Some aspects of the mechanical response of BMI 5250‐4 neat resin at 191°C: Experiment and modeling

The inelastic deformation behavior of BMI‐5250‐4 neat resin, a high‐temperature polymer, was investigated at 191°C. The effects of loading rate on monotonic stress–strain behavior as well as the effect of prior stress rate on creep behavior were explored. Positive nonlinear rate sensitivity was observed in monotonic loading. Creep response was found to be significantly influenced by prior stress rate. Effect of loading history on creep was studied in stepwise creep tests, where specimens were subjected to a constant stress rate loading followed by unloading to zero stress with intermittent creep periods during both loading and unloading. The strain‐time behavior was strongly influenced by prior deformation history. Negative creep was observed on the unloading path. In addition, the behavior of the material was characterized in terms of a nonlinear viscoelastic model by means of creep and recovery tests at 191°C. The model was employed to predict the response of the material under monotonic loading/unloading and multi‐step load histories. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Analysis of the isothermal mechanical response of a shape memory polymer rheological model

In this paper, we derive the isothermal mechanical response of a 4‐element rheological model for shape memory polymers (SMP) in the context of (i) constant stress, (ii) constant strain, (iii) constant stress rate, (iv) constant strain rate, (v) periodic strain. The effect of shape memory strain (modeled by a friction element) and the temperature dependence of the material properties on the SMP response are examined for a polyurethane shape memory polymer of the polyester polypole series. In particular, it is possible to identify a threshold frequency during periodic loading, near which the damping capacity of the SMP is strongly affected by an increasing shape memory strain. On the other hand, when the applied frequency is much greater than the threshold value, an increasing shape memory strain ceases to have any effect on the damping. It is also shown that at a given frequency (significantly greater than the threshold value), the damping capacity as a function of temperature attains a maximum. While this maximum value is frequency‐dependent (being inversely proportional), the temperature at which the maximum is attained is frequency‐independent, and is analytically shown to be the glass transition temperature.     

Viscoplastic analysis of fiber reinforced polymer matrix composites under various loading conditions

The present study aims modeling the viscoplastic behavior of polymer matrix composite laminates under different loading conditions. The adopted model is based on the one‐parameter plasticity model employed to predict the plastic part of the recognized nonlinear behavior of fiber composites [C.T. Sun and J.L. Chen, J. Compos. Mater., 23, 1009 (1989)]. This model evolved to a three‐parameter constitutive viscoplastic model used to describe successfully the strain‐rate dependent mechanical behavior. Based on this model, designated as 3PV, a numerical implementation was made, based on the Classical Laminate Theory (CTL), to simulate non‐linear behavior of general laminates. The validation of this numerical implementation was performed using experimental data reported in literature. The first step was to assess the model predictions under high strain rates. The model was able to model high strain rate mechanical response, of an epoxy system reinforced with glass fibers, between 10 and 2,500 s⁻¹. Furthermore the model proved to be reasonable accurate to simulate creep, stress relaxation and constant strain rate loading of the same material system under high temperatures. Following the experimental observations of vsicoplasticity strain evaluation during load and unloading made by Kim and Tsai [J. Compos. Mater. 36(6), 745 (2002)], a simple model modification is suggested. This modified model proved accurate enough to simulate relaxation successfully of a composite during loading and unloading. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Nonlinear mechanical response of high density polyethylene. Part I: Experimental investigation and model evaluation

The nonlinear behavior of high density polyethylene (HDPE) is investigated for samples cut from thick-walled HDPE pipe. Extensive experimental work has been performed to characterize the non-linear time-dependent response of the material tested under uniaxial compression. Tests were conducted under conditions of constant strain rate, creep, stress relaxation, constant loading rate, abrupt change of strain rate, creep-recovery, cyclic strain rate, and various combinations of these loading conditions. Creep and stress relaxation response after strain reversal and the effect of the transient response on the following stress-strain behavior is examined. Permanent strains for the test specimens and their dependence on loading histories are investigated. Specimens cut at various orientations from the pipe are used to quantify the small amounts of local anisotropy in the pipe specimen. The experimental work has been used to develop both nonlinear viscoelastic (NVE) and viscoplastic (VP) constitutive models in a companion paper. Both the test results and the corresponding model predictions are reported in this paper. It is found that the VP model reproduces the nonlinear viscoelastic-viscoplastic behavior of HDPE very well provided that the current strain is not below the maximum strain imposed (there is no strain reversal). The NVE model predicts the material behavior reasonably well for some loading conditions, but inadequately for others.     

The effect of specimen thickness and stress ratio on the fatigue behavior of polycarbonate

The cyclic residual stresses ahead of fatigue cracks are known to play an important role in the fatigue fracture response of engineering materials. The size of these residual stresses are directly affected by the stress state of the component. In this paper, we examine the effect of stress state for fully compressive and fully tensile cyclic loading of polycarbonate. The role of stress state is studied using two different specimen thicknesses, one thickness will represent a near-plane stress condition and the other will represent a near-plane strain condition. In cyclic compressive loading, it will be shown that the near-plane stress specimen with its larger zone of residual tension will exhibit enhanced crack saturation lengths. While for cyclic tensile loading, the larger zone of residual compression upon unloading will result in crack retardation for the same unloading stress intensity. A series of systematic experiments on the effects of mean stress on fatigue fracture is reported, and the results of the experiments are rationalized with the aid of scanning electron microscopy of the fracture surfaces. The results of this study have strong implications for both constant amplitude fatigue loading and variable amplitude fatigue loading as well as applicability to other engineering materials.     

The effect of strain rate on the deformation and relaxation behavior of 6/6 nylon at room temperature

The influence of strain rate changes in the range from 10^?3 to 10^?6 1/s on the zero-to-tension loading and unloading behavior as well as short term relaxation properties is investigated using cylindrical specimens of circular cross section. A clip-on extensometer measures and controls the axial strain in an MTS servohydraulic, computer-controlled mechanical testing machine. Strains do not exceed twenty percent and all deformation is macroscopically homogeneous. An increase in strain rate causes an increase in stress level. Surprisingly, the total stress drop in a 20 min relaxation period increases with prior strain rate. When the relaxation test is started in the inelastic region with low tangent modulus the total stress drop is nearly independent of the stress and strain at which relaxation commences. Unloading to zero load is not linear but curved and the strain recovery at zero stress is significant. It occurs at an ever decreasing rate and does not exceed three percent in a 12 h period. Like the relaxation behavior the recovery rate increases with prior strain rate. Repeated relaxation periods during zero-to-tension cycling can show a stress magnitude decrease during loading but a stress magnitude increase during unloading. The results suggest that a unified model with an overstress dependence of the inelastic rate of deformation could be useful in modeling.     

Constitutive equations for the viscoplastic response of isotactic polypropylene in cyclic tests: The effect of strain rate

A series of uniaxial tensile loading‐unloading tests are performed on injection‐molded isotactic polypropylene at room temperature. In each test, a specimen is stretched up to the maximal strain ?_max = 0.12 with a constant strain rate, $ \dot \varepsilon $, and retracted down to the zero stress with the same strain rate. The cross‐head speeds vary from 5 to 200 mm/min, which covers practically the entire range of strain rates used in conventional quasi‐static tests. A constitutive model is developed for the viscoplastic response of a semicrystalline polymer at small strains. The stress‐strain relations are determined by five adjustable parameters that are found by matching the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation. Polym. Eng. Sci. 44:548–556, 2004. © 2004 Society of Plastics Engineers.     

An integral constitutive equation for nonlinear plasto-viscoelastic behavior of high-density polyethylene

In the present paper an effort is made to model the time-dependent behavior of high-density polyethylene (HDPE) with a one-dimensional integral representation. Owing to the plasto-viscoelastic behavior of the material, we assume that the total strain can be decomposed into a recoverable viscoelastic strain and an irrecoverable plastic strain. The viscoelastic deformation is represented by the Schapery thermodynamic theory. The plastic deformation is assumed to be accumulated during the loading history. An effective time concept is introduced for the plastic deformation, so that the response due to complex loading can be accounted for. The present representation gives a very good prediction of the responses of creep and recovery, two-step creep, and constant stress rate loading and unloading. It is also applied successfully to describe the process of preconditioning of semicrystalline polymers.     

Temperature-dependent mechanical properties and constitutive equation of cellulose nitrate

The strain-time response under tensile loading (creep tests) and the stress strain response under constant tensile stress rate (proportional loading tests) have been evaluated at 4 temperatures 20, 45, 55, and 65°C, for samples of cellulose nitrate. A time-dependent constitutive equation (or stress-strain relation) for the nonlinear visco-elastic material is deduced from invariant theory with a hypothesis of a creep potential. The procedure for determining the seven material constants involved in the deduced constitutive equation is described for the creep and proportional loading tests and the variation of these constants with temperature is presented. The deduced constitutive equation gives good agreement with the actual observations for the creep and proportional loading tests, independent of the values of temperature, creep stress, or stress rate.     

基于数字图像相关法的熔融沉积聚乳酸材料动态力学性能测试

为研究熔融沉积聚乳酸（PLA）材料动态的力学性能,利用分离式霍普金森压杆（SHPB）装置对PLA材料进行了加载应变率分别为880、1 230、1 650、2 230 s^-1的动态压缩实验,通过高帧率图像采集设备获得了不同应变率下PLA材料的变形图像,结合数字图像相关（DIC）法分析得到PLA试样表面沿加载方向的应变场,并对应变率进行了分析。结果表明,熔融沉积PLA材料在动态载荷作用下的变形过程存在弹性阶段、塑性阶段和卸载阶段;随着应变率的增加,PLA材料在塑性阶段出现了显著的塑性流动区域;PLA材料的压缩强度和最大应变均随应变率增大而增大;利用DIC法测得在整个动态冲击实验过程中,应变在试样中分布基本均匀,应变范围随应变率增大而增大,应变率在整个加载过程中基本保持恒定;DIC法测得的应变与SHPB实验基本一致,应变率误差均小于3 %,表明本研究使用的DIC法能够应用于SHPB实验。     

Cyclic interaction between normal and shear stresses of an epoxy polymer—Experiments and model predictions

This investigation focuses on the axial‐torsional loading interaction of an epoxy polymer, Epon 826/Epi‐Cure Curing Agent 9551. Thin‐walled tubular specimens were subjected to combined constant tensile (or shear) stress and cyclic shear (or tension) loading schemes. Pure tensile creep and shear creep tests were also performed to compare the creep deformation to that with superimposed cyclic shear or cyclic tension. Test data clearly showed that cyclic shear (or cyclic tension) have a readily discernible effect on the tensile (or shear) creep deformation. Similarly, a superimposed constant tensile (or shear) load affects the hysteresis responses in cyclic shear (or cyclic tension). A nonlinear constitutive model developed by the authors was used to simulate the observed normal‐shear stress interaction. Due to the inclusion of an effective stress parameter in its nonlinear function, this model was able to account for the normal‐shear coupling effect. However, the incorporation of a general loading/unloading rule led to inaccurate simulation of the observed oscillatory creep response. A modification of the general rule was proposed and better predictions on both the cyclic and the creep responses could be obtained. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Determination of reversible and irreversible contributions to the polarization and strain response of soft PZT using the partial unloading method

Experimental work is aimed at systematically investigating the non-linear ferroelectric and ferroelastic behavior of a commercially available soft lead zirconate titanate (PZT) material. The fast partial unloading method is used to measure the material properties of unpoled soft PZT under pure electric field and of initially pre-poled soft PZT under compressive stress loading. In the first experiment using unpoled PZT, the evolution of piezoelectric constants and dielectric permittivity is determined as a function of electric field. It is found that the piezoelectric constants and dielectric permittivity depend on the electric field history. The results are used to separate the reversible strain and polarization from the irreversible ones caused by domain switching. In the second experiment using initially pre-poled PZT, it is found that the strain response is significantly dependent on the stress loading rate. The elastic moduli and piezoelectric coefficients are evaluated with respect to the compressive stress history. The measured longitudinal and transverse irreversible strains change significantly during both loading and unloading processes. An attempt is made to discuss the use of irreversible strain and irreversible polarization as internal variables for constitutive modeling. This investigation provides valuable information for modeling to predict the performance and for improving the reliability of piezoelectric devices.     

Residual stress craze and crack formation in poly(methyl methacrylate)

Samples of poly(methyl methacrylate) with a central circular hole are compressed, and crazes form on or after unloading, provided that the strain attains or exceeds a threshold value ?_t. Crazes induced in air are transformed rapidly to cracks, but environmental crazes are more stable. These residual stress crazes form at the diameter of the hole on a plane perpendicular to the applied stress direction. In contrast, during loading, crazes form on the vertical plane containing the hole axis. Unloading crazes are relatively insensitive to changes in strain rate, whereas loading erazes have a pronounced rate dependence. Environmental residual stress crazing exhibits an apparent rate sensitivity at constant time, but the critical applied strain ?_t is essentially constant, irrespective of rate, if the sample is in contact with the environment for a sufficiently long time to ensure that the minimum ?_t is obtained. Residual stress crazes appear to initiate at the equator of the hole, and the maximum tensile residual strain, indicated by a strain gauge, occurs in this position.     

A Model for the Elastoplastic Behavior of Isotactic Poly(propylene) Below the Yield Point

Observations are reported on isotactic poly(propylene) (iPP) in a series of tensile loading‐unloading tests with a constant strain rate at room temperature. A constitutive model is developed for the elastoplastic behavior of a semicrystalline polymer at isothermal uniaxial deformations with small strains. The stress‐strain relations are determined by 5 adjustable parameters which are found by fitting the experimental data.

The stress σ (MPa) versus strain ε in a tensile loading‐unloading test with the maximum strain ε_max = 0.09. Circles: experimental data. Solid line: results of numerical simulation.     

The stress-strain behavior of materials exhibiting andrade creep

The stress-strain behavior of a material exhibiting Andrade creep (for which the creep compliance is linear in the cube-root of time) has been calculated for loading at constant strain rate \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm \varepsilon}\limits^{\rm .} $\end{document} and at constant stress rate \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sigma \limits^. $\end{document} for the limiting case of linear viscoelastic behavior and at constant \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sigma \limits^. $\end{document} for one type of nonlinear viscoelastic response. The recoverable strain after the stress has been removed has also been calculated for these three cases. The results of the calculations are compared with experiment.     

Numerical determination of internal stress and viscoelastic parameters for xerographic papers

A computerized method has been developed for determining, from one experimentally obtained loading curve for a paper sample: (a) the viscoelastic parameters for predicting paper deformation, and (b) the internal or residual stress level in the paper. The loading curve comprises a stress-time curve obtained at a constant straining rate, followed by a stress relaxation curve at a constant strain level. The paper deformation is modeled by the Halsey, White, and Eyring model and a nonlinear viscoelastic model.     

Stress–Strain Behavior of Nicalon-Fiber-Reinforced Calcium Aluminosilicate Composites under Tensile Fatigue Conditions

The unusual stress–strain hysteresis loop shape exhibited by ceramic-matrix composites under cyclic loading has previously been explained as a result of either strain rate dependence of the frictional shear stress or crack closure. This investigation has determined that the response is due to neither mechanism. Instead, it is proposed that a variation of interfacial shear strength occurs during each cycle. A static coefficient of friction dominates immediately after loading or unloading. A much lower dynamic coefficient of friction operates once fiber sliding begins. This dynamic coefficient appears to be very dependent on surface roughness.     

Deformation Mechanisms in Compression-Loaded, Stand-Alone Plasma-Sprayed Alumina Coatings

Cylindrical, stand-alone tubes of plasma-sprayed alumina were tested in compression in the axial direction at room temperature, using strain gauges to monitor axial and circumferential strains. The primary compression-loading profile used was cyclic loading, with monotonically increased peak stresses. Hysteresis was observed in the stress–strain response on unloading, beginning at a peak stress of 50 MPa. The modulus decreased as the maximum applied stress increased. The stress–strain response was only linear at low stresses; the degree of nonlinearity at high stresses scaled with the stress applied. One-hour dwells at constant stress at room temperature revealed a time-dependent strain response. Using transmission electron microscopy and acoustic emission to investigate deformation mechanisms, the stress–strain response was correlated with crack pop-in, growth, and arrest. It is proposed that the numerous defects in plasma-sprayed coatings, including porosity and microcracks, serve as sites for crack nucleation and/or propagation. As these small, nucleated cracks extend under the applied stress, they propagate nearly parallel to the loading direction along interlamellae boundaries. With increasing stress, these cracks ultimately link, resulting in catastrophic failure.     

The Uniaxial Tensile Response of Porous and Microcracked Ceramic Materials

The uniaxial tensile stress–strain behavior of three porous ceramic materials was determined at ambient conditions. Test specimens in the form of thin beams were obtained from the walls of diesel particulate filter honeycombs and tested using a microtesting system. A digital image correlation technique was used to obtain full‐field 2D in‐plane surface displacement maps during tensile loading, and in turn, the 2D strains obtained from displacement fields were used to determine the Secant modulus, Young's modulus, and initial Poisson's ratio of the three porous ceramic materials. Successive unloading–reloading experiments were performed at different levels of stress to decouple the linear elastic, anelastic, and inelastic response in these materials. It was found that the stress–strain response of these materials was nonlinear and that the degree of nonlinearity is related to the initial microcrack density and evolution of damage in the material.     

Tensile Creep and Creep-Recovery Behavior of a SiC-Fiber─Si3N4-Matrix Composite

The tensile creep and creep-recovery behavior of a unidirectional SiC-fiber/Si₃N₄-matrix composite was investigated at 1200°C in air. A primary objective of the study was to determine how various sustained and cyclic creep loading histories would influence the creep rate, accumulated creep strain, and the amount of strain recovered upon specimen unloading. The key results obtained from the investigation can be summarized as follows: (1) A threshold stress of 60 MPa was identified, below which the creep rate of the composite was exceedingly low (∼10⁻¹² s⁻¹). (2) Periodic fiber fracture was identified as a fundamental damage mode for sustained tensile creep at stresses of 200 and 250 MPa. (3) Because of transient stress redistribution between the fibers and matrix, the creep life and failure mode at 250 MPa. were strongly influenced by the rate at which the initial creep stress was applied. (4) Very dramatic creep-strain recovery occurred during cyclic creep; for cyclic loading between stress limits of 200 and 2 MPa, 80% of the prior creep strain was recovered during 50-h-creep/ 50-h-unloading cycles and over 90% during 300-s-creep/ 300-s-unloading cycles. (5) Cyclic loading significantly lowered the duration of primary creep and overall creep-strain accumulation. The implications of the results for microstructural and component design are discussed.