crevprop.fracture

  1. 2024 Jessica Mejia

fracture mechanics used in crevasse propagation model

Linear elastic fracture mechanics scheme for crevasse propagation

LEFM based on Weertman’s dislocation theory and application to crevasses with adaptations from van der Veen (1998)

Theory

STRESS INTENSITY FACTOR For a fracture to propagate

KI >= KIC

stress @ crev tip must >= fracture toughness of ice where KI is the stress intensity factor which describes the stresses at the fracture’s tip the material’s fracture toughness (KIC)

Functions

F(crevasse_depth, ice_thickness[, ...])

Finite ice thickness correction for the stress intensity factor

G(b, d, H)

Functional expression G in KI2 evaluation.

KI1_shielding(d, Rxx, crev_spacing)

KI1 accounting for opening and consider effect of shielding

alpha([dislocation_type, crack_opening_mode])

applied_stress(traction_stress, ...[, ...])

calculated applied stress (sigma_A)

density_profile(depth[, C, ice_density, ...])

empirical density-depth relationship from Paterson 1994

diff_squares(x, y)

calculate the squareroot of the difference of squares :param x: :type x: float, int :param y: :type y: float, int

elastic_displacement(z, sigma_T, mu, ...[, ...])

calculate elastic crevasse wall displacement from applied stress sigma_T.

evaluate_KI1(d, H, Rxx[, simplify, crev_spacing])

Stress intensity factor for tensile normal stress

evaluate_KI2(d, H[, rhoi, rhos, C])

KI(2) in units of MPa

evaluate_KI3(a, d, H)

stress intensity factor component for a water-filled crevasse

evaluate_KInet(d, H, Rxx, a[, rhoi, rhos, C])

f2(b, d, H[, rhoi, rhos, C])

integral within the equation for KI(2) van der veen 1998

f3(a, b, d, H)

find_crev_depth(H, Rxx, KIC[, rhos, ...])

find initial crevasse depth for a water-free crevasse

overburden_stress(b)

ice overburden stress as a function of depth acconting for firn

paterson_empirical_relation(b[, rho_i, rho_s, C])

depth dependant near-surface density

penetration_depth_equ(d, H, Rxx, KIC[, ...])

calculate crevasse penetration depth for a single crevasse

sigma(sigma_T, crevasse_depth, water_depth)

Calculate sigma

sum_over_diff(x, y)

calcualte x+y / x-y

tensile_stress(Rxx, crevasse_depth, ...)

Calculate the stress intensity factor's tensile component.

water_depth(Rxx, crevasse_depth, ice_thickness)

Convert water height in crevasse to depth below surface in meters

water_height(Rxx, fracture_toughness, ...[, ...])

calc water high in crevasse using van der Veen 2007