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Breakdown Mechanism
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When a fracture occurs, it is characterized by an area that can no longer bear load and an edge marked by tension that grows inversely to the radius of the fracture tip. This means that the section is diminished, requiring the remaining section to bear a greater load, exacerbating the situation at the fracture tip and facilitating its propagation. Thus, a catastrophic situation ensues where each increase in the fracture adds to the load to be borne, leading to further fracture growth.

>Model

ID:(2067, 0)

Mechanisms
Description


ID:(15577, 0)

Mechanics breaking
Description

ID:(742, 0)

Tensions in the Vecinity of the Break Tip
Description

The fracture propagates because its tip has an extremely small radius, which implies very high tension, as tension is proportional to the inverse of the square root of the radius.

The advancement of the fracture can be halted if, at some point, the radius increases, reducing the tension at its tip. This is achieved, for example, through material porosity or the insertion of inhomogeneities that act as stress concentration points.

None


ID:(1691, 0)

Model
Description



ID:(15578, 0)

Breakdown Mechanism
Description

When a fracture occurs, it is characterized by an area that can no longer bear load and an edge marked by tension that grows inversely to the radius of the fracture tip. This means that the section is diminished, requiring the remaining section to bear a greater load, exacerbating the situation at the fracture tip and facilitating its propagation. Thus, a catastrophic situation ensues where each increase in the fracture adds to the load to be borne, leading to further fracture growth.

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$\theta$
theta
Angle
rad
$l$
l
Break length
m
$r$
r
Disc radius
m
$F$
F
Force
N
$K_I$
K_I
Intensity factor
$E$
E
Modulus of Elasticity
Pa
$r_p$
r_p
Radio of the break tip
m
$\sigma_1$
sigma_1
Stress on axis $x$
Pa
$\sigma_2$
sigma_2
Stress on axis $y$
Pa

Calculations

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Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
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Translated

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Equations

Examples


(ID 15577)

The fracture propagates because its tip has an extremely small radius, which implies very high tension, as tension is proportional to the inverse of the square root of the radius.

The advancement of the fracture can be halted if, at some point, the radius increases, reducing the tension at its tip. This is achieved, for example, through material porosity or the insertion of inhomogeneities that act as stress concentration points.

None


(ID 1691)



(ID 15578)

The breaking stress is proportional to the intensity factor ($K_I$), which is in turn proportional to the square root of the force ($F$), the modulus of Elasticity ($E$), and the break length ($l$):

$ K_I =\sqrt{\displaystyle\frac{ F E }{ l }}$


(ID 3785)

$\sigma_y(r_p,0)=\displaystyle\frac{K_i}{\sqrt{2\pi r_p}}$

(ID 3786)

$\sigma_x(r,\theta)=\displaystyle\frac{K_i}{\sqrt{2\pi r}}\cos\displaystyle\frac{\theta}{2}\left(1-\sin\displaystyle\frac{\theta}{2}\sin\displaystyle\frac{3\theta}{2}\right)$

(ID 3788)

$\sigma_y(r,\theta)=\displaystyle\frac{K_i}{\sqrt{2\pi r}}\cos\displaystyle\frac{\theta}{2}\left(1+\sin\displaystyle\frac{\theta}{2}\sin\displaystyle\frac{3\theta}{2}\right)$

(ID 3787)

ID:(2067, 0)