- Email: [email protected]
Analysis of fatigue behaviour of notched specimens made of fibreglass reinforced polyamide by means of a cohesive model
Polymer Testing 64 (2017) 337–344
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Material Behaviour
Analysis of fatigue behaviour of notched specimens made of fibreglass reinforced polyamide by means of a cohesive model
MARK
J.A. Casado, F. Gutiérrez-Solana, I. Carrascal, S. Diego, D. Ferreño∗ LADICIM (Laboratory of Science and Engineering of Materials), University of Cantabria, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Av. Los Castros 44, 39005 Santander, Spain
A R T I C L E I N F O
A B S T R A C T
Keywords: Reinforced polyamide Notch Fatigue Crazing Cohesive stress
Fatigue tests until fracture of five notched specimens of short glass fibre reinforced polyamide, with a humidity of 2.5%, were carried out at 23, 28, 33, 38 and 43 °C. A correlation between the environmental temperature and the number of cycles to failure was established. Three different regions of strain were observed, namely, transient, steady-state and pre-failure. Strain and strain-rate during the creep-fatigue process revealed the existence of non-temperature dependent critical strains between these regions. The fractographic study performed after failure suggested the suitability of describing the stress distribution in the remnant ligament through a cohesive model. This is based on the observed fact that, at the crack tip, the matrix and the fibres debond, giving rise to crazing mechanisms so that the ultimate bearing ability of the material relies on the matrix. The calculations involved in the cohesive model were based on the information provided by the fractographic study and the realtime measurements of the crack growth by means of an infrared thermographic camera. Based on this methodology, the cohesive stress of the material was estimated. In a last stage, the surface roughness of the samples was determined after being tested, revealing a reliable correlation between the roughness and the fracture micromechanisms undergone by the underlying material. This correlation makes it possible to use the surface roughness of an in-service component as a parameter to evaluate the level of microstructural damage that it has experienced.
1. Introduction and aim Short glass fibre reinforced polyamide (sgf-PA) is a thermoplastic engineering material which is injected to form technical parts to be used under demanding conditions. The insulating angled guide plates of high-speed railway fastenings are a good example of where this material is employed. These components guarantee the performance of the railway fastening system, ensuring the maintenance of the rail gauge. Fig. 1(a) shows a sketch of the Vossloh W14 railway fastening system, Fig. 1(b) its constitutive parts and Fig. 1(c) a picture of an angled plate. There are currently thousands of kilometers of high-speed lines in the world employing millions of angled guide plates, such as the one shown in Fig. 1. The experience accumulated after years of use shows that this kind of component often undergoes in-service failure [1,2] due to the loads they are subjected to, combined with the environmental conditions, particularly temperature. The fracture of angled plates is a serious drawback, with economic as well as security related consequences. An increase in the number of faults of this type of components is expected as the demands of use intensify. The 453 km long
∗
Corresponding author. E-mail address: [email protected] (D. Ferreño).
http://dx.doi.org/10.1016/j.polymertesting.2017.10.021 Received 18 September 2017; Accepted 26 October 2017 Available online 31 October 2017 0142-9418/ © 2017 Elsevier Ltd. All rights reserved.
Haramain High-Speed Rail project, linking the cities of Medina and Mecca across the Arabian desert, scheduled for 2018, is a good example of new in-service conditions beyond the current operational limits. Fig. 1(c) allows the intricate geometry of the plate, its abrupt changes of section and the central hole, to be appreciated. Without any doubt, all these features act as stress concentrators, similar to notches, facilitating the initiation and propagation of fatigue cracks. Several previous studies have addressed the phenomenon of fatigue in sgf-PA components [3–7]. In particular, some of the authors of this paper have studied this subject in depth. For instance, Casado and Solana [8] analysed the evolution of failure micromechanisms in this material when subjected to fatigue as well as the interrelation between fatigue and creep, which depends on the crack tip local temperature. In addition, they determined the surface damage generated by the fatigue loading on the sgf-PA using the surface roughness as an indicative parameter. The objectives of this study can be grouped into two areas. On the one hand, from a more scientific perspective, the fatigue crack propagation in the sgf-PA material in the presence of stress concentrators was
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
Fig. 1. Picture of the high-speed railway fastening system (a), breakdown with the constitutive elements (b) and detail photograph of an angled guide plate (bottom view).
investigated. In order to provide a conservative description, the extreme case has been examined, consisting of analysing the response of notched components. Fatigue tests were carried out at a range of temperatures between 23 °C and 43 °C, which is considered to be representative of the most demanding in-service conditions for these plates. After identifying the failure micromechanisms in the material, a mechanical model, based on the cohesive stress method, was developed, in order to quantify the stress state both during the propagation and in the critical situation. At the same time, from a more practical perspective, the surface roughness of the specimens has been correlated with the level of damage undergone by the sgf-PA due to propagation; this correlation allows the level of damage in actual components under in-service conditions to be obtained from a simple roughness test. To the best of these authors' knowledge, no previous research has analysed the subjects addressed by the present paper. From our point of view, the information included in this study may be valuable to designers and practitioners, particularly in view of the shortage of specific research focused on the properties of sgf-PA. After the material and experimental methods are described in Sections 2 and 3, the experimental results are introduced and discussed in Section 4. In Section 4.1, the results of the fatigue tests are presented while in Section 4.2 a micromechanical description of the process of failure, based on the fractographic study, is developed. The cohesive model is introduced in Section 4.3 and, in Section 4.4, a correlation between the surface roughness of the specimens as the fatigue damage progresses and the failure micromechanisms in the material is established. Finally, Section 5 presents a discussion of the results obtained in this study.
Fig. 2. Standard tensile notched specimen (dimensions in mm).
were notched (a = 2 mm, see Fig. 2) by pressing a razor blade. The humidity of this hygroscopic material was kept at 2.5%. A total of five fatigue tests were performed.
3. Experimental and analytical methods Stress-controlled tensile fatigue tests were carried out between a maximum stress level of 41.7 MPa and a minimum of 8.3 MPa (in a previous contribution [8], it was shown that these stresses correspond, respectively, to 25% and 5% of the dynamic fracture stress of the material at room temperature on un-notched specimens). A universal INSTRON 8501 hydraulic machine with a dynamic loading capacity of 100 kN was used. The loads were applied with a frequency of 5 Hz, following the procedure described in ASTM D7791 [10]. Due to the thermoplastic nature of the material, the five fatigue tests were carried out in an environmental chamber at temperatures of 23, 28, 33, 38 and 43 °C, respectively (one test at each temperature). Each specimen was maintained at the testing temperature for 45 min before starting the test, in order to guarantee its thermal homogeneity. Obtaining the fatigue propagation rate requires the continuous measurement of the crack length. This measurement is usually carried out using methods such as the electric potential drop or by means of correlations between the crack length and the compliance of the specimen [11]. Bearing in mind that, for polymers, the crack tip undergoes a temperature rise due to the stress concentration and the generation and growth of a plastic zone, the crack growth can be reliably determined using infrared thermographic techniques. In a previous paper [12], this methodology was validated by comparing its results with conventional measurement techniques. This very same technique has been used in this research; thus, temperature measurements were performed with an IRISYS (InfraRed Integrated SYStems) universal thermal imager infrared thermographic camera, type IR 1011 with a resolution of 128x128, and the IRISYS 1011 imager software. During the tests, the following parameters were continuously recorded:
2. Material The worldwide production of PA 6.6 is, roughly, 2 million tons per year, over half of the production being used in the form of fibre-reinforced PA. This material is frequently used when high mechanical strength, rigidity, good stability under heat and/or chemical resistance are required. It is widely employed for manufacturing structural parts, mostly by injection molding. As stated above, sgf-PA is the constitutive material of the angled guide plates used in high speed railway fastening systems all around the world. The fatigue tests of this study were carried out on standard tensile specimens (according to EN-ISO 527 [9]), with a nominal thickness of 4 mm (see the sketch in Fig. 2), manufactured in PA 6.6 reinforced with short fibre glass (35% wt). The specimens were injected by means of an Arburg ALLROUNDER 221 K injection molding machine, with a clamping force of 350 kN. This injector machine is equipped with a twocavities steel mold to fabricate EN ISO 527 standard tensile specimens. Following a general recommendation, fatigue precracking was avoided because it can be very time-consuming since the loading frequency must be kept low in order to minimise hysteresis heating, which may in turn introduce residual stresses at the crack tip. Rather, the specimens 338
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
• Longitudinal strain, measured by means of an extensometer with a clip gauge of 12.5 mm and a travel of ± 5 mm. • Surface temperature of the specimen, determined with the thermographic camera. • Load range, provided by the load cell of the testing machine. • Number of fatigue cycles up to fracture. After the fatigue tests, the fracture surface of the specimens was examined by means of a scanning electron microscope (SEM), model JEOL JSM 5800-LV device, equipped with a microanalyser EDAX OXFORD link eXL. In addition, the roughness of the lateral surface of the specimens, in the proximity of the plane of fracture, was determined using a roughness tester Pherthen, Pherthometer S3P model. The SEM and roughness tester provided valuable information for the analytical cohesive model developed to describe the state during the tests. Regarding the analysis of data, several statistical methods were used. The means of distributions were compared using t-tests, obtaining the p-value (which represents the probability that, when the null hypothesis is true -equal means-, the sample mean difference between two compared groups would be the same as the actual observed results). Moreover, simple linear regression was applied, using the least squares approach. The p-values of the slopes of the linear models were determined (in this case, the p-value tests the null hypothesis that the coefficient is equal to zero, which means that changes in the explanatory variable do not induce changes in the response variable). The level of significance was chosen to be 0.05 in all cases.
Fig. 4. Surface temperature (T) at the crack tip as a function of the number of cycles (N) for the five specimens subjected to fatigue.
4. Experimental results 4.1. Fatigue tests As an arbitrary example, Fig. 3 shows the evolution of the strain (continuous line, left vertical axis) and strain rate (discontinuous line, right vertical axis) as a function of the number of fatigue cycles applied, for the test corresponding to an environmental temperature of 23 °C. It is worth noting that the features present in these graphs are common to the rest of tests/temperatures. In addition, the evolution of surface temperature at the crack tip of the five fatigue tests is represented in Fig. 4. As shown in Fig. 4, as the test evolves, the temperature of the specimen increases slightly, approximately by 5 °C during the test. Moreover, there is a clear correlation between the environmental temperature and the number of cycles to failure, as can be seen in Fig. 5: the higher the temperature, the lower the fatigue lifetime. As shown by Casado et al. [13], under these conditions of stress and temperature, the sgf-PA undergoes coupling between the fatigue and the creep processes. Fig. 3 allows three different regions to be
Fig. 5. Number of cycles to failure as a function of the environmental temperature.
distinguished in the strain and strain rate plots. Region I corresponds to the transient creep-fatigue stage, characterised by a decrease in the strain rate. In Region II, the steady state regime is reached and the material deforms at a constant rate. The final stage, Region III, is characterised by an increasing strain rate preceding the imminent fracture of the specimen. The transition strain levels between these regions were measured, and are represented in Fig. 6 as a function of the external temperature. The figure suggests that these strains correspond to critical values presumably dependent on the material, but not on the temperature.
Fig. 3. Strain (ε) and strain rate (dε/dN) vs. number of cycles (N). Test corresponding to an environmental temperature of 23 °C.
Fig. 6. Transition strains between regions I-II and II-III.
339
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
According to the data, εI-II = 0.009 ± 0.0008 and εII-III = 0.012 ± 0.0008. In order to prove the independency between εI-II and εII-III and the external temperature, a series of statistical procedures were applied. First, linear regression was used (εI-II vs. T and εII-III vs. T, respectively), focusing on the p-values of the slopes of the models. In both cases, these slopes were positive (this fact is suggested by the distribution of points in Fig. 6). For the regression between εI-II (dependant variable) and T (explanatory variable), p = 0.1279 and for εII-III and T, p = 0.0791. Therefore, according to these results, there is not enough information, at the α = 0.05 significance level, to reject the null hypothesis, which states that the slopes are zero. In other words, for practical purposes, it can be assumed that neither εI-II nor εII-III are influenced by the temperature; the effect derived from the scatter of points is stronger than the influence of the explanatory variable. In addition, the statistical ttest was used to compare the means of the two populations (εI-II and εIIIII), obtaining the p-value = 0.0014. Thus, the null hypothesis (equal means) must be rejected at the 0.05 significance level. These calculations support the statement that there is a defined limit between εI-II and εII-III, regardless of the temperature, this limit being εlimit≈0.011. This result does not imply that the temperature is not playing a role in the cracking process. On the contrary, the temperature substantially reduces the number of cycles needed to reach each of the transition strains, εI-II and εII-III, respectively, as well as the time to failure, as clearly shown by Fig. 4 and Fig. 5.
•
•
material shows a smooth appearance. The fractography included in Fig. 7 shows the border between the notch and the initial propagation surface. Zone 2 is characterised by the ductile behaviour of the matrix and the presence of crazing mechanisms. As can be seen in Fig. 7, the matrix shows a dimpled appearance because of its plastic response. Crazes (highly localised deformations that lead to void formation) appear because of the demanding local strain conditions, near the tip of the growing crack. The inability of the material to release heat due to its low thermal conductivity is another factor that facilitates the plasticity as well as the nucleation and creation of crazes. Once the critical crack length is reached, the remaining ligament is unable to withstand the applied forces. Then, the final fracture takes place, which corresponds to the brittle surface that can be appreciated in Zone 3. Note the multifaceted surface of the matrix, typical when the material responds in a brittle manner.
Every specimen was analysed by SEM after being tested to failure. Thus, the size of the three regions described above could be measured. The results of the fractographic study are a consequence of the micromechanisms that develop during fracture process of the sgf-PA. The sketch in Fig. 8 explains the interaction between the matrix and the fibres as the local stress increases (from left to right in the figure). The debonding between the matrix and the fibres starts at the ends of the fibres since this is a location of shear stress concentration. For this reason, debonding may occur even for low applied stress (σ1 in the figure). As the applied stress increases (σ2), new debonding appear, even in the shaft region of the fibres. The local stress makes the matrix yield by crazing which, on the macroscopic level, appears as a stresswhitened region due to a low refractive index [11]. Void coalescence, as for σ3 in Fig. 8, promotes the formation of cracks. In this situation, the loading ability of the specimen rests on the matrix bridges because the bonding between the matrix and the fibres becomes negligible. For this reason, fracture takes place in a zone where the failure of the individual fibrils occurs. Consequently, in this region, the stress state in the matrix corresponds to its cohesive stress. This process is unstable if, when a fibril fails, the redistributed stress is sufficient to break one or
4.2. Fractographic study The SEM examination of the fracture surfaces of the specimens revealed the existence of three different regions. Fig. 7 shows a diagram of the typical cross section of a broken specimen, where the relevant zones are numbered from left to right. A panel of SEM fractographies that allows the morphologies present in each of the three regions to be identified is included in the figure. The main features are described next:
• Zone 1 corresponds to the notch. In this zone, the surface of the
Fig. 7. Schematic description of the regions present on a typical fracture surface.
340
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
the fibres remains intact and both can work collaboratively. For this reason, the stress profile is linear. The stress state in the cross section must balance the applied external stress, σext, which implies the equilibrium in forces and momenta. Some notation is now introduced for the sake of simplicity. Fc is the total force of the cohesive region, which follows equation (1) (‘B’ being the thickness of the specimen). The total force in the linear region, FL, is broken down into two components, which correspond to the rectangular (FLR) and the triangular (FLT) parts of the stress profile, see equation (2). (1)
Fc = σc Lc B
{
FL = FLR + FLT = σ [W − (a + Lc )] +
1 (σc − σ )[W − (a + Lc )] B 2
}
(2) Now, the condition of force equilibrium can be expressed as in equation (3):
Fc + FL = σext WB
(3)
The equilibrium of momenta will be established with respect to the centroid of the cross section (the loading line of the external force), point ‘O’ in the figure. The distances dc, dLR and dLT, represented in Fig. 9, can be obtained, as in equations (4)–(6), by simple geometric manipulation.
W L −a− c 2 2
(4)
dLR =
1 (a + Lc ) 2
(5)
dLS =
2 W (a + Lc ) − 3 6
(6)
dc =
Fig. 8. Sketch showing the different stages of the failure in sgf-PA.
more neighboring fibrils. Then, the brittle failure of the remaining cross section takes place. The multifaceted appearance of the matrix, as in the last fractography in Fig. 7, is the main feature that allows this type of fracture to be identified. 4.3. Estimation of the cohesive stress state
Therefore, the balance of momenta is expressed as in equation (7):
Fc dc − FLR dLR − FLS dLS = 0
Fig. 9 represents a generic situation where the fatigue crack length is ‘a’. The stress state in the region ‘Lc’, near the crack tip, corresponds to the cohesive stress of the matrix, σc. This is a consequence of the debonding between the matrix and the reinforcing fibres that occurs in Region 2 (the total size of Region 2 is represented by the distance (a +Lc), for the critical crack length). Beyond (a+Lc) the material responds in an elastic manner since the bonding between the matrix and
(7)
The cohesive stress of the matrix, σc, and the stress σ, at the end of the remaining ligament (see Fig. 9) are the only unknown factors, provided that the final crack length, a, is measured during the tests (by means of the thermographic camera), and the distance (a+Lc) can be inferred from the SEM inspection of the fracture surface. Therefore, applying equations (3) and (7) allows the cohesive stress of the matrix to be determined. The values of σc obtained are plotted in Fig. 10 as a function of the local temperature at the crack tip. No significant differences between the values or a dependence on temperature is observed. On average, σc = 64 ± 4 MPa.
Fig. 10. Results obtained for the cohesive stress of the matrix, represented against the local temperature at the crack tip.
Fig. 9. Sketch of the stress state during the fatigue test.
341
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
Fig. 11. Micrographs showing the surface effects of the crazes due to loading.
4.4. Surface roughness Previous researchers [14] have reported that the crazes that occur due to the stress state at the crack tip can emerge on the surface of the sample, leaving perceptible traces. The two micrographs gathered in Fig. 11, taken at the surface of one of the fatigued specimens, close to the plane of fracture, confirm this fact. Accordingly, the examination of the surface of the specimens may be used as a source of information regarding the micromechanisms developed during the creep-fatigue process. This can be seen more clearly in Fig. 12, which shows two SEM micrographs, taken at the lateral surface of the specimen tested at 23 °C, in regions 2 and 3 (following the scheme in Fig. 7), respectively. The amount of plasticity of the matrix in Fig. 12(a) (region 2) is substantially larger than in Fig. 12(b) (region 3). Moreover, in this latter case, some broken fibres can be seen, which is a consequence of the brittle failure. Making use of this result, a methodology is proposed in this study, based on the correlation between the surface roughness and the underlying failure mechanisms. Thus, the surface roughness Ra (which is defined as the arithmetic average of the roughness profile) of the previously tested specimens was measured. In Fig. 13, Ra is represented as a function of the region analysed, (1, 2 or 3, in the horizontal axis) and the environmental temperature. The first notable feature is that each of the regions can be identified for its roughness; thus, in region 1, Ra = 0.176 ± 0.005, in Region 2, Ra = 0.253 ± 0.025 and in Region 3, Ra = 0.222 ± 0.014. Moreover, the roughness in Region 2 is apparently affected by the temperature so that, as temperature rises, Ra increases too. This can be interpreted as a consequence of the increase in the ductility of the matrix when temperature rises.
Fig. 13. Plot showing the surface roughness Ra as a function of the region analysed, (1, 2 or 3, in the horizontal axis) and the environmental temperature.
determine the response to fatigue loading of notched specimens, made of short glass fibre-reinforced polyamide. The most relevant experimental findings are summarised as:
• A strong dependency between the environmental temperature and •
5. Discussion This paper describes the experimental study carried out to
the number of cycles to failure has been observed; thus, the higher the temperature, the lower the ability of the material to resist fatigue loads. The evolution of the strain and strain-rate as a function of the number of loading cycles allowed three regions of behaviour to be identified. For ε < 0.009, the material is in Region I, which corresponds to a transient response, characterised by a decrease in the strain-rate. For 0.009 < ε < 0.012, the material is in the steadystate Region II, where the strain-rate of the material remains constant. Finally, for ε > 0.012, a new transient state, with increasing Fig. 12. SEM micrographs, taken at the lateral surface of the specimen tested at 23 °C; (a) regions 2 and, (b), region 3.
342
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
•
•
•
strain-rate is reached, until the final fracture occurs. The statistical analysis carried out has not detected any significant influence of the external temperature and the critical strains between regions, εI-II and εII-III. The study of the fracture surfaces by SEM microscopy has revealed the existence of three zones: Zone 1, corresponds to the notch introduced in the test specimens. In Zone 2, the matrix shows strong plastic deformation and crazing failure mechanisms accompanied by debonding between the matrix and the reinforcing fibres. Finally, when the local critical condition is reached, the fragile fracture of the resistant ligament occurs, giving rise to Zone 3. Based on the information derived from the fractographic study, the cohesive stress of the matrix was obtained. In fact, once the debonding between the matrix and the fibres has occurred, it is the matrix which supports the applied loads (in Zone 3, matrix and fibres collaborate mutually). The cohesive model developed allowed the cohesive stress of the material to be estimated, providing a value of σc = 64 ± 4 MPa (valid for this material and a humidity condition of 2.5%). The surface roughness of the samples was determined after being tested, using the Ra parameter. A correlation between the value of Ra and the fracture micromechanisms undergone by the material in the region examined was established.
as a consequence of the stress concentration due to the internal defects present in the material. The results reported in this study are in agreement with the micromechanisms described in the set of studies mentioned above, since in all these examples crazing was present due to the favorable conditions such as stress concentration, temperature, humidity content, etc., present in the material. A second aspect worthy of consideration refers to the applicability of the results offered in this study for the purposes of design and management under in-service conditions. In this sense, some of the contributions of this paper have a qualitative character. For instance, the relations between the environmental temperature and the number of cycles to failure, as well as the increase of temperature undergone by the material during fatigue, despite their numerical character, are of limited practical interest, since they refer to the very specific experimental conditions in this research (geometry of the specimen, loading frequency, etc.). Nevertheless, they offer valuable qualitative information such as the great importance of the external temperature on the fatigue life of the sgf-PA. This result, although qualitative, is of fundamental importance for new rail applications, as for example the new high-speed rails in the desert. No doubt, specific studies –beyond the scope of the present research– are required under these demanding conditions in order to guarantee the durability of the components manufactured in sgf-PA. The description of the failure micro-mechanisms developed in the material during the fatigue loading, obtained from the fractographic study, provides valuable information for forensic engineering. After the failure of a structural component, it is a common practice to analyze the fracture surface in order to identify the conditions leading to fracture. This research has proved that sgf-PA develops crazing micromechanisms under fatigue loading (under the experimental conditions imposed in the tests); this outcome, as discussed above, contradicts the general belief that identifies the mechanical failure of ductile polymers with shear yielding. In addition, this work also collects a series of experimental results with an evident practical utility. Thus, the mechanical properties derived from the cohesive model are of interest for any structural analysis, as well as for the development of specific numerical models of this composite material. Moreover, the correlation between the values of surface roughness and the material failure mechanism are of application for the inspection of in-service components, as a non-destructive method to measure the amount of damage undergone by the material, facilitating decision-making. The information contained in this paper is particularly relevant considering the scarcity of experimental information in the scientific literature about this material, especially as it is a widely used and highly responsible material. It is worth adding a final remark on the representativeness of the results, in this case in relation to the dimensions of the test specimens. It is a well-known fact that in Fracture Mechanics the triaxiality conditions at the crack tip, during propagation and fracture, depend on the thickness of the specimen. A simplistic calculation based on the results published in a previous paper [19], can help to determine whether plane stress or plane strain conditions prevail in this case. The following material properties were obtained from that paper (for sgf-PA with an humidity of 2%, with specimens similar to those used in this paper): JIntegral fracture toughness, JIc∼12 kPa m; yield stress, σY∼70 MPa; Young's modulus, E∼7 GPa. Moreover, ν∼0.39 is a typical value for the Poisson's ratio for this material. From these data, the fracture toughness can be expressed as a stress intensity factor, (8), following the method in Refs. [11,20]:
The experimental results collected in this research deserve a more detailed discussion. Three topics are analysed next: the failure micromechanisms developed by the material, the practical use of the experimental results and the influence of the crack width on the material behaviour. With regards to the fractographic study carried out, this has revealed some features in apparent contradiction of what might be expected for materials of this nature. Crazing and shear yielding are essentially the two main modes of deformation which are responsible for brittle and ductile fractures of polymers, respectively. Generally speaking, PA 6.6 is considered as a ductile material, so that it is expected that its failure should be accompanied by the presence of shear yielding micromechanisms; nevertheless, this statement contrasts with the results reported in this paper. A craze is defined as a microvoid which develops normal to the main stress. The formation of voids occurs only in tension whereas shear yielding leads to the formation of shear bands. Crazing is a microscopically localised phenomenon, which involves a large degree of localised plastic deformation. The SEM fractographies obtained in the present study allow the distribution of voids that characterise crazing to be appreciated. Thus, for instance, Fig. 7 shows how the region where the crack growth has occurred is covered by the distribution of voids, thus proving the existence of crazes. These results may be in apparent conflict with the identification, mentioned above, between crazing and brittle behaviour; however, this is not an absolute dichotomy and there are a substantial number of scientific contributions that coincide with the results of this research. The presence of cracks is one of the factors that must be taken into consideration in order to understand this apparent discrepancy since the stress state at the crack front is completely different from the uniform stress state in a tensile test. The importance of cracks for the formation of crazing is explicitly addressed in the book by Anderson [12]. Similar considerations are found in the book by Kinloch [15], for example. Despite this, several authors have reported experimental evidence supporting the existence of crazing in reinforced PA. Dibenedetto [16], found similar fatigue behaviour as that reported in this paper for compact samples of polyamide 66 reinforced with graphite fibers. These features are present even in non-cracked components. Thus, Horst [17] established fatigue rupture behaviour conditioned by crazes for polyamide reinforced with short glass fibre with random orientation in tensile specimens. Mouhmid et al. [18] have justified this phenomenon
K JIc =
E ·JIc ≈ 10 MPa·m1/2 1 − υ2
(8)
According to ASTM E 399 [21] and ASTM D5045 [22], the 343
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
[2] J.A. Casado, J.A. Polanco, I. Carrascal, F. Gutiérrez-Solana, International Conference on Fatigue of Composites. Paris, 1997, pp. 454–461. [3] G.P. Koo, M.N. Riddell, J.L. O'Toole, Fatigue properties of polytetrafluoroethylene and related fluoropolymers, Polym. Eng. Sci. 7 (3) (1967) 182–188. [4] R.J. Crawford, P.P. Benham, Cyclic stress fatigue and thermal softening failure of a thermoplastic, J. Mater Sci. 9 (1) (1974) 18–28. [5] I. Constable, J.G. Williams, D.J. Burns, Fatigue and cyclic thermal softening of thermoplastics, J. Mech. Eng. Sci. 12 (1) (1970) 20–29. [6] P.P. Oldyrev, V.M. Parfeev, Fatigue life of polymethyl methacrylate in stationary and stepped nonisothermal cyclic loading regimes, Mech. Compos. Mater. 11 (5) (1975) 682–688. [7] S. Gupta, A. Ray, Fatigue Crack Growth: Mechanics, Behaviour and Prediction, (2009). [8] J.A. Casado, F. Gutiérrez-Solana, J.A. Polanco, I. Carrascal, The assessment of fatigue damage on short-fibre-glass reinforced polyamides (PA) through the surface roughness evolution, Polym. Compos. 27 (4) (2006) 349–359. [9] B. Standard, B. ISO, Plastics—Determination of tensile properties—, Part 1 (1996) 527–521. [10] ASTM D7791-12, Standard, Test Method for Uniaxial Fatigue Properties of Plastics, ASTM International, West Conshohocken, PA, 2012www.astm.org. [11] T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, CRC Press, 2017. [12] I. Carrascal, J.A. Casado, S. Diego, R. Lacalle, S. Cicero, J.A. Álvarez, Determination of the Paris' law constants by means of infrared thermographic techniques, Polym. Test. 40 (2014) 39–45. [13] Casado del Prado, José Antonio. Comportamiento en fatiga de poliamidas reforzadas con fibra de vidrio corta, PhD thesis Universidad de Cantabria, 2010. [14] P. Beardmore, S. Rabinowitz, Longitudinal crazing in isotropic polymers, J. Mater Sci. 7 (6) (1972) 720–723. [15] A.J. Kinloch, R.J. Young, Fracture Behaviour of Polymers, Elsevier Applied Science Publishers Ltd, 0-85334-186-9, 1983. [16] A.T. Dibenedetto, G. Salee, Fatigue crack propagation in Graphite Fiber Reinforced Nylon 66, Pol. Eng. Sci. 19 (1979) 512–518. [17] J.J. Horst, Influence of Fibre Orientation on Fatigue of Short Glassfibre Reinforced Polyamide, PHD Delft University, The Netherlands, 1997. [18] B. Mouhmid, A. Imad, N. Benseddiq, S. Benmedakhène, A. Maazouz, A study of the mechanical behaviour of a glass fibre reinforced polyamide 6,6: Experimental investigation, Polym. Test. 25 (2006) 544–552. [19] D. Ferreño, I. Carrascal, E. Ruiz, J.A. Casado, Characterisation by means of a finite element model of the influence of moisture content on the mechanical and fracture properties of the polyamide 6 reinforced with short glass fibre, Polym. Test. 30 (2011) 420–428. [20] ASTM Standard E1820-17, Standard Test Method for Measurement of Fracture Toughness, ASTM Int. 03 (01) (2017). [21] ASTM Standard E399-12e3, Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIc of Metallic Materials, ASTM Int. 03 (01) (2012). [22] ASTM Standard D5045-14, Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials, ASTM Int. 08 (02) (2014).
following specimen size requirement (9) must be fulfilled in order to guarantee plane strain conditions:
KJ 2 B, b0 ≥ 2.5 ⎛ Ic ⎞ ≈ 0.05 m ⎝ σY ⎠ ⎜
⎟
(9)
Therefore, the thickness required to guarantee plane strain conditions is, approximately, one order of magnitude higher than the specimen's actual thickness. Then, plane stress conditions are expected to prevail during propagation and fracture. This outcome does not lessen the validity or representativeness of the results in this study since the thickness of parts injected in sgf-PA is typically in the order of millimeters due to the technical difficulties in injecting thicker parts. Indeed, this is the case for the angled guide plates that motivated the present research. Moreover, there is at present an open debate about the role of thickness on the fracture resistance of polymers. According to the fractographic analysis presented above, crazing is the fracture micromechanism in sgf-PA for the experimental conditions of the research. According to Anderson [11], the material inside the craze zone is subjected essentially to plane stress, regardless of the specimen thickness. Consequently, the fracture toughness of materials that craze may be relatively insensitive to specimen thickness. Nevertheless, the surrounding material may experience plane strain or mixed conditions; therefore, the stress state in the surrounding material could influence the toughness by dictating the size and shape of the craze zone. Needless to say, this reasoning is purely speculative and requires additional research, beyond the scope of this contribution. Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx. doi.org/10.1016/j.polymertesting.2017.10.021. References [1] J.A. Casado, F. Gutierrez-Solana, J.A. Polanco, R. de la Guerra, The characterization of the resistance to lateral impact of the insulating parts of the P2 rail fastening, WIT Trans. Built Environ. 8 (1970).
344
Contents lists available at ScienceDirect
Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Material Behaviour
Analysis of fatigue behaviour of notched specimens made of fibreglass reinforced polyamide by means of a cohesive model
MARK
J.A. Casado, F. Gutiérrez-Solana, I. Carrascal, S. Diego, D. Ferreño∗ LADICIM (Laboratory of Science and Engineering of Materials), University of Cantabria, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Av. Los Castros 44, 39005 Santander, Spain
A R T I C L E I N F O
A B S T R A C T
Keywords: Reinforced polyamide Notch Fatigue Crazing Cohesive stress
Fatigue tests until fracture of five notched specimens of short glass fibre reinforced polyamide, with a humidity of 2.5%, were carried out at 23, 28, 33, 38 and 43 °C. A correlation between the environmental temperature and the number of cycles to failure was established. Three different regions of strain were observed, namely, transient, steady-state and pre-failure. Strain and strain-rate during the creep-fatigue process revealed the existence of non-temperature dependent critical strains between these regions. The fractographic study performed after failure suggested the suitability of describing the stress distribution in the remnant ligament through a cohesive model. This is based on the observed fact that, at the crack tip, the matrix and the fibres debond, giving rise to crazing mechanisms so that the ultimate bearing ability of the material relies on the matrix. The calculations involved in the cohesive model were based on the information provided by the fractographic study and the realtime measurements of the crack growth by means of an infrared thermographic camera. Based on this methodology, the cohesive stress of the material was estimated. In a last stage, the surface roughness of the samples was determined after being tested, revealing a reliable correlation between the roughness and the fracture micromechanisms undergone by the underlying material. This correlation makes it possible to use the surface roughness of an in-service component as a parameter to evaluate the level of microstructural damage that it has experienced.
1. Introduction and aim Short glass fibre reinforced polyamide (sgf-PA) is a thermoplastic engineering material which is injected to form technical parts to be used under demanding conditions. The insulating angled guide plates of high-speed railway fastenings are a good example of where this material is employed. These components guarantee the performance of the railway fastening system, ensuring the maintenance of the rail gauge. Fig. 1(a) shows a sketch of the Vossloh W14 railway fastening system, Fig. 1(b) its constitutive parts and Fig. 1(c) a picture of an angled plate. There are currently thousands of kilometers of high-speed lines in the world employing millions of angled guide plates, such as the one shown in Fig. 1. The experience accumulated after years of use shows that this kind of component often undergoes in-service failure [1,2] due to the loads they are subjected to, combined with the environmental conditions, particularly temperature. The fracture of angled plates is a serious drawback, with economic as well as security related consequences. An increase in the number of faults of this type of components is expected as the demands of use intensify. The 453 km long
∗
Corresponding author. E-mail address: [email protected] (D. Ferreño).
http://dx.doi.org/10.1016/j.polymertesting.2017.10.021 Received 18 September 2017; Accepted 26 October 2017 Available online 31 October 2017 0142-9418/ © 2017 Elsevier Ltd. All rights reserved.
Haramain High-Speed Rail project, linking the cities of Medina and Mecca across the Arabian desert, scheduled for 2018, is a good example of new in-service conditions beyond the current operational limits. Fig. 1(c) allows the intricate geometry of the plate, its abrupt changes of section and the central hole, to be appreciated. Without any doubt, all these features act as stress concentrators, similar to notches, facilitating the initiation and propagation of fatigue cracks. Several previous studies have addressed the phenomenon of fatigue in sgf-PA components [3–7]. In particular, some of the authors of this paper have studied this subject in depth. For instance, Casado and Solana [8] analysed the evolution of failure micromechanisms in this material when subjected to fatigue as well as the interrelation between fatigue and creep, which depends on the crack tip local temperature. In addition, they determined the surface damage generated by the fatigue loading on the sgf-PA using the surface roughness as an indicative parameter. The objectives of this study can be grouped into two areas. On the one hand, from a more scientific perspective, the fatigue crack propagation in the sgf-PA material in the presence of stress concentrators was
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
Fig. 1. Picture of the high-speed railway fastening system (a), breakdown with the constitutive elements (b) and detail photograph of an angled guide plate (bottom view).
investigated. In order to provide a conservative description, the extreme case has been examined, consisting of analysing the response of notched components. Fatigue tests were carried out at a range of temperatures between 23 °C and 43 °C, which is considered to be representative of the most demanding in-service conditions for these plates. After identifying the failure micromechanisms in the material, a mechanical model, based on the cohesive stress method, was developed, in order to quantify the stress state both during the propagation and in the critical situation. At the same time, from a more practical perspective, the surface roughness of the specimens has been correlated with the level of damage undergone by the sgf-PA due to propagation; this correlation allows the level of damage in actual components under in-service conditions to be obtained from a simple roughness test. To the best of these authors' knowledge, no previous research has analysed the subjects addressed by the present paper. From our point of view, the information included in this study may be valuable to designers and practitioners, particularly in view of the shortage of specific research focused on the properties of sgf-PA. After the material and experimental methods are described in Sections 2 and 3, the experimental results are introduced and discussed in Section 4. In Section 4.1, the results of the fatigue tests are presented while in Section 4.2 a micromechanical description of the process of failure, based on the fractographic study, is developed. The cohesive model is introduced in Section 4.3 and, in Section 4.4, a correlation between the surface roughness of the specimens as the fatigue damage progresses and the failure micromechanisms in the material is established. Finally, Section 5 presents a discussion of the results obtained in this study.
Fig. 2. Standard tensile notched specimen (dimensions in mm).
were notched (a = 2 mm, see Fig. 2) by pressing a razor blade. The humidity of this hygroscopic material was kept at 2.5%. A total of five fatigue tests were performed.
3. Experimental and analytical methods Stress-controlled tensile fatigue tests were carried out between a maximum stress level of 41.7 MPa and a minimum of 8.3 MPa (in a previous contribution [8], it was shown that these stresses correspond, respectively, to 25% and 5% of the dynamic fracture stress of the material at room temperature on un-notched specimens). A universal INSTRON 8501 hydraulic machine with a dynamic loading capacity of 100 kN was used. The loads were applied with a frequency of 5 Hz, following the procedure described in ASTM D7791 [10]. Due to the thermoplastic nature of the material, the five fatigue tests were carried out in an environmental chamber at temperatures of 23, 28, 33, 38 and 43 °C, respectively (one test at each temperature). Each specimen was maintained at the testing temperature for 45 min before starting the test, in order to guarantee its thermal homogeneity. Obtaining the fatigue propagation rate requires the continuous measurement of the crack length. This measurement is usually carried out using methods such as the electric potential drop or by means of correlations between the crack length and the compliance of the specimen [11]. Bearing in mind that, for polymers, the crack tip undergoes a temperature rise due to the stress concentration and the generation and growth of a plastic zone, the crack growth can be reliably determined using infrared thermographic techniques. In a previous paper [12], this methodology was validated by comparing its results with conventional measurement techniques. This very same technique has been used in this research; thus, temperature measurements were performed with an IRISYS (InfraRed Integrated SYStems) universal thermal imager infrared thermographic camera, type IR 1011 with a resolution of 128x128, and the IRISYS 1011 imager software. During the tests, the following parameters were continuously recorded:
2. Material The worldwide production of PA 6.6 is, roughly, 2 million tons per year, over half of the production being used in the form of fibre-reinforced PA. This material is frequently used when high mechanical strength, rigidity, good stability under heat and/or chemical resistance are required. It is widely employed for manufacturing structural parts, mostly by injection molding. As stated above, sgf-PA is the constitutive material of the angled guide plates used in high speed railway fastening systems all around the world. The fatigue tests of this study were carried out on standard tensile specimens (according to EN-ISO 527 [9]), with a nominal thickness of 4 mm (see the sketch in Fig. 2), manufactured in PA 6.6 reinforced with short fibre glass (35% wt). The specimens were injected by means of an Arburg ALLROUNDER 221 K injection molding machine, with a clamping force of 350 kN. This injector machine is equipped with a twocavities steel mold to fabricate EN ISO 527 standard tensile specimens. Following a general recommendation, fatigue precracking was avoided because it can be very time-consuming since the loading frequency must be kept low in order to minimise hysteresis heating, which may in turn introduce residual stresses at the crack tip. Rather, the specimens 338
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
• Longitudinal strain, measured by means of an extensometer with a clip gauge of 12.5 mm and a travel of ± 5 mm. • Surface temperature of the specimen, determined with the thermographic camera. • Load range, provided by the load cell of the testing machine. • Number of fatigue cycles up to fracture. After the fatigue tests, the fracture surface of the specimens was examined by means of a scanning electron microscope (SEM), model JEOL JSM 5800-LV device, equipped with a microanalyser EDAX OXFORD link eXL. In addition, the roughness of the lateral surface of the specimens, in the proximity of the plane of fracture, was determined using a roughness tester Pherthen, Pherthometer S3P model. The SEM and roughness tester provided valuable information for the analytical cohesive model developed to describe the state during the tests. Regarding the analysis of data, several statistical methods were used. The means of distributions were compared using t-tests, obtaining the p-value (which represents the probability that, when the null hypothesis is true -equal means-, the sample mean difference between two compared groups would be the same as the actual observed results). Moreover, simple linear regression was applied, using the least squares approach. The p-values of the slopes of the linear models were determined (in this case, the p-value tests the null hypothesis that the coefficient is equal to zero, which means that changes in the explanatory variable do not induce changes in the response variable). The level of significance was chosen to be 0.05 in all cases.
Fig. 4. Surface temperature (T) at the crack tip as a function of the number of cycles (N) for the five specimens subjected to fatigue.
4. Experimental results 4.1. Fatigue tests As an arbitrary example, Fig. 3 shows the evolution of the strain (continuous line, left vertical axis) and strain rate (discontinuous line, right vertical axis) as a function of the number of fatigue cycles applied, for the test corresponding to an environmental temperature of 23 °C. It is worth noting that the features present in these graphs are common to the rest of tests/temperatures. In addition, the evolution of surface temperature at the crack tip of the five fatigue tests is represented in Fig. 4. As shown in Fig. 4, as the test evolves, the temperature of the specimen increases slightly, approximately by 5 °C during the test. Moreover, there is a clear correlation between the environmental temperature and the number of cycles to failure, as can be seen in Fig. 5: the higher the temperature, the lower the fatigue lifetime. As shown by Casado et al. [13], under these conditions of stress and temperature, the sgf-PA undergoes coupling between the fatigue and the creep processes. Fig. 3 allows three different regions to be
Fig. 5. Number of cycles to failure as a function of the environmental temperature.
distinguished in the strain and strain rate plots. Region I corresponds to the transient creep-fatigue stage, characterised by a decrease in the strain rate. In Region II, the steady state regime is reached and the material deforms at a constant rate. The final stage, Region III, is characterised by an increasing strain rate preceding the imminent fracture of the specimen. The transition strain levels between these regions were measured, and are represented in Fig. 6 as a function of the external temperature. The figure suggests that these strains correspond to critical values presumably dependent on the material, but not on the temperature.
Fig. 3. Strain (ε) and strain rate (dε/dN) vs. number of cycles (N). Test corresponding to an environmental temperature of 23 °C.
Fig. 6. Transition strains between regions I-II and II-III.
339
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
According to the data, εI-II = 0.009 ± 0.0008 and εII-III = 0.012 ± 0.0008. In order to prove the independency between εI-II and εII-III and the external temperature, a series of statistical procedures were applied. First, linear regression was used (εI-II vs. T and εII-III vs. T, respectively), focusing on the p-values of the slopes of the models. In both cases, these slopes were positive (this fact is suggested by the distribution of points in Fig. 6). For the regression between εI-II (dependant variable) and T (explanatory variable), p = 0.1279 and for εII-III and T, p = 0.0791. Therefore, according to these results, there is not enough information, at the α = 0.05 significance level, to reject the null hypothesis, which states that the slopes are zero. In other words, for practical purposes, it can be assumed that neither εI-II nor εII-III are influenced by the temperature; the effect derived from the scatter of points is stronger than the influence of the explanatory variable. In addition, the statistical ttest was used to compare the means of the two populations (εI-II and εIIIII), obtaining the p-value = 0.0014. Thus, the null hypothesis (equal means) must be rejected at the 0.05 significance level. These calculations support the statement that there is a defined limit between εI-II and εII-III, regardless of the temperature, this limit being εlimit≈0.011. This result does not imply that the temperature is not playing a role in the cracking process. On the contrary, the temperature substantially reduces the number of cycles needed to reach each of the transition strains, εI-II and εII-III, respectively, as well as the time to failure, as clearly shown by Fig. 4 and Fig. 5.
•
•
material shows a smooth appearance. The fractography included in Fig. 7 shows the border between the notch and the initial propagation surface. Zone 2 is characterised by the ductile behaviour of the matrix and the presence of crazing mechanisms. As can be seen in Fig. 7, the matrix shows a dimpled appearance because of its plastic response. Crazes (highly localised deformations that lead to void formation) appear because of the demanding local strain conditions, near the tip of the growing crack. The inability of the material to release heat due to its low thermal conductivity is another factor that facilitates the plasticity as well as the nucleation and creation of crazes. Once the critical crack length is reached, the remaining ligament is unable to withstand the applied forces. Then, the final fracture takes place, which corresponds to the brittle surface that can be appreciated in Zone 3. Note the multifaceted surface of the matrix, typical when the material responds in a brittle manner.
Every specimen was analysed by SEM after being tested to failure. Thus, the size of the three regions described above could be measured. The results of the fractographic study are a consequence of the micromechanisms that develop during fracture process of the sgf-PA. The sketch in Fig. 8 explains the interaction between the matrix and the fibres as the local stress increases (from left to right in the figure). The debonding between the matrix and the fibres starts at the ends of the fibres since this is a location of shear stress concentration. For this reason, debonding may occur even for low applied stress (σ1 in the figure). As the applied stress increases (σ2), new debonding appear, even in the shaft region of the fibres. The local stress makes the matrix yield by crazing which, on the macroscopic level, appears as a stresswhitened region due to a low refractive index [11]. Void coalescence, as for σ3 in Fig. 8, promotes the formation of cracks. In this situation, the loading ability of the specimen rests on the matrix bridges because the bonding between the matrix and the fibres becomes negligible. For this reason, fracture takes place in a zone where the failure of the individual fibrils occurs. Consequently, in this region, the stress state in the matrix corresponds to its cohesive stress. This process is unstable if, when a fibril fails, the redistributed stress is sufficient to break one or
4.2. Fractographic study The SEM examination of the fracture surfaces of the specimens revealed the existence of three different regions. Fig. 7 shows a diagram of the typical cross section of a broken specimen, where the relevant zones are numbered from left to right. A panel of SEM fractographies that allows the morphologies present in each of the three regions to be identified is included in the figure. The main features are described next:
• Zone 1 corresponds to the notch. In this zone, the surface of the
Fig. 7. Schematic description of the regions present on a typical fracture surface.
340
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
the fibres remains intact and both can work collaboratively. For this reason, the stress profile is linear. The stress state in the cross section must balance the applied external stress, σext, which implies the equilibrium in forces and momenta. Some notation is now introduced for the sake of simplicity. Fc is the total force of the cohesive region, which follows equation (1) (‘B’ being the thickness of the specimen). The total force in the linear region, FL, is broken down into two components, which correspond to the rectangular (FLR) and the triangular (FLT) parts of the stress profile, see equation (2). (1)
Fc = σc Lc B
{
FL = FLR + FLT = σ [W − (a + Lc )] +
1 (σc − σ )[W − (a + Lc )] B 2
}
(2) Now, the condition of force equilibrium can be expressed as in equation (3):
Fc + FL = σext WB
(3)
The equilibrium of momenta will be established with respect to the centroid of the cross section (the loading line of the external force), point ‘O’ in the figure. The distances dc, dLR and dLT, represented in Fig. 9, can be obtained, as in equations (4)–(6), by simple geometric manipulation.
W L −a− c 2 2
(4)
dLR =
1 (a + Lc ) 2
(5)
dLS =
2 W (a + Lc ) − 3 6
(6)
dc =
Fig. 8. Sketch showing the different stages of the failure in sgf-PA.
more neighboring fibrils. Then, the brittle failure of the remaining cross section takes place. The multifaceted appearance of the matrix, as in the last fractography in Fig. 7, is the main feature that allows this type of fracture to be identified. 4.3. Estimation of the cohesive stress state
Therefore, the balance of momenta is expressed as in equation (7):
Fc dc − FLR dLR − FLS dLS = 0
Fig. 9 represents a generic situation where the fatigue crack length is ‘a’. The stress state in the region ‘Lc’, near the crack tip, corresponds to the cohesive stress of the matrix, σc. This is a consequence of the debonding between the matrix and the reinforcing fibres that occurs in Region 2 (the total size of Region 2 is represented by the distance (a +Lc), for the critical crack length). Beyond (a+Lc) the material responds in an elastic manner since the bonding between the matrix and
(7)
The cohesive stress of the matrix, σc, and the stress σ, at the end of the remaining ligament (see Fig. 9) are the only unknown factors, provided that the final crack length, a, is measured during the tests (by means of the thermographic camera), and the distance (a+Lc) can be inferred from the SEM inspection of the fracture surface. Therefore, applying equations (3) and (7) allows the cohesive stress of the matrix to be determined. The values of σc obtained are plotted in Fig. 10 as a function of the local temperature at the crack tip. No significant differences between the values or a dependence on temperature is observed. On average, σc = 64 ± 4 MPa.
Fig. 10. Results obtained for the cohesive stress of the matrix, represented against the local temperature at the crack tip.
Fig. 9. Sketch of the stress state during the fatigue test.
341
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
Fig. 11. Micrographs showing the surface effects of the crazes due to loading.
4.4. Surface roughness Previous researchers [14] have reported that the crazes that occur due to the stress state at the crack tip can emerge on the surface of the sample, leaving perceptible traces. The two micrographs gathered in Fig. 11, taken at the surface of one of the fatigued specimens, close to the plane of fracture, confirm this fact. Accordingly, the examination of the surface of the specimens may be used as a source of information regarding the micromechanisms developed during the creep-fatigue process. This can be seen more clearly in Fig. 12, which shows two SEM micrographs, taken at the lateral surface of the specimen tested at 23 °C, in regions 2 and 3 (following the scheme in Fig. 7), respectively. The amount of plasticity of the matrix in Fig. 12(a) (region 2) is substantially larger than in Fig. 12(b) (region 3). Moreover, in this latter case, some broken fibres can be seen, which is a consequence of the brittle failure. Making use of this result, a methodology is proposed in this study, based on the correlation between the surface roughness and the underlying failure mechanisms. Thus, the surface roughness Ra (which is defined as the arithmetic average of the roughness profile) of the previously tested specimens was measured. In Fig. 13, Ra is represented as a function of the region analysed, (1, 2 or 3, in the horizontal axis) and the environmental temperature. The first notable feature is that each of the regions can be identified for its roughness; thus, in region 1, Ra = 0.176 ± 0.005, in Region 2, Ra = 0.253 ± 0.025 and in Region 3, Ra = 0.222 ± 0.014. Moreover, the roughness in Region 2 is apparently affected by the temperature so that, as temperature rises, Ra increases too. This can be interpreted as a consequence of the increase in the ductility of the matrix when temperature rises.
Fig. 13. Plot showing the surface roughness Ra as a function of the region analysed, (1, 2 or 3, in the horizontal axis) and the environmental temperature.
determine the response to fatigue loading of notched specimens, made of short glass fibre-reinforced polyamide. The most relevant experimental findings are summarised as:
• A strong dependency between the environmental temperature and •
5. Discussion This paper describes the experimental study carried out to
the number of cycles to failure has been observed; thus, the higher the temperature, the lower the ability of the material to resist fatigue loads. The evolution of the strain and strain-rate as a function of the number of loading cycles allowed three regions of behaviour to be identified. For ε < 0.009, the material is in Region I, which corresponds to a transient response, characterised by a decrease in the strain-rate. For 0.009 < ε < 0.012, the material is in the steadystate Region II, where the strain-rate of the material remains constant. Finally, for ε > 0.012, a new transient state, with increasing Fig. 12. SEM micrographs, taken at the lateral surface of the specimen tested at 23 °C; (a) regions 2 and, (b), region 3.
342
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
•
•
•
strain-rate is reached, until the final fracture occurs. The statistical analysis carried out has not detected any significant influence of the external temperature and the critical strains between regions, εI-II and εII-III. The study of the fracture surfaces by SEM microscopy has revealed the existence of three zones: Zone 1, corresponds to the notch introduced in the test specimens. In Zone 2, the matrix shows strong plastic deformation and crazing failure mechanisms accompanied by debonding between the matrix and the reinforcing fibres. Finally, when the local critical condition is reached, the fragile fracture of the resistant ligament occurs, giving rise to Zone 3. Based on the information derived from the fractographic study, the cohesive stress of the matrix was obtained. In fact, once the debonding between the matrix and the fibres has occurred, it is the matrix which supports the applied loads (in Zone 3, matrix and fibres collaborate mutually). The cohesive model developed allowed the cohesive stress of the material to be estimated, providing a value of σc = 64 ± 4 MPa (valid for this material and a humidity condition of 2.5%). The surface roughness of the samples was determined after being tested, using the Ra parameter. A correlation between the value of Ra and the fracture micromechanisms undergone by the material in the region examined was established.
as a consequence of the stress concentration due to the internal defects present in the material. The results reported in this study are in agreement with the micromechanisms described in the set of studies mentioned above, since in all these examples crazing was present due to the favorable conditions such as stress concentration, temperature, humidity content, etc., present in the material. A second aspect worthy of consideration refers to the applicability of the results offered in this study for the purposes of design and management under in-service conditions. In this sense, some of the contributions of this paper have a qualitative character. For instance, the relations between the environmental temperature and the number of cycles to failure, as well as the increase of temperature undergone by the material during fatigue, despite their numerical character, are of limited practical interest, since they refer to the very specific experimental conditions in this research (geometry of the specimen, loading frequency, etc.). Nevertheless, they offer valuable qualitative information such as the great importance of the external temperature on the fatigue life of the sgf-PA. This result, although qualitative, is of fundamental importance for new rail applications, as for example the new high-speed rails in the desert. No doubt, specific studies –beyond the scope of the present research– are required under these demanding conditions in order to guarantee the durability of the components manufactured in sgf-PA. The description of the failure micro-mechanisms developed in the material during the fatigue loading, obtained from the fractographic study, provides valuable information for forensic engineering. After the failure of a structural component, it is a common practice to analyze the fracture surface in order to identify the conditions leading to fracture. This research has proved that sgf-PA develops crazing micromechanisms under fatigue loading (under the experimental conditions imposed in the tests); this outcome, as discussed above, contradicts the general belief that identifies the mechanical failure of ductile polymers with shear yielding. In addition, this work also collects a series of experimental results with an evident practical utility. Thus, the mechanical properties derived from the cohesive model are of interest for any structural analysis, as well as for the development of specific numerical models of this composite material. Moreover, the correlation between the values of surface roughness and the material failure mechanism are of application for the inspection of in-service components, as a non-destructive method to measure the amount of damage undergone by the material, facilitating decision-making. The information contained in this paper is particularly relevant considering the scarcity of experimental information in the scientific literature about this material, especially as it is a widely used and highly responsible material. It is worth adding a final remark on the representativeness of the results, in this case in relation to the dimensions of the test specimens. It is a well-known fact that in Fracture Mechanics the triaxiality conditions at the crack tip, during propagation and fracture, depend on the thickness of the specimen. A simplistic calculation based on the results published in a previous paper [19], can help to determine whether plane stress or plane strain conditions prevail in this case. The following material properties were obtained from that paper (for sgf-PA with an humidity of 2%, with specimens similar to those used in this paper): JIntegral fracture toughness, JIc∼12 kPa m; yield stress, σY∼70 MPa; Young's modulus, E∼7 GPa. Moreover, ν∼0.39 is a typical value for the Poisson's ratio for this material. From these data, the fracture toughness can be expressed as a stress intensity factor, (8), following the method in Refs. [11,20]:
The experimental results collected in this research deserve a more detailed discussion. Three topics are analysed next: the failure micromechanisms developed by the material, the practical use of the experimental results and the influence of the crack width on the material behaviour. With regards to the fractographic study carried out, this has revealed some features in apparent contradiction of what might be expected for materials of this nature. Crazing and shear yielding are essentially the two main modes of deformation which are responsible for brittle and ductile fractures of polymers, respectively. Generally speaking, PA 6.6 is considered as a ductile material, so that it is expected that its failure should be accompanied by the presence of shear yielding micromechanisms; nevertheless, this statement contrasts with the results reported in this paper. A craze is defined as a microvoid which develops normal to the main stress. The formation of voids occurs only in tension whereas shear yielding leads to the formation of shear bands. Crazing is a microscopically localised phenomenon, which involves a large degree of localised plastic deformation. The SEM fractographies obtained in the present study allow the distribution of voids that characterise crazing to be appreciated. Thus, for instance, Fig. 7 shows how the region where the crack growth has occurred is covered by the distribution of voids, thus proving the existence of crazes. These results may be in apparent conflict with the identification, mentioned above, between crazing and brittle behaviour; however, this is not an absolute dichotomy and there are a substantial number of scientific contributions that coincide with the results of this research. The presence of cracks is one of the factors that must be taken into consideration in order to understand this apparent discrepancy since the stress state at the crack front is completely different from the uniform stress state in a tensile test. The importance of cracks for the formation of crazing is explicitly addressed in the book by Anderson [12]. Similar considerations are found in the book by Kinloch [15], for example. Despite this, several authors have reported experimental evidence supporting the existence of crazing in reinforced PA. Dibenedetto [16], found similar fatigue behaviour as that reported in this paper for compact samples of polyamide 66 reinforced with graphite fibers. These features are present even in non-cracked components. Thus, Horst [17] established fatigue rupture behaviour conditioned by crazes for polyamide reinforced with short glass fibre with random orientation in tensile specimens. Mouhmid et al. [18] have justified this phenomenon
K JIc =
E ·JIc ≈ 10 MPa·m1/2 1 − υ2
(8)
According to ASTM E 399 [21] and ASTM D5045 [22], the 343
Polymer Testing 64 (2017) 337–344
J.A. Casado et al.
[2] J.A. Casado, J.A. Polanco, I. Carrascal, F. Gutiérrez-Solana, International Conference on Fatigue of Composites. Paris, 1997, pp. 454–461. [3] G.P. Koo, M.N. Riddell, J.L. O'Toole, Fatigue properties of polytetrafluoroethylene and related fluoropolymers, Polym. Eng. Sci. 7 (3) (1967) 182–188. [4] R.J. Crawford, P.P. Benham, Cyclic stress fatigue and thermal softening failure of a thermoplastic, J. Mater Sci. 9 (1) (1974) 18–28. [5] I. Constable, J.G. Williams, D.J. Burns, Fatigue and cyclic thermal softening of thermoplastics, J. Mech. Eng. Sci. 12 (1) (1970) 20–29. [6] P.P. Oldyrev, V.M. Parfeev, Fatigue life of polymethyl methacrylate in stationary and stepped nonisothermal cyclic loading regimes, Mech. Compos. Mater. 11 (5) (1975) 682–688. [7] S. Gupta, A. Ray, Fatigue Crack Growth: Mechanics, Behaviour and Prediction, (2009). [8] J.A. Casado, F. Gutiérrez-Solana, J.A. Polanco, I. Carrascal, The assessment of fatigue damage on short-fibre-glass reinforced polyamides (PA) through the surface roughness evolution, Polym. Compos. 27 (4) (2006) 349–359. [9] B. Standard, B. ISO, Plastics—Determination of tensile properties—, Part 1 (1996) 527–521. [10] ASTM D7791-12, Standard, Test Method for Uniaxial Fatigue Properties of Plastics, ASTM International, West Conshohocken, PA, 2012www.astm.org. [11] T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, CRC Press, 2017. [12] I. Carrascal, J.A. Casado, S. Diego, R. Lacalle, S. Cicero, J.A. Álvarez, Determination of the Paris' law constants by means of infrared thermographic techniques, Polym. Test. 40 (2014) 39–45. [13] Casado del Prado, José Antonio. Comportamiento en fatiga de poliamidas reforzadas con fibra de vidrio corta, PhD thesis Universidad de Cantabria, 2010. [14] P. Beardmore, S. Rabinowitz, Longitudinal crazing in isotropic polymers, J. Mater Sci. 7 (6) (1972) 720–723. [15] A.J. Kinloch, R.J. Young, Fracture Behaviour of Polymers, Elsevier Applied Science Publishers Ltd, 0-85334-186-9, 1983. [16] A.T. Dibenedetto, G. Salee, Fatigue crack propagation in Graphite Fiber Reinforced Nylon 66, Pol. Eng. Sci. 19 (1979) 512–518. [17] J.J. Horst, Influence of Fibre Orientation on Fatigue of Short Glassfibre Reinforced Polyamide, PHD Delft University, The Netherlands, 1997. [18] B. Mouhmid, A. Imad, N. Benseddiq, S. Benmedakhène, A. Maazouz, A study of the mechanical behaviour of a glass fibre reinforced polyamide 6,6: Experimental investigation, Polym. Test. 25 (2006) 544–552. [19] D. Ferreño, I. Carrascal, E. Ruiz, J.A. Casado, Characterisation by means of a finite element model of the influence of moisture content on the mechanical and fracture properties of the polyamide 6 reinforced with short glass fibre, Polym. Test. 30 (2011) 420–428. [20] ASTM Standard E1820-17, Standard Test Method for Measurement of Fracture Toughness, ASTM Int. 03 (01) (2017). [21] ASTM Standard E399-12e3, Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIc of Metallic Materials, ASTM Int. 03 (01) (2012). [22] ASTM Standard D5045-14, Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials, ASTM Int. 08 (02) (2014).
following specimen size requirement (9) must be fulfilled in order to guarantee plane strain conditions:
KJ 2 B, b0 ≥ 2.5 ⎛ Ic ⎞ ≈ 0.05 m ⎝ σY ⎠ ⎜
⎟
(9)
Therefore, the thickness required to guarantee plane strain conditions is, approximately, one order of magnitude higher than the specimen's actual thickness. Then, plane stress conditions are expected to prevail during propagation and fracture. This outcome does not lessen the validity or representativeness of the results in this study since the thickness of parts injected in sgf-PA is typically in the order of millimeters due to the technical difficulties in injecting thicker parts. Indeed, this is the case for the angled guide plates that motivated the present research. Moreover, there is at present an open debate about the role of thickness on the fracture resistance of polymers. According to the fractographic analysis presented above, crazing is the fracture micromechanism in sgf-PA for the experimental conditions of the research. According to Anderson [11], the material inside the craze zone is subjected essentially to plane stress, regardless of the specimen thickness. Consequently, the fracture toughness of materials that craze may be relatively insensitive to specimen thickness. Nevertheless, the surrounding material may experience plane strain or mixed conditions; therefore, the stress state in the surrounding material could influence the toughness by dictating the size and shape of the craze zone. Needless to say, this reasoning is purely speculative and requires additional research, beyond the scope of this contribution. Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx. doi.org/10.1016/j.polymertesting.2017.10.021. References [1] J.A. Casado, F. Gutierrez-Solana, J.A. Polanco, R. de la Guerra, The characterization of the resistance to lateral impact of the insulating parts of the P2 rail fastening, WIT Trans. Built Environ. 8 (1970).
344