Viscoelastic state of a three-layer cylindrical shell during impulsive thermomechanical loading

Belorussian Institute of Railroad Transportation Engineers, Gomel'. Translated from Prikladnaya Mekhanika, Vol. 27, No. 3, pp. 46–52, March, 1991.     

Concentration of stresses and strains in a notched cyclinder of a viscoplastic material under harmonic loading

Certain aspects of the correct definitions of stress and strain concentration factors for elastic-viscoplastic solids under cyclic loading are discussed. Problems concerning the harmonic kinematic excitation of cylindrical specimens with a lateral V-notch are examined. The behavior of the material of a cylinder is modeled using generalized flow theory. An approximate model based on the concept of complex moduli is used for comparison. Invariant characteristics such as stress and strain intensities and maximum principal stress and strain are chosen as constitutive quantities for concentration-factor definitions. The behavior of time-varying factors is investigated. Concentration factors calculated in terms of the amplitudes of the constitutive quantities are used as representative characteristics over the cycle of vibration. The dependences of the concentration factors on the loads are also studied. The accuracy of Nueber's and Birger's formulas is evaluated. The solution of the problem in the approximate formulation agrees with its solution in the exact formulation. The possibilities of the approximate model for estimating low-cycle fatigue are evaluated. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 15–22, February, 1999.     

Modeling of coating separation under thermomechanical loading in the beam approximation

The beam approximation is developed to solve some problems of fracture mechanics concerning the formation of separation of thin elastic coatings with allowance for the constraints acting on the connection boundaries and the influence of unsteady temperature actions.The separation end region is modeled by an elastic beam loaded by an external bending moment and by force factors from the connection with the base. This region is subjected to thermoelastic stresses caused by a sudden variation in the temperature of the surface or the adhesive layer. We estimate how the effective fracture strength of the adhesive joint varies for various modes of application of affecting factors, including variations in material properties with temperature and across the coating thickness; we also study buckling phenomena and the kinetics of local fracture processes in the end region. The results can be used when choosing the parameters of an adhesive joint so as to ensure a given effective adhesion fracture strength of the joint.     

Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

We analyze approximate approaches to the modeling of the thermomechanical behavior of physically nonlinear materials under harmonic loading. The approaches are based on various harmonic-linearization schemes and the concept of complex moduli. Mechanical and mathematical features of various schemes are considered. Some modifications of the model are proposed to account for various aspects of material behavior under harmonic loading. The problems of vibration and dissipative heating of physically nonlinear bodies are formulated. The main thermomechanical characteristics are analyzed for some classes of problems.The study was partially sponsored by the State Fund for Basic Research of the Ministry of Education and Science of Ukraine (Grant No. 01.07/00050).Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–34, September 2004.     

The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading

We have examined the problem of the dynamic growth of a single spherical void in an elastic-viscoplastic medium, with a view towards addressing a number of problems that arise during the dynamic failure of metals. Particular attention is paid to inertial, thermal and rate-dependent effects, which have not previously been thoroughly studied in a combined setting. It is shown that the critical stress for unstable growth of the void in the quasistatic case is strongly affected by the thermal softening of the material (in adiabatic calculations). Thermal softening has the effect of lowering the critical stress, and has a stronger influence at high strain hardening exponents. It is shown that the thermally diffusive case for quasistatic void growth in rate-dependent materials is strongly affected by the initial void size, because of the length scale introduced by the thermal diffusion. The effects of inertia are quantified, and it is demonstrated that inertial effects are small in the early stages of void growth and are strongly dependent on the initial size of the void and the rate of loading. Under supercritical loading for the inertial problem, voids of all sizes achieve a constant absolute void growth rate in the long term. Inertia first impedes, but finally promotes dynamic void growth under a subcritical loading. For dynamic void growth, the effect of rate-hardening is to reduce the rate of void growth in comparison to the rate-independent case, and to reduce the final relative void growth achieved.     

Nonstationary oscillations of three-layer cylindrical shells under axisymmetric loading

The nonstationary behavior of three-layer cylindrical shells under an axisymmetric loading is considered with the application of hypotheses to each layer. Independent postulations are proposed for the approximation of displacements and transverse strains across the thickness of each layer. Reissner's variational principle for dynamic processes is used to derive the motion equations. The problem of the dynamic deformation of three-layer cylindrical shells under a nonstationary loading is considered in the case where the ends of the shells are rigidly fixed. The values obtained were compared with those predicted from hypotheses relating to the whole packet of the structure (the Timoshenko-type theory of multilayered shells). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 3–9, August, 1999.     

Stability of layered coatings under biaxial thermomechanical loading

The three-dimensional problem of stability of layered coatings at normal and high temperatures and small precritical strains is formulated and solved and the characteristic equations are derived. The temperature dependence of the physical and mechanical parameters of specific layered coatings is established experimentally. Three-layer coatings on a homogeneous substrate at different temperatures are considered as an example. Recommendations for establishing the optimal service conditions for layered structural members with coatings are formulated.     

Plastic limit state of a thin hollow disk under thermomechanical loading

This paper considers the plastic limit state of a thin hollow axisymmetric disk subjected to thermomechanical loading with a uniform pressure distribution on the inner contour and a temperature increasing during deformation. A semi-analytical solution of the formulated boundary-value problem is obtained. Qualitative features of the behavior of the solution with a loss of the load-carrying capacity of the disk are investigated.     

抛物面型激光推力器的热力冲击响应

通过实验、机理分析和数值模拟系统地分析了大气模式激光推进中抛物面型推力器的热力冲击问题。在分析激光推进中存在的4种热载荷（入射、辐射、透射和运流）的基础上,建立了相应的热力耦合动态计算方法。多脉冲推进的计算温升与实验结果吻合。计算表明,入射吸收和高温辐射是造成抛物面型激光推力器温升的主要原因,并预测推力器在熔化前首先发生拉伸破坏,揭示了激光推进中热力冲击破坏的机理和严重性。     

Dynamic analysis of a disc brake under frictional and thermomechanical internal loading

The study of the vibratory response of a mechanical system as complex as a disc brake needs to consider the complexity of the problem induced by the coupling of tribological, thermomechanical and dynamical effects. Experimental consideration are discussed here for two set ups at the full scale of the disc brake and at a local scale focussed on the third body interface. A numerical model with thermomechanical and dynamical couplings is then presented, followed by a substantial discussion.     

Non-linear response of laminated composite plates under thermomechanical loading

The non-linear response of laminated composite plates under thermomechanical loading is studied using the third-order shear deformation theory (TSDT) that includes classical and first-order shear deformation theories (CLPT and FSDT) as special cases. Geometric non-linearity in the von Kármán sense is considered. The temperature field is assumed to be uniform in the plate. Layers of magnetostrictive material, Terfenol-D, are used to actively control the center deflection. The negative velocity feedback control is used with the constant gain value. The effects of lamination scheme, magnitude of loading, layer material properties, and boundary conditions are studied under thermomechanical loading.     

Deformation of glued beams under harmonic loading

The dynamic deformation of glued beams with a thin adhesive interlayer under harmonic loading is studied. The virtual-work principle is used. The system of ordinary differential equations for the amplitudes in the approximations in coordinate functions is derived and solved. The proposed approach allows determining the stresses and strains at an arbitrary point of the beam, especially in the adhesive interlayer. Numerical results are presented     

Prediction of material thermomechanical response with a unified viscoplastic constitutive model

Results of a research program conducted to develop and apply a unified constitutive model to the prediction of material stress-strain behavior at elevated temperature are presented. Specifically, a model that represents inelastic behavior as coupled plastic and creep response was developed for a nickel base alloy, Hastelloy X, subjected to thermomechanical cycles in which both the mechanical strain and temperature are simultaneously changing. The basis for the constitutive model is the unified approach first proposed by Bodner. Adaptation of the approach to Hastelloy X for variable temperature loading cycles required significant modification of the original model. Prediction of the response of a uniaxial test specimen subjected to a thermomechanical loading cycle, representative of the local conditions present in a gas turbine combustor liner, are presented and serve as the basis for an assessment of the modified model.     

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

The presence of cracks in a structure is usually detected by adopting a linear approach through the monitoring of changes in its dynamic response features, such as natural frequencies and mode shapes. But these linear vibration procedures do not always come up to practical results because of their inherently low sensitivity to defects. Since a crack introduces non-linearities in the system, their use in damage detection merits to be investigated. With this aim the present paper is devoted to analysing the peculiar features of the non-linear response of a cracked beam.The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite elements; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, and quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics, strictly due to the presence of a crack, can be used in non-linear techniques of crack identification.     

Unsteady behavior of an elastic beam floating on shallow water under external loading

A solution is derived for the twodimensional unsteady problem of the behavior of an elastic beam of finite dimensions floating on the free surface of water under external loading. It is assumed that the fluid is ideal and incompressible and its depth is well below the beam length. The simultaneous motion of the beam and the fluid is considered within the framework of linear theory, and the fluid flow is assumed to be potential. The behavior of the beam under various loadings with and without allowance for the inertia of the load is studied.     

Numerical study of the thermomechanical behavior of viscoelastic bodies in plane harmonic deformation

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