Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials

Abstract

The Bodner-Partom nonisothermal flow model and the generalized method of harmonic linearization are used to calculate the complex shear modulus and compliance for AMg-6 aluminum alloy. The strainand stress-controlled cycles of loading in the temperature range 20-400°C are considered. The correspondence between the shear modulus and the compliance is studied. It is similar to the inverse proportionality condition in the theory of linear viscoelasticity. It is established that representing the modulus and compliance as functions of the strain amplitude is better than as functions of the stress amplitude due to the universal description of the characteristics for soft and hard cycles and high accuracy of correspondence Introduction. Modeling the mechanical behavior of inelastic materials and structural members under cyclic loading is of theoretical and practical importance in studying the dissipation and accumulation of energy in materials, evaluating the highand low-cycle fatigue of structural members, damping vibrations, etc. [9,10,15,18,[20][21][22].A fundamental result in the theory of linear viscoelasticity is experimental and theoretical justification of the concept of complex mechanical characteristics that describe the behavior of a material under harmonic loading [1,3,11,17]. In these publications, the concept of complex characteristics was generalized to nonisothermal processes for specific classes (thermorheologically simple) materials. In linear viscoelasticity, the complex characteristics provide an exact description of the mechanical behavior of materials in stationary processes. For physically nonlinear materials, this concept was used together with various schemes of harmonic linearization to develop approximate models. The capabilities of these schemes were studied in [5,7,8]. It was established in [12,13] that determining the complex characteristics is an ambiguous procedure, and its result is greatly dependent on the choice of a functional space whose norm is used to approximate nonlinear (generally, polyharmonic) reactions of a material to harmonic loading by a monoharmonic process. By using a mechanical interpretation for such a norm, it is possible to find an approximation corresponding to the mechanical problem of interest. Relevant results are reviewed in [4,19].The publications cited above deal with isothermal processes. The complex characteristics are assumed independent of temperature. Such a model is applicable when thermal perturbations are small. It is obvious that it cannot describe such important processes as vibrational heating under loading of high amplitudes and vibrations at high external temperatures. Moreover, in justifying the concept of complex characteristics for nonlinear materials, it is of practical and methodological importance to test the principle of correspondence between the modulus and the compliance in the cases of soft (stress-controlled) and hard (strain-controlled) cyclic loading.The present paper uses the complete system of equations of the nonisothermal Bodner-...

Thermal instability of a layered rectangular viscoelastic prism under high-frequency compressive loading

“…The dissipation of energy in viscoelastic bodies undergoing intensive vibrations may cause significant increase in temperature [8,12]. After the temperature reaches the softening or melting point, the material sustains thermal fatigue failure [4,6,12]. At the same time, some polymer technologies, including ultrasonic welding are based on the self-heating phenomenon [5].…”

“…Relevant results are reviewed in [10][11][12]14]. The thermal instability of a rectangular prism with a cylindrical inclusion was examined in [10].…”

Vibration and dissipative heating of a layered rectangular viscoelastic prism under harmonic shear loading

“…The heating process reaches a steady thermal state under kinematic loading and may become avalanche-like (which is typical of thermal instability) under mechanical loading Keywords: viscoelastic material, vibrational heating, layered prism, shear loading Introduction. The vibrational heating of viscoelastic bodies is of theoretical and practical importance for the assessment of the fatigue strength of polymeric, including mechanical-rubber products [3, 5,17] and for the development of efficient polymer processes such as ultrasonic welding [4].Vibrational-heating models for linear and nonlinear viscoelastic and viscoplastic bodies are justified in numerous studies [8,13,15,19,23], their results being systematized and generalized in the monograph [5] and reviews [11,12,22]. An analysis of the experimental and theoretical studies [14,19,23] reveals that the coupled thermomechanical behavior of inelastic bodies under harmonic loading is well described with the help of the concept of complex moduli [14,16,18,20].…”

“…Vibrational-heating models for linear and nonlinear viscoelastic and viscoplastic bodies are justified in numerous studies [8,13,15,19,23], their results being systematized and generalized in the monograph [5] and reviews [11,12,22]. An analysis of the experimental and theoretical studies [14,19,23] reveals that the coupled thermomechanical behavior of inelastic bodies under harmonic loading is well described with the help of the concept of complex moduli [14,16,18,20].…”