2. intro_fracture_materials.pdf

Question 1

What are 5 different types of Failure in Structures?

Answer 1

1) Buckling - failure by elastic instability
2) Jamming - failure by excessive large elastic deformation
3) Yielding - failure by gross plastic deformation
4) Necking - failure by tensile instability
5) Cracking - failure by fast fracture

Question 2

Define General Yielding

Answer 2

A body is said to have undergone general yielding when it is no longer possible to trace a path, across the load-bearing cross section from loading point to loading point, through elastically deformed material only.

Question 3

What curve can be used to determine the surface energy to create a new surface by fracturing the atomic bonds?

Derive an equation for surface energy required using the following image:

Answer 3

half of the area under the curve

Question 4

Given the attached image of a crack in a specimen under tensile loading, what is the max tensile stress (Inglis Solution)

Answer 4

Question 5

Given the attached image of a crack in a specimen under tensile loading, what is the max tensile stress (Griffith Criterion)

Answer 5

(I) A necessary condition for propogation of an elliptical crack is that the max stress at the crack tip is equal to σ_c

(II) An exisitng crack will propagate if this leads ot a reduction of the total energy of the system:

The incremental elastic energy (W_E) due to the propagation of a crack should be equal or more than the work energy necessary to develop a new crack surface (W_S)

Question 6

What symbol(s) represent strain energy release rate?

Answer 6

G_c = γ_s+γ_p

Question 7

When should the strain energy release rate for plastic deformation be included in determining maximum stress of a specimen?

Answer 7

when γp/γs >>1

Question 8

Review derivations from “intro_fracture_materials.pdf”

Answer 8

did you actually tho?

Question 9

How do you find the principle stresses from a stress tensor?

and the direction cosines?

Answer 9

0 = det (σ - λI)

**σ = **σ₁₁ σ₂₁ σ₃₁

  σ<sub>12</sub>  σ<sub>22</sub>  σ<sub>32</sub>

  σ<sub>13</sub>  σ<sub>23</sub>   σ<sub>33</sub>

I = 1 0 0

 0  1  0

 0  0  1

0 = (σ - λI)X

X = {X₁,X₂,X₃}^T

Question 10

What does it mean if the 3 principle stress are:

unequal?

equal?

2 equal, third not equal to 0?

2 equal to 0?

all equal to 0?

Answer 10

unequal: biaxial

equal: hydrostatic

2 equal, third not equal to 0: cylindrical

2 equal to 0: uniaxial

all equal to 0: biaxial or plane stress

Question 11

What are the equations for strain in relation to principle stresses?

Answer 11