PNNL-13501 - Pacific Northwest National Laboratory

• localized motion of the elements in the direction
normal to the plane of the shells
• significant softening in the axial stiffness (change in
axial force/end-feed displacement) indicating
instability of the cross section under axial load.
The combination of both high bending strain and high
normal velocity is a strong indicator that unstable
deformation is occurring. Elevated bending strain is
allowed to occur alone when the tube wall bends to
conform to the die surface. In that case, the bending
strain would be high, but the element normal velocity
low. Softening of the axial stiffness will also result when
a full circumferential wrinkle forms. However, this may
be suppressed if the tube is being formed into a
nonsymmetric die such as a T-section. Therefore, an
additional parameter is calculated to estimate the
circumferential extent of the wrinkle. Rings of elements
along the length of the forming tube are checked and the
ratio of wrinkling elements (both high bending strain and
normal velocity) divided by the total number of elements
in the ring is calculated. A value of one indicates the full
circumference is wrinkling.
The test problem geometry (Figure 1a) involves forming a
tube into a conical die shape. Because this tube is
relatively short, wrinkling is the primary mode of axial
instability (rather than buckling). Both the shell model
and a finer axisymmetric two-dimensional model
(Figure 1b) were used to test the control routine.
Material Data and Constitutive Equations for Modeling
Implementation
The material data and associated constitutive equations
required to develop accurate finite element models of the
hydroforming process were investigated. Most aluminum
alloys for hydroforming are produced by extrusion. The
extrusion process normally results in tubular materials
with crystallographic textures that have the primary slip
planes oriented in particular directions. Therefore,
extrusion produces a tube with the flow stress heavily
dependent upon the direction of material loading. An
experimental investigation of this material anisotropy was
conducted with a typical extrusion material to develop an
anisotropic yield criterion for use in the finite element
model. A tube was instrumented with strain gauges to
measure the circumferential and axial strain and was
subjected to different stress ratios of axial load and
internal pressure. These experiments were conducted on
176 FY 2000 Laboratory Directed Research and Development Annual Report
Figure 1. Tube formed into a conical die shape (top);
Axisymmetry two-dimensional model (bottom)
a new tube and the same tube after 15% plastic strain was
applied. Comparison of the experimental data to an
isotropic von Mises yield criteria showed that the flow
stress is significantly anisotropic.
Hydroforming may be performed using many different
operating conditions. Therefore, a complete description
of the formability of the material under different
directions of loading is required. Biaxial stretching
experiments were conducted on AA6061-T4 material to
determine the forming limit diagram for the material. A
sample population was subjected to a series of
experiments to determine the level of plastic strain that
developed under various ratios of internal pressure and
axial load. A schematic of the experimental apparatus is
shown in Figure 2, which also illustrates typical results
for a single population of samples tested under free
hydroforming conditions. The specimens are arranged in
this figure such that the bottom specimen received the
highest axial compression during testing, and the top
specimen was a uniaxial tensile specimen (with no
internal pressure). If axial compression was imposed on a
tube specimen in excess of the specimens in Figure 2,
buckling and wrinkling began to occur. Regions