Detecting the critical strain of fiber reinforced plastics by means of acoustic emission analysis.
Acoustic emission testing is a quasi-non-destructive testing method to detect and record the ignition and propagation of irreversible damage in materials under load. In tensile testing of fiber reinforced plastics, first micro cracks occur as soon as a critical strain is exceeded. They emit a characteristic sound, which can be detected via acoustic emission analysis. By increasing the load, the amount of acoustic emissions rises. Even, if the plastic's matrix causes a high damping rate, a sudden change in amplitude is indicating the critical strain. Further, the analysis shows signals of the whole frequency range which can be distinguished into three different damage mechanisms (matrix cracking, interfacial failure and fiber breakage) by using pattern recognition techniques. It can be shown that the appearance of micro cracks can be correlated with a specific strain value which is interpreted as the critical strain.
Keywords: critical strain, micro cracks, failure limit, acoustic emission analysis, fiber reinforced plastics
Compared to conventional materials for structural components, the deformation behavior of plastics depends strongly on many different conditions like time, temperature, load etc. Therefore, all these conditions have to be considered during the design process. Till today, the estimation of the plastics material's failure limit is more complex than for linear elastic materials like metal. In most cases, as a failure criterion the principal stress under load is compared to the tensile strength. As tensile strength values are often measured unidirectionally and do not consider the different influences mentioned above, various reduction factors for different conditions are used for the valid calculation of plastic parts. Thus, the full potential of the material often cannot be exploited. Alternatively, plastics can be dimensioned by means of the critical strain as failure limit. The critical strain is the strain, at which first micro cracks occur. There are different estimation methods; however, they are all very time-consuming. The use of acoustic emission analysis in a slightly adjusted tensile test is a promising method with the potential to get quick values for the critical strain of a new material. The occurrence and growth of micro cracks lead to an emission of acoustic sound waves, which are detectable by a piezo transducer. With these signals the critical strain can be measured quick and reliable for fiber reinforced plastics
2. State of the Art
The use of the critical strain as a dimensioning factor was invented in the 1970s by Georg Menges and his group [1, 2]. They found out that an optically detected occurrence of first flow zones [[epsilon].sub.F], for lower loads decreased to lower strains, converging towards an asymptotic value. This is schematically shown in Figure 1. This value was interpreted as the critical strain [1, 3] and its existence could be validated for amorphous transparent and semi crystalline translucent specimens as well. It is remarkable that the value for the critical strain differs insignificantly for thermoplastics with similar mechanical characteristics . But the most important aspect of the critical strain as a dimensioning factor (the so called "permissible strain limit") is that it is mostly independent of
* kind of stressing (static, cyclic, etc.) [2, 4]
* stress distribution (uni- or multiaxial) 
* temperature (assumed no changes in material condition taking place), [2, 5]
* time (short-time, long-term) [1, 3]
* kind of medium (assumed no change of condition is initiated) [2, 6, 7]
[FIGURE 1 OMITTED]
In comparison to stress based dimensioning methods, the critical strain as a permissible strain limit provides several advantages, which are summarized in [8, 9, 10, 11]. One major advantage of the critical strain is its independence of different boundary conditions, which allows for a simplified calculation and design procedure . However, there is a remaining disadvantage, which lies in the measurement of the critical strain being more complex than that of conventional stress limits like the tensile or yield strength. Over the past decades, several different methods were validated to determine the critical strain, of which the most important are listed below.
* Visual examination during tensile testing (quick, but only valid for transparent and translucent specimen):
For amorphous transparent thermoplastics the exceeding of permissible strain leads to a silvery glimmer (crazes), which can be recognized with the naked eye [1, 2, 3]. For semi-crystalline as well as amorphous translucent thermoplastics the exceeding of permissible strain leads to hazing. With a photo-optical measurement during tensile testing, the refraction of light can be measured by the changing intensity .
* Specific fracture energy  (time-consuming, valid also for non-transparent specimen):
During cyclic loading of tensile bars up to different load steps (predefined strain value), the deformation energy can be calculated for each cycle. The specimen gets unclamped for 24 h between two load cycles to relax stresses. After a minimum of four load cycles, the specific fracture energy can be calculated by the difference of the energy loss of the first cycle and a mean value of the subsequent energy losses. Occurring damages at a specific load step will lead to specific fracture energy greater than zero. The lowest load step where first damages occur can be determined as critical strain.
* Pin/ball impression method according to Porth [14, 15, 16] (time-consuming, valid for non-transparent specimen):
This method compares the reduction of tensile strength of different prepared tensile bars. All tensile bars are prepared with a 3 mm bore hole in the middle. The bore hole of different tensile bars is expanded with a stepwise increased steel pin or ball size. Afterwards a tensile test is performed. A critical damage level is exceeded, when the initial strength is reduced by 5 %. The residual corresponding pin oversize is an indicator for the critical strain.
But common to all is that they are either very time-consuming or at limited to certain materials. A quick, universal and robust determination of the critical strain for a wide variety of materials is not possible with these procedures. In contrast to that the acoustic emission analysis can provide a direct detection of micro cracks. In  a method based on the acoustic emission analysis for fiber reinforced epoxy resin is presented. Using a slightly adjusted tensile test, the critical strain can be quickly detected by means of acoustic emission analysis. The occurrence and growth of micro cracks lead to an emission of acoustic sound waves, which are detectable by a piezo transducer. With these signals the critical strain can be estimated for fiber reinforced plastics.
Acoustic emission analysis has also been used since the 1970s for crack characterization of endless fiber reinforced applications, mostly in aerospace [17, 18, 19, 20, 21]. In addition to this, different research for thermoplastics has been performed, likewise for unreinforced thermoplastics [22, 23] and also polymer blends [22, 23] as well as particle and fiber reinforced thermoplastics [24, 25, 26]. Crack initiation and propagation is correlating with the detectable signals of acoustic emission analysis. Thereby, different microscopic failure mechanisms can be distinguished. The signals are analyzed mostly by their amplitude [24, 25, 27]. Recent methods are also using frequency based criteria for determination [21, 28, 29]. Cracks emit higher frequencies with increasing stiffness and decreasing density of the material . Thus, matrix cracks, interfacial failure (fiber pull-out) and fiber breakage can be distinguished by frequency in fiber reinforced plastics [19, 20, 21]. Latest methods are also using pattern recognition techniques to distinguish between different acoustic emission signal types [28, 29, 30].
The determination of the critical strain by means of acoustic emission analysis has also been shown in  for short fiber reinforced thermoplastics and particle reinforced thermoplastics. But a quick, universal and robust method to determine the critical strain for many different materials is still missing. Therefore, a method based on the acoustic emission analyses is presented.
3. Experimental Set-up and Procedure
3.1. Materials and Specimens
A polycarbonate (PC) from Covestro GmbH, Leverkusen, Germany, available with different fiber types and contents was chosen for analysis. The following Table 1 lists the specification of each material.
For all tests, standard tensile bars according to ISO 527-2 , type 1A, were produced on an injection molding machine Allrounder 520S 1600-400 of Arburg, Lo[beta]burg/Germany. The processing conditions were kept constant, except for a slight variation of mold temperature and injection velocity in order to completely fill the cavities. Before processing, the pellets were predried according to the manufacturer's processing guidelines.
3.2. Tensile test and acoustic emission analysis
All tensile tests were performed on a tensile testing machine UPM 1476 of Zwick Roell, Ulm/Germany, at room temperature 23 [degrees]C and a relative humidity of 50 % following ISO 291 . A strain rate of 0.4 mm/min was chosen. The strain is controlled by sensor-arm extensometers with an initial distance of 75 mm. The measured values for force and elongation were steadily transferred to the acoustic emission (AE) system during testing.
For the acoustic emission analysis (AEA) the system PCI-2 AE by MISTRAS, Cambridge/UK, with external amplifiers (40 dB/60 dB) was used. The receiving transducers are wideband differential sensors with a sensitive frequency response ranging from 100 to 900 kHz. The detectable signals were recorded with the software AEWIN, Version E 5.6. The sampling rate was set to 10 MHz and the magnification to 40 dB for the reinforced materials and 60 dB for the unreinforced materials respectively. For the signal acquisition the properties were set to following values: The threshold to 40 dB for the reinforced materials and to 26 dB for the unreinforced materials. All other properties were set equal for all materials: peak definition time PDT = 20 [micro]s, hit definition time HDT = 80 [micro]s and hit lockout time HLT = 300 [micro]s. To raise the signal transmission from the specimens to the sensors, the ultrasound couplant ZG-F from General Electric, Fairfield/USA, was used. The transducers were placed with clamps at the surface of the tensile bar between the sensor arms of the extensometers (Figure 2).
[FIGURE 2 OMITTED]
Before each measurement a sensor response verification test was performed with a pencil lead break source according to Hsu-Nielsen described in ASTM F2174-02:2015 . As clamping the specimens in the tensile testing machine can cause vibrations detectable by the sensors, it has to be made sure that these have faded away when the test begins. Therefore, a waiting period of two minutes was introduced between clamping and testing. Acoustic emissions were recorded while all specimens were stressed with a constant strain rate until failure. Based on this data the permissible strain could be detected by a strong increase of recorded signals, caused by the first micro cracks.
Figure 3 shows the stress-strain-curves of the tested materials. It can be seen that the strain at break decreases dramatically by adding glass fibers to the Polycarbonate. In contrast to that, the Young's modulus increases at the same time. Adding long fibers leads to a higher tensile strength (about twice as high). This effect can be explained by the 'theory of the critical fiber length': only exceeding the critical fiber length can exploit the full reinforcement potential. But, at least for the calculating and design process this diagram offers information about uniaxial tension for the specific testing conditions (for instance: temperature, time, fiber orientation and length distribution within the tensile bars, etc.), only.
[FIGURE 3 OMITTED]
The detailed data determined in tensile tests are summarized in Table 2.
The detected acoustic emissions during continuous testing of a PC-GF20 specimen are shown in Figure 4. Each point in the scatter-plot represents the maximum amplitude of a detected signal occurring at a certain strain value. The shown signals have passed the filters, mentioned in chapter 3.2, only. It can be seen that the first detectable hits are below a threshold of 50 [dB.sub.AE]. When passing a strain value of 0.8 %, the amount as well as the amplitude of the signals increases significantly. This means that beyond this point irreversible damages occur within the specimen and thereby induce acoustic sound waves. Lower amplitudes are observed at the beginning of the damages. Accordingly, further strain leads to higher amplitudes. But considering the amplitude only is insufficient, because of the high damping rate of plastics. However, the sudden change in amplitude is a strong indication for reaching the critical strain.
[FIGURE 4 OMITTED]
In comparison to that, damages can be observed for PC-GF30 by far lower strains. The permissible strain that causes an increase in acoustic emissions is reached already at 0.6 %. According to that, the higher glass fiber content decreases the strain at break, which can be seen in Table 2. Results for PC-GF30 are not presented graphically, because they are close to that of the long fiber reinforced polycarbonate (PC-LGF35), which are shown in Figure 5. The increase of acoustic emissions already starts at a strain of 0.5 %, even though the strain at break of the specimen is slightly higher. However, for this material a threshold of [approximately equal to] 50 [dB.sub.AE] can be observed as well.
Fiber content and length both influence the conduction of the acoustic waves through the specimen. This results not only to a rise in the total amount of detected acoustic emissions with higher fiber content and length, but also to an increase of noise emissions. For non-reinforced PC, hardly any acoustic signals are detected due to high damping. Therefore, the determination of the critical strain for unfilled PC is not possible with this method.
[FIGURE 5 OMITTED]
In addition, the acoustic emissions that occur are classified by their peak frequency. As stated before, the peak frequency can be assigned to the different failure mechanisms. The use of pattern techniques allows to distinguish between different acoustic emission signals. Figure 6 shows the resulting peak frequencies during a tensile test of PC-GF20.
[FIGURE 6 OMITTED]
Frequencies below 200 kHz are attributed to matrix cracks. It has to be noted that noise signals generally have a low frequency and thereby blur with the signals caused by matrix cracks. In Figure 7 this blurring is more obvious since emitted signals are detected during the complete tensile test of the long fiber reinforced polycarbonate (PC-LGF35).
Peak frequencies from 200 kHz to 320 kHz are interpreted as interfacial failure due to a high rate of fiber pull-out. This can be confirmed by SEM images which are shown in each diagram. However, the weak fiber-matrix adhesion could only be found in the short fiber reinforced specimens, whereas the fiber-matrix adhesion is significantly higher in the long fiber specimens (PC-LGF35). All peak frequencies higher than 320 kHz are assigned to fiber breakage.
[FIGURE 7 OMITTED]
The first fiber breakage is observed at a strain of [epsilon] [approximately equal to] 0.8 % for PC-GF20 and [epsilon] [approximately equal to] 0.6 % for PC-LGF35. Finally, these values are correlating with the permissible strain by exceeding a threshold for amplitude.
The difference between the actual beginning of damages and the strain at break for the discontinuous fiber reinforced plastics is compared in Figure 8. It can be stated that first micro cracks appear much earlier than the material fails. In comparison to literature , which gives a range of 1-2 % for stiff thermoplastic reinforced materials, the critical strain values found in this work are lower. Moreover, Figure 8 is showing that even within this material group, detectable differences are found.
5. Conclusion and Outlook
The appearance of micro cracks has been correlated to a specific strain value which is interpreted as the so called critical strain. Tough, the acoustic emission analysis is a fast approach to detect the critical strain of fiber reinforced plastics. The deeper examination of the signal's amplitude provides a better indication of the critical strain. The use of frequency based criteria allows for a better distinction between the occurring fracture mechanisms within the reinforced materials. Finally, the two methods lead to comparable values for the critical strain. The total amount of detected signals in general increases with the fiber content and fiber length.
To validate this method and the determined critical strain values, it has to be verified with different proven methods such as mentioned in Chapter 2. Further investigations on the acoustic emission analysis have to exclude noise signals more reliably. Since non-reinforced thermoplastic's parts are harder to calculate and design, the method should be extended to be applicable to this group of plastics materials.
The authors would like to thank Covestro, Leverkusen/Germany for providing the testing materials. The findings presented in this work were funded by the German Federal Ministry for Economy and Energy (BMWi) administered by the Federation of Industrial Research Association (AIF).
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Fabian WILLEMS (1), Johannes BENZ (1), Christian BONTEN (1)
(1) Institut fur Kunststofftechnik, University of Stuttgart; Stuttgart, Germany Phone: +49 711 685 62883, Fax: +49 711 685 85335; e-mail: Fabian.Willems@ikt.uni-stuttgart.de, Johannes.Benz@ikt.uni-stuttgart.de, Christian.Bonten@ikt.uni-stuttgart.de
Table 1. Material specification Short form Fiber content wt.-% Fiber type Classification PC unreinforced Covestro, Makrolon [R] 3105 PC-GF20 20 short glass fiber Covestro, Makrolon [R] 8025 PC-GF30 30 short glass fiber Covestro, Makrolon [R] 8035 PC-LGF35 35 long glass fiber Covestro, Makrolon [R] 8345 Table 2. Structural properties of the used materials material Young.s modulus in MPa tensile strength in MPa PC 2339 60.62 PC-GF20 4209 53.91 PC-GF30 6486 64.45 PC-LGF35 9730 122.72 material strain at break in % PC 77.35 PC-GF20 3.12 PC-GF30 2.05 PC-LGF35 2.39 strain at break first micro cracks PC-GF20 0.8% 30.% PC-GF30 0.6% 2.0% PC-LGF35 0.5% 2.4% Figure 8. Comparison of the detected micro cracks by different reinforced materials Note: Table made from bar graph.
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|Author:||Willems, Fabian; Benz, Johannes; Bonten, Christian|
|Publication:||Journal of Acoustic Emission|
|Date:||Jan 1, 2016|
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