Determination Of Parameters In The Localised Decrease In Cross Sectional Area In Tensile Specimens Using DIC

Project Summary: The true mechanical response of a material subjected to a tension test is recorded as a plot of true-stress against true-strain. This is only valid up to the instability point (i.e. UTS) when a localised decrease in the cross-sectional area occurs (necking). The onset of necking is accompanied by the establishment of a tri-axial state of stress in the neck: the uni-axial state is destroyed by the geometrical irregularity. Bearing in mind that the flow stress of a material is strongly dependent on the state of stress, a correction has to be introduced to convert the tri-axial flow stress into a uni-axial stress. The tri-axial stresses in the neck, which include the tensile component perpendicular to the axis of the specimen generated by the boundaries of the neck, will depend on the geometry of the neck. A correction can be applied; the most commonly used is that for cylindrical specimens via the Bridgeman equation [1]. This requires a continuous monitoring of the radius of curvature of the neck, and the radius of the cross section at the thinnest part of the neck. In-situ monitoring techniques are required to measure these variables for the purpose of calibrating material damage and fracture models (e.g. modified Armstrong-Zerilli).

The development of experimental techniques to quantify necking in-situ will allow material behaviour to be established beyond the instability point in tension. The use of Digital Image Correlation (DIC) and other advanced optical methods (e.g. prism-based macrophotography and image processing as in Dunnett et al. [2]) will enable a technique to be developed that could continuously monitor the necking parameters (i.e. curvature of the neck and the radius of the cross section) over the entire stress-strain curve to failure, covering the quasi-static to dynamic strain rate range at a variety of test temperatures. Incorporating and relating this additional information to constitutive material models for utilisation by design and theoretical physics simulations is then required. It is common with many empirical and semi-physical models to use strain as a "state" parameter. In general, strain is not appropriate as a state parameter as it limits the models capability of handling situations where a path change occurs, as in the case of a strain rate change or inevitably temperature change due to adiabatic heating during deformation. The work will therefore make use of the Mechanical Threshold Stress (MTS) model, which uses the mechanical threshold stress as an internal state parameter to characterise the "structure" of a material at every deformation state. A working model establishing parameters for a number of metals covering the FCC, HPC and BCC crystal structures will be confirmed.