TY - RPRT
T1 - Modified Dugdale cracks and Fictitious cracks
T2 - Characteristics at critical and sub-critical loading
AU - Nielsen, Lauge Fuglsang
PY - 1998
Y1 - 1998
N2 - A number of theories are presented in the literature on crack
mechanics by which the strength of damaged materials can be
predicted. Among these are theories based on the well-known
Dugdale model of a crack prevented from spreading by self-created
constant cohesive flow stressed acting in local areas, so-called
fictitious cracks, in front of the crack.The Modified Dugdale
theory presented in this paper is also based on the concept of
Dugdale cracks. Any cohesive stress distribution, however, can be
considered in front of the crack. Formally the strength of a
material weakened by a modified Dugdale crack is the same as if it
has been weakened by the well-known Griffith crack, namely
sigma_CR = (EG_CR/phi)^1/2 where E and 1 are Young's modulus and
crack half-length respectively, and G_CR is the so-called critical
energy release rate. The physical significance of G_CR, however,
is different.For brittle materials (considered by the Griffith
theory )G_CR = 2 Gamma where Gamma is surface energy of material
considered. For more tough materials (considered by the modified
Dugdale theory) G_CR is a function f(sigma_L delta_CR) where
sigma_L and delta_CR are theoretical strength and flow limit
(displacement) respectively of material considered. The practical
applicability of the two models is limited such that predicted
strength sigma_CR must be less than sigma_L/3, which corresponds
to an assumption that fictitious cracks are much smaller than real
crack lengths considered. The reason for this limitation is that
G_CR looses its meaning as an independent material property at
higher strengths.Expressions are presented which relate critical
energy release rate G_CR and fictitituous crack geometry of
modified Dugdale cracks to arbitrary cohesive stress
distributions. Examples are presented with cohesive stress
distributions similar to such recently suggested in fracture
analysis of cementitious materials. Other examples are presented
whick demonstrate how fictitious cracks behave with respect to
deformation and cohesive stress distribution when the material
considered is subjected to sub-critical loads. Such information,
which cannot be obtained experimentally, are needed in
viscoelastic lifetime analysis.Finally, the question is considered
whether or not fracture properties experimentally determined are
real (genuine) material properties.
AB - A number of theories are presented in the literature on crack
mechanics by which the strength of damaged materials can be
predicted. Among these are theories based on the well-known
Dugdale model of a crack prevented from spreading by self-created
constant cohesive flow stressed acting in local areas, so-called
fictitious cracks, in front of the crack.The Modified Dugdale
theory presented in this paper is also based on the concept of
Dugdale cracks. Any cohesive stress distribution, however, can be
considered in front of the crack. Formally the strength of a
material weakened by a modified Dugdale crack is the same as if it
has been weakened by the well-known Griffith crack, namely
sigma_CR = (EG_CR/phi)^1/2 where E and 1 are Young's modulus and
crack half-length respectively, and G_CR is the so-called critical
energy release rate. The physical significance of G_CR, however,
is different.For brittle materials (considered by the Griffith
theory )G_CR = 2 Gamma where Gamma is surface energy of material
considered. For more tough materials (considered by the modified
Dugdale theory) G_CR is a function f(sigma_L delta_CR) where
sigma_L and delta_CR are theoretical strength and flow limit
(displacement) respectively of material considered. The practical
applicability of the two models is limited such that predicted
strength sigma_CR must be less than sigma_L/3, which corresponds
to an assumption that fictitious cracks are much smaller than real
crack lengths considered. The reason for this limitation is that
G_CR looses its meaning as an independent material property at
higher strengths.Expressions are presented which relate critical
energy release rate G_CR and fictitituous crack geometry of
modified Dugdale cracks to arbitrary cohesive stress
distributions. Examples are presented with cohesive stress
distributions similar to such recently suggested in fracture
analysis of cementitious materials. Other examples are presented
whick demonstrate how fictitious cracks behave with respect to
deformation and cohesive stress distribution when the material
considered is subjected to sub-critical loads. Such information,
which cannot be obtained experimentally, are needed in
viscoelastic lifetime analysis.Finally, the question is considered
whether or not fracture properties experimentally determined are
real (genuine) material properties.
M3 - Report
BT - Modified Dugdale cracks and Fictitious cracks
ER -