Papers by Keyword: Nonlinear Viscoelasticity

Abstract: A single pocket cage is the SKF product, which is used in Large Size Bearings for wind industry. The function of a bearing cage is to hold, guide and separate rolling elements, and differently from the conventional cage, the current one consists of segments, which eases the bearing assembly and reduces its weight. The long life challenge (25 years!) requires considering fatigue, and since the single pocket cage is made of PEEK polymer, it is also susceptible to creep (in near room temperature), which enhances fatigue damage. The current work proposes the numerical model capturing non-linear viscoelasticity of PEEK. The mechanical behavior of this material is identified in uniaxial tension test and is modeled in Finite Elements (FE) by means of the Parallel Rheological Framework (this numerical tool has been recently implemented in the commercial software ABAQUS). The current FE model enables to apply cyclic loading, simulating the material response of cage when it operates in running bearing. By applying sub-modeling technique only a small domain is modeled which improves the computational time efficiency. The sub-model domain corresponds to the cage region, where the stress is high resulting to the material yielding, fatigue/creep degradation (due to inelastic cyclic deformation) and initiation of fatigue crack. The FE results were combined with the test data, in attempt to relate the numerically predicted damage to the cage life. The development of irreversible deformation during cyclic loading, shakedown analysis and the stress volume effect, are the main focuses of the current work.

Abstract: Two types of carbon fiber-reinforced epoxy composite laminates are chosen for long-term tensile creep tests under different temperatures and load levels. Their time-dependent and non-monotonic deformations indicate clearly both temperature effect and physical aging effect. To characterize these viscoelastic behavior, two phenomenological constitutive models and one physical model are developed. The linear viscoelastic model based on the Boltzmann superposition principle is able to describe reasonably the deformations at relatively lower stress levels and temperatures. The nonlinear viscoelastic model of Schapery’s single-integral form, together with a usage of effective time theory, could describe nicely all the effects of temperature, stress, and physical aging. The physical model based on Ngai’s coupling mechanism concept is further combined with the framework of Schapery’s nonlinear viscoelastic theory, which may provide certain physical understanding about the effect of aging behavior on long-term creep deformation of the laminated composites. Numerical modelling by finite element method are implemented, and comparisons between the experimental and simulation results are demonstrated.

Abstract: The mechanical behaviors were investigated by nonlinear creep tests of poly(methyl methacrylate) under different temperatures. The test duration was 4000 seconds. The corresponding temperature shift factors, stress shift factors and temperature-stress shift factors were obtained according to time-temperature superposition principle, the time-stress superposition principle and the time-temperature-stress superposition principle (TTSSP). The master creep compliance curve up to about 1-month at a reference temperature 22 degrees centigrade and a reference stress 14 MPa was constructed, and the effect of stress-induced damage evolution on the long-term creep behavior of polymeric material was accounted. It was shown that TTSSP provides an effective accelerated test technique in the laboratory, the results obtained from a short-term creep test of poly(methyl methacrylate) specimen at high temperature and stress level can be used to construct the master creep compliance curve for prediction of the long-term mechanical properties at relatively lower temperature and stress level, and the master creep compliance curve with damage considered can be applied to accurately characterize the long-term creep behavior of nonlinear viscoelastic polymer.

Abstract: Uncured, filled rubbers show remarkable nonlinear viscoelasticity as well as cured, filled rubbers. The nonlinearity may come from change in entanglement and filler network structures. Many people use dynamic modulus to characterize rubber materials. However, dynamic modulus cannot be defined at large strain. Hence we must study a viscoelastic function to be defined at large strain. In addition, we need other information to separate the effects of the change in entanglement and filler network structures on nonlinear viscoelasticity. In this work, we have measured simultaneously relaxation modulus G(γ,t) and electrical resistivity ρ(γ,t) for carbon black (CB)-filled, uncured styrene-butadiene copolymers (SBRs) at wide range of strains. Electrical resistivity at equilibrium, ρ(0,t), showed step-like change at the CB loading between 20 and 35 phr, indicating threshold for filler network formation should exist in the range of values in CB loading. Both G(γ,t) and ρ(γ,t) for the samples having CB loading to be higher than the threshold showed nonlinearity at the strain larger than shear strain γ=0.1, indicating rupture in filler network at large strain.

Abstract: Viscoelastic materials are used in automobiles and other products. However, because of theoretical complexity, it has not been easy to put all the energy exhausted into the automotive viscoelastic materials. Since time is the most important factor in the study of viscoelastic material, creep and stress relaxation functions are very important. In this study, a bushing was selected for special viscoelastic material. A bushing is a device used in automotive suspension systems to cushion the force transmitted from the wheel to the frame of the vehicle. A bushing is essentially a hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. The shaft is connected to the suspension and the sleeve is connected to the frame. The cylinder provides the cushion when it deforms due to relative motion between the shaft and sleeve. The relation between the force applied to the shaft or sleeve and their deformation is nonlinear and exhibits features of viscoelasticity. A force-displacement relation for a bushing is important for multi-body dynamics numerical simulations. Hence, an explicit force-displacement relation has been introduced. The relation is expressed in terms of a force relaxation function. With Pipkin-Rogers model, the direct relation of force and displacement that has been derived from experiment and numerical simulation, the sinusoidal displacement was chosen and the relation of frequency and deformation for the viscoelastic material was studied.