Rapid assessment of steady-state creep rates and stress dip effects in solder alloys

Rapid comparisons of traditional and lead-free solders have been made using self stressing spirals. A novel extension of the technique has been used to create stress-dip effects during the steady-state regime. Reverse creep, incubation times, and changed post-dip creep rates have been observed which are free from the uncertainties of conventional stress-dip testing. The time to the re-establishment of forward creep has been used to determine the activation energy of the restoration processes. Re-established creep rates have been shown to be comparable to steady-state creep rates for modest stress dips. Larger stress reductions give higher post-dip creep rates that are closer to primary rates indicating that reverse yielding has disturbed the steady-state dislocation arrangements. Such events could occur in solder joints that are subjected to variable loading.     

Large strain constitutive modelling and computation for isotropic,creep elastoplastic damage solids

A three-dimensional fully coupled creep elastoplastic damage model at finite strain for isotropic non-linear material is developed. The model is based on the thermodynamics of an irreversible process and the internal state variable theory. A hyperelastic form of stress–strain constitutive relation in conjunction with the multiplicative decomposition of the deformation gradient into elastic and inelastic parts is employed. The pressure-dependent plasticity with strain hardening and the damage model with two damage internal variables are particularly considered. The rounding of stress–strain curves appearing in cycling loading is reproduced by introduction of the creep mechanism into the model. A numerical integration procedure for the coupled constitutive equations with three hierarchical phases is proposed. A consistent tangent matrix with consideration of the fully coupled effects at finite strain is derived. Numerical examples are tested to demonstrate the capability and performance of the present model at large strain.     

Effect of stress regime‐dependent creep behaviour on measurement of creep strain rate based on small specimen techniques

Small specimen creep testing technique has become a hot topic of research as bulk materials are not available in many occasions. The stress distributions in the small specimens such as small punch and 3‐point bending specimens are essentially nonuniform. As it is known, the creep deformation/damage accumulation mechanisms exhibited at a high stress regime are not the same as the ones at a lower stress regime for many engineering alloys. The potential measurement errors because of stress regime‐dependent creep behaviour, however, has not been considered in the determination of the creep parameters based on small specimen testing in the previous studies. In this paper, 2 kinds of materials that show different Norton's parameters at the corresponding stress regimes are examined. A simple case of 2‐bar structure is firstly adopted to illustrate the measurement error of creep strain rate because of stress regime‐dependent creep behaviour. Furthermore, clamped beam bending testing and small punch testing are investigated to demonstrate the significance of measurement error using the same materials. It is shown that an error of more than 8 times may occur near the transition point of creep deformation mechanism depending on specimen types and materials. Attention should thus be paid to the selection of stress level in the small specimen testing to avoid significant measurement errors.     

Internal stress and unloading experiments in creep

Internal stresses are developed during deformation and have an important role in determining the mechanical properties and, in particular, the creep properties of crystalline materials. The strain transient dip test is the generally accepted method for the determination of internal stresses developed during creep. The strain transient dip test has been analysed using a number of very general creep models and it is concluded that, for glide-controlled creep, the dip test can only be interpreted if the relation between dislocation velocity and the force on the dislocation is linear. When this is the case it measures not an average internal stress but an average back stress for all the dislocations, mobile and immobile, where the back stress is the resolved component of the internal stress plus the glide component of the line tension force divided by the Burgers vector. The dip test does not allow separation of the back stress into internal stress and line tension components. For recovery models the results of the dip test cannot be simply interpreted because expressions for the creep rate do not define a unique average internal stress or back stress. However, for the recovery model in which strain occurs by athermal or jerky glide there will be a reverse yield stress, i.e. there will be a stress reduction below which there will be instantaneous reverse strain followed by reverse creep. By averaging the instability condition for all the dislocations participating in jerky glide it is shown, subject to assumptions, that the sum of the average internal stress experienced by dislocations involved in both forward and reverse creep can be obtained from the reverse yield stress. Separate values for these internal stresses cannot be obtained, however. Determination of the reverse yield stress for recovery creep is the experiment equivalent to the strain transient dip test for glide-controlled creep.Research visitor from University of Aix-Marseille 11, France.     

Experimental evaluation of the interaction effect between plastic and creep deformation

An experimental study of plasticity-creep interaction effects is reported. The combined stress tests are performed on thin wall tubular specimens of SUS 304 stainless steel at room temperature and high temperature (600° C). The plastic behaviors subsequent to creep pre-strain and creep behaviors subsequent to plastic pre-strain are obtained for loading along straight stress paths with a corner. The inelastic behaviors including both plastic and creep deformations are experimentally investigated. The interaction effects between plastic and creep deformations are quantitatively estimated with the equi-plastic strain surface.     

Primary and Anelastic Creep of a Near α-Ti Alloy and Their Dependencies on Stress and Temperature

The primary creep behaviour of a high temperature near -Ti alloy Ti6242Si has been investigated in the temperature range from 500 to 625°C, and the stress range from 80 to 450 MPa. The results are analysed in terms of the dependencies of stress on strain (strain hardening) and on strain rate (strain rate sensitivity). Furthermore, full unloading experiments were conducted in order to gain additional information as to the nature of primary creep. It is shown that primary creep can be described by an athermal component, strain hardening, with a mean strain hardening coefficient of 0.37, and a thermally activated component, strain rate sensitivity, with a strain rate sensitivity coefficient suggesting a mechanism based on climb controlled recovery. This is confirmed by the activation energy of 259 kJ/mol determined at different stresses, which is similar to the activation energy of Ti self diffusion in -Ti. The anelastic strain obtained on full unloading was analysed in its fast stage in a similar way. The kinetics of anelastic creep and its activation energy are in many aspects very similar to those of primary creep. It is thought that, in the stress and temperature range investigated, primary creep is to a relatively high extent anelastic in nature, and is controlled by the climb controlled bow out of pinned dislocation segments, particularly dislocations pinned at lath boundaries.     

Assessment of power law creep constants of Gr91 steel using small punch creep tests

A method for determining the power law creep constants using the small punch (SP) creep test is studied. We performed elastic-plastic-secondary creep finite-element (FE) analysis of Gr91 (ASTM A387 GR91 CL2) steel using the properties at 565 °C to investigate the evolution of stress and strain rate at the weakest location of the SP creep specimen, i.e. at the annular region located at about 0.7 mm from the centre of the specimen. Empirical relations that correlate the applied load to the equivalent stress and the punch displacement rate to the equivalent creep strain rate are suggested on the basis of the finite-element stress analysis results. These simple relations enable us to achieve the constitutive relation of equivalent stress and equivalent creep strain rate under small punch creep test condition. To validate this approach, SP creep tests were conducted and creep constants were evaluated by using the proposed relations. These evaluated creep constants were then compared with those measured from standard uniaxial creep test. It is shown that creep constants evaluated from the SP creep test and the proposed method are in a good agreement with those from the uniaxial creep test.     

Impression creep behaviour of magnesium alloy-based hybrid composites in the transverse direction

The creep behaviour of a creep-resistant AE42 magnesium alloy reinforced with Saffil short fibres and SiC particulates in various combinations has been investigated in the transverse direction, i.e., the plane containing random fibre orientation was perpendicular to the loading direction, in the temperature range of 175–300 °C at the stress levels ranging from 60 to 140 MPa using impression creep test technique. Normal creep behaviour, i.e., strain rate decreasing with strain and then reaching a steady state, is observed at 175 °C at all the stresses employed, and up to 80 MPa stress at 240 °C. A reverse creep behaviour, i.e., strain rate increasing with strain, then reaching a steady state and then decreasing, is observed above 80 MPa stress at 240 °C and at all the stress levels at 300 °C. This pattern remains the same for all the composites employed. The reverse creep behaviour is found to be associated with fibre breakage. The apparent stress exponent is found to be very high for all the composites. However, after taking the threshold stress into account, the true stress exponent is found to range between 4 and 7, which suggests viscous glide and dislocation climb being the dominant creep mechanisms. The apparent activation energy Q_c was not calculated due to insufficient data at any stress level either for normal or reverse creep behaviour. The creep resistance of the hybrid composites is found to be comparable to that of the composite reinforced with 20% Saffil short fibres alone at all the temperatures and stress levels investigated. The creep rate of the composites in the transverse direction is found to be higher than the creep rate in the longitudinal direction reported in a previous paper.     

Predicting the tensile creep of concrete

Over a four year period, six phases of testing were performed to observe the influence of age at loading, applied stress level, mix composition and relative humidity on the tensile creep of concrete. From these investigations it was possible to develop a model which allowed the prediction of tensile creep based on a knowledge of the compressive strength of the concrete (determined at the age of loading), the applied stress level and the relative humidity. Subsequently, this model was validated using the results from three independent investigations. Compressive creep as well as tensile creep was also obtained. This allowed a comparison of compressive creep with tensile creep and illustrated that on the basis of equal stresses, tensile creep is on average between 2 and 3 times greater than compressive creep (the maximum ratio is in excess of 8). For this investigation, however, on the basis of stress/strength ratio the difference between tensile and compressive creep is less significant. Considering a simply supported flexural reinforced concrete element, the investigation suggests that it is unwise to consider actual compressive creep equal to actual tensile creep as is often the case in design practice.     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

Experimental and numerical investigation of the creep behaviour of Ni‐based superalloy GH4169 under varying loading

The high‐temperature creep experiment of Ni‐based superalloy GH4169 under the constant loading and varying loading conditions was conducted by using the round bar specimens. The creep time‐strain curves under different loading conditions were obtained to study the high‐temperature creep behaviour of GH4169 superalloy. At the same time, the longitudinal and lateral sections near the fracture of creep specimens were observed by the optical microscope, and the specimens with smaller grain corresponded to the larger creep strain rate. In view of the dispersion of the creep curves, the corresponding data processing method was put forward, and on this basis, a model that can describe the 3 stages of creep with certain physical meaning was established. The simulation results are in good agreement with the experimental results, especially the creep deformation under the varying loading condition. The predicted results of the relative time hardening model are closer to the experiment compared with time hardening and strain hardening model. The creep model is realized by the user's material subroutine code in a commercial FEM software package, which can be used as the basis of creep analysis for engineering structures.     

Room temperature creep and its effect on flow stress in a X70 pipeline steel

This paper studied the phenomenon of room creep deformation and its effect on tensile property of a X70 pipeline steel under stress-control loading pattern using round tensile test specimen. Significant time-dependent deformation under constant load was observed in the steel at room temperature, and the deformation is not only dependent on loading stress rate but also dependent on the loading process. It is also found that the loading-unloading-reloading process reduces the subsequent creep strain, while the occurrence of room temperature creep obviously enhances the subsequent yielding strength and the flow stresses.     

The cyclic creep behaviour of Type 316 stainless steel

The cyclic creep behaviour of a Type 316 stainless steel at 625° C has been examined as a function of the maximum applied stress and frequency using trapezoidal loading cycling between zero and a maximum stress. The so-called static-to-dynamic creep transition observed is interpreted in terms of recoverable anelastic strain behaviour without using an internal stress argument. Over the range of experimental conditions examined, failure occurs by static creep modes, namely wedge crack nucleation and growth. The loading strain increments appear to be damaging to about the same extent as the much slower strain occurring at constant load, such that it is the overall strain rate that determines the rate of damage. A cursory examination of square wave load cycling shows that the behaviour is very similar to that observed during trapezoidal loading and suggests that the rate of loading and unloading does not play an important part in determining the creep and rupture behaviour.     

Nanoindentation creep deformation behaviour of high nitrogen nickel-free austenitic stainless steel

Nanoindentation tests of the high nitrogen nickel-free austenitic stainless steel (HNS) were performed with peak load in a wide range of 100–600?mN to investigate the nanoindentation creep deformation behaviours. The results of the nanoindentation creep tests have demonstrated that the load plateaus, creep strain rate and creep stress of the cold-rolled HNS are larger and its creep stress exponent is smaller than the solution-treated HNS. The analysis reveals that the obvious creep deformation behaviour in the cold-rolled HNS arises from the rapidly relaxed dislocation structures in the initial transition regime, while the small creep deformation behaviour of the solution-treatedHNS is mainly attributed to that the stable dislocation structures for the intensive interactions between dislocations.     

Deformation and life assessment of high temperature materials under creep fatigue loading

The knowledge of mechanical long term behaviour under static and cyclic loading for high temperature components requires methodologies for life assessment in order to employ the full potential of materials. A phenomenological life time prediction concept which was developed for multi‐stage creep fatigue loading demonstrates the applicability of rules for synthesis of stress strain path and relaxation including an internal stress concept, as well as mean stress effects. Further, a creep fatigue interaction concept which was also developed covers a wide range of creep dominant loading as well as fatigue dominant loading. Service‐type experiments conducted at different strain rates and hold times for verification purposes demonstrate the acceptability of life prediction method for variation of conventional 1 %Cr‐steels as well as modern high chromium 9‐10 %Cr‐steels. Generally, the service life of components is influenced by multi‐axial behaviour. Multi‐axial experiments with e.g. notched specimens and with cruciform specimens accompanied by advanced methods for calculation of stress strain path and life time prediction stress conditions are of future interest.     

A finite element algorithm to study creep cracks based on the creep hardening surface

This work addresses finite element (FE) modelling of creep cracks under reversed and cyclic loads in steels. A constitutive model based on the creep hardening surface developed by Murakami and Ohno has been selected for this purpose. This model is particularly accurate for describing creep under reversed and cyclic loads and requires no additional material constants. An FE algorithm for this model has been derived and implemented into a research code FVP. The algorithm is verified by comparing the numerical predictions with closed form solutions for simple geometries and loading configurations. FE predictions are compared with experimental data for a stationary crack in a compact tension specimen. The stress and strain fields in the vicinity of a crack under a sustained load are compared with those for the intermediate unloading case. Several integral fracture parameters are investigated as to their appropriateness for describing creep cracks under reversed and cyclic loads.     

Compressive creep of Fe3Al-type iron aluminide with Zr additions

High-temperature creep of a Fe₃Al-type iron aluminide alloyed by zirconium was studied in the temperature range 873–1073 K. The alloy contained (wt.%) 31.5% Al, 3.5% Cr, 0.25% Zr, 0.19% C (Fe balance). It was tested in two states: (i) as received after hot rolling and (ii) heat treated (1423 K/2 h/air). Creep tests were performed in compression at constant load with stepwise loading: in each step, the load was changed to a new value after steady state creep rate had been established. Stress exponent and activation energy of the creep rate were determined and possible creep mechanisms were discussed in terms of the threshold stress concept. A rapid fall of the stress exponent and of the threshold stress with the increasing temperature indicates that creep is impeded by the presence of precipitates only at temperature 873 K. The results were compared with the results of long-term creep tests in tension performed recently on the same alloy. __________ Translated from Problemy Prochnosti, No. 1, pp. 117–120, January–February, 2008.     

Time-dependent creep fracture using singular boundary elements

 This paper presents a procedure for modelling singular crack tip regions of creeping, cracked structural components using singular boundary elements. These special boundary elements correctly simulate the time-dependent singular behaviour of stress and strain fields at the crack tip of creeping materials. The investigated structural components are considered to undergo time-dependent, two-dimensional creep deformation and to be subjected to remote loading conditions. The deformation of the components is assumed to be described by the elastic power law creep model. Examples of various crack problems are investigated to illustrate the efficiency of the proposed singular boundary elements for analysing creep stress and strain distribution problems and for determining some important creep fracture parameters. The effectiveness of the proposed approach is demonstrated and its accuracy is compared with the results obtained by finite element solutions for different creep conditions. Received: 27 February 2002 / Accepted: 28 May 2002 The authors are grateful to Professor D.E. Beskos for encouragement and helpful discussions during the course of this work.     

A three-stage constitutive model for the creep behaviours of high-Cr steels at elevated temperatures

In this paper, a three-dimensional constitutive model is proposed to simulate the creep behaviours of high-Cr steels at elevated temperatures. In the model, the minimum creep rate and the average creep rupture time at different temperatures and stress levels are predicted by adopting two Larson–Miller parameters. The decrease of the creep rate during the primary creep stage is captured by introducing an internal variable representing the strain hardening effect. The material parameters of the model can be identified by using the conventional experimental results. Both the strain- and stress-driven algorithms are designed to solve the constitutive evolution equations. The response of high-Cr steels during the whole creep procedure can be predicted at a quantitative level by the current model. Further implementing the model into a finite element software, the global creep behaviours of high-Cr components under realistic loading conditions can be simulated.     

Comparison of creep strength and intrinsic ductility for serviced and reheat treated T91 steel based on stress relaxation testing

Abstract

High precision stress relaxation tests (SRT) at four temperatures were conducted on T91 (9%Cr) steel after extended boiler service, and also after re-heat treatment. Relative differences in creep strength, measured over five decades in strain rate were dependent on test temperature. Using an established correlation between strain rate sensitivity and elongation at failure, intrinsic ductility values as a function of stress and test temperature were determined. The general trend of a minimum in ductility in terms of stress or strain rate was consistent with long term creep rupture data on T91, and with literature data on alloy steels. However, the precision and repeatability of the SRT analysis contrasted with the appreciable scatter and heat to heat variation in traditional testing. It is argued that the current creep strength evaluation based on the nearly constant state measurement from the SRT test is superior to the measurement of stress dependence of minimum creep rate in traditional creep rupture testing. The complexity of primary creep in laboratory testing, which may not be significant at operating stresses where loading strains may be fully recoverable (anelastic), does not apply to the SRT. Since very low strain rates are achieved in a one day test, the procedures for setting of design allowables and design analysis based on the SRT data should not be significantly different from current practice. This technique offers accelerated alloy development and optimisation for creep strength and also ductility, and hence resistance to notch sensitivity.