Keywords

Introduction

Embedded high frequency signal effects derived from wave impacts on ships can affect failure mechanisms on the structures and have an adverse impact on the fatigue life of the vessel. While operating in a sea environment, ship structures can be subject to many operational loads (wind, pressure, temperature, etc.), one of which is the structural effects derived from the surrounding sea environment. Typically, the wave environment applies an ordinary wave component which drives the primary bending stress of the vessel, along with a more stochastically driven element that manifest itself as wave impacts. This dynamic wave impacts results in a high frequency vibratory response signals load applied to ship structures. The vibratory nature of these high frequency responses makes the design of structures increasingly complex in nature due to their uncertainty, designers and naval design rule societies have relied on methods such as safety factors and/or margins of safety to account for its effects. A typical wave impact on a Naval Structure imparts a time dependent pulse load that exhibits a higher frequency logarithmic decaying sinusoidal response when measured via experimental means and captured utilizing data acquisition systems. The figure below displays one of these signals, where the measured signal can be decomposed into its different components by applying filtering techniques.

Under the current practices, the peaks of these responses are utilized to compare to the quasi-static design stresses, as well as evaluate the fatigue life of the structures either under constant or variable amplitude experimentation. Figure 1 above displays this kind of behavior, where underloads and underloads affect the crack growth rate behavior of material under a simplified signal approach [1].

Fig. 1
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Load Sequencing [2]

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But there are additional higher frequency characteristics to these high frequency signals are not currently taken into consideration. Existing academic research has been centered on capturing a simplified sinusoidal response associated with this slamming event and embedded high frequency response, but has not addressed logarithmic decay, signal frequency, or frequency of occurrence. Work by Sumi et al. has centered on more complex signals, where bounding functions where used to predict crack growth behavior [2], and the results show an influence of crack length predictions based on utilizing these bounding functions.

All these factors have associated uncertainty and cause impact on fatigue life and failure mechanisms exhibited by ship structures, work by researchers such as Fricke et al. has shown damage variation as related to amplitude of high frequency signals [3]. The work presented is a multiphase task that looks to gather fundamental understanding of the effects of this high frequency loading on Aluminum 5xxx material, accounting for some of the signal’s characteristics, and through an experimental evaluation assess its impact on the local failure mechanism and life cycle models. The foundational findings of this research, can then be used in future investigative efforts to develop analytical models addressing heat affected zones, provide underpinnings for high fidelity numerical modelling, eventually providing broader toolsets to designers that can be used to reduce the dependency on safety factors and introduce more rigorous failure mechanism design criterion. The presented work has the following two basic research objectives: develop and execute an experimental evaluation matrix to investigate a bound set of effects of embedded high frequency signals on fatigue crack growth and associated initiation of failure, and develop failure models that incorporate uncertainty in signal parameters variation and their associated influence on material failure. The first is presented as part of this work, and the latter to be presented as part of future efforts.

Experiment Design

This work builds and complements on existing work developed by Hart and Bruck [4] where the investigators looked at failure of aluminum 5052-H32 and the applications of composite patches to aluminum and the effects of crack growth. Whereas their work centered on the utilization of a composite laminate to mitigate crack growth on ultimate failure, this work looks at the effects of crack growth based on loading condition. Figure 2 below displays the aluminum material properties that Hart and Bruck obtained utilizing ATSM 8 [5] and ASTM E466 [6], as well as the layout of their center crack panel specimens. The Modulus listed for the material is 70.9 MPa, the yield at 2% offset is 116 MPa, and the parameters α and n at 9.9 and 0.22 respectively.

Fig. 2
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5052-H32 Material properties and Specimen Failure [5]

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Initial experiments were carried out on this setup for this work, but the results indicated that there was an imbalance of crack growth between the left and right cracks growing from the notch during fatigue loading. Figure 3 above displays the friction wedge grip setup, as well as the crack length visually captured via microscope measurements, the left and right cracks shows differences over 0.5 mm at 80 k cycles. However, one of the promising results from these experiments was that the setup captured effects of crack growth when a high frequency pulse was applied at 80 K cycles, the crack growth shows a variation of the crack growth rate (Da/DN) before and after the pulse is applied.

Fig. 3
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Initial Specimen Setup

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It is important to mention that whereas the experiments by Hart and Bruck utilized a four post MTS servo hydraulic setup since they were interested in the ultimate loading capacity, this work work required flexibility to apply smaller loads with different characteristics, hence a two post Bose ElectroForce frame was used, which has the capacity of applying loadings up to 100 Hz and 3000 N. This device has a built in displacement meter with errors of less than 5 μm, and it has a block waveform generation software that allows for the implementation of unique load signals. Fast Fourier Transforms methods were utilized to ensure that the programmed signal and the applied signals displayed the required frequencies.

The specimen configuration shown in Fig. 4 was developed and it is an amalgamation of several ASTM methods, this was conducted to address the significant asymmetry observed with crack growth as previously described. ASTM E8 [5] guidance was utilized to develop the specimen tapers towards test region, while ASTM E647 [7] middle tension specimen configuration was utilized to size the center notch and test region, maintaining the configuration carried out by Hart and Bruck. Since a clevis pin was utilized, ASTM E338 [8] was utilized to develop end reinforcements and alignment tabs for the end pin connections to ensure the failure would not occur in or adjacent to the clevis pin area. Electrical Discharge Machining (EDM) techniques were utilized to manufacture the specimens, providing a stable level of accuracy for the component geometry, it was also critical to ensure alignment of end pins and size and location of center notch. Several test were carried out in this setup, along with finite element analysis, and microscope evaluations of the clevis pin areas and tapers to ensure no failure was visible and that crack growth would be focused towards the test region and adjacent to the notch. The material for the specimen in marine grade aluminum 5052-H32, with a nominal thickness of 2.29 mm (0.09in) Fig 4. Also shows how the clevis pins were utilized in the loading train, and end adaptors that were used to interface with the Bose frame and to help with specimen load alignment, Universal Grip LLC. components were utilized for this setup: Adapter—Male Bolt 5/8″-18 w/1″ length, Universal Joint Adapter; in addition, Mark-10 G1090 high capacity clevis grip (pair) were utilized. The load capacity of the members was at a minimal load of 9KN, hence far exceeding the capacity of the Bose equipment of 3KN, and ensuring no failure could be accidentally induced to the Bose fixture from a failure of the adapters under load.

Fig. 4
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Clevis Pin Specimen and Setup

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The experimental setup consisted of several components setup to achieve two goals: observe/capture the crack growth on the back of the specimens using a microscope, and to capture the surface strains on the front face of the specimen utilizing digital image correlation techniques. Figure 5 below details the setup utilized for these experiments.

Fig. 5
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Experiment Setup

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In the back face of the specimens, an optics zoom inspection microscope head by Edmunds Optics was used, along with a Dolan-Jenner MI-150 fiber optic illuminator with a fiber optic ring light accessory, was utilized to capture the crack growth on the back side of the specimen. The setup was connected with a rack and pinion positioning system that allowed movement of the microscope along three axis via a hand knob, hence allowing the positioning of the microscope in different locations to capture crack growth. The microscope was able to visualize square areas of 0.5 mm on each side. Several digital pictures were taken on each crack emanating from each notch, which overlapped, and then were stitched together to form an overall view of the crack of the specimen.

In the front face of the specimen, a Point Gray Flea FL3-U3-88S2C-C digital camera attached to a Tamron 28–80 mm f/3.5–22 lens and adapter was used to capture static pictures of the surface of the specimen. In addition, two 250 W halogen Lowel Pro Lights were utilized to provide lighting to the specimen. The lights were not directly aimed at the specimens, but instead aimed at locations adjacent to the mid-point of the specimen, and focused as to provide evenly dispersed light flooding on the specimen. Digital Image Correlation (DIC) was utilized on the front face of the specimens to capture field surface strains [9], in order to capture these images, the area had to be prepped to generate distinct patterns that can be captured with PointGrey FlyCap 2 V2.11.3 and processed utilizing VIC-2D Ver6.0.6 by Correlated Solutions (Lexington, SC).

The figure below shows the typical DIC pattern applied, the generation of this pattern is achieved by first applying a coat of flat white paint as the background, and the black speckle patterns was developed by not directly applying paint, but instead relying on lightweight particles that slowly settle over the specimen. This procedure requires practice as the specimens needs to be rotated over multiple passes, ending with a specimen that has an adequate gray scaling and consistent patterns that would allow for acceptable DIC measurements. Several references were utilized to obtain best practices and recommendations on acceptable DIC techniques to obtain feasible results, one such body of work in conducted by the internationals digital image correlation society [10] (Fig. 6).

Fig. 6
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Specimen and Speckle Pattern

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Experiment Protocol and Matrix

In order to explore the variability of the high frequency pulses, a couple of items das to be developed, first was a consistent process/protocol that was repeatable across experiments, and second was an experimental matrix that varied certain parameters to determine their influence on the response. Figure 7 below outlines the experimental process utilized. It is worth noting that each step below is a top level overview, as there are substantial details on each step that are needed for consistency, i.e. the number of photographs taken during measurements, camera settings, etc.

Fig. 7
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Experimental Process

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The specimen preparation was the initial step in the configuration, the back side of the specimens that faced the microscope was polished to a mirror type finish, this aided in the identification of the crack tip. The front of the specimens received a DIC spackle pattern that had a sigma level equal or below 0.001 [9]. The sigma level was tested during the baseline measurements stages until the desired value was achieved. Prepping the specimens several times was required in some cases to achieve the desired values, as inconsistent baseline measurements would result in unpredictable data during the later stages of the experiments. The baseline measurements also consisted on utilizing DIC to evaluate the displacement of the fixture. i.e. if the load frame indicated a 0.2 mm displacement, do the DIC measurements also show a similar value? This was done by only pining the stationary end of the specimen and comparing the displacement between the load frame and DIC calculations. Additional baseline measurements included static DIC measurements at 200, 1100, and 2000 N, as well as microscope crack measurements at no load and 2000 N. The initial crack growth was a step used to develop a crack and go outside the envelope of the stress-strain effects of the notch radius [11]. The notch radius was 0.17 mm, and an initial starter crack was developed to be around 0.5 mm in length. The HF pulse was applied at 40 K cycles, subsequent measurements monitored the crack growth rates after the HF pulse was applied to evaluate the recovery. It is important to note that the load ranged from 200 N to 2000 N, where the stress ratio R = 0.1, the frequency used for fatigue was 5 Hz, and the nominal Stress intensity ΔK = 6.07 MPa-m0.5.

The experimental matrix utilized is shown in the table below, it consists of a baseline test where no HF pulse is applied, and a 3 × 3 matrix with three level and two factors (amplitude, frequency), resulting in nine treatments, where the amplitude of the pulse is increased in 1/3 amplitude increments, and frequencies that range between 4 and 10 times the baseline frequency i.e. specimen 3C had a peak amplitude of 2900 N, and an HF pulse with a frequency of 50 Hz.

For this matrix, the HF pulse was only applied at the peak of the ordinary wave of 5 Hz, hence the phase shift was held constant, as well as the log decrement of the function as maintained at 0.21. Introduction of other factors would increase the matrix size to a 33 design resulting in 27 treatments.

Initial Results

The initial results provided adequate results, but also highlighted areas of the experiments that required tuning to capture the desired data. Figure 8 below outlines the crack length results of three experiments and the baseline. The frequency is contact at 20 Hz, but the amplitude is varied for each experiment. It can be seen that after the HF pulse is applied at 40 K cycles, the crack growth rate is different over time as compared to the baseline, with block 1C (20 Hz, 2900 N) displaying the longest recovery. These measurements are based on microscope measurements of the crack length on the left and right side of the crack.

Fig. 8
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Initial Results, Amplitude Variability, 20 Hz

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Reviewing the DIC measurements with Vic2D on the front side of the specimens, one can see variation on the strain fields and crack length and dA/dn as shown in Fig. 9 below.

Fig. 9
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Block 2C at HF of 35 Hz and Peak Amplitude of 2900 N

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The data results indicate that a higher fidelity was needed in order to capture the behavior, the data acquisition of every 10 K cycles does not provide sufficient fidelity to address the underlying behavior observed. At the core of this work, models by Wheeler [12] and Willemborg [13]. These models look at the plastic zone behavior, Wheeler relying on crack growth rates, and Willemborg utilizing stress intensity for the calculation, as follows (Fig. 10).

Fig. 10
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Wheeler and Willemborg Models

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More recent research work by Mehrzadi & Taheri [14], and Chen [15] outline the behavior of the plastic zone ahead of the crack tip.

The common thread of all these models is that an overload plastic zone is created once an overload/underload occurs, and the magnitude of this region has an effect on the crack growth rate as long as the cyclic plastic zone stays within its boundaries. In our case, the data obtained indicated that an overload zone is created, but the fidelity of the data does not support the identification of its progression over time. In addition, it is critical to identify the location of the crack tip with respect to the plastic zones around it.

Data Processing

Of the two limitations outlined above, data fidelity improvements can be addressed by capturing a higher number of data points, instead of capturing data every 10 K cycles, capturing data ever 2 K cycles. The drawback of this approach is that the data required for processing increases in magnitude for each test, hence a more robust/automated method of identifying the crack tip location and plastic zone behavior is needed. A unique method for using DIC for crack detection was developed by Bruck [16] while utilizing curve fitting to locate the crack tip location based on the vertical displacement field. Other researchers have tackled this problem, such as Yates who evaluated the vertical displacement field ahead of the crack tip [17]. Since the vertical displacement gradient ahead of the crack tip is much higher than other zones, a threshold can be set based on the gradient, and hence, a crack tip location can be obtained.

This work included extracting DIC output data to MATLAB in order to program algorithms to find the crack tip location. The process for this extraction included exporting output vectors (x, y, V, U, Von Mises strain) from DIC at various pixel locations, for each load set (200, 1100, & 2000 N), and time step (30 K, 32 K cycles, etc.). This data was then brought into MATLAB, where it was arranged in matrix form, and the gradient of V along the vertical direction was calculated. Once this was completed, data could be processed for visualization, where the maximum gradient can be picked from each slide of the notch in the vertical direction. The figure below shows the gradient calculated plotted along the Z axis, hence providing a unique method to visualize the behavior around the crack tip by. Figure 11 below outlines how the data can be plotted in 3D, and then filtered to show a specific range.

Fig. 11
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Vertical Gradient Vp

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This data can also be used to determine the crack path and other output vectors further analyzed to automatically show Von misses strains when compared with the crack tip location. This is a unique way to visualize the behavior shown by Yates et al., uniquely developed to process the output experimental data.

This methods also provides a unique process for the identification of the plastic zone areas and begin the comparison with theoretical models [18] where the approximate size of the plastic zone as a function of angular position, r(ϑ), can be estimated by formulations that are based on yield criterion, as follows:

$$ r\left(\theta \right)=\frac{1}{4\pi }{\left(\frac{K_I}{\sigma_y}\right)}^2\left(\frac{3}{2}{\sin}^2\theta +\cos \theta +1\right) $$
$$ r\left(\theta \right)=\frac{1}{4\pi }{\left(\frac{K_I}{\sigma_y}\right)}^2\left(\frac{3}{2}{\sin}^2\theta +{\left(1-{\nu}^2\right)}^2\left(1+\cos \theta \right)\right) $$

While the work on outlined above displays the complex shapes of the plastic zones under plane stress and plan strain conditions, these items can be simplified to a circular zone ahead of the crack, as shown by Chen [15].

Experimental Results & Follow on Work

The data captured now allows a visualization of the evolution of plastic zones with respect to the crack tip location, Fig. 12 below shows the effects of block 2C which had a HF pulse of 35 Hz and 2900 N in magnitude. The application of this small pulse showed a change is the residual strain ahead of the crack tip and the loaded strain paths. It also allows the inclusion of the calculated crack path using the strain gradient value in the system.

Fig. 12
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eyy strain pre and post Block 2C at HF of 35 Hz and Peak Amplitude of 2900 N

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Work was carried out to compare the error values obtained between microscope measurement and DIC calculated values. Figure 13 below displays the horizontal crack length measurements for the crack propagating form each notch (left and right). The timeline of interest ranges from 36 K cycles to 62 K cycles.

Fig. 13
figure 13

comparison of DIC and microscope crack length, Block 2C at HF of 35 Hz and Peak Amplitude of 2900 N

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Another aspect of the work is evaluating the failure mechanism observed, while the microscope measurements provide a view of the crack propagation, a Barker’s etch method [19] was used for anodizing the aluminum alloy, and then utilizing optical microscopy with polarized lights to observe the grain boundary and the propagated crack. Figure 14 below displays results at 500 μm, 100 μm, and 20 μm magnification levels, allowing the evaluation of the crack propagation through the grain, and the investigation of shielding effects such as contact and deflection on crack growth [20].

Fig. 14
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Barkers Etch of Specimen, Block 2C, HF at 35 Hz and 2900 N

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The work presented has resulted in procedures utilizing DIC for capturing and quantifying details of the fatigue crack growth associated with HF pulse loading. In future work, the dimensions of the HF pulse plastic zone can be captured, and then further utilizing the DIC data, it will be possible to show the plastic zone progression and change over time to evaluate the applicability of failure models such as Willemborg. Another important aspect will be how the added definition of the plastic zone observed affects the crack path. There are several instances, such as the data in Fig. 13, where there is a deviation of the crack path direction following the occurrence of the HF pulse, where strain fields surrounding the crack tip can be taken into consideration to understand the origin of the deviation. Finally, the experiments in Table 1 can be expanded to obtain higher fidelity of data post the application of the high frequency pulse.

Table 1 Experimental matrix
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Conclusions

Existing models, like the Wheeler, Willemborg, and variations of these, have been utilized to predict the crack growth behavior with varying degrees of success. In this study, we created experimental matrices to explore the effects of overload/underload combinations on fatigue crack growth in 5xxx aluminum, typically used in marine applications. Both visual inspection of crack tip location, and using Digital Image Correlation (DIC) techniques for characterization of the crack tip deformation fields. These techniques were used on a designed center crack tension (CCT) panel specimens to measure crack growth. DIC techniques also enabled additional analysis of strain fields to elucidate on the conditions responsible for the change in the crack growth behavior. The development of the experimental protocol was critical for capturing the desired output data for DIC and microscope measurements, and observe the behavior of the plastic zones surrounding the crack tip. Several experiments were conducted until a finalized methods that captured the required data was developed. Unique MATLAB algorithms provided a means to develop innovative approaches to automatically capture the crack tip location and display it along with observed behavior around the crack tip. The next phase of this work includes utilizing this observed data to elucidate the mechanics of crack growth behavior when affected by an embedded high frequency load models for fatigue crack growth.