a basis, the author is involved in a wide-ranging research programme, the objective being to extend the fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. In earlier work, a Mode I fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius . The relation gives the critical elastic flaw-tip peak stress _pcr, and has been derived using a two-extremes procedure, whereby the separate, and indeed exact, solutions for small and large s/ values are blended together to give an all-embracing relation that is valid for all s/ values. _pcr is expressed in terms of the process zone material parameters and geometrical parameters but, for a wide range of flaw geometry parameters, _pcr essentially depends on only one geometrical parameter . This paper provides underpinning for the general thrust of the two-extremes procedure by appealing to exact results for the complete spectrum of s/ values from analyses of appropriate Mode III models. Results obtained by applying the two-extremes procedure are shown to be in very good agreement with the exact results.     

Factors affecting work of fracture of uPVC film

Essential work of fracture (EWF) approach was used to evaluate the fracture toughness of uPVC film. It was found that the specific essential work of fracture, (w_e) is independent of specimen width, specimen gauge length, loading rate and test temperature, but dependent on the geometry of the test specimens. Test temperature and geometry were the only testing parameters affecting the specific non-essential work of fracture (w_p) in a very significant way. The plastic zone shape factor () was found to be very sensitive to both the geometry and temperature. It was established that both w_e and w_p could be partitioned into components that are linked to yielding (i.e. w_e,y and _yw_p,y) and necking/tearing (i.e. w_e,nt and _ntw_p,nt) processes. The only testing parameter that affected w_e,y was test temperature, whereas w_e,nt was affected by test temperature as well as geometry. All testing parameters used in this study affected the values of _yw_p,y and _ntw_p,nt.     

The effects of ageing condition on shear localization from the tip of a notch in maraging steel

An experimental investigation of shear localization at the tip of a notch in several material states of 300 maraging steel is reported. Side-impacted edge-notched plates were tested in the under-aged, peak-aged, and over-aged conditions, and the critical impact velocity above which shear localization occurs at the notch tip is reported for a notch root radius of 175 m. It is found that the critical minimum impact velocity required for shear localization is independent of the ageing condition. Next, the propagation of shear localization in two of the three ageing conditions is recorded using high speed photography at framing rates of 480 000 frames per second. It is seen that, within the uncertainty of the experimental method, shear localization initiates at approximately the same time and stress intensity factor for the two materials. A heavy dependence of the shear band propagation speed and final length upon the ageing condition is seen. For the conditions examined shear failure is seen to propagate at an average velocity of 1000 m s-1 in peak-aged material and 300 m s-1 in under-aged material. The peak-aged material fails fully by shear while the shear failure in under-aged material arrests and is followed by tensile failure. This result demonstrates the effect of material strength, roughly independent of the strain hardening characteristics for these materials, on shear localization propagation. The effects of the specimen and projectile geometry on the results are examined qualitatively using elastodynamic finite element analysis of the stationary notch tip loading. © 1998 Chapman & Hall     

A Local Approach to Brittle Fracture Analysis and Its Physical Interpretation

The paper presents a review of studies dedicated to the development of a local approach to brittle fracture in metals and alloys. To work out a statistical criterion of local fracture in a metal in the vicinity of a stress concentrator is shown to be the key task of the local approach. The author substantiates a possibility of describing the process of brittle (quasibrittle) fracture in metals ahead of the notch on the basis of primary principles, i.e., on the basis of the analysis of the processes of formation and catastrophic growth of crack nuclei. The physical effects have been established, which must be allowed for in the development of the local fracture criterion. The author considers the main factors that govern the size of the process zone. This parameter has been found to depend on the value of the relative gradient of the local plastic strain intensity. The appropriateness of using the Weibull distribution to describe quasibrittle fracture of metals is analyzed. It is demonstrated that the Weibull parameters are not material's constants as postulated in the conventional variant of the local approach. Their values depend on the local plastic strain and the metal stress state in the vicinity of the stress concentrator.     

Measuring toughness and the cohesive stress-displacement relationship by the essential work of fracture concept

The complete fracture behaviour of ductile double edge notched tension (DENT) specimen is analysed with an approximate model, which is then used to discuss the essential work of fracture (EWF) concept. The model results are compared with the experimental results for an aluminium alloy 6082-O. The restrictions on the ligament size for valid application of the EWF method are discussed with the aid of the model. The model is used to suggest an improved method of obtaining the cohesive stress-displacement relationship for the fracture process zone (FPZ).     

Plane stress deformation zones at crack tips in polycarbonate

The plastic deformation produced crack tips in polycarbonate (PC) films stretched in tension, has been characterized by optical and transmission electron microscopy. An extensive and diffuse region of deformation is formed in unannealed specimens. Within this zone the ratio (v _f) of local film thickness to the (undeformed) thickness far away from the crack varies gradually both along and across the zone. The minimum ratio of 0.5 occurs at the crack tip. In contrast to this behaviour, films annealed for a short time just below the glass transition temperature T _g showed a highly localized response, the plastic strain being confined to a well-defined flame shaped deformation zone (DZ) ahead of the crack. Within most of this DZ, v _f is constant at 0.7, rising to 1 over a distance of 10 m at the zone tip, and falling to 0.5 over a distance of 4 m around the crack tip. Bi-refringence measurements show that a high degree of molecular orientation occurs within the zone. These experiments support the idea that an increase in the localization of the plastic strain response upon annealing below T _g is responsible for the embrittlement of PC by such heat treatment.     

On Electronic and Transport “Anomalies” in Layered Oxides

We briefly discuss some electronic and transport anomalies observed in superconducting perovskites. In particular we consider: (i) the complex electronic (and crystallographic) phase diagram, (ii) the symmetry of the gap with a special emphasis on the evidence for s-wave component in various experiments, and (iii) non-Fermi-liquid transport in superconducting Sr₂RuO_4– perovskite (T _c<1 K) that, like LSCO cuprate, exhibits linear resistivity up to 1050 K.     

Non-uniform breaking of molecular bonds,peripheral morphology and releasable adhesion by elastic anisotropy in bio-adhesive contacts

Biological adhesive contacts are usually of hierarchical structures, such as the clustering of hundreds of sub-micrometre spatulae on keratinous hairs of gecko feet, or the clustering of molecular bonds into focal contacts in cell adhesion. When separating these interfaces, releasable adhesion can be accomplished by asymmetric alignment of the lowest scale discrete bonds (such as the inclined spatula that leads to different peeling force when loading in different directions) or by elastic anisotropy. However, only two-dimensional contact has been analysed for the latter method (Chen & Gao 2007 J. Mech. Phys. Solids 55, 1001–1015 (doi:10.1016/j.jmps.2006.10.008)). Important questions such as the three-dimensional contact morphology, the maximum to minimum pull-off force ratio and the tunability of releasable adhesion cannot be answered. In this work, we developed a three-dimensional cohesive interface model with fictitious viscosity that is capable of simulating the de-adhesion instability and the peripheral morphology before and after the onset of instability. The two-dimensional prediction is found to significantly overestimate the maximum to minimum pull-off force ratio. Based on an interface fracture mechanics analysis, we conclude that (i) the maximum and minimum pull-off forces correspond to the largest and smallest contact stiffness, i.e. ‘stiff-adhere and compliant-release’, (ii) the fracture toughness is sensitive to the crack morphology and the initial contact shape can be designed to attain a significantly higher maximum-to-minimum pull-off force ratio than a circular contact, and (iii) since the adhesion is accomplished by clustering of discrete bonds or called bridged crack in terms of fracture mechanics terminology, the above conclusions can only be achieved when the bridging zone is significantly smaller than the contact size. This adhesion-fracture analogy study leads to mechanistic predictions that can be readily used to design biomimetics and releasable adhesives.     

Temperature and deformation rate dependence of the work of fracture in polycarbonate (PC) film

Single edge notched polycarbonate (PC) specimens of thickness 0.175 mm were pulled to complete fracture at temperatures between 25°C and 100°C and at loading rate values of 2, 5 and 50 mm/min. A duckbill-shaped yielded zone was formed ahead of the crack tip in all the specimen tested. Propagation of the crack within the yielded zone was always stable. The method of essential work of fracture (EWF) was used to study the effects of temperature and loading rate on fracture toughness. The specific essential work of fracture, w _e, was found to be independent of both temperature and loading rate. The non-essential work of fracture, w _p, increased with increasing temperature but showed no systematic variation with respect to loading rate. Moreover, plastic constraint factor, m, also increased with increasing temperature. A linear temperature dependence was obtained for both w _p and m giving the extrapolated values of w _p = 0 and m = 0.5 at –23°C.     

The essential work of plane stress ductile fracture of a strain-aged steel

The paper reports the results of an experimental investigation on the essential work of fracture of a strain-aged low carbon (0.1% C) temper-rolled 16-gauge sheet steel which has been subjected to pre-strain levels of 2 to 12% and ageing temperatures of 80 and 100C. Deep edge-notched tension specimens were used to determine the specific essential work by extrapolating the straight-line relationship between the specific work of fracture (W _f) and ligament length (I) to zero ligament length. The strain-aged steels at 80 and 100 give approximately the same specific essential fracture work of 0.18 to 0.20 J mm^–2 which is independent of the amount of prestrain. Advancing crack opening displacements (C.O.D.) have also been analysed, which give 0.60 to 0.63 mm for the strain-aged steels. For comparison, the prestrained but unaged steels have a higher essential work of fracture of 0.275 J mm^–2 and a larger C.O.D. of 0.73 mm. It is concluded, therefore, that the causes of strain-ageing embrittlement are primarily due to the reduction of both the essential work of fracture and the advancing C.O.D. at the crack tip end region.     

Analysis of the essential work of fracture method as applied to UHMWPE

The validity of the basic assumptions behind the method of essential work of fracture (EWF), as applied to ultra-high molecular weight polyethylene (UHMWPE), is evaluated using finite element modelling. To define a suitable model of constitutive behaviour, the mechanical properties of UHMWPE have been measured in both uniaxial tension and compression over a range of strain rates. The observed strain rate dependence of stress, including the observed differences in strain rate sensitivity between tension and compression, is interpreted in terms of a single Eyring process. The constitutive theory is constructed comprising an Eyring process and hyperelastic networks, the latter having responses symmetric with respect to tension and compression. This theory is implemented within a finite element scheme, and used to model fracture measurements made on the same material using double-edge notch tensile specimens. Calculations of the non-essential work and of the extent of the plastic zones are thus made possible. It is concluded that the specific non-essential work is essentially constant, but that the shape factor β, assumed constant in the conventional analysis, varies significantly with ligament length. The implication of this finding on the derived EWF value is evaluated and found to be slight.     

Prediction of Some Important Regularities Using a Statistical Mechanical Equation of State

Four important known regularities for several pure substances have been described using a statistical mechanical equation of state (EOS) derived by Deiters. The equation of state depends on three temperature-independent parameters, which can be obtained from the critical constants. The studied regularities included: (i) near linearity of the reduced isothermal bulk modulus as a function of reduced pressure, (ii) the common bulk modulus point on the isotherms of the reduced bulk modulus versus reduced density, (iii) near linearity of the Zeno contour of reduced temperature against reduced density from the Boyle temperature to the triple point, and (iv) near linearity of the mean density of a saturated liquid and its equilibrium vapor as a function of temperature, called the law of rectilinear diameter. The results for several fluids have been compared to the available experimental data. The predictions are often satisfactory in the sensitive regions.     

Quasi-static mode III fracture in a nonhomogeneous viscoelastic body

Summary An analysis is presented of the quasi-static propagation of a semi-infinite mode III crack in an inhomogeneous isotropic viscoelastic body. A shear modulus is assumed of the formG(t,y)=(t)(y) where |y| denotes the distance measured from the plane of the crack and (t) is a positive, nonincreasing, convex function of time. A closed form expression is derived for the energy release rate (ERR) when a Barenblatt type failure zone is incorporated into the crack model. Numerical and asymptotic results illustrate the combined effects of viscoelastic properties, material inhomogeneity, and the failure zone at the crack tip upon the ERR.     

A realistic theory for the “normal state” and pairing mechanism in the high-tc cuprates

The electronic structure of the high-T _c cuprates is studied on the basis of large-U and smallU orbitals. Two types of charge carriers are predicted: (i) spinless polarons with a very small bandwidth; (ii) anomalous carriers of both charge and spin. The results are consistent with many anomalous properties of the cuprates. The spinless polarons undergo a CDW transition, and transitions between pair states of the two types of carriers provide the pairing mechanism.The author acknowledges stimulating discussions with participants of the workshop. Some numerical work was performed at the Florida State University Computing Center.