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{{Language_sel|LANG=ger|ARTIKEL=GRIFFITH´s Theorie}}
{{PSM_Infobox}}
<span style="font-size:1.2em;font-weight:bold;">GRIFFTH`s theory</span>

'''GRIFFTH`s theory on the strength and Failure of solids'''
__FORCETOC__

==General==

The fundamental scientific work on the [[Strength|strength]] and [[Fracture Behaviour|fracture behaviour]] of solids was carried out by [[Griffith, Alan Arnold|GRIFFITH]] for the [[Material & Werkstoff|material]] glass [1]. The transfer of the results to metallic materials is closely linked to the technical development of nuclear energy. A few years after GRIFFITH's death in 1963, the application of [[Fracture Mechanics|fracture mechanics]] began in the development of materials and component monitoring of [[Plastics|plastics]] and [[Composite Materials Testing|composite materials]].

==The mechanical strength of glass==

In the 1960s, Professor Werner Vogel's research group at the Otto Schott Institute of Friedrich Schiller University in Jena worked on developing general concepts regarding the [[Strength|strength]] of glass and ways of increasing its strength through controlled crystallisation [2].

According to GRIFFITH's theory, the low effective strength of glass is caused by the presence of countless microscopic [[Crack|cracks]] in the glass volume. These [[Crack|cracks]] are said to be semi-elliptical in shape, are also referred to as GRIFFITH pockets, and are thought to act as stress centres. When the glass is subjected to stress, the [[Crack Formation|fracture process]] will start earlier than in flawless glass, starting from these cracks. According to [[Griffith, Alan Arnold|GRIFFTH's]] initial calculations, the pockets should be approximately 5 µm in size. Based on experimental results obtained by various authors using [[Electron Microscopy|electron microscopy methods]], it has been proven that [[Errors|errors]] on the [[Surface|surface]] are the cause of the [[Fracture|failure]]. Therefore, measures to significantly improve the mechanical strength of the glass must primarily consist of surface treatment.

The most significant further development of GRIFFITH's theory was made by E. F. Poncelet (1944 and 1948) [3, 4]. His ideas on the ‘genesis of pockets’ clearly have a strong bearing on glass structure problems. While [[Griffith, Alan Arnold|GRIFFITH]] later changed his original view to assume that pockets were not present throughout the entire volume of glass, but only on the [[Surface|surface]], Poncelet assumes that, apart from coarse surface cracks, there are initially no pockets in the glass. However, they are created throughout the entire glass volume by the application of force. Poncelet's fundamental assumption is that the stress required to form the pockets only needs to be a fraction of the usual fracture stress.

Vogel [2] referred to the connection between droplet-shaped segregation zones, which were first detected in those years, and the formation of GRIFFITH pockets.

According to PONCELET's theory, GRIFFITH pockets should already form when the glass is subjected to tensile stress that is well below the fracture stress. This is equivalent to a slow fracture process around a droplet-shaped segregation zone, which leads to the formation of pockets but not yet to macroscopic [[Fracture|fracture]] of the test [[Specimen|specimen]].

In a glass area under tensile stress that contains a droplet-shaped segregation zone, the primary [[Crack|crack]] will initially always run perpendicular to the direction of tension, but will then bend into a partial ellipse in accordance with the spherical shape of the inhomogeneity ('''Fig. 1''').

[[File:Griffith-Theorie-Bild-1.jpg|200px]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Schematic representation of the formation of a GRIFFTH pocket. Glass area with droplet-shaped segregation zone. Under tensile stress, crack formation generally begins perpendicular to the direction of tension. The [[Crack|crack]] then runs in a semi-elliptical shape around the droplet zone [2].
|}

==Detection of GRIFFTH pockets and GRIFFTH cracks==

The existence of GRIFFTH pockets in glass was experimentally proven using [[Electron Microscopy|electron microscopy]] methods.

'''Figure 2''' shows typical semi-elliptical GRIFFITH pockets that formed as a result of compressive and tensile stress on the glass during the polishing process.

[[File:Griffith-Theorie-Bild-2.jpg|300px]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Droplet-shaped segregation zone in a phosphate-tinted silicate glass. Compressive and tensile stresses on the glass during the polishing process have caused a typical semi-elliptical GRIFFITH pocket to form around the droplet zone (light microscope images). Scale magnification 200:1 [2]
|}

'''Figure 3''' shows an example of [[Crack Initiation|crack formation]] immediately concentric around a segregation zone. In the case of very small segregation zones, [[Crack Formation|crack formation]] occurs immediately at the [[Phase Boundary Surface|phase boundary]].

[[File:Griffith-Theorie-Bild-3.jpg|300px]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px" |Droplet-shaped segregation zone in a phosphate-tinted silicate glass. Concentric cracking around the droplet, but at a certain distance from the [[Phase Boundary Surface|phase boundary]]. In the centre is a bubble formed during the cooling process. (Light microscope image), image magnification 500:1 [2]
|}

Further electron microscope images are included in [2].

==Technical use==

These theoretical considerations regarding the [[Strength|strength]] and failure of glass formed the basis for increasing the strength of glass products in engineering, such as hardening the [[Surface|surface]] by heating a product to [[Glass Transition Temperature|glass temperature]] and then quenching it with cold air. Compressive stresses are formed on the glass surface, while tensile stresses act inside the glass. The [[Crack|cracks]] in the glass surface are compressed and hindered from opening, i.e. initiating the [[Crack Formation|breaking process]] through [[Crack Propagation|crack propagation]]. If the load exceeds the applied breaking stress, there is a risk of failure due to fracture.

A method used industrially today is sodium–potassium ion exchange on the [[Surface|surface]], which also produces the hardening effect described above.

==See also==

* [[GRIFFITH's Criteria|GRIFFITH`s criteria]]
* [[Crack Model according to GRIFFITH|Crack model according to GRIFFITH]]
* [[Griffith, Alan Arnold]]
* [[Crack]]

==References==

{|
|-valign="top"
|[1]
|Griffith, A. A.: The Phenomena of Rupture and Flow in Solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, Vol. 221 (1921) pp. 163–198. JSTOR; DOI: https://www.jstor.org/stable/91192
|-valign="top"
|[2]
|Vogel, W.: Struktur und Kristallisation der Gläser. Deutscher Verlag für Grundstoffindustrie Leipzig (1971) (see AMK-Library under Q 3)
|-valign="top"
|[3]
|Poncelet, E. F.: Fracture and Communication of Brittle Solids. Metals Technol. 11 (1944) Techn. Publ. 1684
|-valign="top"
|[4]
|Poncelet, E. F.: Theory of Static Fatigue for Brittle Solids. Fracturing of Metals. Amer. Soc. Metals (Cleveland) (1948) 201–227
|}

[[Category:Fracture Mechanics]]

GRIFFITH's Theory - Revision history