Structure and Fracture Mechanics of Injection-Molded Composites

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Oct 30, 2013 (3 years and 8 months ago)

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1


International Encyclopedia of Composites
, Ed.:
L. Nicolais

Revised contribution by

J. Karger
-
Kocsis

Tshwane University of Technology, Faculty of Mechanical Engineering and Built
Environment, Department of Polymer Technology, Pretoria, 0001, Republic of S
outh Africa,

and

Budapest University of Technology and Economics, Faculty of Mechanical Engineering,
Department of Polymer Engineering, H
-
1111, Budapest, Hungary

E
-
mail:karger@pt.bme.hu



Structure and Fracture Mechanics of Injection
-
Molded Composites


The

history of fiber
-
reinforced thermoplastic polymers began only a few decades ago, when
industrial production
of the reinforcing fibers (
glass in 1935, carbon in 1959, aramid in 1971
)

and adequate matrix polymers

(e.g.
polyamide 6.6 in 1938 and polyethylene

terephthalate
in
1955
)
was started. Incorporation of
discontinuous

fibers into thermoplastics generally yields
improvements in mechanical and thermal properties, for instance, stiffness, strength,
dimensional stability, service temperature, resistance
to
creep

and fatigue.

These
improvements are, however, connected with reduced strain (ductility) characteristics and
pronounced anisotropy as a result of the structuring of the reinforcement in the molded part
s
.

Fiber reinforcement is a way to make special or

engineering thermoplastics from commodit
y
or high volume thermoplastics, such as
polypropylene
(PP)
.
Note that t
he criteria for
engineering thermoplastics


namely, continuous service temperature above 100°C and tensile

strength higher than 40 MPa [1
]


c
an also be met by several plastics without reinforcement.

T
he relative high annual growth
rate of fiber
-
reinforc
ed composites compared
to neat

plastics
is the result of a total or partial substitution of
metallic and ceramic
parts

by
injection
-
molded
compo
site items manufactured from
discontinuous fiber
-
reinforced polymer
s
.

To characterize these traditional construction materials that are being replaced by polymer
composites, fracture mechanical methods are widely used. Therefore, it seems obvious that
fra
cture mechanical approaches should be used for plastics and composites, too. This topic
has been treated comprehensively in books and papers [
2
-
9
]. Fracture mechanics yield
intrinsic or material parameters that can be reliably used for the design and const
ruction of
composite parts. The main advantage of this concept is that material parameters determined in
different ways can be compared with one another directly. This is not the case with
standardized test methods related to a given property, such as toug
hness. Toughness values
derived by different standard methods

can hardly be compared with one another because of
differences in the loading conditions.

2


It is obvious that the mechanical performance of continuous
-
fiber
-

or fabric
-
reinforced
polymers is supe
rior to that of
discontinuous
-
fiber versions. This disadvantage, which is
attributed to restricted load transfer between the matrix and the fibers, is compensated by

other benefits, i.e. by

design freedom,
easy processing

via

injection and extrusion moldin
g
s
.
Therefore, it is not surprising
that the development of
discontinuous fiber
-
reinforced
thermoplastics

is well reflected

by a steady increase in the aspect ratio (length to diameter,
l/d) of the fibers
both
in the
parent granules and molded parts
.
T
he l
/d ratio of
short fiber
-
reinforced thermoplastics (
SFRTPs
)

produced by extrusion melt

compounding technique was
≈ 20 earlier,

nowadays it lies at

≈ 50. The next milestone in the development of SFRTPs
was
achieved by

pultrusion and powder coating techniques, through which
granule size

fiber
length
was
set
.

The related products are termed t
o long fiber
-
reinforced thermoplastics
(LFRTPs). In their injection and compression moldable grades

the initial

aspect ratio of the
discontinuous
reinforcement

(usually glass fiber)

is ≈ 1000

and ≈ 2500, respectively.

It is doubtless true that the micros
tructure of injection
-
molded composites strongly depends
on the processing mode and its conditions. It is also well known that the mechanical
properties of plastics depend on the testing conditions, especially frequency and temperature.

Therefore, these as
pects have to be considered when
the
fracture and failure performance of
discontinuous fiber
-
reinforced thermo
plastics

are discussed

[10]
.

The mechanical performance of discontinuous fiber
-
reinforced thermoplastics is affected by
the followings (cf. Figure

1):

1
. C
omposition and morphology

2
. T
ype and amount of the reinforcement

3
. I
nterface
(
or interphase
)

between matrix and reinforcement

4
. P
roces
sing methods and conditions

5
. T
esting conditions

There is a strong interrelation amongst items 1) to 5). For
example both the matrix
morphology and reinforcement structuring may be highly dependent on the processing
methods as in the case of injection molding. On the other hand, the type and amount of the
reinforcement dictate the selection of both suitable proce
ssing methods and conditions. Items
1) to 5) list some matrix
-
, reinforcement
-
, interface
-

processing
-

and testing
-
related factors
and serve at the same time as an outline for this contribution.
The mechanical tests are
grouped into static and dynamic frac
ture with monotonic increasing load and static and
dynamic (cyclic) fatigue measurements.
T
he

test results

are
interpreted based on

fracture
mechanical concept
s
.


FIGURE 1
Factors influencing the fracture mechanical performance of discontinuous fiber
-
rei
nforced thermoplastic composites



3


Development
of Microstructure

Changes in the molecular orientation and crystallization behavior in neat and matrix polymers
of S
(L)
FRTP
s

occur during processing. This is accompanied with
fiber
structuring (i.e.
orientatio
n
and layering) in case of the

reinforced grades. Although these changes are rather
complex, the resulting microstructures can be explained by the viscoelasticity of the melt and
by the melt flow fields evolved in the mold. The viscoelastic behavior of the

melt depends on
several parameters of the polymeric material (molecular weight and its distribution, main
chain flexibility,conformation possibilities of the chain, etc) and the processing conditions
(melt and mold temperatures, plunger speed) that affect

the orientation and relaxation of the
polymer. For the flow field consisting of shear and elongational flows, processing conditions
are not the only important factors; the
mold construction (sprue, runner,

gate, and cavity
geometry inducing converging and

diverging flow during processing) is also relevant.

It is widely accepted that fiber orientation in
discontinuous fiber
-
reinforced thermoplastics
c
an adequately be desc
ribed by the model of Tadmor [11
], which involves the fountain or
volc
ano effect discus
sed by Rose [12
]. According to this model, the fiber orientation pattern
produced by injection molding can be approximated by a three
-
layer laminate structure. This
is depicted schematically and as it looks in practice in Figure
2
. In the surface (S) layer
s,
fibers are oriented parallel to the mold filling direction (MFD). This is caused by the shear
flow of the melt along the quickly solidified layer at the mold wall. In the central (C) layer,
fibers adopt an orientation perpendicular to the MFD in the pla
ne of the molded plaque. This
kind of alignment is due to the elongational flow at the midplane of the cavity. Factors
contributing to this elongational flow are diverging flow at the cavity entrance and the
fount
ain effect described by Rose [12
]. An addit
ional argument for the transverse fiber
orientation in the C layer was found in the squeeze flow of the me
lt during the packing stage
.
In the literature, examples of a more complex layering of the particulate reinforcement can be
found, as reviewed
[13
-
14
]
. Quite often a random fiber orientation can be produced in the
solidified layer at the mold wall. In the subsurface layer, however, fibers are aligned in the
MFD is a result of the shear flow evolved in this region. The splitting of the S layers in this
w
ay yields a "five
-
ply" laminate structure. The fiber layeri
ng can be even more complicated,
since particulate

fillers tend to migrate toward the midplane of the molding,
where flow
speeds are higher [15
]. This change, attributed to normal stress effects, a
gain modifies the
flow profile and thus the layering and orientation of the discontinuous reinforcement.


FlGURE
2
:

Fiber

oriention resulting from injection molding
(a)
for 40
wt%

(=
19.4
vol %)
long
G
F
reinforced polypropylene (PP);

(b)
schematically. T
his

picture illustrates p
osition and
design
ation of the
compact tension (
CT
)

specimens
preferentially
used.

Note that the
designation of the CT specimens considers the loading
-

notching (longitudinal, L or
transverse, T) directions in respect to the MFD.


4


Re
sults of numerous investigations carried out on injection
-
molded plaques of 3
-
4 mm
thickness indicate that

(cf. Figure 3)

1.

Both the fiber layering and alignment increase with fiber volume fraction
(
V
f
).

2.

The absolute values of the fiber orientation are close
ly matched in the S and C
layers, and fiber orientation increases with
V
f
.

3.

The processing effects (melt, mold temperature, and injection speed) are of
secondary importance compared with
V
f
.

These findings are for parts of normal thickness (3
-
4
mm)
molded b
y a film gate

[14]
. For
thinner or thicker items, which in addition involve other gate constructions, these statements
are not always valid.


FlGURE
3
:

Effects of cavity thickness (B) and fiber volume fraction (V
f
) on the layering,
planar orientation (f
p
)

and mean fiber length of injection molded discontinuous fiber
-
reinforced composites


Microstructural investigations ca
rried out on long glass fiber (LG
F) reinforced injection
-
molded thermoplastics showed significant analogies with short glass fiber (SGF)

composites
[
16
-
17
]. It was reported that:

1.

The relative thickness of the C layer increases with increasing aspect ratio.

2.

Fiber bunching and bundling may occur.

3.

Fiber bending can be evidenced.

Fiber bunching is connected with the pultrusion pell
etizing proc
ess used for the production of
LGF
-
reinforced injection
moldable composites. The local ordering of fibers during this
process may result in bundles that move cooperatively and do not filamentize enough during
moldin
g
. Fiber bending, on the other hand, is a
n appearance of decreased structural stiffness
due to the hi
g
her length. Both of these effects reduce the effective aspect ratio, of the
reinforci
ng fibers in the molded part [16,18
].

The aspect ratio of the fibers in the molded item depends on material fa
ctors (especially
V
f
),
mold geometry (
e.g.
runner and gate construction),
and processing parameters (e.g.

injection
speed). Higher fiber loading shifts the aspect ratio distribution curve toward lower values

as a
result of increased fiber/fiber and fiber/
w
all interactions, which cause fracture. This effect is
much less pronounced for LGF than for SGF reinforced composites, provided that mold
construction for the former system is adequate. It is due to the preliminary orientation of the
fibers during manufac
turing. The
aspect
ratio distribution curve of the reinforcement may
differ when various layers across the thickness

of th
e molded part are considered [16
]. This is
mainly due
to fiber enrichment in the C lay
er, differences between bunching and
filamentiza
tion in the
S
and C layers, and effects of the flow field on fibers with different
aspect ratios.

For the flow features and microstructural development in
discontinuous
fiber
-
reinforced
thermoplastics, detailed information can be taken from
the Ref. 19
.

5


It

can be concluded that the microstructural parameters of reinforced injection
-
molded
composites are fiber layering, fiber orientation (
the two latter are
commonly termed fiber
structuring), fiber volume fraction, and
effective
fiber aspect ratio and its di
stribution


"Design" of Microstructure

Among the guidelines for processing of SFRTPs

and LFRTPs
, priority is given to processing
parameters and mold constructions that contribute to preserving the initial aspect ratio, that is,
the fiber le
ngth of the rein
forcement
. A
voiding fiber breakage requires molding at minimal
frictional heating. On a given reciprocating injection molding machine this can be achieved
by slow screw rotation, low injection speed, low back pressure, and high barrel temperature.
Processi
ng of LGF reinforced thermoplastics is
very
similar to that of SGF composites. It is
recommended, however, that a 10
-
20°C higher barrel temperature and a special "low work"
screw be chosen. This screw is characterized by a long feed section with constant r
oot and
wide, deep flights. This section is followed by

a low gradual compression zone without
kneading or mixing elements; the screw ends in a constant
-
root metering section with flat
flights. In addition, certain aspects of mold construction have to be c
onsidered (short runner
s,
large film or fan gates)
.

Service conditions for SFRTP composite parts often require a given well
-
defined fiber
structuring. For injection
-
molded items, a new technique called multiple live
-
feed injection
molding was developed. In

this method, a packing head is inserted between the mold and the
head of the injection
-
molding machine. The melt flow, and thus fiber orientation in the
packing stage
, can be modified accordingly
by a programmable movement of the pistons of
the packing he
ad that pressurizes t
he solidifying melt directly [20
].

Computer aided design (CAD) is a new technique that has been successfully applied to
optimization of mold construction for
molded parts
. In CAD design of an injection
-
molded
part, the first step is to

visualize the weak sites, that is, the knit lines (supposing a runner and
gate system). The next step is to change the position and/or type of runner and gate so that
knit lines do not evolve or, if this is impossible,
are
positioned where low stresses in

the part
during service can be predicted. The next phase is modelling the flow in the mold, subdivided
into finite elements, and characterizing the melt flow patterns in these mold segments. For the
calculation of the flow patterns, rheological parameters
, determined experimentally, are used.
The flow modelling is repeated in several steps until op
timized mold filling occurs
. The aim
during extrusion die design is to get the same material flow in all segments of the die resulting
in smooth surfaced, warpag
e
-
free extrudates. For the flow simulations different software
packages are
available
.


Microstructural Characterization

6


As stated before, the microstructural parameters are fiber layering and orientation, fiber
volume fraction, and fiber aspect ratio and
its distribution.

For the determination of fiber layering by imaging of polished sections or thin slices, light
(reflective or transmission), scanning electron microscopy (SEM), and contact
microradiography are preferred. For fiber orientation, microwav
e,
X
-
ray diffraction, sonic,
and thermographic
measurements can also be used. In Figure
2a

SEM micrographs taken
from polished sections along the
t
hickness
-
MFD (
z
-
x
)

and
y
-
x
planes are shown.

The evaluation of fiber alignment and mean fiber orientation in a g
iven plane is very time
-
consuming, as it involves determining the angle distribution under which fibers are aligned. In
this respect, image analysis offers the new possibility of getting information about not only

in
-
plane b
ut also spatial orientations [21
].

Fiber orientation can be described either by using
mean orientat
ion factors, such as Hermans [22], Krenchel [23
], and modified H
ermans [24],
or by vectors [25
].

The aspect ratio (since the diameter of the fibers is mainly constant, it
can
be replaced by

fiber
length) distribution curves are generally determined from microphotographs of the fibers
taken after burning away the matrix. In many cases the matrix polymer can also be removed
by solvents. Instead of histograms showing the relative frequency of f
ibers in a given length
interwall, the use of envelope curves, either in differential or in integral form, is preferred.

The above
-
mentioned microstructural parameters are "integrated" in a reinforcing
effectiveness term

(R)
. This term previously considere
d the effects of fiber structuring with
respect to the loading direction and the fiber loading
[26
].

This was extended later to include
the aspect ratio

and aspect ratio distribution

[
14,16,18],

an
d generalized in the form
:




(
1
)


wh
ere T
rel,i

is the relative thickness of the ith layer normalized to the sample thickness (B, see
Figure 31.4), f
peff,i

is the effective orientation in the i
th

layer calculated using the function of
planar orientation (f
p
) vs. f
p,eff

introduced by Friedrich

[
26
],
V
f,i

is the fiber volume fraction in
the i
th

layer, (l/d)
equ,i

is the equivalent aspect ratio in the i
th

layer, (l/d)
m,i

and (l/d)
n,i

are

the
mean mass
-

and number average aspect ratios in the i
th

layer, respectively

[16]
.

It seems that the fracture

mechanical response of
discontinuous
fiber
-
reinforced plastics can
be appropriately related to this reinfor
cing effectiveness parameter [14
].


Fracture Mechanics

Detailed treatment of fracture mechanics is far beyond the scope of this article; it can be
f
ound in the literature [
2
-
9
]. Here only a brief overview

is given.

A fundamental aspect of fracture mechanics is that the onset of fracture depends not only on
the applied stress but also on the size of intrinsic flaws that act as stress concentrators. The

7


presence of such flaws is the reason, for example, that the real tensile strength of

solids,
including polymers, is ≈1/10 of the theoretical

value [
4
]. Such stress concentration sites are
always present in neat and reinforced molded plastics, either as a result of processing
("notches" at the knit lines resulting from compressed air, bare

fiber segments

as a result of
imperfect wetting by the matrix, voids caused by differences in the thermal expansion
characteristics of the matrix and reinforcement etc.) or caused by use (scratches, damage by
cutting or shaping, impacts etc.). The common
effects of stress and flaw size are combined in
linear elastic fracture mechanics (LEFM)


which deals only with bodies that obey the
Hookian law, that is, whose deformation is fully elastic


in a term called stress intensity
factor

(K) or fracture toughn
ess
:




(
2
)


where


σ = applied stress

a = crack size

Y
= geometrical correction factor taking into consideration the finite size of the specimen used

I = tensile opening mode, mode I


According to the LEFM theory, fracture occurs whe
n K
I

> K
Ic
, where K
Ic
, is a critical value o
f
the stress intensity factor.
This material parameter is also termed
fracture toughness.

From Eq.
(2
) it is obvious that K
I

is a stress
-
related fracture mechanical criterion. K
I
, can be determined
from monoto
nic

static loading measurements, for example
according to ASTM E 399. In the
case of monotonic dynamic loading, K
Ic

can be
computed

by Eq.
(2
) as the slope of the plot
Y·σ against a
-
1/2
.

The other LEFM material parameter is an energy
-
related one that measures the energy
required to extend the crack over a new surface unit. This term is denoted G
Ic
, and is called
fracture energy, critical strain

energy release rate, or specific crack extension force. The onset

of fracture depends again on whether G
I

is less than or greater than G
Ic
. K
c

and G
c

are
interrelated by a function whose exact form depends on the stress state of the specimen (plane
stress

or plane strain). For S
(L)
FRTPs, G
Ic

is generally determined from high
speed
impact
tests

-

using
Charpy
and I
zod
test set ups
-

through

the
method of Plati and Williams [27
] or
its derivatives

(ISO 17281)
.

The main criterion of LEFM, namely fully elastic

deformation, is very severe for plastics that
may undergo pronounced plastic deformation (yielding or tearing) during fracture. In this
case, other approaches, also used originally for metals, were p
ursued for plastics: J
-
integral,
crack opening displacem
ent (COD)
, and essential work of fracture (EWF)

[6,28]
. These
material parameters are included in plastic, elastoplastic, or postyield fracture mechanics
(PYFM). J
Ic

is an energy
-
related term connected with the onset of stable crack growth. For
8


linear elas
tic bodies G
Ic

= J
Ic
. J
Ic

can be determined
for example
by ASTM E813

and ISO/CD
28660
. In addition, J
Ic

can be deduced from high speed impact tests carried out on sharply
notc
hed Izod or Charpy specimens [28
].

The fracture mechanical approach can also be a
pplied for both static and dynamic (cycling)
fatigue of cracked specimens. Static and dynamic fatigue means slow crack growth under
subcritical stresses and stress amplitudes, respectively; that is, the stress intensity factor and
its amplitude lie below K
Ic
. The aim of both measurements is to establish crack extension
characteristics with respect to the stress concentration at the crack tip as a function of either
time (da/dt


static fatigue loading) or number of fatigue cycles (da/dN


dynamic fatigue).

The latter characterization can be performed by the ASTM E 647 standard, originally
developed for metals.


For the determination of the critical values of fracture mechanical parameters related to the
plane strain condition, the specimens used have to meet

different size criteria. These can be
taken from the corresponding standards; alterations to these standards for
discontinuous fiber
-
reinforced thermoplastics

are summarized in Ref. 14
. If these criteria are not met, critical
values of K
I
, are denoted K
c
,

instead of K
Ic
; the same designation is used also for G
c
, and J
c
.


Fracture and Related Failure

In both static and dynamic fracture measurements, breakdown is caused by monotonically
increasing load. The only difference between them is related to the stra
in rate or frequency
range; however, the threshold value is rather arbit
rary. M
easurements carried out below a
cross
-
head speed v of 1 m/min are referred to as static, whereas impact measurements with a
striker speed above 1 m/s are referred to as dynamic
fracture tests.


Static Loading

EFFECT OF MICROSTRUCTURE. Fiber loading. Fiber reinforcement may affect fracture
toughness in different ways. It can be improved, worsened, or held at a constant level by fiber
incorporation, depending on

the matrix of the c
omposite [14
]. The run of K
c
, as a function

of
V
f

can hardly be predicted, because of competitive micromechanisms that either increase or
decrease K
c
.

Nevertheless, discontinuous fiber reinforcement is always the right tool to
increase the fracture toughne
ss of low molecular weight polymers prone for brittle fracture.

The effects of reinforcement
-
matrix bond quality and of matrix toughening are worth
mentioning here. Improving the coupling between fiber and matrix is not necessarily
beneficial for K
c
. Stron
g bonding may hinder the deformability of the composite so that K
c

tends to decrease

[29]
. This is

in accordance
with
the Hahn
-
Rosenfield equation [30
]. This
equation explicitly shows that K
c

does not depend solely on strength but also depends on
ductility

parameters:



(3)

where

9



E
= E modulus



σ
b
, ε
b
= tensile strength and elongation at break, respectively


L

= proportionality constant including strain hardening, in length dimension

It is well known that toughening of the matrix results in increased ductility; however, this is at
the cost of sti
ffness and strength. Thus matrix toughening may also be connected with
deterioration

in K
c
.

The course of J
c

as a function of V
f

depends on the corresponding K
c

-

V
f

and E

-

V
f

functions:



(4
)

provided the plane stress condition sa
tisfies the LEFM theory. If the K
c

increment due to the
square function overcompensates for the increment in E modulus, J
c

increases; when it does
not, the opposite tendency becomes evident. It should be noted here that J
lc

values
can be
found scarcely
for

discontinuous fiber
-
reinforced thermoplastics

in the literature [14,28
].

In spite of the very complex fracture mechanical response to fiber loading, the following
conclusions can be drawn:

1.

An increase in K
c

from fiber loading is more probable the higher t
he E modulus
and the lower the ductility of the unfilled matrix (brittle, low molecular weight,
degraded
polymers, especially polycondenz
ates).

2.

For ductile materials a relative increase in both K
c

and J
c

can be achieved by using
fibers of higher

aspect rat
io (e.g.

LGF

instead of SGF
).

3.

The effects of matrix toughness and fiber
-
matrix bonding are hardly predictable.
For relative improvements in K
c

and J
c
, the strength and ductility characteristics of
the matrix have to be balanced

by the reinforcement
.


Fiber

structuring. The layering and orientation of the fibers in injection
-
molded items were
already shown in connection with Figure
s 2 and

3. On the fracture surface of the specimens,
fibers lying parallel or longitudinal to the crack plane (L fibers) can clea
rly be distinguished
from those oriented perpendicular or transverse to it (T fibers)
(Figure 4
).


FIGURE 4
:

Fracture surface at the razor notch of 40 wt % (=19.4 vol %) SGF reinforced
injection
-
molded PP. (In this
T
-
L

type CT

specimen, L fibers can be fo
und on the surface,
w
hereas

T fibers in the central
layer, as indicated; cf. Fig. 2
. Razor blade notch is marked by
arrow.)


It is doubtless true that the anisotropic structuring of the fibers yields different fracture
mechanical values when specimens with

various notch directions (T and L; see Fig
. 2b
) are
tested [
14,17,26,29
]. The load

bearing capacity of T fibers aligned in the load direction is
consi
derably higher than that of the

L fibers, which have practically no reinforcing effect.
10


Therefore, the fr
acture mechanical response depends on the relative thickness of the layers
containing T and L fibers, respectively.

The degree of fiber orientation in these layers is also important. T fibers completely aligned in
the load direction guarantee the best stre
ss transfer and thus the greatest reinforcement. Fiber
misalignment along the load direction necessarily reduces the overall reinforcing effect.
Friedrich introduced an effective fiber orientation term that takes this fact into account



cf.
Figure 5

[26
].


FIGURE 5:

Relationships between the effective (f
p,eff
) and planar fiber orientations (f
p
)
considering the actual mechanical loading direction


Many investigations carried out on SGF and LGF composites (e.g., Refs.
14,16,17,18
) have
indicated that the ani
sotropy in the mechanical response of the
LGF
-
reinforced
systems is not
very pronounced, in spite of the fact that the three
-
ply laminate structure caused by the
injection molding still exists. This observation suggests the important role of the aspect rat
io.


Fiber aspect ratio. The influence of filler shape on fracture toughness at a given filler loading
strongly depends o
n the matrix characteristics [29
].
However, with

increasing fiber aspect
ratio

K
c

always increases, at least above a given threshold l/
d.

This is connected with an
increase in the loadability of the discontinuous
-
fiber
-
reinforced composites, since their
strength increases with increasing aspect ratio
[
31
]. The l/d ratio can be increased either by
using longer fibers of the same diameter o
r by using smaller diameter fibers of the same
length. Reinforcing with small diameter fibers is beneficial only in a given aspect ratio range.
This is due to the fact that the deleterious effect of stress concentra
tion at the fiber ends
should be compensa
ted for by toughness
-
enhancing effects, such as increasing interface,

improved stress interaction between fibers, and
enhanced

crack path [32
]. A decrease in the
critical fiber length for smaller diameter fibers is expected to lead to an increase in the cl
ack
path length, which promotes fiber pullou
t and reduces fiber fracture [14
].

A definite answer on the effect of fiber aspect ratio distribution cannot be given. There are,
however, several indications [
26,32
] that use of reinforcing fibers with different

aspect ratios
as a result of varying diameters can be beneficial for fracture mechanical characteristics.



EFFECTS OF TESTING CONDITIONS. Temperature.
The fracture toughness, measured
at
low cross
-
head speed
,

decreases
as a function of temperature T
for
both matrix and its fiber
-
reinforced versions
[
16,29
].
A

steeper decrease
in the related plot
can always be found in the
vicinity of the glass transition temperature
(
T
g
)

of the matrix.

Here the enhanced molecular
mobility of the matrix induces a change in

deformation mode from ductile to viscous.
So,
T
g

is always the upper threshold for
the
applicability of the LEFM theory. K
c

values calculated
11


according to Eq.

(1) for temperatures above T
g

no longer have meaning for

fracture
toughness; they can be treated

only as trend

data of a mechanical property thus defined.


Cross
-
head speed. At v = 1000 mm/min, the trend of

K
c

with T is basically different from that
at v = 1

mm/min.
K
c

values start at a relatively low level

in the subambient temperature range
before
they increase

at
the

T
g
[
29, 33, 34
]. This is attributed to

a clear change in the stress
state of the samples (plane

strain to plane stress) and related failure manner (brittle

to viscous
as a result of adiabatic heating at the crack tip).



FAILURE BEHAVI
OR. It is obvious that big differences

due to testing conditions are related
to substantial

changes in microscopic breakdown events. The microscopic

failure mechanisms
occurring in S
(L)
FRTPs are

shown schematically in Figure
6
. They can be grouped

into
mat
rix
-
related (crazing and shear yielding) and fiber
-
related (fiber fracture, pullout, and
debonding)

events. For longer
-
fiber
-
reinforced injection
-
molded

composites, the latter can be
extended by fiber bridging

(unbroken fibers connect the crack sides) and
by cleavage

and slip
of fibers within bundles or rovings during

debonding and pullout.

It should be noted here that
the relative orientation

of the fibers (L and T) strongly influences the relative probability of
the individual fiber
-
related energy absorpt
ion mechanisms [
14,29,35
].


FIGURE
6
:

Failure mechanisms for discontinuous
-
fiber
-
reinforced thermoplastic

at
a
microscopic level


Based on fractographic results, the characteristic failure

modes of the composites can be
summarized in failure

maps. In such
maps the dominant matrix
-

and fiber
-
related

breakdown
processes are indicated as a function

of the testing conditions T and v
[
18,35,36
]
. Failure
maps not only give guidance

for selecting composites for particular circumstances

but also
suggest methods of
increasing the toughness.
In the patent 1iterature one can find abundant
examples and ideas for such improvement.



Dynamic Loading

EFFECTS OF MICROSTRUC
TU
RE.
F
iber loading.

The plot of dynamic fracture toughness
as a function

of V
f
can be as complex as th
at for the static case. Generally

the dynamic
fracture energy
(
G
d
)

decreases with increasing

fiber loading. This effect may or may not be

compensated for by the increasing E modulus with

respect to the resulting K
d
. Since this
effect of the E

modulus is ve
ry closely matched to the static one, the

plot of
K
d

as a function
of
V
f

depends mostly on the
G
d

-

V
f

function of Eq. (4
).

T
he effect of
V
f

on
K
d

is
demonstrated

in Figure
7

for
SGF
-

and

LG
F
-
reinforced com
posites. It can be concluded that
12


increasing the a
spect ratio of the reinforcement yields an improvement in K
d
.

The G
d

-

V
f

function, on the other hand, should depend on the matrix toughness and fiber
-
matrix bond
quality.


FIGURE
7
:

Change in the static
(K
c
)
and

dynamic (
K
d
)

f
racture toughness as a func
tion

of fiber loading
(
V
f
)

at ambient temperature

for SGF
-

and
LGF
-
reinforced injection
-
molded

PP (
K
c

determined on CT specimens

at v = 1
mm/m
in, whereas
K
d

deduced from

lzod
measurements)


At this point attention has to be paid to the internal

flaws induc
ed by specimen machining
(sawing, cutting,

polishing, and the like). The presence of such flaws

causes trouble during
curve fitting and a very big scatter

in
G
d
, especially for long
fiber
-
reinforced systems.

However, if
failure of
the

specimens
occurs

not
at the notch introduced but near to it

means
that

cutting introduced a

flaw


(either by debonding or by intrabundle fiber cleavage) that
acted as a stress concentrator site. In
some

case
s

this threshold or

latent notch


value was
found to be = 0.5
-
0.6 mm

[37
].


Fiber aspect ratio. This effect is surprisingly pronounced

if one compares
K
c

and
K
d

for
SGF
-

and
LGF
-
filled composites (see Fig. 7
). This suggests some

differences in the load transfer
during static and dynamic

measurements that should be clarifie
d.


EFFECTS OF TESTING CONDITIONS.
G
d

and
K
d

values

derived from Izod and Charpy
measurements are

very closely matched. This is due to an analogous stress

state during
impact, which is carried out at practically

the same deformation rate. The plot of
K
d

a
nd
G
d

as a

function of T can

be calculated from Eq.
(4
)

provided that

the E(T)

a
nd
G
d
(T)

o
r
K
d
(T)
functions are known at the

given frequency.
K
d

generally increases with decreasing

T as a
result of the increase in E modulus, whereas
G
d

remains

practically
constant. The

plots of both
fracture mechanical parameters depend on

the temperature range investigated; maxima and
minima

in the plots can also be found. Their appearance is attributed

to primary and
secondary relaxation transitions of

the matrix and its
components [
4,5,38
]
.


FAlLURE BEHAVIOR. It has to be emphasized that

dynamic failure mechanisms are the
same as those

shown and discussed with respect to static loading. Although failure mapping
has not been performed for dynamic measurements, the followin
g findings are expected:

1.

The frequency embrittlement of the matrix promotes brittle matrix cracking, the
onset of which depends on the frequency
-
dependent T
g
. Among the matrix
-
related
failure mechanisms, crazing is more common than shear yielding.

13


2.

Among th
e fiber
-
related failure events, fiber pullout and fracture tend to dominate
.

Their relative proportions depend not only on the testing conditions but also on the
fiber
-
matrix bonding.


Fatigue and Related Failure

S
(L)
FRTP parts are widely used in fields in

which constant

and cyclic subcritical loading
occur. The response to

long
-
term constant loading (static fatigue) is often called

either stress
corrosion (SCC) or environmental stress corrosion

cracking (ESC).

In this case, crack
propagation is

induced in
different environments at the condition K
0

<

K
Ic
, where
K
0

denotes
the initial stress intensity factor.

The result of this kind of measurement is either the

stress

corrosion threshold (
K
I,SCC
) or the crack growth

rate
(da/
dt vs.
K
I
),

or both.
K
I,SCC

means
a
threshold K
I
,

value below which no crack growth takes place in a given

environment.

In dynamic or cyclic fatigue, the crack growth rate per

cycle is established as a function of the
stress intensity

factor amplitude
(
Δ
K
)
. A threshold value
ΔK
th
, which is

connected with the
onset of fatigue growth, can be read

from the fatigue crack propagation (FCP) curve. The

characteristics of static and dynamic fatigue with respect

to the measurements and results to
be discussed are

summarized in Figure
8
.


FIGURE 8
:

T
he fatigue behavior of injection
-
molded composites.


Static Fatigue

EFFECT OF MICROSTRUCTURE. When K
c
, from

static fracture
,

increases with V
f
, one can
expect a similar

trend in the resistance to SCC for the given composite.

I
ncorporation of a
rubbery impa
ct modifier
in the matrix
results in

further improvement in SCC resistance

of the
related composite
. Fractographic

analysis supports the conclusion that this is due to better

wetting of the fibers and thus better protection of

them against acidic attack. O
n the other
hand, when K
c

decreases with V
f
, an acceleration in SCC growth can be

predicted in relation
to the corresponding matrix. The

da/dt
-
K
I

cu
rve
s, or at least their segments in double
logarithmic

representation,
can be approximated

by straight lines
. This indicates the validity
of the Paris
-
Erdog
a
n relationship (o
ften called the Paris power law [
3,4,39
]
)
:




(5
)


The crack growth kinetics depend on both

the micro
structure and the environment [
29,40,41
]
.
Note that t
he

final break
down of the specimens

(usually CT type)

does not necessarily occur
at the K
c

derived from static loading measurement.

In SCC tests, K
I

at the specimen breakdown may be

higher than K
c

when a material with
rather ductile
behavio
r
is investigated
.
This is a c
onsequence of the

very low frequency of this
14


kind of measurement, which

generates a process

or damage zone that is fundame
ntally

different from that found in static
f
racture. Alterations

can be observed in both the size of the
zone and

t
he related failure
mechanisms therein. It can be concluded

that final breakdown of a
specimen with ductile

features (either due to the material or due to the stress

state) takes place
near the static
K
max

value. This value

can be determined by Eq. (1) using the maximum load.

Such response

can be obse
r
ved for composites either in air or in

sur
ro
unding media that
plastify

their matrix.

Final failure of the specimen may also occur at K
I

< K
c

as

a result of
aggressive attack by a given environment. If the

initial stress intensity

factor K
0

is very small
but higher

than
K
I,SCC
, the surrounding medium can penetrate

deeply into the specimen,
causing failure events (e.g.

multiple fiber breakage, surface degradation) that decrease

the
SCC resistance (diffusion
-
assisted SCC).

Therefore,

it is highly reasonable to always indicate
K
0
.

For composites with a ductile matrix or one that is "ductilized"

during the measurement,
the crack tip at its advance

can hardly be resolved. Instead of a sharp crack, a

well
-
evo
lv
ed
damage zone can be observ
ed. The propagation

of this zone as a whole can be treated and
adequately

described by the crack layer theory
(e.g.
[
42
]
)
.

Changes in the time to failure curves due to microstructural

and environmental effects are
very similar to

those discussed above with

respect to SCC growth [
40,41
]
. However,
final
failure
may occur

at

a

K
c

which is either

independent

or dependent

of
K
0
.

The latter

case

suggests that failure depends additionally

on
K
0
,

that is, on the co
rrosi
on loading history of
the

s
pecimen. This corro
sion loading
history is rather complex,

since it involves the
immersion time and all

changes in both the structure and the stress state that

are caused by the
diffusion and penetration of the environment.

T
his observation means t
hat Eq. (5
) no longer

holds
, since da/dt depends in addition on
K
0
;

therefore,

talking about a material parameter
according to the fracture

mechanical concept is very questionable.


EFFE
CT

OF ENVIRONMENT. Both the da/dt
-
K
I
, and

the
K
0
-
time (
t
)

curves depend strongly
on the environme
nt.

They can be grouped by whether their degradative attack

relates mostly
to the matrix, to the fibers, or to the fiber
-
matrix

interface. In addition, the SCC response is
highly

affected by the
corrosion

loading history.


FAILURE. First impressions about

the failure mode

can be got
from

the surface appearance
of the broken

specimens. A nearly planar fracture surface indicates fi
ber degradation, which
mostly occu
rs in acidic environments [43,44
]. A zig
-
zag fracture surface path, reflecting the
fiber alignm
ent, on the other hand, illustrates matrix and matrix
-
fiber interface attacks. The
failure micromechanisms during SCC usually agree with those in static fracture; however,
their relative occurrence varies considerably with the aggressive nature of the envi
ronment
and the K
0

of the test.


15


Dynamic Fatigue

Since flaws are always present in S
(L)
FRTPs, one can conclude

that the main constituent of
durability is the propagation

of such flaws rather than their initiation and

development. In this
case, the results
of FCP measurements

are relevant and important from the point of view

of
construction.


EFFECT OF MICROSTRUCTURE. Fiber loading. It

should be emphasized that FCP
resistance due to fiber

loading changes along with the
K
c
-
V
f

function. Increasing

fracture
tou
ghness thus correlates with improved

FCP resistance (Fig.
9
)
, while decreasing K
c

with V
f

yields

FCP acceleration
[
14,29
]
. Figure
9

again shows the validity

of the Paris power law (Eq.
6
) for the stable FCP range:




(6
)



FIGURE
9
:


Changes in
FCP
behavior due to microstructural parameters, schematically


The exponential term m
of Eq. (6)

generally increases with V
f

(Figure 10).
Th
is

change is
accompanied by a shift of
ΔK
th
, toward higher

ΔK

values; that is, fiber incorporation
enhances the

threshol
d limit below which no crack gr
owth takes

place. The same trend in
ΔK
th

can be
observed when
results achieved on L
-

and T
-
cracked specimens

are
compared.
This is due to a chan
ge in the stress state of

the specimen as it approaches the plane strain
condition

as a result of increasing fiber loading and load direction

aligned fiber structuring.
The onset of unstable crack

growth (final fast fracture) occurs near either K
c

or K
max
,

just as it
does in static fatigue. This upper limit and the

stable FCP range itself are strongly affected by
the vis
co
elasticity

of the material under the given testing condition

(e.g
., crack tip heating
effects [45
]
).


FIGURE 10
:

Paris range in the FCP
curves of PP and its SGF
-

and LGF
-
reinforced grades at
different fiber volume fractions

(indicated in vol.%)


Fiber structuring.
L
-
T

specimens, because of

the higher quantity of T fibers oriented in the
load direction

(see Fig. 2b)
,

exhibit higher FCP resi
stance than
T
-
L
-
cracked ones.

This
finding is again analogous to the results of static

loadings. The effect of fiber structuring
becomes more

and more pronounced with increasing V
f

for SGF
than for LGF reinforcement.

This supports

the statement made before

in connection with monotonic

loading, namely, that
incorporation of LGF diminishes

the mechanical anisot
rop
y.


16


Fiber aspect ratio.
When the FCP curves of SGF
-

and LGF
-
reinforced

PP
s

are compared a
clear improvement

in FCP resistance can be seen as a resul
t of the use of

fibers of higher
aspect ratio

(Figure 9)
. The relative improvement

diminishes with increasing
V
f
. FCP
enhancement of LGF

reinforced systems was attributed to the evolution of a

more extended
damage zone and longer debonding and

pullout rout
es [
46
].

The effects of the above microstructural parameters

on the FCP behavior are summarized
schematically in

F
igure
9. For the microstructural interpretation of th
e
FCP response, a
qualitative [
47
] and a quantitative model

[
16,18,29
]

exist. The latter
is based on the
reinforcing effectiveness

(R)
and microstructural efficiency

(M)

concepts

[
16,26
].

Figure 11

shows the difference in the FCP rates between SGF
-

and LGF
-
reinforced PP composites as a
function of the
M values
. One can clearly see that with in
creasing M the crack rate, at a given
Δ
K value, decreases markedly

[18]
.



FIGURE
11:

FCP
rates

of SGF
-

and

LGF
-
reinforced PP grades
as a function of the
microstructural efficiency (M)
at a given stress intensity
factor
amplitude
(
Δ
K=1.5 MPam
1/2
)



EFFECTS

OF TESTING CONDITIONS. Information on the effects of external testing
conditions (waveform, frequency [
47
], main load, temperature, environment, etc.) on the FCP
response of SFRTPs is very limited. These effects seem to be highly material
-
dependent;
there
fore, general conclusions cannot be drawn.


FAILURE. Analogies between the fracture mechanica1 responses given for fracture and for
fatigue suggest that the individual failure mechanisms at the microscopic level are the same
(
see

Fig.
6
). The first step in

failure is again debonding at the fiber ends. This is followed by
pullout and further debonding for T
-

and L
-
oriented fibers, respectively. Th
e
fatigue crack
path in Figure 12

demonstrates this. In this picture, stress concentration at the fiber ends is
c
learly perceptible. In the damage zone, in addition, a stress concentration field was
developed and preserved by matr
ix deformation.
The matrix underwent

crazing and shear
yielding, initiated by fiber debonding and pullout processes.


FIGURE 12:

Fatigue cr
ack profile on the surface of a
CT

specimen of 20 wt % (= 8.3 vol %)
SGF reinforced PP:
(A)

behind the crack tip;
(B)

before the crack tip. (Crack direction from
left to right.)


Among the discrepancies between fracture and fatigue, the size of the damage
zone and the
sharpness of the crack have to be mentioned; the zone is smaller and the cra
ck is sharper
during fatigue [33
].

17


Further differences between the failure modes are connected with crack tip heating and
accompanying changes in both matrix
-

and fibe
r
-
related micromechanisms caused by cyclic
loading. At the onset of stable FCP, the matrix fails in a semibrittle manner with multiple
fractures. Therefore, the mean pullout length
here
is relatively small. In addition, this multiple
matrix fracture yields

a stress field that promotes fiber bre
akage
.
At the end of stable FCP, the
ductility of the matrix increases considerably; crazed arrays and viscous torn matrix parts can
also be evident. Among the fiber
-
related mechanisms, pullout dominates
-
however; with

an
increased average length

[48,49]
.

On the FCP curves of many S
(L)
FRTPs, a stable delayed crack growth region can also be
resolved jus
t before stable acceleration cra
ck growth occurs (see Fig.
13
a
). This is connected
with an evolution and stabilization o
f the damage zone.
This is the right place to call the
attention to differences in cyclic and static fatigue responses. Under static conditions the
stable crack deceleration occurs at much higher actual stress intensity factor compare
d to the
cyclic one (s
ee Fig. 13
b). This is due to the formation of a more extended “equilibrium”
damage zone the formation of which was supported by the fact that the apparent frequency of
static fatigue is lower than the cyclic one

[18,48]
. Under apparent frequency the recipr
ocal
value of the time causing the specimen fracture is meant.


FIGURE 13
:

S
table
crack deceleration ranges registered during cyclic (a) and static fatigue
(b) for SGF
-

and LGF
-
reinforced PP grades with different fiber volume contents


The fiber
-
related mi
cromechanisms strongly depend on the relative fiber angle to the crack
plane [
29,35,50
]. In addition, crack closure may also appear, especially in T
-
fiber regions
with higher fatigue crack lengths. This decelerates the FCP rate and is connected w
ith a mixe
d
mode (modes I and II
) stress state.

It would be highly reasonable to construct fatigue failure
maps analogous to those for fracture. Because experimental results are lacking, however,
mapping cannot be performed yet.


Design Aspects

It has been shown ab
ove that the fracture mechanical characterization of injection
-
molded
thermoplastics and their composites contributes to a better understanding of their performance
in different loading situations. Although in many cases real plane strain fracture paramete
rs
can hardly be deduced because the mean thickness of injection
-
molded parts (3
-
6 mm) does
not reach the required one, their measured values can be used for design and construction. For
this purpose, however, an adequate fracture mechanical characterizati
on method should be
selected.

The proper choice of method when a fracture
-
resistant part is to be constructed depends on the
behavior of the material. For composites with high stiffness and low ductility, which fail by
18


brittle fracture, stress
-
related term
s (K
c
) are used, whereas for those of high ductility, energy
-
related fracture mechanical terms (G
c

, J
c
,

COD

and EWF
) should be preferred
.

In the case of a part that is to withstand fatigue loading, the first question to be answered is
whether failure occu
rs mainly by crack initiation or by crack propagation. When the cycles to
failure at different stresses are plotted for a given material, the response curve can be divided
into two regions: crack initiation and crack propagation (Fig.
14
). It was shown abo
ve that for
SGF and LGF reinforced injection
-
molded composites, crack propagation is of basic
importance. In this case, therefore, threshold values (K
I,SSC
, ΔK
th
) derived from static and
dynamic fatigue measurements can be used for construction purposes.



FIGURE 14:

Design factors for fatigue
-
resistant composites depending on whether crack
initiation or crack propagation dominates the failure behavior.



Su
mmary

This

article has dealt with microstructural development,

microstructure
-
related fracture, and
fatigue performance

at static and dynamic loadings and corresponding

failure behavior of
short and long discontinuous fiber
-
reinforced injection
-
molded

comp
osites. The response

of
these systems to different loading conditions

was treated by fracture mechanical concepts
using

stress
-

and energy
-
related terms. The accompanying failure

was analyzed by
fractography and grouped into m
atrix
-
and fiber
-
related events
. In addition, the changes

related
to different loading situations were de
m
onstrated

a
nd discussed. Attempts were made to
determine

general trends in microstructural development,

fracture mechanical response, and
connected failure behavior,

and to summariz
e them schematically. Analogies

and
discrepancies between fracture and fatigue were

emphasized and discussed. Finally,
recommendations

were given for design of injection
-
molded thermoplastic

matrix composite
parts under increasing (fracture) and

alternatin
g (fatigue) load. The literature cited offers
further

detail on this topic.





[See
also
Molding
,
Polymer
Injection ???
]


J. Karger
-
Kocsis


References

1.

L.
A. Utracki,
Int. Polym. Process.,
2,

3 (1987).

2.

H. H. Kausch,
Polymer Fracture,
Springer, Berlin,
1978
.

3.

R
.
W.
Hertzberg and J.
A.
Manson,
Fatigue of Engineering

Plastics,
Academic Press,
New York,
1980.

4.

A. J. Ki
n
loc
h

and
R
.
J.

Young
,

Fracture Behavior of Polymers
, A
pplied Scie
nce Publ.,
Barking, United Kingdom, 1983.

19


5.

J.
G
.
Williams,

Fracture Mechanics of P
olymers
,
Ellis
Ho
rwood/J.

Wiley, Chichester,
1984.

6.

A.
G. Atki
n
s and Y.
-
W. Mai,
E
lastic and Plastic Fracture
:

Metals, Po
ly
mers,
Ceramics, Co
mpo
sites,

B
iological Materials,

Ellis Horwoo
d
/J. Wil
e
y,
Chichester
;
1985.

7.

N.
G.
McC
ru
m, C. P. Buckley, and C.
U.
Buck
nall,
Principles

of Po
l
ymer
Engineering
, Oxford

Unive
r
sity Press,
Oxford
,
1988.

8.

K.
Friedrich, Ed.,
Applica
t
ion
of
Fracture Mechanics to

Composite Materials,
Elsevier, Amsterdam,
1989.

9.

L.
A.
Car
l
sson, Ed.,
Thermoplastic Composite Materials,

Elsevier, Amster
dam,
1991
.

10.

J. Karger
-
Kocsis
,


Reinforced polymer blends
” in
D.

R.

Paul and C.

B.

Bucknall
, Eds.,
Polymer Blends, Volume 2: Performance,

J. Wiley, N.Y., 2000, p. 395.

11.

Z
.
Tadmor,
J.
Appl. Polym. Sci.,
18,
1753 (1974
)
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W.
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