Download - Nonlinear Material Guide
-
7/26/2019 Nonlinear Material Guide
1/18
A Guide to HandleNonlinear aterial
in Your Analysis
This guide is made for non-experienced FEA users. It providesbasic knowledge needed to start analyzing plasticity in materials.
Experienced FEA analysts can also use this guide to get used to
the NFX workflow.
http://midasnfx.com/http://midasnfx.com/ -
7/26/2019 Nonlinear Material Guide
2/18
TABLE OF CONTENTS:
Nonlinear Materials in the Industry....... 3
Nonlinear Material Types....... 4
Engineering Stress Strain curve.... 5
True Stress Strain curve. 6
Converting Engineering Data to True Data.. 7
Work Hardening... 8
Why is nonlinear data required in FEA? 10
Nonlinear input in midas NFX 11
Nonlinear analysis types in midas NFX ... 13Examples... 16
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
3/18
Nonlinear Materials in
the Industry
Page 3
1
Nonlinear Materials are omnipresent in various industries which
requires high resistance, light materials and components.
For example: Automotive, Marine, Defense, Aerospace, Heavy
Machinery, Consumer Goods, Electronics, Oil and Gas, Medical
Industry, etc.
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
4/18
Nonlinear Material Types
Page 4
2Nonlinear Materials can be represented using different types of
models and rules.
Material types: Elasto-plastic, Hyper-elastic
Yield Criterions : Von Mises (Metals)
Nonlinear entries: Stress strain curve, Plastic hardening curve, perfect plastic
Hardening Rules: Isotropic, Kinematic, Combined
Dependence: Temperature, Strain rate
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
5/18
Engineering Stress
Strain Curve3
Monotonic tension stress-strain properties are usually reported
in handbooks and are used in many specifications.
Monotonic behavior is obtained from a tension test where a
specimen with circular or rectangular cross sections within the
uniform gauge length is subjected to a monotonically increasing
tensile force until it fractures.
Engineering stress S from a uniaxial test is defined by dividing
the axial force by the original cross sectional area.
Sy - yield strength
Su - ultimate tensile strength
Page 5
Snom - Engineering Stress, nominal
A0 - Original cross sectional area
l - Instantaneous gage length
nom - Engineering Strain, nominal
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
6/18
True Stress Strain Curve
Page 6
4
f- true fracture strength
f- true fracture strain or ductility
True stress sigma is defined by dividing the axial force by the
instantaneous cross sectional area.
True stress in tension is higher than engineering stress
because the cross section area decreases during the loading.
- true stress
- true strain
A - instantaneous cross sectional area
l - instantaneous gage length
L0 - original gage length
For constant volume up to necking assumption:
The following relationships can then be derived:
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
7/18
-
7/26/2019 Nonlinear Material Guide
8/18
Work Hardening5
Loading
UnloadingA
B
C
0
Work hardening is a consequence of plastic deformation, a
permanent change in shape. This is different to elastic
deformation, which is reversible.
Most materials do not exhibit only plastic deformation or elastic
deformation, but rather a combination of the two. The following
discussion mostly applies to metals, especially steels, which
are well studied. Work hardening occurs most notably for
ductile materials such as metals. Ductility is the ability of a
material to undergo plastic deformations before fracture (E.g.:
bending a steel rod until it finally breaks).
Page 8
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
9/18
K - strength coefficient (stress intercept at p = 1)n - strain hardening exponent (slope of the line)
p - plastic strain
Material:
Steel
SuMPa/(ksi)
E
GPa/ksi 103K/K
MPa/(ksi) n/n
1010 331/(48) 203/29.5534/867
(78)/(126)0.185/ 0.244
1020 441/(64) 203/29.5738/1962
(107)/(284)0.190/ 0.321
1038c 582/(84) 201/29.51106/1340
(160)/(195)0.259/ 0.220
Properties of Steel
= K (p)n
When describing Work hardening, Hollomon's equation is
mostly used. Hollomon's equation is a powerful law which
describes the relationship between the stress and the
amount of plastic strain it used to generate the hardening
curve of a nonlinear material.
Page 9
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
10/18
-
7/26/2019 Nonlinear Material Guide
11/18
Nonlinear input in NFX7To assign material nonlinearity in NFX, you can choose to use
stress-strain curve or plastic hardening curve.
Stress-Strain Curve definition takes into account all the
material curves including elastic and plastic domains.
Stress-Strain Curve
Page 11
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
12/18
Plastic Hardening Curve definition takes into account only the
plastic domain, so the initial value should be equal to the yield
stress.
Plastic Hardening Curve
Page 12
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
13/18
Nonlinear analysis Types
in NFX8
Static Analysis: time does not play any role.
Quasi-Static Analysis: is a type of dynamic analysis which
is solved using static loads.
Dynamic Analysis: takes into account the time by
considering fast changing events (load/displacements) and
inertia.
Time
Velocity,
Acceleration
Time
Velocity,
Ac
celeration
TimeVelocityorAcceleration
Page 13
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
14/18
Nonlinear Static
Nonlinear Quasi-Static
Nonlinear Implicit Dynamic
Used to solve true static
equilibrium
Nonlinear Explicit Dynamic
Used to solve true dynamicequilibrium
Sequential Nonlinear
Implicit + Explicit Coupled
In Implicit analysis, the calculation of current quantities in one time
step is based on the quantities calculated during the previous time step.
This is called the Euler Time Integration Scheme. Using this scheme,
the solution remains stable even if large time steps are taken. This is
also called an unconditionally stable scheme. The disadvantage is thatthis algorithm requires you to inverse the stiffness matrix and this is
computationally intensive, especially when nonlinearities are present.
In Explicit analysis, the inversion of the complex stiffness matrix can
be avoided, and only the mass matrix [M] has to be inverted. When
lower order elements are used (always recommended in explicit), the
mass matrix is a lumped matrix, or a diagonal matrix, whose inversion
is a single step process, hence this is very easily done. Thedisadvantage is that the Euler Time integration scheme is not used in
explicit, and thus the solution is not unconditionally stable and very
small time steps have to be used.
Page 14
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
15/18
Static
Structural problems Metal forming Impact problems
IMPLICIT METHOD
EXPLICIT METHOD
In midas NFX all of the Static, Quasi-Static, Dynamic
analysis types can be performed in the functions for the
problem considered
Quasi-Static Dynamic
Page 15
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
16/18
-
7/26/2019 Nonlinear Material Guide
17/18
Examples9
High speed solenoid driven rivet simulation
- Nonlinear Explicit Analysis
Page 17
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx -
7/26/2019 Nonlinear Material Guide
18/18
Now you are
ready to go !
Please contact us if you have any
questions during your trial:
Email: [email protected]
Telephone: +44 (0) 1908 776717
http://www.youtube.com/user/CyprienRhttp://www.youtube.com/user/CyprienRhttps://twitter.com/midasNFXhttps://twitter.com/midasNFXhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttp://www.linkedin.com/company/midas-information-technology-co-ltdhttps://www.facebook.com/midasnfxhttps://www.facebook.com/midasnfx