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 South 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 parts.
Fiber reinforcement is a way to make special or engineering thermoplastics from commodity
or high volume thermoplastics, such as polypropylene (PP). Note that the criteria for
engineering thermoplastics – namely, continuous service temperature above 100°C and tensile
strength higher than 40 MPa [1] – can also be met by several plastics without reinforcement.
The relative high annual growth rate of fiber-reinforced composites compared to neat plastics
is the result of a total or partial substitution of metallic and ceramic parts by injection-molded
composite items manufactured from discontinuous fiber-reinforced polymers.
To characterize these traditional construction materials that are being replaced by polymer
composites, fracture mechanical methods are widely used. Therefore, it seems obvious that
fracture 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 construction 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 toughness. Toughness values
derived by different standard methods can hardly be compared with one another because of
differences in the loading conditions.
1
It is obvious that the mechanical performance of continuous-fiber- or fabric-reinforced
polymers is superior 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 moldings.
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. The l/d ratio of short fiberreinforced 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 to 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 microstructure 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 aspects have to be considered when the fracture and failure performance of
discontinuous fiber-reinforced thermoplastics are discussed [10].
The mechanical performance of discontinuous fiber-reinforced thermoplastics is affected by
the followings (cf. Figure 1):
1. Composition and morphology
2. Type and amount of the reinforcement
3. Interface (or interphase) between matrix and reinforcement
4. Processing methods and conditions
5. Testing 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 processing 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 fracture with monotonic increasing load and static and
dynamic (cyclic) fatigue measurements. The test results are interpreted based on fracture
mechanical concepts.
FIGURE 1 Factors influencing the fracture mechanical performance of discontinuous fiberreinforced thermoplastic composites
2
Development of Microstructure
Changes in the molecular orientation and crystallization behavior in neat and matrix polymers
of S(L)FRTPs occur during processing. This is accompanied with fiber structuring (i.e.
orientation 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
can adequately be described by the model of Tadmor [11], which involves the fountain or
volcano effect discussed 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) layers,
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 plane 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
fountain effect described by Rose [12]. An additional argument for the transverse fiber
orientation in the C layer was found in the squeeze flow of the melt 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
way yields a "five-ply" laminate structure. The fiber layering 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, again 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 GF reinforced polypropylene (PP); (b) schematically. This picture illustrates position and
designation 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.
3
Results 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 (Vf).
2. The absolute values of the fiber orientation are closely matched in the S and C
layers, and fiber orientation increases with Vf.
3. The processing effects (melt, mold temperature, and injection speed) are of
secondary importance compared with Vf.
These findings are for parts of normal thickness (3-4 mm) molded by 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 (Vf) on the layering,
planar orientation (fp) and mean fiber length of injection molded discontinuous fiberreinforced composites
Microstructural investigations carried out on long glass fiber (LGF) reinforced injectionmolded 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 pelletizing process 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
molding. Fiber bending, on the other hand, is an appearance of decreased structural stiffness
due to the higher length. Both of these effects reduce the effective aspect ratio, of the
reinforcing fibers in the molded part [16,18].
The aspect ratio of the fibers in the molded item depends on material factors (especially Vf),
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/wall 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 manufacturing. The aspect ratio distribution curve of the reinforcement may
differ when various layers across the thickness of the molded part are considered [16]. This is
mainly due to fiber enrichment in the C layer, differences between bunching and
filamentization 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.
4
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 distribution
"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 length of the reinforcement. Avoiding 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.
Processing 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 root 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 considered (short runners,
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 head that pressurizes the 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 optimized 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, warpage-free extrudates. For the flow simulations different software
packages are available.
Microstructural Characterization
5
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, microwave, X-ray diffraction, sonic,
and thermographic measurements can also be used. In Figure 2a SEM micrographs taken
from polished sections along the thickness-MFD (z-x) and y-x planes are shown.
The evaluation of fiber alignment and mean fiber orientation in a given plane is very timeconsuming, 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 inplane but also spatial orientations [21]. Fiber orientation can be described either by using
mean orientation factors, such as Hermans [22], Krenchel [23], and modified Hermans [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 fibers 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 considered 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], and generalized in the form:
(l / d ) n,i
l
R   Trel ,i f p , eff ,iV f ,i ( )equ,i
d
(l / d ) m,i
i
(1)
where Trel,i is the relative thickness of the ith layer normalized to the sample thickness (B, see
Figure 31.4), fpeff,i is the effective orientation in the ith layer calculated using the function of
planar orientation (fp) vs. fp,eff introduced by Friedrich [26], Vf,i is the fiber volume fraction in
the ith layer, (l/d)equ,i is the equivalent aspect ratio in the ith layer, (l/d)m,i and (l/d)n,i are the
mean mass- and number average aspect ratios in the ith layer, respectively [16].
It seems that the fracture mechanical response of discontinuous fiber-reinforced plastics can
be appropriately related to this reinforcing effectiveness parameter [14].
Fracture Mechanics
Detailed treatment of fracture mechanics is far beyond the scope of this article; it can be
found 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
6
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 toughness:
( K c ) K I  Y    a1 / 2
(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 when KI > KIc, where KIc, is a critical value of
the stress intensity factor. This material parameter is also termed fracture toughness. From Eq.
(2) it is obvious that KI is a stress-related fracture mechanical criterion. KI, can be determined
from monotonic 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 GI is less than or greater than GIc. Kc and Gc 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, GIc is generally determined from high speed impact
tests - using Charpy and Izod 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 pursued for plastics: J-integral,
crack opening displacement (COD), and essential work of fracture (EWF) [6,28]. These
material parameters are included in plastic, elastoplastic, or postyield fracture mechanics
(PYFM). JIc is an energy-related term connected with the onset of stable crack growth. For
7
linear elastic bodies GIc = JIc. JIc can be determined for example by ASTM E813 and ISO/CD
28660. In addition, JIc can be deduced from high speed impact tests carried out on sharply
notched Izod or Charpy specimens [28].
The fracture mechanical approach can also be applied 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 KIc. 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 fiberreinforced thermoplastics are summarized in Ref. 14. If these criteria are not met, critical
values of KI, are denoted Kc, instead of KIc; the same designation is used also for Gc, and Jc.
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 strain rate or frequency
range; however, the threshold value is rather arbitrary. Measurements 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 composite [14]. The run of Kc, as a function of
Vf can hardly be predicted, because of competitive micromechanisms that either increase or
decrease Kc. Nevertheless, discontinuous fiber reinforcement is always the right tool to
increase the fracture toughness 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 Kc. Strong bonding may hinder the deformability of the composite so that Kc
tends to decrease [29]. This is in accordance with the Hahn-Rosenfield equation [30]. This
equation explicitly shows that Kc does not depend solely on strength but also depends on
ductility parameters:
1/ 2
(3)
Kc  E   B   B  L
where
8
E = E modulus
σb, εb = 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 stiffness and strength. Thus matrix toughening may also be connected with
deterioration in Kc.
The course of Jc as a function of Vf depends on the corresponding Kc - Vf and E - Vf
functions:
K2
J c  Gc   C
(4)
E
provided the plane stress condition satisfies the LEFM theory. If the Kc 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 Kc from fiber loading is more probable the higher the E modulus
and the lower the ductility of the unfilled matrix (brittle, low molecular weight,
degraded polymers, especially polycondenzates).
2. For ductile materials a relative increase in both Kc and Jc can be achieved by using
fibers of higher aspect ratio (e.g. LGF instead of SGF).
3. The effects of matrix toughness and fiber-matrix bonding are hardly predictable.
For relative improvements in Kc and Jc, 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 Figures 2 and 3. On the fracture surface of the specimens,
fibers lying parallel or longitudinal to the crack plane (L fibers) can clearly 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 found on the surface,
whereas 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
considerably higher than that of the L fibers, which have practically no reinforcing effect.
9
Therefore, the fracture 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 stress 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 (fp,eff) and planar fiber orientations (fp)
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 anisotropy 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 ratio.
Fiber aspect ratio. The influence of filler shape on fracture toughness at a given filler loading
strongly depends on the matrix characteristics [29]. However, with increasing fiber aspect
ratio Kc 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 or 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 concentration at the fiber ends
should be compensated 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 clack
path length, which promotes fiber pullout 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 fiberreinforced versions [16,29]. A steeper decrease in the related plot can always be found in the
vicinity of the glass transition temperature (Tg) of the matrix. Here the enhanced molecular
mobility of the matrix induces a change in deformation mode from ductile to viscous. So, Tg
is always the upper threshold for the applicability of the LEFM theory. Kc values calculated
10
according to Eq. (1) for temperatures above Tg 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 Kc with T is basically different from that
at v = 1 mm/min. Kc values start at a relatively low level in the subambient temperature range
before they increase at the Tg [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 BEHAVIOR. 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
matrix-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 absorption 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 MICROSTRUCTURE. Fiber loading. The plot of dynamic fracture toughness
as a function of Vf can be as complex as that for the static case. Generally the dynamic
fracture energy (Gd) decreases with increasing fiber loading. This effect may or may not be
compensated for by the increasing E modulus with respect to the resulting Kd. Since this
effect of the E modulus is very closely matched to the static one, the plot of Kd as a function
of Vf depends mostly on the Gd - Vf function of Eq. (4). The effect of Vf on Kd is
demonstrated in Figure 7 for SGF- and LGF-reinforced composites. It can be concluded that
11
increasing the aspect ratio of the reinforcement yields an improvement in Kd. The Gd - Vf
function, on the other hand, should depend on the matrix toughness and fiber-matrix bond
quality.
FIGURE 7: Change in the static (Kc) and dynamic (Kd) fracture toughness as a function
of fiber loading (Vf) at ambient temperature for SGF- and LGF-reinforced injection-molded
PP (Kc determined on CT specimens at v = 1 mm/min, whereas Kd deduced from lzod
measurements)
At this point attention has to be paid to the internal flaws induced 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 Gd, 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 cases 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 Kc and Kd for SGFand LGF-filled composites (see Fig. 7). This suggests some differences in the load transfer
during static and dynamic measurements that should be clarified.
EFFECTS OF TESTING CONDITIONS. Gd and Kd 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 Kd and Gd
as a function of T can be calculated from Eq. (4) provided that the E(T) and Gd(T) or Kd(T)
functions are known at the given frequency. Kd generally increases with decreasing T as a
result of the increase in E modulus, whereas Gd 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 following findings are expected:
1. The frequency embrittlement of the matrix promotes brittle matrix cracking, the
onset of which depends on the frequency-dependent Tg. Among the matrix-related
failure mechanisms, crazing is more common than shear yielding.
12
2. Among the 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 K0 < KIc, where K0 denotes
the initial stress intensity factor. The result of this kind of measurement is either the stress
corrosion threshold (KI,SCC) or the crack growth rate (da/dt vs. KI), or both. KI,SCC means a
threshold KI, 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 (ΔK). A threshold value ΔKth, 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: The fatigue behavior of injection-molded composites.
Static Fatigue
EFFECT OF MICROSTRUCTURE. When Kc, from static fracture, increases with Vf, one can
expect a similar trend in the resistance to SCC for the given composite. Incorporation of a
rubbery impact 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. On the other
hand, when Kc decreases with Vf, an acceleration in SCC growth can be predicted in relation
to the corresponding matrix. The da/dt-KI curves, or at least their segments in double
logarithmic representation, can be approximated by straight lines. This indicates the validity
of the Paris-Erdogan relationship (often called the Paris power law [3,4,39]):
da
   K Im
dt
(5)
The crack growth kinetics depend on both the microstructure and the environment [29,40,41].
Note that the final breakdown of the specimens (usually CT type) does not necessarily occur
at the Kc derived from static loading measurement.
In SCC tests, KI at the specimen breakdown may be higher than Kc when a material with
rather ductile behavior is investigated. This is a consequence of the very low frequency of this
13
kind of measurement, which generates a process or damage zone that is fundamentally
different from that found in static fracture. Alterations can be observed in both the size of the
zone and the 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 Kmax value. This value can be determined by Eq. (1) using the maximum load.
Such response can be observed for composites either in air or in surrounding media that
plastify their matrix. Final failure of the specimen may also occur at KI < Kc as a result of
aggressive attack by a given environment. If the initial stress intensity factor K0 is very small
but higher than KI,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
K0. 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-evolved
damage zone can be observed. 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 Kc which is either independent or dependent of K0. The latter case
suggests that failure depends additionally on K0, that is, on the corrosion loading history of
the specimen. This corrosion 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. This observation means that Eq. (5) no longer
holds, since da/dt depends in addition on K0; therefore, talking about a material parameter
according to the fracture mechanical concept is very questionable.
EFFECT OF ENVIRONMENT. Both the da/dt-KI, and the K0-time (t) curves depend strongly
on the environment. 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 fiber degradation, which
mostly occurs in acidic environments [43,44]. A zig-zag fracture surface path, reflecting the
fiber alignment, 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 environment
and the K0 of the test.
14
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 Kc-Vf function. Increasing fracture
toughness thus correlates with improved FCP resistance (Fig. 9), while decreasing Kc with Vf
yields FCP acceleration [14,29]. Figure 9 again shows the validity of the Paris power law (Eq.
6) for the stable FCP range:
da
 A(K ) m
dN
(6)
FIGURE 9: Changes in FCP behavior due to microstructural parameters, schematically
The exponential term m of Eq. (6) generally increases with Vf (Figure 10). This change is
accompanied by a shift of ΔKth, toward higher ΔK values; that is, fiber incorporation
enhances the threshold limit below which no crack growth takes place. The same trend in
ΔKth can be observed when results achieved on L- and T-cracked specimens are compared.
This is due to a change 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 Kc or Kmax, just as it
does in static fatigue. This upper limit and the stable FCP range itself are strongly affected by
the viscoelasticity 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 resistance 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 Vf 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 anisotropy.
15
Fiber aspect ratio. When the FCP curves of SGF- and LGF-reinforced PPs are compared a
clear improvement in FCP resistance can be seen as a result of the use of fibers of higher
aspect ratio (Figure 9). The relative improvement diminishes with increasing Vf. FCP
enhancement of LGF reinforced systems was attributed to the evolution of a more extended
damage zone and longer debonding and pullout routes [46].
The effects of the above microstructural parameters on the FCP behavior are summarized
schematically in Figure 9. For the microstructural interpretation of the 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 increasing M the crack rate, at a given
ΔK 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 (ΔK=1.5 MPam1/2)
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;
therefore, 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. The fatigue crack
path in Figure 12 demonstrates this. In this picture, stress concentration at the fiber ends is
clearly perceptible. In the damage zone, in addition, a stress concentration field was
developed and preserved by matrix deformation. The matrix underwent crazing and shear
yielding, initiated by fiber debonding and pullout processes.
FIGURE 12: Fatigue crack 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 crack is sharper
during fatigue [33].
16
Further differences between the failure modes are connected with crack tip heating and
accompanying changes in both matrix- and fiber-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 breakage. 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 just before stable acceleration crack growth occurs (see Fig. 13a). This is connected
with an evolution and stabilization of 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 compared to the
cyclic one (see Fig. 13b). 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 reciprocal
value of the time causing the specimen fracture is meant.
FIGURE 13: Stable 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 micromechanisms 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 with a mixed
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 above 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 parameters
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 characterization 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
17
brittle fracture, stress-related terms (Kc) are used, whereas for those of high ductility, energyrelated fracture mechanical terms (Gc , Jc, 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 occurs 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 above that for
SGF and LGF reinforced injection-molded composites, crack propagation is of basic
importance. In this case, therefore, threshold values (KI,SSC, ΔKth) 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.
Summary
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 composites. 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 matrix-and fiber-related events. In addition, the changes related
to different loading situations were demonstrated and discussed. Attempts were made to
determine general trends in microstructural development, fracture mechanical response, and
connected failure behavior, and to summarize 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 alternating (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. Kinloch and R. J. Young, Fracture Behavior of Polymers, Applied Science Publ.,
Barking, United Kingdom, 1983.
18
5. J. G. Williams, Fracture Mechanics of Polymers, Ellis Horwood/J. Wiley, Chichester,
1984.
6. A. G. Atkins and Y.-W. Mai, Elastic and Plastic Fracture: Metals, Polymers,
Ceramics, Composites, Biological Materials, Ellis Horwood/J. Wiley, Chichester;
1985.
7. N. G. McCrum, C. P. Buckley, and C. U. Bucknall, Principles of Polymer
Engineering, Oxford University Press, Oxford, 1988.
8. K. Friedrich, Ed., Application of Fracture Mechanics to Composite Materials,
Elsevier, Amsterdam, 1989.
9. L. A. Carlsson, Ed., Thermoplastic Composite Materials, Elsevier, Amsterdam, 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).
12. W. Rose, Nature, 191, 242 (1961).
13. M. J. Folkes, Short Fibre Reinforced Thermoplastics, Research Studies Press,
Chichester, 1982.
14. J. Karger-Kocsis, “Microstructure and fracture mechanical performance of short fibre
reinforced thermoplastics” in Ref. 8, p. 189.
15. R. P. Hegler, G. Mennig, and C. Schmauch, Adv. Polvm. Technol., 7, 3 (1987).
16. J. Karger-Kocsis and K. Friedrich, Compos. Sci. Technol., 32, 293 (1988).
17. D. E. Spahr, K. Friedrich, J. M. Schultz, and R. S. Bailey, J. Mater. Sci., 25, 4427
(1990).
18. J. Karger-Kocsis, “Microstructural aspects of fracture in polypropylene and in its
filled, chopped fiber and fiber mat reinforced composites” in J. Karger-Kocsis, Ed.,
Polypropylene - Structure, Blends and Composites, Chapter 4, Vol.3, Chapman and
Hall, London, 1995, p. 142.
19. D. W. Clegg and A. A. Collyer, Eds., Mechanical Properties of Reinforced
Themoplastics, Elsevier Applied Science. London, 1986, especially Chapters 5 (J. L.
White), 6 (L. A. Goettler), and 9 (R. H. Burton and M. J. Folkes).
20. G. Kalay and M. J. Bevis, “Application of shear-controlled orientation in injection
molding of isotactic polypropylene” in J. Karger-Kocsis, Ed., Polypropylene: An A-Z
Reference, Kluwer Academic, Dordrecht, 1999, p. 38.
21. G. Fischer and P. Eyerer, Polym. Compos., 9, 297 (1988).
22. P. H. Hermans, Contribution to the Physics of Cellulose Fibers, Elsevier, New York,
1946.
23. H. Krenchel, Fibre Reinforcement, Akademisk Forlag, Copenhagen, 1964.
24. R. B. Pipes, R. L. McCullough, and D. G. Taggart, Polym. Compos., 3, 34 (1982).
25. S. G. Advani and C. L. Tucker, J. Rheol., 31, 751 (1987).
26. K. Friedrich, Compos. Sci. Technol., 22, 43 (1985).
27. E. Plati and J. G. Wiliams, Polym. Eng. Sci, 15, 470 (1975).
28. W. Grellmann and S. Seidler (Eds.), Polymer Testing, Hanser, Munich, 2007
29. K. Friedrich and J. Karger-Kocsis, "Fracture and fatigue of unfilled and reinforced
polyamides and polyesters," in J. M. Schultz and S. Fakirov, Eds., Solid State
Behavior of Linear Polyesters and Polyamides, Prentice-Hall, Englewood Cliffs, NJ,
1989, p. 249.
30. G. T. Hahn and A. R. Rosenfield, Sources of Fracture Toughness: The Relation
between KIc and the Ordinary Tensile Properties of Metals, ASTM STP 432,
American Society for Testing and Materials, Philadelphia, 1968, p. 5.
31. D. Hull, An Introduction to Composite Materials, Cambridge University Press,
Cambridge, 1981.
19
32. N. Sato, T. Kurauchi, S. Sato, and D. Kamigaito, J. Compos. Mater, 22, 850 (1988).
33. K. Friedrich, L. A. Carlsson, J. W. Gillespie, and J. Karger-Kocsis, “Fracture of
thermoplastic composites” in Ref. 9, p. 233.
34. J. Karger-Kocsis and K. Friedrich, Plast. Rubb. Process. Appl., 7, 91 (1987).
35. K. Friedrich and J. Karger-Kocsis, "Fractography and failure mechanisms of unfilled
and short fiber reinforced semicrystalline thermoplastics," in A. C. Roulin-Moloney,
Ed., Fractography and Failure Mechanisms of Polymers and Composites, Elsevier
Applied Science, London, 1989, p. 437.
36. J. Karger-Kocsis and K. Friedrich, J. Mater. Sci., 22, 947 (1987).
37. J. Karger-Kocsis, J. Appl. Polym. Sci., 45, 1595 (1992).
38. J. Karger-Kocsis and V. N. Kuleznev, Polymer, 23, 699 (1982).
39. P. C. Paris and F. Erdogan, J. Basic Eng., 85, 528 (1963).
40. K. Friedrich, J. Mater. Sci., 26, 3292 (1981).
41. H. Voss, A. Dolgopolsky, and K. Friedrich, Plast. Rubb. Process. Appl., 8, 79 (1987).
42. A. Chudnovsky, "Crack Layer Theory," NASA Contractor Report 174634, Case
Western Reserve University, Cleveland, 1984.
43. C. Lhymn and J. M. Schultz, Polym. Eng. Sci., 24, 1064 (1984).
44. J. N. Price, "Stress corrosion cracking in glass reinforced composites," in A. C.
Roulin-Moloney, Ed., Fractography and Failure Mechanisms of Polymers and
Composites, Elsevier Applied Science, London, 1989, p. 495.
45. R. W. Lang and J. A. Manson, J. Mater. Sci., 22, 3576 (1987).
46. J. Karger-Kocsis and K. Friedrich, Composites, 19, 105 (1988).
47. R. W. Lang, J. A. Manson, and R. W. Hertzberg, “Fatigue crack propagation in shortglass-fiber-reinforced Nylon 6.6: Effect of frequency” in J. C. Seferis and L. Nicolais,
Eds., The Role of the Polymeric Matrix in the Processing and Structural Properties of
Composite Materials, Plenum, New York, 1983, p. 377.
48. J. Karger-Kocsis, K. Friedrich, and R. S. Bailey, Adv. Composite Mater., 1, 103
(1991).
49. J. Karger-Kocsis, R. Walter, and K. Friedrich, J. Polym. Eng. 8, 221 (1988).
50. R. W. Lang, J. A. Manson, and R. W. Hertzberg, J. Mater. Sci., 22, 4015 (1987).
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