K-resistance Curve Research Articles

Research on the effect of thermal treatment on the crack resistance curve of marble using notched semi-circular bend specimen

The crack resistance curve is widely used to describe the complete fracture process of quasi-brittle materials. In the paper, the crack resistance curves of thermally treated marble were tested through the notched semi-circular bend specimens. The acoustic emission (AE) and digital image correlation (DIC) techniques were used to monitor the fracture behaviors of the specimens during the test. The AE results indicated that the crack will initiate from the notch when the axial load is less than the peak load. And, when the axial load reaches the peak load, the DIC results demonstrated that there exists a large fracture process zone (FPZ) in front of the crack notch. The effect crack length was calculated by the compliance method, which is coincided with the DIC results. The amplitude of the crack resistance curves decreases with the increase of treatment temperature, which suggested that the fracture resistance of the specimen declines due to thermal treatment. Based on the K-resistance curves, the initial fracture toughness, unstable fracture toughness, and fracture toughness when FPZ is fully formed have been determined for the thermally treated specimens. The results showed that these parameters both decrease in the increase of treatment temperature. Moreover, The FPZ length first increases and then decreases with the increase of normalized crack length and the critical and maximum non-dimensional FPZ length tends to increase with the increase in treatment temperature.

Experimental and numerical study on the fracture process zone and fracture toughness determination for ISRM-suggested semi-circular bend rock specimen

The semi-circular bend (SCB) method suggested by International Society for Rock Mechanics (ISRM) is demonstrated to yield much conservative mode I fracture toughness. A large fracture process zone observed by both acoustic emission (AE) monitoring and numerical modeling is analyzed to be responsible for that phenomenon. Using numerically simulated effective crack lengths at the peak-load stage in the experiments, the measured toughness values are close to the level I fracture toughness. In addition, numerically simulated K-resistance curves are demonstrated to have great potential for determining the fracture toughness at the level II.

Evaluation of Mode I Fracture Toughness Assisted by the Numerical Determination of K-Resistance

The fracture toughness of a rock often varies depending on the specimen shape and the loading type used to measure it. To investigate the mode I fracture toughness using semi-circular bend (SCB) specimens, we experimentally studied the fracture toughness using SCB and chevron bend (CB) specimens, the latter being one of the specimens used extensively as an International Society for Rock Mechanics (ISRM) suggested method, for comparison. The mode I fracture toughness measured using SCB specimens is lower than both the level I and level II fracture toughness values measured using CB specimens. A numerical study based on discontinuum mechanics was conducted using a two-dimensional distinct element method (DEM) for evaluating crack propagation in the SCB specimen during loading. The numerical results indicate subcritical crack growth as well as sudden crack propagation when the load reaches the maximum. A K-resistance curve is drawn using the crack extension and the load at the point of evaluation. The fracture toughness evaluated by the K-resistance curve is in agreement with the level II fracture toughness measured using CB specimens. Therefore, the SCB specimen yields an improved value for fracture toughness when the increase of K-resistance with stable crack propagation is considered.

Model for the Effect of Fiber Bridging on the Fracture Resistance of Reinforced-Carbon-Carbon

A micromechanical methodology has been developed for analyzing fiber bridging and resistance-curve behavior in reinforced-carbon-carbon (RCC) panels with a 3D composite architecture and a SiC surface coating. The methodology involves treating fiber bridging traction on the crack surfaces in terms of a weight function approach and a bridging law that relates the bridging stress to the crack opening displacement. A procedure has been developed to deduce material constants in the bridging law from the linear portion of the K-resistance curve. This approach has been applied to analyzing R-curves of RCC generated using double cantilever beam and single cantilever bend specimens to establish a bridging law for RCC. The bridging law has been implemented into a micromechanical code for computing the fracture response of a bridged crack in a structural analysis. The crack geometries considered in the structural analysis include the penetration of a craze crack in SiC into the RCC as a single-edge crack under bending and the deflection of a craze crack in SiC along the SiC/RCC interface as a T-shaped crack under bending. The proposed methodology has been validated by comparing the computed R-curves against experimental measurements. The analyses revealed substantial variations in the bridging stress (σo ranges from 11 kPa to 986 kPa, where σo is the limiting bridging stress) and the R-curve response for RCC due to the varying number of bridging ligaments in individual specimens. Furthermore, the R-curve response is predicted to depend on crack geometry. Thus, the initiation toughness at the onset of crack growth is recommended as a conservative estimate of the fracture resistance in RCC. If this bounding structural integrity analysis gives unacceptably conservative predictions, it would be possible to employ the current fiber bridging model to take credit for extra fracture resistance in the RCC. However, due to the large scatter of the inferred bridging stress in RCC, such an implementation would need to be probabilistically based.

The fracture behaviour of intermetallic TiAl alloys with and without warm pre-stressing

The fracture behaviour of near-γ (NG) and fully lamellar (DFL) intermetallic TiAl alloys with and without warm pre-stressing (WPS) is investigated by testing three point bending specimens with fatigue pre-cracks at room temperature and at 700 °C. Detailed fractographic observations and FEM calculations are carried out to find the critical step of cleavage fracture. The results show that the cleavage fracture is induced by direct propagation of the pre-crack and that the stress at the crack tip is the decisive controlling factor. The WPS process improves the fracture initiation toughness of both the NG and the DFL microstructure, but deteriorates slightly the increase of the K-resistance curves, especially for the DFL microstructure. The compressive residual stress induced by WPS plays the main role in improving the fracture initiation toughness.

Ductile fracture of two-dimensional cellular structures

Crack growth initiation and subsequent resistance to propagation are explored numerically for regular and irregular hexagonal honeycomb structures made from ductile cell walls. The elasto-plastic response of the cell walls is described by a bilinear uniaxial stress-strain law, with fracture of the cell walls characterised by the fracture energy per unit area. Estimates for the macroscopic toughness and the associated plastic zone shape are derived analytically on the basis of simple considerations. Crack propagation is simulated numerically by fracturing elements within a finite element model and K-resistance curves are calculated under the assumption of small-scale yielding. The dependence of the crack growth behaviour upon the cell wall material parameters and geometric imperfections of the structure is investigated.

Determination of double-Determination of double- K criterion for crack propagation in quasi-brittle fracture Part I: experimental investigation of crack propagation

The results of experimental investigations using laser speckle interferometry on small size three-point bending notched beams and using photoelastic coating and the strain gauges on very large size compact tension specimens of concrete are presented in detail. The investigations showed that there exists a stage of stable crack propagation before unstable fracture occurs. The results are in agreement with other researchers' investigations using moire interferometry, holographic interferometry, dye-impregnation method and microscope. Further detailed study shows that the three different states, i.e., crack initiation, stable crack propagation and unstable fracture can be distinguished in the fracture process in concrete structures. In order to predict the crack propagation during the fracture process in quasi-brittle materials a double-K criterion is proposed. The double-K criterion consists of two size-independent parameters. Both of them are expressed in terms of the stress intensity factors. One of them reflects the initial cracking toughness, denoted with Kini, which can be directly evaluated by the initial cracking load, Pini, and the precast crack length, a0, using a formula of LEFM. The other one refers to the unstable fracture toughness, denoted with Kun, which can be obtained inserting the maximum load, Pmax, and the effective crack length, a, into the same formula of LEFM. The values of the two parameters, KIcini and KIcun, obtained from the small size three-point bending notched beams and the large size compact tension specimens show that KIcini and KIcun are size-independent. Evaluating with the K-resistance curves obtained from the same test data, it is found that the proposed double-K criterion is equivalent to it in basic principle, but, the double-K criterion can be applied more easily than the K-resistance curve. Finally, as a practical example, the application of the double-K criterion to the prediction of the crack propagation in a concrete dam is discussed.

Determination of Tension-Softening Curve and Fracture Behavior Evaluation in Granite with Crack Tip Toughness.

The tension-softening model has been employed to evaluate the crack growth behavior in rocks. In this paper, the tension-softening relation was determined taking the crack tip toughness into account. The extended J-based technique is applied to determine the tension-softening curve for a granite which has crack tip toughness. Compact tension (CT) specimens were used to conduct J-based fracture toughness tests on the granite. The crack tip toughness was measured using K-resistance curves in the granite. Three sizes of CT specimen were used to examine the specimen size effect on the deduced tension-softening curves. It was shown that the extended J-based technique provides reasonable tension-softening curves irrespective of the specimen size, suggesting the validity of the extended J-based technique. Finally, the necessity of the introduction of the crack tip toughness is demonstrated by performing numerical simulations of the load-displacement behaviors of the granite.

封圧下における岩石のき裂進展抵抗曲線

According to the core-based methods proposed by the authors, fracture toughness testing under confining pressure was carried out for Inada granite and Ogino tuff by using SR and C-RCT specimens, and K-resistance curves of the rocks were measured under confining pressure up to 29.4 MPa. The surfaces of a chevron-notch were sealed with a flexible and tough bellows-shaped film of copper and vinylchloride and other surfaces with a film of vinyl-chloride. In the C-RCT specimen, a fracture propagated parallel to the weakest plane (the bedding plane for the tuff and the rift plane for the granite) while, in the SR specimen, a fracture propagated perpendicular to the weakest plane to evaluate the anisotropy in the Kresistance curve under confining pressure.For both of the rocks, the K-resistance increased remarkably with confining pressure and the increase rate of the K-resistance with crack extension also became greater with confining pressure. Furthermore, the difference in the K-resistance between the two directions became greater with confining pressure. These phenomena were explained by the effects of confining pressure on the formation of process zone ahead of the crack tip. These effects are to reduce the tensile stress ahead of the crack tip by the component perpendicular to the crack plane, to decrease the rate of stress intensity factor with respect to crack extension by the same component of the confining pressure and to close pre-existing microcracks by the components parallel to the crack plane.

ＩＳＲＭ法による溶融石英とＰＭＭＡの破壊じん性評価

Fracture toughness testing of two transparent materials, fused silica and PMMA (polymethyl methacrylate), has been carried out according to a method suggested by ISRM (International Society for Rock Mechnics) in order to know the crack front evolution and also to examine the unloading compliance method for determining the crack length, and a K-resistance curve has been evaluated by the extended ISRM suggested method for these materials.The main results obtained in this study are as follows:(1) The crack front in brittle fused silica preceeds at the ends when the crack length is small, and it approaches to be a straigth line as the crack grows. On the contrary, the crack front in the ductile PMMA always preceeds at the center. Thus, the shape of the crack front depends on the material characteristics.(2) The unloading compliance method according to the ISRM suggested method can evaluate the crack length almost accurately for fused silica while it underestimates the crack length for PMMA, since the time-dependent crack growth occurs in the early stage of unloading. The gradient of a straigth portion in a load-displacement curve during unloading should be used to evaluate the crack length accurately for the materials such as PMMA.(3) A K-resistance curve can be determined almost accurately for brittle fused silica by the extended ISRM suggested method.

Ｃ‐ＲＣＴ試験法の開発と岩石の破壊靭性の異方性評価

In order to evaluate three-dimensional anisotropy in fracture toughness of rocks, a chevron-notched round compact tension (C-RCT) test has been developed. By adding it to the present ISRM Suggested Methods for Determining the Fracture Toughness of Rock, fracture toughnesses in three perpendicular orientations can be determined with a single boring core. A 3-D boundary element analysis has been carried out first for the C-RCT specimen and evaluation formulae on the stress intensity factor and the compliance of CMOD have been presented. Then after verifying the evaluation formulae by comparing a K-resistance curve of a granite between SR tests and C-RCT tests, three-dimensional anisotropy in the K-resistance curve has been evaluated for two rocks by using three specimen types of CB, SR and C-RCT.

Specimen size requirements for determining the inherent fracture toughness of rocks according to the ISRM suggested methods

In order to clarify the specimen size requirements for determining the inherent fracture toughness of rocks according to the Suggested Methods proposed by ISRM, short rod testing has been carried out for eight rocks. The K-resistance curve was evaluated for these rocks as well as for three rocks from a previous study. From the results, the specification of the specimen size requirements in order to determine the inherent fracture toughness of rocks is proposed in terms of the critical crack extension at which the corrected (level II) fracture toughness reaches a constant value.