Application of the crack-bridging model for fracture resistance (R-curve behaviour) to PMMA

The rising fracture toughness behaviour of PMMA was characterized using a crack-bridging model originally developed for coarse-grained alumina that predicts a mechanism for crack resistance from the bridging of unbroken grains behind the crack tip. Based on the published experimental observation of PMMA, the craze zone behind the crack tip was thought to be analogous to the effective grain-bridging zone in the model in which the fibrils in the craze zone were related to the restraining interfacial ligaments. Self-consistent results in terms of the model were obtained which indicates that the crack-bridging model can be used to account for the fibril-toughening mechanism in PMMA.     

Ductile phase toughening and R-curve behaviour in a B4C-Al cermet

The R-curve behaviour of a B₄C-Al cermet was studied experimentally using the indentation/strength technique. Microstructural observations clearly indicate that the dominant mechanism contributing towards increasing toughness with crack length is due to bridging of ductile Al phases. It is inferred that ductile toughening, along with toughening due to residual stresses generated upon cooling of the cermet, contribute to this toughening behaviour. Close agreement between experimental results and a simple model is also established.     

A model for predicting fatigue crack growth behaviour of a low alloy steel at low temperatures

In the present study, a model to predict the fatigue crack growth (FCG) behaviour at low temperatures is proposed for a low alloy steel (16 Mn). The experimental results indicate that fatigue ductile-brittle transition (FDBT) occurs in 16 Mn steel and the FDBT temperature (T_FDBT) is about 130 K. When T > T_FDBT, the FCG mechanism in the intermediate region is the formation of ductile striation and the FCG rates decrease with decreasing temperature. When T ≈ T_FDBT, the FCG mechanism changes into microcleavage and the fatigue fracture toughness K_fc of the steel decreases sharply. The FCG rates tend to increase as the temperature is further reduced. The test data of the FCG rates are well fitted by the formula developed by Zheng and Hirt. An approximate method to predict ΔK_th of the steel at low temperatures is proposed and then a general expression of the FCG rates is given at temperatures ranging from room temperature to T_FDBT. By means of the expressions proposed in this paper, the FCG rates at low temperatures can be predicted from the tensile properties if the endurance limit σ₋₁ and δk_th, at room temperature are known. Finally, a model for FDBT is tentatively proposed. Using this model, one can predict T_FDBT from the ductile-brittle transition curve determined from impact or slow bending tests of cracked Charpy specimens.     

A novel technique to synthesize hydroxyapatite at low temperature

Hydroxyapatite (HAP), a well known biomaterial, was synthesized by a novel technique using agarose gel in a high alkaline medium at a relatively low temperature 85 °C. The XRD analysis of the as-synthesized material revealed the absence of either brushite or or β tricalcium phosphate phases. Sintering studies at 750 and 1200 °C revealed the conversion of HAP into pyrophosphate without leaving any additional phases. A considerable decrease in the transformation temperature of HAP phase to that of -calcium pyrophosphate (-CPP) phase was found compared to the reported values.     

Application of a homogenisation technique to a one-dimensional bar exhibiting strain-softening behaviour

A homogenisation technique is applied to investigate the behaviour of a one-dimensional bar exhibiting tensile strain localisation. For this, an idealised bar containing an inclusion of a strain softening material is first considered and an explicit analytical solution is derived. It is shown that by applying the homogenisation technique, the localised deformation mode of the bar is independent of the dimensions of the zone of homogenisation. Finally, this method is applied to a concrete bar having a double notch and the numerical result is compared with the experimental data available.

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Résumé Une technique d’homogénéisation est appliquée pour étudier le comportement d’une barre unidimensionnelle démontrant une localisation de contrainte de traction. Pour ce faire, une barre idéale contenant une inclusion d’un matériau de radoucissement est d’abord considérée et une solution analytique explicite est dérivée. Il est démontré que, par l’application de la technique d’homogénéisation, le mode de déformation localisée de la barre est indépendant des dimensions de la zone d’homogénéisation. Enfin, la méthode est appliquée à une barre en béton comportant une double entaille et le résultat numérique est comparé avec les données expérimentales disponibles.

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Editorial note Prof. G. Pande is a RILEM Senior Member and Chairman of TC MMM on Computer Modelling of Mechanical behaviours of Masonry structures.     

Corrosion behaviour of steels and refractory metals in flowing Lead-Bismuth Eutectic at low oxygen activity

The corrosion behaviours of AISI 316L and T91 steels, and several refractory metals as W, Mo and Ta, were investigated in flowing lead-bismuth eutectic (LBE) at 400°C. The tests were performed in the LECOR (Lead Corrosion) loop, at low oxygen activity in LBE. The results obtained show that all materials exhibited a weight loss after exposure to the flowing LBE, except for the case of tantalum, which exhibits a weight gain. The resistance to corrosion offered by refractory metals has been found higher in comparison to the case of both steels. Moreover, the austenitic steel behaved more resistance to corrosion induced by LBE than the martensitic steel, under the test condition adopted.     

Thermal diffusivity of solids with a low expansion coefficient: A dilatometric technique

A dilatometric method is presented, suitable to obtain both thermal diffusivity and conductivity of low-conducting solids with a low expansion coefficient. The repeatibility of the measurements of thermal conductivity is 3%, whereas that for diffusivity is 5 %. Data for fused silica at room temperature are given, consistent with those reported in the literature. Since the method is based on detecting the thermal expansion of a copper disk in thermal contact with the specimen, its range of applicability is linked to the sensitivity by which the dilation of copper can be measured: no difficulty arises between liquid nitrogen and 1000°C.     

A neuro-fuzzy technique for fault diagnosis and its application to rotating machinery

Malfunctions in machinery are often sources of reduced productivity and increased maintenance costs in various industrial applications. For this reason, machine condition monitoring is being pursued to recognise incipient faults. In this paper, the fault diagnostic problem is tackled within a neuro-fuzzy approach to pattern classification. Besides the primary purpose of a high rate of correct classification, the proposed neuro-fuzzy approach also aims at obtaining an easily interpretable classification model. The efficiency of the approach is verified with respect to a literature problem and then applied to a case of motor bearing fault classification.     

A method for evaluating the thermal fatigue resistance of ceramics and its application to a fibre reinforced refractory material

An original method of characterizing thermal fatigue of ceramic materials has been proposed. This method is based on after-shock measurements of the degree of damage through a compliance calibration using compact tension (CT) test pieces. This method has been applied to a fibre-reinforced refractory material subjected to repeated thermal shock between 20 and 800° C. It has been demonstrated from both experiments and finite element analysis that the CT specimen is a convenient shape for the evaluation of thermal fatigue behaviour. In these specimens it has been established that the damage primarily affects the notch tip. The thermal fatigue behaviour of the CT specimens depends on notch length: when the notch length is greater than 30 mm, catastrophic failure occurs after a few cycles. When the notch length is less than 30 mm, the crack formed at the notch tip during the first cycle grows slowly during subsequent cycles. This behaviour has been explained by the variation of the stress intensity factor K _I.     

A method to determine the R-curve of flexible materials using a monotonic loading of a single trouser tear specimen

It is shown that the R-curve of flexible materials can be determined using a monotonic loading of a single trouser tear specimen. The load-displacement records of trouser tear specimens are analyzed based on the locus method which determines the critical J-integral value (J _c)) using the locus line of crack initiation points on load-displacement curves of specimens which differ only in initial crack length. Based on this analysis, it is shown that the crack resistance (R) during crack growth including crack initiation and steady state crack propagation can be expressed in terms of quantities that are directly related to the load-displacement plane, and that R can be simplified to a linear function of load. It is also shown that the crack growth (C) can be expressed as a linear function of load-point displacement. The load-displacement record of trouser tearing is then converted to an R-curve simply by changing the scale on each axis. The effectiveness of this method is illustrated experimentally by constructing the R-curve directly from the load-displacement record of a trouser tear specimen made from a thermoplastic rubber sheet.

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Résumé On montre que l'on peut déterminer la courbe R relative à des matériaux flexibles en recourant à un essai charges-déplacements obtenus sur des éprouvettes d'arrachment en se basant sur la méthode des lieux, qui permet de déterminer la valeur critique J _cde l'intégrale J en utilisant la ligne des lieux des points d'amorçage relevés sur des courbes charges-déplacement relatives à des éprouvettes qui ne différent que par la longueur initiale de la fissure.En se basant sur cette analyse, on montre que la résistance à la fissuration au cours de la phase d'amorçage et de croissance stable de la fissure, peut être exprimée en fonction de quantités directement liées à la relation charges-déplacements, et que R peut être ramené de manière simplifiée à une fonction linéaire de la charge, On montre également que la croissance C de la fissure peut être exprimée comme une fonction linéaire du déplacement du point de mise en charge.L'enregistrement charges-déplacement d'un essai d'arrachement se trouve être convertible en une courbe R par un simple changement d'échelle des axes.On illustre l'utilite de cette méthode en construisant expérimentallement la courbe R directement au départ d'un enregistrement charges-déplacements d'une éprouvette d'arrachement réalisée dans une feuille de caoutchouc thermoplastique.

     

Wood: a quasibrittle material R-curve behavior and peak load evaluation

From load-unloading cycles applied on wood notched specimens subjected to three-point bending, we show that the concept of equivalent LEFM, usually used for the quasibrittle materials, can be successfully applied to the fracture behavior of wood in mode I. Within this equivalent linear elastic framework, the quasibrittle fracture behavior of wood leads to an R-curve which is evaluated and discussed. On the other hand, the estimate of the peak load (or maximum load) of a structure as a function of the corresponding R-curve is an important problem for a building material such as wood. After a review of some general results about the connection between the R-curve and the shape of the load-deflection curve, we propose a single equation, i.e., valid for a fracture test under load-control or displacement-control, allowing to estimate the crack length corresponding to every extremum of a load-deflection curve.     

Electrical characterisation as a function of frequency: application to aluminous cement during early hydration

Electrical measurement as a function of frequency is a non-destructive technique which has been applied on numerous ceramic based systems such as single crystals, heterogeneous materials or concentrated suspensions of ceramic powders. It is a method for looking at the dynamic response of the system under test. Several approaches have been developed by different authors to give the associated relaxation times based on a single or on a distribution of times. In order to support the interpretation of the dynamic signal, one has to vary the physical or chemical parameters such as temperature, time, concentration and so on. Application of high frequency measurements (1 MHz–1.8 GHz) on aluminous cement pastes (W/C=0.4) is described. The variations of the capacitance with respect to setting time (from 0 to a few hours after mixing water and cement) and temperature (20 and 30 °C) are related to hydration chronology and to the quantity of formed hydrates. The high frequency response of C₃AH₆, which has been prepared by a chemical route, is also discussed.     

A new method for determining mode II R-curve by the End-Notched Flexure test

A new method for obtaining the mode II R-curve in a End-Notched Flexure test is proposed in the present work. New compliance and energy release rate equations have been derived incorporating shear, local deformation and bending rotation effects.Mode II R-curve, which represents energy release rate as a function of crack extension, is obtained without optical determination of crack tip position. Crack length and energy release rate are determined at each point of the test based on experimental compliance until unstable advance occurs. In order to confirm the theoretical models, unidirectional carbon/epoxy specimens have been tested. Experimental data are evaluated by means of two reduction schemes: an existing data method named Corrected Beam Theory with effective crack length and the new method named Beam Theory including Bending Rotation effects. Shear and local deformation effects are included in both reduction schemes.Results concerning the determination of crack length without crack advance and during stable crack propagation are presented. The agreement between experimental values and theoretical results obtained by the new approach is excellent. Based on the accurate crack length determination at each point of the test, energy release rate is determined point to point and therefore R-curve is obtained.     

Full-field measurement technique and its application to the analysis of materials behaviour under plane strain mode

The purpose of the paper is to provide a comprehensive experimental and numerical analysis of one of the encountered and critical state modes in sheet metal forming processes. The study is carried out with the help of the full-field measurement techniques. In order to confer some generality to the proposed work, several materials and different specimen shapes are considered that exhibit more or less homogeneous strain field. The proposed experimental study of the plane strain test is completed by a preliminary identification of the material parameters for non-linear behaviour at finite strains, using heterogeneous strain field.     

A simple computer implementation of membrane wrinkle behaviour via a projection technique

A simple computer implementation of membrane wrinkle behaviour is presented within the classical elastic plane stress constitutive model. In the present method, a projection technique is utilized for modelling of the wrinkle mechanisms, in which the total strains in wrinkled membranes are decomposed into elastic and zero‐strain energy parts, and a projection matrix that extracts the elastic parts from the total strains is derived. The resulting modified elasticity matrix that represents the stress–strain relations in wrinkled membranes is thus obtained as product of the classical elasticity matrix and the projection matrix. The modified elasticity matrix is straightforward to implement within the context of the finite element method. Numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.