The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law

Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain rate with a stress exponent n ∼ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ∼ 4) nor grain boundary sliding (n ∼ 1.8) have stress exponents that match the value of n ∼ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ∼ 3 dependence of the Glen law by using the “wattmeter” to model grain size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone and (2) as a function of depth within an ice sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

Ambient-Temperature Indentation Creep of Shape Memory NiTi Alloys: Additively Manufactured versus Cast

In this study, depth-sensing indentation creep response of cast and additively manufactured (laser powder bed fusion) NiTi alloys in heat-treated conditions have been investigated at ambient temperature. Indentation creep tests were evaluated with the help of a dual-stage approach comprising a loading segment with a subsequent constant load-holding stage and an unloading phase afterward. The investigation was carried out at a maximum load of 50 mN along with a holding time of 600 s. Different creep parameters comprising indentation creep displacement, creep strain rate, creep stress exponent as well as the indentation size effect have been analyzed quantitatively for the employed materials. In addition, microstructural analysis has been performed to ascertain the processing–microstructure–creep property correlations. A substantial indentation size effect was seen for both cast and printed NiTi samples in heat-treated conditions. According to the creep stress exponent measurements, the dominant mechanism of rate-dependent plastic deformation for all NiTi samples at ambient temperature is attributed to the dislocation movement (i.e., glide/climb). The outcome of this investigation will act as a framework to understand the underlying mechanisms of ambient-temperature indentation creep of the cast and printed NiTi alloy in conjunction with heat-treated conditions.

On the identification of power-law creep parameters from conical indentation

Load and hold conical indentation responses calculated for materials having creep stress exponents of 1.15, 3.59 and 6.60 are regarded as input ‘experimental’ responses. A Bayesian-type statistical approach (Zhang et al. 2019 J. Appl. Mech. 86 , 011002 ( doi:10.1115/1.4041352 )) is used to infer power-law creep parameters, the creep exponent and the associated pre-exponential factor, from noise-free as well as noise-contaminated indentation data. A database for the Bayesian-type analysis is created using finite-element calculations for a coarse set of parameter values with interpolation used to create the refined database used for parameter identification. Uniaxial creep and stress relaxation responses using the identified creep parameters provide a very good approximation to those of the ‘experimental’ materials with stress exponents of 1.15 and 3.59. The sensitivity to noise increases with increasing stress exponent. The uniaxial creep response is more sensitive to the accuracy of the predictions than the uniaxial stress relaxation response. Good agreement with the indentation response does not guarantee good agreement with the uniaxial response. If the noise level is sufficiently small, the model of Bower et al. (1993 Proc. R. Soc. Lond. A 441 , 97–124 ()) provides a good fit to the ‘experimental’ data for all values of creep stress exponent considered, while the model of Ginder et al. (2018 J. Mech. Phys. Solids 112 , 552–562 ()) provides a good fit for a creep stress exponent of 1.15.

Modelling the Creep of Nickel

Many metals and alloys have a stress exponent for the creep rate that is considerably higher than the value of 3 that is typically predicted by creep recovery models. One example is pure Ni. Creep data from Norman and Duran that are analyzed in the paper give a stress exponent of about 7 in the temperature range 0.3 to 0.55 of the melting point. It has recently been shown that the high creep exponent of Al and Cu in the power-law break down regime can be explained by the presence of strain-induced vacancies. By applying a creep recovery model that does not involve adjustable parameters, it is shown that strain induced vacancies can also explain the high-stress exponent of pure nickel.

Inferring ice rheology in Antarctic ice shelves from remotely sensed observations

<p>Glaciers and ice sheets flow as a consequence of ice rheology. At the temperatures and pressures found on Earth, several creep mechanisms allow glacier ice to flow as a non-Newtonian (shear-thinning) viscous fluid. The semi-empirical constitutive relation known as Glen’s Flow Law is often used to describe ice flow and to provide a simple expression for an effective viscosity that decreases with increasing stress and deformation rate. Glen’s Flow Law is a power-law relation between effective strain rate and deviatoric stress, with two parameters defining the rheology of ice: a rate factor, A, and stress exponent, n. The rate factor depends on features such as temperature and grain size, while the stress exponent is primarily representative of the creep mechanism. Neither A nor n are well constrained in natural ice, and the stress exponent is typically assumed to be n = 3 everywhere. Here, we take advantage of recent improvements in remotely sensed observations of surface velocity and ice shelf thickness to infer the values of A and n in Antarctic ice shelves. We focus on areas of ice shelves that flow in a purely extensional regime, where extensional stresses are proportional to observed ice thickness, drag at the base of the ice is negligible, and extensional strain-rates are calculated from the gradients of observed surface velocity fields. In this manner, we use independent observational data to derive spatially dependent constraints on the rate factor A and stress exponent n in Glen's Flow Law. The robust spatial variability provides insights into the creep mechanisms of ice, thereby capturing rheological properties from satellite observations. Our analysis indicates that n ≈ 4 in most fast-flowing areas in an extensional regime, contrary to the prototypical value of n = 3. This finding implies higher non-linearity in ice flow than typically prescribed, influencing calculations of mass flux and the response of ice sheets to perturbations. Additionally, This result suggests that dislocation creep is the dominant creep mechanism in extensional regimes of Antarctic ice shelves, indicative of tertiary creep. This analysis unites theoretical work and synoptic-scale observations of ice flow, providing insights into the rheology and stress-states of ice shelves in Antarctica.</p>

High Temperature Creep Behaviour of Cast Nickel-Based Superalloys INC 713 LC, B1914 and MAR-M247

Cast nickel-based superalloys INC713 LC, B1914 and MAR-M247 are widely used for high temperature components in the aerospace, automotive and power industries due to their good castability, high level of strength properties at high temperature and hot corrosion resistance. The present study is focused on the mutual comparison of the creep properties of the above-mentioned superalloys, their creep and fracture behaviour and the identification of creep deformation mechanism(s). Standard constant load uniaxial creep tests were carried out up to the rupture at applied stress ranging from 150 to 700 MPa and temperatures of 800–1000 °C. The experimentally determined values of the stress exponent of the minimum creep rate, n, were rationalized by considering the existence of the threshold stress, σ0. The corrected values of the stress exponent correspond to the power-law creep regime and suggest dislocation climb and glide as dominating creep deformation mechanisms. Fractographic observations clearly indicate that the creep fracture is a brittle mostly mixed transgranular and intergranular mode, resulting in relatively low values of fracture strain. Determined main creep parameters show that the superalloy MAR-M247 exhibits the best creep properties, followed by B1914 and then the superalloy INC713 LC. However, that each of the investigated superalloys can be successfully used for high temperature components fulfils the required service loading conditions.

Effect of Doped CeO with Si3N4 Powders on the Densification Mechanism During

The densification mechanism of doped CeO with Si3N4 powder during Spark Plasma Sintering (SPS) was investigated under temperatures ranging from 1500 to 1750 °C at soaking pressures of 30, 40, 50 MPa. Results showed that the relative density of Si3N4 ceramics sintered at 1650 °C and 30 MPa was 97.9%. A creep model was employed to determine the mechanism, which can be interpreted on the basis of the stress exponent (n). The results showed that the mechanism was controlled by liquid phase sintering at low effective stress regime (n=1).

The role of grain-size evolution on the rheology of ice: Implications for reconciling laboratory creep data and the Glen flow law

Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain-rate with a stress exponent n ~ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain-size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ~ 4) nor grain boundary sliding (n ~ 1.8) have stress exponents that match the value of n ~ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ~ 3 dependence of the Glen law by using the wattmeter to model grain-size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone, and (2) as a function of depth within an ice-sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

Effect of Loading Rate on Creep Properties of HgCdTe Epitaxial Films

Nanoindentation creep studies were performed on Hg1-xCdxTe (x~0.29) epitaxial films using different loading rates of 0.5 mN.s-1, 1 mN.s-1, 2 mN.s-1 and 4 mN.s-1, keeping a constant peak load of 10 mN. A constant hold time of 20 sec at peak load was maintained for all experiments. The effect of loading rate on creep behaviour of material has been investigated. Creep displacement had shown increasing trend with increase of loading rates. Stress exponents were extracted using creep curve fitting with an empirical equation. A strong dependence of loading rate on stress exponent was observed. The value of stress exponent was found varying in the range 0.60-1.76, 0.96-2.23, 0.98-2,87 and 0.90-2.81 for loading rates 0.5 mN.s-1, 1 mN.s-1, 2 mN.s-1 and 4 mN.s-1, respectively. The change of stress exponent was attributed to change of creep mechanism. Hardness and elastic modulus were extracted from load-displacement curves and it was found that with the increase of the loading rate hardness increases, while elastic modulus remains constant. A correlation between variation of hardness and creep displacement has also been presented.