Compressive creep behaviour of Mg–Li–Al alloy

Abstract

The compressive creep behaviour of as cast Mg–14Li–1·3Al (wt-%) alloy was investigated in the temperature range of 20?85°C and under different compressive stress in the range of 37·3–74·6 MPa with special apparatus. Primary creep deformation and steady creep rate increase with temperature and applied stress. The compressive creep behaviour obeys an empirical equation ln t=C?nln σ + Q/RT, where t is the time to a selected creep strain, σ is the applied stress, T is the absolute temperature, R is the gas constant, and C, n, and Q are constants for the experimental alloy. The average values of the exponent n and the creep activation energy Q are 4·33 and 101·13 kJ mol^?1 respectively. The creep rate controlling mechanism is the dislocation climb and the lattice diffusion of Li in the experimental alloy under the testing conditions.     

Impression creep behaviour of tin based lead free solders

Abstract

Growing concern about the toxic effects of lead in conventional solders has prompted the development of lead free solders. Creep owing to heating in service is one of the causes of solder joint failures in electronic packages. The present study deals with the impression creep behaviour of eutectic Sn – 58Bi, Sn – 57Bi – 1˙3Zn and Sn – 38Pb alloys in the temperature range 303 – 393 K and stress range 2˙6 – 180 MPa. Power law creep with stress exponent n varying from 2 to 6˙3 is observed. All the alloys reveal a strong stress dependence of activation enthalpy with values 155, 120 and 112 kJ mol^-1 for Sn – 58Bi, Sn – 57Bi – 1˙3Zn and Sn – 38Pb, respectively, which are well above those for self-diffusion. The steady state impression velocity varies linearly with punch diameter for all three alloys. It is concluded that a mechanism such as forest intersection involving attractive junctions controls the creep flow in these alloys.     

Effect of superimposed oscillations on creep behaviour of Al – 2 4·.5Cu and Al – 2 4·5Cu – 2 0·1In (wt-%) alloys containing θ′ precipitates

Abstract

The behaviour of both transient and steady state creep of Al – 4·5Cu and Al – 4·5Cu – 0·1In (wt-%) alloys was investigated using a constant stress where torsional oscillations of different frequencies and shear strain amplitudes were operated at various working temperatures. An augment in both transient and steady state creep rates was observed by increasing both frequency and shear strain amplitude of the applied oscillations. The mean values of the activation energy of both alloys for both creep stages were found to be equal to that quoted for dislocation intersection mechanism.     

Impression creep of Sn–40Pb–2·5Sb peritectic solder alloy

Abstract

The power law creep behaviour of the Sn–40Pb–2·5Sb peritectic solder alloy was investigated using an impression test apparatus. The tests were carried out under constant stress in the range 17 to 39 MPa and at temperatures in the range 296 to 363 K. Assuming a power law relationship between the impression velocity and stress, power law stress exponents in the range 1–3 were determined. Analysis of the data showed that for all loads and temperatures, the activation energy was stress independent with values in the range 51–56 kJ mol^-1. Based on the stress exponents obtained and activation energy data, it is proposed that grain boundary diffusion is the major mechanism for creep of the Sn–Pb–Sb peritectic alloy under these test conditions.     

A model based creep equation for 9Cr–1Mo–0·2V (P91 type) steel

Abstract

The isothermal constant stress creep tests data for a 9Cr–1Mo–0·2V (P91 type) steel were submitted for a phenomenological analysis in order to obtain the relevant creep equation for such steel. Namely, the minimum creep strain rate of P91 type steel cannot be described by the simple Arrhenius type power law constitutive model. The incorporation of the threshold stress concept in the analysis of creep data leads to a modified power law, which satisfactorily describes the creep behaviour of the examined P91 steel. However, the threshold stress is not a good material parameter, as it often varies with temperature and/or applied stress. This adds uncertainty to the extrapolation of the creep rates into ranges where experimental data are not available. Besides the fact that the physical foundation for a threshold stress is questionable from a scientific point of view, this is a serious practical limitation of the modified power law creep equation. The second creep equation proposed in the present paper is the improved stress dependent energy barrier model. The improvement of the standard model is based on two assumptions: first, on the hypothesis that the application of a stress also affects the energy barrier to be overcome when a local region transitions from the initial to the final state, and second, by applying a simple power function of stress instead of a hyperbolic sin function in the model based equation. The obtained value of stress exponent, n=5·5, is too high for entirely climb controlled creep. The apparent activation energy of approximately 510 to 545 kJ mol^?1, which is considerably higher than the activation energy for lattice diffusion, is the stress dependent activation energy of the slowest, dominant rate controlling process of the supposed multiple creep mechanisms.     

Effect of isothermal aging on room temperature impression creep of lead free Sn–9Zn and Sn–8Zn–3Bi solders

Abstract

The influence of isothermal aging on the creep behaviour of Sn–9Zn and Sn–8Zn–3Bi solder alloys was studied by impression testing. The tests were carried out under constant impression stress in the range from 90 to 230 MPa at room temperature. Aging affected the microstructure and, thus, the creep behaviour of the materials. The binary Sn–9Zn alloy, with an as cast microstructure characterised by an almost uniform distribution of fine Zn precipitates, was much more creep resistant than the aged condition containing a more sparse precipitate in a softer matrix. In the ternary Sn–8Zn–3Bi alloy, however, isothermal aging enhanced Bi precipitation with almost no change in the distribution and density of Zn particles, the result being an improved creep resistance of the aged material. Irrespective of the processing condition, Sn–8Zn–3Bi showed much lower steady state creep rates than the Sn–9Zn due to both precipitation and a solid solutioning effect of Bi in the Sn matrix. The stress exponents of the as cast and aged conditions were found to be respectively 8·5 and 7·7 for Sn–9Zn and 9·8 and 7·8 for Sn–8Zn–3Bi. These values are in agreement with those determined by room temperature conventional creep testing of the same materials reported in the literature.     

Creep behaviour of AZ61 magnesium alloy at low stresses and intermediate temperatures

Abstract

Tensile creep response was investigated for AZ61 alloy (Mg - 6.4Al - 0.9Zn - 0.2Mn, wt-%) of mean linear intercept grain size ~ 25 μm at stresses in the range 0.9 - 4 MPa over the temperature range 250 - 346°C. Bingham behaviour is obtained with strain rate ? under stress σ given by ?∝σ - σ_o with a threshold stress σ_o decreasing from 1.25 MPa at 210°C to ~ 0.5 MPa at 346°C, which is similar to earlier work on pure magnesium. The corresponding Arrhenius plot of log (Td?/d σ) versus T^-1 indicates an activation energy comparable with that expected for the grain boundary self-diffusion coefficient D _B, and values of D _Bδ (where δ is the effective grain boundary thickness) derived from the Coble equation are also similar to those for pure magnesium. Grain elongation in the direction of the tensile stress is also consistent with the key indicative feature of diffusional creep: deposition of material at grain boundaries nearly transverse to the axis of tensile stressing. Strain rates versus stress are shown to be continuous with published results for superplastic flow of AZ61 at comparable temperatures but higher stresses.     

Creep damage and grain boundary precipitation in power plant metals

Abstract

There is clear evidence that creep damage in power plant steels is associated with grain boundary precipitates. These particles provide favourable nucleation sites for creep damage such as grain boundary cavities and microcracks. Monte Carlo based grain boundary precipitation kinetics is combined with continuum creep damage mechanics (CDM) to model both the microstructural evolution and creep behaviour in power plant metals. It is found that grain boundary precipitates, such as M₂₃C₆ in most Cr containing ferritic steels, are harmful to the creep properties of the material, in line with experimental observations. It is also found that to improve the creep behaviour of the material, means should be found either to increase the proportion of MX type particles, such as VN, or to decrease or remove the larger grain boundary precipitates, such as M₂₃C₆. Hafnium has been ion implanted into thin foils of a 9 wt-%Cr ferritic steel to study the effect of hafnium on the grain boundary precipitation kinetics. It is found that the implantation of hafnium to the steel completely prohibits the formation of the common grain boundary M₂₃C₆ particles. Instead, two new types of precipitates are formed. One is hafnium carbide, which is an MX type precipitate, and is very small in size and has a much higher volume fraction as compared with the volume fraction of VN in conventional power plant ferritic steels. The other is Cr- and V-rich nitride of formula M₂N. CDM modelling shows that implantation of hafnium can markedly improve the creep property of the material. In addition, the replacement of M₂₃C₆ with hafnium carbide increases the concentration of Cr in the matrix and is expected to improve the intergranular corrosion resistance of the material.     

Constitutive modelling and springback prediction for creep age forming of 2124 aluminium alloy

Abstract

In order to improve the mechanical properties and reduce fabrication cost of large sheet metal parts, creep age forming (CAF) technology was developed, which is a process combined creep forming and heat treatment together. Springback of the workpiece in CAF is directly related to process parameters, such as, aging time, experimental stress and temperature. The aim of this paper is to establish a set of creep constitutive model, which can accurately predict the springback of 2124 aluminium alloy in CAF. A series of creep tests were carried out under different stress levels as 200, 225 and 250 MPa, and different temperatures as 185, 190 and 195°C for the solid solution treated and quenched 2124 aluminium alloy. Based on creep test data, a set of classic creep constitutive equations were established. Some important conclusions were drawn: the fitting curves of the constitutive equations could describe the test data in a good way; the creep strain increases with the increasing aging time, temperature and experimental stress. Then the springback of 2124 aluminium alloy during CAF process were analyzed by the finite element software MSC.Marc. Comparisons between the experiment analyses and finite element models show good correlation, and approve the forecast capability of FEM simulation for springback after CAF. At the end, the influence of process parameters on springback is studied, which provides essential foundation for designer to evaluate scheme and to optimise tool system design.     

First order reaction kinetics for transient creep in NiAl hardened austenitic steel

Abstract

Transient creep of an NiAl hardened austenitic steel was analysed in the temperature range of 823 to 923 K at stresses ranging from 150 to 450 MPa in the frame work of first order reaction kinetics. The present analysis is aimed: to correlate various transient creep parameters with steady state creep rate following first order reaction rate theory to obtain correlation constants; and to arrive at a unified equation to describe primary and steady state regimes of the creep curves in terms of correlation coefficients thus derived. Good correlation of transient creep parameters with steady state creep rate has been obtained over the test conditions studied indicating that the basic mechanism of deformation is the same for all the three stages of creep. Unified equation that fits the experimental creep strain time data for different test conditions over transient and steady state regimes has been obtained in terms of correlation coefficients.     

Influence of surface modification and long-term exposure on mechanical creep properties of γ-TiAl G4

Abstract

An investigation of the corrosion processes were performed for coated and uncoated γ-TiAl G4, an alloy designed to work in the temperature range 750 – 800°C, where oxidation and corrosion phenomena occur. An aluminising pack cementation treatment was used to improve the oxidation resistance of this γ-TiAl G4 alloy. Cyclic corrosion tests were performed at 800°C in air for up to 800 1-hour cycles with a Na₂SO₄/NaCl mixture. The influence of both aluminisation and the corrosion phenomena on the creep behaviour was investigated. The cyclic corrosion resistance of the coated γ- TiAl G4 was shown to be improved by aluminising. The pack cementation treatment had no detrimental effect on the creep behaviour. Moreover, neither is creep affected by the corrosion of coated specimens. As corroded uncoated specimen exhibited good creep behaviour, it can be concluded that this alloy is suitable, even without coating, for turbine applications in hot corrosion atmospheres at least up to 800°C.     

Numerical modelling of small disc creep test

Abstract

The small disc creep test is described. The disc creep curves observed need to be related to the creep properties of the material obtained by conventional testing. This relationship should include a means of assessing the creep damage which is initially present in the material and therefore to an estimate of remanent life. There are difficulties with such correlations and these are shown to be related to an imperfect understanding of the complex nature of the small punch test. This understanding can be improved by suitable physical modelling of the deformation occurring. The present paper describes a suitable finite element model and verifies the model against experimental observations of disc creep tests. The model uses a realistic creep deformation law which includes strain hardening, thermal softening and damage accumulation for 0·5Cr0·5Mo0·25V steel. It is shown that the results obtained from the test are sensitive not only to the initial condition of the specimen but also to the conditions of the test (e.g. the values of frictional forces at the punch/specimen interface). The paper makes suggestions of how the model may be used to optimise the disc creep test.     

Deformation behaviour and new constitutive equation utilising the grain size of commercial TC6 titanium alloy

Abstract

Isothermal compression tests on a commercial TC6 titanium alloy have been conducted at deformation temperatures of about 800 – 1040°C, strain rates of 0.001 – 50 s^-1 and height reductions of 30 – 50%. The microstructural evolution is represented through the measured grain size of the prior α-phase. Meanwhile, a new constitutive equation, which includes the grain size, is established for high temperature deformation behaviour. The procedure required to formulate a constitutive equation from the experimental results is presented. The constitutive equation to model the behaviour of the TC6 titanium alloy during high temperature deformation is validated and its formulation is presented. The results show that the present equation is satisfactory for describing the behaviour of the TC6 titanium alloy during high temperature deformation. The maximum difference between the calculated and the experimental results is less than 15%.     

Anisotropic viscoplasticity constitutive model for directionally solidified superalloy

Abstract

The macroscopic deformation behaviour of a Ni-based directionally solidified (DS) superalloy was experimentally investigated, and an anisotropic constitutive model of the material was developed. Monotonic and creep tests were performed on uniaxial test specimens machined from DS plates so that the angle between the loading direction and the solidified grain direction varied between 0 and 90°. Tension-torsion creep tests were also conducted to examine the anisotropic behaviour under multiaxial stress conditions. The material exhibited marked anisotropy under elastic and viscous deformation conditions, whereas it showed isotropy under plastic deformation conditions of high strain rates. Then crystal plasticity analyses were carried out to identify slip systems under creep loading conditions, assuming the anisotropic creep behaviour of the DS material. A viscoplastic constitutive model for expressing both the anisotropic elasticity-viscosity and the isotropic plasticity was proposed. The elastic constants were determined using a self-consistent approach, and viscous parameters were modelled by crystal plasticity analyses. The calculation results obtained using the constitutive model were compared with the experimental data to evaluate the validity of the model. It was demonstrated that the constitutive model could satisfactorily describe the anisotropic behaviour under uniaxial and multiaxial stress conditions with a given set of material parameters.     

The θ projection method applied to small strain creep of commercial aluminium alloy

Abstract

The paper describes the early uniaxial creep behaviour of an airframe aluminium alloy (2419-T851). Tests were conducted over the temperature range 373 to 463 K and for rupture lives up to 7000 ks. The shapes of creep curves were fitted using either the conventional 4-Θ equation or the recently proposed 6-θ equation. Coefficients allowing the interpolation of times to small strains were produced and the accuracy of such interpolations was checked against experimental values. At small strains, the 4-Θ equation produced systematic errors but the 6-θ function gave expected values of errors which could not be distinguished from zero. At larger strains, both methods yielded zero mean errors. The procedures are discussed in terms of the likely deformation mechanisms which might lead to the observed forms of the projection equations. It seems likely that very early creep contains some strain due to anelastic grain boundary relaxation.     

The effect of material behaviour on the analysis of single crystal turbine blades: Part I – Material model

ABSTRACT This paper describes a slip system model developed for the analysis of modern single crystal superalloys – specifically, the first generation alloys RR2000 and SRR99, and the second generation alloy CMSX‐4. The single crystal model is implemented as an ABAQUS User MATerial (UMAT) subroutine, the framework is based on the classical theory of single crystal plasticity. The constitutive equations used have different formulations based on the micromechanisms of deformation and experimental measurements. The emphasis is on the effect of incorporating the micromechanisms of material behaviour on predicted macroscopic results. Several important phenomena and mechanisms, which are required for explaining creep properties as a function of stress, temperature and orientation are identified and included in the model. These include: activation of < 101 > {111} and < 112 > {111} slip systems, rigid body rotation, continuum damage, slip system softening, dislocation interaction, threshold behaviour and rafting. Model simulations are compared with experimental data in various deformation regimes. In a later part of the paper, the model is used to analyse the performance of a single crystal turbine blade. This enables the effect of the micromechanisms of deformation on overall component behaviour to be quantified.     

High temperature creep behaviour of single crystal superalloy

Abstract

Creep behaviour of a newly developed single crystal nickel base superalloy DMSX-l (Ni-7.7Co-6.4Cr-8.4W-0.3Ti-S.S7 Al-7.6Ta-Nf-Y-Nb-Re, wt-%) with 〈001〉 orientation has been analysed and compared with the reported data ofSRR99. It was concluded that the shear stress based model developed for SRR99 is also applicable for the new alloy. Although the material constants for octahedral slip for the new alloy are not exactly the same as those of SRR99, the estimated values of initial creep rate and softening coefficients are nearly of the same order. Therefore it is concluded that in the absence of a material database for cube slip for this new alloy, those available for SRR99 could be used to predict the orientation dependence of its creep behaviour.     

Tensile creep behaviour of coarse grained copper foils at high homologous temperatures and low stresses

Abstract

Tensile creep behaviour of OFHC copper in the temperature range 850 to 1074°C (0·83 to 0·99T_m) under low stress (0·1 to 0·6 MPa) has been investigated in tension for 0·4 and 0·6 mm thick foils with grain size ～1 mm, in the plane of the foils. Increases in creep rate per unit stress at 0·99T_m were two orders of magnitude higher than predicted for Nabarro–Herring diffusional creep and were nearer to values expected from the operation of grain size independent Harper–Dorn creep, but the stress exponent n was closer to 2 than to the n=1 expected in this mechanism. Observations on specimen surfaces revealed some widely spaced slip bands, some small grain boundary movements and occasional cavitation on grain boundaries nearly perpendicular to the stress. Creep rates were comparable with predictions of the movement of dislocations, controlled by the rate of their generation at Bardeen–Herring sources at a spacing similar to that of the observed slip lines.     

Examination of breakdown stress in creep by viscous glide in Al–5·5 at.-%Mg solid solution alloy at high stress levels

Abstract

Creep tests on Al–5·5 at.-%Mg solid solution alloy show that the stress exponent n increases with increasing stress from 3·1 to 5·5. It is demonstrated that the transition to n≈5·5 is not consistent either with normal power law breakdown or with a transition to a region of viscous glide controlled by pipe diffusion, but the results are in good agreement with a breakdown of the dislocations from their solute atmospheres. The activation energies for creep at low and high stresses are 136 and 170 kJ mol^?1 respectively.     

A new creep damage assessment method for metallic material under variable load conditions at elevated temperature

It is significant for structural design and maintenance to assess behaviour and life under varying load conditions. For structures operating in high‐temperature environments, creep is one mechanism responsible for material failures. In this paper, different damage accumulation rules were reviewed, and a new creep damage assessment method was proposed based on the creep damage tolerance parameter λ and load factor Φ. By introducing the creep damage tolerance parameter λ and the minimum creep rate, the loading process and creep behaviour of the material are taken into account in a damage assessment. The parameters in the model can be obtained by the simple variable load creep test, and the remaining life and strain can be predicted using uniaxial creep test data. To analyse the applicability and accuracy of this new model, the strain histories, the life of step load, and the constant load creep from experiments on a titanium alloy at 500°C were obtained, and the prediction results of the novel and previous methods were carefully investigated.