• Steel and Composite Structures
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• v.29 no.2
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• pp.161-173
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• 2018

Point bending is often used for cambering and curving structural steel girders. An analytical solution, applicable in the elasto-plastic range only, that relates applied loads to the desired curve was recently developed for inducing horizontal curves using four-point bending. This solution does not account for initial residual stresses and geometric imperfections built-in hot-rolled sections. This paper presents results from a full-scale test on a hot-rolled steel section curved using four-point bending. In parallel, a numerical analysis, accounting for both initial geometric imperfections and initial residual stresses, was carried out. The models were validated against the experimental results and a good agreement for lateral offset and for strain in the elasto-plastic and post-plastic ranges was achieved. The results show that the effect of initial residual stresses on deformation and strain is minimal. Finally, residual stresses due to cold bending calculated from the numerical analysis were assessed and a revised stress value for the service load design of the curved girder is proposed.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.173-174
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• 2008

The four-point bending test is a widely used method to determine material parameters. The aim of the present study was to evaluate the flexural strength (or modulus of rupture) and the Weibull modulus of cordierite ceramic substrate by means of four-point bending tests. The strength data from experiments followed Weibull statistics. These data indicate that the fatigue effects are more severe when the substrate temperature in the peripheral region is near $200^{\circ}$. At temperatures well above $200^{\circ}C$ the available design strength can be as high as 65% as substrate's initial strength.

• International Journal of Korean Welding Society
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• v.4 no.1
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• pp.46-52
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• 2004

To combine the mechanical advantages of ceramics with those of metals, one often uses both materials within one composite component. But, as known, they have different material properties and fracture behaviors. In this study, a four-point bending test is carried out on $Si_3N_4$ joined to ANSI 304L stainless steel with a Ti-Ag-Cu filler and a Cu interlayer at room temperature to evaluate their longitudinal strain behaviors. And, to detect localized strain, a couple of strain gages are pasted near the joint interfaces of the ceramic and metal sides. The normal strain rates are varied from $3.33{\times}10^5$ to $3.33{\times}10^{-1}s^{-1}$ Within this range, the experimental results showed that the four-point bending strength and the deflection of the interlayer increased with increasing the strain rate.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.12
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• pp.2011-2018
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• 2003

To analyze the bending collapse behavior of an aluminum square tube beam under a bending load, a finite element simulation for the four-point bending test has been performed. Using an aluminum tube beam specimen partly inserted with two steel bars, the local buckling deformation near the center of the tube beam was induced. The maximum bending load and the bending collapse behavior obtained from the numerical simulation were in good agreement with experimental results. Using a combination of the four-point bending test and its finite element simulation, analysis of the local buckling and the accompanied bending collapse behavior of aluminum tube beam could be quantitative accomplished.

• Structural Engineering and Mechanics
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• v.36 no.3
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• pp.343-361
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• 2010

The Discrete Element Method adopting particles for the domain discretization has recently been adopted in fracture studies of non-homogeneous continuous media such as concrete and rock. A model is proposed in which the reinforcement is modelled by 1D rigid-spring discrete elements. The rigid bars interact with the rigid circular particles that simulate the concrete through contact interfaces. The DEM enhanced model with reinforcement capabilities is evaluated using three point bending and four point bending tests on reinforced concrete beams without stirrups. Under three point bending, the model is shown to reproduce the expected final crack pattern, the crack propagation and the load displacement diagram. Under four point bending, the model is shown to match the experimental ultimate load, the size effect and the crack propagation and localization.

• Computers and Concrete
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• v.30 no.4
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• pp.289-299
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• 2022

Based on the random cracking theory, the cylinder RVE model of reinforced concrete is established and the damage process is divided into three stages as the evolution of the cracks. The stress distribution along longitude direction of the concrete and the steel bar in the cylinder model are derived. The equivalent elastic modulus of the RVE are derived and the user-defined field variable subroutine (USDFLD) for the equivalent elastic modulus is well integrated into the ABAQUS. Regarding the tensile rebars and the concrete surrounding the rebars as the equivalent homogeneous transversely isotropic material, and the FEM analysis for the reinforced concrete beams is conducted with the USDFLD subroutine. Considering the concrete cracking and interfacial debonding, the macroscopic damage process of the reinforced concrete beam under four-point bending loading in the simulation. The volume fraction of rebar and the cracking degree are mainly discussed to reveal their influence on the macro-performance and they are calibrated with experimental results. Comparing with the bending experiment performed with 8 reinforced concrete beams, the bending stiffness of the second stage and the ultimate load simulated are in good agreement with the experimental values, which verifies the effectiveness and the accuracy of the improved finite element method for reinforced concrete beam.

• Proceedings of the KWS Conference
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• 2002.10a
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• pp.688-693
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• 2002

Adhesive bonding is becoming one of the popular joining techniques in metal industries, since it has some advantages over other techniques such as welding and diffusion bonding, e.g., any dissimilar metals are easily adhesive-bonded together. In this study, the experiments were carried out in order to provide the statistical data with strength evaluation methods: tension, shear and four-point bending tests for thermoplastic epoxy resin based adhesive-bonded metal joints. We should certificate on the probability of the adhesive strength that has the tendency of brittle fracture, the adhesive bonding strength between metals with thermoplastic adhesive has the best probability at four-point bending test. The strength testing method that has higher probability is four-point bending test, shear test and tensile test in order.

• Journal of the Microelectronics and Packaging Society
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• v.21 no.4
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• pp.33-39
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• 2014

To establish the reliability of a packaging structures, adhesion testing of key interfaces is a critical task. Due to the material mismatch, the interface may be prone to delamination failure due to conditions during the manufacturing of the product or just from the day-to-day use. To assess the reliability of the interface adhesion strength testing can be performed during the design phase of the product. One test method of interest is the four-point bending (4PB) adhesion strength test method. This test method has been implemented in a variety of situations to evaluate the adhesion strength of interfaces in bimaterial structures to the interfaces within thin film multilayer stacks. This article presents a review of the 4PB adhesion strength testing method and key implementations of the technique in regards to semiconductor packaging.

• The Journal of Advanced Prosthodontics
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• v.9 no.6
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• pp.439-446
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• 2017

PURPOSE. To evaluate the effects of different surface treatments on the bond strength of novel CAD/CAM restorative materials to resin cement by four point bending test. MATERIALS AND METHODS. The CAD/CAM materials under investigation were e.max CAD, Mark II, Lava Ultimate, and Enamic. A total of 400 bar specimens ($4{\times}1.2{\times}12mm$) (n=10) milled from the CAD/CAM blocks underwent various pretreatments (no pretreatment (C), hydrofluoric acid (A), hydrofluoric acid + universal adhesive (Scotchbond) (AS), sandblasting (Sb), and sandblasting + universal adhesive (SbS)). The bars were luted end-to-end on the prepared surfaces with a dual curing adhesive resin cement (Variolink N, Ivoclar Vivadent) on the custom-made stainless steel mold. Ten test specimens for each treatment and material combination were performed with four point bending test method. Data were analyzed using ANOVA and Tukey's test. RESULTS. The surface treatment and type of CAD/CAM restorative material showed a significant effect on the four point bending strength (FPBS) (P<.001). For LDC, AS surface treatment showed the highest FPBS results ($100.31{\pm}10.7MPa$) and the lowest values were obtained in RNC ($23.63{\pm}9.0MPa$) for control group. SEM analyses showed that the surface topography of CAD/CAM restorative materials was modified after treatments. CONCLUSION. The surface treatment of sandblasting or HF acid etching in combination with a universal adhesive containing MDP can be suggested for the adhesive cementation of the novel CAD/CAM restorative materials.

• Journal of the Korean Wood Science and Technology
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• v.46 no.5
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• pp.486-496
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• 2018

This study was conducted to confirm an effect of span length on bending properties of larch dimensional lumber in the four point bending test. The size of specimen in this study was 38 (width) ${\times}$ 89 (depth) ${\times}$ 3,600 (length) $mm^3$, and average air-dry density and moisture content of the specimens was $543.5kg/m^3$ and 10.5%, respectively. Visually graded No. 1 dimensional lumbers of 248 were divided by two groups to compare modulus of rupture (MOR) and modulus of elasticity (MOE). One group was tested in the four point bending test with span length of 1,650 mm, and other was tested with span length of 3,000 mm. While MOE was not different according to span length in 5% significance level, MOR was different in accordance with span lengths and was in inverse proportion to change of span length. Fifth percentiles of MOR in span length of 1,650 and 3,000 mm were 28.65 and 25.70 MPa, respectively. It was confirmed that the difference between MORs in each case increased as normalized rank increased. This is because of size effect in Weibull weakest link failure theory. Therefore, KS F 2150, in which there is only regulation about span to depth ratio of 15 or more, is needed to be revised to contain a method considering size effect for MOR. From the method, various results of bending test with different size of lumber could be used to determine design value of lumber.