Asymmetric Four-point Bending Research Articles

Asymmetric Four-Point Crack Specimen

Accurate results for the stress intensity factors for the asymmetric four-point bend specimen with an edge crack are presented. A basic solution for an infinitely long specimen loaded by a constant shear force and a linear moment distribution provides the reference on which the finite geometry solution is based. [S0021-8936(00)03601-1]

Mixed‐Mode Fracture of Ceramics in Asymmetric Four‐Point Bending: Effect of Crack‐Face Grain Interlocking/Bridging

The mixed‐mode fracture of a large‐grain‐size alumina ceramic and a soda‐lime glass is investigated. These ceramics are tested using straight‐through precracked or notched specimens. The straight‐through precrack is introduced by the single‐edge‐precracked beam method. Precracked or notched specimens are subjected to combined mode I/II or pure mode II fracture, under asymmetric four‐point bending, and pure mode I fracture, under symmetric four‐point bending. A pure mode II fracture is never achieved in the precracked polycrystalline alumina by the crack‐face friction inevitably induced by grain interlocking/bridging. The crack‐face friction in sliding mode reduces the local mode II stress intensity factor in the crack‐tip region and produces a sizable amount of mode I deformation. Accounting for the contribution of the crack‐face friction to the crack‐tip local stress intensity factors, KI and KII, in mixed‐mode fracture tests, the experimental results of the KI/KIc versus KII/KIc envelope and the initial angle of noncoplanar crack extension are in good agreement with the theoretical predictions of the maximum hoop‐stress theory.

Two-Dimensional Elastic Stress Analysis of a Beam under Asymmetrical Four-Point Bending.

We first predict using the elementary beam theory that a loading system of asymmetrical four-point bending (AFPB) applied to a beam produces a pure shear loading state through the middle section of the beam. For further investigation, we attempt a detailed analytical study of the stress state in a beam of infinite length subjected to AFPB loading system within the framework of the two-dimensional elasticity theory. The stress function approach is employed, and the principle of the superposition and the method of Fourier transforms are also used in the analysis. The numerical calculations are carried out for the stress components associated with a pure shear stress field.

Promising method for the shear testing of textile composites

The development of the production of textile composites has created the need for the testing of these materials, particularly for their shear strength. The test methods used at present in practice, were developed for laminar and simple 2D woven materials [1, 2], which are characterized by the presence of planes having a low shear strength. For the various 2D and 3D woven, sewn, and knitted composites that have appeared during the last years, the criteria for the preparation and testing of specimens have not-yet been established [3]. These materials are characterized by a significantly higher shear strength than the laminar composites. The textile materials that differ essentially by their mechanical properties, differ from the laminar materials by the scale of the structural inhomogeneity: by a relatively large diameter of the braids, forming the unit cell, and by the space between them, filled with the binder. The unit cell of such materials is defined as the smallest unit which repeats the structure of the fibers and which can be considered as the structural unit of the material. The size of the unit cell, which depends on the size of the braid, the angles and the complexity of interweaving, can be significant and reach 10-12 mm and more. A significant inhomogeneity of the deformation field exists within such a cell. According to [3] the deformation gradient, for instance in a 2D triaxially woven textile composite, can reach 3. The testing of textile composites required new methods, which take into account their peculiar characteristics: a shear strength which is higher than that of the laminar composites, and structural inhomogeneity. The accurate determination of the mechanical properties of the material requires the correct selection of its representative volume and loading, if possible, by a uniform pure shear stress. One of the most promising methods for the testing of this class of materials is the asymmetrical bending of a beam with V-shaped notches [4]. It has been shown in [5] that the method is suited for the testing of three-dimensionally reinforced composites of the carbon-carbon type with orthogonal packing of the tibers. The present article assesses the possibility of expanding the field of applications of this method to the testing of textile composites. It is necessary to select a certain shape and dimensions of the specimen, the parameters of the neck, and the loading scheme. The influence of the parameters of the notch and of the width of the specimen on the shear strength was therefore investigated experimentally. The experimental data were compared with the strength, determined by other methods. The experimental data were obtained on specimens of textile glass fiber plastic; the spatial links in the specimens were formed by the distortion and interweaving of the warp with the rectilinear fibers of the weft, by using the traditional two-thread scheme [2]. The warp fibers linked only the adjacent weft fibers according to height. The configuration and dimensions of the specimen are given in Fig. 1. The specimens were cut out, so that the direction of the warp coincided with the longitudinal axis of the specimen. Variants of the notch geometry and the coefficient of orthotropy of the material are given in Table i. The loading of the samples was based on the asymmetrical four-point bending scheme (AFPB) of the beam (Fig. 2). The dimension of the inner arm b (see Fig. 2) was 10 mm, of the outer arm a 30 mm. The average shear stress ~'av was calculated from the equation

The notched beam in asymmetric four-point bending for brittle material testing

A reliable test in which the stress state approximates that of pure shear is necessary in order to establish a valid failure criterion for brittle materials. One of the possible tests, the notched beam in asymmetric four-point bending, has been analysed using the finite element method. The results show that for brittle materials a stress concentration at or near the notch tip will cause the specimens to fail in the original configuration. A modified version of the test has been developed, which involves the enlargement of the notch angle and the rotation of the beam so that it is loaded with the notches lying in the direction of the loads. The new configuration was applied to graphite specimens which showed a distinctive mode of fracture.

Mixed‐Mode Fracture Toughness of Ceramic Materials

An experimental technique whereby pure mode I, mode II, and combined mode I‐mode II fracture toughness values of ceramic materials can be determined using four‐point bend specimens containing sharp, through‐thickness precracks is discussed. In this method, notched and fatigue‐precracked specimens of brittle solids are subjected to combined mode I‐mode II and pure mode II fracture under asymmetric four‐point bend loading and to pure mode I under symmetric bend loading. A detailed finite element analysis of the test specimen is performed to obtain stress intensity factor calibrations for a wide range of loading states. The effectiveness of this method to provide reproducible combined mode I‐mode II fracture toughness values is demonstrated with experimental results obtained for a polycrystalline Al2O3. Multiaxial fracture mechanics of the Al2O3 ceramic in combined modes I, II, and III are also described in conjunction with the recent experimental study of Suresh and Tschegg (1987). While the mode II fracture toughness of the alumina ceramic is comparable to the mode I fracture toughness KIc, the mode III fracture initiation toughness is 2.3 times higher than KIc. The predictions of fracture toughness and crack path based on various mixed‐mode fracture theories are critically examined in the context of experimental observations, and possible effects of fracture abrasion on the apparent mixed‐mode fracture resistance are highlighted. The significance and implications of the experimental methods used in this study are evaluated in the light of available techniques for multiaxial fracture testing of brittle solids.

Evaluation of the V-Notched Beam Shear Test Through an Interlaboratory Study

In recent years two notched beam flexure tests, the Iosipescu and the asymmetric four-point bending (AFPB) methods, have been proposed for the measurement of shear stress-strain behavior and shear strength of fiber reinforced composite materials. The methods have made significant inroads into the testing community for continuous, woven fabric and discontinuous fiber composites, and a test standard is being developed in ASTM Committee D-30. This paper describes the test methods and summarizes the results of a round-robin test program to define the within- and interlaboratory precision and bias.

A photoelastic investigation of asymmetric four point bend shear test for composite materials

The asymmetric four point bend (AFPB) test, which utilizes a notched specimen and is a modification of the Iosipescu test, is investigated for measuring the shear stress fringe value of orthotropic birefringent model materials. The influence of the notch parameters, such as the notch angle and the notch radius, is first studied in the case of an isotropic model material; a notch angle of 120°, with or without a radius at the notch tip, lowers the shear stress concentration and leads to a better stress fringe value compared to a 90° notch. In the case of a unidirectionally reinforced glass-polyester model material, while the shear stress fringe values given by the 90°, 120°, sharp and radiused notches are reasonably close to the value obtained for an off-axis tensile specimen, no conclusions about the influence of the notch parameters can be drawn due to the peculiarities of the photoelastic response of the inhomogenous orthotropic model material. However, the failure modes indicate that a notch radius and the 120° notch angle reduce the stress concentration. Comparison is made with finite element results.

Measurement of shear strength of granular/discontinuous-columnar sea ice

A method of performing shear tests using asymmetrical four-point bending was applied to sea ice. The method leads to less uncertainty in the stress field created. The tests were performed on specimens of granular/discontinuous-columnar ice obtained from the Beaufort Sea. For a test temperature of −13 ± 2°C and salinity of 4.2%, the average shear strength was 550 kPa with a standard deviation of 120 kPa.

The losipescu shear test as applied to composite materials

A history of the losipescu shear test as applied to composite materials is presented along with a description of the test fixture and specimen design. Iosipescu's shear test is compared to similar test techniques, including the asymmetrical four-point bending (AFPB) test. Finally, in-plane and through-the-thickness shear properties measured using the losipescu shear tests are presented for a variety of materials, including a unidirectional graphite/epoxy, random and continuous-fiber sheet molding compounds, and two polymer materials.