Asymmetric Four-point Bending Test Research Articles

The Effect of Flame Retardant-Aluminum Trihydroxide on Mixed Mode I/II Fracture Toughness of Epoxy Resin.

Fire resistance is a major issue concerning composite materials for safe operation in many industrial sectors. The design process needs to meet safety requirements for buildings and vehicles, where the use of composites has increased. There are several solutions to increasing the flame resistance of polymeric materials, based on either chemical modification or physical additions to the material’s composition. Generally, the used flame retardants affect mechanical properties either in a positive or negative way. The presented research shows the influence of the mixed-mode behavior of epoxy resin. Fracture toughness tests on epoxy resin samples were carried out, to investigate the changes resulting from different inorganic filler contents of aluminum trihydroxide (ATH). Three-point bending and asymmetric four-point bending tests, with different loading modes, were performed, to check the fracture behavior in a complex state of loading. The results showed that the fracture toughness of mode I and mode II was reduced by over 50%, compared to neat resin. The experimental outcomes were compared with theoretical predictions, demonstrating that the crack initiation angle for higher values of KI/KII factor had a reasonable correlation with the MTS prediction. On the other hand, for small values of the factor KI/KII, the results of the crack initiation angle had significant divergences. Additionally, based on scanning electron microscopy images, the fracturing of the samples was presented.

Characterization of Mechanical Properties of 3-D–Printed Materials Using the Asymmetric Four-Point Bending Test and Virtual Fields Method

Abstract The virtual fields method (VFM) is an inverse method for characterizing the mechanical properties of materials that has the advantage that all constitutive parameters can be identified using one test. The accuracy of identification is mainly determined by the load configuration, deformation measurement, and virtual displacement fields. In order to promote the use of VFM, a new load configuration for the asymmetric four-point bending (4PB) test is proposed here. A virtual experiment was performed to examine the feasibility of the asymmetric 4PB test, where the configuration of the proposed test was optimized to achieve high identification accuracy. As an example of a practical application, the proposed method combined with moiré interferometry was used to characterize the constitutive parameters of stainless-steel materials fabricated by selective laser-melting 3-D printing. It was demonstrated that this method is suitable for characterizing the material properties of 3-D–printed materials.

Determination of the Young’s Modulus and Shear Modulus of Solid Wood by the Symmetric and Asymmetric Four-Point Bending Tests

Determination of the Young’s Modulus and Shear Modulus of Solid Wood by the Symmetric and Asymmetric Four-Point Bending Tests

Mode I and II fracture toughness investigation of Laser-Sintered Polyamide

This paper presents experimental investigations on the geometrical and fracture properties of specimens obtained by Additive Manufacturing technology. The experimental tests were performed on Single Edge Notch Bend (SENB) specimens obtained through the Selective Laser Sintering process, based on the polyamide PA2200 material. The SENB specimens were manufactured using three different process energies-PEs (E1, E2 and E3), respectively three different spatial orientations-SOs (Vertical-V, Horizontal-H and Oblique-O). Symmetric and asymmetric four-point bending tests were used to determine the mode I and II fracture toughness (KIC and KIIC). It was observed that the density (ρ) of the 3D printed specimens is highly dependent on the PE and SO, the highest density values being obtained for the highest PE (E1), respectively for the V-SO. Maximum relative errors of the main geometrical parameters (thickness, length and width) of the SENB specimens were obtained for E3-PE and H-SO. With respect to the fracture toughness, it was observed that, regardless of PE and SO, the KIC values are higher than KIIC ones. The highest KIC value was found for E1 and V-SO, while KIIC highlight the highest value for E1 and H-SO. Finally, analysis of variance (ANOVA) method is used to analyze the influence of various factors on outcome parameters.

Measurement of the Shear Properties of Extruded Polystyrene Foam by In-Plane Shear and Asymmetric Four-Point Bending Tests.

The shear modulus and shear strength of extruded polystyrene foam were obtained by the in-plane shear and asymmetric four-point bending tests. In addition, the test data were numerically analysed, and the effectiveness of these tests was examined. The numerical and experimental results suggest that the shear modulus and shear strength obtained from the in-plane shear test are significantly smaller than those obtained from the asymmetric four-point bending test because the influence of the stress concentration was less significant. Although the in-plane shear test is standardised in ASTM C273/C273M-11, it is considerable to adopt the asymmetric four-point bending test as another candidate for obtaining the shear properties of extruded polystyrene foam.

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.

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.

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.

Examination of the Mode II fracture behaviour of wood with a short crack in an asymmetric four-point bending test

Asymmetric four-point bending tests of agathis specimens with a short crack along the neutral axis in a tangential–longitudinal system were conducted onto analyse the failure behaviour of wood with a short crack. The nominal shear strength and Mode II critical stress intensity factors of the specimens with various crack lengths were measured, and the influence of crack length on these properties was examined. The nominal shear strength of the cracked specimens was significantly lower than the strength of a crack-free specimen, even when the crack was extremely short. This finding suggests that the fracture mechanics theory is effective for analysing the failure behaviour of wood with a very short crack in this loading condition. However, the Mode II critical stress intensity factor still depends on the crack length. When the crack length was corrected with considering the formation of fracture process zone ahead of the crack tip, the critical intensity factor could be predicted effectively as well as the nominal shear strength.

Edgewise Shear Properties of 5-Ply Wood Obtained from the Asymmetric Four-Point Bending and Uniaxial-Tension Tests of Notched Specimen

Asymmetric four-point bending and uniaxial-tension tests of notched specimen were conducted using 5-plywood of Lauan in order to obtain the edgewise shear properties such as shear modulus, proportional limit stress in shearing, and shear strength of this representative material. In addition to the experiments, finite element simulations were performed and the validity of the measurement methods was examined. The experimental and numerical analyses reveal that the asymmetric four-point bending test method is more reliable method available for measuring the edgewise shear properties of this material.

Shear properties of wood measured by the asymmetric four-point bending test of notched specimen

Abstract The asymmetric four-point bending test for obtaining shear properties of wood was examined. Rectangular bars with various notches on top and bottom surfaces of western hemlock (Tsuga heterophylla Sarg.) were prepared as a specimen. The shear modulus, proportional limit stress, and shear strength were measured. The influence of notch configuration on the shear properties was examined independently by finite element calculations. The influence of notch configuration was not significant in experiments, while it was found relevant in finite element analyses. Although the pure shear stress condition could not be realized after the initiation of failure, the measurement of shear properties of solid wood simply by the asymmetric four-point bending test was feasible.

Mode II fracture mechanics properties of wood measured by the asymmetric four-point bending test using a single-edge-notched specimen

Using a single-edge-notched specimen of spruce, an asymmetric four-point bending test was conducted to obtain the mode II fracture toughness G IIc and critical stress intensity factor K IIc, and the test method was numerically and experimentally analyzed. A three-point bend end-notched flexure test was also conducted and the results were compared with those of the asymmetric four-point bending tests. The crack length had a small influence on the load/loading-line displacement relationship in the asymmetric four-point bending test, so it was difficult to determine the value of G IIc, which requires the measurement of loading-line displacement. In contrast, the value of K IIc obtained by two tests was similar when the initial crack length ranged from 0.7 to 0.85 times the depth of the specimen. These results show that the asymmetric four-point bending test is a promising means of determining K IIc.

Measurement of the shear modulus of wood by the square-plate twist method

Abstract In this research, square-plate twist test methods for obtaining the shear modulus of wood were examined. Square plates of western hemlock (Tsuga heterophylla Sarg.) were used as specimens. Twist tests were conducted according to three different methods for various length/thickness and span/plate diagonal ratios, and the shear modulus corresponding to each test condition was obtained. To examine the validity of shear modulus obtained by these tests, asymmetric four-point bending tests and finite element calculations were independently conducted and the results were compared. Specimens had a length/thickness ratio greater than 47 and were supported at two or three points close to each corner while applying a load to the remaining corner. Under these conditions, the shear modulus could be properly obtained over a wide range of span/plate diagonal ratios.

Bending and shear properties of compressed Sitka spruce

We examined the bending and shear properties of compressed wood using small and clear specimens of Sitka spruce (Picea sitchensis Carr.). For measuring the bending properties, three-point bending tests were conducted under the span/depth ratio of 14, which is standardized in the American Society for Testing and Materials [ASTM D143-94 (2005a)] and Japanese Industrial Standards [JIS Z2101-94 (1994)]. In the bending test, the load, deflection at the midspan, and strain at the bottom of the midspan were simultaneously measured, and Young’s modulus and bending strength were obtained by elementary beam theory. For obtaining the shear modulus and shear strength, asymmetric four-point bending tests were conducted using the specimens with rectangular and side-grooved cross sections, respectively, and the influence of the compression ratio on the shear properties was examined. The results are summarized as follows: (1) Young’s modulus increased with increasing compression ratio when it was determined by the load–strain relation. Nevertheless, this tendency was rather obscured when Young’s modulus was determined by the load–deflection relation. Hence, it is preferable that Young’s modulus is measured from the load–strain relation. (2) The shear modulus in the longitudinal–tangential plane was maximum at the compression ratio of 50%, whereas that in the longitudinal–radial plane was minimum at the compression ratio of 50%. (3) The influence of the compression on the bending and shear strength ratio was not significant.

Failure Behavior of Spruce Wood under Bending-Shear Combined Stress Field

When a specimen with symmetrical grooves eccentrically cut on its side surfaces is bent, failure due to the bending-shear combined stress field is induced at the grooved portion, so the failure behavior under various combined stress fields can be examined by varying the location of the grooves. Based on this concept, three-point and asymmetric four-point bending tests using spruce specimens with grooves cut on various locations on the side surfaces were conducted. Bending and shear stresses at the occurrence of failure were calculated based on elementary beam theory, and the test results were compared with three failure conditions: maximum stress, Hill-type, and Goldenblat-Kopnov's failure conditions. For a rough approximation of the failure behavior, which might be influenced by the loading pattern, the Hill-type condition was superior to the maximum stress condition, whereas Goldenblat-Kopnov's condition, the expression of which is more complicated, is effective for describing the failure behavior more precisely.