Correlation between crack tortuosity and fracture toughness in cementitious material

This paper proposes a new technique for the evaluation of fractal dimension (D) of fracture surface and a quantitative correlation between D and fracture toughness of cementitious materials. The experimental program has been performed on compact tension (CT) specimens (600 × 525 × 125 mm) with three different aggregate sizes (d _max=4.7 mm, 18.8 mm and 37.5 mm). The fractal geometry concept is utilized in the evaluation of fracture surface roughness. To avoid indirect or destructive experimental procedures that are prohibitively laborious and time consuming, a new non-destructive technique is presented. Results of the analysis indicate that the concept of fractal geometry provides a useful tool in the fracture surface characterization. The results also suggest that the fracture toughness can be correlated with the fractal dimension of fracture surface.     

Size effects in concrete fracture: Part I, experimental setup and observations

This paper presents an experimental investigation on the influence of microstructural parameters, such as aggregate size, and macroscopic parameters, such as specimen dimensions, on brittle fracture. Maximum aggregate size was used as a representative parameter of aggregate distribution in agreement with ASTM C136 standards. Six groups of geometrically similar concrete specimens with various dimensions and aggregate sizes were prepared. Similarity of the specimens was strictly maintained by scaling the specimen dimensions from one group to another by a factor of two starting from a specimen size of (width × total depth × thickness) 105×105×12.5mm to 1680×1680×200mm. Two separate sets of removable pre-cast notches were designed to determine the effect of initial notch size. A considerable effort was devoted to the design of the loading fixture to have a reproducible crack initiation and controlled crack growth. Several loading fixtures were evaluated prior to selection of the one used in the experimental program. Quasi-static splitting cyclic loading in edge cleavage configuration was applied. A servo-hydraulic Instron machine was used for testing. The fracture process was monitored by optical and acoustic imaging techniques. Three forms of comparisons of the test results with respect to the specimen and aggregate sizes were adopted. The first corresponded to the various specimen sizes cast with the same maximum aggregate size. The second comparison was based on the geometrically identical specimens cast with various maximum aggregate sizes. The third form of comparison dealt with complete geometrical similarity, i.e., all dimensionless geometrical characteristics including specimen thickness to maximum aggregate size ratio were identical. Results from this study indicated that as the specimen size decreases, the envelope becomes larger within the first and third forms of comparison. In the second form of comparison, i.e., geometrically identical specimens cast with various maximum aggregate sizes, the area under the envelope was greater as the maximum aggregate size increased. The existence of a trend in dimensionless critical load-CMOD envelopes despite the apparent geometrical and physical similarity of the test conditions is the direct indication of a scale effect, i.e., the modified fracture energy, indicates the existence of a strong scale effect: increases with the specimen dimensions as well as maximum aggregate size.     

Determination of fracture parameters for crack propagation in concrete using an energy approach

Double-G fracture model, a new analytical model describing fracture behaviour on cracked concrete, was recently proposed by Xu and Zhao based on the conception of energy release rate. This model couples the Griffith brittle fracture theory with the bridging softening property of concrete, and it is an extension of double-K fracture model proposed by Xu and Reinhardt. In this model, two fracture parameters, i.e., the initiation fracture energy release and the unstable fracture energy release , are termed to distinguish the different crack propagation stages undergoing during the whole fracture process in concrete. The difference between the two parameters, written as , is assumed to come from the contribution by aggregate bridging interlock, which results in the presence of fracture process zone. In our present work, firstly, the new model is elaborately introduced. Then, fracture tests are conducted, where besides three-point bending beams, a new testing method, called wedge-splitting on compact tension is adopted. In the experiments, electrical strain gauges are used to measure initial cracking load. Based on recorded load-crack mouth opening displacement curve (P-CMOD) or load-displacement curve (P-δ) and load-strain curve (P-ε), double-G fracture parameters are experimentally determined. Further more, based on the assumed three parameters relationship among , and , unstable fracture energy release are calculated. A comparable result between the measured and the calculated confirms this assumption. In order to verify the feasibility of this new model, the effective double-K fracture parameters converted by double-G fracture parameters using are compared with the double-K fracture parameters calculated by double-K fracture model. It is found that there is a good agreement. Another two series of different initial crack-depth ratios three-point bending beams carried out by Refai and Swartz are also collected to provide more experimental verification. It shows that the results obtained from the double-G fracture model agree well with those of double-K fracture model.     

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125mm/min (0.005in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G ₁). There is a well pronounced general trend observed: G ₁ increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G ₁ increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G ₁, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.     

Measurement of fracture toughness of anode used in Solid Oxide Fuel Cell

Reliability prediction and design of multi-layered structure necessitates the knowledge of the mechanical properties of the individual layers, in particular fracture toughness. To measure fracture toughness of typical anode, composed of 60 wt.% NiO and 40 wt.% 3YSZ (60:40 Ni-YSZ) used in Solid Oxide Fuel Cell (SOFC), controlled buckling test was used. A simple set-up was made where a compressive strain was applied on a thin substrate supporting the anode. Both curvature and film strength are calculated from the applied strain, elastic modulus and geometric dimension of the sample. The fracture toughness is calculated to be .     

Investigations of surface structure for thermally evaporated silicon on a Cu(111) surface

The surface structure and composition of semiconductor/Cu(111) films prepared by thermal evaporation in an ultrahigh vacuum condition have been investigated. As Si atoms were deposited on a Cu(111) surface, diffused spots were observed up to 2 monolayers while 1 × 1 spots become dimmer as revealed using low-energy electron diffraction technique. Because of a larger electron affinity of Si than that of Cu, the Cu L₃M₄₅M₄₅ Auger line shifts to a lower kinetic energy. Annealing treatments at 425 K causes a splitting of the Cu L₃M₄₅M₄₅ line. This shows the interdiffusion at the Si/Cu interface and the formation of a Cu-rich surface layer. After annealing treatments, the domains grow and aggregate to form larger domains as revealed by the decreasing full-width at half maximum of diffraction spots. Ge/Cu(111) shows 1 × 1 structure as annealing up to 500 K. Lack of a dominant structure and a large valence diameter of Ge result in different structures as compared to Si/Cu(111).     

Photoemission spectroscopy study of Na-induced phase transitions on Si(1 1 3)

We reinvestigate the Si 2p spectrum of clean to testify two competitive structure models, i.e. adatom-dimer-interstitials and oppositely puckered models, in comparison with recent theoretical calculations. This reveals that only the adatom-dimer-interstitials model reproduces the surface components of the Si 2p spectrum. After decorating Na atoms on clean at room temperature, the 3×2 phase was found to transit into the 3×1 phase by low-energy electron diffraction and photoemission spectroscopy experiments. We will discuss the (3×2)-(3×1) phase transition on the adatom-dimer-interstitials model.     

Diffusion and formation energies of adatoms and vacancies on magnesium surfaces

This paper reports classical molecular statics calculations of magnesium {0 0 0 1}, , , and surfaces, specifically formation energies of defects (adatoms and surface vacancies) and flat surfaces and diffusion energy barriers of the defects. The formation energies show that the surface is thermodynamically more favorable than , and surfaces; in contrast, literature reports have often ignored the surface. The diffusion energy barriers of both adatoms and surface vacancies show strong diffusion anisotropy on , , and surfaces. Based on this anisotropy, the ratio of diffusion distances (of either adatoms or surface vacancies) along two orthogonal directions on is 37–55 at room temperature. Using the results of formation energies and diffusion energy barriers we develop a more complete understanding of surface orientations in Mg nanoblades synthesized by physical vapor deposition [F. Tang, T. Parker, H.-F. Li, G.-C. Wang, T.-M. Lu, J. Nanosci. Nanotechnol. 7 (2007) 3239]. In contrast to previous reports, we postulate that the side surfaces of Mg nanoblades are because (a) they have the second lowest surface formation energy and (b) the ratio of diffusion distances on them agrees with the experimental value of approximately 50.     

Optimization of JK2LB chemical composition for ITER Central Solenoid conduit material

The Japan Atomic Energy Agency (JAEA) has developed a cryogenic structural steel to be used in large superconducting magnets for a fusion machine, and the results of this development will be utilized in the International Thermonuclear Experimental Reactor (ITER). Low carbon and low boron JK2 (JK2LB), which has high strength and fracture toughness at 4 K and thermal contraction from room temperature to 4 K which is lower than that of conventional 316LN steel has been developed as the conduit material for the ITER Central Solenoid (CS) conductor. In order to achieve the ITER requirements (0.2% yield strength ? 1000 MPa, fracture toughness K_IC (J) ? 130 MPa  for CS conduit material, chemical components such as carbon, nitrogen and boron, were optimized. In addition, since the CS is to undergo 6 × 10⁴ load cycles during its lifetime with a maximum principal stress of 490 MPa, fatigue crack growth assessment of the CS conduit was performed. As the result, JK2LB containing nitrogen of 0.2%, boron 15-40 ppm, and low carbon was found to achieve the strength and fracture toughness requirements. For the welding of JK2LB, a filler wire of JK2LB with a low nitrogen content of 0.13% was developed and fracture toughness of more than 130 MPa  was confirmed in the weld metal. Measured fatigue crack growth rates of the base and weld metal at 4 K are low enough to achieve the required CS coil operation cycle lifetime.     

Fracture behavior under mixed-mode loading of ceramic plasma-sprayed thermal barrier coatings at ambient and elevated temperatures

The fracture behavior under modes I and II loading of ceramic plasma-sprayed thermal barrier coatings was determined in air at 25 and 1316 °C in asymmetric four-point flexure. The mode I fracture toughness was found to be K_Ic = 1.15 ± 0.07 and 0.98 ± 0.13 MPa , respectively, at 25 and 1316 °C. The respective ‘nominal’ mode II fracture toughness values were K_IIc = 0.73 ± 0.10 and 0.65 ± 0.04 MPa . The empirical mixed-mode fracture criterion best described the coatings’ fracture behavior under mixed-mode loading. The angle of crack propagation was in reasonable agreement with the minimum strain energy density criterion.     

An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams

An analytical model to predict the effective fracture toughness of concrete was proposed based on the fictitious crack model. Firstly, the equilibrium equations of forces in the section were formed in combination with the plane section assumption. Then a Lagrange function was presented through the equilibrium equations and the relationship formula between the effective crack length and crack tip opening displacement. Taking into account Lagrange Multiplier Method, the maximum load P_max was obtained, as well as the critical effective crack length a_c. Furthermore, was gained in an analytical manner. Subsequently, some material and structural parameters from other literatures were adopted into the proposed model for the calculation. Compared with the experimental results, most of the calculated values show a good agreement for P_max and a_c. In order to study the influence of the softening curve in the fictitious crack on the calculated fracture parameters, three series of constants determining the shape of the softening curve were chosen in the calculation. The results show that the calculated fracture parameters are not sensitive to the shape of the softening curve. Therefore, only if the elastic modulus E_c and flexural tensile strength f_r were measured, P_max, a_c and can be predicted accurately using the proposed model. Finally, the variations of the calculated fracture parameters with the specimen size and a₀/h (i.e., the ratio of the initial crack length to the depth of the specimen) were studied. It was found that both and the pre-critical crack propagation length Δa_c increase with the specimen size. However, the two parameters increase to the maximums and then decrease gradually with a₀/h. Moreover, the theories of free surface effect were utilized to explain the observed size effects.     

Formation and desorption of SiI2 molecules

The chemical etching of Si(100)−(2×1) in I₂ ambient is considered. The desorption activation energy of SiI₂ molecules is evaluated from experimental data. It is found that the desorption activation energy of SiI₂ molecules is equal to . This corresponds to a value of the mean lifetime of adsorbed molecules on the surface of at temperature .