Oluschinski at 06:23, 15 December 2025

2025-12-15T06:23:38Z

← Older revision		Revision as of 08:23, 15 December 2025
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	The [[Crack Model according to GRIFFITH \| GRIFFTITH]] and [[Crack Model according to IRWIN and Mc CLINTOCK \| IRWIN & MC CLINTOCK]] [[Crack Models \| crack models]] have in common that infinitely large stresses occur at the crack tip with a very sharp notch. In order to eliminate this discrepancy between the model conceptions and the practically possible conditions, BARENBLATT developed a model for the elasticity-theoretical description of the stress conditions at the crack tip. The crack is divided into an inner and two outer areas.		The [[Crack Model according to GRIFFITH \| GRIFFTITH]] and [[Crack Model according to IRWIN and Mc CLINTOCK \| IRWIN & MC CLINTOCK]] [[Crack Models \| crack models]] have in common that infinitely large stresses occur at the crack tip with a very sharp notch. In order to eliminate this discrepancy between the model conceptions and the practically possible conditions, BARENBLATT developed a model for the elasticity-theoretical description of the stress conditions at the crack tip. The crack is divided into an inner and two outer areas.

	[[file:~~rissmodellbarenblatt1~~.jpg]]<br>		[[file:CrackModelBarenblatt1.jpg]]<br>
	{\|		{\|
	\|- valign="top"		\|- valign="top"
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	'''Figure 2''' shows the course of the cohesive forces and the resulting stresses in the x-direction over the crack length.		'''Figure 2''' shows the course of the cohesive forces and the resulting stresses in the x-direction over the crack length.

	[[file:~~rissmodellbarenblatt2~~.jpg]]<br>		[[file:CrackModelBarenblatt2.jpg]]<br>
	{\|		{\|
	\|- valign="top"		\|- valign="top"

Oluschinski: Created page with "{{Language_sel|LANG=ger|ARTIKEL=Rissmodell nach BARENBLATT}} {{PSM_Infobox}} Crack model BARENBLATT FORCETOC ==Fundamentals of the model== The GRIFFTITH and IRWIN & MC CLINTOCK crack models have in common that infinitely large stresses occur at the crack tip with a very sharp notch. In order to elimin..."

2025-12-01T06:58:40Z

Created page with "{{Language_sel|LANG=ger|ARTIKEL=Rissmodell nach BARENBLATT}} {{PSM_Infobox}} Crack model BARENBLATT __FORCETOC__ ==Fundamentals of the model== The GRIFFTITH and IRWIN & MC CLINTOCK crack models have in common that infinitely large stresses occur at the crack tip with a very sharp notch. In order to elimin..."

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{{Language_sel|LANG=ger|ARTIKEL=Rissmodell nach BARENBLATT}}
{{PSM_Infobox}}
Crack model BARENBLATT
__FORCETOC__

==Fundamentals of the model==

The [[Crack Model according to GRIFFITH | GRIFFTITH]] and [[Crack Model according to IRWIN and Mc CLINTOCK | IRWIN & MC CLINTOCK]] [[Crack Models | crack models]] have in common that infinitely large stresses occur at the crack tip with a very sharp notch. In order to eliminate this discrepancy between the model conceptions and the practically possible conditions, BARENBLATT developed a model for the elasticity-theoretical description of the stress conditions at the crack tip. The crack is divided into an inner and two outer areas.

[[file:rissmodellbarenblatt1.jpg]] 
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Crack model according to BARENBLATT
|}

In BARENBLATT's crack model, atomic or molecular cohesive forces are assumed, which lead to a smooth closing of the crack surfaces.

The crack opens continuously in the outer area δ, the interpretation is that the atomic and molecular distances in the area δ increase continuously and an interaction takes place in the form of cohesive forces. These can reach the theoretical strength of the material. (Cohesion: Cohesion of the molecules of a body)

==Cohesive forces and cohesive modul==

'''Figure 2''' shows the course of the cohesive forces and the resulting stresses in the x-direction over the crack length.

[[file:rissmodellbarenblatt2.jpg]] 
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Stress distribution at the crack tip according to BARENBLATT
|}

BARENBLATT formulated the integral of the distribution of the cohesive forces over the crack cross-section as a [[Material Parameter | material parameter]] and called it the cohesive modulus

{|
|-
|width="20px"|
|width="500px" | <math>B=\int_{0}^{\delta}\frac{g(s^{*})ds^{*}}{\sqrt{s^{*}}}</math> oder: <math>B=\int_{0}^{\delta}\frac{g(x)}{\sqrt{x}}dx</math>
|}

with
{|
|-
|s*   –
|width="15px" |
|coordinate in x-direction
|-
|g &ensp; –
|width="15px" |
|cohesive force
|}

Although a number of methods for calculating the cohesive modulus have been proposed, an exact determination of this characteristic material parameter remains problematic.

The advantage of BARENBLATT's crack model is that the infinitely large stress values occurring at the crack tip in [[Crack Model according to GRIFFITH | GRIFFITH's crack model]] are avoided, and possible distributions of the stress at an infinitely sharp crack are described.

In recent years, however, there has been an increased interest in this crack model, also known as the cohesive zone model. This is also due, apart from the extension of the model itself, to the immense progress in computer technology.

==Application area==

[[file:CrackModelBarenblatt3.jpg]] 
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px" |Valid ranges of crack models
|}

==Importance of the model==

This theory had relatively little application in practice for a long time. There are examples of application in the analysis of:

* geological fracture processes
* stress corrosion cracking of polymers
* crack propagation at interfaces / in boundary layers (interlaminar crack propagation, crack propagation in adhesive and welded joints etc.)

==See also==

*[[Fracture Mechanics | Fracture mechanics]]
*[[Crack Models | Crack models]]
*[[Crack Model according to GRIFFITH| Crack model according to GRIFFITH]]
*[[Crack Model according to IRWIN and Mc CLINTOCK | Crack model according to IRWIN and Mc CLINTOCK]]
*[[Crack Model according to DUGDALE | Crack model according to DUGDALE]]

'''References'''

* Barenblatt, G. I.: Prikl. Math. i. Mech. XX, 4 (1956), S. 475. In: Blumenauer, H., Pusch, G.: Technische Bruchmechanik. Deutscher Verlag für Grundstoffindustrie, Leipzig (1987) 2. Ed. p. 22 (ISBN 3-342-00096-1; see AMK-Library under E 29-2))

* Barenblatt, G. I.: The Formation of Equilibrium Cracks during Brittle Fracture. General Ideas and Hypotheses. Axially-symmetric Cracks. Journal of Applied Mathematics and Mechanics 23 (1959) 622–636, https://doi.org/10.1016/0021-8928(59)90157-1

* Barenblatt, G. I.: Equilibrium Cracks Formed during Brittle Fracture Rectilinear Cracks in Plane Plates. Journal of Applied Mathematics and Mechanics 23 (1959) 1009–1029; https://doi.org/10.1016/0021-8928(59)90036-X

* Barenblatt, G. I.: Concerning Equilibrium Cracks Forming during Brittle Fracture. The Stability of Isolated Cracks. Relationships with Energetic Theories. Journal of applied Mathematics and Mechanics 23 (1959) 1273–1282; https://doi.org/10.1016/0021-8928(59)90130-3

* Barenblatt, G. I.: The Mathematical Theory of Equilibrium Cracks in Brittle Fracture. Adv. in Appl. Mech. 7 (1962) 55–129; https://doi.org/10.1016/S0065-2156(08)70121-2

[[Category:Fracture Mechanics]]

Crack Model according to BARENBLATT - Revision history

Oluschinski at 06:23, 15 December 2025