Micromechanics Analysis of Damage and Failure in ......Zhiye Li1, Somnath Ghosh2, Daniel J....
Transcript of Micromechanics Analysis of Damage and Failure in ......Zhiye Li1, Somnath Ghosh2, Daniel J....
Top Plate is fixed.
Displacement of Bottom Plate
𝒖𝟐(𝒕) are applied.
Experimental Data : S. Tamrakar, R.
Ganesh, S. Sockalingam, B. Z.
Haque, J. W. Gillespie . 2017
The recent years have seen a surge in research on material
and structural response of composites using homogenization
based hierarchical modeling method. Conventionally, periodic
boundary condition (PBC) is applied on the RVE boundary. The
micromechanical results are inputted to a homogenized-based
constitutive model to give a macro-scale description. However,
when the heterogeneous microstructure is under very high strain
rate loading conditions (103 𝑠−1~106 𝑠−1), PBC do not
represent the accurate effect of stress wave propagation. Thus, it
will reduce the accuracy of the calibrated tensor field in the
multiscale model.
In order to increase the accuracy of the homogenization
model, this study introduces a new space-time dependent
boundary condition (STBC) for 3D microscopic RVE subjected
to high strain rate deformation in explicit FEM simulation. The
advantages of the STBC are discussed by comparing with time-
dependent averaging results of examples using PBC. The
proposed STBC offers significant advantages over conventional
PBC in the RVE-based analysis of heterogeneous materials.
[K. A. Brown. 2010]
Micromechanics Analysis of Damage and Failure in Heterogeneous Composite
Subject to High Strain Rate Impact and Blast
Zhiye Li1, Somnath Ghosh2 , Daniel J. O’Brien3 1Graduate Research Assistant; 2 Michael G. Callas Chair Professor, [email protected], Johns Hopkins University
3Composite and Hybrid Materials Branch, U.S. Army Research Laboratory
Research was sponsored by the Army Research Laboratory and was accomplished
under Cooperative Agreement Number W911NF-12-2-0022. The views and
conclusions contained in this document are those of the authors and should not be
interpreted as representing the official policies, either expressed or implied, of the
Army Research Laboratory or the U.S. Government. The U.S. Government is
authorized to reproduce and distribute reprints for Government purposes
notwithstanding any copyright notation herein.
ACKNOWLEDGEMENT
INTRODUCTION
MULTI-SCALE STUDY OF
COMPOSITE
………………….
EXPRTIMENT
VALIDATION
MICROSCOPIC
FEM MODEL
• Material (VUMAT)
Rate dependent elastic with
Nonlocal CDM
• Interface debonding
(VUEL)
Rate dependent CZM
• Periodic B.C.
HOMOGENIZED
MODEL
• Space Time B.C. (new)
• Unidirectional fibers
RVE
Give precise
prediction and
upgrade
model for
MAT162 (LS-DYNA)
Von Mises Stress Configuration from
FEM Calibration Result
DEVELOPING A CONTINUUM
DAMAGE MODEL FROM
EXPERIMENTS ON DER353
MICROMECHANICAL SPACE-TIME
DEPENDENT BOUNDARY
CONDITION ( STBC )
STBC (continued)
Comment:
• When the heterogeneous microstructure is under very high
strain rate loading conditions (higher than 104𝑠−1), periodic
boundary condition (PBC) do not represent the accurate effect
of stress wave propagation. Space-Time dependent Boundary
Condition (STBC) can give a more accurate prediction for
higher strain rate.
• Apply 1-D solution based STBC on 3D RVE and
calibrated averaged wave speed c from the 3D simulation.
Average wave speed c is a function of volume fraction.
Main idea: In order to increase the accuracy of
the homogenization model, this study introduces
a new space-time dependent boundary condition
(STBC) for 3D microscopic RVE subjected to
high strain rate deformation in explicit FEM
simulation by using characteristics method of
traveling waves.
1×1
1×5
Figure: Deformed local stress contour, volume averaged effective strain and volume
averaged von-Mises stress of 1 × 1 RVE with STBC and PBC for shear simulation.
Comment:
• Homogenization equations consolidates the objective that, the
single fiber RVE can be used in substitute of homogenized
properties of multiple fibers RVEs in order to maintain
accuracy and save computational resources.
HOMOGENIZED PROPERTIES OF
MICROSCOPIC MODEL
Example: 3D FEM 𝑑11= 2 × 106 𝑠−1, uniaxial tension. RVE1 RVE2 RVE3
1×1
1×5
• Effects of adiabatic heating:
∆T=𝛽
𝜌𝑐𝑊 𝐷𝑓(𝑘)
𝑒 𝑉 (𝑘)𝑒
𝑊 𝐷𝑓(𝑘)𝑒 is the dissipative
energy density of the k-th
element in donut. 𝑉 (𝑘)𝑒 is the
volume of the k-th element.
Uniaxial Compression Tests:
• ¼ symmetric model
• Coefficients of friction between
donut and two plate are the
same. (μ= 0.01 )
Deformed stress contour
Material value rate picture reference
Polycarbonate
(PC) polymer
0.5~0.6 1200/s~2200/s
(SHPB)
Z. Li
and J.
Lambros
2000
epoxy resin ~0.45 0.001/s and
300~2500/s
compression
Z. Pan,
B. Sun, V.
P.W. Shim,
B. Gu 2016
PMMA
poly(methyl
methacrylate)
~0.45 1e-2/s ~1e-1/s
SHPB
G. Shao, S.
Zhu,
Y. Wang, Q.
Zhao 2017
PC
(polycarbonate)
~0.8 >1000/s
SHPB
M. Garg
A. D.
Mulliken
M. C.
Boyce 2008
thermoset
epoxy (EPON
862/W)
0.4~0.6 >1000/s
SHPB
glass/epoxy
woven ply
0.4~0.6 visualization
of the portion of
dissipated energy
caused by matrix
cracking
T. Lisle,
C.Bouvet,
M. L.Pastor,
T. Rouault,
P.Margueres
2016
𝛽 is the Taylor-Quinney coefficient. Many experiments
observe that it depends on temperature, strain and strain
rate. A literature review of experiment calibrated 𝛽 value
• Cruciform experiment
[N. Getinet , D. J. O'Brien]
• Droplet experiment
[Sockalingam, et al., 2014]
• DER 353 donut
experiment
[Tamrakar, et al., 2017]
• U-D ply tensile
experiment
[Shokrieh and Omidi, 2009]