Mechanism of crack propagation in brittle and ductile

Theoretical fracture strength is; σ_m = 13,685 MPa

None of the options are correct

Explanation:

We are given;

Nominal applied stress;σ_o = 1060 MPa

Length of surface crack; a = 0.25 mm

Tip radius of curvature; ρ_t = 0.006 mm

Now, the formula for the theoretical fracture strength which is the maximum stress at the crack tip is given as;

σ_m = 2σ_o[a/ρ_t]^(½)

Plugging in the relevant values, we have;

σ_m = 2(1060)[0.25/0.006]^(½)

σ_m = 13,685 MPa

the theoretical fracture strength of the brittle material is 5.02 × 10⁶  psi

Explanation:

Given the data in the question;

Length of surface crack α = 0.25 mm

tip radius ρ = 1.2 × 10⁻³ mm

applied stress σ₀ = 1200 MPa

the theoretical fracture strength of a brittle material = ?

To determine the the theoretical fracture strength or maximum stress at crack tip, we use the following formula;

σ = 2σ₀ α / ρ

where α is the Length of surface crack,

ρ is the tip radius,

and σ₀ is the applied stress.

so we substitute

σ = (2 × 1200 MPa) 0.25 mm / ( 1.2 × 10⁻³ mm )

σ = 2400 MPa × 208.3333

σ = 2400 MPa × 14.43375

σ = 34641 MPa

σ = ( 34641 × 145 )psi

σ = 5.02 × 10⁶  psi

Therefore, the theoretical fracture strength of the brittle material is 5.02 × 10⁶  psi

critical stress = 17.899 MPa

Explanation:

given data

specific surface energy = 0.33 J/m²

flexural strength = 88.1 MPa

elastic modulus values E = 61 GPa

surface crack of length = 0.04 mm

to find out

critical stress (in MPa)

solution

we get here critical stress that is express as

critical stress =      .....................1

here E is elastic modulus values and a is surface crack of length and γ is specific surface energy

put here value we get

critical stress =

critical stress = 1.7899 × N/m²

critical stress = 17.899 MPa

Theoretical fracture strength is; σ_m = 13,685 MPa

None of the options are correct

Explanation:

We are given;

Nominal applied stress;σ_o = 1060 MPa

Length of surface crack; a = 0.25 mm

Tip radius of curvature; ρ_t = 0.006 mm

Now, the formula for the theoretical fracture strength which is the maximum stress at the crack tip is given as;

σ_m = 2σ_o[a/ρ_t]^(½)

Plugging in the relevant values, we have;

σ_m = 2(1060)[0.25/0.006]^(½)

σ_m = 13,685 MPa

theoretical fracture strength is 9916.58 MPa

Explanation:

given data

surface crack of length L = 0.26 mm

radius of curvature r = 0.004 mm

stress So = 1230 MPa

solution

we get here theoretical fracture strength S that is express as

S  =        .................1

here So is stress and L is length and r is radius

put here value and we get

S  =      

solve it we get

S  =  9916.58 MPa

so theoretical fracture strength is 9916.58 MPa

The theoretical fracture strength of the brittle material is 11864.5 MPa

Explanation:

Fracture strength is the ability of a material to withstand fracture. It is also known as the breaking stress, it is the stress at which the material fails as a result of fracture. It usually determined from the stress-strain curve after performing a tensile test.

Given that:

Length (L) = 0.15 mm = 0.15 × 10⁻³ m

radius of curvature (r) = 0.002 mm = 0.002 × 10⁻³ m

Stress (s₀) = 1370 MPa = 1370 × 10⁶ Pa

theoretical fracture strength (s) = ?

The theoretical fracture strength is given as:

Substituting values:

s = 11864.5 MPa

The theoretical fracture strength of the brittle material is 11864.5 MPa

critical stress = 17.899 MPa

Explanation:

given data

specific surface energy = 0.33 J/m²

flexural strength = 88.1 MPa

elastic modulus values E = 61 GPa

surface crack of length = 0.04 mm

to find out

critical stress (in MPa)

solution

we get here critical stress that is express as

critical stress =      .....................1

here E is elastic modulus values and a is surface crack of length and γ is specific surface energy

put here value we get

critical stress =

critical stress = 1.7899 × N/m²

critical stress = 17.899 MPa

34.64Gpa

Explanation:

We can calculate the theoretical fracture strenght by,

Here we have,

Applied stress

Tip radius

lenght of surface crack or half of the lenght of internal crack

Replacing,

Therefore the maximum stress at the crack tip is 34.64Gpa

The theoretical fracture strength of a brittle material is 26465.29 MPa.

Explanation:

Given that,

Length = 0.54 mm

Radius curvature

Stress = 1050 MPa

We need to calculate the theoretical fracture strength of a brittle material

Using formula of strength

Where, l = length of the crack

= tip radius of curvature

Put the value into the formula

Hence, The theoretical fracture strength of a brittle material is 26465.29 MPa.