Scaling characteristics of dislocation link length distributions generated during the creep of crystals

Abstract

The distribution of dislocation link lengths comprising the dislocation network generated during the elevated temperature deformation of NaCl and Al monocrystals has been evaluated at several values of the applied stress, σ, and temperature, T, and at various stages of primary creep up to the steady state condition. The properties of the normalized function, Φ( u) = β 2 ρ −2 φ( L, t), where φ( L, t) dL is the number of dislocation links per unit volume of length between L and L + dL at time t, ρ is the dislocation density, u = L 〈L〉 , 〈 L〉 is the average link length and β is a constant defined by the relationship 〈L〉 = βρ − 1 2 , are analyzed. Within experimental error Φ( u) is independent of t during the primary creep of NaCl. The same appears to be true for Al, although the greater scatter render this conclusion less convincing. For these two materials Φ( u) has the attributes of a dynamic scaling function. It is tentatively concluded that Φ( u) is at most weakly dependent on σ and T and depends primarily on crystal structure. Specifically, Φ( u) ∝ u m as u → 0, with m ~ 1.5 for NaCl and MgO and m ~ 1.33 for Al. Since the data on Al were taken at stresses spanning the Harper-Dorn and power-law creep regimes the results suggest that m is independent of the mode of creep, although it may increase with increasing σ for NaCl. Evidence is presented that β is dependent on the mode of creep. It is smaller (0.75–0.8) for Al deformed in the H-D regime than for materials, including Al, deformed in the power-law regime, where the value of β typically exceeds 0.85 and may also increase with increasing σ. The limiting behavior of Φ( u) is related to the nature of the equation governing the rate of growth g = dL dt , of individual links. In particular, g( L, t) must approach L − m as L → 0. The implications of these observations are discussed.