Cyclic Uniaxial Tensile Tests Research Articles

Fading memory of loading history in polypropylene and a polypropylene/clay nanocomposite

Experimental data are reported for neat polypropylene and a polypropylene/clay nanocomposite in multistep uniaxial cyclic tensile tests at room temperature (oscillations between maximum strains and the zero minimum stress, with the maximum strains increasing monotonically with number of cycles). The fading memory of deformation history is observed: when two test specimens are subjected to loading programs that differ during the first n − 1 cycles and coincide afterwards, their stress–strain diagrams become identical starting from the nth cycle. Constitutive equations are developed in the cyclic viscoelasticity and viscoplasticity of nanocomposites with semicrystalline matrices, and the adjustable parameters of the stress–strain relations are determined by fitting them to experimental data. The ability of the model to predict the fading memory phenomenon is confirmed by numerical simulations.

138 3D-CGモデルを用いた競泳用水着の異方性超弾性モデルによる応力解析(生体負荷の変化と軽減)

A new design method for designing competitive swimsuits using 3-dimensional stress calculation was investigated in this paper. An anisotropic hyperelastic modeling of swimwear fabric was developed from the results of tensile loading tests. 3-dimensional stress distributions of swimwear in swimming motions were calculated by the anisotropic hyperelastic model. The displacement fields of 3D-CG human model which reproduce swimming motion of human body were applied to stress calculation. For the material modeling, the uniaxial cyclic tensile loading tests were conducted to obtain the mechanical characteristics of competitive swimsuits. From loading test results, the mechanical characteristics of swimwear fabrics show anisotropy and the stiffness of the fabric shows hardening along with stretching. The cyclic tensile loading test results show stiffness reduction which depended on the maximum deformation. To take the anisotropy and stress reduction into account for the material modeling, a stress softening model for anisotropic hyperelastic model using stiffness ratio of warp or weft was proposed. In this paper, 3-dimensional stress distributions of swimwear were calculated by the proposed anisotropic hyperelastic model. A polygonal model of the swimwear was prepared and deformation of swimwear was adapted to the skin of 3D-CG human model in swimming motions. From the calculated results, stress distributions were possible to be visualized on the 3D-CG swimwear model.

3D-CG Based Stress Calculation of Competitive Swimwear Using Anisotropic Hyperelastic Model

A new design method for designing competitive swimsuits using 3-dimensional stress calculation was investigated in this paper. An anisotropic hyperelastic modeling of swimwear fabric was developed from the results of tensile loading tests. 3-dimensional stress distributions of swimwear in swimming motions were calculated by the anisotropic hyperelastic model. The displacement fields of 3D-CG human model which reproduce swimming motion of human body were applied to stress calculation. For the material modeling, the uniaxial cyclic tensile loading tests were conducted to obtain the mechanical characteristics of competitive swimsuits. From loading test results, the mechanical characteristics of swimwear fabrics show strong-anisotropy and the stiffness of the fabric shows hardening along with the increase of stretch. The cyclic tensile loading test results shows reduction of stiffness which depended on the maximum deformation previously reached in the history of the material. To take the strong anisotropy and stress reduction into account for the material modeling, a stress-softening model for anisotropic hyperelastic model using stiffness ratio of warp or weft was proposed. The results of the simulation showed good agreement with that of pressure test in a design range of competitive swimsuits. Finally, 3-dimensional stress distributions of swimwear were calculated by the proposed anisotropic hyperelastic model. A polygonal model of the swimwear was prepared and deformation of swimwear was adapted to the skin of 3D-CG human model in swimming motions. From the results, stress distributions were able to be visualized on the 3D-CG swimwear model.

CYCLIC VISCOPLASTICITY OF SEMICRYSTALLINE POLYMERS WITH FINITE STRAINS: OBSERVATIONS AND CONSTITUTIVE MODELING

Observations are reported on low density polyethylene and isotactic polypropylene in uniaxial tensile cyclic tests (oscillations between maximum elongation ratios k max and the zero minimum stress σmin with k max increasing monotonically with number of cycles). Constitutive equations are developed in cyclic viscoplasticity of semicrystalline polymers with finite strains. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Ability of the model to describe the characteristic features of the mechanical behavior and to predict the viscoplastic response in cyclic tests is confirmed by comparison of the results of numerical simulation with observations in additional tests.

Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Original constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histories. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain amplification factor concept applied over material directions according to the Mullins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evolution rule. A computational procedure is defined to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful comparisons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is efficiently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of filled rubbers.

Cyclic viscoplasticity of semicrystalline polymers with finite deformations

Observations are reported on low density polyethylene (LDPE) in uniaxial tensile cyclic tests (oscillations between maximum elongation ratios kmax(n) and the zero minimum stress σmin=0 when kmax(n) increases monotonically with number of cycles n). Experimental data demonstrate fading memory of deformation history: when specimens are subjected to two loading programs that differ along the first n-1 cycles of deformation and coincide afterwards, their stress–strain diagrams become identical starting from the nth cycle. A constitutive model is developed in cyclic viscoplasticity of semicrystalline polymers with finite deformations, and its adjustable parameters are found by fitting the observations. Ability of the stress–strain relations to describe the fading memory phenomenon and to predict the mechanical response of LDPE in cyclic tests with various deformation programs is confirmed by numerical simulation.

Hyperelastic Property Measurements of Heat-Cured Silicone Adhesives by Cyclic Uniaxial Tensile Test

Most of the commonly used linear elastic properties of silicone adhesives cannot precisely represent their material behavior, knowledge of which is crucial to the reliability study of electronic devices. For this reason, in this paper a widely used silicone adhesive, namely Loctite 5404, is chosen for measuring hyperelastic properties via cyclic uniaxial tensile tests. A special sample preparation procedure is developed to avoid the formation of detrimental air bubbles in the samples. Two maximum strain levels, 20% and 40%, are used in the tests. Each test includes five cyclic loadings to produce a stable stress–strain loop. Three orders of magnitude of strain rate changes are studied, and the stress–strain response of the material is found to be strain rate dependent. The measured stress–strain data are imported into Abaqus finite-element software to calibrate the material coefficients of hyperelastic material models (Mooney–Rivlin, Yeoh, Ogden, and van der Waals models). This is the first time that the hyperelastic properties of the studied silicone adhesive are presented. The determined material coefficients can be used directly in finite-element analyses and thus in reliability studies of electronic devices.

Cyclic deformations of polypropylene with a strain-controlled program

Experimental data are reported on isotactic polypropylene in uniaxial tensile cyclic tests with a strain-controlled program (oscillations between fixed minimum and maximum strains). The following characteristic features of stress–strain diagrams are observed: (i) logarithmic decay in maximum and minimum stresses with number of cycles (cyclic softening), (ii) more pronounced reduction in minimum stress than in maximum stress (cyclic strengthening), (iii) independence of rates of decrease in maximum and minimum stresses of strain rate, (iv) decrease in hysteresis energy with number of cycles. To rationalize these observations, a constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers. Numerical simulation demonstrates that the model correctly describes experimental stress–strain curves and quantitatively predicts evolution of maximum and minimum stresses with number of cycles. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers

Stress- and strain-controlled cyclic deformation of polypropylene

Experimental data are reported on isotactic polypropylene in uniaxial tensile cyclic tests with stress- and strain-controlled programs. A constitutive model is developed that adequately describes stress–strain diagrams, and its parameters are found by fitting the observations. Numerical simulation demonstrates that fatigue failure in ratcheting tests is induced by pronounced growth of plastic strain in crystallites.

Elastic–plastic behavior of non-woven fibrous mats

Electrospinning is a novel method for creating non-woven polymer mats that have high surface area and high porosity. These attributes make them ideal candidates for multifunctional composites. Understanding the mechanical properties as a function of fiber properties and mat microstructure can aid in designing these composites. Further, a constitutive model which captures the membrane stress–strain behavior as a function of fiber properties and the geometry of the fibrous network would be a powerful design tool. Here, mats electrospun from amorphous polyamide are used as a model system. The elastic–plastic behavior of single fibers are obtained in tensile tests. Uniaxial monotonic and cyclic tensile tests are conducted on non-woven mats. The mat exhibits elastic–plastic stress–strain behavior. The transverse strain behavior provides important complementary data, showing a negligible initial Poisson's ratio followed by a transverse:axial strain ratio greater than −1:1 after an axial strain of 0.02. A triangulated framework has been developed to emulate the fibrous network structure of the mat. The micromechanically based model incorporates the elastic–plastic behavior of single fibers into a macroscopic membrane model of the mat. This representative volume element based model is shown to capture the uniaxial elastic–plastic response of the mat under monotonic and cyclic loading. The initial modulus and yield stress of the mat are governed by the fiber properties, the network geometry, and the network density. The transverse strain behavior is linked to discrete deformation mechanisms of the fibrous mat structure including fiber alignment, fiber bending, and network consolidation. The model is further validated in comparison to experiments under different constrained axial loading conditions and found to capture the constraint effect on stiffness, yield, post-yield hardening, and post-yield transverse strain behavior. Due to the direct connection between microstructure and macroscopic behavior, this model should be extendable to other electrospun systems and other two dimensional random fibrous networks.

Cyclic strengthening of polypropylene under strain-controlled loading

► Cyclic strengthening is observed in strain-controlled tests on isotactic polypropylene . ► Pre-loading induces a strong increase in the rate of strengthening. ► Strengthening is attributed to alignment of broken lamellar pieces. Experimental data are reported on isotactic polypropylene in uniaxial tensile cyclic tests with a strain-controlled program (oscillations between fixed minimum and maximum strains) at room temperature. The stress–strain diagrams demonstrate that (i) maximum and minimum stresses per cycle decay with number of cycles, (ii) the rate of decrease in minimum stress strongly exceeds that in maximum stress, (iii) secant elastic modulus increases (cyclic strengthening) or decreases (cyclic softening) with number of cycles depending on maximum strain. A physical mechanism is suggested to describe strengthening of semicrystalline polymers that accounts for (i) lamellar fragmentation and (ii) alignment of broken lamellar pieces under cyclic deformation. With reference to this concept, several conclusions are formulated that are confirmed by additional tests on pre-loaded samples.

Effect of the microstructure parameters on the mullins softening in carbon‐black filled styrene–butadiene rubbers

AbstractA quantitative estimate of the Mullins softening is proposed and tested on various carbon‐black filled styrene–butadiene rubbers. To model the behavior of elastomeric materials, some constitutive equations reported in the literature are based on the account of a strain amplification factor, which evolves with the maximum strain history. The amplification factor is grounded on the representation of filled rubbers as heterogeneous materials made of hard rigid domains and soft deformable domains. In this work, this factor is split into two parts with opposite effects that account for the Mullins softening and for the filler reinforcement, respectively. Evolutions of both parts are obtained through a direct analysis of cyclic uniaxial tensile tests performed on a series of materials. The Mullins softening part is shown to linearly depend on the filler volume fraction and on the maximum strain applied, when defined as the first invariant of the Hencky tensor. Its changes with the gum cross‐link density parameter are insignificant. The reinforcement part of the amplification factor shows quadratic dependence on the filler volume fraction. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Multiscale fatigue model for bituminous mixtures

Fatigue failure is one of the main failure mechanisms in flexible pavements, resulting in the decrease of material stiffness due to repeated (traffic) loading, mainly driven by the propagation of microcracks. In this work, a new fatigue model for bituminous mixtures is proposed, which combines multiscale modeling (continuum micromechanics) with fracture mechanics. This model is validated by means of stress-controlled cyclic uniaxial tensile tests. The respective experimental data are obtained at different temperatures, considering different loading amplitudes and frequencies. For these conditions, the fatigue behavior, characterized by a decrease of the complex modulus and an increase of the phase angle with increasing number of load cycles, is well described by the proposed model. The multiscale nature of the proposed model allows determination of the influence of the mix-design, the material behavior of each constituent, and the type of loading on the overall fatigue performance. Finally, performance-based optimization of bituminous mixtures with respect to their fatigue behavior becomes possible.

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–strain 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.

Mechanical Properties of Steel-FRP Composite Bar under Uniaxial and Cyclic Tensile Loads

This paper introduces a newly developed steel-fiber-reinforced polymer (FRP) composite bar (SFCB) and proposes the ideal configuration based on a large number of exploratory tests on handmade products. Based on factory production of SFCB, uniaxial tensile tests and cyclic tensile tests were conducted to determine the initial elastic modulus, postyield stiffness, yield strength, ultimate strength, unloading stiffness, and residual deformation. Test results showed that the stress-strain curve of the SFCB was bilinear before the fiber fractures. After the inner steel yielded, the SFCB showed a stable postyield stiffness, small residual deformation, and good reparability. Because the theoretical model for the stress-strain curve of SFCB under a uniaxial load based on the mixture rule had large error with data from cyclic tests, the corresponding restoring force model under cyclic tensile loading was constructed by statistical analysis of the stress-strain test curve under cyclic tension. The generated restoring force model accurately displayed the trend of unloading stiffness of SFCB degradation with cyclic loads. Furthermore, the predicted results were in good agreement with the experimental results, which proved that the mechanical properties of SFCB could be predicted and designed by the proposed model.

A multiscale approach of nonlinear composites under finite deformation: Experimental characterization and numerical modeling

The present paper is devoted to the study of the mechanical behavior of an ethylene propylene diene monomer (EPDM) rubber reinforced by polypropylene (PP) particles, revealed as compressible. The hyperlastic behavior of this blend has been characterized under cyclic uni-axial tensile tests. The experimental results show a significant effect of the fraction of (PP) particles (5%, 10%, 25% and 30% by weight) on the macroscopic behavior of the composite. In order to model this behavior, we first develop and implement a micromechanically-based nonlinear model for hyperelastic composites. The approach is based on the second order homogenization method proposed by Ponte Castaneda and Tiberio (2000) and for which suitable energy densities are adopted for the matrix and the inclusions phases, both assumed as compressible. We then proceed to the model verification by comparison with Finite Element simulations on a unit cell. Finally, we propose an extension of the model in order to take into account damage due to voids growth phenomena. The comparison of the multiscale damage model predictions with the experimental data obtained on the EPDM/PP composite indicates a very good agreement.

Cyclic thermo-viscoplasticity of high density polyethylene

Observations are reported in uniaxial cyclic tensile tests (loading–unloading with various maximum strains) on high density polyethylene at temperatures ranging from room temperature up to 90 °C. It is demonstrated that the maximum stress per cycle and an apparent residual strain (measured at the instant when the tensile force vanishes under retraction) strongly decrease with temperature. The latter seems unexpected as the interval of temperatures covers the α-relaxation temperature, which is conventionally associated with activation of additional mechanisms for inelastic flow. A model is developed that captures the decrease in residual strain with temperature. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The effects of temperature and maximum strain per cycle on residual strains are studied numerically.

Cyclic viscoplasticity of semicrystalline polymers

Abstract Observations are reported on three grades of isotactic polypropylene in uniaxial cyclic tensile tests with various maximum strains. Constitutive equations are derived for the viscoplastic behavior of a semicrystalline polymer. A characteristic feature of the model is that the rate-of-strain tensor for plastic flow is split into the sum of two components, one of which is proportional to the deviator of the stress tensor, while the other is proportional to the rate-of-strain tensor. The stress–strain relations involve four adjustable parameters that are found by fitting the experimental data. Numerical simulation demonstrates that the model correctly predicts the mechanical response of semicrystalline polymers in cyclic tests.

Determination of tensile crack bridging of PCM-concrete interface subjected to fatigue loading by means of bending test

In this paper, a simple and handy test method for determination of the tensile crack bridging law of PCM-concrete interface is proposed. Based on the fatigue failure mechanism of PCM-concrete interface that is governed by crack propagation as the result of interface bridging degradation, the J-integral method proposed for determining the tension softening relation of concrete under static loading is modified to determine the PCM-concrete interface tensile stress degradation relation. The derived degradation relation is compared to that of normal concrete under cyclic uniaxial tensile tests, and it can be found that the PCM-concrete interface has higher degradation rate so that more attention should be paid to the PCM-concrete interface during the design of PCMretrofitted structures under fatigue loading.

Constitutive model for cyclic deformation of perfluoroelastomers

Observations are reported in uniaxial cyclic tensile tests with a strain-controlled program on perfluoroelastomer Hyflon MFA. A constitutive model is developed for its viscoplastic response and damage at three-dimensional deformations with finite strains. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Numerical simulation demonstrates that the constitutive equations adequately describe the mechanical response of perfluoroelastomer in cyclic tests with complicated deformation programs.