scholarly journals On the contribution of grain boundary sliding type creep to firn densification – an assessment using an optimization approach

2022 ◽  
Vol 16 (1) ◽  
pp. 143-158
Author(s):  
Timm Schultz ◽  
Ralf Müller ◽  
Dietmar Gross ◽  
Angelika Humbert

Abstract. Simulation approaches to firn densification often rely on the assumption that grain boundary sliding is the leading process driving the first stage of densification. Alley (1987) first developed a process-based material model of firn that describes this process. However, often so-called semi-empirical models are favored over the physical description of grain boundary sliding owing to their simplicity and the uncertainties regarding model parameters. In this study, we assessed the applicability of the grain boundary sliding model of Alley (1987) to firn using a numeric firn densification model and an optimization approach, for which we formulated variants of the constitutive relation of Alley (1987). An efficient model implementation based on an updated Lagrangian numerical scheme enabled us to perform a large number of simulations to test different model parameters and identify the simulation results that best reproduced 159 firn density profiles from Greenland and Antarctica. For most of the investigated locations, the simulated and measured firn density profiles were in good agreement. This result implies that the constitutive relation of Alley (1987) characterizes the first stage of firn densification well when suitable model parameters are used. An analysis of the parameters that result in the best agreement revealed a dependence on the mean surface mass balance. This finding may indicate that the load is insufficiently described, as the lateral components of the stress tensor are usually neglected in one-dimensional models of the firn column.

2021 ◽  
Author(s):  
Timm Schultz ◽  
Ralf Müller ◽  
Dietmar Gross ◽  
Angelika Humbert

Abstract. Physics based simulation approaches to firn densification often rely on the assumption that grain boundary sliding,first introduced by Alley (1987) to firn, is the leading process driving the first stage of densification. However, often so calledsemi empirical models are favored against the description of grain boundary sliding due to simplicity and uncertainties regard-ing model parameters. In this study, we are assessing the applicability of grain boundary sliding to firn using a numeric firn5densification model and an optimisation approach, for which we formulate variants of the constitutive relation by Alley (1987).The efficient model implementation based on an updated Lagrangian numerical scheme enables us to perform a large numberof simulations testing different model parameters, to find simulation results suiting 159 firn density profiles from Greenlandand Antarctica best. For most of the investigated locations a good agreement of simulated and measured firn density profileswas found. This implies that the constitutive relation by Alley (1987) characterises the fist stage of firn densification well, if10suitable model parameter are used. An analysis of the parameters that lead to best matches reveals a dependency on the meansurface mass balance. This may indicate an insufficient description of the load situation, as horizontal components of the stresstensor are usually neglected in one dimensional models of the firn column.


2021 ◽  
Author(s):  
Timm Schultz ◽  
Angelika Humbert ◽  
Ralf Müller ◽  
Dietmar Gross

<p>The simulation of firn densification, although first models were already developed in the 1960s, is still a work in progress. Various models and variants of earlier models developed throughout the decades testify for this (e.g. Lundin et al. 2017, Stevens et al, 2020). Here we focus on the first stage of firn densification up to the density of 550 kg m<sup>−3</sup>, hence the first few meters of the firn column. Describing the early stage of the process well is crucial as it proceeds fastest and influences further densification. Alley first applied the process of grain boundary sliding to firn in 1987 and thereby provided a physics based material model for the densification of firn at low densities. Despite being used in many firn densification models, it is sometimes debated if grain boundary sliding is governing the densification at low densities as there are very few observations of intra-crystalline deformation in firn.</p><p>We aim to test to which extent grain boundary sliding can be used to reproduce measured firn density profiles and to constrain the parameter range in the constitutive relation. To this end, we conduct a high number of simulations for various locations, stepping through the parameter space and select the best match with corresponding measured density profiles. By doing so, we are following Alley’s original approach, but we make use of a much larger firn density dataset provided by the SUMup working group (Koenig & Montgomery, 2020).</p><p>Forcing data provided by the regional climate model RACMO (van Wessem et al., 2014, Noël et al., 2015) allows not only to simulate steady state solutions but transient simulations. Our model implementation provides a very fast, complete and flexible simulation environment, allowing to test wide parameter ranges in short time and hence enables us to cover a great amount of firn properties. The broad testing approach allows to evaluate if and in which ways grain boundary sliding might play a role in firn densification at low densities.</p>


Author(s):  
Nancy J. Tighe

Silicon nitride is one of the ceramic materials being considered for the components in gas turbine engines which will be exposed to temperatures of 1000 to 1400°C. Test specimens from hot-pressed billets exhibit flexural strengths of approximately 50 MN/m2 at 1000°C. However, the strength degrades rapidly to less than 20 MN/m2 at 1400°C. The strength degradition is attributed to subcritical crack growth phenomena evidenced by a stress rate dependence of the flexural strength and the stress intensity factor. This phenomena is termed slow crack growth and is associated with the onset of plastic deformation at the crack tip. Lange attributed the subcritical crack growth tb a glassy silicate grain boundary phase which decreased in viscosity with increased temperature and permitted a form of grain boundary sliding to occur.


1983 ◽  
Vol 44 (C9) ◽  
pp. C9-759-C9-764
Author(s):  
E. Bonetti ◽  
A. Cavallini ◽  
E. Evangelista ◽  
P. Gondi

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