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A solution algorithm for the transient analysis of bodies undergoing creep under constant or time varying loads is presented. The constitutive equation adopted is of the form: έc=γσm. The finite element formulation is carried out in terms of displacements and creep strains as internal variables. The time discretization is achieved with a trapezoidal time integration scheme. The creep strains are condensed out to give an equation for displacement increments involving a modified stiffness matrix and force vector. A Newton—Raphson iterative scheme is used for the non‐linear creep strain rate‐stress relation, and creep strains are updated at the end of the time step. The algorithm has been implemented in NOSTRUM for two‐dimensional structural and plane continuum problems, with a von Mises type potential function governing the multiaxial creep constitutive relationship. Numerical results are presented.

This paper aims to present two Anand’s model parameter sets for the multilayer silver–tin (AgSn) transient liquid phase (TLP) foils.

The AgSn TLP test samples are manufactured using pre-defined optimized TLP bonding process parameters. Consequently, tensile and creep tests are conducted at various loading temperatures to generate stress–strain and creep data to accurately determine the elastic properties and two sets of Anand model creep coefficients. The resultant tensile- and creep-based constitutive models are subsequently used in extensive finite element simulations to precisely survey the mechanical response of the AgSn TLP bonds in power electronics due to different thermal loads.

The response of both models is thoroughly addressed in terms of stress–strain relationships, inelastic strain energy densities and equivalent plastic strains. The simulation results revealed that the testing conditions and parameters can significantly influence the values of the fitted Anand coefficients and consequently affect the resultant FEA-computed mechanical response of the TLP bonds. Therefore, this paper suggests that extreme care has to be taken when planning experiments for the estimation of creep parameters of the AgSn TLP joints.

In literature, there is no constitutive modeling data on the AgSn TLP bonds.

The purpose of the investigation was to examine the tertiary creep and the creep fracture characteristics of an aluminium alloy to specification B.S.2L42, subject to complex stressing at 200 dog. C. The scope of the work involved seven pure torsion, pure tension, and combined tension and torsion creep tests, of durations between 300 hrs. and 3,000 hrs., on the aluminium alloy at 200 deg. C., and analysis of the results.

DURING the last few years a programme of creep tests under general stress systems at high temperatures has been carried out at the N.P.L., using four metallic alloys which were chosen as being representative of basic groups of materials used in practice in machinery operating at high temperatures. This work, it was hoped, would fulfil, at least partly, the great need for experimental data in this field, as opposed to the comparative abundance of theoretical work available, and also enable a critical examination of the merits of this theoretical work to be made. The materials chosen in order of examination were a cast 0–17 per cent carbon steel, an aluminium alloy (R.R. 59), a magnesium alloy (containing 2 per cent aluminium), and a nickel‐chromium alloy (Nimonic 75). Each material was tested at temperatures lying within the normal working range of the material in question. Thus the 0–17 per cent carbon steel was tested at 350, 450 and 550 dcg. C. (662, 842 and 1,022 deg. F.), the aluminium alloy at 150 and 200 deg. C. (302 and 392 dcg. F.), the magnesium alloy at 20 and 50 deg. C. (68 and 122 dcg. F.), and the nickel‐chromium alloy at 550 and 650 dcg. C. (1,022 and 1,202 deg. F.).

The lead‐free solder joint reliability of several printed circuit board mounted high‐density packages, when subjected to temperature cycling was investigated by finite element modelling. The packages were a 256‐pin plastic ball grid array (PBGA), a 388‐pin PBGA, and a 1657‐pin ceramic column grid array. Emphasis was placed on the determination of the creep responses (e.g. stress, strain, and strain energy density) of the lead‐free solder joints of these packages.

It is possible to assess the plastic strain associated with yielding under a two‐dimensional stress system X, Y of a disk, by accepting the shear strain energy as the criterion of yielding, and assuming that the principal plastic strains x, y and z for a general stress system of principal stresses X, Y and Z may be represented by

The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method.

A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data.

The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of < 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters.

The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper.

The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss.

The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

Safety analysis has been done for thermal non-homogeneous thick-walled circular cylinder under internal and external pressure. The paper aims to discuss these issues.

Transition theory based on the concept of generalized principal Lebesgue strain measure has been used which simplifies the constitutive equations by prescribing a priory the order of the measure of deformation and helps to achieve better agreement between the theoretical and experimental results.

From the analysis, the paper can conclude that by introducing a suitably chosen temperature gradient, non-homogeneous compressible circular cylinder with internal and external pressure for non-linear measure is on the safer side of the design as compared to the cylinder without temperature because circumferential stresses are less for cylinder with temperature as compared to cylinder without temperature.

Introduction of temperature gradient leads to the idea of “Stress Saving” and minimizing the possibility of fracture of cylinder.

The paper shows that circumferential stresses are less for cylinder with temperature gradient as compared to cylinder at constant temperature, which leads to the idea of “Stress Saving” and minimizing the possibility of fracture of cylinder.

This study aims to investigate the thermal creep behavior of steel frame assemblies with shear tab connections subjected to transient-state fire temperatures. Different key parameters are investigated to study their effect on the global response of the steel frames in fire.

Finite element (FE) models of connection assemblies are first analyzed using Abaqus under transient-state temperature conditions and validated against experimental work available in the literature. Upon acquiring the validated conditions, parametric studies are carried out to study the effect of key geometric and heating parameters on the overall response of the frame assembly to fire temperatures. Thermal creep material is also incorporated in the analyses through a user-defined subroutine, and a comparison between including and excluding creep material is illustrated to show the effect of thermal creep on the structural behavior.

The results reported herein indicate that having a rigid column increases the thermal-induced axial forces, thus increasing the development of thermal creep strains. Slow heating rates can cause axial stress relaxation in the restrained beam and increase the mid-span deflection and consequently the development of beam catenary action. The results also show that reaching higher initial cooling temperatures and having longer cooling phase durations result in more tensile forces at the end of the cooling phase.

Previous studies were limited to isolated steel connections under steady-state conditions. This study investigates the creep behavior of shear tab connection assemblies under transient-state conditions of fire when creep effects are explicitly considered. This can provide a rational and realistic assessment of the steel behavior in fire events.

The purpose of this paper is to derive the exact analytical expressions for torsion and bending creep of rods with the Norton-Bailey, Garofalo and Naumenko-Altenbach-Gorash constitutive models. These simple constitutive models, for example, the time- and strain-hardening constitutive equations, were based on adaptations for time-varying stress of equally simple models for the secondary creep stage from constant load/stress uniaxial tests where minimum creep rate is constant. The analytical solution is studied for Norton-Bailey and Garofalo laws in uniaxial states of stress.

The creep component of strain rate is defined by material-specific creep law. In this paper the authors adopt, following the common procedure Betten, an isotropic stress function. The paper derives the expressions for strain rate for uniaxial and shear stress states for the definite representations of stress function. First, in this paper the authors investigate the creep for the total deformation that remains constant in time.

The exact analytical expressions giving the torque and bending moment as a function of the time were derived.

The material isotropy and homogeneity preimposed. The secondary creep phase is considered.

The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk springs.

The new, closed form solutions with commonly accepted creep models allow a deeper understanding of such a constitutive model's effect on stress and deformation and the implications for high temperature design. The application of the original solutions allows accurate analytic description of creep and relaxation of practically important problems in mechanical engineering. Following the procedure the paper establishes closed form solutions for creep and relaxation in helical, leaf and disk springs.