TEMA 1: TEORÍA DE LAS DISTANCIAS CRÍTICAS (TDC)
ABSTRACT: This paper presents the analysis of the notch effect on granite and limestone fracture specimens. The research is based on the results obtained in an experimental programme composed of 84 fracture specimens, combining the two materials and 7 different notch radii varying from 0.15 mm up to 10 mm. The notch effect is analysed through the evolution of the apparent fracture toughness and the application of the Theory of the Critical Distances.
The results reveal a significant notch effect in the limestone, whereas the notch effect in the granite is negligible for the range of notch radii analysed. Both observations are justified by the corresponding critical distance of the material.
ABSTRACT: The Theory of Critical Distances is actually a group of methodologies, all of them using a characteristic material length parameter when performing fracture assessments on any kind of stress risers. In this paper, the application of the Theory of Critical Distances on Polymethyl methacrylate is analysed, the parameters involved in the analysis are calibrated, and the different versions of this theory are applied, with satisfactory results, to the prediction of the notch effect on the apparent fracture toughness measured on notched specimens. Also, a Scanning Electron Microscopy analysis is performed, establishing relations between the fracture mechanisms and the predictions provided by the Theory of Critical Distances.
ABSTRACT: This paper summarises an attempt to use the theory of critical distances (TCD) to predict static failures in notched brittle components when the applied system of forces results in multiaxial stress states in the vicinity of the stress concentrator apex. In order to reformulate the TCD to coherently address this complex problem, the cracking behaviour of cylindrical specimens of polymethylmethacrylate (PMMA), weakened by different geometrical features and tested under combined tension and torsion, were initially investigated. The direct inspection of the cracked specimens showed that, in an incipient failure condition, the cracking mechanisms changed as the degree of multiaxiality of the stress field damaging the material process zone changed; this held true even though, from an engineering point of view, the investigated material showed a classical brittle behaviour (that is, mode I dominated). In more detail, in tension (and in plain-specimen torsion) failure occurred as soon as a small craze/crack initiated. On the contrary, for notched specimens in torsion failure was preceded by the formation and growth of many small cracks near the notch root. This complex material cracking behaviour resulted in values of the material characteristic length which changed as the degree of multiaxiality of the stress field damaging the material in the vicinity of the stress raiser apex changed. The above phenomena were incorporated into the devised reformulation of the TCD, allowing our method to perform predictions falling in an error interval of about ±20%. Finally, in order to better check the accuracy of our method in predicting static failures in notched brittle materials, it was also applied to some results taken from the literature and generated under combined mode I and II loading. Again the TCD was seen to be highly accurate allowing not only the static strength but also the crack propagation direction to be predicted. These results are very promising, especially in light of the fact that the TCD can easily be used to post-process linear-elastic finite element (FE) models, making it suitable for being successfully employed in an industrial reality.
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The Theory of Critical Distances will be of interest to a range of readers, from academic researchers concerned with the theoretical basis of the subject, to industrial engineers who wish to incorporate the method into modern computer-aided design and analysis.
TEMA 2: EVALUACIÓN DE LA TENACIDAD A FRACTURA
ABSTRACT: This paper describes the advantages and disadvantages of using different methodologies that apply bending fixtures for determining the fracture toughness of different stones. In general, the experimental results tend to show less variability when applying a 4-point bending mode. The comparison of the results obtained using the different experimental procedures also has stressed the great importance of using sharp notches in order to avoid overestimation of fracture toughness. This specific aspect has been also analysed in detail by performing a fractographic examination of unnotched bar specimens submitted to a 4-point bending test. This procedure shows how it is possible to locate and measure the origin of fracture, which contributes, among other things, to discuss the failure mechanisms of stones. Fracture toughness values also have been estimated via fractographic examination and the results compared with those obtained when applying the experimental methodologies.
ABSTRACT: A new approach called the modified maximum tangential stress criterion has been developed for investigating size effects on mode I fracture toughness of quasi-brittle materials. This approach employs the maximum tangential stress criterion while accounting for the higher order term of Williams expansion A3. Having assumed that the FPZ length changes with the specimen size, a formulation was suggested for expressing the variation of FPZ length versus the specimen size. Some experimental results reported for concrete and limestone were employed to assess the proposed criterion. It is shown that the proposed approach provides good estimates for the experimental data.
ABSTRACT: In this paper, the effects of specimen size and geometry on the apparent mode I fracture toughness (K c) of an Iranian white marble (Neyriz) are studied. A number of fracture tests were conducted on center-cracked circular disk (CCCD) specimens with different radii to investigate the size effects on K c. The experimental results demonstrate that the apparent fracture toughness increases in bigger specimens. In order to explain the experimental results, the modified maximum tangential stress (MMTS) criterion is used, where higher order terms of the Williams’ series expansion are included in the maximum tangential stress criterion. It is shown that the MMTS criterion provides good estimates for the apparent fracture toughness of Neyriz marble, obtained from fracture tests of edge-cracked triangular specimens. It is, therefore, concluded that the proposed criterion is able to account for the size and geometry effects on the fracture resistance of rocks simultaneously.
ABSTRACT: A new method called the straight notched disk bending method is developed for mode I fracture toughness determination using rock cores. Disk specimens of andesite and marble having a single straight edge notch were subjected to three-point bending loads. Dimensionless stress intensity factor estimations and fracture toughness tests were conducted for different notch lengths, span lengths, thicknesses and diameters of the cylindrical rock specimens. Stress intensity factors were computed by three-dimensional finite element modeling and the results were presented for a wide range of specimen geometrical parameters. Results of experiments were compared to the results of well-known mode I fracture toughness testing methods. For specimens having thickness equal to the radius, mode I fracture toughness was lower and close to the results obtained by semi-circular bending method. When thickness was increased and doubled, mode I fracture toughness increased and approached to the value found by the suggested cracked chevron notched Brazilian disk method. Advantages of the new method included easy specimen preparation and testing procedure, stiffer specimen geometry, smaller fracture process zone, and flexibility of the specimen geometry for the investigation of the size effect behavior.
ABSTRACT: The two chevron notched rock fracture specimens, CB and SR, recommended by the ISRM to determine rock Mode I fracture toughness have several disadvantages, such as low loads required to initiate failure, a large amount of intact rock core is required, complex loading fixture, difficult sample preparation for SR. The Cracked Chevron Notched Brazilian Disc (CCNBD) and the Cracked Straight Through Brazilian Disc (CSTBD) specimen geometries overcome these problems and are suitable for mixed fracture mode testing.
The general case for the cracked Brazilian disc problem is when the sample is loaded diametrically with the crack inclined at an angle 0 to the loading direction. Different combinations of mode I and mode II fracture intensities can be obtained simply by changing this angle. For the special case when 0 =0° the problem is reduced to the mode I fracture condition.
Former research has only solved the mixed mode CSTBD problem for cases with crack length á(a/R) < 0.6 [1]. However á=0.65-0.80 is more appropriate for practical applications. For the CCNBD specimen, the valid geometrical range should be given so that users can have the choice to select their own geometry according to the availability of rock samples.
ABSTRACT: This paper describes results of experimental research in which the fracture toughness of a granite is determined by means of the J-integral approach and an acoustic-emission (AE) technique. Compact tension specimens and three-point bend specimens of various sizes were tested, and the effects of specimen size and loading condition on the fracture toughness were examined. Concurrently with the fracture toughness tests. AE monitoring was conducted, and the relation between the AE characteristics and fracture behavior was examined. Energy measurements of AE signals and frequency spectral analyses were made to characterize the AE signals. The AE measurements were used to determine a fracture toughness evaluation point and to obtain the critical J-integral value, denoted by JiAE. It is demonstrated that the JiAE value is reasinably constant for a wide range of specimen sizes and specimen types. Based on the result, the fracture toughness of the granite KIc was then computed from the JiAE value using the conversion equation under the assumption of linear elastic response. A comparison of linear elastic fracture toughness values with KIc showed that the J-integral approach combined with the AE technique can be applied to determine a valid fracture toughness of the granite. Finally, a reason for the specimen size dependency observed in the linear elastic toughness value is discussed on the basis of the experimental results.
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This book is a collection of ISRM suggested methods for testing or measuring properties of rocks and rock masses both in the laboratory and in situ, as well as for monitoring the performance of rock engineering structures. The first collection (Yellow Book) has been published in 1981. In order to provide access to all the Suggested Methods in one volume, the ISRM Blue Book was published in 2007 (by the ISRM via the Turkish National Group) and contains the complete set of Suggested Methods from 1974 to 2006 inclusive. The papers in this most recent volume have been published during the last seven years in international journals, mainly in Rock Mechanics and Rock Engineering. They offer guidance for rock characterization procedures and laboratory and field testing and monitoring in rock engineering. These methods provide a definitive procedure for the identification, measurement and evaluation of one or more qualities, characteristics or properties of rocks or rock systems that produces a test result.
TEMA 3: RESISTENCIA A TRACCIÓN (σt)
ABSTRACT: This paper reports on a comparative study of various types of experimental tests for measuring the tensile strength of rocks and rock-like materials. A critical assessment is presented of some widely used laboratory techniques on the basis of experimental data from the literature and from the laboratory investigation performed in this study.
Tests were carried out using a triaxial apparatus recently set up at Milan University of Technology. This was designed to reduce random misalignments between specimen and loading frame, which are typical of conventional triaxial cells with external tie bars. The apparatus was then modified to perform various types of tests for determining the tensile strength of materials. An artificial building stone and a natural calcarenite of the Gravina di Puglia geological formation, sampled at Montescaglioso (Matera-Italy) were tested in this research. The experimental investigation included various types of tests, namely the uni-axial, the Brazilian, the ring, the three and four points bending and the Luong test. Specimens of both materials were also compressed to failure in unconfined conditions and loaded cyclically in unconfined tension and compression, Young’s moduli being measured by means of local instrumentation.
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TEMA 4: DENSIDAD DE ENERGÍA DE DEFORMACIÓN (DED)
ABSTRACT: The paper gives some closed form expressions for the strain energy averaged in a finite size volume surrounding the root of blunt V-shaped notches under Mode I loading. The control volume, reminiscent of Neuber’s concept of elementary structural volumes, is thought of as dependent on the ultimate tensile strength and the fracture toughness KIC in the case of brittle or quasi-brittle materials subjected to static loads. Expressions for strain energy density under plane strain conditions and Mode I loading have been derived from an analytical frame recently reported in the literature, which matches Williams and Creager-Paris’ solutions in the particular cases of plates weakened by sharp V-notches or blunt cracks (U-notches), respectively. In order to validate a local-strain-energy based approach, a well-documented set of experimental data recently reported in this journal by Gómez and Elices has been used. Data refer to blunt and sharp V-specimens of PMMA subjected to static tension loads and characterised by a large variability of notch root radius (from 0 to 4.0 mm) and notch angle (from 0° to 150°). Critical loads obtained experimentally have been compared with the theoretical ones, estimated here by keeping constant the mean value of the strain energy in a well-defined small size volume.
ABSTRACT: A large bulk of experimental data from static tests of sharp and blunt V-notches and from fatigue tests of welded joints are presented in an unified way by using the mean value of the Strain Energy Density (SED) over a given finite-size volume surrounding the highly stressed regions. When the notch is blunt, the control area assumes a crescent shape and R0 is its width as measured along the notch bisector line. In plane problems, when cracks or pointed V-notches are considered, the volume becomes a circle or a circular sector, respectively. The radius R0 depends on material fracture toughness, ultimate tensile strength and Poisson’s ratio in the case of static loads; it depends on the fatigue strength ΔσA of the butt ground welded joints and the Notch Stress Intensity Factor (NSIF) range ΔK1 in the case of welded joints under high cycle fatigue loading (with ΔσAand ΔK1 valid for 5 × 106 cycles).
Dealing with welded joints characterised by a plate thickness greater than 6 mm, the final synthesis based on SED summarises nine hundred data taken from the literature while a new synthesis from spot-welded joints under tension and shear loading, characterised by a limited thickness of the main plate, is presented here for the first time (more than two hundred data).
Dealing with static tests, about one thousand experimental data as taken from the recent literature are involved in the synthesis. The strong variability of the non-dimensional radius R/R0, ranging from about zero to about 1000, makes the check of the approach based on the mean value of the SED severe.
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