which on integration with initial limits of ao and Kmaxo (the Kmax of the fatigue cycle at start of test) produces Kmax = K2 maxo - Q (a-ao) (7) with Q = 2 πσy 2 x y (8) For the case of tests with constant load ratio R, Eqn. 7 can be re-written as ∆K = ∆Ko 2 - Q (1-R)2 (a-a o) (9) Eqn. 9, alongwith Eqn. 8, thus represents an alternate ∆K envelope that may be employed in conducting decreasing ∆K FCGR tests. The conventional technique utilizes a ∆K envelope that is invariant for all types of materials and mean level of fatigue cycles. This is surprising considering that crack tip plasticity, which is thought to be responsible for retardation effects that may be induced, is majorly governed by the flow behaviour of the material and the mean load and amplitude of the fatigue cycle. In the proposed method for accelerating decreasing ∆K FCGR tests, the exact shape of the envelope is determined by the yield stress σy of the material under test (see Eqn. 8), and the R-ratio of the fatigue cycle (see Eqn. 9). A schematic of the ∆K envelope in Eqn. 9 is superimposed in Figure 1. It is not difficult to visualize that for appropriate choice of controlling factors, lower values of ∆K can be attained within much smaller extensions of crack length, as compared to the conventional technique. Having said that, it must be pointed out that despite the nature of the proposed envelope, it may not provide any advantage over the conventional technique in case of material with low σy or for tests at very high R-ratios. conventional exponential procedure: ∆K = ∆Koexp[a-ao] proposed parabolic method Eqn. 9 ao a ∆K ∆Ko Figure 1: Schematic of reduction of ∆K with a as per conventional procedure and the proposed method Other than the σy and R, x and y in Eqn. 8 will also determine the rapidity of the rate of decrease of ∆K. As an informed guess, x and y can be taken as 0.1 and 10 respectively, so that x/y is 0.01. Lumping a user preference parameter t through which the user may exercise control over the rate of ∆K decrement, Eqn. 8 can be explicitly re-written as Q = 0.0628 σy 2 t (10) in which for t=1, x/y assumes a value of 0.01. In order to decide on a value of t that is optimum (i.e. one that allows the fastest rate of reduction of ∆K without inducing any retardation effects) for a given material, the effect of t must be experimentally verified. Such an exercise is detailed below for two varieties of Custrengthened HSLA steel that is used for naval structural applications.
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