Examination of the 4-ENF test for measuring the mode III R-curve of wood

The four-point bend end-notched flexure (4-ENF) test, which was originally developed for measuring the mode II R-curve, is thought to be applicable for measuring the mode III R-curve. In this study, a 4-ENF fracture test of spruce was conducted for obtaining the mode III R-curve, and the test method was numerically and experimentally analyzed. In the numerical analysis, three-dimensional finite element calculations were conducted to determine the distribution of the strain energy release rate along the delamination front by the virtual crack closure technique (VCCT). In the experimental analysis, the mode III R-curve was examined by the modified beam theory and compliance calibration methods of data reduction, which have been conventionally used for analyzing the mode I or mode II R-curve. In addition to these conventional data reduction methods, the strain at each loading point was measured, as was the loading-line displacement and critical load for crack propagation, and the R-curve was obtained by the combination of loading-line compliance, load-longitudinal strain compliance, and critical load for crack propagation, which is named the “compliance combination method”. The finite element analyses suggested that the pure mode III fracture state existed in the mid-section of the specimen in spite of the existence of a small mode II component at the free edges of the delamination front, and the mode III strain energy release rate component calculated by the VCCT coincided well with those obtained by the data reduction methods examined here. The actual R-curve obtained by the compliance combination method coincided well with those by the modified beam theory and compliance calibration methods when the strain was appropriately measured. From these results, therefore, the 4-ENF fracture test is a promising means for obtaining the mode III R-curve of wood.     

R-curve behavior in notched beam tests of rocks

The R-curve for sandstone is obtained from the load-crack mouth opening response of notched specimens subjected to three-point-bending. This approach is used to analyze the fracture behavior under monotonic and cyclic loading. The asymptotic limit of the R-curve compares well with the fracture toughness determined through an effective crack model. The analysis of the relaxation observed before the unloading-reloading cycles in the cyclic tests leads to the conclusion that the fracture toughness remains practically constant while the crack propagates slightly during the load drop.     

Crack path selection in the fracture of fresh and degraded epoxy adhesive joints

The crack paths and fracture surfaces of aluminum–epoxy adhesive joints were characterized as a function of the mode ratio of loading and the amount of degradation that had been generated using the open-faced aging technique. A finite element (FE) model was used to predict the extent of the plastic zone at different crack growth lengths and mode ratios, and a close relationship was found between the evolution of the plastic zone and the previously reported R-curve behavior of these joints. The micro-topography of the fracture surfaces, measured using an optical profilometer, showed that a ductile–brittle transition occurred in the fracture behavior of the joints as degradation progressed. The crack path in the (brittle) degraded specimens was normal to the first principal stress, but could not be predicted in the undegraded joints because of its highly three-dimensional nature. Based on the distribution of the maximum von Mises stress in the adhesive layer ahead of the crack tip, a crack growth mechanism was proposed that is consistent with these experimental observations and explains the highly three-dimensional nature of fracture in these highly constrained joints.     

Comparison of failure mechanisms between rubber-modified and unmodified epoxy adhesives under mode II loading condition

The effect of rubber modification on fracture toughness of adhesive joints under mode II loading condition was investigated in comparison with that under mode I loading, wherein the two adhesives rubber-modified and unmodified were used. To evaluate the fracture toughness on the basis of R-curve characteristics under mode II loading condition, four-point bend tests had been conducted for the adhesively bonded end-notched flexure (ENF) specimens. Thus obtained R-curves revealed the following trend: its behavior did not appear for the unmodified adhesive, whereas the rubber-modified adhesive exhibited a typical behavior. In the initial stage of crack propagation, G _IIC of the rubber-modified adhesive is lower than that of the unmodified adhesive, but becomes greater in the range of Δa > 25 mm. Nevertheless, the significant improvement of the fracture toughness with the rubber modification under mode I loading condition was not observed under mode II loading. Moreover, FEM analysis was made to elucidate the relation between the above fracture behavior and stress distributions near the crack tip. The results gave the reasonable relationship between evolution of plastic zone and the area with high void-fraction as well as the R-curves behavior. In addition, macroscopic and SEM observations for the fracture surfaces were also conducted.     

Effect of geometry and electrical boundary conditions on R-curves for lead zirconate titanate ceramics

R-curve measurements on PZT poled in thickness direction were carried out on CT specimens under different electric boundary conditions. The effect of specimen geometry was evaluated by measuring R-curves in CT specimens of different thickness and comparing these with R-curves in bend bars. A low coercive stress is responsible for the development of a large switching zone. This switching zone is of high relevance for the computation of the actual stress intensity factor at the crack tip and for the R-curve calculation.     

Determination of the length dependence of the threshold for fatigue crack propagation

A rising load amplitude crack growth test on specimens pre-cracked in cyclic compression is presented as a procedure to determine the length dependence of the threshold of fatigue crack propagation described by the R(resistance)-curve for the threshold of stress intensity factor range. The experimental results show that the residual stress field in front of the pre-crack can significantly influence the R-curve.In order to measure the material specific R-curve which is not affected by the pre-cracking condition it is important to use the smallest possible load amplitude. To achieve this goal, a very small notch root radius is essential. It is shown that at notches machined by razor blade polishing technique the load amplitude for pre-cracking can be reduced to values where the load history does not influence the R-curve for the threshold of stress intensity range.     

Fracture load predictions and measurements for highly toughened epoxy adhesive joints

A method to predict the ultimate strength of adhesive joints has been evaluated for the quasi-static loading of a variety of cracked-lap shear (CLS) and single-lap shear (SLS) joints bonded with a high-strength, toughened epoxy adhesive. The adhesive strength was experimentally characterized in terms of the steady-state critical strain energy release rate, , as a function of the loading phase angle, using double cantilever beam (DCB) joints. Comparing the calculated energy release rate using the J-integral with the at the corresponding phase angle, the ultimate failure load in the fracture joint was predicted and compared with experimental results. When the toughening of the adhesive during subcritical crack growth (i.e. its R-curve behavior) was considered in the analysis, good agreement between the predicted and experimental failure loads was achieved, both for joints made with aluminum or steel adherends. The initial condition at the end of joint overlap (fillet or precrack) did not affect the ultimate joint strength because of the significant amount of subcritical crack growth.     

Evaluation of R-curve behavior of ceramic-metal functionally graded materials by stable crack growth

This paper deals with the fracture toughness and R-curve behavior of ceramic-metal functionally graded materials (FGMs). A possibility of stable crack growth in a three-point-bending specimen is examined based on the driving force and resistance for crack growth in FGMs, and the distribution of fracture toughness or R-curve behavior is evaluated on FGMs fabricated by powder metallurgy using partially stabilized zirconia (PSZ) and stainless steel (SUS 304). The materials have a functionally graded surface layer (FGM layer) with a thickness of 1 mm or 2 mm on a SUS 304 substrate. Three-point-bending tests are carried out on a rectangular specimen with a very short crack in the ceramics surface. On the three-point-bending test, a crack is initiated from a short pre-crack in unstable manner, and then it propagates in stable manner through the FGM layer with an increase in the applied load. From the relationship between applied load and crack length during the stable crack growth in the FGM layer, the fracture toughness is evaluated. The fracture toughness increases with an increase in a volume fraction of SUS 304 phase.     

The crack growth resistance of thin steel sheets under eccentric tension

The stable crack growth in thin steel sheets is the topic of this paper. The crack opening was observed using a videoextensometry system, allowing the crack extension determination. J_R-curve and δ_R-curve were established from obtained data. The ductile tearing properties of different thin sheets of steel were determined, including the impact of the specimen orientation, from test performed on compact tension specimens loaded under two conditions. The effect of the material, the rolling direction, and loading rate on the crack growth resistance of thin steel sheets was analyzed. In addition to the crack growth resistance, J-integral values for crack initiation were also estimated. The relation between J _i and J_0.2 was assessed using the basic mathematical and statistical methods. This relation was described by a linear regression model.     

Quantitative fractography of mixed-mode fracture in an R-curve material

Mixed-mode fracture surfaces of an R-curve material were quantitatively assessed using fractography. The R-curve material chosen was a mica glass ceramic. Vickers indentation cracks of different sizes were introduced at the center of tensile surface of glass ceramic bars fractured in flexure. The bars were fractured in flexure by generating mixed-mode (I/II) loading conditions at crack tips by orienting indentation cracks at various angles with respect to the tensile axis. Quantitative fractography indicated that crack-to-mirror size ratios were a function of crack length and mode mixity. Stress intensity at branching for the mirror–hackle transition during mixed-mode (I/II) fracture condition was a constant and was less than the corresponding stress intensity at branching in mode I loading. An empirical relationship is derived for the effective geometric factors in mixed-mode fracture of ceramics from surface cracks in flexure.     

Interlaminar and intralaminar fracture characterization of composites under mode I loading

The interlaminar and intralaminar fracture of laminated composites under mode I loading was studied using the double cantilever beam test. The effect of bridging on the measured fracture energy was assessed by cutting fibres during crack propagation. The fracture energy was evaluated considering a previously developed data reduction scheme based on the beam theory and crack equivalent concept. The model only requires the applied load–displacement data and provides a complete R-curve allowing the definition of the critical energy from the plateau value. A cohesive damage model was used to validate the procedure. It was verified experimentally that bridging phenomenon is pronounced, being more important in intralaminar tests. However, a detailed observation of the intralaminar R-curves showed that the intrinsic toughness, without fibre bridging effects, is similar to the interlaminar one.     

Crack equivalent based method applied to wood fracture characterization using the single edge notched-three point bending test

In this work the single edge notched-three point bending test applied to wood fracture characterization in mode I is analysed. A new data reduction scheme founded on the equivalent linear elastic fracture mechanics with remarkable advantages relatively to classical methods is proposed. The method is based on the beam theory accounting for a triangular stress relief region and on the crack equivalent concept. It does not require crack monitoring during its propagation and provides a complete R-curve which is fundamental for a clear identification of the fracture energy. The model was validated numerically by means of a bilinear cohesive damage model which allows the simulation of damage initiation and growth. The size of the stress relief region in the neighbouring crack zone was estimated and a consistent value was found relatively to the one achieved by other authors.     

Bridging effect on mode I fatigue delamination behavior in composite laminates

This paper discusses the bridging effect of fibres on mode I fatigue delamination growth in unidirectional and multidirectional polymer composite laminates based on a series of double cantilever beam (DCB) tests. From the results, there is sufficient evidence that fibre bridging can decrease the crack growth rate da/dN significantly, and using only one fatigue resistance curve to determine the delamination behavior in composite materials with large-scale fibre bridging may be inadequate. The bridging created in fatigue delamination is different from that of quasi-static delamination at the same crack length. So it is incorrect to use the resistance curve (R-curve) from quasi-static delamination tests to normalize fatigue delamination results.     

Weibull modulus of fracture strength of toughened ceramics subjected to small-scale contacts

The Weibull modulus of toughened ceramics was evaluated. The fracture of the toughened ceramics was assumed to be initiated by surface cracks induced during small-scale contacts such as grinding and polishing and an exponential function was selected to describe the R-curve behavior. Based on a brief theoretical analysis, a numerical simulation procedure was designed to predict the fracture strength for toughened ceramics with different R-curve characteristics. The Weibull modulus of each toughened ceramic was estimated and compared with that of the un-toughened base material. It was concluded that an increase in Weibull modulus can always result from toughening. The increase in Weibull modulus was found to be related directly to the relative crack tolerance, i.e., the ratio of the initial crack size to the critical crack size. This suggests that the improvement in crack stability due to toughening is the main reason for the increased Weibull modulus.     

Mode III interlaminar fracture of carbon/epoxy laminates using the edge crack torsion (ECT) test

The mode III interlaminar fracture of carbon/epoxy laminates was evaluated with the edge crack torsion (ECT) test. Three-dimensional finite element analyses were performed in order to select two specimen geometries and an experimental data reduction scheme. Test results showed considerable non-linearity before the maximum load point and a significant R-curve effect. These features prevented an accurate definition of the initiation point. Nevertheless, analyses of non-linearity zones showed two likely initiation points corresponding to G_IIIc values between 850 and 1100 J/m² for both specimen geometries. Although any of these values is realistic, the range is too broad, thus showing the limitations of the ECT test and the need for further research.     

A finite element analysis of stable crack growth in an aluminium alloy

Extensive stable cracking has been observed in large test pieces of 25 mm thick weldable AlMgZn alloy which is used in the construction of a portable bridge. Standard fracture specimens produced valid K_IC values, with short cracks exhibiting unstable fracture. Finite element analysis of the large specimens determined a valid J_R-curve that can increase the effective K_C by several times the K_IC value. The R-curve has an unusual ‘concave’ shape that is associated with the change from initially flat fracture to fully slant fracture. The early stages of the R-curve are affected by in-plane constraint that can be indexed by the T-stress. The R-curve can be used to explain the stability of long cracks in full-scale tests on a bridge prototype, compared with the instability of short cracks in small, standard test pieces.     

Random growth of crack with R-curve: Markov process model

A probabilistic model for the randomness of the progressive crack growth in a quasi-brittle material such as concrete is presented. The model consists of a Markov chain adapted to R-curve behavior. It yields the crack propagation probability in any loading step as well as the probability of failure at any stage of the fracture process. The R-curve is obtained from the given test data on the effect of structure size on the maximum loads. The standard deviation of the peak load is the minimum statistical information required. According to the available test results, this standard deviation is approximately a linear function of the crack propagation distance. The parameter estimation method is formulated and some applications are illustrated.     

Effect of ion exchange on <Emphasis Type="Italic">R</Emphasis>-curve behavior of a dental porcelain

The objective of this study was to evaluate the effect of the ion exchange treatment on the R-curve behavior of a leucite-reinforced dental porcelain, testing the hypothesis that the ion exchange is able to improve the R-curve behavior of the porcelain studied. Porcelain disks were sintered, finely polished, and submitted to an ion exchange treatment with a KNO₃ paste. The R-curve behavior was assessed by fracturing the specimens in a biaxial flexure design after making Vickers indentations in the center of the polished surface with loads of 1.8, 3.1, 4.9, 9.8, 31.4, and 49.0 N. The results showed that the ion exchange process resulted in significant improvements in terms of fracture toughness and flexural strength as compared to the untreated material. Nevertheless, the rising R-curve behavior previously observed in the control group disappeared after the ion exchange treatment, i.e., fracture toughness did not increase with the increase in crack size for the treated group.