Effects of thermal rates on the thermomechanical behaviors of amorphous shape memory polymers

Shape memory polymers (SMPs) are polymers that can recover a large pre-deformed shape in response to environmental stimuli, such as temperature, light, etc. For a thermally triggered (or activated) amorphous SMP, the pre-deformation and recovery of the shape require the temperature of the material to traverse the glass transition temperature T _g under constrained or free conditions. In this paper, effects of thermal rates on the thermomechanical behaviors of amorphous SMPs are investigated. Under uniaxial compression, during a temperature cycle (cooling followed by heating), the stress decreases to zero as the temperature decreases to below the glass transition temperature, and increases to a value larger than the initial stress (termed stress overshoot) as the temperature is raised above the glass transition temperature. These observations are examined by a thermoviscoelasticity model that couples the nonequilibrium structural relaxation and temperature dependent viscoelastic behavior of the material. In addition, using this model, stress-temperature behaviors during temperature cycles with various thermal rate conditions and tensile loading conditions are studied.     

On the effects of thermal history on the development and relaxation of thermo-mechanical stress in cryopreservation

This study investigates the effects of the thermal protocol on the development and relaxation of thermo-mechanical stress in cryopreservation by means of glass formation, also known as vitrification. The cryopreserved medium is modeled as a homogeneous viscoelastic domain, constrained within either a stiff cylindrical container or a highly compliant bag. Annealing effects during the cooling phase of the cryopreservation protocol are analyzed. Results demonstrate that an intermediate temperature-hold period can significantly reduce the maximum tensile stress, thereby decreasing the potential for structural damage. It is also demonstrated that annealing at temperatures close to glass transition significantly weakens the dependency of thermo-mechanical stress on the cooling rate. Furthermore, a slower initial rewarming rate after cryogenic storage may drastically reduce the maximum tensile stress in the material, which supports previous experimental observations on the likelihood of fracture at this stage. This study discusses the dependency of the various stress components on the storage temperature. Finally, it is demonstrated that the stiffness of the container wall can affect the location of maximum stress, with implications on the development of cryopreservation protocols.     

Uniaxial nonlinear viscoelastic viscoplastic modeling of polypropylene

This paper presents the application of the Schapery viscoelastic and the Perzyna viscoplastic models to strain recovery data of polypropylene. In a previous study, the recovery of strain after monotonic uniaxial tensile loading was measured to gather information on the viscoelasticity and viscoplasticity. The viscoplastic strains from several load histories were determined and are used to calibrate the viscoplastic model. The parameters of the one-dimensional Schapery model are then found by nonlinear optimization using the strain recovery history. The prediction of stress relaxation and creep behavior is investigated.     

TiNi形状记忆合金丝在约束态热循环后的力学特性

研究了TiNi形状记忆合金丝在约束态热循环后的应力-应变特性.结果表明,如果停止加热并加载,或者在母相状态下冷却但是尚未发生正相变时加载,加载应力-应变曲线首先呈线弹性关系,然后才出现应力平台.如果在冷却过程中发生正相变的时候停止冷却并加载,则加载应力-应变曲线只出现应力平台.与之相似,如果在约束态冷却过程中停止冷却并卸载,卸载应力-应变曲线首先呈线弹性关系,然后才出现应力平台.如果在加热过程中停止加热并卸载,则卸载应力-应变曲线立即出现应力平台.     

Viscoplastic–plastic modelling of IN792

At high temperatures metallic materials behave in a viscous manner exemplified by strain rate dependence, stress relaxation and creep deformation. At low temperatures however, these effects are extremely small, and the behaviour is strain rate independent and shows no or very small relaxation effects. Finally there exists an intermediate region, in which the material behaviour is close to strain rate independent for high strain rates but at the same time shows time dependent inelastic effects, such as stress relaxation and creep. For IN792 this occurs at temperatures around 650 °C. The article describes the extension of a power-law viscoplastic model describing the behaviour of IN792 at 850 °C, also to describe the behaviour at 650 °C, by bounding the elastic–viscoplastic stress-space by a plastic yield surface. The model parameters have been estimated using data from creep test and tailored step relaxation tests, and the model fits well to both the step relaxation data aimed at resembling relevant component conditions and long term creep data.     

Viscoplastic analysis of structural polymer composites using stress relaxation and creep data

A structural carbon based composite material has been investigated for its high temperature viscoplastic properties using a model based on an overbearing stress concept and using the data obtained from load relaxation and creep. The time dependent viscoplastic properties were obtained at several load and temperature levels. An elastic–viscoplastic constitutive model (proposed by Gates) was used for the modeling efforts. The model is based on an overstress concept appropriate to inelastic properties of composites. The materials parameters for the model are obtained from a set of load relaxation experiments. The model predictions have been compared to the results of creep tests. The results show that the model is capable of predicting the creep behavior at shorter time periods and lower temperatures. As the temperature is increased or as the creep is prolonged the model predictions deviate from the experimental results.     

Temperature and Time Dependence on Recovery Stress Relaxation in Nickel Titanium Wire during Isothermal Holding at High Temperatures

In this study, the influence of kinematically constrained thermal cycling (heating, isothermal holding and cooling) on the recovery stress in annealed nickel titanium wire was investigated. A 4% pre‐strained nickel titanium wire was heated to temperatures (150, 200, 250 and 300 °C) much higher than the austenite finish temperature. It was observed that the maximum recovery stress obtained at different conditions decreases significantly after the first thermal cycle and reduces gradually with further increasing the number of thermal cycles. It was also seen that the recovery stress increases with time during isothermal holding at 150 °C. During isothermal holding at other temperatures, the recovery stress shows an exponential decrease, and the decrease rate of the recovery stress depends on the isothermal holding temperature. The higher isothermal holding temperature is the more the recovery stress decreases. The decrease rate reduces with increasing the number of thermal cycles.     

GH4169合金高温力学行为本构建模及参数识别

针对涡轮盘用GH4169合金开展了高温下单调拉伸、对称循环及非对称循环的实验工作,结果表明,该材料具有比较明显的循环软化和平均应力松弛特性.采用带Ohno/Wang修正的Chaboche粘塑性理论本构方程,对其表现出的复杂力学现象进行本构建模,介绍了Levenberg-Marquadt非线性优化算法,结合材料实验数据并通过该算法识别了本构方程参数,将本构方程通过用户子程序嵌入到有限元软件ABAQUS中,对GH4169合金的上述实验现象进行了数值模拟,计算曲线与实验曲线取得了较好的一致性.     

Modeling of viscoplastic rate-dependent hardening-softening behavior of hot mix asphalt in compression

The objective of this paper is to model viscoplastic rate-dependent hardening-softening behavior that is experimentally observed from hot mix asphalt (HMA) under repetitive creep and recovery loading in compression. A differential equation is utilized to incorporate the effects of the stress history into yield stress, and an internal variable representing rate dependence in the equation is set as a function of the viscoplastic strain rate to address the change in rate dependence of the material due to gradual hardening. Also, a separate rate-dependent function concept is adopted to describe the difference in rate dependence of the yield stress during unloading and loading. The developed viscoplastic model is applied using the time–temperature superposition principle and shows good agreement with the measured viscoplastic responses of HMA under repetitive creep and recovery loading with various load levels and rest periods.     

Micromechanically Established Constitutive Equations for Multiphase Materials with Viscoelastic–Viscoplastic Phases

A model for viscoelastic–viscoplastic solids is incorporated in a micromechanical analysis of composites with periodic microstructures in order to establish closed-form coupled constitutive relations for viscoelastic–viscoplastic multiphase materials. This is achieved by employing the homogenization technique for the establishment of concentration tensors that relate the local elastic and inelastic fields to the externally applied loading. The resulting constitutive equations are sufficiently general such that viscoelastic, viscoplastic and perfectly elastic phases are obtained as special cases by a proper selection of the material parameters the phase. Results show that the viscoelastic and viscoplastic mechanisms have significant effect on the global stress-strain, relaxation and creep behavior of the composite, and that its response is strongly rate-dependent in the reversible and irreversible regimes.     

The recovery properties under load of a shape memory polymer composite material

In many applications, shape memory alloys are being replaced by shape memory polymers as they have some better properties than shape memory alloys. Nevertheless, shape memory alloys can recover under load which shape memory polymers cannot. Shape memory polymers are not capable of giving full recovery even lifting a tiny load. The melting temperature or the glass transition temperature is the transition temperatures to which shape memory polymers are closely heated. Then a deforming force up to a certain position is applied to the heated shape memory polymers. After that shape memory polymer is permitted to cool while keeping it deformed. After the cooling, shape memory polymer obtains the temporary shape which can be recovered by reheating it at the similar transition temperature (glass transition or melting). Consequently, it recovers at its initial state. Shape memory polymer can achieve constrained recovery and unconstrained recovery, nonetheless; under stress, it is partly recovered. In current work, recovery under load has been investigated of an asymmetrical shape memory composite. It is established that it is capable to recover under various loads. Under various loads, it shows full recovery in reference to initial state. The ability to recover under load can be potentially used in diverse applications.     

A Two-network thermomechanical model of a shape memory polymer

The aim of this work is to demonstrate a Helmholtz potential based approach for the development of the constitutive equations for a shape memory polymer undergoing a thermomechanical cycle. The model is able to simulate the response of the material during heating and cooling cycles and the sensitive dependence of the response on thermal expansion. We notice that the yield-stress of the material controls the gross features of the response of the model, and suggests that the material yields differently depending on not just the current value of the temperature but also on whether the temperature of the material dropped or increased from the previous time-step somewhat similar to the Bauschinger effect in plasticity, except that here the controlling parameter is the rate of temperature change rather than rate of plastic strain. The results of the simulation are in qualitative and quantitative agreement with experiments performed on two different shape memory polymer samples: polyurethane and epoxy resin. We find that modeling the hysteresis of the yield stress of the material during temperature changes is the key to the results.     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

Development of viscoplastic strains during creep in continuous fibre GMT composites

This work is part of a larger study aimed at characterizing the viscoelastic–viscoplastic behavior of a continuous fiber glass mat thermoplastic composite. The purpose of this paper is to experimentally and numerically decouple the viscoplastic strains from total creep response. This enabled the characterization of the evolution of viscoplastic strains as a function of time, stress and loading cycles. The separation also allowed viscoplastic strain development to be corresponded with the progression of failure mechanisms such as interfacial debonding and matrix cracking which were captured in situ. This was achieved by performing creep tests at seven stress levels between 20 and 80 MPa. For each stress level, a series of creep-recovery tests were performed on single specimen for increasingly longer durations from 1 to 24 h. Stress and time dependence of viscoplastic strains were determined experimentally. Using part of the data generated, a viscoplastic model was developed following a method proposed by Nordin. The model had excellent agreement with experimental results for all stresses and times considered. In multiple loading cycles, the viscoplastic strain development is accelerated with increasing number of cycles at higher stress levels. The results further verify the technique for numerical separation of viscoplastic strains proposed in an earlier work. Finally, it was found that the development viscoelastic strains during creep are affected by the previous viscoplastic strain history.     

Characterization and constitutive modeling of stress-relaxation behavior of Poly(methyl methacrylate) (PMMA) across the glass transition temperature

Characterizing the large strain behavior of Poly(methyl methacrylate) (PMMA) across its glass transition temperature is essential for modeling hot embossing. Its mechanical properties vary significantly across the glass transition as well as with strain rate. Several previous models have attempted to capture this behavior with limited success, and none have considered stress relaxation. In this work, stress relaxation experiments are conducted on PMMA at various temperatures spanning the glass transition. The experimental data is then used to develop a new constitutive model. As with earlier models for thermoplastics around the glass transition, the material model consists of two resistances: intermolecular and network. The key advantage of the new model is that the network resistance is represented through an 8-chain hyperelastic model in parallel with a ROuse LInear Entangled POLYmer (Rolie-Poly) element. The structure of the network interactions captures the strain hardening at temperatures less than glass transition and the melt behavior at temperatures greater than glass transition to greatly improve stress relaxation predictions. Strain softening is introduced in the intermolecular branch to predict the stress at small strains. Glass transition is described through temperature dependent material properties. Results have been encouraging for the model’s ability to capture stress relaxation behavior from temperatures 15° below to 25° above glass transition. In addition, it can capture the relaxation behavior at both large and small strains as well as with varying strain rates. This ability to capture stress relaxation suggests it will greatly improve finite element model predictions for hot embossing with PMMA.     

Optical detection of phase transitions in potassium niobate

Abstract

Luminescence data from potassium niobate crystals are reported which show intensity and/or wavelength variations on heating, or cooling, through the phase transition temperatures. The luminescence signals can clearly identify the structural changes between the various crystalline phases. The transition temperatures differ between heating and cooling. They were recorded near 247 and 491 K (heating) or 220 and 478 K (cooling). The hysteresis indicates the presence of metastable material, (e.g. a supercooled structure). The data resolve the previously cited differences in transition temperatures for KNbO₃ from different laboratories. The luminescence signals show further details in the variations of spectra, intensity and transition discontinuities of the luminescence which are related to material quality between samples, even from a single supplier. The luminescence data underline the sensitivity of these crystals to structural damage from electron, X-ray or thermal treatments and offer the opportunity to assess crystalline quality prior to device fabrication.     

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.     

Deformation-induced volume damage in particulate-filled epoxy resins

In this investigation the microstructural deformation and damage mechanisms in an epoxy resin filled with silica flour are investigated. The unfilled resin exhibits bulk shear yielding in both compression and tension which is localized into fine bands by the addition of the particulate filler. In addition, the filled material stress-whitens in compression and at lower rates and higher temperatures in tension. The shear yielding is recoverable upon heating for a time above the glass transition temperature; however, the stress whitening is irreversible. The addition of filler particles introduces several damage mechanisms including particle-matrix debonding, particle fracture and matrix microcracking. In the following report, these damage mechanisms are characterized microstructurally in terms of the rate, temperature and type of loading and their relative contributions to stress whitening.     

A continuous threshold model for the visco-elasto-plastic behavior of PET based multi-layer polymeric films

The envelopes of the super-pressure balloons fabricated by the French space agency (CNES) are made of a multi-layer polymeric film that shows substantial viscoelastic and viscoplastic behavior, both depending nonlinearly on stress. A model is presented that takes into account stress depending viscoelastic and viscoplastic strain response functions observed in uniaxial creep experiments. For easy numerical implementation, the strain response functions are represented by a Prony series, whose coefficients form a continuous spectrum on the logarithmic retardation time scale. The observed response functions are generated by an exponential power law distribution of the Prony coefficients with exponent 3. The distribution is fully characterized by three stress dependent parameters: its center, width, and an intensity factor, corresponding to the maximum coefficient. Creep and recovery experiments show that both viscoelastic and viscoplastic strain are highly stress dependent over a limited stress range and are approximately linear at low stresses and around the maximum stress reached during flight. A continuous threshold function is proposed that approximates well the observed stress dependence of the intensities. It is assumed that the other viscoelastic (viscoplastic) parameters change around the same threshold as the viscoelastic (viscoplastic) intensity and are approximately constant elsewhere. The model reproduces very well the strain response observed in creep and recovery experiments with different creep stresses.     

A model for the Mullins effect during multicyclic equibiaxial loading

In this paper, we derive a model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress–strain cycles with increasing values of the maximum strain, specializing to equibiaxial loading. Since the carbon-filled rubber vulcanizate is initially isotropic, we can show that following initial equibiaxial loading the material becomes transversely isotropic with preferred direction orthogonal to the plane defined by the equibiaxial loading. This is an example of strain-induced anisotropy. Accordingly, we derive nonlinear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These ideas are then combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed includes the effects of hysteresis, stress relaxation, residual strain and creep of residual strain. The model is found to compare extremely well with experimental data.