Experimental Investigation of Dynamic Fracture Initiation in PMMA Submerged in Water
The mode-I dynamic fracture response of notched PMMA plates submerged in water was investigated. The experimental setup utilized was designed to study underwater crack propagation with the aid of visualization techniques to obtain quantitative and qualitative results. High-speed imaging and the method of transmitted caustics were used to complete the measurements. The main objective of this study was to determine the effect of surrounding water on the dynamic fracture behavior of samples as they were impacted. The properties measured to assess the effect of water were the stress intensity factor and crack speed in the initial stages of crack propagation. Experiments were also completed for samples surrounded by air for comparison purposes. Results showed that the presence of water had no effect on the fracture behavior of PMMA at strain rates of the order of 102 s−1.
KeywordsUnderwater Dynamic fracture High-speed imaging Impact loading Caustics
The study of fracture initiation in materials subjected to dynamic loading is necessary to estimate the allowable stresses that structures can withstand at high strain rates. However, an experimental study of structures subjected to extreme conditions, such as underwater dynamic loading, can be particularly challenging since the implementation of visualization techniques and load characterization methods can be complicated compared to air environment experiments. In most cases, these events constitute situations involving significant fluid-solid interactions, which could threaten the integrity of structures and potentially lead to catastrophic failure. For instance, coastal buildings, ship hulls subjected to wave slamming, or submarines subjected to underwater explosions are scenarios where catastrophic failure can occur. Therefore, it is necessary to understand the fracture behavior of structures in underwater situations when subjected to dynamic loading conditions in order to improve future design considerations and minimize damage. The experiments were performed on Poly(methyl methacrylate) (PMMA). Even though not typically used as an underwater structural material, PMMA can be used for windows in submarines. PMMA is a well-characterized material whose dynamic fracture behavior has been studied for different fracture modes and loading conditions [1, 2]. PMMA was used in this work to develop the experimental setup and visualization technique for underwater conditions, as well as to understand its dynamic fracture behavior when submerged in water.
It is well known that the main factors that affect the fracture toughness of a material are the specimen dimensions, geometry, temperature, molecular weight, and loading rate. Furthermore, it has been discovered that the surrounding environment has an important role in the fracture behavior of a material . Specifically, the effects of a liquid environment on a propagating crack have been studied for many types of materials and liquid environments subjected to quasi-static loading. Some of the most relevant studies and their findings will be briefly described in this section.
One of the first studies on the effect of liquid environments on fracture was performed on PMMA and inorganic glass by Williams and Marshall . A fracture mechanics approach was used in conjunction with time-dependent material parameters to describe crack propagation in both air and liquid environments. A fluid flow model was inserted into crack propagation analysis to describe how failure processes were developed under different surrounding environments. This model was applied for crack speeds of up to 10−1 m/s and, among their results, it was stated that water causes plasticization of crack fronts.
Mai  performed an experimental study to examine continuous slow cracking of PMMA in the presence of a variety of liquid environments. Single-edge notched specimens were subjected to uniaxial loading at strain rates on the order of 10−3–10−2 s−1. It was discovered that there is an increase in the energy required for fracture to occur in the presence of liquids, such as water, oils and alcohols, thus, plasticizing the crack-tip and increasing the toughness of the material. These results complement the findings by Williams and Marshall . Additionally, it was discovered that the effect of water on fracture toughness is rate sensitive, which means that the effect of water on crack propagation was dependent on the crack-tip speed. Michalske and Frechette  conducted further studies to analyze the rate sensitivity of fracture toughness and proposed that for crack-tip speeds higher than 10−1 m/s, an accelerating crack is able to completely escape all effects of water. This behavior was attributed to the viscosity of the liquid, which does not allow the liquid to flow into the crack-tip fast enough. In other words, the moment the crack-tip speed is fast enough for it to escape the effect of the surrounding liquid, the fracture behavior of the material is the same as in air.
Additional studies have yielded similar results, which can be summarized in that, at low crack-tip speeds, fracture properties are drastically changed when a crack propagates while immersed in water. At low strain rates, the fracture toughness of PMMA increases to almost double that of the material in air due to the plasticization effect of water. The reason for this behavior is that the duration of the fracture event is longer, which allows more time for water to flow into the crack tip and promote plasticization. On the other hand, as the strain rate is increased, water does not seem to affect the fracture behavior of the material [7, 8].
Alternative mechanisms have been suggested to explain the effect of liquids on low-speed crack propagation. Among some of those mechanisms are surface tension, hydrogen bonding breakage or chemical interactions between the surrounding liquid and the polymer, and the absorption of some of the stored elastic strain energy by the liquid [3, 9, 10, 11]. Nevertheless, it seems that plasticization occurring on the crack-tip at strain rates lower than 10−2 s−1  or crack propagation speeds lower than 10−1 m/s [6, 10] prevails as the most accepted explanation for the variation of fracture behavior of PMMA in the presence of water.
All the previously mentioned experiments have been performed for specimens subjected to quasi-static loading and resulting crack-tip speeds in the range of 3 × 10−5 to 2 × 10−1 m/s. Moreover, no studies were found in the literature for materials subjected to dynamic loading when exposed to a liquid environment. The main difference between quasi-static fracture and dynamic fracture is the presence of stress waves in the latter. The stress waves generate crack initiation and propagation if the stress amplitude overcomes the dynamic fracture toughness of the material [12, 13].
Dynamic fracture toughness is defined as the minimum stress intensity factor (SIF) required to initiate crack propagation, also referred to as the critical SIF. Under dynamic loading, the critical SIF is higher than the quasi-static fracture toughness. Ravi-Chandar and Knauss  proposed that the critical SIF grows with increasing strain rate for dynamic loading conditions because there is an intrinsic time associated with the nucleation and growth of cracking processes. Thus, if the rate of loading is smaller than the rate of microprocesses, quasi-static results would be obtained and the stress intensity factor would remain constant. Conversely, if the loading rate is increased to dynamic loading conditions, the microscopic processes would not be fully developed, leading to a tolerance for higher loads. In other words, when crack-tips are subjected to dynamic loading rates or shorter stress pulses, the stress intensity factor of the material increases monotonically, allowing the material to withstand higher loads before the crack propagates.
There exists a general understanding of the effect of surrounding water on polymer fracture for quasi-static loading and low-speed crack propagation. Nevertheless, most of the studies have used simple fracture tests to quantify the effects of surrounding liquids, and real-time crack-tip behavior under extreme environmental conditions has been much less studied . An extension of these studies to higher strain rates could possibly identify other mechanisms that may affect the dynamic fracture behavior of a material since it is well known that the mechanical response of PMMA changes when it is subjected to dynamic loading. For this reason, in this study, crack initiation in PMMA immersed in water when subjected to an impact were investigated. These experiments were executed to observe if there is any sort of coupling between the surrounding fluid and the solid during the impact event that would affect the dynamic behavior of cracks propagating underwater, e.g., surface energy dissipation into the surrounding water may arise due to higher strain rate. To the best of the authors’ knowledge, there have been no previous experimental studies utilizing high-speed visualization to measure in-situ fracture initiation when the material has been subjected to strain rates in the orders of 102 s−1. The optical method of transmitted caustics with high-speed imaging and simultaneous strain gauge measurements were utilized in these experiments. These experiments quantified the fracture behavior of PMMA, and the SIF and crack-tip speeds were compared for cracks initiated in air and water.
Methods and Material
To simulate dynamic loading conditions on structures immersed in a water environment, an impact was generated using a 10 mm diameter spherical steel projectile launched onto rectangular PMMA notched samples with mid-sections immersed in water.
Commercially available PMMA (from Emco Industrial Plastics, Inc) was used to make the samples for these experiments. The geometry of these samples with dimensions 300 × 40 × 3.125 mm3, similar to the ones utilized by Theocaris and Katsamanis [1, 15, 16], was chosen to obtain mode-I crack propagation during impact. The impact was generated with a spherical projectile to cause a point load, which is convenient for these experiments due to the small thickness of the samples. Once the projectile impinged on the edge of the sample, a compressive pulse travelled down the length of the specimen and reflected back from its free end as a tensile pulse. By applying a point load, the length of the pulse was controlled such that there was no interaction between the compressive and tensile pulse in the vicinity of the crack-tip. When the tensile pulse reached the notch, it promoted mode-I fracture if the stress amplitude of the pulse was sufficiently high . Figure 1 shows the geometry of the sample. The design of this sample was such that plane stress was assumed . Prior to each experiment, one strain gauge was installed on each sample. These gauges were attached at the mid-height of the sample, 50 mm behind the notch as seen from the impact direction, to measure the strain response of the material.
Method of Caustics in Liquid Media
The method of caustics was applied in compliance with the guidelines outlined in . The method of caustics is suitable for these experiments because it allows visualization of crack propagation in transparent media, such as air or water, which was used to quantify the SIF and crack-tip speed of PMMA. The principles of this method have been described in detail elsewhere , so only relevant equations and values used for data analysis will be presented.
Experimental constants and material properties used for the method of caustics
Distance to reference plane
Stress optical coefficient in air
Stress optical coefficient in water
Longitudinal wave speeda
Transverse wave speeda
Results and Discussion
The repeatability of the loading conditions was interpreted by comparing the impact speed for each experiment, and the strain response obtained from the strain gauges attached to each sample. The impact speed was measured using a velocity sensor attached to the exit of the gun barrel. As the projectile passed by this sensor, a square wave was generated. The pulse duration of the square wave, \(\Delta\)t, represents the time it took the sabot to travel through the sensor; thus, \(\Delta\)t combined with the known length of the sabot was utilized to calculate the impact speed. The projectile speed used for these experiments was 37.83 ± 0.4 m/s and 38.83 ± 1.1 m/s for experiments in air and water, respectively. At this impact speed, stress waves with a pulse duration of approximately 70 \(\upmu\)s were generated in the samples.
In this work, it was initially proposed that at high loading rates, a coupling effect between the structure and surrounding liquid may result in a variation of dynamic fracture of the material. However, even though a small difference in the strain response was captured by the strain gauges, namely a dampening effect on the amplitude of the tensile pulse exemplified in Fig. 6, no significant effect on the fracture behavior of the samples was observed. These findings partially agree with previously reported results in which surrounding water showed no effect on cracks propagating faster than 10−1 m/s. These studies indicated that at some point the crack-tip speed was too fast for the liquid to diffuse into the crack-tip and plasticize it. On the other hand, the inability of a liquid to diffuse into a propagating crack does not explain why no plasticizing effect was observed on the notch before crack initiation occurred. Prior to the crack initiation stage, there was sufficient time for surrounding water to plasticize the crack tip, yet the fracture behavior was the same as in air. Therefore, it is suggested that plasticization did occur prior to the fracture event, but the effect of the strain rate, which also increases the fracture toughness of the material, dominated the fracture behavior of the material, resulting in similar results for both environments studied. An analytical model to predict the results obtained here is beyond the present scope of this work but will be addressed in future studies.
An experimental investigation on underwater dynamic fracture initiation of PMMA was completed. To the best of the authors’ knowledge, this constitutes the first study in which dynamic underwater crack propagation is observed and quantitative data is obtained using visualization techniques. The stress intensity factor and crack-tip speeds were measured using the method of caustics coupled with high-speed photography. Results showed that water media has no significant effect on the dynamic fracture initiation of the material when it is subjected to an impact resulting in strain rates of 102 s−1. It was initially proposed that other influencing mechanisms on underwater crack propagation, such as surface energy dissipation into the surrounding water, may arise due to higher strain rate. However, no significant variation was observed in the analysis of the crack tip speed or SIF. Results also imply that the mechanism that prevented water from having an effect on the crack propagation of PMMA subjected to low strain rates prevails at the higher strain rates studied here (up to 102 s−1). Moreover, since the notch of the samples was static prior to crack initiation, it was proposed that water does plasticize the crack tip before fracture occurs, but strain rate effects overcome any effect that water induced. Thus, strain rate seems to dominate the fracture event by overcoming the plasticizing mechanism prior to crack initiation and by generating fast crack-tip speeds that do not to allow water to diffuse into the propagating crack.
Clearly, the aim of this study has been to demonstrate the experimental capabilities available to determine the dynamic fracture of transparent materials underwater. The main limitation in the present work are the assumptions taken to overcome the optical effect that water causes. More accurate results could be obtained if a more robust visualization technique, such as digital image correlation (DIC), could be implemented to quantify the dynamic fracture of materials submerged in water. The use of DIC will require higher temporal and spatial resolution, which can be resolved by using ultra high-speed cameras. While beyond the scope of this work, the aforementioned discussion is part of an ongoing effort to continue the study of dynamic fracture in extreme environments and to contribute to the experimental mechanics community.
The authors gratefully acknowledge the support of the Office of Naval Research through Grant Number N000141310607 (Dr. Y.D.S. Rajapakse, Program Manager) and the National Science Foundation through Grant Number CMMI-1332840.
- 4.Williams JG, Marshall GP (1975) Environmental crack and craze growth phenomena in polymers. In: Proceedings of the royal society of London A: mathematical, physical and engineering sciences, vol 342, pp 55–77. The Royal SocietyGoogle Scholar
- 12.Ravi-Chandar K (2004) Dynamic fracture. Elsevier, AmsterdamGoogle Scholar
- 15.Delpino Gonzales O, Eliasson V (2015a) Influence of water uptake on dynamic fracture behavior of poly (methyl methacrylate). Exp Mech 56(1): 59–68Google Scholar
- 16.Delpino Gonzales O, Eliasson V (2015b) Effect of water content on dynamic fracture initiation of vinyl ester. Exp Mech 56(4): 637–644Google Scholar
- 17.Zukas JA (1982) Impact dynamics. Wiley, New YorkGoogle Scholar
- 21.Takahashi K, Takeda N, Abo-El-Ezz AE (1986) Application of the caustic method to an environmental crack-craze growth problem. In: Photoelasticity, Springer, New York, p 129–134Google Scholar
- 22.Shimizu K, Takahashi S, Danyluk HT (1986) Some new trials on the technique of the method of caustics. In: Photoelasticity, Springer, New York, p 121–128Google Scholar