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Fatigue behaviour of discontinuous carbon-fibre reinforced specimens and structural parts
International Journal of Fatigue 131 (2020) 105289
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue behaviour of discontinuous carbon-fibre reinforced specimens and structural parts
T
Stefan Sieberera, , Susanne Nonna,b, Martin Schagerla,b ⁎
a b
Institute of Structural Lightweight Design, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria Christian Doppler Laboratory for Structural Strength Control of Lightweight Constructions, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria
ARTICLE INFO
ABSTRACT
Keywords: Carbon Fibre Reinforce Polymer (CFRP) Sheet Moulding Compound (SMC) Fatigue testing Composites durability Stiffness degradation
Discontinuous fibre reinforced polymers are increasingly used for structural components in automotive applications. In this paper, specimens made from a carbon-fibre sheet moulding compound are tested in constant amplitude fully reversed cyclic fatigue loading. The obtained fatigue lifetime curves are compared against component fatigue test results. In addition, the evolution of modulus in the specimen is compared to the structural stiffness in the component. A power law is used to describe both, degradations of specimen modulus and component stiffness. The exponent of the power law is proportional to the load amplitude, potentially indicating the existence of a fatigue limit.
1. Introduction Over the last decade, fibre reinforced polymer (FRP) components have been increasingly used as lightweight structural components in automotive applications. In the design phase of such components, fatigue life calculations have to be performed to ensure the durability of structural components over the vehicle lifetime. For this, material parameters for all used engineering materials must be available, and their scalability to component level must be given. In metals, mature theories cover the influence of, amongst others, component size, surface roughness, or load pattern (see e.g. [11,22]), and therefore the material can be used to its full potential. However, for composite materials, the transition from specimen to full-scale component has always been performed with greater caution, because (a) in FRP, material degradation over the lifetime has to be considered [7], (b) material defects from manufacturing can have significant effects [8,18], and (c) the damage progression phase has not been sufficiently studied, and sudden failure at the point of damage initiation is often assumed [19]. The first of these influence factors will be the main focus of this paper. For large-scale series production, discontinuous fibre reinforced polymers are often preferred to unidirectionally continuous fibre composites because of their cost-effectiveness whilst retaining some of the weight-saving potential of FRPs. For short-fibre reinforced polymers with fibre lengths up to 6 mm, the material parameters can be assumed as quasi-isotropic from the random orientation of fibre bundles in the part, and global failure criteria from metals can be applied [20]. For
⁎
long-fibre discontinuously reinforced polymers, e.g. sheet moulding compound (SMC) with typical fibre lengths of 15–25 mm [7], the assumption of isotropic material parameters on the macroscale can be maintained [9]. However, large scatter of the material parameters is encountered [10]. Static material parameters for SMC material can be obtained from tensile testing on specimen [9,10,24] yielding elastic moduli and strength values. Also, fatigue test data in discontinuous FRP specimens is widely available, yielding S-N curves which give the probability of crack initiation in the specimen under pulsating or fullyreversed loading (see e.g. [7,20]). Despite efforts, implemented in general Finite Element software, e.g. Abaqus, and dedicated engineering fatigue software tools, e.g. FEMFAT, to calculate the onset of cracks by expanding static failure criteria for one-stage loading and applying Miner’s rule, so far, no satisfyingly precise and general rule for the calculation of fatigue life in composites has been established. Even before the onset of cracks, especially in SMC and short-fibre FRP, significant reduction in the material stiffness can occur. Schulte reported in [20] the difference in the stiffness reduction in tensiletensile fatigue testing of a cross-ply CFRP laminates: non-crimp continuous UD layers, crimped fabric, and short-fibre aligned layers were considered. Three regions of stiffness reduction were identified for all three laminate types: (i) initial-phase large stiffness reduction, (ii) nearconstant stiffness in the mid-lifetime region, and (iii) a large stiffness drop shortly before specimen failure. The underlying mechanism for these reductions in stiffness are different for the three considered phases. Initially, transverse cracking occurs until saturation is reached.
Corresponding author. E-mail address: [email protected] (S. Sieberer).
https://doi.org/10.1016/j.ijfatigue.2019.105289 Received 18 July 2019; Received in revised form 17 September 2019; Accepted 19 September 2019 Available online 08 October 2019 0142-1123/ © 2019 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
International Journal of Fatigue 131 (2020) 105289
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This ends the initial phase and in the subsequent mid-lifetime region, longitudinal cracks appear, grow and merge with transversal cracks. In addition, delamination occurs, generally starting from free edges or merged cracks. In the last region, widespread delamination leads to fibre overload and failure of the structure. Schulte notes that the midlifetime region spans from about 10% to 90% of the fatigue lifetime of the specimens in continuous and short fibre UD laminates. For the woven fabric, the last region starts at about half of the specimen lifetime. The stiffness reduction up to the end of the mid-lifetime region is comparatively moderate for the CFRP material, and less than 10% of the initial stiffness is lost. In [7], Caprino reviews studies on discontinuous FRP materials and states that the extent of stiffness reduction is largely governed by the type of fibres, with stiffer carbon fibres exhibiting better fatigue performance and less stiffness degradation compared to glass fibres. No definite conclusion on the influence of fibre length could be drawn from the presented data. However, Thomason et al. [25] showed results where a lower bound of fibre length is given, determined by the minimum length necessary to transfer load into the fibres. The influence of the mean stress on the fatigue behaviour in discontinuous fibre composites has been discussed e.g. in [7,15,16]. There are reportedly two factors contributing to the deterioration of fatigue properties under tensile mean stress, which are the mean stress effect and additionally cyclic creep. Whilst the mean stress effect influences the fatigue life directly by adding a constant loading, creep changes the displacement at zero load over time. In the present study, fully reversing loading conditions were used in order to exclude creep effects and to represent the load conditions in the structural component. Recently, the interest in understanding and modelling stiffness degradation in FRP has been rekindled. Quaresimin et al. [21] investigated the early stage damage of glass-fibre epoxy specimens under shear and showed the microcrack formation under shear loading. For these early stages of fatigue and the mid-lifetime region, Movahedi-Rad and co-workers [17] presented experimental results for stiffness reduction of a glass-fibre FRP angle-ply laminate under tension-tension loading. Significant reduction in modulus were recorded, but the testing did not show the last stage of rapid stiffness deterioration before fracture. Adam and Horst [1] considered very high-cycle fatigue on angleply glass-fibre FRP and showed the reduction in bending stiffness in a four-point bending test. The researchers found that the stiffness degradation was reduced at very low loads and suggested the potential existence of endurance strength for composite material. In discontinuous FRP, Mortazavian and Fatemi [16] investigated the fatigue behaviour under different load and environmental conditions of short glass-fibre thermoplastic composites and derived a simple criterion to obtain fatigue strength from tensile strength of the specimens. However, most of the current research in fatigue of composites is focussed on continuous glass fibre reinforced material, and little progress has been made on understanding fatigue in CFRP SMC material on the specimen level. In addition, to the authors knowledge, no verification on larger structures has been performed so far. It is the aim of this paper to investigate the material degradation in stiffness terms of CFRP SMC material under fatigue loading. S-N curves for fully reversed loading are obtained and a stiffness degradation model is presented. The influence of the load level on stiffness degradation and potential for arresting fatigue mechanisms at low load are discussed. For the same material, component testing is performed for an automotive suspension arm. The loading of the component is usually alternating, as cornering forces in both directions have to be transferred between wheel and chassis by the suspension arm [13]. The resulting cycles-to-failure and stiffness degradation is validated for the components against the specimen data. In an accompanying publication [23] to this paper, the stiffness degradation after crack initiation was studied for one component. The content is organised as follows. Section 2 gives the experimental set-up for specimen and component testing, which is followed by the
Fig. 1. Test set-up for the specimen testing with piston of the hydraulic cylinder, load cell, slide bearings, hydraulic grips, and test specimen.
test results for quasi-static and fatigue testing in Section 3. The discussion of the results is given in Section 4 and is followed by the conclusions in Section 5. 2. Test set-up In this section, the test set-ups for the specimen testing and the component testing are described. The tests were performed at room temperature of T = 24 ± 4 °C. A Zwick-Roell BPS-LH0025 hydraulic cylinder with a nominal force of 25 kN and controlled by a CATS Control Cube system was used in all tests. Fig. 1 shows the test rig configured for specimen testing. The test specimen is fixed with MTS 647 hydraulic wedge grips to cylinder and ground. Lateral motion of the cylinder is minimised by guide rails, thus eliminating lateral forces on the specimens and components in fully-reversed cyclic loading. Lowfriction sliding bearings are used to minimise the effect of stick-slip on the load measurement during the fatigue testing. In component testing, the hydraulic grips were replaced by the mounts for the structure. Strains were recorded by a Correlated Solutions digital image correlation (DIC) system, capable of measuring the full surface on one side of the specimens or an area of the components. For this, a so-called speckle pattern, which is a distribution of black dots on a white background, is applied to the specimens. From the relative position of the speckles, the strain is computed. Because the system comprises two cameras, displacements in 3 dimensions are considered when evaluating strains. In addition to strains, the correlation error is considered in the evaluation of results. Correlation is, in this paper, defined as the match in speckle pattern between a reference picture, taken before the test with no load applied, and a picture taken in the test. The correlation error (CE) is evaluated internally by the DIC software, and increase of the CE indicate potential future crack formation. Loss of correlation in an area of high CE gives an indication of crack initiation and growth. 2.1. Specimen testing In a CFRP SMC fabrication process, continuous fibre strands are chopped onto a moving belt covered by an epoxy resin film [2]. The moving direction of the belt gives a deposition direction. The fibre chips in the epoxy matrix were approx. 25 mm long, and between 8 and 12 mm wide. A number of 3.0 mm thick plates made from layers of SMC sheets aligned to the same deposition direction were provided by an industrial partner. Fig. 2 shows part of the plates with specimen cut at 2
International Journal of Fatigue 131 (2020) 105289
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Fig. 2. Plates with cut and labelled specimen. 0 and 90 degree specimen are shown left and right, respectively.
0° and 90° to the deposition direction. The specimen width is 25 mm, and aluminium end tabs were applied before testing. For the tensile specimens, the gauge length was 110 mm, whilst for all other specimen the gauge length was 20 mm. The test programme presented in Table 1 and comprising quasistatic and cyclic fatigue tests was performed. In the quasi-static tensile testing, the test rig was set to displacement controlled operation with head speed of 2 mm/min for the tensile testing, and 0.5 mm/min for the compressive testing. The cyclic fatigue testing was carried out in force controlled mode with a test frequency of 5 Hz. The DIC system measured strains over the width of the specimen in static tension testing. For compression static testing and fatigue testing, the measurement was taken over the thickness of the specimens. This is because the use of hydraulic grips limited the view on the short specimens to the narrow sides. Additional strain gauges (SG) were applied for static compressive testing on both sides of the specimen to validate the DIC measurements. Furthermore, the two strain gauge signals were used to check for lateral buckling of the whole specimen, which would have led to a significant difference between the two signals. For the calculation of the specimen stiffness, DIC- and SG-obtained strains and the load cell output were utilised.
chosen to reproduce the mounting conditions at joints A and B, and linear static displacement steps simulating the test rig motion were applied. Fig. 4 shows stress field results from this FE analysis, indicating the highest-stressed area on one half of the component. Because of the symmetry of the component, two areas with similarly high loading were found. For monitoring purposes of these areas-of-interest, the aforementioned DIC system was used to measure strains and crack formation on one side of the structure, and an industrial digital camera was positioned to monitor the opposite side as only one DIC system was available. The linear FE analysis gave an indication of the stress maxima in the areas-of-interest for a given displacement amplitude or vertical force component in the hinges. Because of the presence of additional flexible parts, e.g. the bushings, in the experimental set-up, the measured displacement at the hydraulic cylinder cannot be used to estimate the component stiffness. The force measurement, on the other hand, can give a measure of the stress maximum. Introducing the stress sensitivity K as
K=
vM,max
(1)
Fz
with the vertical reaction force at the joints Fz and a max. Mises stress vM,max in the component. The obtained stress sensitivity value can be used to estimate the onset of damage when S-N curves from specimen testing are available. Because of the limited number of parts available for testing, one tensile test and four fatigue tests were performed. Quasi-static tensile testing was done with a displacement controlled set-up at a constant rate of 0.1 mm/s. The fully-reversed fatigue test was performed using load control, and test frequencies in the range of 1.0–1.25 Hz were chosen to avoid component heating. For component 2, where the load controlled mode failed to yield stable operation, the displacement amplitude was adjusted manually to maintain the specified load amplitude. For all specimens, stiffness and damage evolution are evaluated. End-of-life conditions were assessed with both available visual inspection systems. End-of-life of the component is defined as the formation of a crack with a minimum length of 3 mm [14]. Such cracks are
2.2. Component testing The components were made from the same SMC material as the flat specimens, and pressed to obtain the part geometry. A visual inspection was performed to ensure that no significant manufacturing defects were visible on the surface. Fig. 3a shows the component on the test rig. The component is fixed to the ground at joint A, where all degrees-of-freedom are restricted. Joint B is guided in the horizontal plane, and is free to rotate about the pivot axis. Fig. 3b shows how the vertical actuation at B is applied by the force Fz via the hydraulic cylinder, yielding global bending-torsional loading in the component. Prior to testing, a Finite Element (FE) analysis of the component was performed in Abaqus 2017. The model consisted of quadratic tetrahedral elements with an element length of approx. 1.0 mm in highly stressed areas. Boundary conditions were Table 1 Overview of specimens tested. Direction on plate
Test performed
Number of specimens
Cross section (in mm): width × thickness
Specimen gauge length (in mm)
0° 0° 0°
Static Tension Static Compression Fully-rev. Fatigue
5 3 10
25.0 × 3.0 25.0 × 3.0 25.0 × 3.0
110 20 20
90° 90° 90°
Static Tension Static Compression Fully-rev. Fatigue
5 3 10
25.0 × 3.0 25.0 × 3.0 25.0 × 3.0
110 20 20
3
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Fig. 3. Component mounted on the hydraulic test rig: (a) actual set-up, and (b) CAD plot of rig.
Fig. 4. Finite element stress plot of the component under normalised displacement using the boundary conditions of the test rig. The area of highest stress on one side is highlighted by the gradient pattern.
specimen dimensions and normalised to the average static tensile strength Rm , and the strains are obtained from the DIC system. In Table 2, the results of the static tests are summarised. In general, dispersion is low for tensile and compressive loading. The specimens cut in 90° direction exhibit higher strength in tensile and compressive directions, however the moduli is not significantly different for 0° and 90° directions in tension.
referred to in this paper as failure-defining cracks and when such a crack appeared, the test was usually stopped. The stiffness of the component was monitored via a load cell mounted between the top alignment guide and the component, therefore eliminating stick-slip force contribution on the measurement. No influence of a horizontal force component on the vertical force measurement is expected because of internal compensation in the cell. For calculation of stiffness of the structure, the load cell and cylinder position transducer readings were used. For the large amplitude cyclic and static displacements, this gives valid results as parasitic influence of the hydraulic stiffness can be neglected. In the next section, the results for specimen and component testing are presented.
3.1.2. Fatigue test results In Table 3, the load amplitude and cycles-to-failure of the specimens is listed, and Fig. 6 shows the obtained S-N-curves from the data. The regression line is yielded using a least-squares algorithm. The 10% and 90% quantiles are calculated by shifting the test results to a single fictitious load level and assuming a log-normal distribution of the samples [12]. Both, the samples cut at 0° and 90° exhibit large scatter in the data. The difference in gradient and offset of the regressed lines are not significant when checked with a t-test to a 95% confidence level for the two populations. Fig. 7a and b show the stiffness evolution of the 0° and 90° specimens, respectively, with normalised cycles-to-failure and the modulus normalised to the initial values of each specimen. Different classes of normalised stress amplitude An , i.e. Ultra High ( An > 0.60), High (0.60 > An > 0.50 ), Mid (0.50 > An > 0.45), and Low ( An < 0.45) are indicated by different line styles. In both graphs, initially, the stiffness reduces sharply over the first approx. 10% of normalised cycles, followed by a phase of moderate decline, before dropping with a large gradient after about 90% of normalised cycles, signalling the onset of specimen failure. Such a pattern is present in all shown classes of normalised stress amplitude. However, regardless of the stress amplitude, some specimens show no notable degradation over their lifetime. It is perceivable that in these specimens, because of their short
3. Test results 3.1. Specimen testing In this section, the specimen static and fatigue test results are presented. For both test series, 0° and 90° samples were used. Quasi-static specimens were tested in tension and compression. To avoid buckling, short specimens were used in compressive testing. All fatigue tests were performed in fully-reversed cyclic loading conditions, thus eliminating creep influence. Again, short specimens were used because of potential buckling instability. 3.1.1. Static test results Fig. 5a shows the stress-strain plots for the tensile tests in 0° and 90° directions, and Fig. 5b shows stress-strain plots for the compressive tests in 0° and 90° directions. The stresses are calculated using nominal 4
International Journal of Fatigue 131 (2020) 105289
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Fig. 5. Stress-strain plot from the static tensile testing of specimens. Tensile results (left) are obtained from long specimens, and compressive results (right) from short specimens. Table 2 Overview of static specimen results. Moduli are reported from DIC and strain gauges (SG) for compressive specimen. Specimen
Specimen orientation
S01L01 S01L02 S01L03 S01L04 S01L05 S02L01 S02L02 S02L03 S02L04 S02L05
0° 0° 0° 0° 0° 90° 90° 90° 90° 90°
Avg. Tens
–
S01L06 S01L07 S01L08 S02L06 S02L07 S02L08
0° 0° 0° 90° 90° 90°
Avg. Comp.
–
Norm. Modulus ×10−3 DIC SG Tensile test specimens 0.168 0.166 0.168 0.183 0.184 0.189 0.145 0.186 0.140 0.205
T/C Strength (normalised) 0.822 0.815 1.032 1.071 1.018 1.032 1.007 0.986 1.024 1.192
0.173
1.000
Compressive test specimens 0.219 0.213 0.195 0.173 0.164 0.135 0.237 0.216 0.199 0.207 0.212 0.144 0.204
Table 3 Overview of static specimen results. ∗ denotes run-outs, i.e. testing was stopped after the maximum considered number of cycles. Note: Because of an error in the data recording for S02L16, there is no modulus data for this specimen.
0.181
−1.321 −1.485 −1.031 −1.474 −1.463 −1.428 −1.367
gauge length, fibre bundles connect both, top and bottom clamped areas. By this, a unidirectional, fibre-dominated part of the specimen cross-section would be formed. Such a section would exhibit very little stiffness degradation, as common in 0°-oriented unidirectional specimens. The stiffness degradation shown in Fig. 7 can be described by the power law
E = aN
or using the logarithm
log(E ) = log(a)
blog(N )
Stress Amp. (norm.)
S01L09 S01L10 S01L11 S01L12 S01L13 S01L14 S01L15 S01L16 S01L17 S01L18
0.56 0.42 0.42 0.49 0.49 0.49 0.56 0.42 0.56 0.42
S02L11 S02L12 S02L13 S02L14 S02L15 S02L16 S02L17 S02L18 S02L19 S02L20
0.71 0.63 0.56 0.49 0.42 0.35 0.42 0.42 0.49 0.56
Init. Modulus (norm.) 0° specimens
90° specimens
Cycles to Failure
0.21 0.17 0.24 0.25 0.21 0.18 0.21 0.19 0.22 0.19
9,469 23,070 2,000,000* 1,340,000 21,740 248,700 8,262 633,800 17,270 573,200
0.22 0.25 0.25 0.26 0.19 – 0.17 0.31 0.32 0.21
1,508 13,600 145,100 39,820 44,690 2,000,000* 553,300 2,000,000* 2,000,000* 5,258
amplitude. A linear regression line highlights the trend towards lower bvalue at lower stresses. Towards the end of the life of the specimens, above 90% of the fatigue life, the stiffness of the specimens drops and onset of progressive damage is observed. The final normalised modulus can be as low as 20% of the initial value. Fig. 9 shows examples of the final fracture of specimens as recorded by the DIC system. It can be seen that in the specimens at the end of their fatigue life, widespread delamination has occurred and buckling of layers of chips have most likely led to the collapse of the specimens. The fracture zones are outside the clamping and tab area, therefore no failure initiation from the stress conditions in the grip area is observed. In the next section, the component testing will show whether the fatigue life predictions and the stiffness degradation obtained on the specimen level is scalable to the component which is subjected to a more complex load case.
(2)
b
Specimen
(3)
where E is a normalised stiffness, a and b are the degradation coefficient and degradation exponent, respectively and are obtained from data fitting. For a cycle count of one, a can be interpreted as a virtual static value for the stiffness. This virtual value does not include the initial-phase stiffness drop which is not considered in the model. A range of b = 0.05–0.24 in the central fatigue region was obtained from the test data. Values of b in the region of 0.05–0.09 are reported for 45° angle-ply GFRP in [17]. Fig. 8 shows a plot of the b-value for each test specimen which showed degradation over the applied stress
3.2. Component testing For the component testing, results of the quasi-static tensile test are 5
International Journal of Fatigue 131 (2020) 105289
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Fig. 6. Fatigue life S-N regression lines and data points from testing for specimen testing.
presented first, followed by the fatigue test results.
recorded in the second attempt is 5.39 at a displacement of 89 mm. Because of the load cell position above the lateral guidance, in the second attempt, a stick-slip influence can be observed at the start of the test. Fig. 11 shows the area-of-interest at the start of the tensile test and at the first detection of a crack at 22.5 mm displacement of the cylinder, and a normalised load of 1.07. This load is the reference load Fz , r / Fz, m for the subsequent fatigue testing. The colour gradation in the area-of-interest shows the degree of correlation error, with blue the least and red the largest correlation error. Formation of a crack usually occurs in areas of large correlation error. When a crack is formed, correlation is lost in the cracked area (see Fig. 11b).
3.2.1. Tensile test results One component was tested in a quasi-static tensile test. Because of the large displacement in the component testing, the cylinder position transducer was utilised for measuring the deflection, and the load cell was utilised for the force output. The normalised load over displacement plot is shown in Fig. 10. The load is normalised with respect to a nominal maximum load defined by the stress sensitivity K from FE (see Eq. (1)) and the specimen average tensile strength Rm , i.e. Fz , m = K Rm . Initially, no lateral alignment device was used (dashed line). However, for large displacements, the lateral force on the hydraulic cylinder prevented safe operation, and the test was aborted. In a second attempt, the lateral alignment was installed (solid line), and the displacement amplitude could be increased up to 100 mm. Near-linear behaviour is yielded in both tests, and the normalised chord stiffness of the component obtained between 2 and 16 mm displacement, before any damage is observed, gives 0.048 and 0.057 mm−1 for the first and second attempt, respectively. The first discontinuity in the force signal is obtained in the first attempt at a normalised load of approx. 0.78. At this force, the correlation error recorded by the DIC system in the highest stressed area is large, but no crack is formed. A failure-defining crack is found by the DIC system at a normalised load of 1.07, but does not yield a significant discontinuity in the force-displacement diagram. The maximum normalised load
3.2.2. Fatigue test results In the fatigue tests, four components were tested in fully-reversed fatigue tests. Of these, two were tested at 40% of the reference load, and two at 60% of the reference load. Because the load levels are very low, the load cell was repositioned to exclude the stick-slip effect. In Fig. 12, DIC-plots of one area-of-interest of component 2 at the start and after finishing of a test are depicted. In the component testing, failure is defined as the number of cycles at which the first macro-crack, defined with length above 3 mm, is visible in one of the area-of-interest, monitored by the DIC system or the industrial digital camera. The failure-defining crack for this component occurred on the non-DIC side and is shown in Fig. 13. After the crack was detected at 72,000 cycles (Fig. 13b), there was no detectable growth of the crack until the
Fig. 7. Stiffness degradation curves normalised to the cycles and the initial modulus of the specimen. 6
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Fig. 8. Influence of normalised load on the parameter b.
constant load amplitude test was stopped at 835,000 cycles (Fig. 13c). Fig. 12b shows the cracks that have formed on the DIC side up to this cycle count. They are about 2.5 and 1.5 mm long (see also Fig. 17). Plotting the cycles at failure of the components in the normalised specimen S-N diagram gives Fig. 14. The 10% and 90% quantiles of the specimen testing are represented by dashed and solid lines, respectively. All four tested components exhibit failure within the scatter bands of the specimen testing. However, large variation in the fatigue life is recorded. One of the 40% components was declared a run-out and testing was stopped after 2,000,000 cycles without a failure-defining crack. This limit was chosen as it is representative of endurance limits applied in the European automotive sector for suspension and chassis parts, see e.g. [5,6]. The stiffness degradation was considered as the increase in displacement amplitude at constant force amplitude in the fatigue testing. Figs. 15 and 16 show the evolution of the stiffness of two components. The blue lines are the measured stiffness values, and regression lines are drawn in red. Component 4 is the run-out component, whereas for component 1 the test was stopped after 107,000 cycles because of the presence of a failure-defining crack. Generally, there is a significant noise and fluctuations in the measured stiffness, attributed to the controller which adjusts the amplitude, and external influences on the force measurement, e.g. in the guide rails or temperature changes in the environment and component during the testing. In Fig. 16 for component 4, an increase in stiffness over the first approx. 5,000 cycles can be noted. This could be attributed to load re-distribution from matrix to fibres. After this initial phase, all components exhibit a stiffness reduction over cycles. The regression line for the
stiffness evolution is calculated according to the power law in Eq. (3). Table 4 shows the summarised results of the fatigue testing, including cycles to failure and stiffness evolution parameters a and b. It can be seen that on average, lower values for the exponent b are obtained at lower loads. Testing of component 2 continued after a failure-defining crack was recorded at 72,000 cycles. The test at constant load was eventually stopped at 835,000 cycles, and progressive damage testing followed, which is reported by the authors in [23]. Additionally, the relative stiffness value at the end of the cyclic test is given for the components. Component 1 shows the lowest residual stiffness value with 0.78, and for the run-out component, a value of 0.96 is recorded at the end of the test. For component 2, the relative stiffness at 835,000 cycles is given. At 72,000 cycles, the relative stiffness was 0.96. The significance of the degradation exponent b, the degradation coefficient a, and the residual stiffness are discussed and compared to specimen results in the next section. 4. Discussion of results 4.1. Specimen testing results The strength values in static test results in Table 2, are normalised to the average tensile value. There is generally low scatter in the tensile and compressive strength results, but a larger average compressive strength is yielded. This is not uncommon for composite materials, as different failure mechanisms apply. Because of the different gauge
Fig. 9. Fractured specimens in fatigue testing. 7
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Fig. 10. Tensile test results of a pristine component, with and without alignment. The fatigue reference load Fz ,r / Fz, m is indicated by the horizontal dash-dotted line.
Fig. 11. DIC images indicating CE at the start and at the detection of a crack at 22.5 mm displacement and normalised load of 1.07. An arrow points to the crack.
length of tensile and compressive specimens, an additional statistical size influence cannot be ruled out. The significantly lower compressive strength of S01L08 compared to the rest of the sample could originate from an imperfect bonding of two SMC layers and delamination leading to buckling-failure of the specimen. In Table 2, the modulus is given for each specimen. The average tensile modulus is about 15% lower compared to the average compressive modulus. This is potentially because of opening of matrix cracks which could have formed early on near stress concentrations in the material. For the compressive specimens, the strain gauge and DIC measurements are generally in good agreement, however for specimen S02L08, the strain gauge measured stiffness is about 32% lower than
the DIC value. Potentially, this may originate from early onset of delamination of layers at the strain gauges. The modulus for SMC material relies on the measurement device and method because of the heterogenic mesoscale material make-up. Feraboli and co-authors have discussed this topic [3] and compared different techniques to measure the strains, i.e. DIC systems and strain gauges. From their viewpoint, the DIC can give the best insight into the material. Their results are however obtained by strain gauges for most specimens. Results presented in this publication have been relying mostly on full-field DIC measurements, and the additional strain gauges for the compressive quasi-static specimens support the obtained results. Therefore, the reported modulus values are generally an average of the
Fig. 12. DIC images at the start and end of the component 2 cyclic testing. The areas of increased correlation error (red areas in colour print) and crack length are marked by arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 8
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Fig. 13. Crack formation and propagation on the non-DIC side of component 2.
tests were stopped at 2 × 106 cycles. The regression and endurance strength are specific for the tested CFRP SMC material. Despite this lack of generality, the stiffness degradation is a well known phenomenon in reinforced polymers and it is conceivable that similar effects of load dependent stiffness reduction are encountered in many other FRP materials. Furthermore, the results are valid for zero mean stress only, as mean stress effects have not been investigated in this study. Because the damage mechanisms in tensile and compressive loading conditions are fundamentally different for composite materials, a dependency of the stiffness degradation behaviour on loading conditions is not unlikely. Assuming that the matrix material has a significant influence on the shown stiffness reduction, it is worth hypothesizing what a change in matrix material properties would yield in terms of stiffness evolution. Generally it is assumed that a more brittle matrix material performs worse in low-cycle fatigue, but the gap to tough materials becomes narrower at larger cycles. This may mean that also the stiffness degeneration behaves differently. The gradient c1 of the linear regression could potentially be steeper for more brittle material, or a different regression function may be better suited for these matrix materials. The degradation coefficient a can be used to calculate an initial material stiffness. This is not the actual pristine material stiffness, as the regression model does not account for the initial-phase stiffness drop. In the current study, a was obtained from the test data by regression. Having an a priori estimate for the virtual static value of the material may be valuable for damage summation in variable amplitude loading. Assuming a damage parameter D which is described by the reduction in stiffness e.g. in [26] by
full specimen surface measurement. As reported in [3], such a surface measurement represents the volume of flat specimen well as behaviour through the thickness is covered. In fatigue testing, the initial modulus has a large dispersion, which may be from the mesostructure influence in the short-gauge specimens. In the mid-lifetime region, however, the reduction in the stiffness of the specimens in 0° and 90° orientation can be described by a power law, which fits the data well in the normalised cycle range of 0.1 to 0.9. The power law exponent b in Eq. (3) decreases towards lower load amplitudes. This is indicative of a slowing rate of deterioration in the material and can itself be described by a linear law. Fig. 8 shows the linear fitted regression line R with
R = c0 + c1 An
(4)
where An is the normalised stress amplitude, c0 is the static offset, and c1 is the slope. An offset c0 = 0.0174 and a slope c1 = 0.0206 are obtained, and assuming the validity of the approach, an extrapolation of the regression to lower amplitudes can be performed. Then, the stress amplitude where the value of b reaches zero can be described as the endurance strength of the material, because all stiffness reducing fatigue mechanisms cease to progress at this load. For the SMC material considered, the calculated endurance strength is Lendur = 0.87 kN, or 6% of the static tensile strength. This indicates that there is a very low endurance limit in terms of load for this material. A reason for such a low endurance strength might be the inherent stress concentrations at tow ends of SMC material [4]. Furthermore, extrapolating the S-N curve to the endurance strength gives approx. 1012.6 and 1010.8 cycles at the endurance limit for the S-N curves of the 0° and 90° specimens, respectively. Such large endurance limit cycles are generally not obtained in either, laboratory testing or automotive applications. Also, the extrapolation to such large cycle counts is naturally prone to error as the S-N curves are obtained from a relatively small number of specimen, and per definition of run-outs, the
D=1
EN E0
(5)
where EN and E0 are the current and virtual static stiffness, an
Fig. 14. Fatigue life upper and lower (90% and 10%) Quantiles from specimen testing and component cycles to failure. 9
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Fig. 15. Stiffness evolution of component 1, 107,000 cycles at 60%.
Fig. 16. Stiffness evolution of component 4, run-out at load level 40%. Table 4 Overview of component results in fatigue. ∗ Component 2 showed a failure-defining crack at 72,000 cycles. Specimen
Load level (rel. to Fz, r /Fz ,m )
Load level (normalised)
Reference
–
1.00
0.60 0.60 0.40 0.40
0.12 0.12 0.08 0.08
comp comp comp comp
1 2 3 4
Cycles
Degradation exp. b
Degr. coeff. a
Rel. Stiffness end of cycling
0.048 0.023 0.030 0.005
0.1406 0.0923 0.0915 0.0143
0.78 0.91 0.86 0.96
Tensile test specimen Fatigue test specimen 107,000 835,000* 150,000 2,000,000
evaluation of the damage progression in the mid-lifetime range could be performed. However, the start of the progressive failure range has to be further investigated to obtain a critical D-value and formulate a usable end-of-life criterion.
pronounced overall behaviour in terms of stiffness evolution is expected, and stress re-distribution can occur in the material over the fatigue test until failure conditions are fulfilled. However, the first failure-defining crack is detected via the DIC system at a normalised load of 1.07, i.e. only 7% higher than expected from the ultimate tensile stress average from specimen testing. This result gives confidence in the transferability of specimen results to components. A discontinuity in the load-displacement signal at a normalised load of 0.78 has not led to any visible cracks, but could be indicative of start of crack formation at resin-rich areas of the component, originating e.g. from manufacturing. Such effect of
4.2. Component testing results The loading in the component is more complex than in the specimen and not as uniform over the cross-section. Also, stress concentrations exist in the identified areas-of-interest and there, regions of high stress and low stress exist in close vicinity. As a result of this, a less 10
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Fig. 17. Correlation error (CE) and crack length evolution in component 2, the crack appearance on the non-DIC side is indicated as a vertical line.
inhomogeneities are difficult to predict in simulations and zero-defect production is hardly possible when using SMC material. However, the static test showed that the component was tolerant to this discontinuity: the stiffness was not immediately affected and sufficient safety to the maximum strength of the component was given. Cycles to failure is defined as the appearance of a failure-defining crack in the areas-of-interest. Because of the anisotropic material on the meso-scale, and subsequent variation of the properties in the highest stressed area, the cycles to failure have a large dispersion. However, as shown in Fig. 14, the fatigue life of the components were within the 10% and 90% quantiles of the specimen testing. For component 2, the test was prolonged after failure conditions were fulfilled. The subsequent cycling showed a constant log rate of stiffness decrease, indicating that the component can withstand the applied load sufficiently well despite the crack. Fig. 17 shows the CE and crack evolution on the component. The crack on the non-DIC side immediately exceeds 3 mm in length, but does not grow significantly in the following cyclic testing. On the DIC side, no crack appears until 680,000 cycles, however, large areas of high CE are recorded. The ongoing stiffness decrease together with non-DIC side crack growth arrest indicates some re-distribution of load in the material and continuous deterioration (i.e. small-scale damage evolution). A failure criterion based on local crack appearance may therefore lead to overly conservative judgement of component failure. Conceivably, using the global stiffness reduction as the failure criterion could yield more realistic determination of the state of damage in the structure. For the run-out component, the stiffness decrease was minimal, i.e. damage progression per load cycle was very low and thus the long life was gained. It could be argued that despite the small b-value, there is a finite life because of the stiffness reduction, and only when b is zero, infinite life is gained. Similar considerations are reported in [1], where the authors concluded that for the very high-cycle fatigue specimens, all fatigue driving mechanisms almost completely vanished. The test results have also highlighted that fatigue life stiffness degradation analysis in components may be necessary in stiffness-sensitive applications, as significant reductions over the mid-lifetime region are yielded. For components 1 and 3, the relative stiffness drops were 22 % and 14 %, respectively (see Table 4). In the application of the suspension component, design engineers should include such findings in the lifetimeanalysis of their systems.
level and stiffness degradation exponent over the lifetime for specimen and component were found. From the results, the following main findings can be drawn: – Specimen tensile strength corresponds with the stress level at failure-defining fracture in the component. – In fatigue testing, specimens exhibit characteristic stiffness degradation over the lifetime, which can be described by a power law. – The exponent b of the power-law relationship reduces linearly with decreasing specimen load amplitude. – Components also show stiffness degradation in fatigue, and a similar trend to lower b-values for low load amplitudes can be observed. – In the tested component, the presence of a failure-defining crack did not lead to structural failure. – The stiffness degradation could be used to define an endurance limit load for materials and structures. From these findings it can be concluded, that for the considered SMC material, stiffness reduction is more significant in structural damage and durability considerations than single cracks at highly-stressed areas of a component. It could be argued, that a lower stiffness limit gives a better end-of-life definition than the appearance of surface cracks in limited areas. Future work in the field of CFRP SMC fatigue should focus on expanding the presented stiffness degradation law to the initial and final lifetime periods, and deduce fatigue limits for the use of SMC components in terms of residual stiffness or accumulated damage law. Estimating a safe limit of stiffness reduction to ensure fail-safe operation while utilising the damage tolerance of the material will be one of the most challenging tasks connected with fatigue of SMC components in the near future. Acknowledgements The financial support by the Christian Doppler Research Association, the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. References [1] Adam TJ, Horst P. Fatigue damage and fatigue limits of a GFRP angle-ply laminate tested under very high cycle fatigue loading. Int J Fatigue 2017;99:202–14. [2] Bunsell AR, Renard J. Fundamentals of fibre reinforced composite materials. IOP Publishing; 2005. [3] Feraboli P, Peitso E, Cleveland T, Stickler PB. Modulus measurement for prepregbased discontinuous carbon fiber/epoxy systems. J Compos Mater
5. Conclusion In this paper, the experimental results of quasi-static and fatigue testing of CFRP SMC specimens and components are reported. S-N curves and stiffness degradation are shown, and a link between load 11
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S. Sieberer, et al. 2009;43:1947–65. [4] Feraboli P, Peitso E, Cleveland T, Stickler PB, Halpin John C. Notched behavior of prepreg-based discontinuous carbon fiber/epoxy systems. Composites Part A 2009;40(3):289–99. [5] Friedrich HE. Leichtbau in der Fahrzeugtechnik. Springer-Verlag; 2017. [6] Hägele N, Sonsino CM. Structural durability design recommendations for forged automotive aluminium chassis components submitted to spectrum and environmental loadings by the example of a tension strut. Int J Fatigue 2014;69:63–70. [7] Harris B, editor. Fatigue in composites. Cambridge, UK: Woodhead Publishing Limited; 2003. [8] Hörrmann S, Adumitroaie A, Viechtbauer C, Schagerl M. The effect of fiber waviness on the fatigue life of CFRP materials. Int J Fatigue 2016;90:139–47. [9] Ionita A, Weitsman YW. On the mechanical response of randomly reinforced chopped-fibers composites: data and model. Compos Sci Technol 2006;66:2566–79. [10] Li Y, Pimenta S, Singgih J, Ottenwelter C, Nothdurfter S, Schuffenhauer K. Understanding and modelling variability in modulus and strength of tow based discontinuous composites. In: ICCM21, Xi’an, China; 20–25 Aug. 2017, 12p, 2017. [11] Forschungskuratorium Maschinenbau. FKM Richtlinie Rechnerischer Festigkeitsnachweis für Maschinenbauteile. 6. Auflage Darmstadt, Germany: FKM; 2012. [12] Masendorf R, Müller C. Execution and evaluation of cyclic tests at constant load amplitudes - DIN 50100:2016. Fatigue Test 2018;60:961–8. [13] Matschinski W. Radführungen der Strassenfahrzeuge. Berlin Heidelberg: SpringerVerlag; 2007. [14] May M, Hallett SR. Damage initiation in polymer matrix composites under highcycle fatigue loading - a question of definition or a material property? Int J Fatigue 2016;87:59–62. [15] Mortazavian S, Fatemi A. Fatigue behavior and modeling of short fiber reinforced
polymer composites: a literature review. Int J Fatigue 2015;70:297–321. [16] Mortazavian S, Fatemi A. Fatigue of short fiber thermoplastic composites: a review of recent experimental results and analysis. Int J Fatigue 2017;102:171–83. [17] Movahedi-Rad AV, Keller T, Vassilopoulos AP. Fatigue damage in angle-ply gfrp laminates under tension-tension fatigue. Int J Fatigue 2018;109:60–9. [18] Nonn S. Effects of defects and damage localization in carbon fiber reinforced polymer lightweight structures PhD thesis Johannes Kepler University Linz; 2018. [19] Department of Defense. MIL-HDBK-17-3F: Composite Materials Handbook. Polymer matrix composites materials usage, design, and analysis vol. 3. United States: Department of Defense; 2002. [20] Pritchard G, editor. Reinforced plastics durability. Cambridge, UK: Woodhead Publishing Limited; 1999. [21] Quaresimin M, Carraro PA, Maragoni L. Early stage damage in off-axis plies under fatigue loading. Compos Sci Technol 2016;128:147–54. [22] Radaj D, Vormwald M. Ermüdungsfestigkeit: Grundlagen für Ingenieure. Berlin Heidelberg: Springer-Verlag; 2007. [23] Sieberer S, Nonn S, Schagerl M. Experimental study on the stiffness evolution and residual strength of a pre-damaged structural component made from SMC CFRP material. Proceedings of the 13th international conference on damage assessment of structures. Springer; 2020.. p. 827–36. [24] Stokes VK. Random glass mat reinforced thermoplastic composites. Part IV: characterization of the tensile strength. Polym Compos 1990;11:354–67. [25] Thomason JL, Vlug MA, Schipper G, Krikor HGLT. Influence of fibre length and concentration on the properties of GFRP: Part 3. Strength and strain at failure. Composites Part A 1996;27A:1075–84. [26] Wang SS, Chim ES-M. Fatigue damage and degradation in random short-fiber SMC composite. J Compos Mater 1983;17:114–34.
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue behaviour of discontinuous carbon-fibre reinforced specimens and structural parts
T
Stefan Sieberera, , Susanne Nonna,b, Martin Schagerla,b ⁎
a b
Institute of Structural Lightweight Design, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria Christian Doppler Laboratory for Structural Strength Control of Lightweight Constructions, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria
ARTICLE INFO
ABSTRACT
Keywords: Carbon Fibre Reinforce Polymer (CFRP) Sheet Moulding Compound (SMC) Fatigue testing Composites durability Stiffness degradation
Discontinuous fibre reinforced polymers are increasingly used for structural components in automotive applications. In this paper, specimens made from a carbon-fibre sheet moulding compound are tested in constant amplitude fully reversed cyclic fatigue loading. The obtained fatigue lifetime curves are compared against component fatigue test results. In addition, the evolution of modulus in the specimen is compared to the structural stiffness in the component. A power law is used to describe both, degradations of specimen modulus and component stiffness. The exponent of the power law is proportional to the load amplitude, potentially indicating the existence of a fatigue limit.
1. Introduction Over the last decade, fibre reinforced polymer (FRP) components have been increasingly used as lightweight structural components in automotive applications. In the design phase of such components, fatigue life calculations have to be performed to ensure the durability of structural components over the vehicle lifetime. For this, material parameters for all used engineering materials must be available, and their scalability to component level must be given. In metals, mature theories cover the influence of, amongst others, component size, surface roughness, or load pattern (see e.g. [11,22]), and therefore the material can be used to its full potential. However, for composite materials, the transition from specimen to full-scale component has always been performed with greater caution, because (a) in FRP, material degradation over the lifetime has to be considered [7], (b) material defects from manufacturing can have significant effects [8,18], and (c) the damage progression phase has not been sufficiently studied, and sudden failure at the point of damage initiation is often assumed [19]. The first of these influence factors will be the main focus of this paper. For large-scale series production, discontinuous fibre reinforced polymers are often preferred to unidirectionally continuous fibre composites because of their cost-effectiveness whilst retaining some of the weight-saving potential of FRPs. For short-fibre reinforced polymers with fibre lengths up to 6 mm, the material parameters can be assumed as quasi-isotropic from the random orientation of fibre bundles in the part, and global failure criteria from metals can be applied [20]. For
⁎
long-fibre discontinuously reinforced polymers, e.g. sheet moulding compound (SMC) with typical fibre lengths of 15–25 mm [7], the assumption of isotropic material parameters on the macroscale can be maintained [9]. However, large scatter of the material parameters is encountered [10]. Static material parameters for SMC material can be obtained from tensile testing on specimen [9,10,24] yielding elastic moduli and strength values. Also, fatigue test data in discontinuous FRP specimens is widely available, yielding S-N curves which give the probability of crack initiation in the specimen under pulsating or fullyreversed loading (see e.g. [7,20]). Despite efforts, implemented in general Finite Element software, e.g. Abaqus, and dedicated engineering fatigue software tools, e.g. FEMFAT, to calculate the onset of cracks by expanding static failure criteria for one-stage loading and applying Miner’s rule, so far, no satisfyingly precise and general rule for the calculation of fatigue life in composites has been established. Even before the onset of cracks, especially in SMC and short-fibre FRP, significant reduction in the material stiffness can occur. Schulte reported in [20] the difference in the stiffness reduction in tensiletensile fatigue testing of a cross-ply CFRP laminates: non-crimp continuous UD layers, crimped fabric, and short-fibre aligned layers were considered. Three regions of stiffness reduction were identified for all three laminate types: (i) initial-phase large stiffness reduction, (ii) nearconstant stiffness in the mid-lifetime region, and (iii) a large stiffness drop shortly before specimen failure. The underlying mechanism for these reductions in stiffness are different for the three considered phases. Initially, transverse cracking occurs until saturation is reached.
Corresponding author. E-mail address: [email protected] (S. Sieberer).
https://doi.org/10.1016/j.ijfatigue.2019.105289 Received 18 July 2019; Received in revised form 17 September 2019; Accepted 19 September 2019 Available online 08 October 2019 0142-1123/ © 2019 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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This ends the initial phase and in the subsequent mid-lifetime region, longitudinal cracks appear, grow and merge with transversal cracks. In addition, delamination occurs, generally starting from free edges or merged cracks. In the last region, widespread delamination leads to fibre overload and failure of the structure. Schulte notes that the midlifetime region spans from about 10% to 90% of the fatigue lifetime of the specimens in continuous and short fibre UD laminates. For the woven fabric, the last region starts at about half of the specimen lifetime. The stiffness reduction up to the end of the mid-lifetime region is comparatively moderate for the CFRP material, and less than 10% of the initial stiffness is lost. In [7], Caprino reviews studies on discontinuous FRP materials and states that the extent of stiffness reduction is largely governed by the type of fibres, with stiffer carbon fibres exhibiting better fatigue performance and less stiffness degradation compared to glass fibres. No definite conclusion on the influence of fibre length could be drawn from the presented data. However, Thomason et al. [25] showed results where a lower bound of fibre length is given, determined by the minimum length necessary to transfer load into the fibres. The influence of the mean stress on the fatigue behaviour in discontinuous fibre composites has been discussed e.g. in [7,15,16]. There are reportedly two factors contributing to the deterioration of fatigue properties under tensile mean stress, which are the mean stress effect and additionally cyclic creep. Whilst the mean stress effect influences the fatigue life directly by adding a constant loading, creep changes the displacement at zero load over time. In the present study, fully reversing loading conditions were used in order to exclude creep effects and to represent the load conditions in the structural component. Recently, the interest in understanding and modelling stiffness degradation in FRP has been rekindled. Quaresimin et al. [21] investigated the early stage damage of glass-fibre epoxy specimens under shear and showed the microcrack formation under shear loading. For these early stages of fatigue and the mid-lifetime region, Movahedi-Rad and co-workers [17] presented experimental results for stiffness reduction of a glass-fibre FRP angle-ply laminate under tension-tension loading. Significant reduction in modulus were recorded, but the testing did not show the last stage of rapid stiffness deterioration before fracture. Adam and Horst [1] considered very high-cycle fatigue on angleply glass-fibre FRP and showed the reduction in bending stiffness in a four-point bending test. The researchers found that the stiffness degradation was reduced at very low loads and suggested the potential existence of endurance strength for composite material. In discontinuous FRP, Mortazavian and Fatemi [16] investigated the fatigue behaviour under different load and environmental conditions of short glass-fibre thermoplastic composites and derived a simple criterion to obtain fatigue strength from tensile strength of the specimens. However, most of the current research in fatigue of composites is focussed on continuous glass fibre reinforced material, and little progress has been made on understanding fatigue in CFRP SMC material on the specimen level. In addition, to the authors knowledge, no verification on larger structures has been performed so far. It is the aim of this paper to investigate the material degradation in stiffness terms of CFRP SMC material under fatigue loading. S-N curves for fully reversed loading are obtained and a stiffness degradation model is presented. The influence of the load level on stiffness degradation and potential for arresting fatigue mechanisms at low load are discussed. For the same material, component testing is performed for an automotive suspension arm. The loading of the component is usually alternating, as cornering forces in both directions have to be transferred between wheel and chassis by the suspension arm [13]. The resulting cycles-to-failure and stiffness degradation is validated for the components against the specimen data. In an accompanying publication [23] to this paper, the stiffness degradation after crack initiation was studied for one component. The content is organised as follows. Section 2 gives the experimental set-up for specimen and component testing, which is followed by the
Fig. 1. Test set-up for the specimen testing with piston of the hydraulic cylinder, load cell, slide bearings, hydraulic grips, and test specimen.
test results for quasi-static and fatigue testing in Section 3. The discussion of the results is given in Section 4 and is followed by the conclusions in Section 5. 2. Test set-up In this section, the test set-ups for the specimen testing and the component testing are described. The tests were performed at room temperature of T = 24 ± 4 °C. A Zwick-Roell BPS-LH0025 hydraulic cylinder with a nominal force of 25 kN and controlled by a CATS Control Cube system was used in all tests. Fig. 1 shows the test rig configured for specimen testing. The test specimen is fixed with MTS 647 hydraulic wedge grips to cylinder and ground. Lateral motion of the cylinder is minimised by guide rails, thus eliminating lateral forces on the specimens and components in fully-reversed cyclic loading. Lowfriction sliding bearings are used to minimise the effect of stick-slip on the load measurement during the fatigue testing. In component testing, the hydraulic grips were replaced by the mounts for the structure. Strains were recorded by a Correlated Solutions digital image correlation (DIC) system, capable of measuring the full surface on one side of the specimens or an area of the components. For this, a so-called speckle pattern, which is a distribution of black dots on a white background, is applied to the specimens. From the relative position of the speckles, the strain is computed. Because the system comprises two cameras, displacements in 3 dimensions are considered when evaluating strains. In addition to strains, the correlation error is considered in the evaluation of results. Correlation is, in this paper, defined as the match in speckle pattern between a reference picture, taken before the test with no load applied, and a picture taken in the test. The correlation error (CE) is evaluated internally by the DIC software, and increase of the CE indicate potential future crack formation. Loss of correlation in an area of high CE gives an indication of crack initiation and growth. 2.1. Specimen testing In a CFRP SMC fabrication process, continuous fibre strands are chopped onto a moving belt covered by an epoxy resin film [2]. The moving direction of the belt gives a deposition direction. The fibre chips in the epoxy matrix were approx. 25 mm long, and between 8 and 12 mm wide. A number of 3.0 mm thick plates made from layers of SMC sheets aligned to the same deposition direction were provided by an industrial partner. Fig. 2 shows part of the plates with specimen cut at 2
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Fig. 2. Plates with cut and labelled specimen. 0 and 90 degree specimen are shown left and right, respectively.
0° and 90° to the deposition direction. The specimen width is 25 mm, and aluminium end tabs were applied before testing. For the tensile specimens, the gauge length was 110 mm, whilst for all other specimen the gauge length was 20 mm. The test programme presented in Table 1 and comprising quasistatic and cyclic fatigue tests was performed. In the quasi-static tensile testing, the test rig was set to displacement controlled operation with head speed of 2 mm/min for the tensile testing, and 0.5 mm/min for the compressive testing. The cyclic fatigue testing was carried out in force controlled mode with a test frequency of 5 Hz. The DIC system measured strains over the width of the specimen in static tension testing. For compression static testing and fatigue testing, the measurement was taken over the thickness of the specimens. This is because the use of hydraulic grips limited the view on the short specimens to the narrow sides. Additional strain gauges (SG) were applied for static compressive testing on both sides of the specimen to validate the DIC measurements. Furthermore, the two strain gauge signals were used to check for lateral buckling of the whole specimen, which would have led to a significant difference between the two signals. For the calculation of the specimen stiffness, DIC- and SG-obtained strains and the load cell output were utilised.
chosen to reproduce the mounting conditions at joints A and B, and linear static displacement steps simulating the test rig motion were applied. Fig. 4 shows stress field results from this FE analysis, indicating the highest-stressed area on one half of the component. Because of the symmetry of the component, two areas with similarly high loading were found. For monitoring purposes of these areas-of-interest, the aforementioned DIC system was used to measure strains and crack formation on one side of the structure, and an industrial digital camera was positioned to monitor the opposite side as only one DIC system was available. The linear FE analysis gave an indication of the stress maxima in the areas-of-interest for a given displacement amplitude or vertical force component in the hinges. Because of the presence of additional flexible parts, e.g. the bushings, in the experimental set-up, the measured displacement at the hydraulic cylinder cannot be used to estimate the component stiffness. The force measurement, on the other hand, can give a measure of the stress maximum. Introducing the stress sensitivity K as
K=
vM,max
(1)
Fz
with the vertical reaction force at the joints Fz and a max. Mises stress vM,max in the component. The obtained stress sensitivity value can be used to estimate the onset of damage when S-N curves from specimen testing are available. Because of the limited number of parts available for testing, one tensile test and four fatigue tests were performed. Quasi-static tensile testing was done with a displacement controlled set-up at a constant rate of 0.1 mm/s. The fully-reversed fatigue test was performed using load control, and test frequencies in the range of 1.0–1.25 Hz were chosen to avoid component heating. For component 2, where the load controlled mode failed to yield stable operation, the displacement amplitude was adjusted manually to maintain the specified load amplitude. For all specimens, stiffness and damage evolution are evaluated. End-of-life conditions were assessed with both available visual inspection systems. End-of-life of the component is defined as the formation of a crack with a minimum length of 3 mm [14]. Such cracks are
2.2. Component testing The components were made from the same SMC material as the flat specimens, and pressed to obtain the part geometry. A visual inspection was performed to ensure that no significant manufacturing defects were visible on the surface. Fig. 3a shows the component on the test rig. The component is fixed to the ground at joint A, where all degrees-of-freedom are restricted. Joint B is guided in the horizontal plane, and is free to rotate about the pivot axis. Fig. 3b shows how the vertical actuation at B is applied by the force Fz via the hydraulic cylinder, yielding global bending-torsional loading in the component. Prior to testing, a Finite Element (FE) analysis of the component was performed in Abaqus 2017. The model consisted of quadratic tetrahedral elements with an element length of approx. 1.0 mm in highly stressed areas. Boundary conditions were Table 1 Overview of specimens tested. Direction on plate
Test performed
Number of specimens
Cross section (in mm): width × thickness
Specimen gauge length (in mm)
0° 0° 0°
Static Tension Static Compression Fully-rev. Fatigue
5 3 10
25.0 × 3.0 25.0 × 3.0 25.0 × 3.0
110 20 20
90° 90° 90°
Static Tension Static Compression Fully-rev. Fatigue
5 3 10
25.0 × 3.0 25.0 × 3.0 25.0 × 3.0
110 20 20
3
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Fig. 3. Component mounted on the hydraulic test rig: (a) actual set-up, and (b) CAD plot of rig.
Fig. 4. Finite element stress plot of the component under normalised displacement using the boundary conditions of the test rig. The area of highest stress on one side is highlighted by the gradient pattern.
specimen dimensions and normalised to the average static tensile strength Rm , and the strains are obtained from the DIC system. In Table 2, the results of the static tests are summarised. In general, dispersion is low for tensile and compressive loading. The specimens cut in 90° direction exhibit higher strength in tensile and compressive directions, however the moduli is not significantly different for 0° and 90° directions in tension.
referred to in this paper as failure-defining cracks and when such a crack appeared, the test was usually stopped. The stiffness of the component was monitored via a load cell mounted between the top alignment guide and the component, therefore eliminating stick-slip force contribution on the measurement. No influence of a horizontal force component on the vertical force measurement is expected because of internal compensation in the cell. For calculation of stiffness of the structure, the load cell and cylinder position transducer readings were used. For the large amplitude cyclic and static displacements, this gives valid results as parasitic influence of the hydraulic stiffness can be neglected. In the next section, the results for specimen and component testing are presented.
3.1.2. Fatigue test results In Table 3, the load amplitude and cycles-to-failure of the specimens is listed, and Fig. 6 shows the obtained S-N-curves from the data. The regression line is yielded using a least-squares algorithm. The 10% and 90% quantiles are calculated by shifting the test results to a single fictitious load level and assuming a log-normal distribution of the samples [12]. Both, the samples cut at 0° and 90° exhibit large scatter in the data. The difference in gradient and offset of the regressed lines are not significant when checked with a t-test to a 95% confidence level for the two populations. Fig. 7a and b show the stiffness evolution of the 0° and 90° specimens, respectively, with normalised cycles-to-failure and the modulus normalised to the initial values of each specimen. Different classes of normalised stress amplitude An , i.e. Ultra High ( An > 0.60), High (0.60 > An > 0.50 ), Mid (0.50 > An > 0.45), and Low ( An < 0.45) are indicated by different line styles. In both graphs, initially, the stiffness reduces sharply over the first approx. 10% of normalised cycles, followed by a phase of moderate decline, before dropping with a large gradient after about 90% of normalised cycles, signalling the onset of specimen failure. Such a pattern is present in all shown classes of normalised stress amplitude. However, regardless of the stress amplitude, some specimens show no notable degradation over their lifetime. It is perceivable that in these specimens, because of their short
3. Test results 3.1. Specimen testing In this section, the specimen static and fatigue test results are presented. For both test series, 0° and 90° samples were used. Quasi-static specimens were tested in tension and compression. To avoid buckling, short specimens were used in compressive testing. All fatigue tests were performed in fully-reversed cyclic loading conditions, thus eliminating creep influence. Again, short specimens were used because of potential buckling instability. 3.1.1. Static test results Fig. 5a shows the stress-strain plots for the tensile tests in 0° and 90° directions, and Fig. 5b shows stress-strain plots for the compressive tests in 0° and 90° directions. The stresses are calculated using nominal 4
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Fig. 5. Stress-strain plot from the static tensile testing of specimens. Tensile results (left) are obtained from long specimens, and compressive results (right) from short specimens. Table 2 Overview of static specimen results. Moduli are reported from DIC and strain gauges (SG) for compressive specimen. Specimen
Specimen orientation
S01L01 S01L02 S01L03 S01L04 S01L05 S02L01 S02L02 S02L03 S02L04 S02L05
0° 0° 0° 0° 0° 90° 90° 90° 90° 90°
Avg. Tens
–
S01L06 S01L07 S01L08 S02L06 S02L07 S02L08
0° 0° 0° 90° 90° 90°
Avg. Comp.
–
Norm. Modulus ×10−3 DIC SG Tensile test specimens 0.168 0.166 0.168 0.183 0.184 0.189 0.145 0.186 0.140 0.205
T/C Strength (normalised) 0.822 0.815 1.032 1.071 1.018 1.032 1.007 0.986 1.024 1.192
0.173
1.000
Compressive test specimens 0.219 0.213 0.195 0.173 0.164 0.135 0.237 0.216 0.199 0.207 0.212 0.144 0.204
Table 3 Overview of static specimen results. ∗ denotes run-outs, i.e. testing was stopped after the maximum considered number of cycles. Note: Because of an error in the data recording for S02L16, there is no modulus data for this specimen.
0.181
−1.321 −1.485 −1.031 −1.474 −1.463 −1.428 −1.367
gauge length, fibre bundles connect both, top and bottom clamped areas. By this, a unidirectional, fibre-dominated part of the specimen cross-section would be formed. Such a section would exhibit very little stiffness degradation, as common in 0°-oriented unidirectional specimens. The stiffness degradation shown in Fig. 7 can be described by the power law
E = aN
or using the logarithm
log(E ) = log(a)
blog(N )
Stress Amp. (norm.)
S01L09 S01L10 S01L11 S01L12 S01L13 S01L14 S01L15 S01L16 S01L17 S01L18
0.56 0.42 0.42 0.49 0.49 0.49 0.56 0.42 0.56 0.42
S02L11 S02L12 S02L13 S02L14 S02L15 S02L16 S02L17 S02L18 S02L19 S02L20
0.71 0.63 0.56 0.49 0.42 0.35 0.42 0.42 0.49 0.56
Init. Modulus (norm.) 0° specimens
90° specimens
Cycles to Failure
0.21 0.17 0.24 0.25 0.21 0.18 0.21 0.19 0.22 0.19
9,469 23,070 2,000,000* 1,340,000 21,740 248,700 8,262 633,800 17,270 573,200
0.22 0.25 0.25 0.26 0.19 – 0.17 0.31 0.32 0.21
1,508 13,600 145,100 39,820 44,690 2,000,000* 553,300 2,000,000* 2,000,000* 5,258
amplitude. A linear regression line highlights the trend towards lower bvalue at lower stresses. Towards the end of the life of the specimens, above 90% of the fatigue life, the stiffness of the specimens drops and onset of progressive damage is observed. The final normalised modulus can be as low as 20% of the initial value. Fig. 9 shows examples of the final fracture of specimens as recorded by the DIC system. It can be seen that in the specimens at the end of their fatigue life, widespread delamination has occurred and buckling of layers of chips have most likely led to the collapse of the specimens. The fracture zones are outside the clamping and tab area, therefore no failure initiation from the stress conditions in the grip area is observed. In the next section, the component testing will show whether the fatigue life predictions and the stiffness degradation obtained on the specimen level is scalable to the component which is subjected to a more complex load case.
(2)
b
Specimen
(3)
where E is a normalised stiffness, a and b are the degradation coefficient and degradation exponent, respectively and are obtained from data fitting. For a cycle count of one, a can be interpreted as a virtual static value for the stiffness. This virtual value does not include the initial-phase stiffness drop which is not considered in the model. A range of b = 0.05–0.24 in the central fatigue region was obtained from the test data. Values of b in the region of 0.05–0.09 are reported for 45° angle-ply GFRP in [17]. Fig. 8 shows a plot of the b-value for each test specimen which showed degradation over the applied stress
3.2. Component testing For the component testing, results of the quasi-static tensile test are 5
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Fig. 6. Fatigue life S-N regression lines and data points from testing for specimen testing.
presented first, followed by the fatigue test results.
recorded in the second attempt is 5.39 at a displacement of 89 mm. Because of the load cell position above the lateral guidance, in the second attempt, a stick-slip influence can be observed at the start of the test. Fig. 11 shows the area-of-interest at the start of the tensile test and at the first detection of a crack at 22.5 mm displacement of the cylinder, and a normalised load of 1.07. This load is the reference load Fz , r / Fz, m for the subsequent fatigue testing. The colour gradation in the area-of-interest shows the degree of correlation error, with blue the least and red the largest correlation error. Formation of a crack usually occurs in areas of large correlation error. When a crack is formed, correlation is lost in the cracked area (see Fig. 11b).
3.2.1. Tensile test results One component was tested in a quasi-static tensile test. Because of the large displacement in the component testing, the cylinder position transducer was utilised for measuring the deflection, and the load cell was utilised for the force output. The normalised load over displacement plot is shown in Fig. 10. The load is normalised with respect to a nominal maximum load defined by the stress sensitivity K from FE (see Eq. (1)) and the specimen average tensile strength Rm , i.e. Fz , m = K Rm . Initially, no lateral alignment device was used (dashed line). However, for large displacements, the lateral force on the hydraulic cylinder prevented safe operation, and the test was aborted. In a second attempt, the lateral alignment was installed (solid line), and the displacement amplitude could be increased up to 100 mm. Near-linear behaviour is yielded in both tests, and the normalised chord stiffness of the component obtained between 2 and 16 mm displacement, before any damage is observed, gives 0.048 and 0.057 mm−1 for the first and second attempt, respectively. The first discontinuity in the force signal is obtained in the first attempt at a normalised load of approx. 0.78. At this force, the correlation error recorded by the DIC system in the highest stressed area is large, but no crack is formed. A failure-defining crack is found by the DIC system at a normalised load of 1.07, but does not yield a significant discontinuity in the force-displacement diagram. The maximum normalised load
3.2.2. Fatigue test results In the fatigue tests, four components were tested in fully-reversed fatigue tests. Of these, two were tested at 40% of the reference load, and two at 60% of the reference load. Because the load levels are very low, the load cell was repositioned to exclude the stick-slip effect. In Fig. 12, DIC-plots of one area-of-interest of component 2 at the start and after finishing of a test are depicted. In the component testing, failure is defined as the number of cycles at which the first macro-crack, defined with length above 3 mm, is visible in one of the area-of-interest, monitored by the DIC system or the industrial digital camera. The failure-defining crack for this component occurred on the non-DIC side and is shown in Fig. 13. After the crack was detected at 72,000 cycles (Fig. 13b), there was no detectable growth of the crack until the
Fig. 7. Stiffness degradation curves normalised to the cycles and the initial modulus of the specimen. 6
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Fig. 8. Influence of normalised load on the parameter b.
constant load amplitude test was stopped at 835,000 cycles (Fig. 13c). Fig. 12b shows the cracks that have formed on the DIC side up to this cycle count. They are about 2.5 and 1.5 mm long (see also Fig. 17). Plotting the cycles at failure of the components in the normalised specimen S-N diagram gives Fig. 14. The 10% and 90% quantiles of the specimen testing are represented by dashed and solid lines, respectively. All four tested components exhibit failure within the scatter bands of the specimen testing. However, large variation in the fatigue life is recorded. One of the 40% components was declared a run-out and testing was stopped after 2,000,000 cycles without a failure-defining crack. This limit was chosen as it is representative of endurance limits applied in the European automotive sector for suspension and chassis parts, see e.g. [5,6]. The stiffness degradation was considered as the increase in displacement amplitude at constant force amplitude in the fatigue testing. Figs. 15 and 16 show the evolution of the stiffness of two components. The blue lines are the measured stiffness values, and regression lines are drawn in red. Component 4 is the run-out component, whereas for component 1 the test was stopped after 107,000 cycles because of the presence of a failure-defining crack. Generally, there is a significant noise and fluctuations in the measured stiffness, attributed to the controller which adjusts the amplitude, and external influences on the force measurement, e.g. in the guide rails or temperature changes in the environment and component during the testing. In Fig. 16 for component 4, an increase in stiffness over the first approx. 5,000 cycles can be noted. This could be attributed to load re-distribution from matrix to fibres. After this initial phase, all components exhibit a stiffness reduction over cycles. The regression line for the
stiffness evolution is calculated according to the power law in Eq. (3). Table 4 shows the summarised results of the fatigue testing, including cycles to failure and stiffness evolution parameters a and b. It can be seen that on average, lower values for the exponent b are obtained at lower loads. Testing of component 2 continued after a failure-defining crack was recorded at 72,000 cycles. The test at constant load was eventually stopped at 835,000 cycles, and progressive damage testing followed, which is reported by the authors in [23]. Additionally, the relative stiffness value at the end of the cyclic test is given for the components. Component 1 shows the lowest residual stiffness value with 0.78, and for the run-out component, a value of 0.96 is recorded at the end of the test. For component 2, the relative stiffness at 835,000 cycles is given. At 72,000 cycles, the relative stiffness was 0.96. The significance of the degradation exponent b, the degradation coefficient a, and the residual stiffness are discussed and compared to specimen results in the next section. 4. Discussion of results 4.1. Specimen testing results The strength values in static test results in Table 2, are normalised to the average tensile value. There is generally low scatter in the tensile and compressive strength results, but a larger average compressive strength is yielded. This is not uncommon for composite materials, as different failure mechanisms apply. Because of the different gauge
Fig. 9. Fractured specimens in fatigue testing. 7
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Fig. 10. Tensile test results of a pristine component, with and without alignment. The fatigue reference load Fz ,r / Fz, m is indicated by the horizontal dash-dotted line.
Fig. 11. DIC images indicating CE at the start and at the detection of a crack at 22.5 mm displacement and normalised load of 1.07. An arrow points to the crack.
length of tensile and compressive specimens, an additional statistical size influence cannot be ruled out. The significantly lower compressive strength of S01L08 compared to the rest of the sample could originate from an imperfect bonding of two SMC layers and delamination leading to buckling-failure of the specimen. In Table 2, the modulus is given for each specimen. The average tensile modulus is about 15% lower compared to the average compressive modulus. This is potentially because of opening of matrix cracks which could have formed early on near stress concentrations in the material. For the compressive specimens, the strain gauge and DIC measurements are generally in good agreement, however for specimen S02L08, the strain gauge measured stiffness is about 32% lower than
the DIC value. Potentially, this may originate from early onset of delamination of layers at the strain gauges. The modulus for SMC material relies on the measurement device and method because of the heterogenic mesoscale material make-up. Feraboli and co-authors have discussed this topic [3] and compared different techniques to measure the strains, i.e. DIC systems and strain gauges. From their viewpoint, the DIC can give the best insight into the material. Their results are however obtained by strain gauges for most specimens. Results presented in this publication have been relying mostly on full-field DIC measurements, and the additional strain gauges for the compressive quasi-static specimens support the obtained results. Therefore, the reported modulus values are generally an average of the
Fig. 12. DIC images at the start and end of the component 2 cyclic testing. The areas of increased correlation error (red areas in colour print) and crack length are marked by arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 8
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Fig. 13. Crack formation and propagation on the non-DIC side of component 2.
tests were stopped at 2 × 106 cycles. The regression and endurance strength are specific for the tested CFRP SMC material. Despite this lack of generality, the stiffness degradation is a well known phenomenon in reinforced polymers and it is conceivable that similar effects of load dependent stiffness reduction are encountered in many other FRP materials. Furthermore, the results are valid for zero mean stress only, as mean stress effects have not been investigated in this study. Because the damage mechanisms in tensile and compressive loading conditions are fundamentally different for composite materials, a dependency of the stiffness degradation behaviour on loading conditions is not unlikely. Assuming that the matrix material has a significant influence on the shown stiffness reduction, it is worth hypothesizing what a change in matrix material properties would yield in terms of stiffness evolution. Generally it is assumed that a more brittle matrix material performs worse in low-cycle fatigue, but the gap to tough materials becomes narrower at larger cycles. This may mean that also the stiffness degeneration behaves differently. The gradient c1 of the linear regression could potentially be steeper for more brittle material, or a different regression function may be better suited for these matrix materials. The degradation coefficient a can be used to calculate an initial material stiffness. This is not the actual pristine material stiffness, as the regression model does not account for the initial-phase stiffness drop. In the current study, a was obtained from the test data by regression. Having an a priori estimate for the virtual static value of the material may be valuable for damage summation in variable amplitude loading. Assuming a damage parameter D which is described by the reduction in stiffness e.g. in [26] by
full specimen surface measurement. As reported in [3], such a surface measurement represents the volume of flat specimen well as behaviour through the thickness is covered. In fatigue testing, the initial modulus has a large dispersion, which may be from the mesostructure influence in the short-gauge specimens. In the mid-lifetime region, however, the reduction in the stiffness of the specimens in 0° and 90° orientation can be described by a power law, which fits the data well in the normalised cycle range of 0.1 to 0.9. The power law exponent b in Eq. (3) decreases towards lower load amplitudes. This is indicative of a slowing rate of deterioration in the material and can itself be described by a linear law. Fig. 8 shows the linear fitted regression line R with
R = c0 + c1 An
(4)
where An is the normalised stress amplitude, c0 is the static offset, and c1 is the slope. An offset c0 = 0.0174 and a slope c1 = 0.0206 are obtained, and assuming the validity of the approach, an extrapolation of the regression to lower amplitudes can be performed. Then, the stress amplitude where the value of b reaches zero can be described as the endurance strength of the material, because all stiffness reducing fatigue mechanisms cease to progress at this load. For the SMC material considered, the calculated endurance strength is Lendur = 0.87 kN, or 6% of the static tensile strength. This indicates that there is a very low endurance limit in terms of load for this material. A reason for such a low endurance strength might be the inherent stress concentrations at tow ends of SMC material [4]. Furthermore, extrapolating the S-N curve to the endurance strength gives approx. 1012.6 and 1010.8 cycles at the endurance limit for the S-N curves of the 0° and 90° specimens, respectively. Such large endurance limit cycles are generally not obtained in either, laboratory testing or automotive applications. Also, the extrapolation to such large cycle counts is naturally prone to error as the S-N curves are obtained from a relatively small number of specimen, and per definition of run-outs, the
D=1
EN E0
(5)
where EN and E0 are the current and virtual static stiffness, an
Fig. 14. Fatigue life upper and lower (90% and 10%) Quantiles from specimen testing and component cycles to failure. 9
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Fig. 15. Stiffness evolution of component 1, 107,000 cycles at 60%.
Fig. 16. Stiffness evolution of component 4, run-out at load level 40%. Table 4 Overview of component results in fatigue. ∗ Component 2 showed a failure-defining crack at 72,000 cycles. Specimen
Load level (rel. to Fz, r /Fz ,m )
Load level (normalised)
Reference
–
1.00
0.60 0.60 0.40 0.40
0.12 0.12 0.08 0.08
comp comp comp comp
1 2 3 4
Cycles
Degradation exp. b
Degr. coeff. a
Rel. Stiffness end of cycling
0.048 0.023 0.030 0.005
0.1406 0.0923 0.0915 0.0143
0.78 0.91 0.86 0.96
Tensile test specimen Fatigue test specimen 107,000 835,000* 150,000 2,000,000
evaluation of the damage progression in the mid-lifetime range could be performed. However, the start of the progressive failure range has to be further investigated to obtain a critical D-value and formulate a usable end-of-life criterion.
pronounced overall behaviour in terms of stiffness evolution is expected, and stress re-distribution can occur in the material over the fatigue test until failure conditions are fulfilled. However, the first failure-defining crack is detected via the DIC system at a normalised load of 1.07, i.e. only 7% higher than expected from the ultimate tensile stress average from specimen testing. This result gives confidence in the transferability of specimen results to components. A discontinuity in the load-displacement signal at a normalised load of 0.78 has not led to any visible cracks, but could be indicative of start of crack formation at resin-rich areas of the component, originating e.g. from manufacturing. Such effect of
4.2. Component testing results The loading in the component is more complex than in the specimen and not as uniform over the cross-section. Also, stress concentrations exist in the identified areas-of-interest and there, regions of high stress and low stress exist in close vicinity. As a result of this, a less 10
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Fig. 17. Correlation error (CE) and crack length evolution in component 2, the crack appearance on the non-DIC side is indicated as a vertical line.
inhomogeneities are difficult to predict in simulations and zero-defect production is hardly possible when using SMC material. However, the static test showed that the component was tolerant to this discontinuity: the stiffness was not immediately affected and sufficient safety to the maximum strength of the component was given. Cycles to failure is defined as the appearance of a failure-defining crack in the areas-of-interest. Because of the anisotropic material on the meso-scale, and subsequent variation of the properties in the highest stressed area, the cycles to failure have a large dispersion. However, as shown in Fig. 14, the fatigue life of the components were within the 10% and 90% quantiles of the specimen testing. For component 2, the test was prolonged after failure conditions were fulfilled. The subsequent cycling showed a constant log rate of stiffness decrease, indicating that the component can withstand the applied load sufficiently well despite the crack. Fig. 17 shows the CE and crack evolution on the component. The crack on the non-DIC side immediately exceeds 3 mm in length, but does not grow significantly in the following cyclic testing. On the DIC side, no crack appears until 680,000 cycles, however, large areas of high CE are recorded. The ongoing stiffness decrease together with non-DIC side crack growth arrest indicates some re-distribution of load in the material and continuous deterioration (i.e. small-scale damage evolution). A failure criterion based on local crack appearance may therefore lead to overly conservative judgement of component failure. Conceivably, using the global stiffness reduction as the failure criterion could yield more realistic determination of the state of damage in the structure. For the run-out component, the stiffness decrease was minimal, i.e. damage progression per load cycle was very low and thus the long life was gained. It could be argued that despite the small b-value, there is a finite life because of the stiffness reduction, and only when b is zero, infinite life is gained. Similar considerations are reported in [1], where the authors concluded that for the very high-cycle fatigue specimens, all fatigue driving mechanisms almost completely vanished. The test results have also highlighted that fatigue life stiffness degradation analysis in components may be necessary in stiffness-sensitive applications, as significant reductions over the mid-lifetime region are yielded. For components 1 and 3, the relative stiffness drops were 22 % and 14 %, respectively (see Table 4). In the application of the suspension component, design engineers should include such findings in the lifetimeanalysis of their systems.
level and stiffness degradation exponent over the lifetime for specimen and component were found. From the results, the following main findings can be drawn: – Specimen tensile strength corresponds with the stress level at failure-defining fracture in the component. – In fatigue testing, specimens exhibit characteristic stiffness degradation over the lifetime, which can be described by a power law. – The exponent b of the power-law relationship reduces linearly with decreasing specimen load amplitude. – Components also show stiffness degradation in fatigue, and a similar trend to lower b-values for low load amplitudes can be observed. – In the tested component, the presence of a failure-defining crack did not lead to structural failure. – The stiffness degradation could be used to define an endurance limit load for materials and structures. From these findings it can be concluded, that for the considered SMC material, stiffness reduction is more significant in structural damage and durability considerations than single cracks at highly-stressed areas of a component. It could be argued, that a lower stiffness limit gives a better end-of-life definition than the appearance of surface cracks in limited areas. Future work in the field of CFRP SMC fatigue should focus on expanding the presented stiffness degradation law to the initial and final lifetime periods, and deduce fatigue limits for the use of SMC components in terms of residual stiffness or accumulated damage law. Estimating a safe limit of stiffness reduction to ensure fail-safe operation while utilising the damage tolerance of the material will be one of the most challenging tasks connected with fatigue of SMC components in the near future. Acknowledgements The financial support by the Christian Doppler Research Association, the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. References [1] Adam TJ, Horst P. Fatigue damage and fatigue limits of a GFRP angle-ply laminate tested under very high cycle fatigue loading. Int J Fatigue 2017;99:202–14. [2] Bunsell AR, Renard J. Fundamentals of fibre reinforced composite materials. IOP Publishing; 2005. [3] Feraboli P, Peitso E, Cleveland T, Stickler PB. Modulus measurement for prepregbased discontinuous carbon fiber/epoxy systems. J Compos Mater
5. Conclusion In this paper, the experimental results of quasi-static and fatigue testing of CFRP SMC specimens and components are reported. S-N curves and stiffness degradation are shown, and a link between load 11
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