Elastoplastic mechanics of porous materials with varied inner pressures

A micromechanics model and a computational homogenization method were developed to examine the macroscopic elastoplasticity and yield behavior of closed-cell porous materials with varied inner gas pressures. For the uniaxial stress–strain relation of the porous material, the micromechanics model coincides well with the numerical homogenization, especially for the case of relatively low porosity and gas pressures. The effects of the combination of the different gas pressures on the uniaxial stress–strain curve, the nominal Poisson’s ratio, yield surface and initial yield strength of the material are systematically investigated. The multiple gas pressures can induce the tension–compression asymmetry of the uniaxial stress–strain curves and the nominal Poisson’s ratio of nonlinear deformation. In particular it is shown that when the multiple gas pressures coincide, the yield surface of the porous material with inner gas pressures can be simply obtained from that of the porous material without inner pressures by a shift along the negative direction of the hydrostatic stress axis. However, when the multiple pressures are different, in addition to a translation along the hydrostatic axis, the yield surface undergoes a change in shape and size, and the maximal equivalent stress is lowered by a difference in gas pressures. Furthermore, the multiple gas pressures have a significant effect to reduce the yield strength of the closed cell porous materials.     

复杂面内应力状态下平面编织高铝纤维增强氧化铝基复合材料强度及疲劳寿命预测方法

针对平面编织氧化铝基复合材料提出了一种复杂面内应力状态下的强度准则和疲劳寿命预测方法。通过拉伸、压缩及纯剪切试验,分别获得了材料的静强度指标。考虑材料拉、压性能的差异和面内拉-剪联合作用对材料强度的影响机制,提出了修正的Hoffman强度理论。采用该强度理论预测得到的偏轴拉伸强度与试验结果基本一致,偏差不超过10%。开展了偏轴角θ=0°、15°、30°、45°,应力比R=0.1,频率f=10 Hz的拉伸疲劳试验,试验结果表明随着偏轴角的增加,相同轴向拉伸载荷下的疲劳寿命逐渐降低。由于面内剪切应力分量的作用,疲劳失效由纤维主导逐渐过渡到纤维和基体共同主导的模式。基于单轴疲劳寿命曲线,采用Broutman-Sahu剩余强度模型表征剩余强度随疲劳循环次数的变化规律,结合剩余强度演化模型和修正的Hoffman强度理论,提出了一种面内复杂载荷条件下的疲劳寿命预测模型,并引入疲劳剪切损伤影响因子表征拉-剪应力联合作用对材料疲劳行为的影响。采用本文提出的疲劳寿命预测模型,预测不同偏轴角拉伸疲劳寿命,预测结果与试验结果基本一致,偏差在1倍寿命范围内。比较结果表明在给定应力比、温度和疲劳载荷频率条件下,该疲劳寿命预测模型可以用来预测平面编织氧化铝基复合材料拉-剪复杂面内载荷条件下疲劳寿命。      

On the mechanical characterization of materials by Arcan-type specimens

The simple circular notched specimen was originally proposed by Arcan to characterize the elastic properties of fibre-reinforced composites. Unfortunately, its optimized geometry does not allow to measure with reasonable accuracy both the material shear strength and the conditions of failure under a generic biaxial stress state, since the effects of stress concentration on the fillets of the two V-grooves and on the inner circular edges are responsible of premature fractures due to the uniaxial stress states of the notch edges.In a previous numerical study carried out by a parametric two-dimensional finite element model, some of the Authors of this paper found a new optimal geometry of the Arcan specimen able to minimize the notch effect and achieve a uniform pure shear stress field in the gauge cross-section. In the present paper, starting from such a geometry, a new type of Arcan specimen is proposed, having not uniform thickness. An extensive three-dimensional parametric finite element analysis has been done to define its optimal shape. The numerical results show that the new specimen is able to achieve, with a higher probability, material fracture in the minimum cross-section under a pure shear stress distribution which is more uniform than those acting in the Arcan specimen typologies until now proposed.     

Determination of material parameters of a viscoplastic model by genetic algorithm

Macroscopic (continuum) and microscopic models, used for simulation of material behaviors under different loading conditions, contain a large number of material parameters and determination of these parameters is an important and difficult issue in the modeling. The aim of this work essentially deals with parameter determination procedure of any viscoplasticity model. In this study, genetic algorithm (GA) parameter optimization procedure has been proposed to determine material parameters of viscoplastic models. Parameter determination capability of the GA optimization method was tested by using VBO model which one of the viscoplasticity theory with no yield surface and loading–unloading conditions. Fourteen material parameters of VBO model are determined using uniaxial loading–unloading stress strain curves of high density polyethylene (HDPE). Using these material parameters, creep and relaxation behaviors of HDPE are simulated. A good match with experimental results is obtained. Apart from many existing studies in the literature, GA optimization procedure is applied to determine material parameters instead of trial and error procedure. This method can also be used to determine materials parameters of other viscoplasticity theories for all kinds of materials.     

The macroscopic yielding behaviour of polymers in multiaxial stress fields

Experimental data on yielding of polyoxymethylene (POM) and polypropylene (PP) have been obtained in a wide range of complex triaxial stress conditions. These complex triaxial stress states have been produced by superimposition of simple stresses such as uniaxial compression, uniaxial tension and pure shear on hydrostatic pressure of various intensities. The actual yield surfaces of both polymers were constructed using the data. The yield surface of POM is a cone-shaped with a pointed apex and straight edges, while the yield surface of PP is cone-lime and non-linear, also with a pointed apex. A yield criterion is shown to very closely predict the observed behaviour of both polymers.     

Development of a stress-mode sensitive viscoelastic constitutive relationship for asphalt concrete: experimental and numerical modeling

Asphalt binder is responsible for the thermo-viscoelastic mechanical behavior of asphalt concrete. Upon application of pure compressive stress to an asphalt concrete specimen, the stress is transferred by mechanisms such as aggregate interlock and the adhesion/cohesion properties of asphalt mastic. In the pure tensile stress mode, aggregate interlock plays a limited role in stress transfer, and the mastic phase plays the dominant role through its adhesive/cohesive and viscoelastic properties. Under actual combined loading patterns, any coordinate direction may experience different stress modes; therefore, the mechanical behavior is not the same in the different directions and the asphalt specimen behaves as an anisotropic material. The present study developed an anisotropic nonlinear viscoelastic constitutive relationship that is sensitive to the tension/compression stress mode by extending Schapery’s nonlinear viscoelastic model. The proposed constitutive relationship was implemented in Abaqus using a user material (UMAT) subroutine in an implicit scheme. Uniaxial compression and indirect tension (IDT) testing were used to characterize the viscoelastic properties of the bituminous materials and to calibrate and validate the proposed constitutive relationship. Compressive and tensile creep compliances were calculated using uniaxial compression, as well as IDT test results, for different creep-recovery loading patterns at intermediate temperature. The results showed that both tensile creep compliance and its rate were greater than those of compression. The calculated deflections based on these IDT test simulations were compared with experimental measurements and were deemed acceptable. This suggests that the proposed viscoelastic constitutive relationship correctly demonstrates the viscoelastic response and is more accurate for analysis of asphalt concrete in the laboratory or in situ.     

弹塑性比例叠加的锥压入半解析模型与试验方法

基于能量密度等效,考虑圆锥压入(锥压入)过程中线性律纯弹性和幂律纯塑性的应变能比例叠加,提出了弹塑性应变能比例叠加的锥压入载荷-位移模型(Load vs. Displacement Model based on Proportional Superposition of elastoplastic-energy under conical indenting,LDM-PS),进而提出了获取材料Ramberg-Osgood律(R-O律)应力-应变关系的锥压入试验方法。针对80种设定材料,通过LDM-PS预测的载荷-位移曲线(正向预测)与有限元分析结果密切吻合,并且以有限元分析(Finite Element Analysis,FEA)所得载荷-位移曲线作为试验模拟曲线,采用两种锥角圆锥压头分别对平滑材料表面进行两次单锥压入加载(双锥压入),可通过对双锥压入的两个载荷-位移曲线的加载阶段按抛物律(Kick律)回归可实现R-O律参数的求解。由LDM-PS预测的R-O律应力-应变关系曲线(反向预测)与FEA的条件关系曲线密切吻合;针对8种金属材料完成了双锥压入试验,通过锥压入试验新方法预测的应力...     

Verification of the prediction of deformation-induced anisotropy for simple deformation modes: uniaxial state and pure shear state of stress

Deformation texture with preferred orientation is developed by external disturbance applied to the grain during the deformation process such as rolling. The formation of deformation texture is strongly influencing the mechanical property of the product, and material anisotropy is observed from the deformation texture, macroscopically. Therefore, the proper consideration and analysis of deformation texture is required. In the present work, the method for prediction of deformation-induced anisotropy employing the phenomenological yield potential is proposed. The proposed algorithm is applied to the anisotropic evolution for simple deformation modes, such as uniaxial stress state and pure shear stress state in X–Y direction. In order to verify the effectiveness of the method, the result from the proposed algorithm is then compared with that from the crystallographic texture analysis.     

Cyclic uniaxial and multiaxial loading with yield surface distortion consideration on prediction of ratcheting

In this study, the yield surface distortion was incorporated in the cyclic plasticity modeling as well as its center movement. The combination of Chaboche’s model and the yield surface distortion model of Baltov was used in a set of uniaxial and multiaxial loadings. The variation of the stress amplitude and the mean stress and different multiaxial loadings such as tension-torsion tests were studied. It was shown that the consideration of the distortion of the yield surface via the distortion parameter and its sign in modeling has an important effect on the plastic strain increment determination and so on the ratcheting rate. The combined model was applied to the experimental results. It was shown that the combination of the nonlinear kinematic hardening model of Chaboche and the yield surface distortion leads to a good estimation of the ratcheting strain increment in different uniaxial and multiaxial tests.     

Characterization of interlaminar shear failures of graphite/epoxy composite materials

Research undertaken to develop a more fundamental understanding of interlaminar shear failure in laminated graphite/epoxy composites is described. A test method capable of producing a state of pure interlaminar shear stress within a specified region of a composite test specimen was devised. The test method consisted of the four-point flexural testing of a unique test sample constructed of a coupon of Hercules AS4/3501-6, unidirectional, graphite/epoxy material bonded between two strips of steel using a room-temperature-curing epoxy adhesive. The major advantage of the test method is that the interlaminar shear failure of the composite coupon results from an induced state of pure shear stress, rather than from damage resulting from a complex stress state affecting the region of loading as typically occurs in the case of conventional flexural-type shear tests. The resulting shear failures were characterized with respect to fracture surface appearance, mode of failure, and stress state on the failure plane. A specially designed crack detection device was used to determine the site of fracture initiation and the direction of crack propagation.     

Evaluation of constitutive models for textured aluminium alloys using plane-strain tension and shear tests

The constitutive modelling of the strongly textured aluminium alloys AA6063-T6 and AA7003-T6 is studied. The materials were delivered in the form of flat extruded profiles. Plane-strain tension and shear tests in the plane of the flat profiles are performed. The tests are then used to evaluate a constitutive model including an anisotropic yield function, the associated flow rule and a nonlinear isotropic work-hardening rule. The parameters of the yield criterion and the work-hardening rule were identified primarily from uniaxial tension tests in different in-plane directions. It is suggested how analytical considerations and the results from the plane-strain tension and shear tests may be used to obtain a more accurate calibration of the anisotropic yield criterion. To further assess the constitutive model, finite element simulations of the plane-strain tension and shear tests are carried out and the results compared with the experimental force-elongation curves. Significant deviations in the experimental and predicted results are disclosed, and attributed partly to the parameter identification, primarily based on uniaxial tension tests, and partly to the assumption of isotropic work-hardening. Polycrystal plasticity calculations are carried out for simple shear of the AA7003-T6 material, indicating that texture evolution plays an important role in determining the response in this test already at moderate strains.     

A PATH-INDEPENDENT PARAMETER FOR FATIGUE UNDER PROPORTIONAL AND NON-PROPORTIONAL LOADING

Abstract— A path-independent multiaxial fatigue damage criterion is proposed based on critical plane concepts: fatigue crack growth is controlled by the maximum shear strain, and an important secondary effect is due to the normal strain excursion over one reversal of the maximum shear strain. The effect of loading path on fatigue endurance is quantified by the normal strain excursion. Only one multiaxial material constant is required in the model which can be determined from uniaxial test data plus one torsional result. The parameter can be easily integrated with a shear strain-life relationship to predict low cycle fatigue lifetime. Experimental data of four different materials: En15R steel, 1% Cr-Mo-V steel, 304 stainless steel, and 316 stainless steel at two temperatures were used to verify the criterion. It is shown that the proposed parameter can satisfactorily correlate test results for various proportional and non-proportional straining paths.     

剪切连接件的受力机理理论分析与试验验证

基于剪切连接件（SLD）的典型构造建立力学模型,应用弹性力学半逆解法对其腹板的应力分布进行求解,并对剪切连接件的初始刚度K、屈服后刚度K'、屈服荷载F_y、屈服位移u_y等关键性能指标进行了理论分析。针对以往屈服点确定方法存在的不足,提出了一种基于Bouc-Wen模型和模拟退火算法的等效屈服点确定方法。最后采用单调拟静力加载试验进行验证。研究结果表明:剪切连接件腹板应力分布和各项力学性能指标的理论解与有限元分析结果及试验实测结果吻合较好;该文提出的屈服点确定方法能够有效识别剪切连接件的相关力学性能指标,且拟合曲线与单调加载试验曲线良好吻合。理论分析成果将为剪切连接件的工程设计、性能评估及后续研究提供理论参考。     

An equivalent uniaxial fatigue stress model for analyzing landing gear fuse pins

We study the biaxial stress state conditions in landing gear fuse pins in the fuse groove. This biaxial state comprises a combination of shear stresses which are usually the largest stresses in the fuse pin by design, and compressive stresses which keep the half-section of the fuse pin in equilibrium. Conventional fatigue analysis techniques use an equivalent uniaxial stress, based on the Mises stress of a pure-shear condition. The respective predicted fatigue damages are much higher than those obtained from fuse pin cyclic tests. A new equivalent uniaxial fatigue stress model is proposed that includes the additional compressive stress as a relief on the fatigue damage in the fuse groove, thereby explaining the observations from fuse pin tests. The model is used in conventional uniaxial strain-life fatigue software (Goodrich Aerospace’s Fatigue Life V2) to predict the fatigue damage on a landing gear fuse pin with a sample load spectrum. The results are then compared to the pure shear model, and to a biaxial finite element fatigue analysis. As compared to the equivalent Mises model, the proposed model provides less conservative estimation of the fuse pin fatigue life, the latter value being higher than that provided by the two-dimensional finite element calculation. __________ Translated from Problemy Prochnosti, No. 3, pp. 85–98, May–June, 2006.     

Anisotropic Gurson‐Tvergaard‐Needleman plasticity and damage model for finite element analysis of elastic‐plastic problems

Implementation and analysis of the anisotropic version of the Gurson‐Tvergaard‐Needleman (GTN) isotropic damage criterion are performed on the basis of Hill's quadratic anisotropic yield theory with the definition of an effective anisotropic coefficient to represent the elastic‐plastic behavior of ductile metals. This study aims to analyze the extension of the GTN model suitable for anisotropic porous metals and to investigate the GTN model extension. An anisotropic damage model is implemented using the user material subroutine in ABAQUS/standard finite element code. The implementation is verified and applied to simulate a uniaxial tensile test on a commercially produced aluminum sheet material for three‐dimensional and plane stress test cases. Spherical and ellipsoidal micro voids are considered in the matrix material, and their effects on the uniaxial stress‐strain response of the material are analyzed. Hill's quadratic anisotropic yield theory predicts substantially large damage evolution and a low stress‐strain curve compared with those predicted by the isotropic model. An approximate model for anisotropic materials is proposed to avoid increased damage evolution. In this approximate model, Hill's anisotropic constants are replaced with an effective anisotropy coefficient. All model‐generated stress‐strain predictions are compared with the experimental stress‐strain curve of AA6016‐T4 alloy.     

A method to determine the shear and compressive stress–strain curves from torsion and bending tests of thin wires

Some materials are provided as wire or other slender geometries and are commonly used as mechanical parts, especially in medical applications. If slender geometries are well adapted to quasistatic tensile tests, such geometries cannot be properly tested under shear and compressive loads. The shear and compressive stress–strain curves nevertheless remain of major interest to engineers and designers. This paper proves and illustrates that material shear and compressive stress–strain curves can efficiently be extracted from torsion and bending tests on thin wires, even in noisy situations. The method is first presented to analyze torsion tests. This method is then developed and adapted to extract the material compressive stress–strain curve from both pure bending and uniaxial tensile tests.     

A plasticity model for multiaxial cyclic loading and ratchetting

Summary The nonlinear behavior of metals when subjected to monotonic and cyclic non-proportional loading is modeled using the proposed hardening rule. The model is based on the Chaboche [1], [2] and Voyiadjis and Sivakumar [3], [4] models incorporating the bounding surface concept. The evolution of the backstress is governed by the deviatoric stress rate direction, the plastic strain rate, the backstress, and the proximity of the yield surface from the bounding surface. In order to ensure uniqueness of the solution, nesting of the yield surface with the bounding surface is ensured. The prediction of the model in uniaxial cyclic loading is compared with the experimental results obtained by Chaboche [1], [2]. The behavior of the model in multiaxial stress space is tested by comparing it with the experimental results in axial and torsional loadings performed by Shiratori et al. [5] for different stress trajectories. The amount of hardening of the material is tested for different complex stress paths. The model gives a very satisfactory result under uniaxial, cyclic and biaxial non-proportional loadings. Ratchetting is also illustrated using a non-proportional loading history.     

Characterising the shear–tension coupling and wrinkling behaviour of woven engineering fabrics

Modelling the forming process for engineering fabrics and textile composites using a mechanical approach, such as the finite element method, requires characterisation of the material’s behaviour under large shear deformation. For woven engineering fabrics, a coupling between in-plane tension and both shear compliance and the onset of wrinkling is to be expected. This paper focuses on a novel testing technique, the biaxial bias extension test, as a means to investigate this shear–tension coupling and fabric wrinkling. Novel methods of determining the wrinkling behaviour are demonstrated. The main difficulty with the technique lies in extracting the material contribution to the recorded signal. To do this, an experimental method is proposed and demonstrated using a plain weave glass fabric. Biaxial bias extension test results are compared against picture frame and uniaxial bias extension results.     

A Generalized Yield Criterion

A generalized yield criterion is proposed based on the metai plastic deformation mechanics and the fundamental formula in theory of plasticity. Using the generalized yield criterion, the reason is explained that Mises yield criterion and Tresca yield criterion do not completely match with experimental data. It has been shown that the yield criteria of ductile metals depend not only on the quadratic invariant of the deviatoric stress tensor J2, but also on the cubic invariant of the deviatoric stress tensor J3 and the ratio of the yield stress in pure shear to the yield stress in uniaxial tension κ/σs. The reason that Mises yield criterion and Tresca yield criterion are not in good agreement with the experimental data is that the effect of J3 and κ/σs is neglected.     

基于数字图像相关技术测量刨花板材料力学参数

刨花板作为一种人造板材,其表面多孔性致使应变片的粘贴过程十分困难,且涂胶量的多少会直接影响测量的精度。基于对样品变形前后图像分析的数字图像相关(Digital Image Correlation,DIC)技术被用于测量刨花板的力学参数。相比于传统的贴应变片法,该技术具有高精度、非接触性及全场测量等优势。“横观各向同性”模型被考虑用来模拟刨花板的力学行为。于是,表征材料力学性能的弹性张量取决于5个独立的弹性参数:纵向、横向弹性模量EL、ET,纵向、横向泊松比νL、νT及纵向剪切模量GL。为了实现这一测量过程,刨花板被切割成一批梁样品,随后被应用于三点弯曲试验。通过比较感兴趣区域(Region Of Interest,ROI)内网格节点位移的测量值与铁木辛柯梁理论解析解,及有限元模型修正(Finite Element Model Updating,FEMU)方法的应用,4个弹性参数ET、GL、EL和νL被成功测量。对比相关文献,该文的测量方法简单易行,测量结果准确,可应用于刨花板材料并推广至各向异性材料的弹性参数测量之中。