There are two equations that are primarily used in context of the facture stress one with sqrt(2 *gamma*E/a0) and the other with sqrt(2*gamma*E/pi*C).I do not understand which one to use while finding the critical crack length.
Dear Rajorshi
In fracture mechanics, there are many distinct formulas for calculating different parameters such as theoretical cohesive strength, fracture strength, critical crack length, and fracture toughness. In the following, two different formulas will be explained:
a) 𝝈𝒕𝒉=((𝑬.𝜸𝒔)/𝒂𝟎) (𝟏/𝟐)
where 𝑬 is young's modulus, 𝝈𝒕𝒉 is the theoretical cohesive strength,𝜸𝒔 is the surface energy, and 𝒂𝟎 is the interatomic spacing.
However, the observed fracture strength is always lower than the theoretical cohesive strength. Therefore, eq.(b), known as "Griffith’s equation", was developed:
b) 𝝈f=((2𝑬.𝜸𝒔)/πc)(𝟏/𝟐)
where 𝝈f and c are the fracture strength, and half of the center crack length. Consequently, if the material contains a center crack with length of 2c, then the fracture stress will be equal to 𝝈f . However, this equation is used for brittle materials. You can use Irwin’s modification if your material is ductile-brittle.
You might use eq.(b) considering that 𝝈f is the fracture strength of your material and 2c is the critical crack length. However, in linear elastic fracture mechanics, “fracture toughness” of the material (K1c) is calculated, and the critical crack length is determined with respect to the amount of applied stress.
I hope this answer could be useful.
Kind regards
Dear Rajorshi
In fracture mechanics, there are many distinct formulas for calculating different parameters such as theoretical cohesive strength, fracture strength, critical crack length, and fracture toughness. In the following, two different formulas will be explained:
a) 𝝈𝒕𝒉=((𝑬.𝜸𝒔)/𝒂𝟎) (𝟏/𝟐)
where 𝑬 is young's modulus, 𝝈𝒕𝒉 is the theoretical cohesive strength,𝜸𝒔 is the surface energy, and 𝒂𝟎 is the interatomic spacing.
However, the observed fracture strength is always lower than the theoretical cohesive strength. Therefore, eq.(b), known as "Griffith’s equation", was developed:
b) 𝝈f=((2𝑬.𝜸𝒔)/πc)(𝟏/𝟐)
where 𝝈f and c are the fracture strength, and half of the center crack length. Consequently, if the material contains a center crack with length of 2c, then the fracture stress will be equal to 𝝈f . However, this equation is used for brittle materials. You can use Irwin’s modification if your material is ductile-brittle.
You might use eq.(b) considering that 𝝈f is the fracture strength of your material and 2c is the critical crack length. However, in linear elastic fracture mechanics, “fracture toughness” of the material (K1c) is calculated, and the critical crack length is determined with respect to the amount of applied stress.
I hope this answer could be useful.
Kind regards
The critical crack length indicates the transition from a stable crack growth regime to unstable crack growth (stage 3) regime that leads to catastrophic fracture or failure. From an initial crack length of 'a' to the critical crack length 'ac', the crack growth behavior can be predicted using fracture mechanics principles. This stage is considered as 'stable crack growth' regime.
The critical crack length is a term used to describe the defects in materials. It is the length of the crack that grows after the fracture occurs rapidly at the same stress. Therefore, according to Erwin and Griffith theory related to the geometric shape of the crack in the standard sample dimensions, the length of the notch (crack) that applied before the test should not exceed the width of the sample exposed to the external stress. The fracture toughness is considered as an essential mechanical property of the brittle materials.
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