Advanced Non-Associated Plasticity with Enhanced Isotropic and NonIsotropic Hardening for Sheet Metal

Advanced Non-Associated Plasticity
with Enhanced Isotropic and Non-
Isotropic Hardening for Sheet Metal

Contents
CHAPTER 1....................................................................................................................................1
Introduction..................................................................................................................................1
1.1 Anisotropic metal plasticity...................................................................................................2
1.2 Ductile fracture with anisotropy............................................................................................3
1.3 Thesis outline.........................................................................................................................5
REREFENCES..............................................................................................................................13

CHAPTER 1
Introduction
In automotive industries, military and automotive industry engineering structures are one
of the most important things which is laid emphasis on. In engineering structures metal sheets
and their ductile fracture plays a n important and vital role. Even in military it is an important
thing which should be focused on. Especially in military and automotive industry its use and
importance are continuously increasing (Sumikawa, Ishiwatariand Hiramoto, 2017). In
automotive industry it is laid more emphasis on as it is used in variety of ways and in future it
can be used for manufacturing light-weight car body materials, For example Advanced High
Strength Steels (AHSS), aluminium alloys magnesium alloys and many more. Many automotive
industry organizations are focusing on using metal sheets specifically for some its features such
as superior strength especially for light weight ratio and have extremely lower ductility as
compared to others. This helps in making fracture an important thing to be focused on for
efficient vehicle design. But these metallic sheets have one main challenging issue which is
ductility or it can also be said as fracture anisotropy of metal sheets or metallic materials
(Abedini, Butcher and Worswick, 2018). In crack propagation and initiation this directionality
has been observed as one of the main manufacturing problems which is faced by automation
industry organizations. This can be explained with the help of a figure. In the below figure1-1 a
explains Courty of General Motors in which fracture mostly run in the direction in which it is
rolling regardless of the direction in which it has been loading. Another figure 1-1 b helps in
explaining that all kinds of cracks open themselves in a crosswise especially when hole
expansion operation is being taken place. It is a kind of validating model which has helped in
explaining anisotropic properties of the metel which has helped in explaining that it was of great
value optimizing performance of the materials during a process which is based on simulation-
based design (Markiewicz, Langrand and Notta-Cuvier, 2017).
Metallic material that have been thermodynamically processed or plastically deformed
have most common property of anisotropic mechanical properties like in rolled sheets. There are
three main aspectis from which these anisotropic fracture properties come from: anisotropic
plastic 28 properties; anisotropic damage accumulation/fracture strain envelope; stress/strain
history induced anisotropy (Hassan, Salawdeh and Goggins, 2018). The main and final aim of
this thesis is to develop all kinds of model materials that incorporate all the three features that
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have be listed above and for it is extremely important to have complete and detailed
understanding and modelling of ductile fracture and plasticity of both anisotropic metal as it is
absolutely necessary.
(a) (Courty fo General Motors) Crack tends to open In T.D.
(b) (Courtesy of US Steel)
Fig. 1-1: Anisotropic ductile fracture observed in industrial forming tests. (a) 3 Marciniak
forming tests specimens of TRIP780 steel, where crack always runs along rolling direction; (b)
hole-expansion experiments of a DP780 steel where cracks tend to open in transverse direction.
1.1 Anisotropic metal plasticity
For decades anisotropic plasticity of models has been one of the most important and hot
favourite topics and has been used for various purposes in various kinds of models. It includes
two different kinds of models at two different levels that are crystal plasticity models at the
microstructure level and phenomenological models at the macroscopic level. There are various
kinds of phenomenological yield functions that have been majorly developed for metals plastic
anisotropy (Kim, Park and Kim, 2019). From all those kinds of functions one of the main
functions that drew attention was linearly transformed stress tensors this was mainly because of
higher flexibility and convexity consideration of metal sheet’s anisotropic behaviour. After this
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