Kinetic theory approach to fatigue crack propagation in terms of dislocation dynamics

Abstract

As for the model of kinetic theory of fatigue crack propagation it may be classified into the following two types:Thefirst type: The model in which a microcrack nucleates in the neighbourhood of the tip of the main crack through the mechanism of separation of atoms caused by stress concentration due to the notch effect [1--4] (Fig. la) or due to slip (Fig. lc) or the mechanism of the condensation of vacancies [5] (Fig. lb), and the main crack join this, the process being repeated. The second type: The model in which the main crack itself extends by the mechanism of separation of atoms [6] (Fig. l d) or the mechanism of offset by slip (Fig. le) without nucleating a microcrack and joining it in front of the tip of the main crack.With respect to the model of the first type, some theoretical approaches have been attempted in the previous papers [1][2][3][4][5]. In the present article, from the viewpoint of the second type an attempt has been made based on dislocation dynamics.In the present article it is assumed that an irreversible slip occurs at the tip of crack every L W--° (a) (e) Figure 1. Typical examples of models in kinetic theory of fatigue crack propagation. half cycle under tension, but not during half cycle under compression. As far as this respect is concerned, the model is not inconsistent with those of McEvily et al. [7], Tomkins [8] and Laird et al. [9]. The number Z of Frank-Read sources along the crack tip edge of the length L~ of the main crack may be denoted by L 1 P~, that is Z = L1 p½, where p = the dislocation density at the concerned edge area. The relative offset ~ of the two parts of the crack at the edge between the distance L~ may be written as ~= Z n b = L l p * n b , where n=the number of dislocations emitted from the crack tip, b is Burgers vector. Then fatigue crack propagation rate, dc/dN is written as :where c = half length of crack and N is repeated cycles and 0~ is geometrical factor. For instance, in the case of tension-compression loading as shown in Fig. 2, ~ is 2 -½. lnt, Journ. of Fracture, 10 (1974)467-470

Dislocation dynamics theory for fatigue crack growth

“…On the other hand, it may be assumed that offset [1] is caused by the dislocation emission from the surface of the crack front on opening and closing. On the other hand, it may be assumed that offset [1] is caused by the dislocation emission from the surface of the crack front on opening and closing.…”

“…One of the authors however has made an initial attempt [1] to treat the subject, but in this first approximation, a crude power type simplification was made in relating the dislocation velocity and applied stress. One of the authors however has made an initial attempt [1] to treat the subject, but in this first approximation, a crude power type simplification was made in relating the dislocation velocity and applied stress.…”

Effect of a second phase particle on the rate of growth of fatigue cracks

“…In applying the above equation to a two-phase medium two types of particles namely with a planar interface or with a circular interface are considered. Comparison of the results obtained by Hahn and 544 K. Jagannadham, E. G. Ramachandran Rosenfield [7] in a homogeneous medium and those obtained for a pile-up at a planar interface [5] gives (2) where k=(G2-G,)/(G2WG,), Gz is the shear modulus of the matrix, G 2 that of the second phase and L the distance travelled by the leading dislocation. has been estimated to be [4], p = 8fT/bd where f is the volume fraction of the particles, d is the average diameter of the particle with circular cross-section.…”

“…An average value of At, the effective stress at the tip of a crack under fatigue has been determined to be [2] An average value of At, the effective stress at the tip of a crack under fatigue has been determined to be [2] …”

“…In the past many attempts have been made to determine the fatigue crack growth rate in homogeneous media [1,2] using the theory of dislocations. In the Bilby, Cottrell and Swinden model proposed by Weertman [1], the crack and the plastic zone at the tip are represented by arrays of dislocations.…”