Optical response and yield behavior of a polyester model material

A mixture of flexible and rigid polyester resins is one of the materials that has been used in the past to model elasto-plastic prototype behavior. As a result of recent curtailments in plastic production, one of the constituents of the mixture is no longer available. A different flexible resin of the same family is available, however, and has been shown in this program to be suitable for optical-model studies involving deformations into the plastic range of material response. In this paper, complete mechanical and optical properties for the new model material are presented for both uniaxial tensile and compressive loadings. Results from a series of thin-walled cylinder tests under internal-pressure loadings are also presented which provide some information on the optical and yield characteristics of the polyester model material under a biaxial state of stress. Results of the study indicate that stress-strain curves for the material can be modified significantly by changing the mixture ratio or the test temperature. Optical data from the study indicate that the fringe order in the material is a function of the instantaneous principal-strain difference. Data from the uniaxial tension and compression tests, together with limited data from the cylinder tests, indicate that the polyester material may follow a modified von Mises yield criterion which accommodates differences in tensile and compressive yield strengths of a material.     

A new direct biaxial testing machine for anisotropic materials

A screw-driven new biaxial testing machine for the realization of experimental investigations on anisotropic sheet materials, such as composite plates or rolled sheet metals, is presented. The described mechanical concept and servocontrol system allow cruciform specimens to be subjected to large strain biaxial tensile and compressive tests without kinematic incompatibilities. Moreover, for the proper implementation of biaxial tensile tests, the specific problems linked to the anisotropic properties of the investigated materials are taken into account; therefore, for the first time, the biaxial machine is supplied with the original ‘off-axes testing device,’ consisting of hinged fixtures with knife-edges at each arm of the cruciform specimen. A recently developed optimization method for the optimal design of flat tensile cruciform specimens is shortly reviewed. Numerical simulations illustrate the decisive superiority of the optimized specimen compared with specimen designs proposed in the literature, as well as the necessity to use the ‘off-axes’ testing technique in biaxial tests on anisotropic materials.     

Experimental studies on the yield behavior of ductile and brittle aluminum foams

Specimen size effects are a major cause of the unreliability of foam models in finite element codes. Here, the modified Arcan apparatus is used to investigate the biaxial yielding of ductile and brittle Al foams. This apparatus subjects a central section of a “butterfly-shaped” specimen to a uniform state of plane stress. The stresses have local maxima at the central section, thus ensuring that yielding occurs there. A yield envelope, which directly relates to the crushing process, can then be determined. Size effects are introduced when using conventional methods such as tri-axial or plate-shear tests. In such tests, averages of stress and strain are measured. These measures do not represent the actual yield event, because foam's internal structure is inhomogeneous and so is the deformation field. Strain localization and failure can occur at any weak layer of cells in the bulk. In this study, we have performed a series of biaxial tests on isotropic Alporas and anisotropic Hydro closed-cell Al foams of approximately equal densities. Alporas failed locally by a ductile phenomenon of progressive crushing of cells. It also possessed uniaxial strength asymmetry. Hydro specimens parallel and perpendicular to ‘foam rise’ were investigated. The Hydro foam developed a local, characteristic brittle crack at loads in the vicinity of the yield point. Phenomenological yield surfaces, which incorporate these features are obtained for the foams, and show dependence on both the deviatoric and hydrostatic stresses. We also provide expressions for the shear and hydrostatic strengths in terms of the uniaxial strengths. Finally, the size-independence of the yield surface is verified using the uniaxial compression of tapered specimens.     

Measurement of the shapes of foil bulge-test samples

Accurate measurements of important tensile properties of thin metal foils are often quite difficult to achieve in uniaxial tests because of sample-preparation difficulties and the tensile instability called necking. Consequently, hydraulic bulge tests have been introduced as a successful means of suppressing these problems through the use of a simplified specimen geometry and biaxial rather than uniaxial tensile-stress states. Considerable effort has been made by various investigators to relate such biaxial stress-strain and ductility data to uniaxial data, generally following the assumption that the bulge is shaped like a spherical cap. The present study evaluates this assumption for foils by measuring actual shapes with unprecedented accuracy and detail using the two-source holographic technique and a polynomial-spline computer analysis of the resulting interferograms. These measurements were made on nine specimens of 0.127-mm-thick annealed rolled copper foil which had been deformed into bulges of varying heights up to rupture. A comparison is made between the measured shapes and the spherical-cap shape generally assumed in the interpretation of bulge-test data. The spherical assumption gives results which are reasonably valid for the later stages of deformation. Indeed, the stress-strain curve obtained from bulge testing corresponds closely with the uniaxial tensile curves for this material. The strain at failure (i.e., elongation) was greater in the biaxial bulge test than in the uniaxial test but not nearly as great as the strain expected from a theoretical model proposed by Hill. However, all the specimens measured exhibited localized areas with larger radii of curvature. The presence of these “flats” may be associated with a mode of failure in the bulge test which corresponds to necking instability in the uniaxial test, and thereby account for the limited strain to failure.     

A new method for the biaxial testing of cellular solids

Commercial cellular solids such as metal foams and honeycombs exhibit deformation and failure responses that are dependent on specimen size during testing. For foams, this size dependence originates from the fabrication-induced material and structural inhomogeneities, which cause the uncontrolled localization of deformation during the testing of foam cubes. Different peak loads and failure modes are observed in honeycomb specimens in the plate-shear configuration depending on specimen height. This size dependence causes difficulty in obtaining a more representative constitutive behavior of the material. It has recently been established that the size dependence under uniaxial compression can be eliminated with tapered cellular specimens, which enable controlled deformation at a given region of the specimen. This concept is extended in this paper to the biaxial testing of butterfly-shaped cellular specimens in the Arcan apparatus, which focuses deformation at the central section of the specimen. The Arcan apparatus has been modified such that all displacements at the boundaries of the specimen could be controlled during testing. As a consequence of this fully displacement controlled Arcan apparatus, a force perpendicular to that applied by the standard universal testing machine is generated and becomes significant. Thus, an additional load cell is integrated on the apparatus to measure this load. Example responses of butterfly-shaped specimens composed of aluminum alloy honeycomb, aluminum alloy foam and hybrid stainless-steel assembly are presented to illustrate the capabilities of this new testing method.     

混凝土动态双轴拉压破坏准则细观数值模拟研究

正常服役期内的混凝土结构往往处于复杂应力状态,并且不可避免地会受到偶发动力载荷作用.对于复杂载荷作用下的混凝土力学性能研究,破坏准则是基础.受试验设备等条件限制,现有的动态双轴拉压破坏准则形式复杂、缺乏更高应变率和侧应力比范围且尚未综合考虑应变率和侧应力比的耦合作用.为进一步提出适用范围更高且更准确的混凝土动态双轴拉压...     

滑轨导向式静/动态双轴拉伸实验技术

基于液压伺服高速加载系统,发展了一种材料双轴拉伸力学性能测试技术。利用锥面接触导向驱动方法,把加载锤竖直方向的驱动力转化为水平方向的双轴驱动力,从而实现对十字形试样平面双轴加载。借助有限元数值模拟手段优化了锥面接触角和十字形试样尺寸。当接触锥角为45°时,既有较好的水平驱动转化效率,同时又保持较小的接触力,确保水平驱动加载各组件在弹性变形范围内,可多次重复使用。确定了加载臂狭缝个数、狭缝与减薄区边缘长度和标距段厚度等试样设计关键参数,在十字形试样测试标距段内实现了均匀变形。设计了测力夹持一体化导杆和非接触光学全场应变测试系统,准确获得了试样的应力和应变。利用此平面双轴拉伸加载装置,开展2024-T351铝合金板单轴拉伸实验和激光探测同步性验证实验,验证装置设计的可行性;开展铝合金板材在不同加载速率下的双轴拉伸实验,得到在双轴加载下铝合金板材应力应变曲线,并与单轴加载下实验结果进行了对比分析。     

Determining Stress–Strain in Rubber with In-Plane Biaxial Tensile Tester

The nominal stress–strain relationships of industrial rubber materials under multiaxial deformation are essential for precisely determining the constitutive laws of those materials. This paper proposes a new method for precisely estimating the nominal stress–stretch relationships of carbon-black-filled styrene butadiene rubbers (SBRs) under uniaxial tension, pure shear, and equibiaxial tension by using an in-plane biaxial tensile tester. The proposed method employs sheet-shaped rubber samples with notches for the pure-shear and equibiaxial tension tests to mitigate the influence of non-uniform deformation around the clamps. Finite element analysis and biaxial tensile tests were performed to verify the effectiveness of the proposed method. Performance evaluations based on both numerical calculations and experiments revealed that the proposed method enabled the precise calculation of the nominal stress–stretch relationship for uniform deformation from a tensile load and deformation of the reference area defined at the center of the samples.     

高密度聚乙烯的复合应力蠕变

本文通过实验方法确定多重积分型蠕变方程中的各个时间函数,并在认识材材料非线性粘弹特征的基础上作出合理修正,最后得到适用于单轴及复合应力条件下的蠕变方程。     

Cyclic stress-strain data analysis under biaxial tensile stress state

A new device was developed to assess fatigue life under biaxial tensile loading at elevated temperatures. It makes use of an annular disk specimen and can be easily mounted onto a standard push-pull machine so that the axial force is converted into radial forces extending across the disk specimen. Therefore, a positive ratio of the tangential to the radial stress can be imposed at the reduced section of the disk specimen; this ratio depends on the specimen configuration and may be fixed to a value ranging from 0.5 to 0.9 by varying the inner diameter of the disk. The proposed device has performed successfully and was used to study the cyclic behavior of Type-304 stainless steel subjected to various biaxial tensile stress states at room temperature and at 200°C. The data obtained from this experimental procedure have been analyzed to evaluate the effectiveness of some correlations already available for treating the biaxial cyclic stress-strain response in terms of the uniaxial behavior. This analysis shows that a successful correlation should account for all the stress components. The authors discuss the concept used in the modeling of the material cyclic behavior and the formulation of a biaxial fatigue damage parameter necessary for an effective analytical life prediction methodology.     

Damage evolution and crack propagation in rocks with dual elliptic flaws in compression

To give an insight into the understanding of damage evolution and crack propagation in rocks,a series of uniaxial and biaxial compression numerical tests are carried out.The investigations show that damage evolution occurs firstly in the weak rock,the area around the flaw and the area between the flaw and the neighboring rock layer.Cracks mostly generate as tensile cracks under uniaxial compression and shear cracks under biaxial compression.Crack patterns are classified and divided.The relationship between the accumulated lateral displacement and the short radius(b)is fitted,and the equation of crack path is also established.     

A plane stress formulation for elastic-plastic deformation of unidirectional composites

A plane stress analysis of the elastic-plastic deformation of unidirectional composites is presented. A continuum model based on the solid-mixture concept is selected as the basis for the analysis. Model parameters, including process-dependent variables, are deduced from experiments performed on unidirectional composites. A computer program MET1MAT has been developed accordingly and tested for a few simple in-plane loading cases. Experimental data for uniaxial tests performed in longitudinal and transverse directions and for a few biaxial tests are presented to substantiate the analysis. And, finally, application of the results to laminated metal matrix composites is discussed.     

Mullins�� effect in semicrystalline polymers: experiments and?modeling

Experimental data are reported on isotactic polypropylene in uniaxial cyclic tensile tests with various maximum strains at room temperature. It is demonstrated that polypropylene reveals all characteristic features (hysteresis of energy, damage accumulation, and strain-hardening) of the Mullins effect. Constitutive equations are derived for the viscoplastic behavior of semicrystalline polymers at three-dimensional deformations with small strains. Adjustable parameters in the stress?Cstrain relations are found by fitting the observations. Numerical simulation shows that the model adequately predicts the viscoplastic response of polypropylene in uniaxial and biaxial cyclic tests.     

Hardening of a rolled sheet submitted to radial and complex biaxial tensile loadings

Biaxial tensile tests are performed on cruciform specimens with the help of direct biaxial testing machine. Small offset-strain yield curves are detected on an aluminium alloy (AL1200) rolled sheet submitted to irreversible radial and complex biaxial tensile loadings. A predominant kinematic hardening and an important isotropic expansion are observed. A yield curve distortion is observed as well but, unlike the traction–torsion case, its intensity appears to be linked to the loading type. Moreover, the strain responses are analyzed in order to point out the pronounced anisotropy of the rolled sheet and to check if the sheet behavior is in agreement with a plastic flow associated with the yield curve.     

Constitutive modeling of ice in the high strain rate regime

The objective of the present work is to propose a constitutive model for ice by considering the influence of important parameters such as strain rate dependence and pressure sensitivity on the response of the material. In this regard, the constitutive model proposed by Carney et al. (2006) is considered as a starting basis and subsequently modified to incorporate the effect of brittle cracking within a continuum damage mechanics framework. The damage is taken to occur in the form of distributed cracking within the material during impact which is consistent with experimental observations. At the point of failure, the material is assumed to be fluid-like with deviatoric stress almost dropping down to zero. The constitutive model is implemented in a general purpose finite element code using an explicit formulation. Several single element tests under uniaxial tension and compression, as well as biaxial loading are conducted in order to understand the performance of the model. Few large size simulations are also performed to understand the capability of the model to predict brittle damage evolution in un-notched and notched three point bend specimens. The proposed model predicts lower strength under tensile loading as compared to compressive loading which is in tune with experimental observations. Further the model also asserts the strain rate dependency of the strength behavior under both compressive as well as tensile loading, which also corroborates well with experimental results.     

基于S准则发展的混凝土动态多轴强度准则

通过对经典强度理论或准则的强度参数分析,将强度参数转化为由混凝土的单轴压缩和单轴拉伸强度表示,结合S准则给出的混凝土单轴强度的率效应规律,得出了强度参数受应变率影响的率效应函数,进而将常用的静态多轴强度准则摩尔-库伦强度理论、松岗-中井强度理论、德鲁克-普拉格强度理论、拉得-邓肯强度准则和胡克-布朗强度准则发展为动态多轴强度准则.利用混凝土动态单轴压缩和动态单轴拉伸试验结果统计分析给出的S准则率效应参数,分析了5种强度准则中强度参数随应变率的变化规律以及取值范围.基于混凝土单轴压缩和单轴拉伸强度,分别给出了5种强度准则在子午面、偏平面和平面应力条件下的强度曲线与主应力空间中的强度曲面,对比分析了5种强度准则间的异同,以及每种强度准则随应变率的变化规律.利用混凝土材料的动态双轴和动态真三轴强度试验结果,分析评价了5种动态多轴强度准则,并且阐述了各动态多轴强度准则的应变率适用范围.德鲁克-普拉格强度理论与试验结果相差甚远,不适于描述混凝土材料的强度规律.动态双轴加载时,在拉压区各强度准则差别不大,都可较好地描述试验规律;在压压区各强度准则差别较大,松岗-中井强度理论与试验结果吻合最好.在动态真三轴比例加载时,摩尔-库伦强度理论和胡克-布朗强度准则无法考虑中主应力的影响;松岗-中井强度理论和拉得-邓肯强度准则都可较好地描述试验规律.      

混凝土率型内时损伤本构模型

混凝土是一种典型的率敏感材料,为了更好地描述混凝土结构在动力、冲击荷载作用下的强度和变形特征,本文结合内时理论和损伤理论建立了一种考虑混凝土率效应的内时损伤本构模型。该模型的特点:将混凝土材料的受力软化效应分解为密实状态的塑性效应和由微裂缝扩展引起的刚度退化效应。前者由内时理论来描述,这使该模型摆脱了一般弹塑性模型中屈服面的概念,从而更符合混凝土的变形特性,并且简化了非线性计算过程;后者由损伤理论来描述,根据混凝土的动力试验结果建立了增量型的损伤演变方程,从而使该模型能够较好地反映混凝土的动力特性。最后,应用本文建议的模型对一钢筋混凝土简支梁进行了非线性分析,结果表明:当结构承受快速荷载作用时,应变率对结构的受力性能影响较大,在进行结构分析时必须予以考虑。     

The influence of biaxial stresses on high-cycle fatigue-crack propagation

Arising from a design study, an examination has been made of the problems associated with evaluating the fatigue behavior of an I-beam section joined to a transverse stiffener, loaded in biaxial bending. A laboratory test rig has been designed to study high-frequency (40–230 Hz) fatigue-crack propagation in the tensile flange of a composite aluminum I-section, for a range of stress biaxiality ratios (λ) from 0 to +1 (equibiaxial tension), λ being varied by adjusting the ratios of loading spans in the two orthogonal axes for the same amount of uniaxial deflection. The results obtained are considered in the context of the significantly contradictory information currently available in the literature. Crack geometry and test procedure (as influenced by load/stress measurement) are found to considerably influence the effect of biaxial stresses on fatigue. Thus, the growth rate of corner-initiated cracks increases with increasing stress biaxiality (monitored in terms of nominal applied stresses), but the reverse is true for center-cracked specimens. When tests are conducted in terms of combinations of local stresses, or data reduced using corrections, there is no significant effect of biaxial stresses on fatigue-crack growth.     

A 3-phase model for the numerical analysis of semi-crystalline polymer films in finite elastoplastic strains

In this paper, the mechanical behavior of semi-crystalline polymer films in finite elastoplastic strains is investigated. A 3-phase constitutive model has been specially developed in a previous paper and validated for various materials in both uniaxial and biaxial uniform hot drawing. In the present study, the numerical implementation of this 3-phase model in a finite element software is outlined in the perspective of using this model in more general non-uniform cases of complex geometries and/or loadings. In the present case, only polyethylene films at room temperature are considered. First, uniaxial tensile experimental tests are performed so as to calibrate the model parameters. Then, for validation purposes, two series of experimental tests are conducted on tensile specimens with central holes and double edge notched tensile (DENT) specimens. During these tests, digital image correlation is used to analyze the strain (or displacement) field history during loading. Finally, numerical computations are performed with the help of the finite element software including the 3-phase model previously implemented (cohesive elements are also needed for the simulation of the crack propagation in DENT specimens). In both cases, the comparison between the experimental and numerical force–displacement curves, together with the comparisons between the experimental and numerical strain fields at different times, give very satisfactory results.