de-DEen-GB
Mikrostruktur
und mechanisches Verhalten des Schaumglases
 
von Dr. sc. techn. ETH Rudolf Trinkner
 

List of Symbols

 

a(mm)

Half length of the Griffith crack

a(mm)

Edge length of the base polyhedron of the “TOP” model foam glass  

a(mm)

Length for description of the base polyhedra of the model foam glasses "Beta" and "Ortho"

C𝚒J(N/mm2)

Element of the matrix of the moduli of elasticity

[C𝚒J]

Matrix of the moduli of elasticity

d(N/mm)

Linear load

D(mmN)

Plate stiffness of the cell wall films of the model foam glasses

D(mm)

Diameter of a test cylinder

𝚎𝚒j(-)

Differentiation of the displacement  according to the coordinates xj

E(N/mm2)

Modulus of elasticity

E(n)(N/mm2)

Modulus of elasticity of the spherical foam glass with the porosity n

Ev(N/mm2)

Modulus of elasticity of the polyhedron foam glass according to Voigt

 

E(z)(N/mm2)

=:

F(ξ,η)(N)

Stress function according to Airy F(ξ, η)

Fo(mm2)

Cross-sectional surface of a test piece

K(mm-1)

Mean curvature of a cell wall film of the polyhedron foam

F(mm2)

Cross-sectional surface of a fictitious edge beam of a material sub-unit of the model foam glass

g(mm/sec2)

Gravitational acceleration

G(n)(N/mm2)

Shear modulus of the spherical foam glass with the porosity n

G(N/mm2)

Shear modulus

h(N /mm)

Linear load

(mm4)

on the ξ -axis of the cross-section of the fictitious edge beam-related second moment of area

(mm4)

On the η -axis of the cross-section of the fictitious edge beam-related second moment of area

Jp(mm4)

polar moment of inertia of the fictitious edge beam

k(-)

Form factor of the spherical pores in the elastic medium

k(-)

Ratio

L(mm)

Length of a test cylinder

3(mm)

Mean sectional length of the space-filling elementary polyhedron of the polyhedron foam glass on a test line

mξ(N)

Unit sectional length of the planar cell wall film-related Bending moment

mη(N)

Unit sectional length of the planar cell wall film-related bending moment

mξη(N)

Unit sectional length of the planar cell wall film-related torsional moment

Mt(mmN)

Torsional moment

MtB(mmN)

Torsional moment at fracture

n(-)

Porosity of a foam glass body

n(-)

Porosity of the spherical foam glass

n(-)

Porosity of the cell wall films of the polyhedron foam glass alone

nz(-)

Relationship between the gas volume included in the polyhedron bubbles of a polyhedron foam glass sample and the sample volume

nξ(N/mm)

Unit sectional length of the planar cell wall film-related Normal force

nn(N/mm)

Unit sectional length of the planar cell wall film-related Normal force

NB(N)

External tensile force at fracture -->

NL(mm−1)

Number of sections of the base polyhedron of the polyhedron foam glass per unit length of the test line in an intersecting plane

p(N/mm2)

Internal pressure of the cell bubbles of a foam

ρ(ξ,η)(N/mm2)

Surface loading acting normally to the ξ η -plane

p(x)(N/mm)

Linear load acting in direction  of the space

p(y)(N /mm)

Linear load acting in direction  of the space

p(z)(N/mm)

Linear load acting in direction  of the space

P(N)

Force, load

qξ(N /mm)

Unit sectional length of the planar cell wall film-related Lateral force

r(mm)

Radius of the plateau edge

Vector

Vector

Vector

R1(mm)

Curvature radius of a cell wall film

R2(mm)

Curvature radius of a cell wall film

Displacement vector

Sv(mm-1)

The volume unit-related centre surface of the polyhedron foam glass wall films of the polyhedron foam glass

t(mm)

Thickness of the assumed planar surface cell wall films of the polyhedron foam glass

Ts(°C)

Expansion temperature of the foam glass

u(mm)

Displacement in direction ξ of the coordinate system ξ,η,ζ

ui(mm)

Displacement

v(mm)

Displacement in direction η of the coordinate system ξ,η,ζ

w(mm)

Displacement in the direction ζ of the coordinate system ξ,η,ζ

Displacement vector in the coordinate system ξ,η,ζ

w(ξ,η)(mm)

Bending normal to the ξ η -plane

Wt(mm3)

Torsional resistance moment

x(mm)

Coordinate

Xi(N)

Force

y(mm)

Coordinate

z(mm)

Coordinate

α(N /mm)

Surface stress of the liquid film of a foam

γo(N /mm)

Specific surface energy

γξη(-)

Angle change

δ1(mm)

Thickness of the cell wall film in its centre

δ2(mm)

Thickness of the cell wall film at its edge

Δ(mm-2)

Laplace - Operator (=:)

ε(-)

Ratio

εi(-)

Distortion

εiJ(-)

Distortion

Distortion vector

εq(-)

Measured lateral strain of the foam glass test cylinder

ε1(-)

Measured longitudinal elongation of the foam glass test cylinder

ζ(mm)

Coordinate

η(mm)

Coordinate

λ(-)

Slenderness ratio

λ(W /m⋅°C)

Thermal conductivity of the foam glass

λD (mg / m⋅h⋅Pа) water vapour permeability of foam glass

λdB(mm)

Specific compressive strength of foam glass

ν(-)

Poisson’s ratio nt-->

ν(n)(-)

Poisson’s ratio of the spherical foam glass with the porosity n

νv(-)

Poisson’s ratio according to Voigt

ν(z,x)(-)

=:-

ν(z,y)(-)

=:-

ζ(mm)

Coordinate

ρ(gr /cm3)

Density of foam glass

ρGlas(gr /cm3)

Density of the solid glass making up the foam glass body

ρ(gr /cm3)

Density of the cell wall films of Spherical foam glass

σ(N /mm2)

Stress

σc(N /mm2)

Critical stress according to Griffith

σ(x)(N /mm2)

External surface loading in direction x of the space

σ(y)(N /mm2)

External surface loading in direction y of the space

σ(z)(N /mm2)

External surface loading in direction z of the space

(n∗)(N /mm2)

Tensile strength of the base material of the spherical foam glass

σB(n)(N /mm2)

Tensile strength of the spherical foam glass with porosity n

σB(N /mm2)

Tensile strength

σB(N /mm2)

Measured tensile strength of the foam glass

(N /mm2)

Tensile strength in direction x of the space

(N /mm2)

Tensile strength in direction y of the space

(N /mm2)

Tensile strength in direction z of the space

σdB(N /mm2)

Tensile strength

σdB(N /mm2)

Measured compressive strength

(N /mm2)

Compressive strength in direction x of the space

(N /mm2)

Compressive strength in direction y of the space

(N /mm2)

Compressive strength in direction z of the space

σξ(N /mm2)

Normal stress (membrane action)

ση(N /mm2)

NNormal stress (membrane action)

σij(N /mm2)

Stress

σi(N /mm2)

Stress

Stress vector

τξη(N /mm2)

SShear stress (membrane action)

τB(N /mm2)

Shear strength

τB(N /mm2)

Measured torsional shear strength

(N /mm2)

Shear strength in relationship to the normal stress-free planes E(φ=45o) or E(φ=135o)

(N /mm2)

Shear strength in relationship to the normal stress-free planes E(φ=450) or E(φ=135o)

ω(-)

Ratio 

ωt°C-1

Linear coefficient of thermal expansion

(N /mm2)

Torsional vector

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