Cycle-dependent creep under random loading

An important aspect of the response of a metal subjected to cyclic loading and a superimposed mean load is its capacity for progressive strain accumulation. In the present investigation, random loading with tensile mean loads is applied to carbon-steel specimens. The cycle-dependent creep properties are described and a phenomenological approach to predict the number of cycles to ductile failure is proposed. At lower stress values, the fatigue-type brittle failure occurs. To predict the failure lives, the familiar fatigue-damage theory is modified for the case of random loading, and the effect of mean stress is included.     

The total creep of viscoelastic composites under hydrostatic or antiplane loading

The problem of bounding the total creep (or total stress relaxation) of a composite made of two linear viscoelastic materials and subjected to a constant hydrostatic or antiplane loading is considered. It is done by coupling the immediate and the relaxed responses of the composite, which are pure elastic. The coupled bounds provide the possible range of the total deformation at infinite time as a function of the initial deformation of the composite. For antiplane shear existing bounds for coupled two-dimensional conductivity yield the required coupled bounds, and these are attained by doubly coated cylinder assemblages. The translation method is used to couple the effective bulk moduli of a viscoelastic composite at zero and infinite time. A number of microgeometries are found to attain the bulk modulus bounds. It is shown that the Hashin's composite sphere assemblage does not necessarily correspond to the maximum or minimum overall creep, although it necessarily attains the bounds for effective bulk moduli. For instance, there are cases when the doubly coated sphere microstructure or some special polycrystal arrangements attain the bounds on the total creep.     

Subcritical growth of a crack in a transversally isotropic aging composite under long-term static loading

The problem of long-term fracture of an aging reinforced composite array having hexagonal symmetry and weakened by a flat circular macrocrack is considered based on the Boltzmann-Volterra principle and the theory of long-term fracture of viscoelastic bodies. The array is under the action of stationary tensile forces applied at infinity and normal to the crack plane. The Maslov-Arutyunyan operator is used to describe the aging strain properties of the array. The irrational functions of integral Volterra operators obtained during the solution are determined by expanding them into continued fractions. The crack growth equations derived are numerically solved for a specific material (ferroconcrete). Curves of the rupture life of the composite array, kinetics of crack growth, and safe loading are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 72–79, December, 1999.     

Study on the static properties of spiral springs under static loading

Applied Mathematics and Mechanics - Spiral springs have a wide range of applications in various fields. As a result of the complexity of friction, few theoretical analyses of spring belts under...     

Failure of spot welds under in-plane static loading

Under in-plane loading conditions, two independent modes contribute to the failure of a spot weld: the in-plane shear mode and the in-plane rotational mode. In this work, the failures of both modes under large static load are examined individually. To study the combined failure of these two modes, two special test coupons are designed. The first coupon contains one spot weld. The second coupon contains five spot welds. Tests conducted in this work show that a very simple force-based failure criterion can be used to predict the failure of a spot weld under large in-plane combined static loads. Current multiaxial failure theory cannot explain this combined failure. This force-based spot weld failure criterion fits current automotive industry needs for body shell finite element application very well.     

Grip pressure distribution under static and dynamic loading

The dynamic response of a vibrating handarm system is strongly related to the grip force. While the relationship between total grip force and vibration characteristics of the hand-arm system has been extensively studied, no attempts have been made to investigate the distribution of grip pressure at the hand-handle interface. The local grip-pressure distribution may be more closely related to the finger blood flow, fatigue and loss of productivity than total grip force. In the present study, distribution of static and dynamic forces at a hand-handle interface is investigated using a grid of pressure sensors mounted on the handle. The pressure distribution is acquired for different values of static and dynamic grip forces in the range of 25–150 N. The dynamic measurements were conducted at various discrete frequencies in the 20–1000 Hz range with peak acceleration levels of 0.5 g, 1.0 g, 2.0 g and 3.0 g. The grip-pressure distribution under static loads revealed a concentration of high pressures near the tips of the index and middle fingers, and the base of the thumb. This concentration of high pressures shifted towards the middle of the fingers under dynamic loads, irrespective of grip force, excitation frequency and acceleration levels. These local pressure peaks may be related to impairment of blood flow to finger tips and the possible causation of vibration white finger. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

History-sensitive accumulation rules for life-time prediction under variable creep loading

A general form of temporal strength conditions under variable creep loading is employed to formulate several new phenomenological accumulation rules based on the constant-loading durability diagram. Unlike the well-known Robinson rule of linear accumulation of partial life-times, the new rules allow to describe the life-time sensitivity to the load sequence observed in experiments. Comparison of the new rules with experimental data shows that they fit the data much more accurately than the Robinson rule.     

Variational analysis of gradient elastic flexural plates under static loading

Gradient elastic flexural Kirchhoff plates under static loading are considered. Their governing equation of equilibrium in terms of their lateral deflection is a sixth order partial differential equation instead of the fourth order one for the classical case. A variational formulation of the problem is established with the aid of the principle of virtual work and used to determine all possible boundary conditions, classical and non-classical ones. Two circular gradient elastic plates, clamped or simply supported at their boundaries, are analyzed analytically and the gradient effect on their static response is assessed in detail. A rectangular gradient elastic plate, simply supported at its boundaries, is also analyzed analytically and its rationally obtained boundary conditions are compared with the heuristically obtained ones in a previous publication of the authors. Finally, a plate with two opposite sides clamped experiencing cylindrical bending is also analyzed and its response compared against that for the cases of micropolar and couple-stress elasticity theories.     

Calculating creep strains in linear viscoelastic materials under nonstationary uniaxial loading

The creep strains in linear viscoelastic materials under nonstationary loading of various types (incremental loading, complete unloading, and cyclic loading) are determined. Boltzmann–Volterra hereditary theory with fractional exponential kernel is used. Nonstationary loads are specified by Heaviside functions. The calculated results are validated by experimentally determining nonstationary creep strains of glass-reinforced plastic, plastic laminate, polymer concrete, duralumin, and nylon     

Damage accumulation stages in polycrystalline duralumin under static fatigue loading

Two groups of mode changes in the internal structure of a cyclically loaded tension specimen containing a circular hole are analyzed. Their association with order-dependent parameters are also identified. Solutions are obtained and they show that stage I and II deformation in the vicinity of a macroscale stress concentrator is caused by an occupation wave where the velocity is bounded below certain limiting value. Stage III deformation occurs in the strain-localization region.     

Frictional Hertzian contact problems under cyclic loading using static reduction

In this study we investigate an axisymmetric Hertzian contact problem of a rigid sphere pressing into an elastic half-space under cyclic loading. A numerical solution is sought to obtain a steady state, which demands a large amount of computer memory and computing speed. To achieve a tractable problem, the current numerical model uses a “static reduction” technique, which employs only a contact stiffness matrix rather than the entire stiffness of the problem and is more accurate than the approach used by most finite element codes. Investigation of the tendency of contact behavior in the transient and steady states confirms that a steady state exists, showing converged energy dissipation. The dependence of dissipation on load amplitude shows a power law of load amplitude less than 3, which may explain some deviations in the experimental findings.     

Some results of testing simple structures under constant and variable loading during creep

The design of two rigs for room-temperature creep testing is described. One is for testing beams in pure bending and the other for testing circular plates simply supported at the outer edge and loaded through a rigid central boss. A system for giving reproducible step-loading cycles is also described. Typical creep-deformation curves for commercially pure aluminum beams and plates under steady and variable loading are given. These test results are compared with predictions based on the tensile-creep behavior. The repeatability and accuracy of these results are also discussed.     

Stability and limit states of elastoplastic spherical shells under static and dynamic loading

The problem of elastoplastic deformation, buckling, and postcritical behavior of spherical shells is solved using a finite element method and a cross-type explicit scheme of time integration. Stability problems for hemispherical shells under external pressure and compression between rigid plates are considered. The influence of holes and boundary conditions on shell deformation is investigated. It is shown that the calculation results are in good agreement with experimental data.