Creep behavior material models

The material behaviors considered will include linear elasticity plus linear or nonlinear creep behavior. The nonlinear case will be restricted to power-law rheologies. In some cases the elasticity will be idealized as rigid. In ceramics, it is commonly the case that creep occurs by mass transport on the grain boundaries.1 This usually leads to a linear rheology. In the models considered,... 

First, consider a composite with a volume fraction/of fibers, all of which are broken. There are two possible models for the steady-state creep behavior of such a material. In one, favored by Mileiko18 and Lilholt,19 among others, the matrix serves simply to transmit shear stress from one fiber to another and the longitudinal stress in the matrix is negligible. The kinematics of this model requires void space to increase in volume at the ends of the fibers. However,... 

The scheme also assumes that the redistribution of the secondary phase changes the size distribution of cavities within the material, which is supported by experimental observations [23,46], Final proof of the cavitation creep model is the fact that Eq. (2) fits the experimental data over a wide range of stresses for both SN 88 and NT 154. Thus, the model shovm in Figure 13.16 provides an understanding of the overall creep behavior of silicon nitride. Cavitation is the main creep mechanism in silicon nitride, and in other similarly bonded ceramics. 

The present contribution has shown that the creep behavior of amorphous polymers under the influence of progressing aging can be well described and predicted under any thermal prehistory applying the multiparameter model based on free volume. The only condition necessary is the knowledge of any measured equilibrium creep curve. For each material the multiparameter model with the given set of parameters allows the prediction of the behavior in volume under any complicated thermal history as well. Introducing some additional postulations, the free volume model is adapted to work at low temperatures, i.e., at temperatures below T. Next, the theory should be extended to measurements at still lower temperatures as well as to some other amorphous polymers. 

Finally, it is worth mentioning another approach used to describe nonlinear viscoelastic solids nonlinear differential viscoelasticity [49, 178, 179]. This theory has been successfully applied to model finite amplitude waves propagation [180-182]. It is the generalization to the three-dimensional nonlinear case of the rheological element composed by a dashpot in series with a spring. Thus in the simplest case, the stress depends upon the current values of strain and strain rate rally. In this sense, it can account for the nonlinear short-term response and the creep behavior, but it fails to reproduce the long-term material response (e.g., relaxation tests). The so-called Mooney-Rivlin viscoelastic material [183] and the incompressible version of the model proposed by Landau and Lifshitz [184] belraig to this class. 

Sometimes it is advantageous to combine Voigt and Maxwell models. The series combination known as the Burgers model contains four experimental constants, which describe the creep behavior of a material. Numerous other com-... 

Service lifetime prediction of polymers and/or polymer based materials may be undertaken from different types of tests, such as creep behavior tests (linear and non-linear creep, physical aging, time-dependent plasticity), fatigue behavior tests (stress transfer and normalized life prediction models, empirical fatigue theories, fracture mechanics theory and strength degradation) and standard accelerated aging tests (chemical resistance, thermal stability, liquid absorption) [32]. 

Upon associating a Voigt element and a Maxwell element in series, one obtains the Bni ers model, which is well-suited to describe the creep behavior of a thermoplastic polymer the behavior of such a material is characterized by an instantaneous elasticity followed by a phase of retarded elasticity, but the strain retains in this case an irreversible character. 

Another important characteristic of adhesives is their time-dependent response to loads. Adhesives may exhibit viscoelastic or visco-plastic material behavior, such as creep and relaxation, resulting in time-dependent stresses and strains. In adhesives with a high glass transition temperature relative to the operating temperature it maybe acceptable to model the adhesive with a time-independent material model. However, as temperature, absorbed moisture, stress level, and time under load increase, there is an increased likelihood of errors in using such a model. Selection of a time-dependent material model will depend on a number of... 

The comparison of calculated and experimental data of the creep curves showed a good correlation. After comparing the calculated results it can be concluded that the viscoelastic behavior of the technical fabric can be described by the one-integral model. In warp and weft directions the numerical curve fitting resulted in a difference of 3.5-9.9% and 0.3-2.6% respectively. Therefore, the Schapery model with the power function characterized more accurate creep behavior in weft direction than warp direction. Also the power function described the strain evaluation better than the exponential function. This research concluded that both the linear and nonlinear viscoelastic identifications based on different material models can be brought together and the results of linear characterization can be applied to the nonlinear description of the material. 

Transient Response Creep. The creep behavior of the polymeric fluid in the nonlinear viscoelastic regime has some different features from what were foimd with the linear response regime. First, there are no ready means of relating the creep compliance to the relaxation modulus as was done in the linear viscoelastic case. In fact, the relationship between the relaxation properties and the creep properties depends entirely on the exact constitutive relationship chosen for the response of the material, and numerical inversion of the specific constitutive law is ordinarily necessary to predict creep response from the relaxation behavior (or vice versa). For most cases, the material properties that appear in the constitutive equations are written in terms of the relaxation response. We discuss this subsequently in the context of the K-BKZ model. 

Voyiadjis, G. Z., and Zolochevsky, A., "Modeling of secondary creep behavior for anisotropic materials with different properties in tension and compression." IntemationalJoumal of PlasticitylAlQ (1998) 1059-1083. 

The accuracy of Finite Element Analysis is wholly dependent on the precision of the material model employed. In the realm of elastomers, accurate material models are difficult to create due to the nonlinear behavior of the material as well as other viscoelastic effects, such as creep, stress relaxation, compression set, and cyclic softening. 

An area of continued research is in development of elastomeric material models which can incorporate cyclic behavior into one model casting aside the need to switch from non-cyclic to cyclic models. Further, other areas of research involve more accurately predicting viscoelastic behavior such as stress relaxation, creep, and most importantly for cyclic applications, compression set. As these models are developed, the accuracy and abilities of Finite Element Analysis of elastomers will improve dramatically and provide a much better method to predict the complex loading conditions over time that elastomeric parts commonly see. 

We shall follow the same approach as the last section, starting with an examination of the predicted behavior of a Voigt model in a creep experiment. We should not be surprised to discover that the model oversimplifies the behavior of actual polymeric materials. We shall continue to use a shear experiment as the basis for discussion, although a creep experiment could be carried out in either a tension or shear mode. Again we begin by assuming that the Hookean spring in the model is characterized by a modulus G, and the Newtonian dash-pot by a viscosity 77. ... 

Very simple models can illustrate the general creep and stress-relaxation behavior of polymers except that the time scales are greatly collapsed in the models compared to actual materials. In the models most of the in-... 

Since the relaxation mechanisms characteristic of the constituent blocks will be associated with separate distributions of relaxation times, the simple time-temperature (or frequency-temperature) superposition applicable to most amorphous homopolymers and random copolymers cannot apply to block copolymers, even if each block separately shows thermorheologically simple behavior. Block copolymers, in contrast to the polymethacrylates studied by Ferry and co-workers, are not singlephase systems. They form, however, felicitous models for studying materials with multiple transitions because their molecular architecture can be shaped with considerable freedom. We report here on a study of time—temperature superposition in a commercially available triblock copolymer rubber determined in tensile relaxation and creep. 

This review is intended to focus on ceramic matrix composite materials. However, the creep models which exist and which will be discussed are generic in the sense that they can apply to materials with polymer, metal or ceramic matrices. Only a case-by-case distinction between linear and nonlinear behavior separates the materials into classes of response. The temperature-dependent issue of whether the fibers creep or do not creep permits further classification. Therefore, in the review of the models, it is more attractive to use a classification scheme which accords with the nature of the material response rather than one which identifies the materials per se. Thus, this review could apply to polymer, metal or ceramic matrix materials equally well. 

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