Evolution of mechanical properties for a dual-phase steel subjected to different loading paths

The evolution of the mechanical properties of a dual-phase (DP590) steel sheet after being prestrained by uniaxial tension, plane strain and equal biaxial stretching was investigated. Specimens were first loaded using the three prestraining modes. Then, from the prestrained specimens, a few sub-sized samples were machined along the rolling direction and the transverse direction for further uniaxial tension testing. Six loading paths were provided. Equal biaxial stretching was performed using a cruciform specimen. The evolution of work hardening performance, elastic modulus, yield stress and tensile stress under the six loading paths were discussed in detail. The results indicate that loading paths can affect the latent work hardening performances, strain hardenability, yield stress and tensile stress evolution as well as the elastic modulus decrease during plastic deformation. The uniaxial tension–uniaxial tension path results in a cross-softening phenomenon, the largest yield stress enhancement and a mild maximum tensile stress increase. The equal biaxial stretching-uniaxial tension path leads to a cross-hardening phenomenon, the least yield stress enhancement and the largest tensile strength increase maximum tensile strength. The elastic modulus of DP590 steel not only changes with the accumulated plastic strain but also varies with the loading paths. The largest decrease of the elastic modulus equal biaxial stretching–uniaxial tension can reach 12.7% beyond 8% equivalent strain, which is 5.2% greater than that in the monotonic uniaxial tension path.     

Energy dissipation capacity of fibre reinforced concrete under biaxial tension–compression load. Part I: Test equipment and work of fracture

The objective of this research was to analyse the differences in the dissipated energy under uniaxial tension and biaxial tension–compression load of fibre reinforced concretes using the Wedge Splitting Test. Under biaxial load the specimens were subjected to compressive stress ratios from 10% to 50% of the concrete compressive strength perpendicular to the direction of the tensile load.Under biaxial tension–compression load the energy dissipation capacity of the specimens decreases compared to the uniaxial tension load case on average 20–30%. It is believed that the decrease is a result of the damage mechanism of the concrete matrix and deterioration of the fibre–matrix and/or aggregate–cement paste interfaces in case the section is additionally loaded with compression stresses. This indicates that dimensioning of concrete elements under biaxial stress states using material parameters obtained from tests conducted on specimens under uniaxial tensile load is unsafe and could potentially lead to a non-conservative design.In the second part of this paper the extent of the fracture process zone under uniaxial tension and biaxial tension–compression load will be examined with the Acoustic Emission technique and the reasons for decrease of the energy dissipation capacity under biaxial load will be further discussed.     

Polymer foams for personal protection: cushions, shoes and helmets

Three areas, where polymer foam products are used in personal protection, are reviewed to contrast the foam micromechanisms and the use of Finite Element Analysis (FEA) for engineering design. For flexible open-cell foams used for seating cushions, the main deformation mechanism is cell edge bending; regular cell models can predict much of the compressive response. Hyperelastic FEA models can then predict the forces for foam indentation. For flexible closed-cell foams used in shoe midsoles, cell air compression dominates the response; diffusive air loss leads to foam deterioration with use. Hyperelastic FEA models can predict the interaction between the foam and the heelpad. Finally, for rigid closed-cell foams used in helmets, the permanent stretching and wrinkling of cell faces dominates the response. Crushable foam FEA models, which consider the yield surface and hardening, predict different responses for impacts on the road and on a kerbstone.     

Modeling multiaxial impact behavior of a glassy polymer

In many applications of polymers, impact performance is a primary concern. Impact tests experimentally performed on molding prototypes yield useful data for a particular structural and impact loading case. But, it is generally not practical in terms of time and cost to experimentally characterize the effects of a wide range of design variables. A successful numerical model for impact deformation and failure of polymers can provide convenient and useful guidelines on product design and therefore decrease the disadvantages that arise from purely experimental trial and error. Since the specimen geometry and loading mode for multiaxial impact test provides a close correlation with practical impact conditions and can conveniently provide experimental data, the first step of validating a numerical model is to simulate this type of test. In this paper, we create a finite element analysis model using ABAQUS/Explicit to simulate the deformation and failure of a glassy ABS (acrylonitrile-butadiene-styrene) polymer in the standard ASTM D3763 multiaxial impact test. Since polymers often exhibit different behavior in uniaxial tensile and compression tests, the uniaxial compression or tensile tests are generally not representative of the three-dimensional deformation behavior under impact loading. A hydrostatic pressure effect (controlled by the parameter γ) is used to generalize a previously developed constitutive model ("DSGZ" model) so that it can describe the entire range of deformation behavior of polymers under any monotonic loading modes. The generalized DSGZ model and a failure criterion are incorporated in the FEA model as a user material subroutine. The phenomenon of thermomechanical coupling during plastic deformation is considered in the analysis. Impact load vs. displacement and impact energy vs. displacement curves from FEA simulation are compared with experimental data. The results show good agreement. Finally, equivalent stress, strain, strain rate and temperature distributions in the polymer disk are presented. Electronic Publication     

钢纤维混凝土多轴损伤比强度准则EI北大核心CSCD

以损伤比强度理论为基础,建立了钢纤维混凝土真三轴损伤比强度准则,并根据钢纤维混凝土试验资料,推荐了钢纤维混凝土损伤比变量表达式中的6个经验参数。利用钢纤维混凝土在单轴、双轴和三轴受力状态下的应力-应变曲线试验结果验证了损伤比取值合理性,对比了单轴受拉、单轴受压和双轴等压等典型受力状态下钢纤维混凝土和普通混凝土损伤比变量取值的差异。通过与国内外共104组钢纤维体积率为0.5%~2.5%的钢纤维混凝土三轴强度试验资料的比较,表明六经验参数钢纤维混凝土损伤比强度准则的三维破坏包络面接近已有认识;通过与国内外强度准则比较,表明损伤比强度准则与钢纤维混凝土三轴试验数据有较高的吻合度。对于围压三轴受力状态,提出简化的钢纤维混凝土常规三轴强度准则,并与已有常规三轴强度准则进行比较分析。此外,对于材料处于二轴受力,推荐了简化的损伤比二轴强度准则中的经验参数取值。     

Influence of stress softening on energy-absorption capability of polymeric foams

The energy-absorption capability of the polymeric foam used in vehicle bumpers is investigated through cyclic loading tests in different loading types, including uniaxial compression, biaxial compression and three-point bending. The test results indicate, due to significant stress softening, the energy-absorption capability of the bumper foam is greatly reduced after it is repeatedly loaded from the raw state. It is also revealed that both the softening effect and the reduction of energy-absorption are dependent on the deformation history. To account for the softening effect as well as its dependence on deformation history in simulation of the bumper foam, appropriate material models are identified and a modeling approach is developed. Using consecutive low-speed impact tests on a bumper system, the influence of the stress softening on the structural performance is studied. Both the experimental and modeling results indicate that the stress softening of the foam cushion compromises to a certain extent the bumper impact performance in subsequent impacts.     

Estimation of biaxial tensile and compression behavior of polypropylene using molecular dynamics simulation

The polymeric materials in general exhibit strong time–temperature dependence and viscoelastic behavior. The time–temperature superposition principle is typically used to estimate the long-term viscoelastic behavior. In addition, Mises criterion and Tresca criterion have been proposed to estimate the yield or failure stresses in a multiaxial stress state and Christensen failure criterion can be applied in the case of different tensile and compressive strengths. In this study, using molecular dynamics method, uniaxial and biaxial tensile and compression test simulations were performed for polypropylene at various strain rates and temperatures. It was observed that the compressive fracture stresses were higher than the tensile fracture stresses. In addition, the fracture stress was high at a low temperature and high strain rate and these fracture stresses are in good agreement with Christensen failure criterion curves. Furthermore, the long-term viscoelastic behavior can almost be predicted from the short-term viscoelastic behaviors at three different temperatures using time–temperature superposition principle. But, the simulations at a wide range of temperatures is important to predict the more accurate long-term viscoelastic behavior.     

On the identification of an effective cross section for a cruciform specimen

Biaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (a) partial unloading method, where stresses are determined based on force–strain curves; (b) identification with uniaxial tensile testing; (c) an analysis of equivalent biaxial tests; and (d) numerical simulations. Considering experimental results for an AA1050 aluminium alloy and for a low‐carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: The uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method, because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress–strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm² for the considered specimen.     

Determination of mechanical properties of PVC foam using a modified Arcan fixture

The design and development of a modified Arcan fixture (MAF) is described. The purpose of the fixture is to characterise polymer foam materials with respect to their tensile, compressive, shear and bidirectional mechanical properties. The MAF enables the application of pure compression or high compression to shear bidirectional loading conditions that is not possible with conventional Arcan fixtures. The tensile and shear behaviour to failure of a cross-linked Divinycell H100 PVC foam core material are studied using Digital Image Correlation (DIC). A detailed investigation of the parasitic effects of the fixture and misalignment of the fixture and loading machine are discussed. Thermoelastic Stress Analysis (TSA) is used to directly examine and validate the uniformity and symmetry of the stress fields obtained for both tensile and shear specimens. To account for the inhomogeneity of the strain field across the specimen cross sections, a “correction factor” for the measured “gauge section” surface strains has been determined using nonlinear finite element analysis (FEA). The outcome is a set of validated mechanical properties that are in excellent agreement with material property measurements conducted using conventional test tensile and shear test fixtures.     

基于颗粒流离散元模型的弹丸侵彻细观混凝土数值模拟方法研究

利用颗粒离散单元法,研究弹丸侵彻细观混凝土模型中弹丸受到介质的阻应力与侵彻速度的关系。采用蒙特卡罗法随机生成并投放混凝土骨料且骨料的粒径分布满足级配曲线。通过对混凝土颗粒离散元细观力学模型进行单轴压缩实验、巴西劈裂实验和双轴压缩实验的参数反演,确定细观模型参数,能使细观混凝土模型具有和一般混凝土等效的力学性能。分析了骨料、过渡层和砂浆三相材料各细观参数对混凝土单轴压缩应力应变关系影响以及锥形弹和平头弹弹丸直径对侵彻阻应力的影响。将颗粒离散元细观力学模型方法计算的弹丸阻应力与空腔膨胀理论计算模型相比较,表明计算离散元方法具有良好的精度和实用性。     

泡沫镍力学性能的实验研究

本研究在室温下控制位移,先以5mm/min的位移速度对泡沫镍进行了单轴拉伸、压缩实验,然后在不同应变率情况下进行了一系列单轴拉伸实验,得到了相应的应力-应变曲线,讨论了材料的应变率相关性.结果表明在普通拉伸试验范围内(准静态),改变变形速度会影响应力-应变曲线,屈服应力、强度极限随变形速度增大而下降;单轴拉伸时,应力应变关系明显分为线弹性变形、塑性变形、线性硬化和破坏4个阶段;单轴压缩时,具备其他泡沫材料受压典型应力-应变曲线的3阶段特征,即明显的弹性变形段、屈服平台段和紧实段.     

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

A procedure for non‐proportional size scaling of the strength of concrete based on the weakest‐link statistics is proposed to synchronize strength data from specimens of different geometries and different loading modes. The procedure relies on proportional size scaling of strength to determine the parameters of the statistical model and often on finite element analysis to calculate the coefficient of the equivalent strength. The approach for non‐proportional size scaling is capable to synchronize the uniaxial strength data of concrete from uniaxial tensile specimens and 3‐point bending specimens, or the biaxial tensile strength data of circular plates in different loading mode. The non‐transference of the uniaxial strength data to the biaxial strength data is unclear in its mechanism but possibly due to the variation of statistical distribution of microcracks with stress states in different specimens.     

Bending analyses for 3D engineered structural panels made from laminated paper and carbon fabric

This paper presents analysis of a 3-dimensional engineered structural panel (3DESP) having a tri-axial core structure made from phenolic impregnated laminated-paper composites with and without high-strength composite carbon-fiber fabric laminated to the outside of both faces. Both I-beam equations and finite element method were used to analyze four-point bending of the panels. Comparisons were made with experimental panels. In this study, four experimental panels were fabricated and analyzed to determine the influence of the carbon-fiber on bending performance. The materials properties for finite element analyses (FEA) and I-beam equations were obtained from either the manufacturer or in-house material tensile tests. The results of the FEA and I-beam equations were used to compare with the experimental 3DESP four-point bending tests. The maximum load, face stresses, shear stresses, and apparent modulus of elasticity were determined. For the I-beam equations, failure was based on maximum stress values. For FEA, the Tsai-Wu strength failure criterion was used to determine structural materials failure. The I-beam equations underestimated the performance of the experimental panels. The FEA-estimated load values were generally higher than the experimental panels exhibiting slightly higher panel properties and load capacity. The addition of carbon-fiber fabric to the face of the panels influenced the failure mechanism from face buckling to panel shear at the face–rib interface. FEA provided the best comparison with the experimental bending results for 3DESP.     

Fracturing behaviour of sandstone specimens with a cavity formed by intersecting excavations under compression: Experimental study and numerical modelling

To investigate the mechanical properties, damage characteristics, and fracturing behaviour of specimens with a cavity formed by intersecting excavations, a series of uniaxial compression tests were conducted incorporating digital image correlation (DIC) and acoustic emission (AE) techniques. PFC^2D modelling was conducted to further study the failure modes and crack evolution under biaxial loading. The results showed that the mechanical properties are significantly weakened by the cavity and influenced by its shape. The failure of the specimens containing a cavity under uniaxial compression can be considered as a progressive process of crack initiation, propagation, and coalescence of different cracks with each other, leading to forming macrofractures, which can be visually displayed by the DIC technique. A new method for determining the crack closure stress is proposed, and the crack initiation stress and the crack damage stress of specimens are also obtained by the AE measurements. The failure mode of the intact specimen changed from the tensile–shear failure mode under the uniaxial compression to the shear‐dominated failure mode under the biaxial compression. Failure of the specimens with a cavity is dominated by shear cracks rather than tensile cracks. Under high confining stresses, almost no macrotensile cracks appeared on the roof or floor of the cavity; instead, several spalling fractures were visible on the two sides of the cavity. The fracturing mechanism is well explained by the evolution of the internal stresses in the specimens.     

Biaxial Yield for Nonlinearly Viscoelastic Materials with a Strain Clock

A constitutive equation with a dilatation dependent reduced time is used to model the mechanical response of solid amorphous polymers such as polycarbonate. Such constitutive equations have the property that stress relaxation occurs faster with increasing dilatation. In previous work, it has been shown that this constitutive equation can account for yield in materials undergoing uniaxial strain or stress control histories. In the present work, yield is discussed when materials described by this constitutive equation undergo homogeneous biaxial and triaxial strain histories. Four sets of conditions are considered: in-plane biaxial constant strain rate histories and in-plane biaxial constant stress rate histories, for both plane stress and plane strain states. Yield is defined in a manner analogous to that in the corresponding strain and stress control conditions in the uniaxial case.     

正方形断面钢管混凝土短柱轴心受压极限承载力的研究

本文根据钢管混凝土柱轴压实验及有限元分析的结果，首次提出正方形断面钢管混凝土短柱轴心受压极限承载力计算模型．该模型将钢管视为平面应力状态，将核心的混凝土划分为双轴受压区与三轴受压区，利用Ｍｉｓｅｓ屈服曲面以及复杂应力状态混凝土的强度理论，可将钢管混凝土柱的承载力表示为钢管模向应力的函数．根据塑性理论中的下限定理，即可确定钢管混凝土柱的极限承载力。     

Strain Measures for Rigid Crushable Foam in Uniaxial Compression

Abstract:  Progressive collapse deformation mechanisms in Rohacell-51WF foam during uniaxial compression has been studied. Measures of a macroscopic engineering strain are identified. The elastic and plastic parts of a macroscopic engineering strain can be predicted by using the compression failure strain, lock-up strain, and time dependent elastic and plastic parts of lock-up strain, which are material parameters. Identification of strain measures in a uniaxial compression test is essential to get material parameters for an elastoplastic model. The viscoelastic recovery property of Rohacell-51WF foam is also described.     

单轴压缩载荷下闭孔泡沫铝的变形机制

基于X射线计算机断层扫描技术,重构了能够反映闭孔泡沫铝真实细观结构的三维有限元模型。采用数值模拟与试验测试相结合的方法,研究了泡沫铝在准静态单轴压缩载荷作用下的力学响应及其变形机制,重点关注了平台阶段及致密化阶段的变形模式。结果表明:试件中变形带的出现是压缩过程进入平台阶段的一个标志,此时棱杆和孔壁的变形以塑性弯曲为主;平台阶段,棱杆及孔壁的变形逐渐向塑性起皱与塑性屈曲转变;伴随致密化阶段的发生,变形带内部的胞孔严重坍塌,呈‘双凹圆盘’状。闭孔泡沫铝细观结构变形模式的数值模拟与试验结果相符,验证了该模型的有效性,为进一步研究各相关物理量(相对密度、加载速率等)及变形机制对其宏观吸能性能的影响奠定了基础。