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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.

In this addendum, the purpose of this paper is to introduce the new creep law for the description of the different stages of creep. The introduced creep law generalizes the creep law used in Kobelev (2014).

The new generalized creep law demonstrates the relationship between creep rate and stress as well as accounts the time dependence in different creep regimes. In the stage of primary creep there is explicit time dependence of creep rate. In the stage of secondary creep the creep rate exhibits – analogously to the original creep law – no explicit dependence on time.

The closed form expressions giving the torque and bending moment as a function of the time are provided. The method is applicable for definite other stress functions in the creep law.

The arbitrary creep law allows the separation of time and spatial variables; exponential and power-law time dependence.

The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk spring, driveshafts, torque elements of machine dynamics.

The new creep model with fractional derivative of time dependence is introduced. The closed form solutions for new creep model allow simple formulas for creep effect on stress and deformation and the implications for high temperature design.

Solder joint long‐term reliability is an ultimate requirement for electronics packaging. Solder joint failure, however, can involve complex mechanisms. One of many basic failure processes in metals/alloys is the creep phenomenon. Creep is defined as a time‐dependent deformation when a material is subjected to a stress for a prolonged period of time. This time‐dependent deformation can theoretically occur at any temperature above absolute zero. However, creep‐dominant failure normally occurs under high temperature in relation to the melting point of the material. Common solders are low temperature alloys with melting point or liquidus/solidus temperature in the range of 120–320°C. Therefore a detectable creep process under low level of mechanical load is expected even at ambient temperature. This paper presents the preliminary data on the comparative creep rate of twenty‐two common solder alloys and attempts to correlate the creep rate to the tensile strength, modulus, melting point and microstructure of alloys. The alloys under study include Sn/Pb, Sn/Pb/Ag, Sn/Ag, Sn/Sb, Sn/Pb/Bi, Sn/Pb/Sb, Sn/Bi, Sn/In, and Pb/In systems. This paper also discusses the proposed mechanisms for solder creep phenomena. It is hoped that the data in this work will provide additional fundamental mechanical properties of various solder alloys, which are much needed to facilitate the design of reliable solder joint structure.

In an attempt to improve service life of lead‐free Sn‐based electronic solder joints, compatible reinforcements were introduced by in‐situ and mechanical mixing methods. The reinforcements affect the steady‐state creep rate and the strain for the onset of tertiary creep of the solder joints. However, neither of these parameters, when considered alone, can be used for evaluating the reliability of solder joints. The Larson‐Miller parameter, and a new parameter proposed in the paper, can incorporate test parameters to arrive at a reliability prediction methodology. The role of these reinforcements in homogenising creep strain within the joint is analysed. The observed creep behaviour of these composite solders is discussed on the basis of interfacial bonding strength between the reinforcement and the solder matrix.

A mathematical model has been developed to predict steady state creep response of a rotating disc made of SiC (particle/whisker) reinforced 6061Al matrix composite. The model is used to investigate the effect of SiC morphology on the creep behavior of composite disc. The steady state creep behavior has been described by Sherby’s creep law. The creep stresses and creep rates are significantly affected by the morphology of SiC. The steady state creep rates in whisker reinforced disc are observed to be significantly lower than those observed in particle reinforced disc.

The purpose of this paper is to investigate the creep properties of Sn‐0.7Cu composite solder joints reinforced with optimal nano‐sized Ag particles in order to improve the creep performance of lead‐free solder joints by a composite approach.

The composite approach has been considered as an effective method to improve the creep performance of solder joints. Nano‐sized Ag reinforcing particles were incorporated into Sn‐0.7Cu solder by mechanically mixing. A systematic creep study was carried out on nano‐composite solder joints reinforced with optimal nano‐sized Ag particles and compared with Sn‐0.7Cu solder joints at different temperatures and stress levels. A steady‐state creep constitutive equation for nano‐composite solder joints containing the best volume reinforcement was established in this study. Microstructural features of solder joints were analyzed to help determine their deformation mechanisms during creep.

The creep activation energies and stress exponents of Ag particle‐enhanced Sn‐0.7Cu lead‐free based composite solder joints were higher than those of matrix solder joints under the same stress and temperature. Thus, the creep properties of nano‐composite solder joints are better than those of Sn‐0.7Cu solder joints.

The findings indicated that nano‐sized Ag reinforcing particles could effectively improve the creep properties of solder joints. A new steady‐state creep constitutive equation of nano‐composite solder joints was established. Deformation mechanisms of Sn‐0.7Cu solder and nano‐composite solder joints during creep were determined.

This paper aims to propose a methodology to remove inherent implicit creep from the Eurocode 3 material model for steel and to present a creep-free analysis on simply supported steel members.

Most of the available material models of steel are based on transient coupon tests, which inherently include creep strain associated with particular heating rates and load ratios.

The creep-free analysis aims to reveal the influence of implicit creep by investigating the behaviour of simply supported steel beams and columns exposed to various heating regimes. The paper further evaluates the implicit consideration of creep in the Eurocode 3 steel material model.

A modified Eurocode 3 carbon steel material model for creep-free analysis is proposed for general structural fire engineering analysis.

The discrete element method (DEM) was used to stimulate creep processes in granular materials. The authors present the main features of the numerical model, which include a new viscous mechanism for particle sliding, a new feedback technique for maintaining constant stress during creep, and a scaling technique that allowed monitoring the long‐term creep behaviour of a granular assembly. The creep behaviour of the numerical model exhibited the essential characteristics of soil creep—a creep rate that decreased rapidly with time, an increase in the creep rate with the applied deviator stress, and the beginning of creep rupture. The model's numerical performance is discussed, and representative 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 this study is to describe the mechanism of single-crystal high-temperature creep deformation, predict the creep life more accurately and study the creep constitutive and lifetime models with microstructure evolution.

The mechanical properties of nickel-based single-crystal superalloy are closely related to the γ' phase. Creep tests under four different temperature and stress conditions were carried out. The relationship between creep temperature, stress and life is fitted by numerical method, and the creep activation energy is obtained. The creep fracture surface, morphology and evolution of strengthening phase (γ') and matrix phase (γ) during different creep periods were observed by scanning electron microscope. With the increase of creep temperature, the rafting time is advanced. The detailed morphology and evolution of dislocations were observed by transmission electron microscope (TEM).

With the increase of creep temperature, the rafting time is advanced. The detailed morphology and evolution of dislocations were observed by TEM. Dislocations are mainly concentrated in the γ channel phase, especially at high temperature and low stress.

A creep constitutive model based on the evolution of γ' phase size and γ channel width was proposed. Compared with the experimental results, the predicted creep life is within 1.4 times error dispersion band.