1

Structural Analysis of Components Obtained by

the Injection Molding Process

André Antunes Oliveira

andre.antunes.oliveira@tecnico.ulisboa.pt

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

6 References

[1] M. Medraj, "Injection Molding lecture

16," [Online]. Available:

http://users.encs.concordia.ca/~mmedraj/

mech421/lecture%2016%20plastics%203.

pdf?q=injection-molding.

[2] Flying Eagle, "Reliable & Economic

Mold Solutions," Flying Eagle, [Online].

Available: http://www.cnf-

moldmaking.com/.

[3] Autodesk Inc., "Autodesk Helius PFA

2016 User's Manual," 2015. [Online].

Available:

http://help.autodesk.com/view/ACMPAN/

2016/ENU/.

[4] J. N. Reddy and J. N. Reddy, Mechanics

of Laminated Composite Plates and

Shells: Theory and Analysis, CRC Press,

2004.

[5] S. G. Advani and C. L. Tucker III, "The

Use of Tensors to Describe and Predict

Fiber Orientation in Short-Fiber

Composites," Journal of Rheology, vol.

31, pp. 751-784, 1987.

[6] ABAQUS, Inc., "Abaqus Analysis User's

Manual," 2014. [Online]. Available:

http://abaqus.software.polimi.it/v6.14/boo

ks/usi/default.htm.

[7] Simulia Inc., "Abaqus Interface for

Moldflow User's Manual," [Online].

Available:

http://abaqus.ethz.ch:2080/v6.11/books/us

b/default.htm.

[8] Autodesk Inc., "Autodesk Simulation

Moldflow Insight 2015 Help," [Online].

Available:

https://knowledge.autodesk.com/support/

moldflow-

insight#?p=MFIA&p_disp=Moldflow%2

0Insight&sort=score.

[9] ABAQUS Inc., "ABAQUS/Explicit:

Advanced Topics - Elements," 2005.

[10] C. L. Tucker III e E. Liang, “Stiffness

Predictions for Unidirectional Short-Fiber

Composites: Review and Evaluation,”

Composite Science Technology, 1999.

[11] B. N. Nguyen e J. Paquette, “EMTA’s

Evaluation of the Elastic Properties for

Fiber Polymer Composites Potentially

Used in Hydropower Systems,” Pacific

Northwest National Laboratory, August

2010.