Nabarro (1948) pointed out theoretically that any polycrystalline solid yields to an applied shear stress to change its shape due to self-diffusion within crystal grains. Since 1957 Kumagai and Itô have carried out the long-term creep experiment on granite beams. Their experimental results over 24 years show that granite flows viscously without a yield stress. It may be essential that a solid has no yield stress. In this chapter the author compiles long-term creep experiments on rock, and discusses the creep, referring to the theory by Nabarro and Herring (1950).
Nabarro (1948) a fait remarquer theoriquement que tout solide polycristallin cède à une contrainte de cisaillement appliquee pour se transformer par l'auto-diffusion de grains cristalises. D'après les experiences à long terme que Kumegai et Itô ont faites sur le poutre en granit pendant 24 ans depuis 1957, le granit se montre fluent et visqueux sans seuil de plasticite. Un solide ne doit, peut-être, pas avoir de seuil de plasticite. Dans ce rapport, les auteurs recueillent les fruits de leurs experiences à long terme sur le fluage de roche et les expliquent en se referant à la theorie etablie par Nabarro et Herring (1950).
Nabarro (1948) wies darauf theoretisch hin, daβ sich jeder feste polykristallinische Körper infolge seiner Selbstdiffusion innerhalb des Kristallkorns der ange1egten Scherspannung ergibt und deformiert. Seit 1957 haben Kumagai und Itô einen langfristigen Kriechenversuch mit Granitbalken gemacht. Ihr ueber 24 Jahre fortdauernder Versuch zeigt, daβ Granit viskos ohne Flieβgrenze flieβt. Es duerfte sich darum im wesentlichen handeln, daB ein fester Körper keine Flieβgrenze hat. In der vorliegenden Arbeit soll das Kriechen, fuer das Daten aus den langfristigen Versuchen mit Gesteinskriechen gesammelt worden sind, in Verbindung mit der Theorie nach Nabarro und Herring diskutiert werden.
In a material test, a test-piece is first deformed elastically, then after reaching the yield point, flows plastically. Atoms are fixed at their lattice points in the elastic range, but they are moved in the plastic range. It is well known in a study of metals that the moving mechanism is due to the dislocation within a crystal grain. The yield stress is a strength of material against the plastic flow, while the breaking stress is another strength against rupture. In a creep test, the lowest stress under which the secondary creep (steady flow) takes place is the yield stress. When only the primary creep occurs but the secondary creep does not, atoms are fixed at lattice points. In this case, when stress is released, the strain is perfectly recovered. Determine the yield stress of material for creep is very laborious, although the value has been known to be smaller than the yield stress obtained by the material test curried out for a short time. Griggs (1940) tried to determine the yield stress for creep of rock. The chosen material is alabaster of gypsum. The alabaster was immersed in water chemically saturated by itself. The wet creep tests were carried out at different compressive stresses from 300 to 103 kg/cm2. The test at 103 kg/cm2 was continued over 520 days. Strain rates ε of the secondary creep thus obtained are plotted against the compressive stresses σ as shown in Fig.l (Griggs, 1940, Fig.7 and Table 1), which the author draws using the abscissa (ε) scaled ordinarily, though Griggs used a log-scale. The strain rate at 300 kg/cm2 is too large (23xl0–9) to be shown in the figure. The empirical formular got by Griggs is represented by a hyperbolic sine shown in the figure. If the formular were correct, the strain rate would become zero at a stress of 92 kg/cm2. This is the yield stress of the alabaster under the given condition. However, there is no experimental evidence that the secondary creep does not take place at stresses smaller than 92 kg/cm2.
Nabarro (1948) pointed out that self-diffusion within grains of a polycrystalline solid can cause the solid to yield to an applied shear stress and the yielding is caused by a diffusional flow of matter within each crystal grain away from boundaries where there is a compression and toward those where there is a tension, as shown in Fig.2. This yielding can cause the solid to. behave macroscopically as viscous fluid with an viscosity proportional to the square of the grain size. In actual crystal there are always lattice defects; a lattice vacancy or an interstitial atom is a point defect. The diffusional flow takes place through these point defects. As Herring (1950) perfected the theory, it is called "Nabarro-Herring creep" or the lattice diffusion creep. On the other hand, creep caused by the dislocation within a crystal grain as mentioned at the top of this paper is called "dislocation creep".