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.

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.

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.

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.

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.

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.

Bending Resistance of Steel Plate-Reinforced Concrete Beam

The formulas for calculating bending-resistant capacity of a steel plate-reinforced concrete composite beam are derived. To validate the formulas, experiments of the composite beam under three-point bending are carried out. Calculated results based on the formulas are in good agreement with experimental results.

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.

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.

Mesoscale fracture behavior of Longmaxi outcrop shale with different bedding angles:Experimental and numerical investigations

The mechanical properties and fracturing mechanism of shale containing beddings are critically important in shale gas exploitation and wellbore stability.To investigate the effects of shale bedding on crack behavior and fracturing mechanism,scanning electron microscope(SEM)with a loading system was employed to carry out three-point bending tests on Longmaxi outcrop shale.The crack initiation and propagation of Longmaxi shale were observed and recorded by taking photos during loading.The cracking paths were extracted to calculate the crack length through a MATLAB program.The peak load,fracture toughness and fracture energy all increase with the bedding angle from 0°to 90°.The crack length and energy were also found to increase with the bedding angle in the range of 0°-600 and then drop slightly.The fracturing mechanism of shale includes the main crack affected by the bedding angle and disturbed by randomly distributed particles.The main cracking path was accompanied by several microcrack branches which could form an interconnected crack system.When the main crack encounters larger sedimentary particles,it will deflect around the particles and then restore to the initial direction.A numerical technique using extended finite element method(XFEM)coupled with anisotropic cohesive damage criteria was developed,which is able to capture the dependence of crack propagations on bedding angle and sedimentary particles.This study sheds light on understanding and predicting mesoscale fracture behavior of shale with different bedding angles.

An Experimental Study of Several Special Issues Regarding the Ice Force on Conical Structures

The effect of the cone spacing of a conieal structure on the ice force is studied by model experiments. The ice force reduction coefficient presented in this paper expresses the relationship between the ice force and the arrangement of cones. The experiments prove that the mode of the ice failure before the boundary of upward-downward bending cone (UDBC) is crushing. A conclusion can also be drawn from the experiments that the ice force on the boundary of UDBC is by far less than that on a vertical pile with the same diameter. Moreover, the ice force frequencies on upright and inve-rted cones are obtained under the field condition of the platform JZ20-2, respectively. The results show that the alterna-tion of the ice force on UDBC can hardly induce resonance of platform JZ20-2.

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.

高黏橡胶改性沥青制备及其流变性能研究

排水路面是促进可持续发展和建设海绵城市的有效方法之一,该文研究适用于排水沥青路面的高黏改性沥青,采用主要成分为SBS颗粒和高黏橡胶颗粒对基质沥青进行改性,通过正交试验,分别采用60℃动力黏度、软化点、针入度、延度、弹性恢复指标确定高黏橡胶改性沥青的最佳掺量。选择常用的TPS改性剂和XC改性剂作为对照组进行对比分析,利用弯曲梁流变试验(BBR)和动态剪切流变试验(DSR)对三种高黏沥青的低温抗裂性和高温稳定性进行分析和评价,结果表明根据正交试验获得的最佳配方所制得的高黏橡胶改性沥青性能优良,为高黏改性沥青在道路工程领域中的开发和应用提供有价值的参考。

船体梁总纵弯曲载荷识别方法及试验验证

基于结构应变动态响应,采用时域反卷积算法建立了船体梁总纵弯曲载荷识别理论模型.结合Tikhonov正则化理论及FFT(快速傅里叶变换)滤波算法,有效提高了载荷识别精度.并采用系列箱型梁结构模型动载试验验证了载荷识别理论模型的有效性.结果表明:建立的载荷识别理论模型可以准确地反演得出施加载荷时程曲线,误差小于5%.

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.

碳纤维复合材料车门防撞梁多尺度高效变形模拟及实验验证

以碳纤维复合材料车门防撞梁为例,开发了一种面向工程零部件的多尺度高效变形模拟技术,建立了自洽聚类分析方法及多尺度渐进损伤本构模型,通过多尺度单元与唯象单元混合建模,有效降低了模型的求解成本,通过将有限的计算资源分配在恰当的位置,结果表明计算资源的利用效率得到显著提升,实现了工程零部件损伤行为的高效预测,实际计算时间缩短至原来的1/4。对三点弯状态下复合材料防撞梁的宏微观渐进损伤过程进行了分析。基于真空袋成形工艺进行了防撞梁样件试制以及三点弯破坏实验,验证了仿真结果的准确性。

Heterogeneous Fracture Simulation of Three-point Bending Plain-concrete Beam with Double Notches

Plain concrete is regarded as a two-phase material comprising randomly distributed aggregates and mortar matrix. A series of three-point bending concrete beams with symmetric or asymmetric double notches are modeled using the modified random aggregate generation and packing algorithm. The cohesive zone model is used as the fracture criterion and the cohesive el- ements are inserted into both the mortar matrix and the aggregate-mortar interfaces as potential micro-cracking zones. The dead and alive crack phenomena are studied experimentally and nu- merically; and the influences of notch location, aggregate distribution and gradation on fracture are numerically evaluated. Some important conclusions are given.

Crystal plasticity finite element simulations on extruded Mg-10Gd rod with texture gradient

The mechanical properties of an extruded Mg-10Gd sample, specifically designed for vascular stents, are crucial for predicting its behavior under service conditions. Achieving homogeneous stresses in the hoop direction, essential for characterizing vascular stents, poses challenges in experimental testing based on standard specimens featuring a reduced cross section. This study utilizes an elasto-visco-plastic self-consistent polycrystal model(ΔEVPSC) with the predominant twinning reorientation(PTR) scheme as a numerical tool, offering an alternative to mechanical testing. For verification, various mechanical experiments, such as uniaxial tension, compression, notched-bar tension, three-point bending, and C-ring compression tests, were conducted. The resulting force vs. displacement curves and textures were then compared with those based on the ΔEVPSC model. The computational model's significance is highlighted by simulation results demonstrating that the differential hardening along with a weak strength differential effect observed in the Mg-10Gd sample is a result of the interplay between micromechanical deformation mechanisms and deformation-induced texture evolution. Furthermore, the study highlights that incorporating the axisymmetric texture from the as-received material incorporating the measured texture gradient significantly improves predictive accuracy on the strength in the hoop direction. Ultimately, the findings suggest that the ΔEVPSC model can effectively predict the mechanical behavior resulting from loading scenarios that are impossible to realize experimentally, emphasizing its valuable contribution as a digital twin.