A Time-Strain Separable K-BKZ Constitutive Equation to Describe the Large Amplitude Oscillatory Shear (LAOS) Flow Behavior of Viscoelastic Polymer Liquids

안혜진,장갑식,송기원,Ahn, Hye-Jin,Chang, Gap-Shik,Song, Ki-Won The Korean Fiber Society 2017 한국섬유공학회지 Vol.54 No.4

The present study has been designed to describe the nonlinear viscoelastic behavior of concentrated polymer systems in large amplitude oscillatory shear (LAOS) flow fields using a time-strain separable K-BKZ constitutive equation (i.e., Wagner model). Using an Advanced Rheometric Expansion System (ARES), the dynamic viscoelastic behavior of aqueous poly(ethylene oxide) (PEO) solutions with various molecular weights and different concentrations has been investigated with a various combination of several fixed strain amplitudes and constant angular frequencies. The linear dynamic data (storage modulus and loss modulus) over a wide range of angular frequencies were obtained to determine the relaxation spectrum parameters and the stress relaxation moduli at various deformation magnitudes were measured to determine the damping function. The effects of the number of relaxation spectrum parameters and damping functions on the prediction results of the Wagner model were examined in depth. The nonlinear viscoelastic functions were analyzed by the aid of 3D plots and predicted over a wide range of strain amplitudes to evaluate the overall predictability of the Wagner model. The main findings obtained from this study are summarized as follows : (1) The Lissajous patterns predicted by the Wagner model are in good coincidence with the experimentally obtained stress-strain rate hysteresis loops both in linear and nonlinear viscoelastic regions and are independent of the number of relaxation spectrum parameters used in the calculation of memory function. (2) The effect of damping function on the predictive ability of the Wagner model is more sensitive than that of memory function. When the damping function is smaller than that of the experimental data, the stress amplitude predicted by the Wagner model also becomes smaller. (3) The Wagner model predictions are closely coincident with the experimental results in the linear viscoelastic region. As the strain amplitude is increased, the predicted nonlinear viscoelastic functions are somewhat larger than that of the experimental data. Nevertheless, all trends of the nonlinear viscoelastic behavior are in good agreement with the experimental results in a qualitative sense. (4) The Wagner model predicts the first harmonic loss modulus more exactly than the first harmonic storage modulus. As the strain amplitude is increased, the first harmonic storage modulus is somewhat overpredicted. The third and fifth harmonic storage and loss moduli exhibit an overshoot or an undershoot at large strain amplitudes. This constitutive equation has an ability to qualitatively describe well such dramatic behavioral changes.

일래스토메릭 부싱의 축방향모드에 대한 리아니스 모델연구

이성범 ( Seong Beom Lee ) 한국고무학회 2002 엘라스토머 및 콤포지트 Vol.37 No.3

본 연구에서 고려된 elastomeric bushing은 자동차 현가장치에 사용되는 기계요소로서, 가깥쪽의 실린더형 슬리브와 안쪽의 실린더형 축 사이에서 가운데가 완전히 비어있는 실린더의 형태를 가진다. 본 연구에서는 일래스토메릭 부싱에 적용되는 힘과 변형의 관계가 비선형이고 점탄성의 특성을 보이므로, Lianis에 의해 발전되어진 비선형 점탄성 비압축 재료에 대한 구조방정식을 사용하여, 부싱의 축방향 응답에 대한 힘과 변위의 관계를 얻었다. 또한 변위에 의존하는 force relaxation function은 extrapolation method에 의한 ramp displacement control test로부터 완성되고, 이는 step displacement control test로부터 얻게된 결과와 비교하여, 두 결과가 매우 잘 일치됨을 확인하였다. An elastomeric bushing which has been considered in this research is a device used in automotive suspension systems to reduce the force transmitted from the wheel to the frame of the vehicle. A bushing is modeled as a hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. Lianis constitutive equation for a nonlinear viscoelastic incompressible material is used to model the elastomeric material of the bushing. It is used to derive a force-displacement relation for axial response of the bushing. The displacement dependent force relaxation function for the bushing is obtained from the ramp displacement control tests with an extrapolation method. This is compared with the exact result obtained from the step displacement control test and the results are in very good agreement.

자동차 부싱에 대한 Pipkin-Rogers 모델의 실험적 연구

김성진(Sung Jin Kim),이수용(Su Young Lee),이성범(Seong Beom Lee) Korean Society for Precision Engineering 2005 한국정밀공학회지 Vol.22 No.11

An automotive bushing is a device used in automotive suspension systems to reduce the load transmitted from the wheel to the frame of the vehicle. A bushing is a hollow cylinder, which is bonded to a solid steel shaft at its inner surface and a steel sleeve at its outer surface. The relation between the force applied to the shaft and the relative deformation of a bushing is nonlinear and exhibits features of viscoelasticity. In this paper, an automotive bushing is regarded as nonlinear viscoelastic incompressible material. Instron 8801 equipment was used for experimental research and ramp-to-constant displacement control test was used for data acquisition. Displacement dependent force relaxation function was obtained from the force extrapolation method and expressed as the explicit combination of time and displacement. Pipkin-Rogers model, which is the direct relation of force and displacement, was obtained and comparison studies between the experimental results and the Pipkin-Rogers results were carried out.

반경방향모드에 대한 자동차 부싱의 실험적 연구

이성범(Seong Beom Lee),정재영(Jae Young Jeong),박종식(Jong Sik Park),이우현(Woo Hyun Lee) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.6

An automotive bushing is a device used in automotive suspension systems to reduce the load transmitted from the wheel to the frame of the vehicle. A bushing is a hollow cylinder, which is bonded to a solid steel shaft at its inner surface and a steel sleeve its outer surface. The relation between the force applied to the shaft and the relative deformation of a bushing is nonlinear and exhibits features of viscoelasticity. In this paper, an automotive bushing is regarded as nonlinear viscoelastic incompressible material. Instron 8801 equipment was used for experimental research and ramp-to-constant displacement control test was used for data acquisition. Displacement-dependent force relaxation function was obtained from the force extrapolation method and expressed as the explicit combination of time and displacement. Pipkin-Rogers model, which is the direct relation of force and displacement, was obtained and comparison studies between the experimental results and the Pipkin-Rogers results were carried out.

Nonlinear Viscoelastic Behavior of Concentrated Xanthan Gum Systems in Large Amplitude Oscillatory Shear (LAOS) Flow Fields : Fourier Transform Rheology

안혜진,국화윤,송기원,Ahn, Hye-Jin,Kuk, Hoa-Youn,Song, Ki-Won The Korean Fiber Society 2017 한국섬유공학회지 Vol.54 No.5

The present study has been performed to quantitatively characterize the nonlinear rheological behavior of concentrated xanthan gum systems in large amplitude oscillatory shear (LAOS) flow fields by means of the methodology of Fourier transform (FT) rheology. Using an Advanced Rheometric Expansion System (ARES), the dynamic viscoelastic behavior of aqueous xanthan gum solutions with different concentrations has been experimentally investigated in LAOS flow conditions with a various combination of several fixed strain amplitudes and constant angular frequencies. The nonlinear viscoelastic functions were derived from the Fourier spectra of stress responses, and then the fundamental and higher harmonic contributions were calculated from discrete Fourier transform (DFT). The nonlinear viscoelastic behavior was interpreted by displaying 3D plots, and then the effects of strain amplitude and angular frequency on the nonlinear behavior were discussed in depth. A comparison of the experimentally obtained stress response with the stress waves calculated from higher harmonic nonlinear viscoelastic functions was made to clarify the role of higher harmonic contributions. The main findings obtained from this study are summarized as follows : (1) When the strain amplitude becomes larger than a critical value of 50%, the higher nonlinear viscoelastic functions must be considered to explain the nonlinear viscoelastic behavior. However, the fundamental stress amplitude is dominantly larger than those of higher harmonics. (2) As the strain amplitude is increased, the fundamental stress amplitude is steeply increased within the linear viscoelastic region beyond which followed by an approximately constant magnitude at large deformations. This strain dependence may be explained as a distinction between linear and nonlinear viscoelastic behavior. (3) When the strain amplitude exceeds a critical value of 50%, the higher stress amplitudes are sharply increased with an increase in strain amplitude at large deformations, indicating that the higher stress harmonics exert an influence on the nonlinear viscoelastic behavior. (4) In order to interpret the complicated nonlinear viscoelastic behavior occurring at large deformations, the fundamental terms as well as the higher harmonics of phase angles defined at the odd terms should be deliberated for a quantitatively advanced analysis. (5) An overall shape of the experimentally obtained stress response is strongly affected by the higher harmonic contributions. As the angular frequency is decreased, a more distorted and a sharper stress waveform is observed at LAOS deformations. (6) A distorted stress waveform is qualitatively inclined to the left side with respect to a sinusoidal curve. In order to explain the nonlinear viscoelastic behavior of concentrated xanthan gum systems in LAOS flow fields, the nonlinear viscoelastic functions from the first to at least seventh harmonics should be considered for an accurate analysis.

Discrete Fourier Transform Analysis to Characterize the Large Amplitude Oscillatory Shear (LAOS) Flow Behavior of Viscoelastic Polymer Liquids

장갑식,안혜진,송기원,Chang, Gap-Shik,Ahn, Hye-Jin,Song, Ki-Won The Korean Fiber Society 2016 한국섬유공학회지 Vol.53 No.5

The objective of the present study is to systematically characterize the nonlinear viscoelastic behavior of concentrated polymer systems in large amplitude oscillatory shear (LAOS) flow fields by means of discrete Fourier transform (DFT) analysis. Using an Advanced Rheometric Expansion System (ARES), the dynamic viscoelastic behavior of aqueous poly(ethylene oxide) (PEO) solutions with various molecular weights and different concentrations has been investigated with several fixed strain amplitudes and constant angular frequencies. The nonlinear viscoelastic functions and the degree of nonlinearity were derived from the Fourier spectra of stress responses, and then the nonlinear behavior was interpreted by the use of 3D and contour plots, respectively. The effects of strain amplitude and angular frequency on the nonlinear viscoelastic behavior were nextly discussed in depth. In addition, the strain limits of linear viscoelastic response were determined from the ratio of harmonic contributions, and then the validity of Pipkin diagram with regard to characteristic time was evaluated for all PEO solutions. The main findings obtained from this study are summarized as follows: (1) At small strain amplitudes, the influence of the first harmonic contribution is dominant. As the strain amplitude becomes larger, however, the effect of higher odd harmonic contributions is increased, resulting in an occurrence of a nonlinear viscoelastic behavior. (2) The degree of nonlinearity is increased with an increase in strain amplitude. This is also increased with increasing angular frequency until reaching the maximum value at a certain angular frequency and then decreased with a further increase in angular frequency. (3) The Pipkin diagram with regard to characteristic time is a very effective method to explore the nonlinear regime of viscoelastic polymer liquids in LAOS deformations.

The Doi-Edwards Constitutive Equation to Predict the Large Amplitude Oscillatory Shear (LAOS) Flow Behavior of Viscoelastic Polymer Liquids

안혜진,장갑식,송기원,Ahn, Hye-Jin,Chang, Gap-Shik,Song, Ki-Won The Korean Fiber Society 2017 한국섬유공학회지 Vol.54 No.4

The present study has been designed to predict the nonlinear viscoelastic behavior of concentrated polymer systems in large amplitude oscillatory shear (LAOS) flow fields by means of the Doi-Edwards constitutive equation. Using an Advanced Rheometric Expansion System (ARES), the dynamic viscoelastic behavior of aqueous poly (ethylene oxide) (PEO) solutions with various molecular weights and different concentrations has been investigated with a various combination of several fixed strain amplitudes and constant angular frequencies. The linear dynamic data (storage modulus and loss modulus) over a wide range of angular frequencies were also obtained to determine the relaxation spectrum parameters. The experimentally obtained Lissajous patterns (stress-strain rate hysteresis loops) were compared with the Doi-Edwards model predictions over a wide range of strain amplitudes and angular frequencies for all polymer solutions prepared in this work. The nonlinear viscoelastic functions were analyzed by the aid of 3D plots and predicted over a wide range of strain amplitudes to evaluate the overall predictability of the Doi-Edwards model. The main findings obtained from this study are summarized as follows : (1) The Lissajous patterns predicted by the Doi-Edwards model represent a good agreement with the experimentally obtained stress-strain rate hysteresis loops both in linear and nonlinear viscoelastic regions. (2) The predictions of the Doi-Edwards model are closely coincident with the experimental results in the linear viscoelastic region. As the strain amplitude is increased, the predicted nonlinear viscoelastic functions are somewhat larger than that of the experimental data. Nevertheless, all trends of the nonlinear viscoelastic behavior are qualitatively in good agreement with the experimental results. (3) The Doi-Edwards model gives a very good prediction for the first harmonic storage modulus and loss modulus up to the nonlinear viscoelastic region. The third and fifth harmonic storage and loss moduli exhibit an overshoot or an undershoot at large strain amplitudes. This constitutive equation can describe well such excessive behavioral changes in a qualitative sense. (4) The Doi-Edwards model has a slightly better ability than the Wagner model to predict the LAOS flow behavior of concentrated polymer systems.

Nonlinear thermal vibration of FGM beams resting on nonlinear viscoelastic foundation

M. Alimoradzadeh,Ş.D. Akbaş 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.44 No.4

Nonlinear free vibration analysis of a functionally graded beam resting on the nonlinear viscoelastic foundation is studied with uniform temperature rising. The non-linear strain-displacement relationship is considered in the finite strain theory. The governing nonlinear dynamic equation is derived based on the finite strain theory with using of Hamilton’s principle. The Galerkin’s decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The influences of temperature rising, material distribution parameter, nonlinear viscoelastic foundation parameters on the nonlinear free response and phase trajectory are investigated. In this paper, it is aimed that a contribution to the literature for nonlinear thermal vibration solutions of a functionally graded beam resting on the nonlinear viscoelastic foundation by using of multiple time scale method.

점탄성 고분자 액체의 정상유동함수와 과도적 유동함수의 상관관계 연구: Gleissle 밀러 관계식들의 실험적 검증 및 이론적 고찰

곽윤정,안혜진,송기원,Kwak, Yun-Jeong,Ahn, Hye-Jin,Song, Ki-Won 한국섬유공학회 2015 한국섬유공학회지 Vol.52 No.3

The objective of this study is to systematically investigate the relationships between steady flow functions and transient flow functions for viscoelastic polymer liquids. Using a strain-controlled rheometer (Advanced Rheometric Expansion System (ARES)), the steady shear flow properties and the transient shear flow properties of concentrated poly(ethylene oxide) (PEO) solutions have been measured over a wide range of shear rates and times. The validity of the three forms of the Gleissle mirror relations was examined by comparing them with the experimentally obtained results. In addition, the effect of nonlinearity on the applicability of these Gleissle mirror relations was discussed from a theoretical view-point by introducing the concept of a nonlinear strain measure. The main findings obtained from this study can be summarized as follows: (1) A nonlinear strain measure is decreased with an increase in strain magnitude, after reaching the maximum value at small strain range. This behavior is quite different from the theoretical prediction to satisfy the conditions of the Gleissle mirror relations. (2) The first mirror relation describing the equivalence between steady shear flow viscosity and shear stress growth coefficient is valid over a wide range of shear rates and is hardly affected by the nonlinearity of polymer solutions. (3) The second mirror relation expressing the equivalence between first normal stress coefficient and first normal stress growth coefficient is also applicable over a wide range of shear rates. This relation is, however, significantly influenced by the degree of nonlinearity (i.e., shape of a nonlinear strain measure) of polymer solutions. (4) The third mirror relation can be regarded as a very useful empirical model to predict the first normal stress coefficient from steady shear flow viscosity data, provided that an appropriate value of a shift factor is given.

대진폭 전단변형하에서 폴리이소부틸렌 농후용액의 비선형 점탄성 거동

장갑식 한국유변학회 1998 Korea-Australia rheology journal Vol.10 No.3

본 연구에서는 Advanced Rheometric Expansion System(ARES)를 사용하여 대진폭 진동 전단 변형하에서 발생하는 폴리이소부틸렌(PIB) 농후 용액의 비선형 점탄성 거동을 저 장탄성율과 동적점도의 변형량 의존성 및 응력파형의 fast Fourier transform(FFT) 해석을 통해 고찰하였다. 스트레인 진촉을 단계적으로 증가시키면서 측정한 동적 점탄성으로 부터 저장탄성율 및 동적점도의 선형응답한계를 결정하고 이들에 미치는 각주파수의 영향을 조사 하였다. 그리고 응력파형의 Fourier 전개로부터 유도되는 비선형 점탄성함수를 사용하여 비 선형 거동을 설명하였다. 끝으로 비선형 점탄성 거동의 정도를 나타내는 비선형 거동 지수 를 정의하고 이들에 미치는 각주파수의 영향에 대해 검토하였다. 이상의 연구를 통해 얻어 진 결과를 요약하면 다음과 같다.(1) 선형 응답한계는 고분자 용액의 특성시간의 역수보다 높은 각주파수 범위에서는 일정한 값을 유지하지만 특성시간의 역수보다 낮은 각주파수 영 역에서는 각주파수가 감소할수록 증가한다. (2)선형응답한계 이상의 대변형하에서는 3차비선 형 점탄성 함수 이상의 고차항의 영향이 크게 작용하며 이로인해 비선형 거동이 발생된다. (3) 스트레인 진폭을 단계적으로 증가시키면서 측정한 저장탄성율 및 동적점도의 변형량 의 존성은 응력파형의 Fourier transform으로부터 유도된 1차 비선형 점탄성 함수의 변형량 의 존성을 나타낸다 (4) 저장탄성율 및 동적점도의 변형량 의존성으로부터 유도된 비선형 거동 지수는 탄성적 서질과 점성적 성질에 대한 비선형 특성을 평가하기 위한 유요한 방법으로 인정된다. (5) 비선형 점탄성 거동의 정도를 나탄는 비선형 거동지수는 특정한 각주파수에서 최대치를 가지며 또한 탄성적 거동이 점성적 거동에 비해 더욱 큰 각주파수 의존성을 나타낸다.