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1
Structural Analysis of Components Obtained by
the Injection Molding Process
André Antunes Oliveira
Instituto Superior Técnico, Lisboa, Portugal
April 2016
Abstract
The mechanical properties of components manufactured using the injection molding process
depend on the characteristics of its constituent material, the processing conditions used and, ultimately, on
the part’s geometry. This parameters have a strong influence on process resultant variables, like the material
flow, the fiber orientation, the internal stress fields and, consequently, the warpage. Thus, the material
obtained under these conditions has different properties than the ones initially provided by the
manufacturer, causing structural changes in each component, which subsequently modify its load
performance.
Injection simulation programs, such as Autodesk Moldflow, computationally reproduce each step
of this process. In order to implement the manufacturing history of each injection molded component on
the reproduction of its loading behavior, it is required the integration of the injection simulation results in
programs able to carry out its structural analysis. This way, the finite element analysis programs, such as
Simulia Abaqus, allow the determination of the mechanical behavior of a loaded part considering its
manufacturing biography (in cavity stress field, residual strains, fiber orientation). The interaction between
these software can be accomplished directly, or using external interfaces, like Helius PFA.
This work aims to couple the manufacturing history of injection molded components, as well as
the material experimental information, in the prediction of its loading behavior. Thus, this study intends to
increase the accuracy of structural analysis performed on injection molded parts.
Keywords: Injection Molding Simulation, Autodesk Moldflow, Finite Element Analysis, Simulia Abaqus,
Residual Stress, Product Performance
1 Introduction
The injection molding process causes
structural changes in each component, which
subsequently modify its performance under a
service load. These changes are caused by the
accumulation of stress during the part’s filling in
the mold cavity, resulting on warpage that
deforms its geometry after manufacture. Thus,
the component’s deformation and shrinkage
generate residual stress fields, functioning as an
indicator of the effects caused by the
manufacturing process on the part’s structural
integrity. Therefore, in order to accurately
reproduce the loading performance of injection
molded components, it’s required an upgrade on
the prediction of process resultant residual stress
fields.
This work aims for two fundamental
accomplishments. The first one is the
optimization of forecasting injection molded
components’ loading behavior, which results on
the improvement of the prediction of process
resultant residual stress distribution. This is
intended to be achieved coupling the parts’
manufacturing history in its structural analysis
and, subsequently, evaluating its effects on the
product performance. The second
accomplishment of this work is to increase the
accuracy of structural analyses of injection
2
molded components, using the material
experimental data as well.
2 Background
2.1 Injection Molding Process
The injection molding process is one of the
most common manufacturing techniques for the
mass production of polymer components. It is
based on four major stages [1]:
1. Filling - Initially the polymer contained
in a hopper, usually in the form of pellets,
is leaked to the surface of a rotating
screw that pushes it into the mold. The
screw rotation causes the contact of the
plastic pellets with the hot cylinder walls,
melting due to the heat of compression,
the friction and the high surface
temperature. When there is enough
molten material in the screw end, it
paralyzes and injects the molten plastic
in the mold cavity through a feed system;
2. Packing – this phase begins when 95% to
98% of the cavity has been filled. This
moment is called the velocity/pressure
switch-over point, when there is a
switch-over from ram speed control to
packing pressure. During this phase,
further pressure is applied to the material
in an attempt to pack more material into
the cavity. This is intended to produce a
reduced and more uniform shrinkage
with less component warpage.
3. Cooling – Simultaneously, the mold is
cooled down using a coolant to lower the
temperature of the plastic part. Once the
polymer solidifies, the cavity pressure is
reduced to atmospheric pressure. This
stage ends when the part reaches a safe
extraction temperature;
4. Ejection – Finally, when the component
is fully solidified, the mold is opened and
the part is ejected. The mold is then
closed so that a new cycle can begin.
The injection molding process has many
advantages, such as its suitability to large
production volumes, obtaining complex
geometry parts that require fewer finishing
operations. However, the high cost of the
required equipment and the great
competitiveness of this market, emerge as the
major drawbacks of this process.
2.1.1 Residual Stress
By definition, residual stresses are
elastic stress fields that remain in a solid material
without any external loads or temperature
gradients applied. These stresses are the result of
the part’s deformation and shrinkage after its
ejection from the mold, when the in cavity
constraints are released. Furthermore, residual
stresses have a similar effect on a structure than
externally applied forces, which can lead to the
part’s resistance reduction and, ultimately, its
early failure. There are two kinds of residual
stresses: the flow induced and the thermal
induced [2].
The flow induced residual stresses are
developed during the filling phase. Subsequently,
they are the result of contact between the oriented
and disoriented layers of material, due to high
cooling rates and shear stresses [2].
The thermal induced residual stresses
are the result of the part’s unbalanced cooling
and differential shrinkage [2].
2.1.2 In-Cavity Stress Field
While the component is still confined
into the mold cavity, the internal stress field that
is developed during the material solidification is
called in-cavity stress. In practice, in-cavity
stresses are the driving force of the part’s
warpage and shrinkage after ejection [2].
2.1.3 Residual Strain
The configurations before and after the
part’s ejection are exhibited in Figure 1. In A the
part is still confined into the mold cavity, while
cools down to achieve room temperature. Using
the Hooke’s Law of equation (1), the stress and
strain fields of configuration A are easily
obtained (equation (2)). In this configuration the
resulting stress field, {𝜎𝐴}, is nonzero, unlike the
strain field, {𝜀𝐴}. However, there are residual
strains, {𝜀𝑛𝑚}, due to shrinkage when the part is
into the mold, calculated using the in-cavity
stress field, {𝜎𝐴} (equation (2)) [3].
When the mold is removed the scheme
B it’s obtained, in which the part warps and
develops residual stresses, {𝜎𝐵}. This way, the
3
effect of residual strain can be incorporated in the
residual stress field calculation (equation (3)),
accounting for process resultant shrinkage [3].
{𝜎} = [𝐶]{𝜀} (1)
{𝜎𝐴} = [𝐶]({𝜀𝐴} − {𝜀𝑛𝑚})⇔
⇔{𝜀𝐴} − [𝐶]−1{𝜎𝐴} = {𝜀𝑛𝑚}⇔
⇔{𝜀𝑛𝑚} = −[𝐶]−1{𝜎𝐴}
(2)
{𝜎𝐵} = [𝐶]({𝜀𝐵} − {𝜀𝑛𝑚}) (3)
Figure 1 – Stress and strain fields before and
after the part’s ejection [3].
2.2 Injection of Fiber Reinforced
Thermoplastics
A fiber reinforced material, also named
as a composite, is a combination of two
constituent materials: the matrix and the fibers.
Therefore, the matrix main function is to keep the
fibers together, securing them and acting as a
mean of load transfer. There are short and long
fiber reinforced materials, as well as different
fiber orientations available (for instance,
perfectly aligned or randomly aligned).
Composite materials are in fact commonly used
in the injection molding process, in order to
improve components’ stiffness, resistance and
other mechanical properties [4].
2.2.1 Fiber Orientation Tensor
The second and fourth order fiber
orientation tensors, shown in equations (4) and
(5), provide a statistical description of the
direction of the fibers in a certain point of the
domain. This way, the probability density
function, 𝜑(𝑝), describes the behavior of a set of
fibers in a given direction [5].
These tensor’s eigenvectors indicate the
main directions of fiber alignment, assuming that
the material is orthotropic. Thus, its eigenvalues
provide a measure of the degree of fiber
alignment of the material. A perfectly aligned
composite has fiber orientation tensor
eigenvalues of (1,0,0), unlike a randomly aligned
material, whose eigenvalues are (1/3,1/3,1/3) [3].
𝑎𝑖𝑗 = ∫𝑝𝑖𝑝𝑗𝜑(𝑝)𝑑𝑝 (4)
𝑎𝑖𝑗𝑘𝑙 = ∫𝑝𝑖𝑝𝑗𝑝𝑘𝑝𝑙𝜑(𝑝)𝑑𝑝 (5)
2.2.2 Mori Tanaka micro-mechanics
Model
The mechanical properties of fiber
reinforced materials depend on the direction, as a
result of fiber alignment, being often called
orthotropic materials. The micro-mechanical
models provide a theoretical way to obtain the
mechanical properties of a composite based on
properties of its constituents (matrix and fibers).
The Mori Tanaka micro-mechanical
model is widely used to calculate the mechanical
properties of a composite material. Initially, the
matrix and fiber constituent materials stiffness
matrixes are combined (𝐶𝑚 and 𝐶𝑓, respectively)
in order to obtain the composite stiffness matrix,
𝐶𝐶, as shown in equations (6) to (8). Afterwards,
this model calculates the material mechanical
properties using the Hooke’s Law in equation
(1).
𝐶𝐶 = 𝐶𝑓 + 𝑣𝑓(𝐶𝑓 − 𝐶𝑚)𝐴 (6)
𝐴 = 𝑇[(1 − 𝑣𝑓)𝐼 + 𝑣𝑓𝑇]−1
(7)
𝑇 = [𝐼 + 𝑆(𝐶𝑚)−1(𝐶𝑓 − 𝐶𝑚)]−1 (8)
Nevertheless, 𝑆 represents the Eshelby
tensor, 𝐴 is the strain concentration tensor and is
𝑣𝑓 the fiber volume fraction.
2.3 Numerical Analysis Tools
2.3.1 Injection Simulation
The selected software to perform
injection simulations was Autodesk Moldflow
Insight 2016. This software allows the user to
simulate the various steps of the injection
molding process, through different analysis
modules that can be used alone or sequentially,
4
such as filling, packing, cooling and warpage.
Moldflow has also an extensive material
properties database.
2.3.2 Finite Element Analysis
Abaqus 6.14-1 was the chosen structural
analysis software, which has a wide range of
FEM solutions. [6]:
The current research aims to integrate the
injection simulation results in structural analysis.
Thus, it is essential to implement a solution that
allows Abaqus receive all information from
Moldflow without affecting these results.
One of the key elements of a structural static
analysis is the application of constraints, limiting
certain degrees of freedom of the model. An
Abaqus structural analysis is a group of
sequential steps, which are sets of time
increments, each with the respective loads and
boundary conditions. Thus, the nature of the
boundary conditions of each step requires further
study, and especially in the initial step, since it’s
the one in which the injection simulation results
are managed.
2.4 Coupling of Injection
Simulation Results to
Structural Analysis
In order to couple the manufacturing
history of a component in its structural analysis
and, this way, predict the process resultant
residual stress field, it’s mandatory to import the
injection simulation results to a FEA software.
Therefore, this can be accomplished using two
different methods:
1. Direct transfer of the injection
simulation data to structural analysis,
using the Abaqus Interface for
Moldflow as a compiler. This method
doesn´t require any mapping between
meshes, using the same configuration in
both analysis (injection simulation and
structural analysis);
2. Transmitting the injection simulation
results to external interfaces, which
have solvers that allow its mapping to
structural programs. This method
involves the use of an injection mesh
(donor mesh) different from the one
used for the structural analysis
(receiving mesh), mapping information
from one model to another. The
interface used for this study was Helius
Progressive Failure Analysis.
Thus, these two methods combine the
structural analysis and the part’s manufacturing
history, using injection simulation results such as
in-cavity stress field, residual strains or the fiber
orientation tensor of a composite material.
3 Implementation
3.1 Direct Method of Data
Transfer
The initial study aims to define
methodologies and settings to be implemented
during the injection simulation, allowing to
accurately transfer its results to the structural
analysis. In addition, it requires the creation of
suitable conditions in the structural analysis to
process the injection data. The assessment made
in this chapter was based on the observation of
deformations and residual stresses of each model.
The direct transfer method enables the
usage of the injection mesh in the structural
analysis, allowing a closer observation and
assessment of the different responses of the mesh
deformed shape depending on the various
settings implemented. This way, that was the
selected method in this chapter to transfer the
injection simulation results to Abaqus.
Figure 2 shows the flowchart of the
direct transfer method using Abaqus Interface for
Moldflow as a compiler. Moldflow imports to
Abaqus data related to the mesh undeformed
shape, the material properties, the in-cavity stress
field and the fiber orientation tensor. In addition,
this method automatically adds constraints in
three degrees of freedom of the part, in order to
eliminate its rigid body motion. Abaqus Interface
for Moldflow then converts this information into
a structural model, in order to be Abaqus
compatible [7].
Figure 2 - Flowchart of the direct transfer of the Moldflow simulation data to Abaqus analysis.
3.1.1 Mesh
Moldflow offers three different types of
mesh: Midplane, Dual Domain and 3D.
Midplane and Dual Domain meshes are suitable
for shell models, due to its bi-dimensional
triangular elements. Nevertheless, 3D meshes are
built on 4-node tetrahedrons, especially designed
for thick solid parts. For that matter, 3D mesh
was adopted for this work injection simulations
[3].
3.1.1.1 Quality
Mesh quality is one of the major factors
for the accuracy of the final results. The most
important indicator of an injection 3D mesh
quality is the aspect ratio. The aspect ratio of an
element is the relation between its width and
height, a/b of Figure 3. A perfect element
exhibits an aspect ratio of 1 [8].
Figure 3 – Triangular aspect ratio [8].
Both injection and structural meshes
require limit values of aspect ratio of its
elements, in order to be considerate a
qualitatively approved mesh. The maximum
allowable aspect ratio of an injection 3D mesh is
30, while for a structural mesh is 10.
When transferring directly the injection
simulation results to the structural analysis, the
injection mesh is imported to Abaqus as a 4-node
tetra element mesh (C3D4 in Figure 4).
Subsequently, Abaqus Interface for Moldflow
enables its translation from C3D4 to C3D10
(Figure 4), a 10-node tetra mesh. That way, this
transfer method keeps the mesh topology intact,
giving the option of changing its elements
constitution in the structural analysis [7].
Figure 4 – a) C3D4. b) C3D10. [9]
As a result, the injection mesh quality
standards of aspect ratio need to be compatible
with the structural limits as well. However, the
automatic repair of 3D elements aspect ratio,
performed in Moldflow, can’t overcome this
problem in every single mesh element, leaving
elements with insufficiently refined aspect ratios
in complex geometry and thickness variation
zones (dark blue in Figure 5). This elements can
damage the accuracy of the structural analysis.
Figure 5 - 3D injection mesh repair results in
Autodesk Moldflow.
(a) (b)
6
3.1.1.2 Aggregation
The injection simulation analysis
sequence was established as filling, packing and
warpage. Thus, Moldflow assumes the uniform
cooling of the part during the process simulation.
Furthermore, Moldflow has three mesh options
in order to perform its warpage analysis [8]:
1. Using the 3D mesh with linear
elements, as in the filling and packing
analysis phases;
2. Update the linear tetrahedral elements
of the 3D mesh to second order
(quadratic) using a different mesh than
in the filling and packing stages;
3. Mesh aggregation. This technique
reduces the mesh number of layers for
two (instead of the six used by default),
while updating each element to the
second order.
The assessment of the influence of the type
of element and the mesh aggregation option in
the injection simulation, required the analysis of
four models in parallel:
1. Moldflow Quadratic → Abaqus
C3D10
2. Moldflow Linear → Abaqus C3D4
3. Moldflow Aggregation → Abaqus
C3D10
4. Moldflow Aggregation → Abaqus
C3D4
3.1.2 Boundary Conditions
In order to allow the part’s shrinkage
and warpage using the in-cavity stress field, it
was implemented in the structural analysis an
initial step free from loading or constraints.
However, it demands the application of artificial
mechanisms in this step to remove the rigid body
motion. Thus, there were two studies performed:
1. Strategic application of low stiffness
springs (Figure 6);
2. Energy stabilization of the model.
Abaqus automatic energy stabilization
mechanism applies damping in the
structural model, dissipating a small
fraction of the deformation energy.
Thus, it is required the energetic balance
of the model to validate this study [6].
Figure 6 – Weak springs applied in the structural and injection models.
3.2 Helius PFA
Moldflow’s inability to incorporate the
material experimental data in the injection
simulation and, subsequently, transfer directly
this results to Abaqus, demanded the study of a
new interface. Thus, Figure 7 shows the
flowchart of the direct transfer method using
Helius PFA.
Helius PFA is a program developed by
Autodesk, which has a tool called Advanced
Material Exchange (AME) that allows the
mapping of fiber orientation tensor and residual
strains from the injection simulation to the
structural analysis. This transfer method maps
information from a donor mesh (injection) to a
receiving mesh (structural), both different from
each other. AME has different tools to optimize
the mapping ability, such as the model alignment
or mapping suitability plot [3].
Furthermore, Helius PFA homogenizes
and decomposes the material stress and strain
fields into their constituent (matrix and fibers)
average values, in order to improve the structural
analysis accuracy. The homogenization and
decomposition process is established using the
Mori Tanaka micromechanical model, as well as
the fiber orientation averaging [3].
Helius PFA implements the material
experimental stress-strain data in the structural
analysis, using a combination of the modified
Ramberg-Osgood model (equation (9)) and the
modified Von Mises stress (equation (10)), to
predict its plastic behavior. The yielding occurs
when equations (8) and (9) have equal values [3].
𝜎𝑌ℎ = 𝐸1/𝑛(𝜎0)
(𝑛−1)/𝑛(𝜀𝑒𝑓𝑓𝑝
)1/𝑛
(9)
𝜎𝑒𝑓𝑓 = √1
2[(𝛼𝜎11 − 𝛽𝜎22)
2 + (𝛽𝜎22 − 𝛽𝜎33)2 +
(𝛽𝜎33 − 𝛼𝜎11)2 + 6(𝜎12
2 + 𝜎232 + 𝜎31
2 )]
(10)
7
𝜎0 is the matrix yield stress, 𝐸 is the matrix
Young’s modulus and 𝜀𝑒𝑓𝑓𝑝
is the matrix plastic
strain. 𝛼 and 𝛽 are directional dependence
coefficients, accounting for the fibers direction in
the effective stress equation. They are obtained
using equations (11) and (12), where 𝜆 is the
largest fiber orientation tensor eigenvalue and 𝜃
is the fiber randomness parameter. 𝜆𝑚, 𝛼𝑚, 𝛽𝑚
correspond to the case of a strongly aligned
material [3].
𝛼 = 𝜃 + (𝛼𝑚 − 𝜃
𝜆𝑚 − 1/2)(𝜆 −
1
2)
(11)
𝛽 = 𝜃 + (𝛽𝑚 − 𝜃
𝜆𝑚 − 1/2)(𝜆 −
1
2)
(12)
This chapter aims to implement the
material experimental data in the structural
analysis, mapping the injection simulation results
from one model to another. This way, the study
performed was based on the comparison between
the material experimental stress-strain curves and
a specimen structural analysis results.
Figure 7 - Flowchart of transferring Moldflow simulation data to Abaqus analysis using Helius PFA. -
3.3 Case Study
In order to reproduce an injection molded
component loading behavior, it was developed a
study using three different approaches:
1. Structural Analysis considering the
undeformed part shape and the material
properties used in Moldlow, during
injection simulation. Thus, this model
does not account for the manufacturing
effects of the part;
2. Application of the direct method of
transferring the injection simulation
results to structural analysis, now
applying a load step;
3. Use Helius PFA to map injection
simulation resultant variables to
Abaqus, implementing the experimental
material data as well. It was considered
one structural analysis with the residual
strain field and another without it.
The load step implemented in each of the
analysis performed in this chapter is represented
in Figure 8, showing the displacements and
constraints applied on the part.
Figure 8 – Load step displacements and
constraints.
8
(c)
(a)
(d)
(b)
4 Results and Discussion
4.1 Direct Method of Data
Transfer
4.1.1 Mesh
The results of the mesh study are in the
Tables 1 and 2, showing the effects on the
structural analysis caused by the type of element
used and the mesh aggregation option in the
injection simulation.
Table 1 - Total deflection and residual stress of
the models without mesh aggregation.
U [MM]
MIN - MAX
𝝈𝑽𝑴 [MPA]
MIN - MAX
MOLDFLOW
QUADRATIC
1.12
x10-15
6.01 - -
ABAQUS C3D10 0.0 9.79 0.22 123.22
MOLDFLOW
LINEAR
4.37
x10-16
5.58 - -
ABAQUS C3D4 0.0 7.81 0.54 66.87
Table 2 - Total deflection and residual stress of
the models with mesh aggregation.
U [MM]
MIN - MAX
𝝈𝑽𝑴 [MPA]
MIN - MAX
MOLDFLOW
AGGREGATION
3.22x10-15
5.94 - -
ABAQUS C3D10 0.0 4.06 0.57 55.17
ABAQUS C3D4 0.0 3.53 0.37 46.05
This study shows that the quadratic
elements are more flexible, reaching higher
levels of deformation due to its constitution (10-
node rather than the linear 4-node).
The models without mesh aggregation
reached higher stress and deflection results.
Figures 9 a) and b) show the maximum stress
verified in these models, located on areas of
thickness variation, in high aspect ratio elements
(Figure 5). Thus, this values of stress are
considered to be heterogeneities caused by the
existence of elements with aspect ratio higher
than the mesh quality standards.
Figures 9 c) and d) represent the same
location in the models with mesh aggregation, as
the maximum stress of the models without it.
These models obtained lower results of stress and
defection. Furthermore, its maximum stress
location is not this one (Figure 9 c) and d)),
revealing that the mesh aggregation option
reorganizes the injection mesh elements with
high aspect ratio, softening the stress results in
those areas. Basically, the mesh aggregation
option performs an isoparametric mapping in the
critical areas of the injection mesh, allowing the
repair of the element which present an
insufficiently refined aspect ratio.
Figure 9 – Stress locations. a) Max stress,
quadratic model without aggregation. b) Max
stress, linear model without aggregation. c)
Quadratic model with mesh aggregation. d)
Linear model with mesh aggregation
4.1.2 Boundary Conditions
Table 3 shows the results of the studies
used to define the boundary conditions of the
initial step of the structural analysis, allowing the
part to deform and shrink using the in-cavity
stress field and, simultaneously, removing the
rigid body motion.
Table 3 - Total deflection and residual stress of
each boundary conditions approach.
U [MM]
MIN - MAX 𝝈𝑽𝑴 [MPA]
MIN - MAX
MOLDFLOW
MOLAS
0.0071 2.962 - -
ABAQUS
MOLAS
0.0955 2.126 0.55 55.17
MOLDFLOW
ESTAB.
0.2164 2.954 - -
ABAQUS
ESTAB.
0.231 2.138 0.57 55.17
The application of weak springs affects
the structural analysis and the injection
9
simulation, reaching lower levels of minimum
deflection in the spring application zone.
The energy stabilization performed in the
structural analysis achieved similar values of
minimum deflection as in the injection
simulation, showing it affects insignificantly the
results. This way, this mechanism is considered
to be the right choice to allow the component’s
free shrinkage and deformation.
4.2 Helius PFA
4.2.1 Mapping
The usage of Helius PFA to transfer the
injection simulation results to the structural
analysis, demands the mapping of the fiber
orientation tensor and residual strain form one
model to the other. The injection model used in
this study was a plaque and the selected structural
model was a specimen. The experimental
material data available has stress-strain results in
three different fiber orientations: 0°, 45° e 90°.
As a result, the specimen needs to be aligned in
these directions to perform the mapping, in order
to accurately reproduce the part’s behavior in all
three fiber orientations of the experimental
stress-strain curves. The mapping results are
shown in the Figures 10 and 11.
Figure 10 – Fiber orientation tensor mapping.
Figure 11 – Residual strain mapping.
4.2.2 Material Experimental
Properties
Figure 12 shows the comparison
between the material experimental tensile curves
(EXP), in each fiber direction, and the stress-
strain fields obtained in the structural analysis
with (STRAIN) or without (NO STRAIN) the
injection simulation residual stress.
The models without residual stress
reproduced accurately the behavior of the
experimental tensile curves, for 45° and 90° of
fiber alignment. Nevertheless, for 0° of fiber
orientation, these models achieved lower levels
of stress and strain prior to the rupture, due to the
fact that the fiber in Moldflow’s injection
simulation is not perfectly aligned.
Figure 12 - Stress-strain graphs comparing the
experimental tensile curves of the material and
the results of structural analysis, in each fiber
direction. a) 0°. b) 45° .c) 90°.
The models considering the residual
strain, showed a similar behavior. However, the
residual stress field cause the negative translation
of the curves, forcing the initial shrinkage of the
part.
0
100
200
-0,005 0 0,005 0,01 0,015 0,02 0,025
STR
ESS
[MP
A]
STRAIN
EXP STRAIN NO STRAIN
0
50
100
-0,01 0 0,01 0,02 0,03
STR
ESS
[MP
A]
STRAIN
EXP STRAIN NO STRAIN
0
50
100
150
-0,012 -0,002 0,008 0,018 0,028
STR
ESS
[MP
A]
STRAIN
EXP STRAIN NO STRAIN
0o
0o
90o
90o
(a)
(b)
(c)
10
4.3 Case Study
Tables 4 and 5 present the results of the
case study performed, in which were applied
three different approaches to predict the loading
behavior of an injection molded component.
Table 4 - Total deflection and stress in the
direction of loading, obtained in the Abaqus
Standard and the direct transfer case studies.
U [MM]
MIN - MAX
𝝈𝒙𝒙 [MPA]
MIN - MAX
ABAQUS
STANDARD
0.0 13.51 -73.46 46.40
DIRECT 0.0 14.70 -760.13 293.58
Table 5 – Total deflection and stress in the
direction of loading, obtained in the Helius PFA
case study.
U [MM]
MIN - MAX
𝝈𝒙𝒙 [MPA]
MIN - MAX
STRAIN 0.03 6.56 -86.73 32.99
NO STRAIN 0.0 7.34 -72.65 23.86
The first approach (Abaqus Standard)
shows that a structural analysis without
considering the part’s manufacturing effects,
using only its undeformed shape and material
properties, assumes a linear elastic behavior of
the material, keeping its characteristics constant
during the simulation. This case has reached the
smaller deformations, showing that the linear
relationship between the stress and strain fields is
not enough to increase the analysis reliability.
The direct transfer model presents the
greatest deflections and residual stresses. Thus,
the effect of the in cavity stress field, applied in
the first step of the analysis, overcharges the
system with stress, warping prior to the
application of load and after it. It should be noted
that this case also considers a linear elastic
behavior of the material, due to the inability of
implementing any experimental tensile curves in
the structural analysis via direct transfer.
The third approach, using Helius PFA as an
interface between Abaqus and Moldflow,
endorses the inclusion of the residual stress field
as mean to implement the part´s manufacturing
history in the structural analysis. The model
using residual stresses (STRAIN) stands less
deformation levels prior to rupture, than the other
one (NO STRAIN), in which these fields were
not considered. Furthermore, the residual strains
cause a stress boost in the system.
Therefore, the coupling of the residual
strains in the structural analysis decreases the
part’s resistance to failure, forecasting its loading
behavior with much more reliability. Thus, this
study showed the importance of considering the
part’s manufacturing history in the FEM
analysis, allowing the forecast of its true
deformation limits.
5 Conclusions
This work allowed to increase accuracy of
the structural analysis of injection molded
components, establishing a set of methodologies
and definitions, as well as considering the part’s
manufacturing history and the material
experimental data.
The mesh aggregation during the injection
simulation revealed to be crucial to overcome the
mesh existing elements with high aspect ratio.
This way, this work endorses the mesh quality as
a major milestone to the accuracy of the final
results.
The direct transfer method is
computationally very slow, that being a setback
from the start. Additionally, this method reached
exaggerate levels of stress and strain, which
compromised its results accuracy. The biggest
drawback of this method is the inability of
implementing any material experimental data.
Helius PFA assumed to be the more
accurate methodology of interaction between
Abaqus and Moldflow. Beyond enabling the
implementation of the experimental tensile
curves of the material, as well its mapping
capability, this interface provides a set of tools
that optimize the reproduction of the
performance of an injection molded component.
Besides, the comparison between the results
obtained by Helius and the material experimental
tensile curves showed a broad convergence,
endorsing the usage of this interface in order to
increase the structural analysis reliability.
11
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