Asymmetric Four-point Bending Research Articles

Residual shear strength of a severely ASR-damaged flat slab bridge

Although the residual shear strength of ASR-damaged slab bridges without shear reinforcement has been discussed for several decades, the amount of published research on this topic is very limited. This paper presents the results of a test series on 18 reinforced beams sawn from a severely ASR-damaged flat slab bridge. Flexural failure as well as shear failure were observed. The test results indicate that the ASR cracks in the beams strongly influenced the propagation of load-induced cracks. Generally, the calculated moment capacity of beams tested in three-point bending was lower than the maximum moment carried by the beams. For the beams tested in asymmetric four-point bending, an increase in the shear span-to-effective depth ratio resulted in a decrease in the measured shear strength. The measured shear strengths were compared with calculated shear strengths using the Eurocode 2. Calculations based on the compressive strength of drilled cores were rather conservative at low shear span-to-effective depth ratios. However, the conservatism of the Eurocode 2 decreased with increasing shear span-to-effective depth ratios. With the inclusion of ASR-induced pre-stress effect, the calculated shear strengths correlated better with the measured shear strengths. The test results indicated that the ASR-induced pre-stress effect can, to some extent, compensate for the significant loss in material properties.

Characterization of mixed mode fracture properties of nanographene reinforced epoxy and Mode I delamination of its carbon fiber composite

Abstract Motivated by previous research performed by the authors investigating Mode I toughness enhancement using nanographene in EPON 862 epoxy, this article aims to investigate (a) the changes in mixed mode fracture properties of a thermoset polymer (EPON 862) reinforced with hydrogen passivated nanographene platelets (HP-NGPs) and, (b) Mode I fracture properties of EPON 862/IM7 unidirectional laminate with and without dispersed HP-NGPs. For (a), mixed mode fracture experimentation was performed using an asymmetric four-point bending specimen on baseline (0 wt%), 0.1 wt% and 0.5 wt% HP-NGP reinforced EPON 862 polymer. Three different mode mix (KII/KI) ratios (0.78, 1.53, 117) were used to obtain an experimental fracture envelop encompassing pure Mode I to Mode II. Remarkable increase in the fracture envelop both in Mode I (∼3 times) and Mode II (∼2.5 times) was observed with only 0.5 wt% of HP-NGP. For case (b), Double Cantilever Beam (DCB) experiments were used to obtain the fracture toughness of the unidirectional laminates with the HP-NGP reinforced matrices as in (a), in accordance with ASTM D5528. Significant increase (∼100%) in resistance to crack propagation was observed for 0.5 wt% NGP reinforced system in comparison to baseline samples.

Effect of particle size on mixed-mode fracture of nanographene reinforced epoxy and mode I delamination of its carbon fiber composite

Motivated by the lack of available mixed-mode test data in the literature on graphene nanocomposites, this article aims to investigate two cases: (a) the changes in mixed-mode fracture properties of a thermoset polymer (EPON 862) reinforced with hydrogen passivated nanographene platelets (HP-NGPs) and, (b) Mode I fracture properties of EPON 862/IM7 unidirectional laminate with dispersed HP-NGPs. For case (a), mixed mode fracture experimentation was performed using an asymmetric four-point bending specimen on baseline (0wt%), 0.1wt% and 0.5wt% HP-NGP reinforced EPON 862. Three different mode mix (KII/KI) ratios (0.78, 1.53, 117) were used to obtain a fracture envelop encompassing pure Mode I to Mode II. Remarkable increases in the fracture envelop both in Mode I (3 times) and Mode II (2.5 times) was observed with only 0.5wt% of HP-NGP. For case (b), Double Cantilever Beam (DCB) experiments were used to obtain the fracture toughness of the unidirectional IM7/EPON 862 laminates with the HP-NGP reinforced matrices. Significant increase (100%) in resistance to crack propagation in DCB specimens was observed. A brittle to ductile transition at the crack tip due to a novel nanoscale size effect is postulated and verified using TEM as the reason for the toughness increase.

Modeling of toughness enhancement mechanisms in graphene nanocomposites

ABSTRACTThe objective of this paper is to develop a mechanism-based theoretical model to explain fracture experiments conducted on nanographene platelet (NGP) reinforced thermoset polymer nanocomposite tested in pure Mode I and in mixed mode by the authors and other researchers. Remarkable improvement in fracture toughness, KIC (∼200%), and critical strain energy release rate, GIC (∼570%), was observed with only 0.5 wt% NGP addition to the EPON 862 polymer system. Interestingly, very large increase in ductility of the fracture specimens at peak load was observed with increasing NGP loading. Asymmetric four-point bend tests were also performed for three different mode mix (tan−1(KII/KI)) ratios (38°, 57°, and 89.5°). Significant enhancement in toughness as well as ductility for each mode mix case was observed with increasing NGP loading. Further, significant increases of 48% and 100% in delamination initiation toughness and resistance to crack propagation, respectively, were observed for 0.5-wt% NGP-reinforced IM7/EPON 862 unidirectional laminate. In this article, the reinforcement capacity of NGPs is explained through a length-scale based toughness enhancement mechanism, which is then employed to predict the critical length and orientation of nanoparticles for maximum fracture toughness improvement. It is envisioned that the application of this model could lead to significant toughness enhancement in composite laminates through (a) reduced intralaminar matrix cracks, (b) improved fiber/matrix interfacial toughening by controlling the size of nanoparticle growth on fuzzy fibers, and (c) improved delamination toughening as already demonstrated by the authors. For conclusive verification of our proposed model, there is a need for in-situ experiments to fully verify the nanoscale toughening effect by observing the process zone size near the tip of a nanoscale crack in a polymer thin film in-situ while it is being loaded, visualizing the brittle–ductile transition postulated by our theory and MD simulations. Work is currently underway in collaboration with the Air Force Research Laboratory to accomplish this objective.

Application of an average strain energy density criterion to obtain the mixed mode fracture load of granite rock tested with the cracked asymmetric four-point bend specimens

Mixed mode brittle fracture behaviour of granite rock is studied experimentally and theoretically using Asymmetric Four Point Bend (AFPB) specimens containing pre-cracks subjected to different mixed mode loading conditions, ranging from pure mode I to pure mode II. The main aim of this paper is twofold. First, to present a complete set of experimental results on fracture of pre-cracked granite samples under various in-plane loading mixities, and second, to predict the fracture loads of the tested rock samples under mixed mode I/II conditions using an energy-based criterion, namely the Average Strain Energy Density (ASED) criterion. Good agreement is found between the experimentally obtained fracture loads and the theoretical predictions based on the constancy of the mean strain energy density over the material volume. It is shown that the ASED criterion is able to provide well predictions for the fracture loads of the investigated rock material containing a pre-crack.

In-plane shear properties of medium-density fibreboard measured by asymmetric four-point bending of a notched specimen

In this research, asymmetric four-point bending (AFPB) tests were used to obtain the in-plane shear (IPS) properties of medium-density fibreboard (MDF). Circular notches were cut on the top and bottom surfaces of rectangular MDF bars with variable distances between the notch roots. Both tab-free and tabbed specimens were prepared from these bars. The AFPB tests were conducted using these specimens, and three IPS properties, that is, the shear modulus, proportional limit stress, and stress at failure, were measured. When using tabs, the IPS properties could be obtained for a wide range of the notch root distances, although the failure initiated at the notch roots led to the catastrophic failure.

Crack propagation direction in a mixed mode geometry estimated via multi-parameter fracture criteria

A numerical parametric study on the crack growth direction under mixed mode conditions (I+II) is introduced. An eccentric asymmetric four-point bending of a single edge notched beam specimen is considered as an example, since various levels of mode mixity can be thus obtained. The crack growth direction is estimated using the maximum tangential stress (MTS) criterion, the strain energy density (SED) criterion and the crack tip displacement (CTD) criterion. Multi-parameter fracture mechanics based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series is employed. It was found out that whereas the use of the CTD and SED criteria should be accurate enough even in their classical (or two-parameter) form for most geometries and distances of their application from the crack tip, the generalized form of the MTS criterion with at least four terms of the series should be applied, if the distance of its application is not less than 0.01 of the specimen width. Moreover, it is able to describe the typical dependence of the initial kink angle on the distance from the crack tip where the criterion is applied.

Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria

The presented work introduces a numerical parametric study on the crack propagation direction under mixed-mode conditions (mode I + II). It is conducted for the geometry of an eccentric asymmetric fourpoint bending of a single edge notched beam specimen; various levels of mode-mixity are ensured by modifications in the crack length and crack eccentricity. The direction of crack propagation is estimated semianalytically using both the maximum tangential stress criterion and the strain energy density criterion (implemented as a procedure within the used finite element computational code) as well as numerically (from verification reasons). Multi-parameter fracture mechanics is employed in the presented work for precise analytical evaluation of the stress field in the cracked specimen. This theory is based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series. Recent studies show that utilization of only first term of the series, which corresponds to the stress intensity factor (SIF), the single controlling parameter for the crack initiation and propagation assessment in brittle materials, is insufficient in many crack problems. It appears also in this study that the higher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarly to a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extent estimation, etc.).

Multi-parameter fracture criteria for the estimation of crack propagation direction applied to a mixed-mode geometry

A parametric study has been performed on an eccentric asymmetric four-point bending specimen in order to investigate initial crack propagation direction. Under various levels of mixed-mode conditions, the generalized form of the maximum tangential stress criterion and the strain energy density criterion has been derived by means of the multi-parameter description of the crack-tip stress field. A discussion on the need to consider several more initial terms of the Williams expansion during fracture behaviour assessment is presented and some recommendations are stated based on the results of the analyses.

Mixed-Mode Testing for an Asymmetric Four-Point Bending Configuration of Polyurethane Foams

Many efforts have been made recently to determine the fracture toughness of different types of foams in static and dynamic loading conditions. Taking into account that there is no standard method for the experimental determination of the fracture toughness of plastic foams, different procedures and specimens were used. This paper presents the polyurethane foam fracture toughness results obtained experimentally for three foam densities. Asymmetric four-point bending specimens were used for determining fracture toughness in mode I and in a mixed one, and also the influence of the loading speed and geometry of the specimen were investigated.

In-plane shear strength of paper measured by asymmetric four-point bending test

Abstract The in-plane shear strengths (IPSS) of copy paper, filter paper, and sack paper were obtained from an asymmetric four-point bending (AFPB) test. Rectangular tabs of medium-density fibreboard (MDF) were bonded to the paper specimen. The length of the clearance between the tabs was varied, and the influence of the clearance on the IPSS value was investigated. The IPSS obtained from the AFPB test was compared with that obtained from a 35° off-axis tension (OAT) test, which was proposed in a previous study. The IPSS values obtained from the AFPB tests on the copy paper and sack paper were significantly lower than those obtained from the 35° OAT tests because of the localised buckling caused by the negative principal stress. In contrast, the IPSS values obtained from the AFPB and OAT tests on the filter paper were in agreement when the clearance length was >5 mm because the buckling effect was excluded.

Effect of Specimen Configuration and Lamination Construction on the Measurement of the In-plane Shear Modulus of Plywood Obtained by the Asymmetric Four-point Bending Test

In this study, the in-plane shear modulus of 3-, 5-, and 7-ply lauan wood (Shorea sp.) was measured by conducting an asymmetric four-point bending (AFPB) test with various specimen depth/length ratios and subsequently performing a flexural vibration (FV) test and finite element analysis (FEA). The results obtained from the experiment and the FEA revealed that the in-plane shear modulus was dependent on the depth/length ratio of the specimen. The dependence of the in-plane shear modulus obtained from the AFPB test was more significant than that obtained from the FV test. Additionally, the in-plane shear modulus values obtained from the AFPB test varied more significantly than those obtained from the FV test. In determining the in-plane shear modulus of plywood, the FV test was therefore superior to the AFPB test.

Mode II Critical Stress Intensity Factor of Medium-Density Fiberboard Measured by Asymmetric Four-Point Bending Tests and Analyses of Kink Crack Formation

Using medium-density fiberboard specimens, asymmetric four-point bending tests were conducted to obtain the Mode II critical stress intensity factor for this in-plane system. Because the medium-density fiberboard is in-plane quasi-isotropic about its board plane, the crack propagates obliquely with respect to the initial crack direction under the asymmetric four-point loading condition. A finite element analysis is required to obtain the Mode II stress intensity factor. The analysis herein was conducted to take into account the kink crack formation. In addition, a three-point bend end-notched flexure test was also conducted, and the results obtained by the experiments and numerical calculations were compared. When the initial crack’s length-to-specimen’s depth ratio ranged from 0.85 to 0.95 and when the additional crack length was taken into account, the Mode II critical stress intensity factor KIIc was appropriately obtained by the asymmetric four-point bending test.

Interlaminar Shear Strength of Medium-Density Fiberboard (MDF) Measured by Three-Point Short-Beam Shear Test and Comparison with that Obtained by Asymmetric Four-Point Bending Test

In this research, interlaminar shear strength of medium-density fiberboard (MDF) as obtained by a three-point short-beam shear test was examined. The three-point short-beam shear tests were conducted on MDF, which were used in a previous research on the asymmetric four-point bending tests. Interlaminar shear strength was measured using the specimens with rectangular and I-shaped cross sections with varying the span lengths. It is less useful to obtain the interlaminar shear strength by the three-point short-beam shear test than the asymmetric four-point bending test because the effective span length for obtaining an appropriate value of interlaminar shear strength is extremely restricted.

Determination of the Shear Buckling Load of a Large Polymer Composite I-Section Using Strain and Displacement Sensors

This paper presents a method and procedure of sensing and determining critical shear buckling load and corresponding deformations of a comparably large composite I-section using strain rosettes and displacement sensors. The tested specimen was a pultruded composite beam made of vinyl ester resin, E-glass and carbon fibers. Various coupon tests were performed before the shear buckling test to obtain fundamental material properties of the I-section. In order to sensitively detect shear buckling of the tested I-section, twenty strain rosettes and eight displacement sensors were applied and attached on the web and flange surfaces. An asymmetric four-point bending loading scheme was utilized for the test. The loading scheme resulted a high shear and almost zero moment condition at the center of the web panel. The web shear buckling load was determined after analyzing the obtained test data from strain rosettes and displacement sensors. Finite element analysis was also performed to verify the experimental results and to support the discussed experimental approach.

The consolidation and bond strength of rafted sea ice

The consolidation and bond strength of rafted sea ice were investigated through a series of experiments undertaken in the Ice Physics Laboratory at the UCL. To simulate a section of rafted sea ice, blocks of laboratory grown saline ice were stacked in an insulated tank with spacers between adjacent blocks to allow saline water to flood in. The rate of consolidation was then monitored using a combination of temperature readings recorded in the ice and liquid layer, salinity measurements of the liquid layer, and cores taken at specific times of interest. Two states of consolidation were observed: thermodynamic consolidation where the ice blocks were physically bonded but the bond strength was weak, and mechanical consolidation where the bond had reached full strength. Results showed that the rafted ice had physically bonded in less than a day, however it took many more days (6 to 30 depending on the environmental conditions) for the bond to reach maximum strength. Increasing the thickness of the ice, the salinity of the water and the inter-block gap size all increased the consolidation time. Once consolidated, ice cores were taken and sheared using the asymmetric four-point bending method to measure the strength of the bond between the ice blocks. These were then compared to the shear strength of solid ice blocks simulating level sea ice. Our results show that the shear strength of the bond between the rafted ice blocks is about 30% weaker than that of level ice.

Mode II critical stress intensity factor of wood measured by the asymmetric four-point bending test of single-edge-notched specimen while considering an additional crack length

No abstract available.

Discussion of: “Mode II fracture mechanics properties of wood measured by the asymmetric four-point bending test using a single-edge-notched specimen of Hiroshi Yoshihara Eng. Frac. Mech. 75 (2008) 4727–4739”

A discussion is given of the article mentioned in the title. The conclusions of this article, based on classical fracture mechanics, are shown to be questionable in the light of new theory and the there preferred mode II asymmetric four point bending test is shown to be problematic in giving the right values of fracture toughness and release rate. The in the article given data provide information on equivalent mode II softening behaviour and confirms that the strength of the intact fracture plane then is determining, the same as applies for mode I.

Interlaminar shear strength of medium-density fiberboard obtained from asymmetrical four-point bending tests

The interlaminar shear strength was obtained by conducting an asymmetrical four-point bending test. Four types of specimens including rectangular, side-grooved, side-tapered, and notched specimens, were prepared. In the test, the span lengths varied, and the influence of the span length with respect to the specimen depth was examined. The specimen configuration was also examined. The interlaminar shear strength was effectively obtained, except for the notched specimens, when the span length was appropriately determined. When considering convenience in the preparation of the specimen, the rectangular specimen is particularly recommended, although the effective span length is restricted. In contrast, the side-tapered specimen is particularly recommended when considering a wide range of span lengths, although the fabrication of the specimen is somewhat time-consuming.

Shear Modulus and Shear Strength Evaluation of Solid Wood by a Modified ISO 15310 Square-Plate Twist Method

Square-plate twist (SPT) tests were conducted to measure the shear modulus and shear strength using the method, which was a modifi cation of the International Organization for Standardization (ISO 15310) standardized method. In the SPT test, the length/thickness ratio varied. In addition, asymmetric four-point bend- ing (AFPB) tests were conducted, and the shear modulus and shear strength obtained were compared with those obtained by the SPT tests. The shear modulus was obtained effectively by the SPT test when the specimen was thin enough. Although the shear strength was evaluated as higher than that obtained by the AFPB tests, it might be regarded as an apparent value of shear strength when the range of length/thickness is limited. To obtain the actual shear strength by the SPT test, some modifi cation of the equation is required.