The strain rates in the non-uniform and the uniform portion, Sn and Su, are analyzed from a viewpoint of interaction between Si (i=u, n) and Q which is an element with a given strain rate. The prediction is compared with the experimental results: (1) The magnitude of strain rate deviation, ΔR∗i(=Δ\dotεi⁄\bar\dotε), normalized by a given strain rate, \bar\dotε, in the portion, Si, is expressed as:(This article is not displayable. Please see full text pdf.) \ oindentwhere C is a constant, m a strain rate sensitivity parameter, Ai a cross-sectional area in the portion Si, and λi(=li⁄L) a normalized length of Si divided by a specimen length, L. (2) The calculated results agree well with the experimental results, that is, |ΔR∗i| shows a maximum value at a certain length, λ∗i, which becomes smaller with decreasing m-value and |ΔR∗i| decreases with increasing m-value. (3) The length of necking region, which occurs during deformation, increases with increasing m-value, and the growth rate of necking becomes lower as the m-value increases. (4) The interaction force between Q and Si is an attractive force (or a repulsive force), when Δ\dotε and \bar\dotε have the same signs (or different signs), where \bar\dotε and Δ\dotε are a given strain rate and a strain rate deviation of Si from \bar\dotε, respectively.
Flow and fracture behaviors of superplastic Al-Cu eutectic and Zn-Al eutectoid alloys are investigated under various conditions of the strain rate sensitivity index m. The main results are as follows: (1) The normalized strain rate \dotεn*⁄\bar\dotε at fracture, where \dotεn* is the apparent fracture strain rate in the non-uniform part of the specimen and \bar\dotε is a given strain rate, decreases as \bar\dotε approaches the strain rate \dotε∞′ at m=0 in a higher strain rate side. (2) In the typical superplastic conditions well-developed dimples are found. This fact suggests that grain deformations on the fracture surfaces are remarkably high, and that the fracture part passes through the higher strain rate region where the deformation mechanism is not the grain boundary sliding but the dislocation motion in grains. (3) The fracture diameter, which depends not only on the m-value at a given strain rate \bar\dotε but on the distribution-curve of the m-value to the strain rates, shows a lower value for the higher ratio of \dotε∞′⁄\bar\dotε and for the more gradual change in the m-value with the strain rate. (4) On the basis of the above results, it seems reasonable to consider that the fracture of superplastic materials occurs when a fracture part gets the strain rate \dotε∞′.
The dependence of flow stress on deformation time (strain) is examined under various conditions of the strain rate sensitivity parameter, m, for superplastic Al-Cu and Al-Cu-Si eutectic alloys, and is analized from a kinematical viewpoint. Results obtained are as follows: (1) The period of deformation, T∗0, is expressed as T∗0=2nT∗ (n=…, 1/3, 1/2, 1, 2, 3,…), where T∗ is the time between the onset of the initial elastic deformation and the sub-sequent plastic deformation. (2) The variation in flow stress, Δσ/σ, for a deformation period is approximately expressed as(This article is not displayable. Please see full text pdf.) \ oindentwhere C is a constant and J=∂m⁄∂ln\dotε. (3) From the above equation, it is expected that for the work hardening parameter, γ≡(1⁄σ)(∂σ⁄∂ε), γ>0, γ=0 and γ<0 when J>0 J=0, and J<0, respectively, and these relations show a good agreement with the experimental results obtained from Al-Cu and Al-Cu-Si eutectic alloys. (4) The value measured by the strain rate change method depends on the strain rate ratio, N. The value within N<10 increases with increasing N when J>0. It decreases with increasing N when J<0. In the case of J=0, it becomes constant. (5) Defining m+ and m− to be the m-value for the increment and decrement in the strain rate, respectively, it is suggested that m+>m− when J>0, m+
The relation between the fracture strain and the strain rate sensitivity index m is analized, and it is compared with experimental results obtaind from Al-Cu eutectic and Zn-Al eutectoid alloys. The results are as follows: (1) Most of the fracture strain is made in the strain rate region where the m-value of the non-uniform part of the specimen is approximately equal to that at a given strain rate. (2) Using the m or M-value at a given strain rate, the fracture strain εf is described by the following theoretical equations:(This article is not displayable. Please see full text pdf.) \ oindentwhere Am and AM are constants which depend not only on the m-value at a given strain rate \bar\dotε but on the distribution-curve of the m-values to the strain rates. They become larger, the higher the ratio of the strain rate \dotε∞′ at m=0 to a given strain rate (\dotε∞′⁄\bar\dotε) and the more gradual the change in the m-value with the strain rate. (3) It is indicated that the uniform strain εh depends on the m or M-value as the following equations:(This article is not displayable. Please see full text pdf.)
