Abstract
The two parameters, C and m, which characterize the Paris equation for fatigue crack growth are explained in relation to the crack closure concept suggested by Elber. It is proposed that the range of effective incremental change in stress intensity factor (ΔK) needed for crack growth should have a second power correlation with the growth rate. The crack growth is essentially determined by cumulative damage to the material in cycled plastic zone near the crack tip, and is relatively insensitive to the applied ΔK-values and the mechanical properties of material. However, the crack closure behavior is expected to depend on both the stress range and the material properties. Thus it is concluded that the exponent parameter m reflects mainly the dependency of crack closure behavior on ΔK. For example, in the case of m=4 the crack opening level increases linearly with increase in ΔK, while in the case of m=2 it remains constant. It is suggested that the cyclic straining at the crack tip possibly varies with ΔK, thus changing primarily the crack closure behavior rather than the damage accumulation process in the plastic zone.
Résumé
Les deux paramètres, C et m, qui caractérisent l'équation de Paris pour la propagation des fissures de fatigue sont expliqués en relation avec le concept de fermeture d'une fissure suggéré par Elber. On propose que la grandeur du changement effectif du facteur d'intensité de contrainte ΔK nécessaire à l'accroissement d'une fissure figure à une puissance deuxième dans une corrélation avec le taux de croissance. La croissance d'une fissure est essentiellement déterminée par le dommage cumulatif infligé au matériau dans la zône de déformation plastique cyclique au voisinage de l'extrémité de la fissure; il est relativement insensible aux valeurs appliquées de ΔK et aux propriétés mécaniques du matériau. Toutefois, le comportement à la fermeture d'une fissure devrait dépendre à la fois du taux de contrainte et des propriétés du matériau. Il est donc conclu que le paramètre exponentiel m représente principalement la dépendance du comportement à la fermeture d'une fissure par rapport à ΔK. A titre d'exemple, dans le cas de m=4, le niveau de fermeture de la fissure augmente linéairement avec un accroissement de ΔK, tandis que, dans le cas de m=2, il demeure constant. On suggère que les déformations cycliques à l'extrémité de la fissure peuvent varier avec ΔK et modifient ainsi en premier lieu le comportement à la fermeture de la fissure plutôt que le processus d'accumulation de dommages dans la zône plastique.
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Tanaka, K., Matsuoka, S. A tentative explanation for two parameters, C and m, in Paris equation of fatigue crack growth. Int J Fract 13, 563–583 (1977). https://doi.org/10.1007/BF00017293
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DOI: https://doi.org/10.1007/BF00017293