Asymmetric Four-point Bending Research Articles

Testing of wood shear modulus based on cantilevered square plate torsional vibration method

ABSTRACT The application of the energy method has proposed a dynamic testing method for the shear modulus in two mutually perpendicular directions on the principal surface of wood using a cantilevered square plate torsional vibration method. In the study, this method was applied to measure the shear modulus of larch wood in the LT and TL directions, as well as the longitudinal and transverse shear modulus of Laminated Veneer Lumber (LVL) sheets. The validity of the results was confirmed through experimental verification using the asymmetric four-point bending beam method, the free plate torsional vibration method, and the free square plate torsional mode method. Simulation calculations of the principal shear modulus for six species of trees with width-to-thickness ratios ranging from 10 to 25 were also conducted using this method. The conclusions drawn suggest that a width-to-thickness ratio of 15 for the cantilevered square plate provides sufficient accuracy for testing the principal shear modulus of wood. Furthermore, the difference in shear modulus between two mutually perpendicular directions on the principal surface of wood is dependent on the width-to-thickness ratio of the cantilevered square plate, indicating that this method outperforms other dynamic methods for testing wood shear modulus.

Dynamic test study of twelve elastic constants of larch timber

The elastic modulus, shear modulus, and Poisson’s ratio of timber are the elastic constants characterizing its material properties. In this paper, the transient excitation method was used to dynamically measure the 10 elastic constants of the falling larch wood under the condition of the free board and cantilever board, that is, 3 elastic moduli E, 3 shear moduli G, and 4 Poisson’s ratios μ. The other two Poisson’s ratios μ were derived using the principle of orthogonality. At the same time, the elastic modulus, shear modulus, and Poisson’s ratio under static conditions were tested and verified by symmetrical four-point bending, asymmetrical four-point bending, and tensile methods. This study is expected to have good application value and practical significance for timber as an engineering structural material, which is widely used in architecture, decoration, furniture, transportation, musical instruments, and in other fields.

Analytical, experimental and computational study of composite beams in asymmetric four-point bending

In this work, an analytical/theoretical, computational and experimental study is performed to investigate the behavior of polymer matrix and glass-fiber chopped strand mat composites when are loaded in asymmetric four-point bending. The theory of elasticity is used to find analytical/theoretical expressions for the stresses, strains and mainly deflections both flexural and shear. Several parameters concerning this bending method can be taken into consideration for the calculations and assessment of the results. It is shown that the magnitude of the deflection depends on the force, the span to thickness ratio but mainly on the parameter λ, referred to as loading factor and introduced in this method, which may, also determine the transition between flexural and shear failure. Finally, the convergence of the analytical and computational values with those received from experiments carried out on chopped strand mat composite beams is investigated.

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.

Effects of the presence or absence and the position of glued edge joints in the lamina on the shear strength of glued laminated timber

Four kinds of glued laminated timber were produced (i.e., one with a glued edge-joint and the other three with nonglued edge joints) in the lamina at different positions toward the depth direction. Shear tests using an asymmetric four-point bending method were then conducted for these glued laminated timber specimens. The results showed that although the glued edge-joint specimens had the highest shear strength in all groups, the shear strength decreased as the distance from the adjacent nonglued edge-joint plane decreased. Furthermore, the shear strength of all specimens exceeded the standard shear design strength value (2.1 N/mm2) set by the Ministry of Land, Infrastructure, Transport and Tourism, Japan. Next, the shear strength of the nonglued edge-joint specimens was estimated based on that of the glued edge-joint specimens. Although the mean-estimated shear strength was lower than the mean-measured shear strength, the possibility of the shear strength changing based on the position of the nonglued edge-joint plane specimens from that of the glued edge-joint specimens was still estimated.

Investigation of fracture toughness in mixed mode for hybrid laminated polymer composites using an A4PB type specimen

In this paper, the fracture toughness of hybrid composites for with and without fly ash composites is evaluated for asymmetric four-point bend test specimens. The preparations of specimens are by simple hand layup technique. Specimens are tested under a universal testing machine for peak load. And concluded that the specimens with fly ash composition yield better fracture toughness compared to without flyash. The scanning electron microscope study shows that the crack starting and progression is mainly dependent on s/d ratios.

Mode II critical stress intensity factor of solid wood obtained from the asymmetric four-point bend fracture test using groove-free and side-grooved samples

Asymmetric four-point bend fracture (AFPBF) tests and three-point bend end-notched flexure (3ENF) tests were performed on groove-free and side-grooved samples of western hemlock, and the Mode II fracture critical stress intensity factor (KIIc) was obtained. Differences in the KIIc values obtained from the AFPBF and 3ENF tests were significant. However, these differences were effectively reduced when the additional crack length Δ was introduced into the data reduction process. These results indicate that the KIIc value can be determined by considering the Δ value and the results obtained from previous Mode II fracture mechanics tests.

Comparison of the shear behavior in graphite-epoxy composites evaluated by means of biaxial test and off-axis tension test

Abstract Characterization of shear behavior in composite materials remains a not fully solved problem. In the last fifty years, many different approaches have been proposed to solve this problem (rail shear, thin-walled tube torsion, off-axis tensile, ±45° tensile, Arcan, Iosipescu, asymmetric four-point bend, plate twist, v-notched rail shear, off-axis flexural, and shear frame), although none of these approaches have achieved an unquestionable solution. For this reason, proposals of alternative methods and comparison between different experimental techniques are of interest. In the present work, the use of cruciform samples with the fiber oriented at 45° with respect to the load directions, and subjected to tension-compression (creating a pure shear stress state at the central part of the samples), is studied. The experimental results of the cruciform samples have been compared with the off-axis tests (with the fiber at 10°) for the same material (AS4/8552), finding a good agreement between the shear experimental curves, especially at the initial part of the curve, where the shear modulus is calculated. Nevertheless, the shear strength value obtained by means of the cruciform specimen has shown to be significantly lower than that obtained using the off-axis test. A Finite Element numerical model of the cruciform specimen has been developed to analyze the stress field of the samples. Numerical results have shown that there is a central area of the cruciform specimens where a pure and uniform shear stress state is developed, which is suitable for the evaluation of the shear constitutive law of the material. It has been observed that there is a (σ 22) stress concentration in the transition between the straight and curved parts of the boundary geometry of the samples, which explain some premature failures of the samples. This premature failure could be avoided with tabs extended up to the beginning of the central part of the sample.

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.

Evaluation Method for Cohesive Crack Propagation in Fragile Locations of RCC Dam Using XFEM

Roller compacted concrete (RCC) dams own a large number of horizontal construction layers, which can easily lead to weak joints among layers and generate interlayer joints with different scales to reduce the dam bearing capacity. In this study, extended finite element method (XFEM) is used to simulate crack propagation, the finite element description is first taken on the strong discontinuity. Subsequently, the displacement function of the crack-tip in the quadrilateral element and the geometric determination method of the crack-tip strengthening region are established. Afterwards, the discrete form of the governing equation is derived and the XFEM increment discretization method of the cohesive crack with the crack-tip reinforcement is proposed using the virtual node method to represent the discontinuity of the fracture element. These methods are validated through simulating mixed-mode cracking of one-sided notched asymmetric four-point bending beam. Eventually, the proposed methods are applied to RCC gravity dam to study the development rule and propagation path of the interlayer joints, so as to evaluate the effect of different lengths of the interlayer joints on the dam structural performance. The estimated critical values of dam deformation are helpful to prevent the dam failure during long term operation.

Experimental investigation of rate dependency of freeze bond strength

The effects of deformation rate on the shear strength of freeze bonds have been investigated through a series of Asymmetric Four-Point Bending (AFPB) experiments. Two submersion times of 30 min and 24 h have been considered, while the deformation rate has been varied from 0.01 to 100 mm/s. Ice specimens with an initial temperature of −18 °C have been subjected to a constant confinement of 25 kPa during formation and shearing of the freeze bonds. Failure of the bonds proved to be highly dependent on deformation rate, where more strain was observed prior to failure of the bond for slower deformation rates. The shear strength of the bond for both submersion times showed a general decreasing trend with increased deformation rate, which is of significant importance in characterizing the properties of ice ridge/rubble strength. Previous ice rubble strength experiments, as well as ice ridge keel gouging tests, have reported the same failure rate-dependency, highlighting the role of freeze bond failure on rate effects. Compressive strength measurements of solid ice presented in the literature have been observed to follow similar trends within the range of strain rates used in present study, where the failure mode appears to transition from ductile to brittle with increasing deformation rate. While more work is needed to understand the mechanisms associated with the rate dependency of freeze bond, this general observation suggests the rate dependency of ice ridges/rubble may indeed be related to the behavior of ice as a material, rather than being associated primarily with factors such as inertial and pore pressure effects, which have been previously proposed as the principal controlling mechanism.

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.

Experimental study of the effect of submersion time on the strength development of freeze bonds

Freeze bonds have been found to influence the mechanical properties of ice rubble and ridges, and it is therefore important to study the fundamental physical properties affecting these features. The shear strength of freeze bonded ice blocks has been investigated through a series of asymmetric four point bending (AFPB) experiments for different submersion times and initial ice temperatures. Ice blocks were subject to a confinement of 25 kPa and were sheared at an actuator rate of 5 mm/s. Effects of submersion time on shear strength of freeze bonds was investigated by varying the submersion time from 1 min to 14 days, for two initial ice temperatures of −18 °C and −10 °C. Shear strength values measured are believed to be dominated by two concurrent mechanisms. Thermal bond growth is the first mechanism, where an initial increase in strength with submersion time is observed, reaching a peak after four (4) minutes of submersion time and gradually decreasing to a constant value. Sintering-creep bond development is the second mechanism that significantly influences the bond strength in submersion times longer than 24 h, where the strength increases and eventually asymptotes to the strength of solid ice. An empirical equation which estimates the bond strength as a function of submersion time and initial ice temperature is developed.

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.

Study on crack propagation based on extended finite element and optimized adhesion structure

The basis of numerical simulation in this paper is discontinuous finite element analysis named extended finite element method. The description of the theory is helpful to understand the basis for the realization of cohesive constitutive relation in software. The characteristics of linear cohesive constitutive relation, bilinear cohesive constitutive relation, turning point and implicit function cohesive constitutive relation are studied. A new cohesive constitutive relation is optimized with analysing the advantages and disadvantages of each cohesive constitutive relation. Comparing the experimental results of classical mode I crack propagation with the numerical simulation of the cohesive constitutive relationship, show that the simulation results of the optimized constitutive relationship are closer to the experimental structure than those of the bilinear constitutive relationship. Optimized cohesive constitutive model is used to simulate an asymmetric four-point bending beam with a single notch. The results show that the crack propagation trajectory is highly consistent with the experimental structure. The rationality of optimizing the cohesive constitutive relation is verified by comparing two experiments.

On the evaluation of energy release rate and mode mixity for ductile asymmetric four point bend specimens

A method for evaluating the contributions from mode I and II components of loading to the energy release rate J in ductile asymmetric four-point bend (4-PB) specimens is proposed. The validity of the method is established by conducting elastic-plastic finite element analysis of several asymmetric 4-PB specimens exhibiting a range of mode mixities from pure mode I to II and having different crack length to width (a / W) ratios. Further, a definition of plastic mode mixity is introduced based on the near-tip opening and sliding displacements. This definition and the proposed method to evaluate J are easy to apply since the required crack opening and sliding displacements can be determined from in-situ optical imaging coupled with Digital Image Correlation (DIC) technique. The application of the proposed methodology is demonstrated by analyzing mixed-mode fracture experiments being conducted with a magnesium alloy. It is found that the critical value of J at crack initiation reduces as loading changes from mode I to II.

Fracture load prediction under mixed mode I + II using a stress based method for brittle materials tested with the asymmetric four-point bend specimen

Fracture load prediction for brittle cracked components under mixed mode tensile-shear loading is an essential task for integrity assessments and reliability analysis of structures containing flaws or cracks. Most of the available fracture criteria are usually derived based on the crack tip stress /strain fields that consider a limited terms of William’s infinite series expansion that are related to singular stress term (KI and KII), first non-singular stress term (T-stress) and sometimes other higher order terms. However, an approach is proposed in this research for mixed mode fracture prediction that does not need direct determining the crack tip fracture parameters (i.e. the coefficients of the William’s series expansion) and instead takes into account the total tangential stress component in predicting the corresponding fracture load under any desired mode I/II mixity. For employing this simple model which is called “Tangential stress contour-TSC”, it is only required to obtain the contour of tangential stress component ahead of the crack tip via performing a numerical finite element analysis. Based on this model at the onset of fracture which corresponds to the critical fracture load of the cracked specimen the maximum tangential stress (σθθ) at a critical distance rc from the crack tip becomes identical with the tensile strength (σt) of the material. The TSC criterion was utilized for predicting the mixed mode I/II fracture loads of two rock materials (granite and marble) tested with the edge cracked asymmetric four-point bend (AFPB) specimen. It was demonstrated that the suggested TSC model can predict very well the fracture loads of tested materials for the whole mode mixities ranging from pure mode I to pure mode II.

Polyurethane foam behavior in mixed mode bending

Mixed mode four-point bending testing is performed on polyurethane foams. This paper presents only the results on the stress intensity factors (SIFs) obtained experimentally for a density of 325 kg/m3 , although tests were done for three foam densities. An asymmetric four-point bending setup was used for determining the critical SIFs in Mode I and Mode II, and discussions on the influence of the initial crack length on the SIF values are done. As initial crack length is increased the theoretical predictions give a better comparison to experimentally obtained results. Mode II testing is also performed on a polyurethane foam as a particular case of mixed-mode four-point testing. Crack initiation and propagation in Mode II depends on the geometrical parameters of the testing configuration. Numerical XFEM simulations are done in order to clarify the situations in which the crack doesn't propagate, and failure is produced in the region of supports. A combined experimental-XFEM analysis is recommended to fully understand the particularities of the behavior of cellular materials.

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.