GRIFFITH's Theory
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GRIFFTH`s theory
GRIFFTH`s theory on the strength and Failure of solids
General
The fundamental scientific work on the strength and fracture behaviour of solids was carried out by GRIFFITH for the 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 began in the development of materials and component monitoring of plastics and 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 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 cracks in the glass volume. These 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 fracture process will start earlier than in flawless glass, starting from these cracks. According to GRIFFTH's initial calculations, the pockets should be approximately 5 µm in size. Based on experimental results obtained by various authors using electron microscopy methods, it has been proven that errors on the surface are the cause of the 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 later changed his original view to assume that pockets were not present throughout the entire volume of glass, but only on the 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 of the test specimen.
In a glass area under tensile stress that contains a droplet-shaped segregation zone, the primary 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).
| Fig. 1: | 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 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 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.
| Fig. 2: | 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 formation immediately concentric around a segregation zone. In the case of very small segregation zones, crack formation occurs immediately at the phase boundary.
| Fig. 3: | Droplet-shaped segregation zone in a phosphate-tinted silicate glass. Concentric cracking around the droplet, but at a certain distance from the 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 and failure of glass formed the basis for increasing the strength of glass products in engineering, such as hardening the surface by heating a product to 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 cracks in the glass surface are compressed and hindered from opening, i.e. initiating the breaking process through 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, which also produces the hardening effect described above.
See also
References
| [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 |
| [2] | Vogel, W.: Struktur und Kristallisation der Gläser. Deutscher Verlag für Grundstoffindustrie Leipzig (1971) (see AMK-Library under Q 3) |
| [3] | Poncelet, E. F.: Fracture and Communication of Brittle Solids. Metals Technol. 11 (1944) Techn. Publ. 1684 |
| [4] | Poncelet, E. F.: Theory of Static Fatigue for Brittle Solids. Fracturing of Metals. Amer. Soc. Metals (Cleveland) (1948) 201–227 |