Abstract

The ASME pressure vessels for human occupancy (PVHO) codes and standards are engineering standards developed to provide a reliable design method for pressure vessel windows. This empirical method is based primarily on years of government-sponsored testing and development and does not directly use engineering theory. This empirical algorithm makes it challenging to revise without additional large-scale physical testing. The industries using the PVHO code need a way to incorporate advances in material science, manufacturing technology, and overall engineering advances without spending years in code case review. Verification and validation techniques, coupled with stochastic finite element analysis (FEA) to address operational variables, can be the basis for a “design by analysis” method to complement the existing testing requirements to produce a full engineering package consistent with other pressure vessel and pressure vessel component design. A design method sufficiently reliable for PVHO could be used in other applications.

1 Introduction and Background

Pressure vessels for human occupancy (PVHO) are those pressurized systems which have living people within them. The engineering code for designing PVHOs is ASME PVHO-1, which defines its scope as “all pressure vessels that enclose a human within their pressure boundary while under internal or external pressure exceeding a differential pressure of 15 kPa (2 psi). PVHOs include, but are not limited to, submersibles, diving bells, and personnel transfer capsules, as well as decompression, recompression, hypobaric, and hyperbaric PVHOs [1].” These are all safety-critical applications, as a sudden decompression can cause injury with pressures as low as 15 kPa (2 psig) and certain death at higher pressures. While many PVHOs are intended for stable medical facility environments, others are subject to extremes in weather while in transportation and operations, often with impact loading, thermal shock, and complex heat transfer conditions.

A key safety aspect of pressure vessels is the entire pressure boundary that is only as reliable as its weakest component. Structurally, the novel aspect of a PVHO is the window, which is needed to either observe people under treatment or for occupants to look out in order to accomplish a task. The windows are part of a “viewport” assembly incorporated into the overall pressure vessel structure. The assembly often includes elastomer or polymer gaskets and significant preloads, potentially increasing the complexity of loading on a window. Figure 1 shows the window seats incorporated into the titanium hull of the deep submergence vehicle (DSV) ALVIN prior to being installed as part of the deep-sea vessel's refit. Figure 2 shows the illustration of the updated DSV Alvin with the new hull and the windows incorporated into viewports.

Fig. 1
A section of the titanium personnel hull of the Wood Holes Oceanographic Institute's DSV ALVIN, with its PVHO-designed window seats, rated for 6500 m (2100 feet), prior to the new personnel section's installation in the 2013 upgrade for the deep submergence vehicle. The seats for the 90 deg conical frustums are covered to protect the surface from damage which could create a leak. The outer diameter of the windows is 430 mm (17 in.) (Photo by Bart Kemper).
Fig. 1
A section of the titanium personnel hull of the Wood Holes Oceanographic Institute's DSV ALVIN, with its PVHO-designed window seats, rated for 6500 m (2100 feet), prior to the new personnel section's installation in the 2013 upgrade for the deep submergence vehicle. The seats for the 90 deg conical frustums are covered to protect the surface from damage which could create a leak. The outer diameter of the windows is 430 mm (17 in.) (Photo by Bart Kemper).
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Fig. 2
The DSV ALVIN with the spherical hull installed and viewports assembled. The acrylic conical frustum windows are held in place by an outside ring (Artist's rendition by Megan Carroll, Woods Hole Oceanographic Institute) (used with permission by Woods Hole Oceanographic Institute).
Fig. 2
The DSV ALVIN with the spherical hull installed and viewports assembled. The acrylic conical frustum windows are held in place by an outside ring (Artist's rendition by Megan Carroll, Woods Hole Oceanographic Institute) (used with permission by Woods Hole Oceanographic Institute).
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1.1 Pressure Vessel for Human Occupancy Code Development.

Historically, glass windows in PVHOs demonstrated two key challenges: a tendency to leak along any imperfection of the steel/glass interface and a tendency to fail rapidly once its capacity is exceeded. These limitations constrained diving depths and durations, such as with the DSV TRIESTE [2]. As the need for underwater depth increased, glass windows transitioned to fused quartz and the geometry transitioned to conical frustums. In addition to fused quartz, two other materials suitable for PVHO windows are identified: polymethyl methacrylate (PMMA), or “acrylic”; and polycarbonate [1,2]. PMMA is used in the vast majority of PVHO windows.

Early PVHO code development in the 1960s questioned how to evaluate these materials for a variety of uncertainties and performance-related phenomena. This included how well the window conformed to the seat, how fast defects propagated once they occurred, and how well could manufacturing flaws or in-service defects could be detected. Validation & Verification (V&V) techniques were not a formal procedure in this time period but are now a defined process [3]. Retroactively applying V&V to the published literature which formed the current code captures key aspects of the original intent while shaping a modern design by analysis method.

Modern tools such as finite element analysis (FEA) are not only an established part of modern pressure vessel design, but they have also been used for acrylics in a variety of applications [4]. FEA is being used to address issues not explicitly provided for in the current PVHO code, such as creep under load [5] and cyclic failure modes [6], in a manner consistent with other pressure vessel technology. This illustrates the need for a systematic method to supplement the existing empirical algorithm used to design PVHO windows.

1.2 Challenges and Shortfalls of an Empirical Algorithm.

The current window design process is contained in Sec. 2 of PVHO-1 [1]. Detailed review shows little technical differences from the rationale and recommendations established in 1973 [7] and the first codified form in PVHO-1 in 1977. The process can be simplified as follows:

  1. Select the window geometry from the pre-approved list.

  2. Select the maximum values for external pressure, internal pressure, ambient temperature, and internal temperatures.

  3. Based on the above, determine the correction factor from the appropriate table.

  4. Multiply the correction factor by the operational maximums, then use the adjusted pressure with the code-specified curves for that geometry to determine the window thickness. An example design curve is shown in Fig. 3.

Fig. 3
A conical frustrum window design table from PVHO-1 with illustrations of “one-way” (elevated pressure on one side” and “two way” (elevated pressure on either side) assembled viewports [1]. The window is the acrylic component with the viewport being the full assembly, including window seat, retaining ring, and bolts. Given the desired design pressure (modified by the correction factor), the chart returns a ratio of window thickness to the diameter of the opening. Deflections, stresses, and strains of the window are not considered in the process (from ASME PVHO-1. Used with permission).
Fig. 3
A conical frustrum window design table from PVHO-1 with illustrations of “one-way” (elevated pressure on one side” and “two way” (elevated pressure on either side) assembled viewports [1]. The window is the acrylic component with the viewport being the full assembly, including window seat, retaining ring, and bolts. Given the desired design pressure (modified by the correction factor), the chart returns a ratio of window thickness to the diameter of the opening. Deflections, stresses, and strains of the window are not considered in the process (from ASME PVHO-1. Used with permission).
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Despite no calculation of “allowable stresses” or similar traditional pressure design methods, there have been no incidents attributed to PVHO-1 window design [8]. This algorithm has resulted in over four decades of successful, reliable window designs spanning thousands of PVHO windows across medical chambers, diving chambers, recompression chambers, and other permutations, including submarine windows with over 20 times the PVHO baseline of 10,000 cycles [6,9] and full-ocean depth submarines that exceed the PVHO pressure chart [10].

The fundamental challenge is that the algorithm is constrained to the specific tested and validated geometries. The ASME PVHO code does not incorporate a range of other mechanical and material properties typically considered in a pressure vessel design. For example, temperature is used to identify a “correction factor,” but that does not determine material response at a given temperature nor does it consider localized temperatures. Similar to traditional pressure vessel materials like steel, changing temperatures change the compressive and tensile yield strength, compressive and tensile ultimate strength, modulus of elasticity, modulus of flexure, and other properties. While metallic pressure vessels' material properties are specified at 27.8 °C (50 °F) intervals [11], acrylic has pronounced changes in properties with temperature increments of only 5.6 °C (10 °F) [7,1214]. This indicates that the windows are more temperature sensitive than the metallic portions of the pressure boundary.

Using an empirically developed algorithm instead of a more robust series of engineering calculations locks the design process into a closed-loop set of materials, geometries, and loads tested. A novel design for a PVHO requires a “code case review,” a time-consuming process where the information is submitted to the ASME PVHO committee for consideration for inclusion as a stand-alone exception to the code. These code cases do not change the code process itself. Pressure vessel components other than acrylic windows have design processes that allow for alternate methods such as “design by rule” (Section VIII, Div. 2, Part 4) and “design by analysis” (Section VIII, Div. 2, Part 5) [11]. Design by analysis provides a methodology to use FEA to include material curve development and load cases. There are similar “by rules” and “by analysis” for postconstruction modifications, repairs, and useful remaining life assessments in ASME/API Fitness-for-Service [15]. While there are methods for repair or derating acrylic structures in other applications, there are no provisions in ASME PVHO-2, the postconstruction safety code, for evaluating in-service acrylic windows other than addressing minor surface issues [16].

The assumptions used to numerically model a structure are important. The original window materials were discussed in detail while developing the initial PVHO code. The current PVHO specifications do not consider changes in polymer technology from the original “Plexiglass G” and “MIL-P 8184” grades used in the original testing [2] to the modern crosslinked PMMA [17,18]. Implicitly, it assumes that a material that meets the PVHO-1 requirements in PVHO-1 Tables 2-3.4-1 and -2 [1] will be sufficient. Closer examination of the PVHO-1 material specification tables shows that this assumption is flawed. Materials have a specified “minimum elongation at break” to provide a measure of plastic deformation after yield, which is a measure of ductility. The PVHO code-specified minimum required elongation at break is 2% strain at an ultimate strength of 62 MPa (9000 psi), yet the elongation calculated using only the modulus of elasticity at the same ultimate strength yields an elongation of 2.25%. This results in the PVHO-1 specification allowing fully brittle behavior for acrylics [19].

The lack of a specified measure of ductility violates the historical criteria for selecting acrylic, as illustrated in Table 1. Table 1 is an example Phenomena Identification and Ranking Table (PIRT) method applied to the original body of research [2]. It uses two methods to compare window materials using importance of window characteristics: a simple tally of the scores and dividing the score by the importance value, providing a weighted result. The table's italicized values indicates PMMA had the greatest total and weighted total score, indicating that it could be a better choice for PVHO window applications. The same methodology used to recreate why acrylics were chosen can be used to evaluate grades of acrylics or new materials that may be suitable.

Table 1

PIRT chart for window material

PhenomenaImportanceFused quartzPMMAPolycarbonate
Optical transparency1101010
Sealing (ductility)2498
“Leak before failure” (failure speed)2697
Internal defects readily observed2488
Size of parts (larger is better)3785
Biologically safe in elevated temps31075
Weight4488
Total and weighted total (score/importance)45/23.759/30.051/28.8
PhenomenaImportanceFused quartzPMMAPolycarbonate
Optical transparency1101010
Sealing (ductility)2498
“Leak before failure” (failure speed)2697
Internal defects readily observed2488
Size of parts (larger is better)3785
Biologically safe in elevated temps31075
Weight4488
Total and weighted total (score/importance)45/23.759/30.051/28.8

Another premise typical of pressure vessels is they are designed using “thin wall” or “membrane” assumptions. The combination of strength of acrylic, design pressure, and the dimensions needed to hold a person requires the majority of PVHO acrylic applications to require “thick wall” pressure vessel theory. The PVHO code specifies that a joint in a spherical section must be “pure membrane compressive stress” [1]. This is not possible when the joint material between the acrylic half-spheres have 50% the strength of the cast acrylic sections. The joint cannot be considered “membrane stress” nor can it achieve “pure compressive stress” [20]. Unlike the detailed methods offered for joints in the boiler and pressure vessel code, the empirical nature of PVHO-1 and PVHO-2 precludes an analytical basis to design or evaluate joint stress.

The PVHO algorithm does not have provisions to address transient nonuniform reduced strength across the polymer thickness due to elevated ambient surface conditions. Polymers act as insulators compared to the steel hulls, slow to change temperature. The code's omission of this relationship indicates an assumption that these time-related factors can be neglected [13]. In diving systems and submersibles working in warmer climates, the ambient air temperatures are over 28 °C (100 °F) but the working depth water temperatures are 10 °C (50 °F). The acrylic windows will retain heat potentially for hours, resulting in “soft centers” with reduced mechanical strength and lower modulus of elasticity as these PVHOs dive [21]. Full ocean depth submersibles have the thickest windows and have been analyzed in order to determine the time needed to allow the windows to come to thermodynamic equilibrium [14]. Unlike the boiler and pressure vessel code, there is no method to determine stresses or deflections with different temperatures for a given pressure. This temperature sensitivity increases the uncertainty for design as well as the complexity of material loads and response. The empirical design method has proven itself over time, but the lack of direct application of engineering principles locks the entire design process into what was adopted in the early 1970s with no way to incorporate material changes, examine new geometries, or examine new types of applications and loading.

2 Introducing a New Methodology

Finite element analysis is an accepted industry tool, with codified rules for design and in-service evaluations using linear and implicit nonlinear methods [11,15]. Transient thermal conditions can be modeled using computational fluid dynamics, another computational tool available to industry [21]. Modeling acrylic applications using the classic V&V two-pronged method of numerical modeling and experimentation is well within the established use of FEA for PMMA applications ranging from biomedical [22] to aerospace [12,23] to structural [24]. The issues regarding PMMA properties, particularly the viscoelastic response, have been quantified in a manner consistent with implicit nonlinear FEA when using the previously discussed PVHO application constraints on strain rates, cyclic loading, and temperature range [4,17,2527].

Due to its current use in conventional pressure vessels, finite element analysis is a reasonable tool to advance new designs and types of glassy polymer pressure vessel components in lieu of the previous empirical method. FEA has been found to correlate well to known failure modes as well as correlate to the demonstrated reliability of ASME PVHO design [6]. FEA was part of the early development of the ASME PVHO safety standard [28,29]. NASA uses it to qualify critical structures [30]. Submarine makers outside of PVHO jurisdictions use FEA to qualify their window designs [10,14,31]. FEA is a specified method for designing a window seat in Sec. 2 of PVHO-1 [1,32], so the use of FEA to design metallic structures is acceptable for PVHO applications. There is nothing in the current PVHO code to exclude its use. However, accepted engineering practice indicates FEA alone is not sufficient.

The complex transient pressure and temperature loading regimes have been simplified in the past, as demonstrated with the limitations of the PVHO window design algorithm. Unlike in ASME BPVC Section II, there are no code-specified material values for different temperatures and conditions [11]. There are no code-specified methods to set design margins for stress, strain, or deflection in order to adjust designs for new shapes, materials, or applications. Polymer components loaded plastically often have “shape factor” design considerations, where the manner in which a material is constrained has significantly more impact on mechanical response than the same design using metallic components. This is not addressed, either. These are just some of the engineering issues that arise when trying to qualify a design that is outside the empirical PVHO method.

Stochastic FEA can harness modern computing power to address a range of interacting variables to build a more reliable design by not limiting design to a single deterministic design [3,27]. Using stochastic methods in conjunction with V&V methods can replace the lack of specified material grades and properties as well as mitigate risks associated with uncertainty through evaluating the design using a wider range of variables. For example, instead of evaluating a “full ocean depth” thick window for a single uniform temperature, the design would evaluate temperature variations based on the users design specification and the potential for transient thermal gradients. Conversely, a thin window used for a hyperbaric stretcher could be assumed to have uniform temperatures through the thickness but would have more attention to flexure at different temperatures. These principles will guide a given design to have an endstate reliability consistent with conventional pressure vessel and piping design by analysis methods.

3 Need for Design by Analysis

The current design method in Sec. 2 of PVHO-1 is similar to the ASME BPVC “by rules” methods of Section VIII, Div. 1. This initial examination of available data demonstrates that the previously published experimental results can be used as a starting point for establishing an additional design by analysis method to complement the existing PVHO algorithm. There is sufficient historical data to serve as a starting point to examine failure modes.

Most significantly, acrylic is being adopted by the ASME BPVC Codes and Standards committee as a conventional pressure vessel material. It has been specifically allowed for pharmaceutical chromatography columns [33] and is in the process of being fully integrated into the BPVC code. These new rules will refer to PVHO-1 for design and PVHO-2 for postconstruction. This expanding acrylic use for pressure vessels, coupled with forecasted increased involvement by the National Board of Boiler and Pressure Vessel Inspectors (NBBI), indicates that the acrylic pressure vessel components for non-PVHOs will be subject to review by ASME Authorized Inspectors.

Pressure vessels for human occupancy are a small percentage of the pressure vessel industry. In the process of opening acrylics for all conventional pressure vessels, the Section VIII code committee expressed the need to address design considerations outside of PVHO-1. A sufficiently robust design by analysis would provide a means to address this within the existing ASME framework. This need alone is sufficient to drive a design by analysis method development. It puts the design, testing, and validation on the users, to be reviewed by ASME Authorized Inspectors for non-PVHOs, in lieu of replicating the work and time needed to expand the current empirical system beyond its current diving, submersibles, and supporting hyperbaric medical systems.

A reliable design code for glassy polymers has applications beyond PVHO. Design margins would be adjusted to meet the risk mitigation needed, such as reducing design margins when no humans are at risk. One current application is camera and instrumentation housings ranging from deep-sea remotely operated vehicles to high-altitude unmanned aerial systems [34]. A future application could include human-occupied systems for space, lunar, and other extra-terrestrial applications. Regardless of application or industry, a robust design by analysis method suitable for the risks associated with a human-occupied system would be readily applied in other industries as new applications, materials, and geometries are identified. Unlike conventional pressure vessel materials, glassy polymers are currently less defined than ASME-approved metallic alloys and are more sensitive to pressure and temperature variations. Simply using FEA and the Section VIII design by analysis rules is insufficient. A more comprehensive approach is needed.

3.1 Verification and Validation and Stochastic Finite Element Analysis.

Verification and validation techniques provide a framework for developing a new section of the ASME PVHO code. Unlike traditional pressure vessels, there are not established material models similar to Section II of BPVC, so testing will be needed for materials. Geometry outside the established PVHO-1 methods would also require some form of testing. Combining numerical modeling to the existing testing requirements will allow a reduced amount of physical testing by leveraging testing to verify the model instead of being the primary means of validation. Current testing for code cases is primarily performance based, which requires significantly more testing and higher proof loading than conventional PVHO windows in the absence of a systematic design methodology and criteria tied to the testing process.

The conventional V&V two-prong “model” and “experiment” paths [3] would address designs for a given application and assumed conditions. Addressing the variables such as seat fit tolerances, window friction, temperatures over time, and material property variance was originally addressed through multiple experimental studies. Guidelines similar to design by analysis in Section VIII, Div. 2, Part 5 [11] would provide load sets, material model criteria, and PVHO-specific stochastic methods to address the applicable variables due to tolerances, material variances, and complex operating environments. PVHO-1's existing physical testing requirements would be expanded compared to conventional PVHO windows but reduced in comparison to code case methods. Stochastic FEA methods would address specified variables, such as geometric tolerances or temperature variations, to leverage modern computing to increase reliability [27]. A window designed for a medical treatment facility will typically have less variables to address than a window designed for an ocean vessel that must operate in arctic to tropical conditions.

3.2 Applying to Glassy Polymer Pressure Vessel Components.

Ideally, the ASME PVHO committee would establish parameters for materials and analyses similar to what is currently done in the existing metallic pressure vessel technology and provide FEA guidance incorporating material responses within operational boundaries. Comparing experimental results to simulations that use increased precision of modern FEA would create an accurate representation of PVHO windows. Revisiting the foundation work would not only reduce testing requirements, it would align the criteria with a known, reliable process. Maintaining the same family of materials such as acrylics would avoid introducing unforeseen biological interactions due to pressure and artificial gas mixes. V&V techniques also integrate testing, which is implicitly used through established material specifications in conventional pressure vessel design and explicitly required in PVHO design. Testing and comparison to the literature is critical to establish material properties and overall performance.

An example V&V framework for PVHO design by analysis is shown in Fig. 4, based on Ref. [3]. This shows a proposed method to compare simulations to experimental results. The experimental results are those experiments performed specifically for the project, previous data with appropriate documentation (such as historical stress–strain curves for acrylic samples for a specific grade from a specific source), or published results such as Dr. Stachiw's reports published by the U.S. Navy [7,13,28 and others not cited herein]. Assessing the nature of these results and associated uncertainty is part of the process. This two-pronged approach is typical of V&V methods and is presented as a guide. That actual “model” and “experimental” efforts are often iterative and only fits the five step progression in a broad manner.

Fig. 4
Conceptual V&V flowchart for a PVHO window “design by analysis” process. The endstate of following this process is a validated and documented PVHO-compliant design which can be directly reviewed by a jurisdictional authority instead of going through an ASME PVHO code case process.
Fig. 4
Conceptual V&V flowchart for a PVHO window “design by analysis” process. The endstate of following this process is a validated and documented PVHO-compliant design which can be directly reviewed by a jurisdictional authority instead of going through an ASME PVHO code case process.
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A summary of the five step V&V approach is the following:

  1. Conceptual Window. Establish the conceptual design requirements through the user's design specification.

  2. Preliminary Design. Determine the geometry requirements, specify pressures and temperatures, specify life cycle in terms of cycles and years, select specific grades of materials, and establish tolerances. The tolerances and variables for the stochastic aspect of the work are established at this point.

  3. Calculations. Size the components using conventional means, including the methods in PVHO-1 and historical results, as appropriate. Use these parameters to establish the experimental requirements in order to comply with design of experiment (DOE) methodology. These parameters, coupled with the stochastic variables, are also used to establish boundary conditions and model parameters for simulations, including accounting for variables in material properties, tolerances due to fabrication limitations, and measurements available in the quality assurance/quality control process. Previous experiments and literature data will be considered. It will also specify the number and types of material tests and at which temperatures to offset the uncertainties associated with the material properties needed to be consistent with the metallic components. This is different from conventional pressure vessel design which typically uses a more limited set of design parameters. This is due to many variables in the conventional process which are addressed implicitly or explicitly in other parts of the code process or with standardized specifications. The stochastic examination of the interaction of variables reduces the uncertainty to levels consistent with conventional pressure vessel technology.

  4. Review. Evaluate the results of the simulations and experiments to ensure that each simulation and experiment is sufficiently accurate and precise as well as consistent with the bounding parameters. A potential source for error is to allow one prong to automatically drive the other. While they have linked starting points and criteria, each prong must be separately developed, executed, and reviewed in order to conform with V&V methodology. Comparisons to past experiments or published literature are a key step.

  5. Quantitative Comparison. Once the simulations and experiments are reviewed, they can be compared. Ideally, the experiments validate the design efforts by returning physical results consistent with the predictions of the simulations. These results are also compared to ensure that they meet the design criteria, are within fabrication limitations, and are within inspectable tolerances for quality assurance. Deviations are examined for significance and may require additional iterations. The end result is a complete engineering package demonstrating that the design is validated by calculation (including simulations) and verified by experimentation (project-specific, historical, and published sources). Assuming that proper documentation and inspections occur within an approved framework, this would replace the need for a multi-year “code case” process.

In the simulation prong, a design's theoretical response can be compared to the experimental response. Items such as allowable stress, maximum deflection, and temperature variation can be examined in detail. The stochastic variations within different grades of materials, material property variances, service conditions, or other factors can be varied over their specification range to ensure that the variations do not change design outcomes.

An example of the existing variance is in PVHO-1, Section 2-2.9.4 (requirements for large openings) where the angular variation between the seat and the window can be up to 0.5 deg. There is no basis to evaluate the stresses due to dimensional variances or the effects of thermal expansion. Past work shows that the angular differences create elevated stresses [20], but 0.5 deg seat angle variation with a 10 mm thickness PVHO window for a given diameter will have significantly less stress due to misalignment than a 50 mm thickness with the same diameter at its PVHO-1 design pressure. The proposed method would verify whether this variation is acceptable when coupled with other variables. It may result in allowing for greater variance (and less need for dimensional precision) or requiring a reduced tolerance with a greater need for dimensional precision. These results would go into the design package for the Authorized Inspector, who in turn would verify that the components are within specification.

3.3 Pressure Vessel Design Envelope.

The intent is to develop a design by analysis methodology for glassy polymers a design envelope sufficiently consistent with other pressure vessel design-by-analysis methods such that the full system is limited by the conventional metallic portions. The established pressure vessel design envelope is illustrated in Fig. 5 [35]. This design envelope is embedded as a well-defined framework for pressure vessel design [11] and postconstruction evaluation [15]. The design envelope is established using specific stress ratios with respect to the material's yield strength at a specified temperature. The use of membrane stress (Pm) and bending stress (Pb) indicates that this is using thin wall pressure vessel theory, which is not compatible with the thickness typical of many acrylic windows. Glassy polymers have different failure modes than metallic materials, particularly without using thin wall pressure vessel theory. Between failure modes and geometry considerations, different variables such as strain may be needed to achieve the same or more conservative design envelope as shown in Fig. 5.

Fig. 5
An illustration of how conventional metallic pressure vessel design methods in ASME BPVC, Section VIII, Division 2 using “design by analysis” methods are constrained to a design envelope to avoid failure. A successful polymer structural design by analysis method would similarly define failure modes and establish a safe, reliable design envelope similar tothe conventional pressure vessel design envelope. Given thetypical window geometries and polymer material response to loads, it is likely that the design margins will be based onstrain instead of stress (graph from PTB-1-2014 ASME Section VIII—Division 2 Criteria and Commentary. Used with permission).
Fig. 5
An illustration of how conventional metallic pressure vessel design methods in ASME BPVC, Section VIII, Division 2 using “design by analysis” methods are constrained to a design envelope to avoid failure. A successful polymer structural design by analysis method would similarly define failure modes and establish a safe, reliable design envelope similar tothe conventional pressure vessel design envelope. Given thetypical window geometries and polymer material response to loads, it is likely that the design margins will be based onstrain instead of stress (graph from PTB-1-2014 ASME Section VIII—Division 2 Criteria and Commentary. Used with permission).
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The current PVHO-1 design algorithm was developed so the windows themselves as well as the assembled viewports have higher design margins than the rest of the pressure boundary [2,7]. It uses a simple deterministic modeling method which obscures potential failure modes, such as neglecting stresses due to viewport seat-to-window angular mismatch as long as it is within 0.5 deg. The proposed methodology mitigates uncertainties with respect to the window design to be consistent with the existing design-by-analysis methods applicable to the rest of the pressure boundary, thereby remaining within ASME design envelope.

To develop analysis and modeling guidelines to remain within this design envelope, V&V methodology would be used to examine known failure modes in relevant literature to establish FEA criteria indicating the onset of failure modes. This, in turn, will be used to develop the acrylic-specific design-by-analysis guidance which avoids failure mode at quantified points. Establishing the onset of failure conditions enables design-by-analysis guidelines to incorporate design margins consistent with Fig. 5.

The foundational work used to develop the existing PVHO algorithm includes many examples of load testing to failure [2,7]. These examples can be modeled using modern methods. While testing would still be required, the updated testing would be part of a deliberate V&V process, would be less burdensome than the current performance-only requirements and obviate the need for code case review. One of the outcomes of establishing the testing guidelines is to lay the foundation for gathering properly qualified data over time to develop material tables, which in turn would allow for updated guidelines for reduced testing consistent with other pressure vessel design-by-analysis methods used for the metallic parts of PVHOs as well as other pressure vessels [35,36]. As documented in 2004 in one of his last papers, this is consistent with Dr. Stachiw's vision of using FEA and experimental procedures while building upon the existing information used to develop the proven empirical method [37].

3.4 Reducing Code Cases to Safely Speed Innovation.

Design-by-analysis is not to eliminate the existing, proven window design algorithm. There are still ways to improve the existing PVHO algorithm. As discussed previously, an example of such a change is that the minimum material specifications need to be revised to require a plastic response prior to failure [19]. The acrylic joints cannot be considered “membrane stresses” and need updated characterization [20]. Such changes are more about correcting errors and omissions within PVHO codes.

These changes do not expand the scope of shapes, sizes, or materials of PVHO windows. It does not address new applications, which introduces questions regarding service factors, maintenance, and other issues. These variations from PVHO-1 are currently handled by the cumbersome provisional “code case” process. Based on experience, a PVHO code case can take over 3 years to complete.

A comprehensive design by analysis methodology would reliably address the life-safety critical components in uncertain and complex environments. It would allow the user to develop, validate, and document designs which can be code-qualified by the jurisdictional authority in a timely manner consistent with other aspects of pressure vessel technology as well as the current PVHO-1 design algorithm's safety record. Future PVHO code cases may be reduced or eliminated depending on how the PVHO Committee's concerns are met.

This is likely to have far reaching effects. The ASME PVHO safety standard has been adopted by a variety of regulatory bodies around the world. It will safely speed innovation in the existing areas as well as developing fields of PVHO technology such as “dry diving” with tunnel boring machines [36]. As acrylics are incorporated as an ASME BPVC Section VIII pressure vessel material [33], this method will also reduce the need for code cases in Section VIII. In turn, it is likely that the design rules will expand to polymer applications which are not “pressure vessels” nor for “human occupancy” just as the original PVHO design information were adapted for aquaria [2,38], remotely operated vehicle/AUSs [33,37], and critical laboratory equipment [24,39]. Acrylic structures are used in innovative architectural applications such as the world's tallest indoor waterfall [40]. Acrylic windows have a long history in aviation [12,41] and have replaced glass in spacecraft in order to reduce weight and increase reliability [42]. A robust, flexible method for design could speed innovation while enhancing safety and reliability in all of these endeavors.

The proposed process allows for design adjustments based on specific risks and conditions, providing the flexibility to address any industry. Currently, a specified geometry is indexed against a single pressure and temperature to determine a thickness. In a manner similar to design by analysis in Section VIII, the more rigorous engineering method could be used to optimize thicknesses. For example, it could justify a window in a protected laboratory environment be thinner than a window for similar geometry and pressure for an ocean-going PVHO.

This goes beyond PVHO-specific applications. The fully developed process would reduce the need for code cases overall. Potentially, it allows all non-PVHO ASME pressure vessels to use the existing Authorized Inspector system for acrylic components. This will avoid situations such as non-PVHO acrylic design code cases being reviewed by the PVHO committee whose members have little or no exposure to a given industry and use, prolonging a multiyear process further.

4 Conclusion

Window design methodology from landmark work resulted in the ASME PVHO code and remains largely unchanged from the original recommendations. This empirical method is based primarily on years of testing, but does not directly use engineering theory. This makes changing the existing system exceedingly challenging to revise without a large-scale government funded effort. The industries using the PVHO code need a way to incorporate advances in material science, manufacturing technology, and overall engineering technology to explore weight and cost reductions, application-specific risk mitigation, and other design considerations. It is recommended that the existing PVHO code-specified methods be retained for continuity and established design, similar to ASME BPVC Section VIII, Div. 1, and provide a methodology to allow engineers to use modern tools such as Finite Element Analysis and Computational Fluid Dynamics, similar to ASME BPVC Section VIII, Div. 2, coupled with V&V methodology and stochastic modeling techniques, to produce designs outside the scope of the current ASME PVHO codes. It is likely that a successful structural design method that is reliable enough for the risks associated with human occupancy will be used in not only conventional pressure vessel applications but other structural use of glassy polymers.

Acknowledgment

The authors are volunteer members of the ASME Pressure Vessels for Human Occupancy Codes and Standards committee and subcommittees. Their participation has given them insight to the history of the development of the PVHO code. This paper does not represent the opinions of ASME Codes and Standards, the PVHO Committee, any of the subcommittees, or of the other volunteers. The authors are grateful for the ASME allowing the use of images from other codes as well as the support of the Woods Hole Oceanographic Institute for the information and use of images regarding the DSV ALVIN.

Nomenclature

     
  • Pb =

    primary bending stress. This represents the stress in a thin wall pressure vessel where typically a moment is applied to the structure to create “out-of-plane” stresses, using 2D simplification. An example is a lateral load on a pressure vessel flange

  •  
  • Pm =

    primary membrane stress. This represents the stress in a thin-walled pressure vessel due to internal pressure where the walls are placed in a tension-only loading, or “in-plane” stress using 2D simplification

  •  
  • r/t =

    inner radius (r) of the window divided by the thickness (t). Used to evaluate whether thin-wall or thick-wall theory applies. r/t > 10 is “thick wall,” otherwise it is “thin wall.” Thin wall pressure vessel theory allows the wall to be modeled as 2D membranes where the stress and strain due to internal pressure is assumed to be uniform through the thickness

  •  
  • Sy =

    yield stress. The stress value below which the material response to load is considered “elastic” and recovers without deformation after loading. Stresses above the yield value indicate some degree of “plastic,” or permanent, deformation

  •  
  • t/D =

    thickness of the window divided by the window opening diameter. Used for several established PVHO window geometries in PVHO-1

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