The effect of VBHF on formability and instability analysis, incorporating strain gradient effect on neck evolution

In this dissertation, the effect of variable blank holder force (VBHF) is studied. The emphasis is placed on the understanding of the mechanics of its effects on formability through its effect on the deformation history (strain path).; First, the effects of variable blank holder pressure (VBHP) on the outcome of the deep drawing process of non-axisymmetric square part were studied by using an explicit finite-element method. Different blank holder pressures (BHP) are applied locally in different locations in the flange (location-scheme), whose magnitudes vary with respect to punch penetration (time-scheme). It is found that the maximum drawability can be achieved when the proper time-scheme is incorporated with the suitable location-scheme. The critical material points which are located in potential failure sites are significantly affected by the BHP pattern. An implicit FEM method was then used to study the strain paths and strain distributions at different stages of deformation. Similar to the non-axisymmetric cup drawing, it is shown that the overall trend of the strain path in axisymmetric deep drawing process can be sorted into two types: linear for the nodes in the flange and under punch face; and bi-linear for the nodes around the punch nose, with the second segment of the path being plane-strain. This overall trend is not affected by different VBHF schemes. However, the slopes (strain ratios) of the first linear segment of the strain paths are different under different VBHF schemes. This means that the drawing deformation that the material in the flange area undergoes before it is drawn into the die cavity is affected by the VBHF. The effects on formability caused by this change in the bi-linear strain path were studied in detail using M-K method. A strain path dependent modified Forming Limit Diagram (MFLD) was proposed and constructed based on the actual strain paths. With the knowledge of the strain path effects on formability, the dependency of MFLD on VBHF was studied through the strain paths obtained under different VBHF conditions. The performances of different VBHF schemes were evaluated by comparing the MFLD with the corresponding strain distributions. A calibration diagram that is used to construct the MFLD was suggested and provided.; In the instability analysis a standard power law constitutive equation has been used which does not distinguish the properties of the material inside the imperfection area from those of the uniform region. In this dissertation, a new instability model was developed by considering the effects of higher order strain gradient terms on the neck formation during the post-localization period. The detailed information on the behavior of neck growth was obtained. It is shown that the strain path of neck during its elongation deviates from the strain path of uniform region, which includes and clearly indicates the localized deformation inside the imperfection. After this strain state, the limit strain in the uniform region does not change while the strain inside the imperfection changes dramatically which corresponds to the collapse of the neck. This critical strain is taken as necking strain and the FLD based on this strain is constructed, together with the limit strain based on the deformation of uniform region, for the middle strength aluminum. (Abstract shortened by UMI.)...