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.

Three-point bending behavior of aluminum foam sandwich with steel panel

Static three-point bending tests of aluminum foam sandwiches with glued steel panel were performed. The deformation and failure of sandwich structure with different thicknesses of panel and foam core were investigated. The results indicate that the maximum bending load increases with the thickness of both steel panel and foam core. The failure of sandwich can be ascribed to the crush and shear damage of foam core and the delamination of glued interface at a large bending load, The crack on the foam wall developed in the melting foam procedure is the major factor for the failure of foam core. The sandwich structure with thick foam core and thin steel panel has the optimal specific bending strength. The maximum bending load of that with 8 mm panel and 50 mm foam core is 66.06 kN.

Three-point bending performance of a new aluminum foam composite structure

A new composite structure based on aluminum foam sandwich and fiber metal laminate was proposed. A layer of glass fiber was provided at the interface between the metal panel and the aluminum foam core in this composite structure, using adhesive technology to bond the materials together by organic glue in the sequence of metal panel, glass fiber, aluminum foam core, glass fiber and metal panel. The experimental results show that the new composite structure has an improved comprehensive performance compared with the traditional aluminum foam sandwiches. The optimized parameters for the fabrication of the new aluminum foam composite structure with best bending strength were obtained. The epoxy resin and low porosity aluminum foams are preferred, the thickness of aluminum sheets should be at least 1.5 mm, and the type of glass fiber has little effect on the bending strength. The main failure modes of the new composite structures with two types of glues were discussed.

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.

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.

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.

Influence of heat treatment conditions on bending characteristics of 6063 aluminum alloy sheets

Bending deformation behaviors of solution treated(ST),natural aged(NA)and T6tempered6063aluminum alloy sheetswere studied by three-point bending tests.The changes of bending force,interior angle,bending radius and sheet thickness in thefillet region were analyzed by experimental measurements and numerical simulations.The results showed that the bendingcharacteristics were strongly dependent on the heat treatment conditions.The T6alloy sheets were bent more sharply and localplastic deformation occurred severely in the fillet region.However,the ST and NA alloy sheets exhibited relatively uniform bendingdeformation and large bending radius.The bending force of T6alloy was the highest,followed by the NA alloy and that of the STalloy was minimum.After unloading,as compared with the ST and NA alloys,the springback of T6alloys was markedly larger.Theaging time showed a positive sensitivity on the springback and non-uniform bending deformability.The bending characteristics areattributed to the combined effects of yield strength,yield ratio and coefficient of neutral layer.

Extending application of asymmetric semi-circular bend specimen to investigate mixed mode Ⅰ/Ⅱ fracture behavior of granite

The asymmetric semi-circular bend(ASCB)specimen has been proposed to investigate the cracking behavior in different geo and construction materials and attracted the attention of researchers due to its advantages.However,there are few studies on the fracture toughness determination of rock materials.In this work,a series of fracture tests were performed with the ASCB specimens made of granite.The onset of fracture,crack initiation angle and crack propagating trajectory was analyzed in detail combined with several mixed mode fracture criteria.The influence of the crack length on the mode Ⅰ/Ⅱ fracture toughness was studied.A comparison between the fracture toughness ratios predicted by varying criteria and experimental results was conducted.The relationship between experimentally determined crack initiation angles and curves of the generalized maximum tangential stress(GMTS)criterion was obtained.The fracture process of the specimen was recorded with the high-speed camera.The shortcomings of the ASCB specimens for the fracture toughness determination of rock materials were discussed.The results may provide a reference for analysis of mixed mode I and II fracture behavior of brittle materials.

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.

A New Method for Determining J_(IC) of High StrengthHigh Fracture Toughness Steels by SingleThree Point Bend Specimen

A single three point bend specimen compliance method for determining JIC of high strength high fracture toughness steels is presented and a formula for calculatinff J-integral is proposed as follows.It is simple and valid for high strength high fracture toughness steels. The values of JIC and KIC measured by this method are in good agreement with those measured by standard test method.

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.

应力状态对三点弯曲小试样蠕变性能评价的影响

针对大部分小试样技术没有规范化的标准,试样在尺寸上的变化往往会引起所受应力状态的变化,进而影响蠕变参数反演的准确性的问题,采用有限元法,基于三点弯小试样梁弯曲本构模型和Norton蠕变方程,分析试样在不同横截面宽厚比下的应力状态,及其对三点弯小试样蠕变性能的影响。研究结果表明,当横截面宽厚比b:2h<1:2时,试样趋向于平面应力状态;当b:2h>2:1时,试样趋向于平面应变状态;当1:2≤b:2h≤2:1时,试样介于两种应力状态之间。对于加载点稳态位移速率、蠕变应力、转换系数、蠕变参数反演结果,平面应力状态的影响明显大于平面应变状态;与单轴蠕变试验数据的对比结果表明,将试样横截面宽厚比控制在1:1≤b:2h≤2:1范围之内,能够提高蠕变参数反演结果的准确性。研究结果为三点弯小试样试验方法的合理应用提供依据。

3D打印混凝土弯曲疲劳性能研究

为研究3D打印混凝土弯曲疲劳性能,通过216根3D打印试件弯曲疲劳试验,分析不同钢纤维体积率ρ_(f)和纤维长度l_f对构件弯拉强度和弯曲疲劳性能的影响规律,基于双参数Weibull分布理论推导不同失效概率下的疲劳寿命计算公式,提出不同失效概率下的疲劳方程lg S=lg a-b lg N,并进一步分析钢纤维ρ_(f)l_(f)/d_(f)对构件疲劳性能的影响规律。研究结果表明:3D打印混凝土构件疲劳破坏实际是钢纤维发挥阻裂作用的过程,在裂缝产生、扩展、收缩、再扩展、再收缩直至破坏的过程中,裂缝的宽度、长度和深度一直在发生变化,从宏观角度是材料强度和弹性模量不断下降的过程,而微观角度是材料内部组织结构不断劣化的过程。3D打印构件中掺入的钢纤维能够有效阻止横向裂缝的产生和扩展,显著提升混凝土构件的抗弯拉强度、阻裂能力和耐疲劳性能,使其破坏形式由突然脆性破坏过渡为具有韧性的塑性破坏。钢纤维ρ_(f)l_(f)/d_(f)是影响构件抗弯拉疲劳性能的重要因素,在相同的应力比S=0.65作用下,钢纤维ρ_(f)l_(f)/d_(f)由0增至0.60时,构件疲劳次数N提高了252%;相同的疲劳次数N=10^(6)作用下,钢纤维ρ_(f)l_(f)/d_(f)由0增至0.60时,应力比提高了9.15%。3D打印混凝土试件中,钢纤维体积率ρ_(f)比钢纤维长度l_f对疲劳性能的影响程度更明显。研究结果为进一步推动3D打印技术在道路、桥梁等基础设施领域的应用,促进交通行业智能化、工业化发展具有重要意义。

基于RA-AF特征的橡胶自密实混凝土裂缝扩展研究

为探究橡胶自密实混凝土断裂扩展模式,结合声发射RA-AF特征和高斯混合模型(GMM),利用带预制裂缝的半圆盘弯曲试件进行三点弯曲试验,选取橡胶掺量(0%、10%、20%、30%)及跨径比(0.45、0.54、0.72)为试验变量,分析橡胶自密实混凝土裂缝开展种类及变化规律。结果表明:橡胶掺量为20%时,橡胶自密实混凝土表现出较好的工作性能;橡胶掺量增加,拉伸断裂声发射事件占比增大,说明裂缝向Ⅰ型拉伸裂缝发展,并且裂缝发展具有连续的特点;增大跨径比会导致试件承载能力下降,但相同加载阶段其损伤程度逐渐降低,试件内部的断裂模式发生变化,跨径比为0.54时试件表现出较好的工作性能;GMM法显示,拉伸裂缝与剪切裂缝并非简单地以直线作为分界,而是在某些区域内共同存在,GMM法能更为合理地表述不同工况下拉伸断裂事件与剪切断裂事件发生比例的变化规律。

Multi-Objective Optimization of Aluminum Alloy Electric Bus Frame Connectors for Enhanced Durability

The widespread adoption of aluminumalloy electric buses,known for their energy efficiency and eco-friendliness,faces a challenge due to the aluminum frame’s susceptibility to deformation compared to steel.This issue is further exacerbated by the stringent requirements imposed by the flammability and explosiveness of batteries,necessitating robust frame protection.Our study aims to optimize the connectors of aluminum alloy bus frames,emphasizing durability,energy efficiency,and safety.This research delves into Multi-Objective Coordinated Optimization(MCO)techniques for lightweight design in aluminum alloy bus body connectors.Our goal is to enhance lightweighting,reinforce energy absorption,and improve deformation resistance in connector components.Three typical aluminum alloy connectors were selected and a design optimization platform was built for their MCO using a variety of software and methods.Firstly,through three-point bending experiments and finite element analysis on three types of connector components,we identified optimized design parameters based on deformation patterns.Then,employing Optimal Latin hypercube design(OLHD),parametric modeling,and neural network approximation,we developed high-precision approximate models for the design parameters of each connector component,targeting energy absorption,mass,and logarithmic strain.Lastly,utilizing the Archive-based Micro Genetic Algorithm(AMGA),Multi-Objective Particle Swarm Optimization(MOPSO),and Non-dominated SortingGenetic Algorithm(NSGA2),we explored optimized design solutions for these joint components.Subsequently,we simulated joint assembly buckling during bus rollover crash scenarios to verify and analyze the optimized solutions in three-point bending simulations.Each joint component showcased a remarkable 30%–40%mass reduction while boosting energy absorption.Our design optimization method exhibits high efficiency and costeffectiveness.Leveraging contemporary automation technology,the design optimization platform developed in this study is poised to facilitate intelligent optimization of lightweight metal components in future applications.

Effects of Temperature and Liquid Nitrogen(LN2)on Coal’s Mechanical and Acoustic Emission(AE)Properties

Liquid nitrogen has shown excellent performances as a good fracturing medium in the extraction of unconventional natural gas,and its application in coalbed methane extraction is currently a research hotspot.This study focuses on the acoustic emission properties of coal specimens treated utilizing liquid nitrogen with varying initial temperatures in a three-point bending environment.Through examination of the load-displacement curves of the considered coal samples,their mechanical properties are also revealed for different initial temperatures and cycling frequencies.The findings demonstrate a gradual decline in the maximum load capacity of coal rock as the temperature rises.Similarly,when subjected to the same temperature,an escalation in the cycling frequency leads to a reduction in the peak load of coal rock.This suggests that both temperature and cycling frequency exert a notable impact on the fracturing efficacy of liquid nitrogen.Freeze-thaw cycling treatments and exposure to high-temperature conditions can activate preexisting damage in the coal rock,and,accordingly,influence its mechanical properties.In particular,throughout the progressive loading of coal rock samples,the failure mechanisms are predominantly characterized by the occurrence of tensile cracks,succeeded by the development,spread,and fracture of shear fissures.

柔度法测算三点弯曲试样疲劳裂纹长度的影响因素

使用柔度法对不同厚度三点弯曲试样的疲劳裂纹长度进行测算,结合有限元仿真分析方法,研究了试样厚度、柔度函数关系式的适用条件、材料的弹性模量、裂纹前缘弯曲程度、引伸计标距等因素对柔度法测算裂纹长度准确性的影响。结果表明:归一化实际裂纹长度不小于0.3是保证柔度法测算结果准确性的必要条件;用有限元方法模拟平直的贯穿型裂纹,归一化模拟裂纹长度不小于0.3时,柔度函数关系式与模拟结果的吻合程度较高;当试样厚度不大于40 mm时,在柔度函数关系式中使用材料的弹性模量可以获得较为准确的测算结果;随着试样厚度的增加,裂纹前缘圆弧角度增大,裂纹平直度降低,导致测算裂纹长度比实际裂纹长度偏小。

Experimental and numerical investigation of mechanical behavior of plain woven CFRP composites subjected to three-point bending

The mechanical behavior of plain woven Carbon Fiber-Reinforced Polymer(CFRP)composites under Three-Point Bending(TPB)is investigated via experimental and numerical approaches.Multiscale models,including microscale,mesoscale and macroscale models,have been developed to characterize the TPB strength and damages.Thereinto,Representative Volume Elements(RVEs)of the microscale and mesoscale structures are established to determine the effective properties of carbon-fiber yarn and CFRP composites,respectively.Aimed at accurately and efficiently predicting the TPB behavior,an Equivalent Cross-Ply Laminate(ECPL)cell is proposed to simplify the inherent woven architecture,and the effective properties of the subcell are computed using a local homogenization approach.The macroscale model of the TPB specimen is constructed by a topology structure of ECPL cells to predict the mechanical behavior.The TPB experiments have been performed to validate the multiscale models.Both the experimental and numerical results reveal that delamination mainly appears in the top and bottom interfaces of the CFRP laminates.And matrix cracking and delamination are identified as the significant damage modes during the TPB process.Finally,the quasi-static and dynamic behaviors of plain woven composites are discussed by comparing the results of Low-Velocity Impact(LVI)and TPB simulations.

Determination of dynamic modeⅠfracture toughness of rock at ambient high temperatures using notched semi-circular bend method

To investigate the influence of loading rate and high temperature on the dynamic fracture toughness of rock,dynamic fracture tests were carried out on notched semi-circular bend specimens under four temperature conditions based on the split Hopkinson pressure bar system.Experimental and analytical methods were applied to investigating the effect of temperature gradient on the stress waves.A high-speed camera was used to check the fracture characteristics of the specimens.The results demonstrate that the temperature gradient on the bars will not significantly distort the shape of the stress wave.The dynamic force balance is achieved even when the specimens are at a temperature of 400°C.The dynamic fracture toughness linearly develops with the increase of loading rate within the temperature range of 25-400°C,and high temperature has a strengthening effect on the dynamic fracture toughness.