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Abstract

The present study is concerned with an experimental study into the effect of superimposed creep deformation, varying local fiber orientation distributions, and more complex multiaxial stress states on the fatigue of short fiber reinforced thermoplastics. The cross-interaction of these effects is a relevant feature in all fields of applications of short fiber composites since molding related variations of the local fiber orientation states cannot be avoided for injection molded structures. Long term loading will result in a combined occurrence of fatigue and creep and thus an interaction of the related effects. The study is based on a short glass fiber reinforced polyamide 66 as reference material which is a common material grade in many automotive applications. A basic characterization is performed by means of tensile and DMA experiments. Subsequently, creep and creep fatigue experiments are performed at ambient and elevated temperatures. In order to include the effects of locally varying fiber orientation situations and locally multiaxial loading situations, the coupon experiments are complemented by experiments on breadboard specimens featuring notches, holes, and structural component related external geometries. Superimposed creep deformation might accelerate fatigue failure, however, for notched specimens might also result in an increased fatigue lifetime due to creep-induced stress relief at the notch roots. The results reveal that care has to be taken when transferring the results on idealized coupon specimens to generalized, realistic problems. The results also serve as a development and validation data base for a continuum damage mechanics material model presented in an oncoming contribution.

Keywords

Short fiber composites creep fatigue experimental characterization multiaxial loads

Introduction

Short fiber reinforced plastics with disordered microstructure are popular materials in many fields of modern lightweight construction. Advantageous features are a reasonable stiffness and strength obtained at a rather low specific weight. Furthermore, these materials can easily be processed by injection molding as a standard and well-established manufacturing process for polymeric materials. The injection molding process also enables the easy manufacturing of highly integrated components with complex shapes. These advantages motivate the use of short fiber reinforced composites as materials for many semi-structural parts in the transport sector and other technological fields.

For short fiber reinforced composites, the use of thermoplastic matrix systems is advantageous due to their superior mechanical and manufacturing properties, their capabilities for inherent structural damping and the enhanced possibilities for material recycling at the end-of-life for the respective components. Nevertheless, a disadvantage is their tendency towards creep deformation due to the limited cross-linking of their molecular microstructure.

In engineering applications, the durability and fatigue lifetime of short fiber reinforced polymers are usually assessed in terms of classical Wöhler-Miner type $S$ - $N$ -curve approaches. A number of different options for the mathematical formulation of the S-N-curve are discussed, e.g., by Haibach¹ and Vassilopoulos et al.² These approaches define the number of cycles to failure as a function of a – usually uniaxial – effective stress amplitude. Consequently, a considerable body of the pre-existing literature on fatigue of short fiber composites is related to the normalization of experimental data and the definition of effective load measures using a variety of criteria (Mortazavian and Fatemi³). A stress-based approach in this sense, considering temperature and fiber orientation effects has, e.g., been proposed by Guster et al.⁴ Vervoort⁵ proposes a critical action plane approach using a Goodman-type mean stress correction. Different fiber orientation states are included by an interpolation. Modified Wöhler-Miner type approaches have been presented by Hartmann et al,⁶ Hinkelmann et al.⁷ as well as Zago and Springer.⁸ For assessment of notched situations, Moosbrugger et al.⁹ have presented a nonlocal approach based on the most stressed material volume whereas Sonsino and Moosbrugger¹⁰ use a stress gradient-based approach. Gaier et al.¹¹ propose a critical plane approach in conjunction with a linear damage accumulation assumption.

As an alternative approach to the mentioned uniaxial approaches, a number of multiaxial stress-based approaches have been proposed. Bernasconi et al,¹² De Monte et al.¹³ as well as Mortazavian and Fatemi¹⁴ presented $S$ - $N$ -curve normalization approaches based on the Tsai-Hill^15,16 failure theory. Jen and Lee¹⁷ presented an approach in this sense directed especially to thermoplastic matrix systems. Strain energy density-based approaches are essentially three-dimensional approaches avoiding some of the problems of stress-based approaches. Schaaf et al.¹⁸ use a strain energy density-based concept in conjunction with a hybrid reference volume to define a normalized $S$ - $N$ -curve. A similar normalization approach has been presented by Klimkeit et al.¹⁹ Launay et al.²⁰ employ a strain energy density approach to assess the effect of multiaxial loading.

The micromechanics of fatigue degradation and failure of fiber reinforced composites have been extensively studied^21,22 and compiled,²³ by Talreja for unidirectionally fiber reinforced polymers. For short fiber composites, it has been shown that the main degradation and damage mechanism consists of debonding of the fiber and matrix interfaces for the fibers oriented perpendicular to the principal loading direction. The evolving micro defects then trigger the cracking of the matrix. This finding has been confirmed by Corbetta et al.²⁴ and especially in tomographic analyses by Arif et al,²⁵ identifying debonding and pore formation at the fiber ends as the leading damage mechanism for short fiber reinforced polymers.

All of the cited studies are directed to fatigue degradation and failure only whereas superimposed creep effects are neglected. Creep effects become relevant especially for short fiber reinforced polymers with thermoplastic matrix systems due to the limited cross-linking of their macromolecular microstructure. The effect has been reported e.g., by Perreux and Joseph,²⁶ in a study on the fatigue of tubular specimens under biaxial loads. It is relevant, especially in tension-tension fatigue with positive $R$ -ratios and thus tensile mean stresses.

The present study addresses the interaction of creep and fatigue in an experimental approach. The interaction is studied on coupon level using unnotched and notched specimens as well as on breadboard specimens with more complex geometry and loading conditions. It is found that the interaction of creep and fatigue might accelerate the damage accumulation. However, contradictory effects might occur at notches and other stress and strain concentrations where creep might cause a stress and strain relief.

Material and methods

Material and test specimens

The reference material investigated in the present contribution was a short glass fiber reinforced polyamide 66 material with a fiber content of $35 wt . %$ (PA66GF35). The identical material from the same material supplier, however, from another batch has already been investigated in previous contributions by de Monte et al,¹³ Sonsino and Moosbrugger¹⁰ and others, making the results directly comparable.

From the raw material, plane plates with dimensions of $120 mm \times 80 mm$ and a plate thickness of $2 mm$ according to Figure 1(a) were manufactured using injection molding. The plane plates were injected across their full width of 80 mm using a fishtail distributor with integrated baffle. During the molding process, a specially designed gate section has been used to reduce the development of a layered fiber orientation structure to a minimum.

Figure 1.

Coupon specimens. (a) Injection molded plate, (b) Test specimens.

From the injection molded plates, plane test specimens according to Figure 1(b) were manufactured using waterjet cutting. Three different specimen geometries with and without notches were used. Both mild and sharp notches with notch root radii of $r = 2.5 mm$ and $r = 0.2 mm$ , respectively, were used. For isotropic homogeneous materials, the employed notch root radii would result in notch factors of $K_{t} = 2.3$ and $6.8$ , respectively. Furthermore, straight plane bars with dimensions of $60 mm \times 10 mm \times 2 mm$ were cut for a dynamical-mechanical analysis.

To secure comparable conditions and to prevent humidity effects due to the waterjet cutting process, the specimens were dried at $T = 30 ° C, \dots, 35 ° C$ and 3% to 10% relative humidity prior to testing. The drying process was controlled by periodic weight checks until constant weights were achieved. The drying process lasted for about 1 month. Exemplary humidity tests revealed final moisture contents in the range between $0.21 %$ and $0.25 %$ .

To investigate the effect of stress concentrations and general multiaxial loading conditions, three different types of breadboard specimens were considered. The first specimen type is the “T”-specimen according to Figure 2(a). The specimens were molded in either the longitudinal ( $x_{1}$ -) or the transverse ( $x_{2}$ -) directions to study fiber orientation effects caused by the molding process. The specimens were supplied with three different notch root radii of $r = 0.2 mm$ , $0.5 mm$ , and $1.0 mm$ , respectively.

Figure 2.

Breadboard specimens. (a) “T” specimen, (b) “Submarine” specimen, (c) “MultiTester” specimen.

As specimens with even more complex geometry, “Submarine” and “MultiTester” specimens according to Figure 2(b) and (c) respectively were investigated. The specimens were injection molded from the right hand and top ends, respectively as sketched in Figure 2. The breadboard specimens were conditioned in a similar manner as the coupon specimens.

Test procedures

Microstructural investigation

Prior to mechanical testing the microstructure of the material has been investigated using both, metallographic sectioning in conjunction with optical microscopy and X-ray computed tomography. In-plane metallographic sections were taken from the center of three plates according to Figure 1(a) not used for specimen manufacture. Both near-surface locations and locations from the plate midplane were investigated. For an investigation of the fiber orientation distribution through the plate thickness, sections oriented in the $x_{1}$ - $x_{3}$ -plane were taken from a location at the lower left end of the plates according to Figure 1(a) close to the gate section. The sections were ground, polished, and investigated using optical microscopy.

In addition, cuboidal specimens with $2 mm$ edge length were taken from six positions on one of the plates not used for specimen manufacture. The specimen positions were chosen such that they match with the center and end positions of the gauge sections of the tensile specimens cut in $0 °$ - $30 °$ -, and $90 °$ directions as well as two positions of the specimen heads. The microstructure of the cuboidal specimens was investigated by X-ray computed tomography and an in-house digital image correlation procedure for identification of the individual fibers. The results of both, metallographic sectioning and the X-ray computed tomography investigation were evaluated in terms of the second order fiber orientation tensor.

Basic mechanical characterization

A basic characterization of the mechanical response has been performed by tensile experiments on specimens oriented at angles of $0 °$ and $90 °$ to the flow ( $x_{1}$ -) direction. The specimens were tested under quasi-static loading conditions using a servo hydraulic testing machine. The experiments were performed on unnotched specimens according to Figure 1(b). All experiments were performed at ambient temperature under strain control at a strain rate of $10^{- 3} / \min$ until failure. During the experiments, the crosshead displacement, relative displacement of the strain gauge, and resultant force were continuously recorded. The results were evaluated in terms of engineering stress-strain curves for the two test directions.

For a preliminary characterization of the viscoelastic and damping properties, a dynamic mechanical analysis (DMA) was performed under three-point bending using a Netzsch DAM 242 E/1/G testing machine. The tests were performed at excitation frequencies of $0.1 Hz$ , $1 Hz$ , and $10 Hz$ . Temperature sweeps were made at a heating rate of $2 K / \min$ over the interval from $- 50 ° C$ to $+ 150 ° C$ , thus covering the entire relevant temperature range for ground transport applications. Experiments were made for specimens cut in $0 °$ , $30 °$ , and $90 °$ to the flow direction, testing four specimens each. The results were evaluated with respect to the storage and loss moduli $E^{'}$ and $E^{″}$ as a function of temperature and excitation frequency.

Creep

For evaluation of the creep response of the reference material, creep experiments were performed at constant temperature and constant applied stresses using a standard deadweight test rig in a climatic chamber to control temperature and humidity. The load levels were chosen related to the tensile strength of the material within the respective test direction. However, integer numbers were used rather than direct fractions of the ultimate tensile stresses, choosing identical creep loads for the different loading directions where feasible in order to provide comparable results.

During the experiments, the elongation of an initial gauge length of

l_{0} = 10 mm

was continuously recorded in

50 s

intervals using clip-on extensometers. The experiments were performed for a duration of

200 h

at constant test temperatures of

T = 23 ° C

80 ° C

, and

130 ° C,

respectively. These test temperatures represent temperatures well below, close to and well beyond the glass transition temperature

T_{G}

of the material (see Section 3.2). The tests were performed on unnotched specimens in

0 °

30 °

-, and

90 °

-orientation (see Figure 1). Furthermore, creep experiments were performed for selected cases on notched specimens. Due to the different creep rates at the different conditions, the test stresses were defined individually rather than using unified stress levels for all conditions. To keep the overall effort within acceptable bounds, not all possible conditions were combined with each other. The test matrix is presented in Table 1.

Table 1.

Test matrix for creep characterization.

Geometry (Figure 1)	$T$	$φ$	$σ$	No. of tests
(-)	(°C)	(°)	(MPa)	(-)
Unnotched	23	0	70, 80, 90	3, 4, 2
		30	80, 90	3, 3
		90	60, 70, 80, 90	3, 3, 4, 3
	80	0	50, 60	3, 3
		90	40, 45, 50	3, 4, 3
	130	0	60	4
		90	90	4
Mild notch	80	30	40, 55, 60, 65	1, 3, 1,1
Sharp notch	80	0	40, 60, 65, 70	1, 1, 2, 2

Fatigue and creep-fatigue

The fatigue response has been determined in force-controlled experiments under harmonic sinusoidal cyclic loads in the tensile and alternating ranges with load ratios of

R = σ_{\min} / σ_{\max} = 0

and

- 1

, respectively. The test matrix is provided in Table 2. The experiments were performed using a servohydraulic testing machine equipped with a temperature chamber (Figure 3). During the experiments, the applied force and the resulting strain were recorded continuously using the internal load cell and a tactile extensometer, respectively. Under alternating loads, a low friction buckling support was used. The test frequency was set to

4 Hz

for all experiments, limiting the self-heating of the specimen by internal friction even at high load levels to less than

3 K

. The load level for each specimen was chosen individually based on the experiment progress, aiming on the failure cycle interval

N_{f} \in [10^{3}, 10^{6}]

. The results were evaluated in terms of

S

N

curves for complete specimen failure as well as for crack initiation. To detect crack initiation, a photographic documentation of the specimen state was used. The frequency of taking photographs was chosen depending on the expected fatigue life of the respective specimen in order to obtain a sufficiently detailed documentation of the crack initiation and propagation. E.g., in the low-cycle fatigue regime, photographs were taken at intervals of 100 load cycles whereas in the high-cycle fatigue regime an interval of 5000 load cycles was used..

Table 2.

Test matrix and fatigue properties for fatigue characterization coupon specimens.

Geometry (Figure 1)	$T$	$φ$	$R$	Type of test	Failure type	$k$	$σ_{a, 10^{6}}$	$T_{σ}$
(-)	(°C)	(°)	(-)	(-)	Failure type	(-)	(MPa)	(-)
Mild notch	23	0	−1	Fatigue	Rupture	8.7	37.9	1:1.05
					Crack	9.2	37.5	1:1.06
				Creep-fatigue	Rupture	7.2	32.1	1:1.09
					Crack	7.1	31.4	1:1.07
Mild notch	130	30	−1	Creep-fatigue	Rupture	11.3	18.0	1:1.18
					Crack	-	-	-
Sharp notch	23	90	−1	Fatigue	Rupture	18.3	21.0	1:1.04
					Crack	18.5	19.4	1:1.03
				Creep-fatigue	Rupture	8.8	19.4	1:1.20
					Crack	9.4	16.8	1:1.24
Sharp notch	130	0	0	Fatigue	Rupture	8.8	11.5	1:1.08
					Crack	6.9	9.4	1:1.10
				Creep-fatigue	Rupture	9.3	19.4	1:1.20
					Crack	9.4	16.8	1:1.24
Sharp notch	23	30	0	Fatigue	Rupture	10.4	16.9	1:1.02
					Crack	9.1	15.8	1:1.03
				Creep-fatigue	Rupture	13.0	18.4	1:1.06
					Crack	9.4	16.8	1:1.21
Mild notch	130	90	0	Creep-fatigue	Rupture	13.9	9.6	1:1.02
					Crack	-	-	-

Figure 3.

Generic test setup for fatigue experiments similar to those of the present study. (a) $R = 0$ , (b) $R = - 1$ with anti-buckling device.

In order to investigate the interaction between creep and fatigue damage, interrupted fatigue experiments were performed. In these experiments, harmonic sinusoidal loads were applied in blocks of $20 000$ cycles. Between each of these blocks, the specimens were subjected to a constant tensile load of $σ_{creep} = σ_{UTS} / 2$ , i.e., half of the static failure stress. This static load was applied for all creep-fatigue tests regardless of the respective fatigue load levels, because it was expected to produce a measurable effect of creep during a reasonable length of time while not leading to failure during the first static loading phases. The creep phases lasted for $1 / 3$ of the periods for the fatigue blocks, i.e., for $0.463 h$ whereas the fatigue blocks for $20 000$ cycles at $4 Hz$ lasted for $1.388 h$ each.

The fatigue and creep-fatigue experiments were performed on coupon specimens with mild and sharp notches according to Figure 1. All three test directions, $0 °$ , $30 °$ , and $90 °$ were investigated. The experiments were performed at ambient temperature and $130 ° C$ , respectively. In order to keep the overall effort within acceptable bounds, not all possible parameter combinations were investigated but the experimental range was restricted to the test matrix presented in Table 2.

Fractography

To provide further details of the fracture mechanisms, the fracture surfaces of selected specimens were investigated in a fractographic analysis using scanning electron microscopy. For this purpose, the fracture surfaces were sputtered with a metallic coating of approximately $2 nm$ thickness. The investigation was performed in a Hitachi S-3400N scanning electron microscope at a primary electron beam voltage of $5 kV$ under secondary electron (SE) mode. The investigation comprised a total of seven specimens from the creep experiments and eight coupon specimens from the fatigue tests. In both cases, specimens tested at ambient and elevated temperatures were investigated. Both notched and unnotched specimens as well as specimens tested in different test directions were investigated.

Fatigue under complex loading conditions

In order to assess the effects of more complex loading situations, breadboard specimens according to Figure 2 were tested. Three different types were considered. Different general specimen geometries being used in previous investigations were chosen. As generalization compared to the coupon specimens, geometries with different types of notches, cross-sectional variations, as well as general external geometries and loading conditions were considered.

All specimens were injection molded as indicated in Figure 2. The different geometries resulted in the formation of locally varying fiber distribution states. The “T” specimens according to Figure 2(a) were clamped at their two horizontal ends extending towards the positive and negative

x_{1}

-directions and loaded by alternating bending loads in

x_{1}

-direction applied to the vertical leg pointing towards the

x_{3}

-direction. Four different configurations were tested, considering different notch root radii

r

and different molding directions as indicated in Figure 2(a): longitudinally molded specimens with

r = 0.1 mm

and

0.5 mm

as well as specimens molded in the transverse direction with

r = 0.5 mm

and

1.0 mm

, respectively (Table 3). By these means, the effect of stress and strain concentrations induced by different notch root radii can be studied. To include the effect of variable loads onto the damage accumulation, the first

10^{5}

cycles were applied at ambient temperature. Subsequently, the specimens and the test rig were heated at zero load to

130 ° C

and the specimens were fatigued on to failure at the same load level as for the first

10^{5}

cycles. In both loading phases, the specimens were fatigued under harmonic sinusoidal loads at

2 Hz

Table 3.

Test matrix and fatigue properties for fatigue characterization of “T”-specimen.

Geometry (Figure 2(a))	$T$	$φ$	$R$	Type of test	Failure type	$k$	$F_{a, 10^{5}}$	$T_{F}$
(-)	(°C)	(°)	(-)	(-)	Failure type	(-)	(N)	(-)
r = 0.1 mm	23/130	0	0	Fatigue	Rupture	3.5	35.5	1:1.19
r = 0.5 mm	23/130	0	0	Fatigue	Rupture	4.9	37.8	1:1.08
r = 0.5 mm	23/130	90	0	Fatigue	Rupture	2.4	39.4	1:1.18
r = 1.0 mm	23/130	90	0	Fatigue	Rupture	3.7	45.6	1:1.10

Table 4.

Randomized block loading program.

Block no.	$N$	Relative load level
(-)	(-)	(-)
1	166	0.749
2	11	0.895
3	37 380	0.236
4	645	0.661
5	4	1.000
6	2 495	0.558
7	43	0.827
8	9 656	0.431

The “MultiTester” and “Submarine” specimens are designed to include the effects of cross-sectional variations (especially the “MultiTester”) and internal holes under more general local loading situations (“Submarine”). Both types also include the effect of generalized external shapes, closer to the situation in real injection molded components, thereby also including the effect of locally varying fiber orientation distributions due to the molding process. The specimens were tested at variable internal pressure at a load ratio of

R = p_{\min} / p_{\max} = 0

after sealing the aperture sections with caps. Hydraulic oil has been used as pressurizing medium in order to avoid humidity absorption effects when using water. Air pressure could not be used for reasons of the need for rapid variation of the internal pressure without effects of time-dependent in- and outflow of the pressurization medium. To include the effects of complex loading conditions and random excitations, internal pressure spectra with variable amplitudes were applied. In order to keep the effort within acceptable bounds, the load history was defined by a block spectrum defined as an approximation of a normally distributed (Gaussian) spectrum. The cumulative frequency

H

of the spectrum was expressed as a function of the relative (i.e., relative to the maximum amplitude) load amplitude

x

H = H_{0}^{1 - x^{ν}}

(1)

where

ν = 2

and

H_{0}

is the total number of load cycles in the spectrum. The maximum load level was defined as the maximum of the Gaussian spectrum, i.e., at

x = 1

. The remaining load levels intersect the spectrum’s curve so that the areas enclosed between it and the respective level are of equal size on both sides of the intersection. The sequence of the blocks within the spectrum was randomized. During the fatigue-tests, this same sequence was then repeated until the failure of the respective specimen. The load levels relative to a nominal load level together with the respective cycle numbers are listed in Table 4. Not unusually, preliminary tests showed that blocks with high load levels and low cycle numbers triggered significantly more damage than those with low load levels and high cycle numbers. In the present case, this effect led to specimens either failing during the first run of the block-spectrum or not failing at all. To generate valid results, however, the spectrum should be applied several times before failure. Therefore, the three highest load levels were excluded from the block-spectrum.

Table 5.

Test matrix and fatigue properties for fatigue characterization of “MultiTester” and “Submarine” specimens.

Geometry (Figure 2(b) and (c))	$T$	$R$	Type of test	Conditioning	Failure type	$k$	$p_{a, 10^{5}}$	$T_{p}$
(-)	(°C)	(-)	(-)	Conditioning	Failure type	(-)	(Bar)	(-)
MultiTester	23	0.05	Fatigue	Moist	Rupture	11.3	8.8	1:1.08
Submarine	23	0.05	Fatigue	dry	Rupture	9.8	35.5	1:1.16
MutiTester	23	0.05	Randomized block loading program	Moist	Rupture	27.2	10.9	1:1.51
MultiTester	23	0.05	Randomized block loading program	dry	Rupture	89.0	14.0	1:1.06

Further to the effect of complex loading conditions, the effect of humidity was examined in the experiments on the “MultiTester” specimens. For this purpose, a series of these specimens were conditioned in a wet environment in contrast to all other specimens being conditioned as described before. The different test conditions are compiled in Table 5.

In addition to the experimental investigations of the present study, the coupon and breadboard experiments also serve as development and validation data base for a damage mechanics material model accounting for short fiber composites presented in a companion paper (Abdul Hamid et al,²⁷ Spancken et al.²⁸).

Results

Microstructure

Selected results of the metallographic section investigation are presented in Figure 4, considering the in-plane fiber orientation distribution near the plate surface (Figure 4(a)) and in the specimen midplane (Figure 4(b)) as well as the transverse fiber orientation distribution (Figure 4(c)). No distinct differences are observed between the in-plane fiber orientation distribution in the specimen midplane and a plane near the plate surface. Consequently, only a slight formation of a central layer with a fiber orientation perpendicular to the flow direction ( $x_{1}$ -direction) is observed whereas the majority of the fibers are oriented parallel to the flow direction in the boundary layers, covering most of the specimen thickness.

Figure 4.

Microstructural investigation. (a) In-plane section, near-surface position, (b) in-plane section, midplane, (c) transverse section, (d) transverse distribution of $a_{11}$ and $a_{33}$ , (e) transverse distribution of $a_{22}$ .

This result is confirmed by the results of the three-dimensional tomographic investigation. In Figure 4(d) and (e), the distribution of the main diagonal parameters $a_{11}$ , $a_{22}$ , and $a_{33}$ through the plate thickness is evaluated for the six specimen positions investigated. The exact locations of the specimens used for the evaluation within the plate are sketched to scale in the inlay figures. The microstructure features a distinct preference orientation of the fibers towards the flow ( $x_{1}$ -) direction with large $a_{11}$ and low $a_{22}$ . In the plate center a thin central layer with large $a_{22}$ and low $a_{11}$ , indicating a fiber preference orientation perpendicular to the flow direction is observed. Nevertheless, the central layer covers only a small part of the entire plate thickness. Small transverse fiber orientation components $a_{33}$ throughout the entire thickness indicate that the fibers are mostly oriented within the plate’s $x_{1}$ - $x_{2}$ -plane.

The full set of the components

a_{i j}

of the second order fiber orientation tensor obtained from the metallographic sections at the plate center considering both, the midplane and the near-surface location is presented together with a statistical evaluation in Table 6. The results indicate a distinct fiber preference orientation towards the flow direction with only minor contributions towards the transverse (

x_{3}

-) direction, again confirming the previous qualitative and quantitative findings. The scatter in the results between the different plates and section locations is limited, indicated by rather small standard deviations.

Table 6.

Fiber orientation tensor components.

Plate	Position	$a_{11}$	$a_{22}$	$a_{33}$	$a_{23}$	$a_{13}$	$a_{12}$
(-)	(-)	(-)	(-)	(-)	(-)	(-)	(-)
1	Near surface	0.81	0.17	0.02	0.05	0.05	0.14
1	Midplane	0.90	0.09	0.01	0.03	0.02	0.05
2	Near surface	0.84	0.15	0.01	0.03	0.01	0.01
2	Midplane	0.85	0.13	0.02	0.03	0.01	0.05
3	Midplane	0.85	0.12	0.03	0.04	0.02	0.06
Average		0.85	0.13	0.02	0.04	0.02	0.06
Standard deviation		0.03	0.03	0.01	0.01	0.02	0.05

Basic mechanical characterization

The results of the quasi-static tensile experiments are presented in Figure 5 for both, the $0 °$ and the $90 °$ test direction. For both test directions, an initially approximately linear stress-strain characteristic is obtained which becomes increasingly nonlinear in the upper half of the stress range. For the tests in the $90 °$ direction perpendicular to the flow direction (and thus to the fiber preference direction), stronger nonlinearities are observed due to the more distinct matrix effects. Failure in all cases occurs in a sudden, brittle failure mode, irrespective of the loading direction. For both loading directions, only limited scatter between the individual stress-strain curves is observed. This observation holds for both, stiffness, and strength.

Figure 5.

Quasi-static tensile characterization. (a) Testing in $0 °$ -direction, (b) testing in $90 °$ -direction.

In Figure 6, the DMA test results for the storage and loss moduli $E^{'}$ and $E^{″}$ for the three test directions are presented as a function of temperature. For all three test directions, the storage moduli $E^{'}$ are found on a plateau at high levels and decrease rapidly towards lower levels once the glass transition temperature $T_{G} \approx 70 ° C$ is reached. At the same temperature, the loss moduli $E^{″}$ attain their maximum values. Beyond the glass transition, the thermal variation of the storage moduli $E^{'}$ decreases again. As in the quasi-static experiments, the highest moduli are obtained for the tests in the $0 °$ - and thus the fiber preference direction, followed by the specimens cut in $30 °$ direction and the $90 °$ specimens. In all three test directions, a moderate effect of the excitation frequency is observed. The viscoelasticity of the matrix results in a frequency dependency of the material response. Due to the uncertainty of the microstructure, variations between the results based on the individual specimens are observed. Nevertheless, the variability again proves to be limited.

Figure 6.

Dynamic mechanical analysis. (a) Storage modulus, (b) loss modulus.

Creep

The creep curves obtained on unnotched specimens at ambient temperature are presented in Figure 7, considering test directions of $0 °$ and $90 °$ . Within the fiber preference direction ( $0 °$ test direction, Figure 7(a)), a standard creep response is observed, consisting of a primary creep phase with decelerating creep rate followed by a secondary creep phase with a constant creep rate. Even for a couple of creep experiments extended to 1000 h creep time, no tertiary creep phase with accelerated creep and creep rupture is observed. Increasing load levels exhibit a tendency towards a nonlinear increase in the creep rate. For all load levels, a distinct scatter in the creep curves is observed, caused by the disordered and uncertain microstructure of the material.

Figure 7.

Creep curves of unnotched specimens below, at, and beyond the glass transition. (a) Ambient temperature, test direction $0 °$ , (b) ambient temperature, test direction $90 °$ , (c) $80 ° C$ , test direction $0 °$ , (d) $80 ° C$ , test direction $90 °$ , (e) $130 ° C$ , test direction $0 °$ , (f) $130 ° C$ , test direction $90 °$ .

The creep response for a test direction of $90 °$ is presented in Figure 7(b) where the inlay figure is an enlarged representation of the initial creep range. The creep response is qualitatively similar to the response observed for the $0 °$ test direction. Nevertheless, larger creep strains are attained for similar load levels due to the lower creep constraint by the fibers preferably oriented towards the $0 °$ direction. For the higher load levels, a number of creep ruptures are observed in the initial range during the first 2 hours of the experiments (see the inlay figure in Figure 7(b)). In all cases, rupture occurred in a sudden brittle failure mode without any indication of a tertiary creep phase with accelerating creep deformation. The rupture strains are found in a scatter band in the same range as the scatter band for the failure strains under quasi-static loading conditions as presented in Figure 5. For a test direction of $30 °$ , qualitatively similar results are obtained as for the 0° and 90° test directions. The results are found in between the results for tests within and perpendicular to the fiber direction.

The results of the creep experiments at $80 ° C$ and thus close to the glass transition temperature are presented in Figure 7(c) and (d) considering both, the fiber preference ( $0 °$ -) direction and the direction perpendicular to the preference orientation of the fibers ( $90$ °-direction). A distinct primary and secondary creep phase are observed in both test directions. Although the applied load levels are comparatively high for the applied test temperature, the creep rate decreases to almost vanishing values in both test directions for all applied load levels. Nevertheless, due to the softer material response at elevated temperatures, compared to the experiments at ambient temperature larger creep strains are accumulated at similar load levels. In the experiments perpendicular to the fiber preference directions, two ruptures are observed in the initial, primary creep range (see the inlay figure in Figure 7(d)). Again – although subject to scatter – the rupture strains are found in a similar order of magnitude. Interestingly, another specimen tested at the same load level ( $50 MPa$ ) as the ruptured ones does not exhibit a failure and enters into a secondary creep phase at an almost vanishing creep rate as observed also for the specimens tested at lower load levels. Noticeably, the uncertainty and scatter in the creep results are found to be much less pronounced than observed in the experiments at ambient temperature.

The creep results obtained at a test temperature of $130 ° C$ and thus well beyond the glass transition temperature are presented in Figure 7(e) and (f) concerning experiments within and perpendicular to the fiber preference direction, respectively. The results are found to be qualitatively similar to the results at $80 ° C$ . Nevertheless, the creep rates in the secondary creep rates are higher again. Also, the scatter is found to be more pronounced, although not as pronounced as in the experiments at ambient temperature.

Complementing the experiments on unnotched specimens, a limited number of experiments on notched specimens considering selected cases were performed. The results are presented in Figure 8(a) for mild notched specimens tested at an angle of $30 °$ to the fiber preference direction and in Figure 8(b) for specimens with sharp notches tested within the fiber preference direction. The inlay figures provide enlarged representations of the respective initial ranges. The results are presented in terms of nominal strains $ε_{nom} = Δ l / l_{0}$ with a reference length of $l_{0} = 10 mm$ across the notched section. All specimens were tested at $80 ° C$ , thus close to the glass transition temperature. As for the unnotched specimens, secondary creep phases with rather small creep rates are observed in both cases. Nevertheless, a more pronounced scatter is observed for the notched specimens due to the strong stress and strain localization in small volumes around the notch roots. Thus, local variations of the microstructure have a larger impact, circumventing the self-averaging effect for larger highly deformed volumes as in unnotched tensile specimens. For both specimen configurations, a number of creep ruptures were observed within the first 30 minutes of the experiments. For the mildly notched specimens, the rupture again occurs in a sudden brittle failure mode without any visible tertiary creep deformation. For the sharp notched configuration – in contrast to all preliminary observations – some slight acceleration of the nominal creep rate $d ε_{nom} / d t$ precedes the rupture events. Some accelerated (nominal) creep deformation is also observed for the specimen tested at the third highest load level of $60 MPa$ (see Figure 8(b)). However, as it is confirmed by the results of the fractographic investigation (Section 3.5), these accelerations in the nominal creep deformation $ε_{nom}$ are caused by crack formation and propagation prior to complete specimen failure rather than being true tertiary creep effects on the material level.

Figure 8.

Exemplary creep experiments on notched specimens at $80 ° C$ . (a) Mild notch, test direction $30 °$ , (b) sharp notch, test direction $0 °$ .

Fatigue and creep-fatigue

The results of the fatigue and creep-fatigue experiments on coupon specimens for the different conditions compiled in the test matrix in Table 2 are presented in Figure 9. The characteristic values of the $S$ - $N$ -curves, $k$ , σ_a,10⁶ and T_σ are listed in Table 2. For simplicity, the $S$ - $N$ curves for the notched configurations are presented in terms of nominal stress amplitudes computed from the applied force distributed over the net cross-section. For information, the stress level $σ_{creep}$ for the creep phases – where applicable – is marked in the diagrams.

Figure 9.

Fatigue and creep-fatigue experiments. (a) Test direction $0 °$ , mild notch, $R = - 1$ , $23 ° C$ , (b) test direction $30 °$ , mild notch, $R = - 1$ , $130 ° C$ , (c) test direction $90 °$ , sharp notch, $R = - 1$ , $23 ° C$ , (d) test direction $0 °$ , sharp notch, $R = 0$ , $130 ° C$ , (e) test direction $30 °$ , sharp notch, $R = 0$ , $23 ° C$ , (f) test direction $90 °$ , mild notch, $R = 0$ , $130 ° C$ .

All $S$ - $N$ -curves shown in Figures 9 and 16 are statistically evaluated according to their parameters: the stress amplitude at $N = 10^{6}$ , the slope $k$ , and the scatter width $T_{σ}$ . For the double-logarithmic representation of the test results, a linear fit, based on a Basquin-type formulation⁵ is generated. Therefore, the inclination $m$ and interception $b$ are evaluated according to

y = m x + b

(2)

By using the inclination $m$ , the slope $k$ of the $S$ - $N$ -curve is calculated according to

k = - \frac{1}{m}

(3)

Subsequently, any value of stress amplitudes concerning the number of load cycles can be calculated by

σ_{a, N 1} = σ_{a, N 2} {(\frac{N_{2}}{N_{1}})}^{\frac{1}{k}}

(4)

To evaluate survival probabilities and the scattering, the experiments of the $S$ - $N$ -curve must be evaluated statistically. For this purpose, the standard deviation $s_{n}$ and the mean value $\log (m)$ are calculated according to

s_{n} = \sqrt{\frac{1}{n - 1} \cdot \sum_{i}^{n} {(\log (N_{i}) - \log (m))}^{2}}

(5)

\log (m) = \log (N_{50 %}) = \frac{1}{n} \cdot \sum_{i}^{n} \log (N_{i})

(6)

where

$n$ : amount of valuable tests

$N_{i}$ : number of cycles to failure of the $i$ -th test, $i = 1, \dots, n$

With the parameter $u_{P A}$ of the standard normal distribution for the required survival probabilities $P_{s}$ (here exemplified $10 %$ ( $u_{P A} = 1.28$ ) and $90 %$ ( $u_{P A} = - 1.28$ )) from,¹ the stress amplitudes for the respective survival probabilities are calculated according :

\log (σ (P_{s 10 %}) = \log (σ (P_{A 90 %}) = u_{P A 90 %} \cdot s_{n} + \log (σ_{P s 50 %}))

(7)

\log (σ (P_{s 90 %}) = \log (σ (P_{A 10 %}) = u_{P A 10 %} \cdot s_{n} + \log (σ_{P s 50 %}))

(8)

$P_{s} = 1 - P_{A}$ applies, where analogously stresses $σ$ can be substituted with numbers of load cycles $N$ .

The scattering $T_{σ}$ Tσ is calculated according to equation (9), as shown here, for example, as the ratio of the stress amplitude $σ_{P s 10 %}$ at a survival probability of $10 %$ and the stress amplitude $σ_{P s 90 %}$ at a survival probability of $90 %$ :

T_{σ} = 1 : \frac{σ_{P s 10 %}}{σ_{P s 90 %}}

(9)

For the case of alternating fatigue loads applied in the fiber preference ( $0 °$ -) direction to mildly notched specimens at ambient temperature in Figure 9(a) similar $S$ - $N$ curves are obtained whether the final fracture of the specimen or the detection of a fatigue crack is considered. Failure occurs in a predominantly brittle mode where crack initiation is followed almost directly by unstable crack propagation and thus specimen rupture. Comparing the results for pure fatigue and fatigue load interrupted by creep phases, the intermediate creep phases are found to reduce the fatigue lifetime for similar stress amplitudes or to reduce the allowable stress amplitude for prescribed fatigue lifetimes. In principle, this could at least in part be due to additional fatigue damage incurred by increasing and decreasing the load at the beginning and end of the creep phase, respectively. However, creep loads are applied as the maximum loads of the creep phases, not as their amplitudes. Thus, creep load levels in case of $R = 0$ (Figure 9) would correspond to amplitudes of one half of the given values. If the creep-load levels were applied as constant amplitude fatigue loads (without holding), fatigue lives of several thousand cycles could be expected based on the $S$ - $N$ -curves shown for pure fatigue loading. Therefore, the additional fatigue damage accumulated by the small number of creep phases is negligible. The reduction of the fatigue lives under combined creep-fatigue loading is therefore due to additional creep damage accumulated during the creep (holding) phases.

At a test direction of $30 °$ and an elevated temperature of $130 ° C$ , only creep-fatigue experiments considering specimen rupture have been performed. The results are presented in Figure 9(b). The elevated temperature and the off-axis test direction of 30° to the fiber preference direction result in a further decrease in the fatigue lifetime. Nevertheless, in both cases, the $S$ - $N$ curves approximately approach the static failure stress $σ_{UTS}$ as the extreme case of a fatigue load with a single cycle only. For a further rotation of the test direction to 90° and a change in the load ratio to $R = 0$ , a further decrease in the fatigue lifetime is observed in Figure 9(f). Again, only creep-fatigue experiments were performed for this case.

The results for the fatigue experiments in the sharply notched specimen configuration are presented in Figure 9(c) to (e). For the specimens tested perpendicular to the fiber preference direction at ambient temperature and a load ratio of $R = - 1$ in Figure 9(c), partially contradictory results to the findings in Figure 9(a) are obtained. On the one hand, a significant difference between the $S$ - $N$ curves based on specimen rupture and crack initiation is observed. In the sharply notched specimen configuration crack initiation thus does not trigger immediate specimen rupture by unstable crack propagation. Instead, a stable fatigue propagation extends the fatigue lifetime significantly. This observation holds for both, pure fatigue and creep-fatigue loading. On the other hand, the effect of the creep phases on the fatigue lifetime is different to the effect observed in the mildly notched case in Figure 9(a). The $S$ - $N$ curves for the creep-fatigue case feature steeper slopes and thus shorter or longer fatigue lifetimes are obtained, depending on the applied load level. This observation indicates the simultaneous action of different effects triggered by the intermediate creep phases. On one hand, the creep deformation causes the development of additional damage effects as in the mildly notched case. On the other hand, the creep deformation in the highly stressed and strained notch root areas causes a stress and strain redistribution and thus a reduction of the notch effect, resulting in lower local stresses and an increase in the size of the process zone. This effect is obviously more distinct for the sharply notched specimen configuration with its smaller process zone and its much more pronounced stress and strain concentration.

Qualitatively similar results – although less distinct – are obtained in the experiments in $0 °$ -direction at elevated temperature and a load ratio of $R = 0$ (see Figure 9(d)). Quantitatively the fatigue lifetimes are slightly lower. The results for a test direction of $30 °$ at a load ratio of $R = 0$ at ambient temperature in Figure 9(e) are found qualitatively and quantitatively similar to their counterparts obtained in a test direction of $90 °$ at $R = - 1$ in Figure 9(c), except that in the former in contrast to the latter, the slopes of the $S$ - $N$ curves under pure fatigue and creep-fatigue are similar.

Fractography

In a first approach, the fracture surfaces of the ruptured creep specimens were investigated. Figure 10 presents the total fracture surface on the right side of a specimen tested perpendicular to the fiber preference direction at $90 MPa$ and ambient temperature, together with successive magnifications of the details at selected positions as indicated in the figure.

Figure 10.

Creep fracture surface (unnotched, test direction $90 °$ , temperature $23 ° C$ , $90 MPa$ ).

The matrix exhibits a mostly brittle fracture surface without relevant formation of ductile dimples. Due to the testing direction perpendicular to the fiber preference direction, most fibers are found within the fracture surface. To a large amount, rupture has occurred in an inter-fiber fracture mode with only a few visible fibers. In the – in the present material rather thin – central layer (see Figure 4) fibers are predominantly oriented normally to the fracture surface. Here, brittle matrix failure together with fiber pull-out is found to be the dominating failure mode. The fiber surfaces in most cases are free from matrix adherences, thus indicating fiber matrix interface failure as the most relevant microstructural failure mechanism. Together with the visible fiber pull-out, this finding indicates that void formation at the fiber ends might also play an important role in the damage and failure process, despite not being visible on the fracture surface. No evidence of fiber fracture during the specimen rupture is found. The visible fiber fracture surfaces are probably due to the fracture of the fibers during the manufacturing process.

Similar observations are made at the opposite end of the fracture surface. Nevertheless, the fracture surface on the left side in general exhibits a rougher appearance than on the right side presented in Figure 10. It is assumed that rupture was triggered in the smoother right side of the specimen whereas crack branching effects during crack propagation are assumed to have caused the rougher appearance of the fracture surface towards its left end.

The creep experiments in Section 3.3 indicate a different material response close to the glass transition temperature. For this reason, the fracture surface of a specimen oriented at $90 °$ to the fiber preference orientation and tested at $50 MPa$ and a temperature of $80 ° C$ was investigated in detail. Figure 11 presents the full fracture surface on one end of the specimen together with an enlarged detail as indicated together with an enlarged detail from the opposite end of the fracture surface. Again, the appearance of the fracture surface on the right end shown in full was found to be much smoother than the opposite end. Nevertheless, in this example, a significant crack branch with a macroscopic breakout gives evidence of crack propagation from the smooth right end towards the rougher left end of the fracture surface.

Figure 11.

Creep fracture surface (unnotched, test direction $90 °$ , temperature $80 ° C$ , $50 MPa$ ).

The fracture surface on the right side of the specimen – the side of the fracture initiation –indicates a brittle failure of the matrix together with fiber matrix interface failures, indicated by blank fiber surfaces without matrix adhesions. Already in this range, indications for crack branching are visible as in the case of the sub-surface crack in the detail from the right end of the fracture surface. In contrast to the observations on the specimen tested at ambient temperature, a predominantly ductile failure is observed at the opposite end of the fracture surface. Thus, a mixed failure mode with a brittle initiation but partly ductile propagation develops in the creep rupture at $80 ° C$ .

A similar investigation has been performed for the specimens tested under fatigue loads. Figure 12 shows the left end of the fracture surface of a mildly notched specimen tested in $0 °$ direction at ambient temperature under fatigue without holding phases with a load ratio of $R = - 1$ , together with a magnified detail as well as a detail of the opposite end of the fracture surface. At both ends the fracture surface exhibits a brittle failure mode of the matrix together with pull-out of fibers oriented normally to the fracture surface. It cannot be directly determined whether the visible fiber breakages are failure events which occurred during the fatigue failure of the specimen or already during the manufacturing process. Nevertheless, the amount of blank fiber surfaces indicates an extensive fiber matrix interface failure together with fiber pull-out. Thus, the breakages can be traced back to the material manufacturing process. Whether the failure was triggered at the right or left end of the specimen cannot be determined.

Figure 12.

Fatigue fracture surface (mild notch, test direction $0 °$ , $23 ° C$ , load ratio $R = - 1$ ).

For comparison, the fracture surface of a specimen with mild notch tested under pure fatigue with $R = - 1$ at $130 ° C$ in an orientation of 30° is investigated in Figure 13. In the full view, the development of failure along the inclined fiber preference orientation and thus off the ligament is clearly visible. Considering the stress and strain concentration at the notch root, it is evident that the crack was initiated at the notch root at the left end of the fracture surface. In the magnified detail view, again a brittle failure mode is observed in the crack initiation region. In contrast, the fracture surface features a ductile mode towards the right end after some amount of crack propagation. Nevertheless, even in this range, the debonding of the fiber and matrix interfaces plays an important role.

Figure 13.

Fatigue fracture surface (mild notch, test direction $30 °$ , $130 ° C$ , load ratio $R = - 1$ ).

In order to assess the effect of the load ratio $R$ , the fracture surface of a sharply notched $0 °$ -specimen fatigued at $R = 0$ and a temperature of $130 ° C$ is investigated in Figure 14. Here, the macroscopic shape of the fracture surface indicates a crack initiation from both notch roots. During the crack propagation, the evolving cracks showed a tendency to a reorientation towards the fiber preference direction prior to the rupture of the remaining ligament in the specimen center. Consistent with the previous observations, a predominantly brittle failure mode is observed in the presumed crack initiation zones at the notch roots whereas a ductile failure mode is observed in the range of the final rupture. Again, a significant amount of fiber and matrix interface debonding is observed at all stages of the fatigue failure. In comparison to the fracture surface of specimens tested under alternating fatigue load with $R = - 1$ (Figure 13) no significant differences are observed.

Figure 14.

Fatigue fracture surface (sharp notch, test direction $0 °$ , $130 ° C$ , load ratio $R = 0$ ).

For a direct comparison, details of the fracture surfaces of specimens tested under creep, pure fatigue load, and creep-fatigue are presented in Figure 15. All specimens were tested at elevated temperature. Fatigue loads were applied as tension-tension fatigue with a load ratio of $R = 0$ . All specimens were tested in the fiber preference ( $0 °$ -) direction. No significant differences are observed. In all three cases, fracture was initiated by brittle failure of the matrix in conjunction with fiber matrix interface debonding and subsequent fiber pull-out. Presumably, this failure mechanism also involves void formation at the fiber ends.

Figure 15.

Fracture surfaces for different loading types.

Fatigue under complex loading conditions

The results of the fatigue experiments on the “T”-specimens with intermediate change in the thermal conditions are presented in Figure 16(a) for all four specimen configurations considered. The characteristic values $k$ , $F_{a, 10^{5}}$ and $T_{F}$ of the $S$ - $N$ -curves are listed in Table 3. Specimens which failed prior to the temperature shift from $23 ° C$ to $130 ° C$ at $10^{5}$ cycles were not included in the evaluation of the $S$ - $N$ curves. However, the respective data are included in the diagram for information. Notice that the presented $S$ - $N$ curves provide structural component related $S$ - $N$ curves rather than directly material related ones, although the “structure”, i.e., the breadboard specimen is still quite simple. One on the relevant structural features – further to the notch with different notch root radii – is the presence of varying, molding dependent local fiber orientation states in the highly loaded volume.

Figure 16.

Fatigue under complex loading situations. (a) “T”-specimens, (b) “MultiTester”- and “Submarine” specimens.

For all four test configurations, $S$ - $N$ curves with similar slopes were obtained except for the longitudinally molded case with a notch root radius of $0.5 mm$ . However, the lower slope in this case is caused by a single outlier, i.e., the datum at $30 MPa$ with a failure at approximately $320 000$ cycles. Concerning the effects of the specimen configuration, the most significant effect is due to the notch root radius where larger notch root radii are observed to increase the fatigue lifetime significantly. Regarding the molding direction, the fatigue lifetime of the specimens with a notch root radius of $r = 0.5 mm$ molded in the longitudinal direction is found to be slightly larger than for their counterparts molded in the transverse direction. This effect is due to the fiber preference orientation which is the direction along the notch ( $x_{2}$ -direction) for the transversally molded specimens whereas the fibers for the longitudinally molded specimen tend to align towards the $x_{1}$ - and $x_{3}$ -directions and thus the main loading direction in the notch root under bending loads applied to the vertical leg of the specimens.

The (structural component related) $S$ - $N$ curves for the experiments on the “MultiTester” and “Submarine” specimens under variable internal pressure according Table 5 are presented in Figure 16(b). The characteristic values $k$ , $p_{a, 10^{6}}$ and $T_{p}$ are listed in Table 5 In all cases, linear $S$ - $N$ curves are obtained in the same manner as for the coupon experiments under harmonic sinusoidal fatigue loads. Due to the larger wall thickness in the critical regions, the “Submarine” specimens feature significantly higher fatigue lifetimes than the “MultiTester” specimens tested with the same variable pressure load spectrum. For the “MultiTester” specimens, failure occurred at the thin and strongly curved section at the upper end of the larger nearly cylindrical section. Failure of the “Submarine” specimens was observed on the outside at the intersection of the two tubular sections with a suspicion of being originally triggered at the hole connecting the two tubular chambers. The “MultiTester” results on wet conditioned specimens reveal that the loading scenario with variable (block-) amplitudes yields a $S$ - $N$ curve with a lower slope than a harmonic sinusoidal loading with constant amplitudes. A similar, nearly horizontal $S$ - $N$ curve is also obtained for the “MultiTester” specimens tested under fatigue with variable amplitudes but conditioned to a dry state. However, the fatigue lifetime for the dry specimens is higher than for their wet-conditioned counterparts.

Complementing the investigations of the present contribution, the experiments on the three types of breadboard specimens will serve as validation experiments for a continuum damage mechanics material model developed in an oncoming contribution (Abdul Hamid et al.²⁷).

Discussion

The results of the experimental investigation reveal a strong effect of the flow direction on the fiber orientation and thus the mechanical properties of the material, as to be expected. In this context, only a limited development of a layered structure as it would be usual for injection molded components is observed in the plates used for coupon specimen manufacture due to the special design of the gate section in the manufacture of the plates. Thus, the coupon specimens could be considered as specimens with a uniform fiber orientation distribution through the specimen thickness. In general, both stiffness and strength are found to correlate with the number of fibers oriented towards the loading direction. In this context, more pronounced nonlinearities are observed in the material response for 90° test orientation due to more pronounced matrix effects perpendicular to the fiber direction. Accordingly, the material response strongly depends on the flow direction during the molding process. This becomes obvious in the experiments on “T” specimens, where specimens with identical geometry were molded alternatively in two spatial directions.

The dynamic mechanical analysis revealed a distinct viscoelastic effect with significant loss moduli especially in the range of the glass transition temperature at approximately $T_{G} \approx 70 ° C$ . Both, the quasi-static tensile experiments, and the dynamical mechanical analysis (DMA) showed a good repeatability of the results. However, due to the viscoelasticity of the material, the DMA results at different test frequencies proved to be different. Based on the DMA results, test temperatures for creep and fatigue well below (23°C), close to (80°C) and beyond (130°C) the glass transition temperature were chosen.

The creep experiments featured a primary creep phase with decelerating creep rate with a subsequent secondary creep phase at an almost constant creep rate as expected. However, no tertiary creep phase with accelerating creep rate prior to creep rupture was observed in the experiments on unnotched specimens. Instead, creep rupture occurred in a sudden brittle failure mode without any preliminary indication. For the ruptured specimens, the failure strains were found in the same range as the failure strains in the quasi-static experiments. Nevertheless, in both cases, the failure strains depend on the fiber orientation state and the testing direction. This observation indicates a strain-driven failure mechanism.

Similar results were obtained in the experiments on notched specimens at elevated temperature, except for a minor development of a tertiary creep phase on specimen level prior to rupture. Nevertheless, the apparent tertiary creep is suspected to be related to a crack propagation process from one of the notch roots into the unnotched area rather than being a material creep effect. This observation is confirmed by the fractographic investigation which revealed a brittle failure mode in the crack initiation range of all specimens – whether notched or unnotched – whereas a mixed and ductile failure mode is observed on the fracture surfaces in the crack propagation ranges. A generally rougher appearance of the fracture surface in conjunction with breakouts gives evidence of a crack propagation process with crack branching induced by the fibrous microstructure, increasing the macroscopic fracture toughness further.

The crack propagation is observed to follow the fiber preference direction as far as possible and thus to occur in a matrix-dominated mode. For fiber orientation states and loading directions, where a failure in fiber direction is essential, a large amount of fiber pull-out is observed. In this context, the fibers are mostly found blank without matrix adhesions, indicating fiber matrix interface debonding as the leading micromechanical failure mode. In conjunction with the observed fiber pull-out, void formation at the fiber ends is also likely. No evidence of fiber breakage during the specimen rupture process is observed. Brittle failure surfaces on fibers are probably due to fiber breakages during the manufacturing process.

The creep curves feature a distinct scatter due to the disordered microstructure. The effect is found more pronounced in test directions other than the fiber preference direction, i.e., in the more matrix-dominated test directions due to lower creep constraint imposed by the fibers oriented in directions off the loading direction. In the range of the glass transition temperature, the scatter for the unnotched test configurations becomes much less pronounced. At the same time, secondary creep phases with rather low creep rates are observed even when creep strains in the range of the failure strain are reached. This effect could be caused by an easier local stress relief at stress concentrations on the microstructural level, making stress concentrations less severe and thus preventing them from triggering failure. For notched specimens, a distinct scatter is observed even close to the glass transition temperature due to the smaller size of the highly loaded (stressed and/or deformed) volume causing a much less pronounced self-averaging effect of the material.

The effect of crack propagation is also observed in the fatigue response. More pronounced differences between the $S$ - $N$ curves based on specimen failure and first crack detection are observed in the sharp notch configuration. For specimens with mild notches only minor differences between the $S$ - $N$ curves are observed, indicating that for sharp notches, crack propagation forms a more significant part of the specimen lifetime. As for the specimens tested under creep loads, the fracture surface in the crack initiation zone features a predominantly brittle appearance. In the crack propagation zones mixed or ductile fracture surfaces are observed, especially for experiments under elevated temperatures. Due to crack branching, a rougher appearance of the fracture surfaces is observed in this region. Crack branching with the development of a larger total crack surface than the projected crack surface acts as a mechanism to increase the fracture toughness. For the present short fiber reinforced material, the development of non-straight crack paths and crack branching is mainly triggered by the fibrous microstructure of the material.

In the interaction of different deformation types, creep is found to have distinct, non-negligible effects on the fatigue resistance and lifetime of the material. The results indicate the simultaneous action of different and contradictory effects. Basically, intermediate creep phases – and thus also creep deformation developing during the high-stress phases of the cyclic fatigue loads – might accelerate the fatigue failure. The reason is the accumulation of additional damage due to the creep deformation. On the other hand, especially for sharply notched test configurations, creep deformation of the material results in stress relief in the stress concentrations at the notch roots. Thus, a stress redistribution to the surrounding area occurs, resulting in an increase in the highly loaded area at lower load levels and thus a partial relief of the notch effect. This effect is suitable for an apparent increase in the fatigue lifetime on the specimen level (although not on the material level in the rigorous sense). Consequently, a decrease in the fatigue lifetime is observed in the experiments on mild notched configurations with limited notch effect. On sharp notch test configurations, the opposite effects are observed with a partial increase in the fatigue lifetime of the specimen due to a creep-induced partial relief of the notch effect.

Regarding the local failure modes, no pronounced and systematic differences are observed considering creep, creep-fatigue, or pure fatigue loading conditions in the fractographic investigations. This finding confirms the observation that failure is triggered in a strain-driven mechanism with a similar, temperature and fiber orientation distribution dependent, failure strain for all loading types. In all cases, the $S$ - $N$ curves are found to approach either half of ( $R = 0$ ) or the full static tensile failure stress ( $R = - 1$ ) as the extreme case of a fatigue load consisting of a single cycle.

In the experiments on breadboard specimens, it is found that wet conditioning of the material results in decreased fatigue lifetime compared to testing in dried condition. Variable amplitude loading is found to affect not only the position of the $S$ - $N$ curves in the Wöhler $S$ - $N$ diagram but also their slope.

Conclusion

The present contribution was concerned with the effect of creep and multiaxial loading conditions on the fatigue strength and lifetime of short fiber reinforced thermoplastics. In an experimental approach, the effects were studied using a PA66GF35 short glass fiber reinforced polyamide 66 material as reference material. The material response was investigated in quasi-static experiments under proportional loading, dynamic mechanical analyses, creep, fatigue, and creep-fatigue experiments as well as in experiments on breadboard specimens under more complex loading conditions including variable temperature and variable load levels.

The material was found to fail in all cases in a strain-driven failure mode. For all the different loading modes, failure was initiated at similar, failure strains. Nevertheless, the failure strains depend on the respective experimental conditions such as temperature, fiber orientation distribution, and testing direction. The failure modes on material level were found to be predominantly brittle. More ductile and a generally tougher response developed in cases where at least partially stable crack propagation occurred, i.e., at elevated temperatures and especially in case of failure initiation from notches with strong stress and strain gradients. Both, the predominantly brittle failure of the material under all considered static and long-term loading situations and the strain-driven failure initiation provide important features to be taken into account in a damage mechanics material model for short fiber reinforced composites. Thus, the strain or the strain energy density rather than the stress state would serve as an appropriate damage driver in such an approach. Furthermore, a damage model can be formulated based on an elastic base model. The present results form an experimental data base for development and validation of a material model in this sense, developed in an oncoming contribution.

The interaction of creep and fatigue was found to be governed by two different contradictory effects. On one hand, superimposed creep deformation might increase the damage accumulation and thus reduce the fatigue lifetime whereas at the same time, creep deformation might have a beneficial effect by triggering a stress and strain redistribution at stress concentrations, thus reducing notch effects. This finding gives evidence that superimposed creep deformation essentially needs to be considered in the fatigue assessment of short fiber reinforced thermoplastics. Since the creep deformation usually exhibits a distinct nonlinear stress dependence, the superposition principle does not apply. Damage effects by superimposed creep deformation will be most relevant in the range of the upper tensile and lower compressive peaks of the fatigue load cycles rather than being relevant in an averaged manner smeared over the entire range of the load cycle. Again, for continuum mechanics modelling and simulation the necessity for a combined treatment of creep and fatigue damage becomes evident.

Footnotes

Acknowledgements

The present contribution has been funded by AiF under grant no. IGF 20374N in accordance with a resolution of the German Federal Parliament. The financial support is gratefully acknowledged.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the AiF (IGF 20374N).

ORCID iDs

Benedikt Rohrmüller

Jörg Hohe

Dominik M Laveuve

Data availability statement

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.*

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Characterization of the effect of creep and multiaxial loading situations on fatigue of short fiber reinforced thermoplastics

Abstract

Keywords

Introduction

Material and methods

Material and test specimens

Test procedures

Microstructural investigation

Basic mechanical characterization

Creep

Fatigue and creep-fatigue

Fractography

Fatigue under complex loading conditions

Results

Microstructure

Basic mechanical characterization

Creep

Fatigue and creep-fatigue

Fractography

Fatigue under complex loading conditions

Discussion

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iDs

Data availability statement

References