Worked example tensile test properties

In materials in which the properties depend on direction, the state of anisotropy is usually indicated by the R-value. This is defined as the ratio of width strain, ε w = lnww , to thickness strain, ε t = lntt . In some cases, the thickness strain is measured directly, but it may be calculated also from the length and width measurements using the constant volume assumption, i.e. wtl = w t l or t t = w l wl The R-value is therefore, R = ln w w ln w l wl 1.17 If the change in width is measured during the test, the R-value can be determined con- tinuously and some variation with strain may be observed. Often measurements are taken at a particular value of strain, e.g. at e eng. = 15. The direction in which the R-value is measured is indicated by a suffix, i.e. R , R 45 and R 90 for tests in the rolling, diagonal and transverse directions respectively. If, for a given material, these values are different, the sheet is said to display planar anisotropy and the most common description of this is R = R + R 90 − 2R 45 2 1.18 which may be positive or negative, although in steels it is usually positive. If the measured R-value differs from unity, this shows a difference between average in-plane and through-thickness properties which is usually characterized by the normal plastic anisotropy ratio, defined as R = R + 2R 45 + R 90 4 1.19 The term ‘normal’ is used here in the sense of properties ‘perpendicular’ to the plane of the sheet.

1.1.6 Rate sensitivity

For many materials at room temperature, the properties measured will not vary greatly with small changes in the speed at which the test is performed. The property most sensitive to rate of deformation is the lower yield stress and therefore it is customary to specify the cross-head speed of the testing machine – typically about 25 mmminute. If the cross-head speed, v, is suddenly changed by a factor of 10 or more during the uniform deformation region of a tensile test, a small jump in the load may be observed as shown in Figure 1.7. This indicates some strain-rate sensitivity in the material that can be described by the exponent, m, in the equation σ = Kε n ˙ε m 1.20 Material properties 9