Deformation and fracture behaviour under combined creep and fatigue

An examination of deformation and fracture has been made for the nickel base superalloy IN597 at 850°C for relatively high stress short life cyclic torsional loading programmes. The cycles combine low cycle fatigue with creep and relaxation dwell from the repeated application of a closed hysteresis loop under strain control. From a consideration of the changing shape of the hysteresis loop throughout cyclic life the effects of dwell stress, inelastic strain range and cycle number on creep deformation are examined together with the variation of peak stress softening with cycle number and relaxation time. Their effects on fracture in a high-temperature oxidising environment are appraised in relation to various predictive techniques; the Coffin-Manson equation, the universal slopes method, the linear damage rule, strain range partitioning and various incremental life prediction laws.Observations made on transgranular and intergranular crack paths are shown to provide the necessary metallographic evidence for the relative contributions to fracture from the repeated action of creep, fatigue and relaxation processes.     

A non-linear uniaxial integral constitutive equation incorporating rate effects,creep and relaxation

A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.     

Quasi-static properties of a photoviscoelastic material

This paper describes the results of mechanical and optical measurements in plasticized polyvinyl chloride under conditions of creep and relaxation at room temperature. It covers one task of a broader investigation aimed at developing experimental methods for viscoelastic stress analysis. The moiré method of strain analysis was found well suited for continuous recording of axial and transversal deformation in creep tests. The material exhibits linear viscoelastic behavior, both mechanical and optical. Strain, stress and birefringence measured from creep and relaxation tests gave straightline plots on log-log scale and, thus simple empirical formulas were possible to derive. The theoretical prediction that birefringence in a linear viscoelastic material not exhibiting flow can be expressed as a linear relationship of stress and strain was satisfactorily substantiated.     

Stress–strain relations for hydrogels under multiaxial deformation

Constitutive equations are derived for the elastic response of swollen elastomers and hydrogels under an arbitrary deformation with finite strains. An expression is developed for the free energy density of a polymer network based on the Flory concept of flexible chains with constrained junctions and solvent-dependent reference configuration. The importance of introduction of a reference configuration evolving under swelling is confirmed by the analysis of experimental data on nanocomposite hydrogels subjected to swelling and drying. Adjustable parameters in the stress–strain relations are found by fitting observations on swollen elastomers, chemical gels (linked by covalent bonds and sliding cross-links), and physical gels under uniaxial stretching, equi-biaxial tension, and pure shear. Good agreement is demonstrated between the observations and results of numerical simulation. A pronounced difference is revealed between the effect of solvent content on elastic moduli of chemical and physical gels.     

Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers

The inelastic deformation behaviors of metals and polymers are discussed with the aim of finding a common base that would simplify academic and engineering analyses. Only monotonic loading conditions at room temperature are considered. For loading at different rates, nonlinear relations between loading rate and stress level, creep stress level and creep strain, and relaxation rate and stress were common to both type of materials. There are, of course, significant differences in elastic properties, strength levels and the strains involved. Special properties such as relaxation behaviors and creep anomalies can be qualitatively and quantitatively reproduced by the state variable model VBO (viscoplasticity theory based on overstress). Since experimental investigations typically concentrate on one particular aspect of inelastic deformation behavior such as creep or strain-rate dependence, it is often difficult to gather a comprehensive data set for a given material. In spite of this, considerable similitude in the deformation behavior of metals and polymers in various test conditions has nevertheless been established.     

Dynamic study of gelatin gels by creep measurements

We have investigated the dynamical properties of gelatin gels using creep measurements. A commercial apparatus (Carrimed CSL500) was modified in order to increase the deformation of the gel and to take advantage of the inertia of the system. When a step stress is applied, the very first response of these materials is an oscillating strain owing to a coupling of the high elasticity of the gelatin gels and the inertia of the apparatus. From these damped oscillations, we have extracted the elastic and loss moduli as a function of frequency, which allows us to widen the frequency range (toward high frequencies) of measurement. After subtraction of the oscillations, we have obtained the compliance funtion from which, using Ferry's formalism, we can calculate the relaxation time distribution function over a very large time range (10^–3–10⁴ s). We show that the dynamics of gelatin gels is governed by two very different characteristic times. We interpret the faster relaxation time as relaxation at the scale of the gel network mesh-size, while the slower time we assign to relaxations involving the lifetime of the gelatin gel cross-links. It is now possible to use creep measurements as an alternative to the forced oscillatory function determination, as the same data can be obtained but, more quickly, and over a large frequency range. This gives us more indication of the gel's structure (gel network behaviour, kinetics of ageing) than all the laborious methods previously necessary.     

Modeling deformation behavior of polymers with viscoplasticity theory based on overstress

The nonlinear strain rate sensitivity, multiple creep and recovery behavior of polyphenylene oxide (PPO), which were explored through strain rate-controlled experiments at ambient temperature by Khan [The deformation behavior of solid polymers and modeling with the viscoplasticity theory based overstress, Ph.D. Thesis, Rensselaer Polytechnic Institute, New York], are modeled using the modified viscoplasticity theory based on overstress (VBO). In addition, VBO used by Krempl and Ho [An overstress model for solid polymer deformation behavior applied to Nylon 66, ASTM STP 1357, 2000, p. 118] and the classical VBO are used to demonstrate the improved modeling capabilities of VBO for solid polymer deformation. The unified model (VBO) has two tensor valued state variables, the equilibrium and kinematic stresses and two scalar valued states variables, drag and isotropic stresses. The simulations include monotonic loading and unloading at various strain rates, multiple creep and recovery at zero stress. Since creep behavior has been found to be profoundly influenced by the level of the stress, the tests are performed at different stresses above and below the yield point. Numerical results are compared to experimental data. It is shown that nonlinear rate sensitivity, nonlinear unloading, creep and recovery at zero stress can be reproduced using the modified viscoplasticity theory based on overstress.     

Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels

A polymer network can imbibe copious amounts of solvent and swell, the resulting state is known as a gel. Depending on its constituents, a gel is able to deform under the influence of various external stimuli, such as temperature, pH-value and light. In this work, we investigate the photo-thermal mechanics of deformation of temperature sensitive hydrogels impregnated with light-absorbing nano-particles. The field theory of photo-thermal sensitive gels is developed by incorporating effects of photochemical heating into the thermodynamic theory of neutral and temperature sensitive hydrogels. This is achieved by considering the equilibrium thermodynamics of a swelling gel through a variational approach. The phase transition phenomenon of these gels, and the factors affecting their deformations, are studied. To facilitate the simulation of large inhomogeneous deformations subjected to geometrical constraints, a finite element model is developed using a user-defined subroutine in ABAQUS, and by modeling the gel as a hyperelastic material. This numerical approach is validated through case studies involving gels undergoing phase coexistence and buckling when exposed to irradiation of varying intensities, and as a microvalve in microfluidic application.     

Explicit and implicit viscoplastic models for polymeric composite

The viscoplastic behavior of a carbon-fiber/polymer matrix composite was investigated through two different modeling efforts. The first model is phenomenological in nature and utilizes the tensile and stress relaxation experiments to predict the creep strain. The phenomenological model was constructed based on the overstress viscoplastic model. In the second model, the composite viscoplastic behavior is captured via neural networks formulation. The neural networks model was constructed directly from the experimental results obtained via creep tests performed at various stress–temperature conditions. The neural network was trained to predict the creep strain based on the stress–temperature–time values. The performance of the neural model is evaluated through the mean squared error between the neural network prediction and the experimental creep strain results. To minimize this error, several optimization techniques were examined. The minimization of the error when carried out by the Truncated Newton method outperforms the standard back-propagation and the conjugate gradient method in terms of convergence rate and accuracy. Using neural network with truncated Newton training algorithm, the prediction of the creep strain was very satisfactory compared to the phenomenological model.     

Finite deformation of a polymer: experiments and modeling

The response of a polymer (polytetrafluoroethylene) to quasi-static and dynamic loading is determined and modeled. The polytetrafluoroethylene is extremely ductile and highly nonlinear in elastic as well as plastic behaviors including elastic unloading. Constitutive model developed earlier by Khan, Huang and Liang (KHL) is extended to include the responses of polymeric materials. The strain rate hardening, creep, and relaxation behaviors of polytetrafluoroethylene were determined through extensive experimental study. Based on the observation that both viscoelastic and viscoplastic deformation of polytetrafluoroethylene are time dependent and nonlinear, a phenomenalogical viscoelasto–plastic constitutive model is presented by a series connection of a viscoelastic deformation module (represented by three elements standard solid spring dashpot model), and a viscoplastic deformation module represented by KHL model. The KHL module is affected only when the stress exceeds the initial yield stress. The comparison between the predictions from the extended model and experimental data for uniaxial static and dynamic compression, creep and relaxation demonstrate that the proposed constitutive model is able to represent the observed time dependent mechanical behavior of polytetrafluoroethylene polytetrafluoroethylene qualitatively and quantitatively.     

Experimental investigation of cyclic and time-dependent deformation of titanium alloy at elevated temperature

A novel cyclic deformation test program was undertaken to characterize macroscopic time dependent deformation of a titanium alloy for use in viscoplastic model development. All tests were conducted at a high homologous temperature, 650 °C, where there are large time dependent and loading rate dependent effects. Uninterrupted constant amplitude tests having zero mean stress or a tensile mean stress were conducted using three different control modes: strain amplitude and strain rate, stress amplitude and stress rate, and a hybrid stress amplitude and strain rate. Strain ratcheting occurred for all cyclic tests having a tensile mean stress and no plastic shakedown was observed. The shape of the strain ratcheting curve as a function of time is analogous to a creep curve having primary, steady state and tertiary regions, but the magnitude of the ratchet strains are higher than creep strains would be for a constant stress equal to the mean stress. Strain cycles interrupted with up to eight 2-h stress relaxation periods around the hysteresis loop, including hold times in each quadrant of the stress–strain diagram, were also conducted. Stress relaxation was path-dependent and in some cases the stress relaxed to zero. The cyclic behavior of these interrupted tests was similar even though each cycle was very complex. These results support constitutive model development by providing exploratory, characterization and validation data.     

螺旋压缩弹簧应力松弛特性试验分析及其应用

本文通过应力松弛试验、理论推导及数值模拟研究了高温下螺旋压缩弹簧的应力松弛规律,并利用加速模型对工况下弹簧应力松弛服役寿命做出预测.首先,根据螺旋压缩弹簧的结构特点搭建了弹簧应力松弛连续动态测试装置,该装置不仅避免了传统测试方法存在的缺陷,而且能够保证试验过程中位移载荷恒定,并实时监测载荷变化.本文以某飞机舱门单锁机构...     

Characterization of polyacrylamide gels as an elastic model for food gels

Serving as an elastic model system for food gels, characteristics of polyacrylamide (PAAm) gels were investigated using small amplitude and large deformation rheological tests. The PAAm gels displayed elastic or viscoelastic behavior depending on network crosslink density. For elastic PAAm gels, the rheological properties obeyed the theory of rubber elasticity; whereas for viscoelastic PAAm gels, shear modulus depended on temperature. The elastic PAAm gel fracture parameters did not change with deformation rate (0.2–5.5 s^–1), indicating insignificant viscous flow during deformation. Fracture stress was correlated with gel monomer concentration, whereas the fracture strain remained constant regardless of the monomer concentration. In addition, the stress was linearly proportioned with strain up to fracture, indicating that PAAm gels did not experience finite network chain extensibility during large deformation. Consequently, the fracture of PAAm gels did not result from the extensional limitation of network chains, nor did gel fracture result from the nonlinear force–distance relationship between polymer connections. Purportedly, the fracture of PAAm gels was caused by external force overcoming the gel cohesive forces, and low strength of PAAm gels compared to rubbers caused fracture prior to experiencing nonlinear stress-strain deformation.Paper No. FSR04-20 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, NC 27695-7643. The use of trade names does not imply endorsement by the North Carolina Agricultural Research Service of products named, nor criticisms of similar ones not mentioned.     

Experimental investigation and modeling of non-monotonic creep behavior in polymers

The deformation behavior of two unfilled engineering thermoplastics, ultra high molecular weight polyethylene (UHMWPE) and polycarbonate (PC), has been investigated in creep test conditions. It has been found that a loading history (prior to the creep test) comprising of loading to a maximum stress or strain value followed by partial unloading to arrive at the target stress value can greatly modify the strain-time behavior. Under such a test protocol, while the expected increase in strain during creep (constant tensile load) is observed, at relatively low creep stresses specimens have also demonstrated a monotonic decrease in strain. In an intermediate stress range, specimens have demonstrated time dependent behavior comprising of a transition from decreasing to increasing strain during creep in tension. This paper presents experimental results to delineate these findings and explore the effect of prior strain rate on the qualitative and quantitative changes in the output (strain-time) behavior. Furthermore, modification of the viscoplasticity theory based on overstress (VBO) model into a double element configuration is introduced. These changes confer upon the model the ability to yield non-monotonic behavior in creep, and supporting simulation results have been included. These changes, therefore, allow the model to simulate strain rate sensitivity, creep, relaxation, and recovery behavior, but more importantly address the issue of non-monotonic changes in creep and relaxation when a loading history involves some degree of unloading.     

Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

Swelling and instability of a gel annulus

We study the swelling of a gel annulus attached to a rigid core when it is immersed in a solvent.For equilibrium states,the free-energy function of the gel can be converted into a strain energy function,and as a result the gel can be treated as a compressible hyperelastic material.Asymptotic methods are used to study the inhomogeneous swelling in order to obtain the leading-order solution.Some analytical insights are then deduced.Because of the compressive hoop stress in this state,at some stage instability can occur,leading to wrinkles in the gel.An incremental deformation theory in nonlinear elasticity is used to conduct a linear bifurcation analysis for understanding such instability.More specifically,the critical loading for the onset of a wrinkled state is obtained.Detailed discussions on the behaviors of various physical quantities in this critical state are given.It is found that the critical mode number,while insensitive to the material parameters,is greatly influenced by the ratio of the inner and outer radii of the gel.Also,an interesting finding is that the critical swelling ratio is an increasing function of this geometrical parameter,which implies that a thin annulus is more likely to be unstable than a thick one.     

A viscoplastic constitutive model incorporating dynamic strain aging effect during cyclic deformation conditions

In this paper, a viscoplastic constitutive model previously proposed by the authors was extended to apply to the cyclic deformation analysis of the modified 9Cr-1Mo steel. A series of cyclic deformation tests were conducted on modified 9Cr-1Mo steel at various temperatures, including those under anisothermal conditions. Furthermore, cyclic evolution of state variables used in the authors' constitutive model was experimentally measured. Based on the test results, cyclic softening behavior depending on the temperature and its history was introduced into the constitutive model. The extended model was applied to simulations of inelastic deformation behavior under monotonic tension, stress relaxation, creep, isothermal cyclic deformations including stress relaxation and anisothermal cyclic deformations. It was found that the present constitutive model has a capability of describing the inelastic deformation behavior of modified 9Cr-1Mo steel adequately at various loading conditions.     

关节软骨两相多孔介质非线性模型的有限元方法

基于混合物理论的两相多孔介质模型可以准确描述关节软骨的力学行为，关节软骨的渗透率与固体相体积应变相关。本文研究这一模型的非线性有限元法。具体采用伽辽金加权残值法得到有限元平衡方程，编制了有限元程序，进而对关节软骨围限压缩蠕变和应力松弛行为进行了数值模拟。与视渗透率为常数的线性模型的计算结果比较表明，在变形较大时，渗透率随固体相体积应变变化这一非线性效应不容忽视。