Inelastic material behavior of polymers – Experimental characterization,formulation and implementation of a material model

In this contribution an experimental procedure based on displacement controlled tensile tests at different rates of loading, relaxation experiments and deformation controlled loading and unloading processes with intermediate relaxations to experimentally characterize and classify the nonlinear, inelastic mechanical behavior of polymers is presented. These experiments provide data for a structured approach to parameter identification. In line with the experiments, a small strain uniaxial viscoplastic material model is derived, subsequently generalized to multiaxial loadings and implemented into a finite element program. The combination of the experimental procedure and the proposed material model is then used to characterize and model the mechanical behavior of the thermoplastic polypropylene. After the identification of the necessary material parameters, stress–strain curves have been computed for different uni- and multiaxial loadings and are compared with experimental results.     

A nonlinear fractional viscoelastic material model for polymers

In this contribution a test scheme based on tensile tests at different velocities, relaxation experiments and deformation controlled loading and unloading processes with intermediate relaxations has been used to experimentally characterize the nonlinear, inelastic material behavior. Based on the experimental observations a small strain nonlinear fractional viscoelastic material model is derived. In order to use the model within a finite element analysis, the constitutive equations have been generalized for the multiaxial case. The experimental test scheme and the fractional viscoelastic material model are subsequently applied to characterize and compute the mechanical behavior of the thermoplastic Polypropylene. After the identification of the material parameters several uniaxial and multiaxial simulations have been carried out and compared with experimental results.     

Fatigue behavior of laminated composites with a circular hole under in-plane multiaxial loading

A modified fiber failure fatigue model is presented for characterizing the behavior of laminated composites with a central circular hole under in-plane multiaxial fatigue loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane multiaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Analytical predictions are compared with the experimental results for uniaxial and multiaxial fatigue loading cases. A good match is observed. Further, studies are carried out for different in-plane biaxial tension–tension and biaxial compression–compression loading cases.     

Anisotropic viscoplasticity constitutive model for directionally solidified superalloy

Abstract

The macroscopic deformation behaviour of a Ni-based directionally solidified (DS) superalloy was experimentally investigated, and an anisotropic constitutive model of the material was developed. Monotonic and creep tests were performed on uniaxial test specimens machined from DS plates so that the angle between the loading direction and the solidified grain direction varied between 0 and 90°. Tension-torsion creep tests were also conducted to examine the anisotropic behaviour under multiaxial stress conditions. The material exhibited marked anisotropy under elastic and viscous deformation conditions, whereas it showed isotropy under plastic deformation conditions of high strain rates. Then crystal plasticity analyses were carried out to identify slip systems under creep loading conditions, assuming the anisotropic creep behaviour of the DS material. A viscoplastic constitutive model for expressing both the anisotropic elasticity-viscosity and the isotropic plasticity was proposed. The elastic constants were determined using a self-consistent approach, and viscous parameters were modelled by crystal plasticity analyses. The calculation results obtained using the constitutive model were compared with the experimental data to evaluate the validity of the model. It was demonstrated that the constitutive model could satisfactorily describe the anisotropic behaviour under uniaxial and multiaxial stress conditions with a given set of material parameters.     

Uniaxial and biaxial failure behaviors of aluminum alloy foams

Combined shear–tensile test have been performed on a closed-cell aluminum alloy foams with three relative densities over a wide range of loading rates in order to probe their failure behaviors under biaxial loading conditions. Quasi-static uniaxial compressive and tensile tests have also been conducted to investigate uniaxial failure behaviors of the aluminum alloy foams. The materials exhibit uniaxial failure stress asymmetry due to different failure mechanism in the uniaxial tensile and compression. Comparison is made between three phenomenological failure criteria and the measured failure stresses under different loading conditions to verify these criteria. The experimental failure surfaces of the aluminum alloy foams provide support for the three phenomenological failure criteria when suitable Poisson’s ratio is employed. The shape of the experimental failure surface in principal stress plane was not significantly influenced by variation in the relative density. The slight expansion of the failure surfaces with loading rate happened to be isotropic for this investigated closed-cell aluminum alloy foams in combined shear–tensile testes.     

单向受拉状态下的钢纤维混凝土本构模型

在混凝土中添加随机分布的钢纤维能有效提高混凝土力学性能。为了更好地考虑纤维对单向受拉状态下钢纤维混凝土（SFRC）的增强作用，提出一个钢纤维混凝土的弥散开裂本构模型。在弹性阶段，纤维混凝土被视为简单复合材料，基于两相复合材料理论，对SFRC的弹性刚度矩阵进行修正；在受拉开裂后，混凝土的塑性变形量被视为纤维与混凝土界面脱粘过程中滑移量，利用粘结滑移模型计算纤维在混凝土开裂面上的桥接作用。该文通过有限元软件ABAQUS中子程序二次开发接口Umat，进行Fortran编程，在ABAQUS中实现该本构模型。通过数值模拟结果与受拉实验数据进行对比，验证了该本构模型的准确性。通过数值模拟分析，进一步探究钢纤维混凝土相关参数对抗拉性能的影响，为钢纤维混凝土在实际的工程中的应用提供建议。     

An analysis of the Brazilian disk fracture test using the Weibull probabilistic treatment of brittle strength

It is pointed out that the Weibull multiaxial treatment of brittle strength contains limitations which are not present in the more familiar uniaxial formulation. Provided these limitations are satisfied, it is possible to use tension or bending data to predict multiaxial behavior when at least one principal stress is tensile. This is illustrated for the Brazilian disk test (diametral compression of a disk). Predictions based on bending tests agree well with observed strength values in disk tests on two types of rocks.     

Behavior of high performance fiber reinforced cement composites under multi-axial compressive loading

Experiments were conducted to better understand the behavior of strain hardening, high performance fiber reinforced cement composites (HPFRCC) when subjected to uniaxial, biaxial, and triaxial compression. The experimental parameters were: type of fiber, fiber volume fraction, and loading path. Two types of commercially available fibers, namely high-strength hooked steel fiber and ultra high molecular weight polyethylene fiber, with volume fractions ranging from 1.0% to 2.0%, were used in a 55-MPa mortar matrix. The selected loading paths consisted of uniaxial compression and tension, equal biaxial compression, and triaxial compression with two levels of lateral compression. The test results revealed that the inclusion of short fibers can significantly increase both strength and ductility under uniaxial and biaxial loading paths, but that the role of volume fraction is rather small for the range of fiber volume contents considered. The results also showed that the confining effect introduced by the fibers becomes minor in triaxial compression tests, where there is relatively high external confining pressure. The experimental information documented herein can serve as input for the development of multiaxial constitutive models for HPFRCCs.     

Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression

Uniaxial compression experiments were performed for brittle sandstone samples containing a single fissure by a rock mechanics servo-controlled testing system. Based on the experimental results of axial stress-axial strain curves, the influence of single fissure geometry on the strength and deformation behavior of sandstone samples is analyzed in detail. Compared with the intact sandstone sample, the sandstone samples containing a single fissure show the localization deformation failure. The uniaxial compressive strength, Young’s modulus and peak axial strain of sandstone samples with pre-existing single fissure are all lower than that of intact sandstone sample, which is closely related to the fissure length and fissure angle. The crack coalescence was observed and characterized from tips of pre-existing single fissure in brittle sandstone sample. Nine different crack types are identified based on their geometry and crack propagation mechanism (tensile, shear, lateral crack, far-field crack and surface spalling) for single fissure, which can be used to analyze the failure mode and cracking process of sandstone sample containing a single fissure under uniaxial compression. To confirm the subsequence of crack coalescence in sandstone sample, the photographic monitoring and acoustic emission (AE) technique were adopted for uniaxial compression test. The real-time crack coalescence process of sandstone containing a single fissure was recorded during the whole loading. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle sandstone sample containing a single fissure is analyzed under uniaxial compression. The present research is helpful to understand the failure behavior and fracture mechanism of engineering rock mass (such as slope instability and underground rock burst).     

A temperature dependent creep damage model for polycrystalline ice

We present a continuum damage model for the temperature dependent creep response of polycrystalline ice under a multiaxial state of stress, suited for ice in polar regions. The proposed model is based on a thermo-viscoelastic constitutive law for ice creep and a local orthotropic damage accumulation law for tension, compression and shear loadings. Orthotropic damage is represented by a symmetric second-order damage tensor and its effect on creep is incorporated through the effective stress concept. The unknown model parameters are first calibrated using published experimental data from constant uniaxial stress tests and then predictions are made for constant strain rate and multiaxial loadings. The predicted results are in good agreement with both experimental and numerical results in the literature illustrating the viability of the proposed model. The model is mainly intended for studying the failure mechanisms of polar ice at low deformation rates with depth varying temperature profiles.     

橡胶隔振器大变形有限元分析

以橡胶隔振器为研究对象,基于超弹性本构模型,对拉伸、压缩、剪切状态下分别进行有限元计算,探讨橡胶等不可压缩材料大变形有限元建模技术;重点研究橡胶结构不同受载方式下变形模式及有限元分析所需要的材料试验数据。经与试验结果对比分析,得到隔振器三种状态下,填充超弹本构模型最优的材料数据类型,为橡胶结构件的数值模拟提供有益参考。     

钢纤维高性能轻骨料混凝土多轴强度和变形特性研究

为了研究钢纤维掺量和三轴应力比对高性能轻骨料混凝土破坏准则和本构关系的影响规律,进行了钢纤维全轻混凝土和钢纤维次轻混凝土多轴强度和变形特性的试验研究,考虑到试验机加载能力和新拌高性能轻骨料混凝土的工作性能,选取的钢纤维体积掺量为0、0.5%、1.0%和1.5%,试验加载路径有单轴拉、压,双轴等压和真三轴压。结果发现在单轴应力和低应力比条件下,钢纤维能够明显地发挥增强阻裂作用,随着钢纤维掺量的增加,中间主应力对极限抗压强度和峰值应变的影响越来越大,且钢纤维体积掺量对两种轻骨料混凝土应力-应变曲线下降段有一定的影响;在高应力比条件下,钢纤维体积掺量对峰值强度、峰值应变和应力-应变曲线下降段无明显影响,但对高应力比下轻骨料混凝土应力-应变曲线上特有的应力平台区域有较大的影响。考虑钢纤维含量特征参数的影响,对普通骨料混凝土的Kotsovos破坏准则进行了相应的修正,得出了适合钢纤维增强轻骨料混凝土的破坏准则表达式。     

未硫化橡胶非线性粘弹性本构模型研究

建立一种新的未硫化橡胶力学行为的描述方法。为了充分研究未硫化橡胶在不同变形模式下复杂的应力-应变行为,设计了3种不同的力学特性实验:单轴拉伸、压缩与剪切试验。发现未硫化橡胶的应力-应变关系表现出很强的非线性和率相关性。提出结合Yeoh应变能函数的广义Maxwell粘超弹性模型,拟合分析表明试验结果与模拟结果一致性较好。发现与硫化橡胶一样,必须采用多工况下的实验数据才能得到变形协调的粘弹性本构模型。实验结果和建立的本构模型有助于工程师更好的理解未硫化橡胶的力学行为,为橡胶的制造过程仿真提供理论基础。     

Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture

A coupled plasticity-damage model for plain concrete is presented in this paper. Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a plasticity model is proposed in order to effectively predict and simulate plain concrete fracture. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations and for the easiness in the numerical implementation, in the CDM framework the strain equivalence hypothesis is adopted such that the strain in the effective (undamaged) configuration is equivalent to the strain in the nominal (damaged) configuration. The proposed constitutive model has been shown to satisfy the thermodynamics requirements. Detailed numerical algorithms are developed for the finite element implementation of the proposed coupled plasticity-damage model. The numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus. Special emphasis is placed on identifying the plasticity and damage model material parameters from loading-unloading uniaxial test results. The overall performance of the proposed model is verified by comparing the model predictions to various experimental data, such as monotonic uniaxial tension and compression tests, monotonic biaxial compression test, loading-unloading uniaxial tensile and compressive tests, and mixed-mode fracture tests.     

Deformation characteristics of low carbon steel subjected to dynamic impact loading

The effects of impact loading on changes in microstructure have been studied in low carbon steel. Low to moderate shock loading tests have been carried out on steel specimens using a single stage gas gun with projectile velocities ranging from 200 to 500 m/s. Stress history at the back face of the target specimen and projectile velocity prior to impact were recorded via manganin stress gauges and velocity lasers, respectively. A Johnson-Cook constitutive material model was employed to numerically simulate the material behavior of low carbon steel during impact and obtain the particle velocity at the impact surface as well the pressure distribution across the specimens as a function of impact duration. An analytical approach was used to determine the twin volume fraction as a function of blast loading. The amount of twinning within the α-ferrite phase was measured in post-impact specimens. A comparison between experimental and numerical stress histories, and analytical and experimental twin volume fraction were used to optimize the material and deformation models and establish a correlation between impact pressure and deformation response of the steel under examination. Strain rate controlled tensile tests were carried out on post-impact specimens. Results of these tests are discussed in relation to the effects of impact loading on the yield and ultimate tensile strength as well as the hardening and strain energy characteristics.     

Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. II: Calibration and validation

The Lattice Discrete Particle Model (LDPM) formulated in the preceding Part I of this study is calibrated and validated in the present Part II. Calibration and validation is performed by comparing the results of numerical simulations with experimental data gathered from the literature. Simulated experiments include uniaxial and multiaxial compression, tensile fracture, shear strength, and cycling compression tests.     

Stochastic modelling of low-cycle fatigue damage in 316L stainless steel under variable multiaxial loading

In the present study, a stochastic model is developed for the low-cycle fatigue life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. In the proposed model, fatigue phenomenon is considered as a Markov process, and damage vector and reliability are defined on every plane. Any low-cycle fatigue damage evaluating method can be included in the proposed model. The model enables calculation of statistical reliability and crack initiation direction under variable multiaxial loading, which are generally not available. In the present study, a critical plane method proposed by Kandil et al . ( Metals Soc., London 280, 203–210, 1982) maximum tensile strain range, and von Mises equivalent strain range are used to calculate fatigue damage. When the critical plane method is chosen, the effect of multiple critical planes is also included in the proposed model. Maximum tensile strain and von Mises strain methods are used for the demonstration of the generality of the proposed model. The material properties and the stochastic model parameters are obtained from uniaxial tests only. The stochastic model made of the parameters obtained from the uniaxial tests is applied to the life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. The predicted results show good aggreement with experimental results.     

The damage tolerance of GRP laminates under biaxial prestress

The damage tolerance of E-Glass reinforced/polyester laminated plates subjected to a low velocity impact while under an in-plane prestress is investigated. Prior to test, the plates are subjected to either uniaxial or biaxial loading by means of a specially designed test rig which enables independent tension/tension, tension/compression or compression/ compression testing in all stress/strain quadrants. Impact tests are carried out for a single strike energy for a comprehensive range of pre-strains. Absorbed energy, damage area, peak impact loads and the maximum permanent indentation depth are assessed in characterising the resulting damage.

It is shown that the shape, orientation and size of the damage zone is strongly influenced by the nature and magnitude of the pre-strain. Impact specimens subject to shear loading give rise to the largest increase in damage area when compared to unstressed plates.     

钢渣粗骨料混凝土单轴受压应力-应变关系试验研究

为探究钢渣粗骨料混凝土稳定性及其应力-应变关系全曲线,该文对包头某钢铁公司的钢渣粗骨料进行了浸水膨胀率试验及压蒸粉化率试验并测其f-CaO含量;完成了6组不同钢渣替代率下的立方体抗压试验及棱柱体单轴受压试验,分析其破坏形态及受力变形特征,建立钢渣粗骨料混凝土本构关系模型。研究表明:该文所选钢渣的f-CaO含量、浸水膨胀率、压蒸粉化率均符合现行规范规定,稳定性良好;钢渣粗骨料混凝土单轴抗压强度随钢渣掺量的增加而提高,并高于普通混凝土抗压强度,破坏呈现的脆性特征也更为显著;钢渣粗骨料混凝土棱柱体抗压强度与立方体抗压强度的比值相较于普通混凝土更高。根据过镇海本构模型及Wee模型,并引入钢渣粗骨料含量的修正系数,对钢渣粗骨料混凝土应力-应变关系采用分段式表达。该文提出应力-应变模型与试验结果拟合程度较好,可以更加全面的描述钢渣粗骨料混凝土的单轴受压力学行为。     

An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule

Predicting the unloading and/or cyclic deformation behavior of polymers is a challenge for most nonlinear viscoelastic constitutive models. Experimental data of an epoxy polymer under uniaxial loading/unloading and two other types of cyclic loadings are used to assess the predictive capabilities of three types of nonlinear viscoelastic models. A general loading/unloading criterion and a switching rule, proposed recently by the authors, are further modified and incorporated into each of the three models. For each model, predictions by both the original formulations and that incorporating the proposed loading/unloading rule are compared with the test data. It is clearly shown that such a rule is essential to correctly simulate the unloading and cyclic loading behavior of polymers. By introducing such a rule to constitutive models, the quantitative predictions can be improved, to various degrees of success, with respect to cyclic deformation features such as ratcheting under cyclic loading with a mean stress and stress relaxation under cyclic straining with a mean strain.