Abstract
Mathematical modelling of deformation mechanisms in
polycrystalline isotropic ice over wide temperature and
strain rate ranges was investigated in this thesis. The
proposed 3dimensional constitutive equations describe
both timedependent ductile deformation mechanisms and
microcracking associated with Hookean deformation showing
a brittle nature.
A model to describe the high strain rates operative
mechanisms, which form the microcrack nucleus, was
introduced. It was assumed that the required four
independent deformation systems were: basal glide (2
systems) and twinning (2 systems). At very high strain
rates, when the dislocation motion on the basal plane is
not fast enough, the total permanent response of the
icebody causing microcracking may be resulting from
twinning.
The prominent microcracking (damage) at high strain rates
is described by a fourthorder tensor. The damage
evolution law is based on the potential energy theorem.
The observed micromechanisms in ice are modelled for both
the condition for microcrack formation and the effects of
microcracks on the mechanical properties of ice. The
proposed approach connects continuum damage mechanics
with fracture mechanics.
The proposed theory reveals the HallPetch type of
relation, although the frictional stress vanishes.
Computed examples satisfactorily gave the measured
compressive strength of ice and predicted the ratio of
the peak compressive stress to the peak tensile stress as
1.85: 1, which is much lower than the measured one  8.6
: 1.
At elevated temperatures when the strain rate is low, the
ductile response of ice is dominant. The following
mechanisms are modelled: Hookean deformation, delayed
elasticity associated with grain boundary sliding and
viscoplaticity associated with dislocation movement. The
uniaxial material model is based on the equation proposed
by Sinha. However, a more effective approximate time
integration method was applied in computing the delayed
elastic strain. This work gives a micromechanical
representation for the (viscoclastic) delayed elasticity.
This was applied during the derivation of the
3dimensional constitutive SADSequation, which coincides
in uniaxial tension with the Ashby and Duval modification
of Sinha's model.
A Schapery's nonlinear viscoelasticity theory based time
integration method, which is a modification to the
procedure applied in the uniaxial case, was proposed for
the SADSequation. Although this method gives realistic
predictions during loading it does not allow the material
to relax correctly.
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Supervisors/Advisors 

Award date  19 Apr 1990 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9513836177 
Publication status  Published  1990 
MoE publication type  G4 Doctoral dissertation (monograph) 
Keywords
 ice
 deformation
 mechanical properties
 mechanics
 microstructure
 mathematical models
 fractures (materials)
 cracking (fracturing)
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Santaoja, K. (1990). Mathematical modelling of deformation mechanisms in ice: Dissertation. VTT Technical Research Centre of Finland.