A review on evaluation of crack resistance of asphalt mixture by semi-circular bending test

Although there are many kinds of fracture tests to choose from in evaluating the crack resistance of asphalt mixture,the semi-circular bending(SCB)test has attracted a lot of attention in the academic road engineering community because of its simplicity,stability,and flexibility in testing and evaluation.The SCB test has become a common method to study the cracking resistance of asphalt mixture in recent years.This paper mainly summarizes the overview of the SCB test,summarizes some research results and common characterization parameters of the SCB test method in monotone test and fatigue test in recent years,and predicts and suggests the research direction of the SCB test in the future.It is found that the research on the monotonic SCB test is more comprehensive,and the research on the SCB fatigue test needs to be further improved in the aspects of loading mode,characterization parameter selection,and so on.Researchers can flexibly adjust the geometric dimensions and the test parameters of semi-cylindrical specimens,and conduct comprehensive analysis combined with the results of numerical simulation.The crack resistance of asphalt mixture can be comprehensively evaluated by fracture energy,fracture toughness,stiffness,flexibility index and other fracture indicators,combined with the crack propagation of the specimen.The analysis of numerical simulation can confirm the test results.In order to standardize the setting of fatigue parameters for future application,it is necessary to standardize the setting of bending performance.

Determination of Concrete Fracture Parameters from a Three-Point Bending Test

The mechanical behavior within the processing zone of concrete material can be well described by the crack bridging performance. The material properties related to the crack bridging are cracking strength, tensile strength, and the stress-crack width relationship. In general, the cracking strength is lower than the tensile strength of concrete. Crack propagation is governed by the cracking strength. This paper presents a method to determine the above material parameters from a three-point bending test. In the experiment, a pre-notched beam is used. Corresponding values of load, crack mouth opening displacement, and load point displacement are simultaneously recorded. From experimentally determined load-crack mouth opening displacement curves, the above-mentioned crack bridging parameters are deduced by a numerical procedure. The method can be used to evaluate the influence of coarse aggregate and cementitious matrix strength on the stress-crack width relationship, tensile strength, and fracture energy of concrete.

Numerical analysis of bending property of bi-modulus materials and a new method for measurement of tensile elastic modulus

In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.

Three-point bending of honeycomb sandwich beams with facesheet perforations

A novel square honeycomb-cored sandwich beam with perforated bottom facesheet is investigated under threepoint bending,both analytically and numerically.Perforated square holes in the bottom facesheet are characterized by the area ratio of the hole to intact facesheet（perforation ratio）.While for large-scale engineering applications like the decks of cargo vehicles and transportation ships,the perforations are needed to facilitate the fabrication process（e.g.,laser welding）as well as service maintenance,it is demonstrated that these perforations,when properly designed,can also enhance the resistance of the sandwich to bending.For illustration,fair comparisons among competing sandwich designs having different perforation ratios but equal mass is achieved by systematically thickening the core webs.Further,the perforated sandwich beam is designed with a relatively thick facesheet to avoid local indention failure so that it mainly fails in two competing modes：（1）bending failure,i.e.,yielding of beam cross-section and buckling of top facesheet caused by bending moment;（2）shear failure,i.e.,yielding and buckling of core webs due to shear forcing.The sensitivity of the failure loads to the ratio of core height to beam span is also discussed for varying perforation ratios.As the perfo-ration ratio is increased,the load of shear failure increases due to thickening core webs,while that of bending failure decreases due to the weakening bottom facesheet.Design of a sandwich beam with optimal perforation ratio is realized when the two failure loads are equal,leading to significantly enhanced failure load（up to 60%increase）relative to that of a non-perforated sandwich beam with equal mass.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

Interfacial toughness evaluation of thermal barrier coatings by bending test

Determining the interfacial properties of thermal barrier coatings(TBCs) is imperative for their durability evaluation and further improvements. A ceramic coating(topcoat) and a NiCoCrALY bondcoat were atmospheric-plasma-sprayed(APS) on a stainless steel substrate. A modified three-point bending test was adopted to initiate and propagate the topcoat/bondcoat(TC/BC)interfacial crack. After a complete delamination, the fracture surfaces were examined by an optical microscope, which shows that the cracking plane was merely on the TC/BC interface. Based on the experimental results of load–displacement and crack length–displacement,the strain energy release rate G for crack propagation was calculated, and the averaged magnitude was 77.1 J/m^2.Repeatable results have indicated that the method can be used for the evaluation of interfacial fracture toughness in thermal barrier coatings and other multi-layer structures.

Dynamic Fracture Behaviors of Selected Aluminum Alloys Under Three-point Bending

The dynamic fracture behaviors of the extruded 2024-T4 and 7075-T6 aluminum alloys are investigated by using an instrumented drop tower machine.The specimens are made from a 25 mm diameter extruded circular rod.The dynamic three-point bending tests of each alloy are carried out at different impact velocities.The initiation fracture toughness and average propagation fracture toughness of 2024-T4 and 7075-T6 are determined at different loading rates.The results show that both the initiation toughness and the propagation toughness increase with the loading rate.Further,the difference between the fracture toughness behaviors of 2024-T4 and 7075-T6 is found to be dependent on the variation of fracture mechanism.The comprehensive fractographic investigations of the fracture surfaces clearly demonstrate that the fracture mode of 2024-T4 is predominantly transgranular fracture with high density small-sized dimples,and the fracture mode of 7075-T6 is mainly intergranular fracture with many intermetallic particles in the bottom of voids located in the fracture surface.

Modelling and Simulation on the Effect of Hot Forming Damage on Three-Point Bending Performance of Beam Components

The effects of forming damage are analyzed,which occur during hot stamping process,on the load-carrying capacity and failure mode of hot stamped beams.A damage-coupled pre-forming constitutive model was proposed,in which the damage during hot stamping process was introduced into the service response.The constitutive model was applied into the three-point bending simulation of a hot stamped beam,and then the influences of forming damage on the load-carrying capacity and cracks propagation were investigated.The results show that the forming damage reduces the maximum load capacity of the hot stamped beam by 7.5%.It also causes the crack to occur earlier and promotes crack to propagate along the radial direction of the punch.

Experimental and theoretical analyses of package-on-package structure under three-point bending loading

High density packaging is developing toward miniaturization and integration, which causes many difficulties in designing, manufacturing, and reliability testing. Package-on-Package （POP） is a promising three-dimensional high- density packaging method that integrates a chip scale package （CSP） in the top package and a fine-pitch ball grid array （FBGA） in the bottom package. In this paper, in-situ scanning electron microscopy （SEM） observation is carried out to detect the deformation and damage of the PoP structure under three-point bending loading. The results indicate that the cracks occur in the die of the top package, then cause the crack deflection and bridging in the die attaching layer. Furthermore, the mechanical principles are used to analyse the cracking process of the PoP structure based on the multi-layer laminating hypothesis and the theoretical analysis results are found to be in good agreement with the experimental results.

Evaluation of Contact Pressure in Bending under Tension Test by a Pressure Sensitive Film

The contact pressure acting on the sheet/tools interface has been studied because of growing the concern about the wear of tools. Recent studies make use of numerical simulation software to evaluate and correlate this pressure with the friction and wear generated. Since there are many studies that determine the coefficient of friction in sheet metal forming by bending under tension (BUT) test, the contact pressure between the pin and the sheet was measured using a film that has the ability to record the applied pressure. The vertical force applied to pin was also measured. The results indicate that the vertical force is more accurate to set the contact pressure that using equations predetermined. It was also observed that the contact area between the sheet and the pin is always smaller than the area calculated geometrically. The friction coefficient was determined for the BUT test through several equations proposed by various authors in order to check if there is much variation between the results. It was observed that the friction coefficient showed little variation for each equation, and each one can be used. The material used was the commercially pure aluminum, alloy Al1100.

Bending Analysis of a Filament-Wound Composite Tube

The aim of this paper is to present finite element model of a filament-wound composite tube subjected to three-point bending and bending in accordance with standard EN?15807:2011?(railway applications-pneumatic half couplings) along with its experimental verification. In the finite element model, composite reinforcement plies have been characterized by linear orthotropic material model, while rubber liners have been described by a two-parameter MooneyRivlin model. Force-displacement curves of three-point bending show fairly good agreement between simulation results and experimental data. Reaction forces of FE simulation and experiment of standard bending test are in good agreement.

Spring-back deformation in tube bending

The spring-back of a bending metal tube was studied through extensive experiments and finite element method （FEM） analysis. An approximate equation for the spring-back angle of bending was deduced. It is noted that the mechanical properties of the material （in a tubular form） are quite different from those found in the standard tensile tests （when the materials are in bar forms）. This is one of the major reasons that result in the discrepancies in the outcomes of experimental study, FEM calculations, and spring-back analysis. It is therefore of crucial importance to study the mechanical properties of the materials in their tubular forms. The experiments and FEM simulations prove that the spring-back angle is significantly affected by the mechanical properties of the materials. The angle decreases accordingly with plastic modulus, but changes inversely with the hardening index and elastic modulus The spring-back angle is also affected by the conditions of tube deformation： it increases accordingly with the relative bending radius but changes inversely with the relative wall thickness. In addition, the spring-back angle increases nonlinearly with the bending angle.

Influence of Characteristics on Bending Strength of Layered Steel Fiber Reinforced Concrete

The influence of two main characteristics of steel fiber, the aspect ratio （Df） and volume fraction （ρf）, on the bending strength of Layered Steel Fiber Reinforced Concrete （LSFRC） is investigated by using orthogonal test. Via the variance analysis on the experimental results and trend analysis on the two characteristics, Df is found significantly related to the bending strength of LSFRC. The influence ratio is 63.3%. The bending strength of LSFRC increases if Df increases, makes better when Df reaches 100. ρf has ordinary influence on the bending strength of LSFRC. The influence ratio is 29.2%. Other characteristics, such as the shape of steel fiber and the mix proportion, have less influence. The best ρf contributing to the bending strength of LSFRC is 1.5 %. If ρf is greater than 1.5%, it has negative influence on the bending strength of LSFRC. So, ρf makes a limited contribution to the bending strength of LSFRC.

Effect of bending temperatures on the microstructure and springback of a TRIP steel sheet

Transformation-induced plasticity(TRIP)steel possesses high strength and formability,enabling the use of a thinner gauge material and allowing for the fabrication of complex shapes.In this research,we measured the effect of bending temperatures on the microstructure and air-bending springback angle of TRIP steel at temperatures from 25 to 600
C.Real-time in situ X-ray diffraction and scanning electron microscopy were used for pre-and postbending analysis.As the prebending temperature increased from 25
C to 600
C,the retained austenite(RA)volume fraction decreased,and the RA transformed to bainite at temperatures above 400
C.The springback angle was positively correlated with the prebending RA volume fraction,with the smallest springback angle achieved at 400
C.Additionally,the springback angle was positively correlated with the bending angle,because the RA transformation ratio contributed to increased strain hardening.Further microstructure analysis revealed that the RA became elongated in the tension direction as the bending temperatures increased.

Strain localization and damage development in 2060 alloy during bending

The microstructure evolution and damage development of the third-generation Al-Li alloy 2060 （T8） were studied using in situ bending tests. Specimens were loaded with a series of punches of different radii, and the microstructure evolution was studied by scanning electron microscopy, electron backscatter diffraction, and digital image correlation （DIC） methods. The evolution of the microscopic fracture strain distribution and microstructure in 2060 alloy during bending was characterized, where the dispersion distribution of precipitates was recorded by backscattered electron imaging and later inputted into a DIC system for strain calculations. The experimental results showed that strain localization in the free surface of bent specimens induced damage to the microstructure. The region of crack initiation lies on the free surface with maximum strain, and the shear crack propagates along the macro-shear band in the early stages of bending. Crack propagation in the later stages was interpreted on the basis of the conventional mechanism of ductile fracture.

Nodes Effect on the Bending Performance of Laminated Bamboo Lumber Unit

This research studied the ultimate bearing capacity of laminated bamboo lumber(LBL)unit and thereby calculated the maximum bending moment.The load-displacement chart for all specimens was obtained.Then the flexural capacity of members with and without bamboo nodes in the middle section was coMPared.The bending experiment phenomenon of LBL unit was concluded.Different failure modes of bending components were analysed and concluded.Finally,the bending behaviour of LBL units is coMPared with other bamboo and timber products.It is shown that the average ultimate load of BS members is 866.1 N,the average flexural strength is 101 MPa,the average modulus of elasticity is 8.3 GPa,and the average maximum displacement is 17.02 mm.The average ultimate load of BNS members is 1008.1 N,the average flexural strength is 118.02 MPa,the average modulus of elasticity is 9.9 GPa,and the average maximum displacement is 18.26 mm.Laminated bamboo lumber(LBL)unit without bamboo nodes(BNS)has relatively higher flexural strength coMPared with LBL unit with bamboo nodes(BS).The presence of bamboo nodes reduces the strength of the entire structure.Three failure modes were concluded for BS members,and two failure modes were observed for BNS members during the experimental process.According to a coMParison between the LBL unit and other products,the flexural strength and bending modulus of elasticity of the LBL unit are similar as bamboo scrimber and raw bamboo components,which is much higher than timber components.

Experimental Study on the Influence of Cross-Section Type of Marine Cable Conductors on the Bending Performance

Through the development of marine energy,marine cables are the key equipment for transmission of electrical energy between surface platforms and underwater facilities.Fatigue failure is a critical failure mode of marine cables.The bending performance of the cable conductor has a major influence on both bending and fatigue performances of the overall cable structure.To study the influence of different types of the conductor cross-section on the bending performances of marine cable conductors,three types of copper conductors with the same cross-sectional area,i.e.,noncompressed round,compressed round,and shaped wire conductors,were selected.The experimental results demonstrated that the cross-section type significantly affects the bending performances of copper conductors.In particular,the bending stiffness of the shaped wire conductor is the highest among the three conductor types.Four key evaluation parameters,i.e.,the bending stiffness,maximum bending moment,envelope area,and engineering critical slip point,were selected to compare and analyze the bending hysteresis curves of the three copper conductors.The differences in the key evaluation parameters were analyzed based on the structural dimensional parameters,processing methods,and classical bending stiffness theoretical models of the three copper conductor types.The results provide an important theoretical guidance for the structural design and engineering applications of marine cable conductors.

Failure analysis of polycrystalline diamond compact cutters for breaking rock by bending waves theory

The breakage mechanism of the polycrystalline diamond compact(PDC) cutters was analyzed by the energy theory of bending waves. The cutting tests of granite block were conducted on a multifunctional testing device by using the cutter at three kinds of negative fore angles of 30°, 45° and 60°. The results show that, when the edge of the PDC layer is broken, the layer of tungsten cobalt is broken a little under the angle of 30°, while the layer of tungsten cobalt is broken continuously under the angle of 60°, their maximum depths are about 2 and 7 mm respectively in the two cases. The eccentric distance mainly depends on the negative fore angle of the cutter. When the cutter thrusts into the rock under an attack angle of 60°, the energy of bending waves reaches the maximum since the eccentric distance is the maximum. So the damage of cutter is the most serious. This test result is consistent with the conclusion of theoretical analysis well. The eccentric distance from the axial line of cutter to the point of action between the rock and cutter has great effect on the breakage of the cutter. Thus during the process of cutting, the eccentric distance should be reduced to improve the service life of PDC cutters.