The paper deals with experimental and numerical analysis of end-notched flexure (ENF) test of GRFP unidirectional laminates. The numerical analyses were performed in the ANSYS® program based on the ...finite element method. The fracture zone under mode II shear loading was modelled with the application of Virtual Crack Closure Technique (VCCT) associated with Linear Fracture Criterion and with the use of Cohesive Zone Method (CZM) coupled with bilinear delamination law. The problem of ENF test was solved with the use of one- and three-dimensional models with the implementation of linear interface element or contact element and by modelling the test in an accurate way (support and load rollers) and simplified by using boundary conditions. The benchmark studies confirmed the usefulness of several data reduction schemes and ruled out the Corrected Beam Theory as ineffective for determining the mode II critical energy release rate as well as highlighted the superiority of the CZM method over the VCCT has been confirmed by: (i) the possibility of applying the method for coarse meshes; (ii) convergence of results achieved for both two- and three-dimensional models; (iii) significantly shorter CPU time; and (iv) no need of the initial delamination front assumption.
•True mode II fracturing is compared to the conventional mode II fracturing.•A criterion is suggested to predict the fracturing type (tensile- or shear-based).•The superiority of the DNBD test over ...the existing ones is discussed.•True mode II DNBD tests are conducted on three different rock types.•True mode II values of the fracture toughness are compared to the mode I ones.
This paper discusses the use of the double-edge notched Brazilian disk test (DNBD) for measuring true mode II fracture toughness of rocks. The term true emphasises that in this test, not only is the crack tip loading shear-based, but also the material failure is shear-induced. Conventional mode II tests typically experience dominantly tensile failure. We introduce a fracture growth criterion that explains where and how a shear-based fracture extension occurs. Our theoretical analysis demonstrates that large values of compressive T-stress in the DNBD specimen significantly help inducing a true mode II fracturing. Crack tip parameters are computed by finite element analyses for various notch lengths and loading angles. These values are then employed to determine the geometry and loading condition for the optimal performance of the test. We also compare the DNBD with two other available tests for measuring true mode II fracture toughness, and show that the DNBD test typically has a lower contribution of mode I loading than the two alternative approaches and, therefore, better approximates the true mode II condition while at the same time being the experimentally simplest. Three types of rocks (limestone, marble and granite) were tested using the new approach and their true mode II fracture toughness is reported for two different crack lengths. The measured true mode II fracture toughness is compared with the mode I fracture toughness obtained from the semi-circular bending test.
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•The FPZ was studied under pure mode II load condition using the DIC method.•A BDCN specimen was used in this experimental study due to simple test setup.•A Mode II traction-free ...crack detection and localisation methodology is proposed.•The measured FPZ length is compared with multiple analytical predictions.•CTOD and CTSD vector components are measured and compared.
In this paper, the fracture process zone (FPZ) of a high-performance concrete (HPC) is studied. The analysis is done under a pure mode II load, making use of a digital image correlation (DIC) technique. The experimental test was performed on Brazilian disc with central notch (BDCN) specimens with a relative notch ratio a/R of 0.267. The main focus of this experimental study was the traction-free crack ahead of the notch tip, together with the FPZ extent ahead of the crack. This is done by adjusting the current method for mode I crack localisation to pure mode II cracks. Additionally, a traditional analytical formulation to predict FPZ length was substituted with the fracture toughness for mode II to cover mode II load cases. To verify the adjustments to the mode I crack identification, crack tip opening (CTOD) and crack tip sliding (CTSD) displacements were measured by DIC, which showed a mode II dominance in the crack tip displacement components.
The dynamic mode-II energy release rate of the end-notched flexure (ENF) test with applied time-dependent displacement is derived for the first time with the effect of vibration included. A dynamic ...Euler-Bernoulli beam theory is employed together with a deflection condition to simulate contact. To investigate the dynamic effect and the relative dynamic contribution from each vibration mode, a dynamic factor and a spatial factor are defined. It is found that the contribution of the ith vibration mode is dependent on the spatial factor (which is a function of the delamination length and the total length of the ENF specimen) and that certain vibration modes are dominant (depending on the delamination-length ratio). In addition, for a given spatial factor, there may be a certain vibration mode with a zero contribution to the ERR. The developed theory is verified against results from finite-element-method simulation for two cases of ENF tests and they are in excellent agreement. This work now allows the loading rate-dependent mode-II delamination toughness of layered materials to be determined using ENF tests. In addition, it provides understanding of the structural dynamic response in the presence of mode-II delamination and can guide the design of structures to mitigate the vibration-driven delamination.
•KIIc cannot completely reflect crack propagation resistance for layered rocks.•Fracture process initiation and acceleration were found during shearing for notched specimens.•More than one high ...strain zone may appear ahead of notch front for layered rocks.•Tensile fractures may generate even during shear process.
Shear-sliding mode fracture, i.e., mode II fracture, is a very common rupture mode of layered rocks. To achieve a better understanding of the anisotropy in the real mode II fracture, which propagates in a self-similar manner, a series of direct shear tests were conducted on single-notched specimens made of shale with three bedding angles, i.e., β = 0°, 45° and 90°. The ranking of the anisotropic mode II fracture toughness (KIIc) with different bedding angles is KIIc,45° >KIIc,90° >KIIc,0°, which is different from that of the anisotropic mode II fracture energy release rate (GIIc), i.e., GIIc,90° >GIIc,45° >GIIc,0°, suggesting that, unlike isotropic rocks, the crack propagation resistance of a layered rock cannot be completely characterized by its fracture toughness. From the acoustic emission monitoring results, it is found that the fracture process initiates and accelerates from the notch front once the applied mode II stress intensity factor (SIF) reaches its first and second thresholds, KII, FPI (approximately 50%∼70% of the fracture toughness) and KII, FPA (approximately 85%∼95% of the fracture toughness), respectively; generally, both KII, FPI and KII, FPA show noticeable anisotropies. The results of the b value indicate that more small-scale events occur in the specimen with β = 0°, and large-scale events account for a greater proportion in the specimen with β = 45°. A dominant high strain zone along the prefabricated crack direction and a secondary high strain zone along the bedding planes were discovered. Combining the acoustic emission and digital image correlation results, three typical fracture mechanisms were observed: (1) shear fracture along bedding planes when shearing along beddings; (2) shear fracture in matrix and along bedding planes for β = 45°; and (3) shear fracture in matrix and tensile fracture of bedding planes when shearing perpendicular to the beddings.
End-Notched Flexure (ENF) and Compact Shear (CS) tests were performed on Australian Radiata Pine to quantify Mode II fracture properties in wood. Capabilities and limitations of each fracture test ...are compared with respect to ease of testing, underlying reduction schemes to determine Mode II fracture toughness (or strain-energy release rate), stable crack growth and mixed mode behaviour during crack growth. In particular, different reduction schemes are presented with and without the need for cumbersome crack length measurements. In contrast to CS tests, it is found that ENF tests yield stable and reliable Mode II fracture with negligible mixed-mode behaviour. Considering resistance curves, crack length measurements are only needed to determine initial fracture energy values associated with crack length values up to 20 mm while compliance-based beam theory can be used to calculate steady-state fracture energies by means of an equivalent crack length that only requires global load–displacement test data.
•Direct comparison of End-Notched Flexure (ENF) and Compact Shear (CS) tests.•Both tests result in similar energy release rate values in the RL and TL planes ranging from 1.34 N/mm up to 1.49 N/mm.•ENF tests yield stable and reliable Mode II fracture with negligible mixed-mode behaviour.•CS tests include unwanted Mode I contributions of up to 35%.
•The mode I SIF decreases and mode II SIF increases with increasing dislocation ratios or crack ratios.•The mixed mode I/II crack propagation trajectory in the ZCCDS sandstone specimen changes from ...kinked to straight when the mode I SIF decreases.•The JRC of ZCCDS sandstone specimens first increases and then stabilizes with increasing the mixed factors.
Mode II fracture often occurs in rock, which often result in violent ruptures of rock and catastrophic failure of rock engineering. However, attempts to replicate mode II crack extension on a laboratory scale generally fail due to the existence of tensile stress at the notch tip. In this study, a novel testing method named the Z-shaped centre cracked direct shear (ZCCDS) test was developed to examine the mode II fracture of rock, and a series of tests were performed on sandstone with various dislocation ratios (α1) and crack ratios (α2). The equation for calculating the mode II fracture toughness (KIIC) of rock was determined using the finite element method. The validity and reliability of this test method were verified by digital image correlation analysis and comparison with KIIC values determined by the other methods. The testing results showed that the peak shear load changes slightly with increasing α1 and decreases with increasing α2. The mode I stress intensity factor (SIF) decreases while mode II SIF increases with increasing α1 or α2. When α1 = 0.25 and α2 = 0.3, relative sliding deformation at the notch tip was captured via displacement vector analysis, corresponding to a true KIIC of 4.16 MPa∙m0.5. In addition, the effect of α1 and α2 on the failure characteristics of ZCCDS sandstone specimens is slight, and the pure mode II crack of the sandstone satisfies “self-similar extension”. The fracture surface becomes smoother with increasing contribution of the mode II component due to the wide distribution of transgranular fractures. The findings of this study can facilitate better understanding of mode II fracture behaviour of rock.
•Debonding occurred at the matrix–fiber interface.•A global width effect was not observed.•After the onset of debonding friction contributed to the increase of the load.•The effective bond length ...leff due to bond was estimated to be 255mm.•Cohesive material law and fracture energy were obtained from strain profiles.
The results of single-lap shear tests, conducted on specimens with fiber reinforced cementitious matrix (FRCM) composite strips bonded to concrete blocks, are presented in this paper. The FRCM composite was comprised of polyparaphenylene benzobisoxazole (PBO) fibers and polymer-modified cement-based mortar. This study indicates that in PBO FRCM–concrete joints debonding mainly occurs at the matrix–fiber interface. Friction between fiber filaments and between fibers and matrix is observed after the debonding process initiates. The experimental data suggest that a width effect does not exist among the fiber bundles, and an effective bond length can be defined and is approximately 260mm. Axial strain profiles along the bonded length are analyzed to investigate the stress-transfer mechanism at the matrix–fiber interface.
This study aimed at estimating crack tip position in adhesive bonded joints under mode II quasi‐static loading using experimental and numerical approaches. Experimental techniques were utilized and ...compared, including optical backscatter reflectometry, visual testing, and a novel strategy based on digital image correlation. Additionally, a finite element analysis was employed to identify the numerical crack tip position and the extent of damage within the bondline. This analysis revealed that a significant portion of the crack propagation region in the adhesive is occupied by the fracture process zone. Moreover, optical backscatter reflectometry shows the potential to detect this process zone within the adhesive that the other methods may not detect. This capability is particularly beneficial for detecting damage at early stages.
Highlights
OBR and DIC were used for crack initiation and propagation in ENF joint under mode II.
OBR back‐face strain demonstrated its ability to detect potential early‐stage damage.
Trapezoidal TSL outperformed bi‐linear TSL in FE crack propagation modeling.
A significant portion of crack propagation region was occupied by FPZ in adhesive.
Multi-walled carbon nanotubes (MWCNTs) were added to an epoxy resin in an effort to improve the fracture toughness of bulk epoxy and also when used as matrix for carbon fibre reinforced epoxy ...composites (CFRPs). The incorporation of MWCNTs to bulk epoxy and CFRPs moderately increased the mode-I fracture energy, and significantly increased the mode-II fracture energy, i.e. the average mode-II fracture energy of CFRPs increased from 2026 J/m2 to 3406 J/m2 due to the addition of 0.5 wt% MWCNTs, and further to 5491 J/m2 due to the addition of 1 wt% MWCNTs. The superior toughening performance of MWCNTs in mode-II fracture is attributed to two reasons: 1) increased MWCNT breaking and crack deflection mechanisms under shear load; and 2) large fracture process zone accompanied with extensive hackle markings and micro-cracks ahead of the mode-II crack tip of CFRPs, which resulted in significant number of MWCNTs contributing to toughening mechanisms.
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•MWCNTs were used to enhance epoxy and carbon fibre composites.•Mode-I and Mode-II fracture behaviour was studied.•The addition of MWCNTs moderately increased Mode-I fracture toughness.•The addition of MWCNTs significantly increased Mode-II fracture toughness.
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