Primary Creep Rate Research Articles

Investigation into Stress Relaxation and Creep Rate of C47200 Copper Alloy

Copper alloys have high thermal conductivity, relatively high mechanical strength, and toughness over a wide range of temperature; hence they are highly sorted for complex structural applications that required extreme heat flux under load. Creep of materials is classically associated with time-dependent plasticity under a constant stress/load at an elevated temperature, often greater than the absolute melting temperature. This research is aimed to study the evaluation of stress and creep rate in copper, identifying the mechanisms at which copper can easily be exposed to stress and creep deformations in structures. A 12 mm diameter copper rod with the composition of 52.05 % CuO and 30.26 % SnO2 was procured locally. Samples from the procured rod were heat treated to 650°C for 30 minutes and cooled in the still air as well as inside the furnace. Creep test was carried out at 760uC with a constant load corresponding to an initial stress (between 1.5 MPa and 350 MPa) and stress relation was carried out on a 98 kN capacity stress relaxation frame (from 350 MPa to 300 MPa). Rockwell hardness test and metallographic analysis (at 200 mm) were also conducted on the heat treated and unheated control samples. It was established that heat treatment reduced the hardness property of stress relaxed copper, accelerated the stress relaxation process up to 60 %, speed up both primary creep rate and the tertiary creep rate as well altered the linear creep pattern and behaviour.

History effects in the creep of a disordered brittle material

We study the creep behavior of a disordered brittle material (concrete) under successive loading steps, using acoustic emission and ultrasonic sensing to track internal damage. The primary creep rate is observed to follow a (Omori-type) power-law decay in the strain rate, the number of acoustic emission events, as well as the amplitudes of the ultrasonic beams, supporting a brittle-creep mechanism. The distribution of acoustic emission event energies is observed to have a scale-free power-law distribution instead of a truncated one expected for a system approaching a critical point at failure. The main outcome is, however, the discovery of unexpected history effects that make the material less prone to creep when it has been previously deformed and damaged under primary creep. With the help of a progressive damage model implementing thermal activation, we interpret this as an aging-under-stress phenomenon: During an initial creep step at relatively low applied stress, the easy-to-damage sites are exhausted first, depleting the excitation spectrum at low stress gap values. Consequently on reloading, although previously damaged, the primary creep restarts but the material creeps (and damages) less than it would under the same stress but without precreeping. Besides shedding a new light on the fundamental physics of creep of disordered brittle materials, this has important practical consequences in the interpretation of some experimental procedures, such as stress-stepping experiments.

Creep Behavior ofγ-TiAl-Based Alloys with Fully Lamellar Microstore

AbstractRecent investigations have demonstrated that the interface spacing in fully lamellar microstructures has a major influence on the creep behavior of γ-TiAl-based alloys. In this paper, the dependence of the creep properties on interface spacing in fully lamellar Ti-46.5 at.% Al-4 at.% (Cr, Nb,Ta, B) sheet material was studied. Creep tests were conducted over a temperature range of 700 to 800 °C and at stresses between 100 and 260 MPa. The results indicate that the primary creep strain as well as the minimum creep rate decrease with decreasing interface spacing. A model which considers the limitation of the free dislocation path by stored dislocations as well as by geometrical obstacles was applied to explain the role of the interface spacing on both the primary creep strain and secondary creep rate. The applicability of the model has been verified by comparing calculated creep curves with experimentally obtained ones.

Creep Deformation Behavior of Inconel 617 Alloy in the Temperature Range of 650 °C to 800 °C

Creep behavior of the Inconel 617 alloy has been investigated through tests carried out in the temperature range of 650 °C to 800 °C under 95 to 350 MPa. Creep curves obtained from tests on the alloy exhibit a non-classical nature, with the primary creep rate decreasing to a minimum value, followed by a typical increase, which is either continuous at temperatures ≤ 700 °C or has an intermediate steady-state regime at 750 °C or 800 °C. The variation of minimum creep rate (έmin) with stress (σ) obeys the power law relationship (έmin = Aσn), with the stress exponent, n, increasing with temperature to a peak value at ~ 700 °C. The value of n > 5 has been rationalized by considering the existence of threshold stress, which like n has been found to decrease sharply with temperature beyond 700 °C. Investigation of the post-creep microstructures by transmission electron microscope has revealed the formation of γ′ and M23C6 precipitates, which obstruct dislocation motion during the primary stage. Microstructures of the samples creep-tested at ≥ 750 °C have exhibited relatively smaller amounts of γ′. The existence of threshold stress and the steady-state regime in the tertiary creep stage has been ascribed to obstruction of dislocation motion by M23C6 and γ′ precipitates.

Changes in Monkman-Grant relation among four creep regions of modified 9Cr-1Mo steel

The relation of creep rupture life to minimum creep rate, namely Monkman-Grant (MG) relation is examined by using a creep database of modified 9Cr-1Mo steel. The database covers wide ranges of creep rupture life up to 1.2 × 105 h and of minimum creep rate down to 7.6 × 10−8 h−1. The MG plot exhibits a low overall value of MG exponent (p = 0.85) together with wide scatter of data points at long rupture life. Causes of the low p value and the wide scatter are discussed in the present study paying attention to change in creep curve shape with creep rupture life. There are four regions H, M, L1 and L2 showing different creep behavior in the steel. Regional MG relations are examined also in each region. Values of p are less than unity and change among the four regions. The p value is especially low (0.62) in long-term region L2. The regional p values less than unity result in the low overall p value of 0.85. The especially low regional value of p in the long-term region causes the wide scatter of data points in the overall MG plot. A modified Monkman-Grant equation (Eq. (29)) is proposed taking account of creep deceleration rate A (=−1/(dln ε˙/dε), where ε˙ and ε are the creep strain rate and the creep strain) in primary creep and creep acceleration rate B (=1/(dln ε˙/dε)) in tertiary creep. The rates characterize shape of a creep curve. The modified equation can explain the difference of p values among the four regions.

A homogenized primary creep model of nickel-base superalloys and its application to determining micro-mechanistic characteristics

A primary creep model of nickel-base superalloys is developed for the low-temperature-high-stress regime, which provides insight into the active micro-mechanisms, extracted from features of the experimental creep curves. A two-parameter model is established to account for the accumulated primary creep strain, which contains a “threshold stress” representing the possible shear resistance during primary creep. Consideration of this threshold stress leads to a stress exponent n in the order of 3∼4, in sharp contrast to the conventional analysis that gives an ultra high value of n>10. A general stress-dependence of dislocation velocity is then proposed based on the framework of thermally-activated deformation, which leads to another two-parameter model for the primary creep rate. Applications to two superalloys demonstrate a good agreement between the model and experimental data. In addition, two micro-mechanistic characteristics of creep, i.e., dislocation drag coefficient and activation volume, can be unambiguously determined from the model parameters. The values of these physical quantities obtained for the two superalloys considered suggest a coupled dislocation motion of glide and climb at the γ/γ' interface as the rate-controlling mechanism during primary creep in superalloys.

Effect of prior deformation on the subsequent creep and anelastic recovery behaviour of an advanced martensitic steel

The creep and anelastic recovery characteristics of a 10%Cr steel have been systematically investigated at 600°C after subjecting the test material to various prior deformation histories. Constant-load forward creep tests on specimens, either with a tensile or compressive preloading history, indicated that over- and reverse-preloading respectively decreases and increases the early primary creep rate of the steel. The extent of decrease (or increase) in early primary creep rate is also found to be directly proportional to the magnitude of stress during prior loading while such a correlation is not clearly evident for material deformation in the secondary and tertiary stages. Specifically, the creep rate in the secondary and tertiary stages is lower for specimens with a compressive prior loading while the rupture time is notably shorter for tensile pre-loaded specimens. The observed effect of prior loading on the early primary creep behaviour can be explained by considering micro-backstress development (as a consequence of dislocation pile-up formation during the prior loading phase) that subsequently introduces a kinematic hardening effect to the material's viscoplastic response. The second set of experiments involve monitoring the anelastic recovery behaviour immediately after accumulation of a similar amount of time-dependent strain either under forward creep (load control mode) or stress relaxation (strain control mode) condition in completely unloaded 10%Cr steel specimens at 600°C. Experimental observations indicate that the higher the stress magnitude during the prior loading phase, the greater and faster the anelastic recovery at zero stress. Further findings show the mode of prior deformation (creep or relaxation) to also not noticeably influence the subsequent anelastic recovery behaviour. The observed anelastic recovery characteristic can be mechanistically interpreted by consideration of the time-dependent material back-flow due to the relaxation of dislocation bows and pile-ups generated during the prior deformation.

Effects of minor Cu and Mg additions on microstructure and material properties of 8xxx aluminum conductor alloys

Abstract

Effect of Nitrogen on Primary and Steady State Creep Deformation Behaviour of 316LN Austenitic Stainless Steel

Effect of nitrogen on primary and steady state creep deformation behaviour of 316LN austenitic stainless steel has been studied. Nitrogen content was varied between 0.07 and 0.22 wt%. Creep tests have been carried out on the steels over the stress range of 120–225 MPa at 923 K. The creep behaviour of the steels has been assessed based on Garofalo relationship, \(\varepsilon = \varepsilon_{o} + \varepsilon_{T} \left[ {1 - exp\left( { - rt} \right)} \right] + \dot{\varepsilon }_{s} t\). The rate of exhaustion of primary creep rate ‘r’ and steady state creep rate ‘\(\dot{\varepsilon }_{s}\)’ decrease and time to onset the secondary creep stage increases with nitrogen content. The relationships between the initial creep rate ‘\(\dot{\varepsilon }_{i}\)’and rate of exhaustion of primary creep rate ‘r’ with steady creep rate ‘\(\dot{\varepsilon }_{s}\)’ reveal that the same deformation mechanism prevails during the transient and steady state creep deformations. Attempt has been made to generate a master transient creep curve for the steels having different nitrogen contents using the above parameters. Even though for a steel of specific nitrogen content, master curve has been generated for different stress levels, a master curve for all the steel could not be established. Different deformation characteristics of the steel having different nitrogen content which effect the stacking fault energy as well as precipitation behaviour is considered for the disagreement.

Lattice continuum and diffusional creep.

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

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.

Effect of Tungsten on Primary Creep Deformation and Minimum Creep Rate of Reduced Activation Ferritic-Martensitic Steel

Effect of tungsten on transient creep deformation and minimum creep rate of reduced activation ferritic-martensitic (RAFM) steel has been assessed. Tungsten content in the 9Cr-RAFM steel has been varied between 1 and 2 wt pct, and creep tests were carried out over the stress range of 180 and 260 MPa at 823 K (550 °C). The tempered martensitic steel exhibited primary creep followed by tertiary stage of creep deformation with a minimum in creep deformation rate. The primary creep behavior has been assessed based on the Garofalo relationship, \( \varepsilon = \varepsilon_{\text{o}} + \varepsilon_{\text{T}} [1-\exp (-r^{\prime} \cdot t)] + \dot{\varepsilon }_{\text{m}} \cdot t \), considering minimum creep rate \( \dot{\varepsilon }_{\text{m}} \) instead of steady-state creep rate \( \dot{\varepsilon }_{\text{s}} \). The relationships between (i) rate of exhaustion of transient creep r′ with minimum creep rate, (ii) rate of exhaustion of transient creep r′ with time to reach minimum creep rate, and (iii) initial creep rate \( \dot{\varepsilon }_{\text{i}} \) with minimum creep rate revealed that the first-order reaction-rate theory has prevailed throughout the transient region of the RAFM steel having different tungsten contents. The rate of exhaustion of transient creep r′ and minimum creep rate \( \dot{\varepsilon }_{\text{m}} \) decreased, whereas the transient strain ɛT increased with increase in tungsten content. A master transient creep curve of the steels has been developed considering the variation of \( \frac{{\left( {\varepsilon - \varepsilon_{\text{o}} } \right)}}{{\varepsilon_{\text{T}} }} \) with \( \frac{{\dot{\varepsilon }_{\text{m}} \cdot t}}{{\varepsilon_{\text{T}} }} \). The effect of tungsten on the variation of minimum creep rate with applied stress has been rationalized by invoking the back-stress concept.

A thermally activated model for room temperature creep in nanocrystalline Au films at intermediate stresses

Uniaxial tension creep experiments conducted on free-standing nanocrystalline Au films with 40 nm grain size showed high initial primary creep rates of 3.3 × 10−8–2.7 × 10−7 s−1, reaching steady-state creep rates of 5.5 × 10−9–1.1 × 10−8 s−1 after 5–6 h. The isochronous creep curves pointed to the need for a nonlinear creep model based on the kinetics of thermal activation, which captured well the effect of applied stress amplitude. The implications of this model on the long term stability of nanocrystalline films were explored numerically for periodic stress profiles.

Work hardening during primary creep of copper

An analysis of primary creep curves in copper in the temperature range 423–573 K indicated results that were consistent with the view that hardening is due to athermal rather than thermally activated processes. It was assumed that the strain rate could be divided into a steady state component and primary creep deformation. By subtracting the steady state component, curves of primary creep rates against primary creep strains were plotted. Using a rate equation that has frequently been used to describe thermally activated glide controlled deformation, flow stresses were calculated from primary creep deformation rates. Curves of flow stress against primary creep strains were obtained. If initial strains accounting for plastic deformation during application of the steady loads were added to the strains, results could be superimposed to lie on a single curve, irrespective of creep load and temperature.

Mechanical and microstructural observations during compression creep of a short fiber reinforced AlMg metal matrix composite

The constant load compression creep behavior of a short fiber reinforced aluminium-5 wt.% magnesium alloy (AlMg5) containing 15 vol.% Al 2O 3 fibers (Saffil) was investigated. Creep of the matrix alloy and the metal matrix composite (MMC) was studied at 300 °C and 500 °C. Stresses ranging from 10 MPa to 120 MPa result in minimum creep rates between 10 −9 s −1 and 10 −3 s −1. MMC creep is characterized by an initial decrease of the creep rate before a distinct creep rate minimum is reached, while the matrix alloy shows increasing primary creep rates at 500 °C. It is difficult to rationalize the stress dependence of the minimum creep rates by a simple Norton law, because the stress exponent n is not always constant. The orientation of Al 2O 3 fibers with respect to the loading axis is found to affect minimum creep rates. Fiber breakage represents an important damage mechanism. Fiber agglomerates are observed in the initial microstructure which may well affect the entire process of creep.

Microstructure and Creep of γ-TiAl Containing β-Stabilizer

Fully lamellar structures of powder metallurgy (PM), investment cast, and directionally solidified (DS) TiAl alloys containing β stabilizer were produced after stepped cool heat treatment, and interface β precipitates were formed after aging at 950°C. In addition, a columnar grain structure combined with a fully lamellar structure aligned with the load direction and interface β precipitates were formed by directional solidification and subsequent heat treatments. Creep test results of PM TiAl indicate that controlling the initial microstructures is also critical for balancing the primary and steady-state creep resistance during short and long-term tests. DS TiAl alloy exhibits a significant reduction of the primary strain and creep rate compared to polycrystalline TiAl due to the unique DS microstructure. Therefore, a DS microstructure with proper lamellar orientation and controlled interface β precipitation is the ideal if maximum time to a relatively small (<0.5%) strain is the design criterion of merit.

Comparison of the Microstructure, Tensile, and Creep Behavior for Ti-22Al-26Nb (At. Pct) and Ti-22Al-26Nb-5B (At. Pct)

The effect of the addition of 5 at. pct boron on the microstructure and creep behavior of a nominally Ti-22Al-26Nb (at. pct) alloy was investigated. The boron-modified alloy contained boride needles enriched in titanium and niobium, and because to these borides, this material was considered to be a discontinuously reinforced metal matrix composite. These needle-shaped borides made up to 2 pct of the volume and were up to 158-μm long and 22-μm wide. The effect of boron on the mechanical properties was evaluated through in-situ creep testing and tensile testing at room temperature (RT) and 650 °C. Overall, the addition of 5 at. pct boron proved to be detrimental to the tensile and creep behavior. The composite exhibited a brittle failure and lower elongations-to-failure than the monolithic material. The in-situ tensile and creep experiments revealed that the deformation process initiated in the boride needles, which cracked extensively, and significantly greater primary creep strains and creep rates were exhibited by the composite.

Compressive creep behaviour of Mg–Li–Al alloy

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.

Strengthening of a fully lamellar TiAl + W alloy by dynamic precipitation of β phase during long-term creep

In a fully lamellar Ti–48Al + W alloy, β phase precipitated by aging lowers the primary creep rate significantly. However, dynamic precipitation of the β phase during long-term creep reduces the steady-state creep rate of the unaged alloy close to that of the alloy in the aged condition.

Creep behavior of γ-TiAl sheet material with differently spaced fully lamellar microstructures

Recent investigations have shown that the interface spacing in fully lamellar microstructures has a major influence on the creep behavior of γ-TiAl based alloys [Scr. Mater. 37 (1998) 1025; Scr. Mater. 35 (1996) 1391; Mater. Sci. Eng. A239–240 (1997) 419; Intermetallics 7 (1999) 171]. In order to study the dependence of interface spacing on creep, fully lamellar microstructures exhibiting different interface spacings but comparable colony size were adjusted in Ti–46.5 at.% Al–4 at.% (Cr, Nb, Ta, B) sheet material by appropriate heat treatments. Creep tests were conducted in a temperature range of 700–800 °C and stresses between 100 and 260 MPa. The results indicate that the primary creep strain as well as the minimum creep rate decreases with decreasing interface spacing. In addition, apparent activation energies and stress exponents were determined as a function of the interface spacing in order to describe the creep controlling mechanisms. A model assumption, which considers the limitation of the free dislocation path by stored dislocations as well as by geometrical obstacles was applied to explain the role of the interface spacing on primary creep strain and secondary creep rate.