<P> There is a growing interest in magnesium and its alloys due to their high strength
to weight ratio. Magnesium is of particular interest to the automotive industry as a
consequence of the current pressure to reduce green house gas emissions from the
transportation sector through vehicle weight reduction. However, there is a lack of
knowledge concerning the formability of magnesium. As a result, the application of
magnesium as a commercial material has not been fully exploited. Much has been learned
from the constitutive modeling of materials such as aluminum and steel. Therefore, this
thesis considers the constitutive modeling of magnesium and its alloys. </p> <p> Based on this motivation, polycrystal plasticity theories that have been established
and used to characterize aluminum and steel are studied. The validity of these theories is
examined with respect to magnesium and its alloys. The magnesium system is composed
of the hexagonal closed-packed (HCP) crystal structure. Therefore, a strong plastic
anisotropy is induced in magnesium crystals due to the limited number of slip systems
that may be activated with ease. The models proposed by Taylor and Sachs neglect strain
and stress heterogeneities respectively. As a result, the models are either too stiff or too
soft to study magnesium due to the anisotropic nature of the crystal structure. The
intermediate models; self-consistent models, which are able to consider the
heterogeneities among the grains in polycrystals, are believed to be more suitable to study
magnesium and its alloys. Therefore, a large strain elastic-viscoplastic self-consistent
(EVPSC) model is developed for polycrystalline materials. Both rate sensitive slip and
twinning are included as mechanisms of plastic deformation, while elastic anisotropy is
accounted for in the elastic modulus. The transition from single crystal plasticity to
polycrystal plasticity is based on a completely self-consistent approach. It is shown that
the differences in the predicted stress-strain curves and texture evolutions based on the
EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and
Tome (1993) are negligible at large strains for monotonic loadings. For the deformations
involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic
transition, while the VPSC model gives a discontinuous response because the model is
incapable of modeling elastic deformation. In addition, it is demonstrated that the EVPSC
model can capture some important experimental features which cannot be simulated by
using the VPSC model. </p> <p> Various self-consistent schemes exist for EVPSC and VPSC models. However,
the evaluations of these models are not complete. Therefore, an examination of various
polycrystal plasticity models is made, based on comparisons of the predicted and
experimental stress responses as well as the R values, to assess their validity. It is
established that, among the models examined, the self-consistent models with grain
interaction stiffuess values halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options,
the Affine self-consistent scheme results in the best overall performance. Furthermore, it
is demonstrated that the R values under uniaxial tension and compression within the sheet
plane show a strong dependence on the imposed strain. This suggests that the
development of anisotropic yield functions using measured R values, must account for
the strain. dependence. </p> <p> The recently developed large strain elastic visco-plastic self-consistent (EVPSC)
model, which incorporates both slip and twinning deformation mechanisms, is used to
study .the lattice strain evolution in extruded magnesium alloy AZ31 under uniaxial
tension and compression. The results are compared against in-situ neutron diffraction
measurements done on the same alloy. For the first time, the effects of stress relaxation
and strain creep on lattice strain measurements in respectively displacement controlled
and load controlled in-situ tests are numerically assessed. It is found that the stress
relaxation, has a significant effect on the lattice strain measurements. It is also observed
that although the creep does not significantly affect the trend of the lattice strain
evolution, a better agreement with the experiments is found if creep is included in the
simulations. </p> <p> In conjunction with the M-K approach developed by Marciniak and Kuczynski
(1967), the EVPSC model is applied to study the sheet metal formability of magnesium
alloys in terms of the forming limit diagram (FLO). The role of crystal plasticity models
and the effects of basal texture on formability of magnesium alloy AZ31 B sheet are
studied numerically. It is observed that formability in HCP polycrystalline materials is
very sensitive to the intensity of the basal texture. The path-dependency of formability is
examined based on different non-proportional loading histories, which are combinations
of two linear strain paths. It is found that while the FLO in strain space is very sensitive
to strain path changes, the forming limit stress diagram (FLSO) in stress space is much
less path-dependent. It is suggested that the FLSO is much more favourable than the FLO
in representing forming limits in the numerical simulation of sheet metal forming
processes. The numerical results are found to be in good qualitative agreement with
experimental observations. </p> / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/19384 |
| Date | 09 1900 |
| Creators | Wang, Huamiao |
| Contributors | Wu, Peidong, Mechanical Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
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