Deformation and failure of ice under constant stress or constant strain-rate

Fine-grained isotropic ice was tested in uniaxial compression at ?5°C. Tests were made under: (1) constant strain rate, and (2) constant stress, with total axial strains up to about 7%. Constant rate tests for the range 10^?7 to 10^?3 s^?1 gave stress/strain curves which exhibited two distinct yield points for rates up to about 10^?4 s^?1. The “initial yield point”, at which internal cracks begin to form at a high rate, occurred at strains in the range 0.03–0.6%, the strain for initial yielding increasing with strain rate. A secondary yield point occurred at axial strains close to 1%. However, above 10^?4 s^?1 the initial yield point became dominant and the secondary yield point disappeared. At the lowest rates (10^?7–10^?6 s^?1), the secondary yield point was distinct, but the initial yield occurred at a stress level equal to, or greater than, that for secondary yield. Constant stress tests for the range 0.8–3.8 MPa gave creep curves which had a minimum strain rate at strains close to 1%. For strains less than 0.2% the resolution and data sampling were inadequate for accurate determination of strain rate as a function of time or strain, but there were fairly clear indications of another strain rate minimum in the range of 0.01%–0.1% axial strain.Direct comparison of the results for constant stress and constant strain rate suggests that the two tests give much the same information when interpreted suitably. Detailed comparisons and interpretations of the data will be given in a subsequent paper.     

Stress/strain/time relations for ice under uniaxial compression

Results of mechanical tests involving uniaxial compression of isotropic ice at ?5°C were analysed and interpreted. Constant load (CL) creep tests were made for applied stresses in the range 0.8 to 3.8 MPa, and “strength” tests under constant displacement rate (CD) were made for applied strain rates in the range 10^?7 to 10^?3 s^?1. Results from CL tests and CD tests corresponded closely, giving much the same information about failure strains, strength, creep rates, time to failure, stress/strain-rate relations, and suchlike. Empirical stress/strain-rate relations were developed for three distinct states of strain: (1) for the initial yield point, where axial strains are typically of the order of 0.1%, (2) for the ductile yield point, where axial strains are typically of the order of 1%, (3) for an axial strain of 10%. Stress/strain-rate relations and stress/strain relations for constant duration of CL loading were examined for load durations up to half an hour. The elapsed time up to the ductile yield point (～1% strain) was related to stress and to strain rate for CL tests and CD tests, and correspondence of the results was demonstrated both for interrelationship between CL and CD tests and for compatibility with the appropriate stress/strain-rate relations. The elapsed time up to the initial yield point was also considered. It was shown that CD stress/strain curves can be constructed from a suitable family of CL creep curves, and vice versa.The characteristics of CL creep curves and CD stress/strain curves were examined in some detail, considering relations between strain rates for certain identifiable points on creep curves, and relations between stresses for certain identifiable parts of stress/strain curves. Effective values for quasi-elastic moduli were considered. The strains for various critical points were compared with each other and with the strains at which rates of acoustic emissions reach maximum values.     

Creep deformation behaviour of AZ31 magnesium alloy over wide range of temperature and stress

Abstract

The creep deformation behaviour of coarse grained AZ31 magnesium alloy was examined in the temperature range from 423 to 673 K (0·46–0·73T_m) under various constant stresses covering low strain rate range from 4×10^?9 to 2×10^?2 s^?1. Most shape of the creep curve was typical of class II behaviour. However, only at low stress and low temperature, the shape of the creep curve was typical of class I behaviour. At very low stress at 673 K, the stress exponent for the secondary creep rate was ～2. At low stress level, the stress exponent was ～3 and the present results were in good agreement with the prediction of Takeuchi and Argon model. At high stress level, the stress exponent was ～5 and the present results were in good agreement with the prediction of Weertman model. The transition of deformation mechanism from solute drag creep to dislocation climb creep could be explained in terms of solute atmosphere breakaway concept.     

Tensile creep behavior of Sn–Ag–Cu–Ni multicomponent lead-free solder alloy

In the process of electronic packaging, the dissolution of under bump metallizations, such as Cu and Ni, into liquid solder occurs during soldering, which can change the original solder to a multicomponent one. Under the trend of miniaturization, it is quite necessary to evaluate the properties of multicomponent solder with excessive Cu and Ni compositions. In this study, the tensile creep behavior of Sn–3.5Ag–2.0Cu–0.5Ni multicomponent lead-free solder alloy is investigated at three temperatures, i.e., 303, 348 and 393 K. The steady-rate creep rates are obtained in the range of 10^?4–10^?8 s^?1, when the normalized stress, σ/E, is in the range of 10^?4–10^?3. Based on the Dorn equation, the apparent stress exponent (n _a), threshold stress (σ _th), and activation energy of creep (Q _C) are calculated at the three temperatures. It is found that the Sn–3.5Ag–2.0Cu–0.5Ni solder alloy shows a better creep performance than pure tin and eutectic Sn–3.5Ag solder due to the strengthening effect of Ag₃Sn and (Cu,Ni)₆Sn₅ IMC precipitations. The true stress exponent for creep is identified to be 7, indicating that the creep behave is controlled by the dislocation-pipe diffusion in the tin matrix.     

Compression stress–strain and creep properties of the 52In–48Sn and 97In–3Ag low-temperature Pb-free solders

Lead (Pb)-free, low melting temperature solders are required for step-soldering processes used to assemble micro-electrical mechanical system (MEMS) and optoelectronic (OE) devices. Stress–strain and creep studies, which provide solder mechanical properties for unified creep-plasticity (UCP) predictive models, were performed on the Pb-free 97In–3Ag (wt.%) and 58In–42Sn solders and counterpart Pb-bearing 80In–15Pb–5Ag and 70In–15Sn–9.6Pb–5.4Cd alloys. Stress–strain tests were performed at 4.4 × 10^?5 s^?1 and 8.8 × 10^?4 s^?1. Stress–strain and creep tests were performed at ?25, 25, 75, and 100°C or 125°C. The samples were evaluated in the as-fabricated and post-annealed conditions. The In–Ag solder had yield stress values of 0.5–8.5 MPa. The values of ΔH for steady-state creep were 99 ± 14 kJ/mol and 46 ± 11 kJ/mol, indicating that bulk diffusion controlled creep in the as-fabricated samples (former) and fast-diffusion controlled creep in the annealed samples (latter). The In–Sn yield stresses were 1.0–22 MPa and were not dependent on an annealed condition. The steady-state creep ΔH values were 55 ± 11 kJ/mol and 48 ± 13 kJ/mol for the as-fabricated and annealed samples, respectively, indicating the fast-diffusion controlled creep for the two conditions. The UCP constitutive models were derived for the In–Ag solder in the as-fabricated and annealed conditions.     

Tensile creep study of copper with alumina dispersions prepared by high rate physical vapour deposition

Mott has suggested that the ideal creep-resistant material will be one with a fine grain size in which the grain boundaries are filled with some substance, say a refractory oxide, to inhibit the motion of grain boundaries. Such a system, alumina-dispersed copper, was prepared by high rate physical vapour deposition. The process parameters and their effect on structure and texture have been studied. The room temperature mechanical properties have also been reported. This paper deals with a high temperature mechanical property, i.e. tensile creep. Tests were made on a constant-stress vacuum creep rig with a Ferrometic feedthrough to ensure a zero leakage rotary seal. A vacuum of 1.33 X 10^?3 Pa was maintained. The test temperatures were 500°C (0.57T_m) and 700°C (0.72T_m). The stresses applied were 2.07, 3.45, 4.14 and 6.89 X 10⁷ Nm^?2. Tests were made on as-deposited films and on cold-rolled condensates.Minimum creep rate curves showed the effect of the alumina content in raising the creep resistance of copper. Cold rolling also reduced the minimum creep rate markedly. Varying the temperature and stress affected the shape of these curves. Stress-rupture plots were used to summarize the data.Grain refinement together with a fine stable dispersion seem to give improved creep strength. The critical barrier of the Orowan stress was noted. The stress exponent for a low alumina deposit (0.21 vol.%) was about 8, and the apparent activation energy for creep was about 202 kJ mol^?1 (0.13 vol.%). There was an inverse relationship between the rupture life and the minimum creep rate, their product being constant (about 0.2).     

Creep behavior of nanocrystalline Au films as a function of temperature

Freestanding nanocrystalline Au films, subjected to nominally elastic loads at 25–110 °C, demonstrated high primary (10^?7–10^?4 s^?1) and steady-state creep rates (10^?8–10^?5 s^?1). The deformation mechanisms for creep were strongly temperature dependent: grain boundary sliding-based creep dominated at room temperature and 50 °C, while the contribution of dislocation-mediated creep increased at 80 and 110 °C. The effect of applied stress on primary and steady-state creep strain at different temperatures was captured well by a non-linear model that was based on the kinetics of thermal activation. Multi-cycle creep experiments showed that at room temperature virtually all the primary strain accumulated during each forward creep cycle was recovered upon complete unloading. As the contribution of dislocation-mediated creep increased with temperature, the ratio of strain recovery to primary strain accumulated during each cycle was reduced due to the accumulation of plastic strain at higher temperatures. Notably, at all temperatures, the steady-state creep rate decreased after the first creep cycle. Moreover, the entire creep response remained virtually unchanged in all subsequent cycles, which implies that the first creep cycle resulted in mechanical annealing. This conclusion was further supported by calculations of the activation entropy: A reduction in its magnitude between the first and all subsequent creep cycles at all temperatures pointed out to mechanical annealing of initial material defects during the first loading cycle. The negative values of the calculated activation entropy indicated that entropy changes due to annihilation of defects-dominated entropy changes associated with the generation of new defects. Finally, the activation entropy for steady-state creep was temperature insensitive, but increased with stress, which is consistent with an increase in defect generation at higher stresses.     

Hot deformation behaviour of precipitation hardening stainless steel

Abstract

The behaviour of 17-4 precipitation hardening (PH) stainless steel was studied using the hot compression test at temperatures of 950–1150°C with strain rates of 0·001–10 s^?1. The stress–strain curves were plotted by considering the effect of friction. The work hardening rate versus stress curves were used to reveal whether or not dynamic recrystallisation (DRX) occurred. Using the constitutive equations, the activation energy of hot working for 17-4 PH stainless steel was determined as 337 kJ mol^?1. The effect of Zener–Hollomon parameter Z on the peak stress and strain was studied using the power law relation. The normalised critical stress and strain for initiation of DRX were found to be 0·89 and 0·47 respectively. Moreover, these behaviours were compared to other steels.     

Creep of silicon nitride-titanium nitride composites

The effect of particulate TiN additions (0–50 wt%) on creep behaviour of hot-pressed (5 wt%Y₂O₃ + 2 wt%Al₂O₃)-doped silicon nitride (HPSN)-based ceramics was studied. Creep was measured using a four-point bending fixture in air at 1100–1340 °C. At 1100 °C, very low creep rates of HPSN with 0–30 wt% TiN are observed at nominal stresses up to 160 MPa. At 1200 °C the creep rate is slightly higher, and at 1300 °C the creep rate is increased by three orders of magnitude compared to 1100 °C and rupture occurs after a few hours under creep conditions. It was established that the formation of a TiN skeleton could detrimentally affect the creep behaviour of HPSN. An increase in TiN content leads to higher creep rates and to shorter rupture times of the samples. Activation energies of 500–1000 kJ mol^?1 in the temperature range of 1100–1340 °C at 100 MPa, and stress exponentsn?4 in the stress range 100–160 MPa at 1130–1200 °C were calculated. Possible creep mechanisms and the effect of oxidation on creep are discussed.     

Creep behaviour of carbon containing Fe3Al alloy

Abstract

Tensile creep of a Fe–16 wt-%Al–0·5 wt-%C alloy was investigated over a temperature range of 773 to 873 K and stress range of 80 to 200 MPa. Creep curves exhibited very limited primary and secondary creep regimes. An extended tertiary creep regime was observed for all the test conditions. Stress dependence of minimum creep rate can be represented by a power-law equation with stress exponents being in the range 4 to 5. The activation energy for creep was found to be ～340 kJ mol^?1. The observed stress exponent and activation energy for creep suggest that creep is controlled by dislocation climb. Creep fracture in Fe₃Al–C alloy is predominantly by transgranular ductile mode by nucleation, growth and coalescence of microvoids formed at FeAlC_0·5 particle/matrix interface by decohesion as well as fracture of elongated particles. Extended tertiary creep observed in the alloy was analysed in the light of the mechanisms proposed for nickel based superalloys.     

Rate-dependent deformation of Sn–3.5Ag lead-free solder

Compression experiments on bulk Sn-3.5Ag lead-free solder specimens have been carried out to help formulate the material constitutive behaviour of this alloy using the concept of an evolving internal stress. Tests covered the temperature range 0–125 °C and fixed strain rates between 3 × 10⁻⁷–3 × 10⁻³ s⁻¹. Flow behaviour was found to be compatible with that for a deforming a tin-rich matrix (stress exponent n = 7, activation energy Q = 46.7 kJ/mol) in which the external applied stress is reduced by an internal back stress due to the presence of precipitate phase particles. Stress–strain curves have been satisfactorily modelled using rate equations incorporating linear hardening and diffusion-controlled recovery. Comparison with supplementary tension and creep experiments, and with data from other researchers, indicates that inconsistencies in reported flow behaviour is most likely to be due to variations in initial microstructure rather than the nature of the applied loading.     

Creep of Pb–2·5Sb–0·2Sn alloy at low stresses

Abstract

The creep of a Pb–2·5Sb–0·2Sn alloy has been studied at stresses up to 6·5 MN m^?2 in the temperature range 318–348 K (0·53–0·58T_m) using helical specimens. At 333 K, a transition in the stress exponent from ~1 to 3 occurred at ~3 MN m^?2. The observed good agreements below the transition stress, both for experimental dE/do and predictions for Coble diffusional creep of lead, and for measured activation energy for creep and the activation energy for grain boundary self-diffusion in lead, suggest that grain boundary diffusional creep is the dominant mechanism. at low stresses. The presence of antimony does not seem to affect the magnitude of dE/do appreciably, and the results suggest that the grain boundary self-diffusivity of lead is not influenced by the presence of segregated antimony on the grain boundaries. The diffusional creep occurred above a threshold stress of magnitude ~0·5 MN m^?2, and its temperature dependence was characterised by an activation energy of ~20 kJ mol^?1, similar to the value of 23 ± 7 kJ mol^?1 typical of pure metals in the temperature range investigated. The stress exponent of ~3 observed for the power law regime suggests control by viscous glide of dislocations constrained by dragging of solute atmospheres. Preliminary tests on sagging beam specimens of as-worked material at an applied stress of 2·5 MN m^?2 and a test temperature of 333 K has provided the first direct evidence that anisotropic grain shape affects Coble creep. The specimen with the longest grain dimension along the stress axis underwent slower creep than the specimen with the longest grain dimension perpendicular to the stress axis. This observation is in qualitative agreement with theoretical predictions.

MST/1139     

Annealing effect to constitutive behavior of Sn–3.0Ag–0.5Cu solder

Sn–Ag–Cu based solder alloys are replacing Sn–Pb solders in electronic packaging structures of commercial electric devices. In order to evaluate the structural reliability, the mechanical property of solder material is critical to the numerical simulations. Annealing process has been found to stabilize material properties of Sn–37Pb solder material. In the current study, the annealing effect on tensile behaviour of Sn–3.0Ag–0.5Cu (SAC305) solder material is investigated and compared with Sn–37Pb solder. It is found that the tensile strength for both materials are more stabilized and consistent after the annealing process, nevertheless, the annealing process will improve the plasticity of SAC305 solder dominated by dislocation motion, and impede the occurrence of hardening deformation in Sn–37Pb solder dominated by grain-boundary sliding mechanism. Furthermore, the annealing effect is quantified in the proposed constitutive model based on unified creep–plasticity theory. The parameters are calibrated against the measured stress–strain relationships at the tensile strain rates ranging from 1?×?10^?4 to 1?×?10^?3 s^?1. The numerical regressions for dominant parameters in the proposed model reveal the intrinsic differences between SAC305 and Sn–37Pb solders under annealing treatment.     

Microstructural evolution and flow behaviour during hot compression of twin roll cast ZK60 magnesium alloy

Abstract

Microstructural evolution and flow behaviour during hot compression of twin roll cast ZK60 magnesium alloy were characterised by employing deformation temperatures of 300, 350 and 400°C and strain rate ranging from 10^?3 to 100 s^?1. When compressed at 10^?3 s^?1, all stress–strain curves at different temperatures (300, 350 and 400°C) showed a flow softening behaviour due to active dynamic recrystallisation. When compressed at 10^?2 s^?1 and elevated temperatures (300, 350 and 400°C), all stress–strain curves showed a flow stress drop after peak stress due to twinning for 300 and 350°C deformation and recrystallisation for 400°C deformation. The balance between shear deformation and recrystallisation resulted in a steady flow behaviour after the true strain reached 0·22. When strain rate increased to 10^?1 s^?1, a small fraction of dynamic recrystallisation in shear deformation region was responsible for slight flow softening behaviour during compression. A flow hardening appeared due to basal and non-basal slips when deformed at 100 s^?1. It is suggested that the flow behaviour during hot compression of twin roll cast ZK60 alloy depends on the separating effect or combined effects of shear deformation, twinning and recrystallisation.     

Tensile and creep properties of Al–7Si–0.3Mg alloy with Zr and Er addition

The combined and singular effects of Zr and Er addition on the microstructure, tensile and impression creep behaviour of the cast A356 alloy were investigated. The Zr and Er refined the α-Al dendrites and secondary dendrite arm spacing (SDAS) and modified the eutectic morphology. The simultaneous addition of Zr and Er exhibited the smallest α-Al dendrites and SDAS with a fibrous eutectic morphology, resulting in the highest yield (～118?MPa) and tensile (～190?MPa) strength, and the largest creep resistance. The stress exponent, and the activation energy, were within the range of 6.28–7.22 and between 121.6 and 148.2?kJ?mol^?1, respectively. The lattice self-diffusion climb-controlled creep was the dominant creep mechanism. The constitutive creep equation was developed for each alloy.     

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.     

Hot working and crystallographic texture analysis of magnesium AZ alloys

Abstract

The hot working behaviour of magnesium AZ (e.g. AZ31; Al: 3%, Zn: 1%) alloys and their associated crystallographic texture evolution is reviewed. Under hot working conditions, the stress–strain curves show flow softening at all the temperatures and strain rates indicating dynamic recrystallisation (DRX) is predominant. The mean size of the recrystallised grains in all the alloys decreases as the value of Zener–Hollomon parameter Z increases. The hot working range of the alloys dwell between 200 and 500°C and the strain rates between 10^?3 and 5 s^?1. The hot working of AZ series alloy shows discontinuous DRX as the main mechanism. Equal channel angular processing shows continuous DRX. The constitutive equation development shows a linear relationship between the stress and the Z parameter. The activation energy for the alloys ranges from 112 to 169 kJ mol^?1 and Z values range from 10 to 10 s^?1. Textural examinations show basal texture as the predominant orientation.     

Creep deformation and crack growth rates of a super α2 titanium aluminide alloy

The influences of stress and temperature on creep deformation behavior and the creep crack growth rates of the super α₂ Ti₃Al alloy were investigated with respect to its safe application at high temperatures. In a temperature range of 1033–1093 K at low applied stress levels, the stress exponent was equal to 1.5. At an intermediate stress range (10^?3 < σ/E < 3 × 10^?3), a stress exponent of 3.3 was observed. As the applied stress was increased, the stress exponent changed from 3.3 to 4.4. The high temperature crack growth rate of the Ti₃Al alloy can be correlated with stress intensity factor K rather than C1 at 1033 K due to environmental embrittlement.     

Effect of nitrogen on tensile flow behaviour of type 316 LN austenitic stainless steel

Abstract

The influence of nitrogen content on the tensile flow behaviour of type 316 LN austenitic stainless steel has been studied. Nitrogen content in the steel has been varied in the range 0·07 to 0·22 wt-%. Tensile tests were carried out over the temperature range of 300–1123 K at a nominal strain rate of 3×10^?3 s^?1. The tensile flow behaviour of the steels has been analysed based on the constitutive equation proposed by Voce. The Voce’s parameters of initial stress (σ_i) and saturation stress (σ_s) were found to increase linearly with increase in nitrogen content at all the test temperatures. Tensile properties of the steels were predicted from Voce constitutive equation parameters.