Ratcheting and shakedown anomalies are investigated for impulsively loaded vessels. Calculated results for explosive containment vessels subjected to repeated dynamic loading are used to illustrate behaviors that differ markedly from classical ratcheting/shakedown (i.e., the phenomenon associated with purely static loading and elastic-perfectly plastic material) and from the shakedown assessment procedure in API 579-1/ASME FFS-1. Results are similar to ‘pseudo-shakedown’ reported for other dynamically loaded structures. In addition, a simplified analytical model subjected to repeated impulsive loading is shown to demonstrate related characteristics. Experimental data presented elsewhere for explosive containment vessels subjected to repeated loading are used to further demonstrate the differences between conventional ratcheting and that observed for repeated loading of impulsively loaded vessels. These differences are believed to be associated with energy-based response as opposed to load-based response of statically loaded vessels.

in FY17. This report presents the results of those studies. An EPP strain limits methodology assessment was based on recent two-bar thermal ratcheting test results on 316H stainless steel in the temperature range of 405 to 7050C. Strain range predictions from the EPP evaluation of the two-bar tests were also evaluated and compared with the experimental results. The role of sustained primary loading on cyclic life was assessed using the results of pressurized SMT data from tests on Alloy 617 at 9500C. A viscoplastic material model was used in an analytic simulation of two-bar tests to compare with EPP strain limits assessments using isochronous stress strain curves that are consistent with the viscoplastic material model. A finite element model of a prior 304H stainless steel Oak Ridge National Laboratory (ORNL) nozzle-to-sphere test was developed and used for an EPP strain limits and creep-fatigue code case damage evaluations. A theoretical treatment of a recurring issue with convergence criteria for plastic shakedown illustrated the role of computer machine precision in EPP calculations.

A methodology of fitness-for-service evaluation (FFSE) for explosive containment vessels (ECVs) is introduced that utilizes change-in-thickness measurements pre- and post-test to determine the propensity of the structure to ratchet or to shake down. The method focuses on ductile failure and complements previously developed brittle failure methodologies associated with fatigue fracture of flaws introduced during manufacture or subsequent service. The methodology is illustrated using measured thickness changes on a spherical vessel and is intended to eliminate or diminish the need for detailed, challenging finite element calculations of ratcheting and shakedown. An example is presented, based upon measured thickness changes in an explosively loaded containment vessel. Current limitations of the procedure are discussed. Applicable consensus code requirements and issues with the numerical modeling of ratcheting are briefly presented.

High-explosive containment vessels are often designed for repeated use, implying predominately elastic material behavior. Each explosive test imparts an impulse to the vessel wall. The vessel subsequently vibrates as a result of the internal blast loading, with amplitude diminishing exponentially in time after a few cycles due to structural damping. Flaws present in the vessel, as well as new flaws induced by fragment impact during testing, could potentially grow by fatigue during these vibrations. Subsequent explosive tests result in new sequences of vibrations, providing further opportunity for flaws to grow by fatigue. The obvious question is, How many explosive experiments can be performed before flaws potentially grow to unsafe limits? Because ASME Code Case 2564-5 (Impulsively Loaded Pressure Vessels) has just been incorporated in Section VIII, Division 3 of the 2019 ASME Boiler and Pressure Vessel Code, evaluation of remaining life and fitness-for-service of explosive containment vessels now draws upon two interrelated codes and standards: ASME Section VIII-3 and API-579/ASME FFS-1. This paper discusses their implementation in determining the remaining life of dynamically loaded vessels that have seen service and are potentially damaged. Results of a representative explosive containment vessel are presented using actual flaw data for both embedded weld flaws and fragment damage. Because of the potentially large number of flaws that can be detected by modern nondestructive inspection methods, three simplifying assumptions and a procedure are presented for conservatively eliminating from further consideration the vast majority of the flaws that possess considerable remaining life.

Guidance for the appropriate preload for bolted joints is well established for static pressure loading as well as cyclic loading. The goal for bolt-preload selection in these cases is generally leak prevention, alleviation of bolt loosening, and minimization of fatigue loading of the closure bolts. For impulsively loaded containment vessels, such as those governed by the rules of ASME Code Case 2564 in Section VIII, Div. 3, much less is known regarding appropriate bolt-preload selection. In this paper, a simplified, upper-bound bolt-preload methodology is developed to evaluate the role of bolt preload on peak bolt stress, including the effect of transient vessel motions. The simplified model for the bolted joint and vessel is solved in closed form for exponential pressure-pulse loading on the interior of a spherical containment vessel. Detailed finite element calculations are also performed using a refined model to more precisely examine the role of bolt preload. Comparisons of the approximate bolt-preload methodology with the detailed finite element results are then presented, along with comparisons to a lower-bound solution reported earlier. It is shown that the peak bolt stress predicted by the detailed finite element model is bounded from above and below by the simplified solutions. Implications on the role of bolt preload on peak dynamic bolt stress are given for sudden pressure-pulse loading. Goals and requirements for selecting bolt preload for impulsively loaded vessels are briefly discussed.

Significant changes were recently made in design limits for pressurized vessels in Section VIII, Division 3 of the ASME Code. There is now a local damage-mechanics based strain-exhaustion limit as well as a separate global plastic collapse limit. In addition, Code Case 2564 (Sec VIII, Div 3) has recently been approved to address impulsively loaded vessels. Recent studies have shown that local strain limits play a particularly important role for these impulsively loaded vessels. In this paper, the new local strain-exhaustion procedure, originally intended for static-pressure-loaded vessels, is evaluated for adequacy in conservatively predicting failure for impulsively loaded vessels. Based upon a symmetrically loaded cylindrical shell geometry, it is found that direct extension of the new local failure rules in the ASME Code to impulsively loaded vessels is unconservative. However, a hoop-strain local failure criterion predicts failures reasonably well.

Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME code (Sec. VIII, Div. 3) and 2008 and 2009 Addenda, and these are now a part of the 2010 code. There is now a local damage-mechanics based strain-exhaustion limit, including the well-known global plastic collapse limit. Moreover, Code Case 2564 (Sec. VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement-controlled and short-duration dynamic pressure loading is given. This instability condition is evaluated for six plastic and viscoplastic constitutive relations. The role of strain rate sensitivity on the instability point is investigated. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared with the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.

Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME Code (Section VIII; Div. 3) and 2008 and 2009 Addenda. There is now a local damage-mechanics based strain-exhaustion limit, including the well-known global plastic collapse limit. Moreover, Code Case 2564 (Section VIII, Div. 3) has recently been approved to address impulsively loaded vessels.It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, a literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement controlled and short-duration dynamic pressure loading is given. This instability condition is evaluated for six plastic and visco-plastic constitutive relations. The role of strain-rate sensitivity on the instability point is investigated. Calculations for statically and dynamically loaded spherical shells are presented, illustrating the formation of instabilities. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared to the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain-rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.

Numerous theoretical investigations on the natural frequencies for complete spherical shells have been reported over the past four decades. However, attempts at correlating the theoretical results with either experimental or simulated results (both for axisymmetric and nonaxisymmetric modes of vibration) are almost completely lacking. In this paper, natural frequencies and mode shapes obtained from axisymmetric and nonaxisymmetric theories of vibration of complete spherical shells and from finite element computer simulations of the vibrations, with and without geometrical imperfections, are presented. Modal tests reported elsewhere on commercially available, thin spherical marine floats (with imperfections) are then utilized as a basis for comparison of frequencies to both the theoretical and numerical results. Because of the imperfections present, “splitting” of frequencies of nonaxisymmetric modes is anticipated. The presence of this frequency splitting phenomenon is demonstrated. In addition, results of a “whole field” measurement on one of the imperfect shells using dynamic holography are presented.

Plastic instabilities that could potentially develop in spherical shells under a variety of symmetric loading conditions are examined. First, a literature survey of both static and dynamic instabilities associated with spherical shells is presented, with emphasis on plastic tensile instability. Then, building upon work done elsewhere for cylindrical shells, a plastic instability condition for spherical shells subjected to displacement controlled and impulsive loading is developed and compared with earlier results reported in the literature. It is found that the instability point for displacement controlled loading and impulsive loading of a spherical shell is the same as for a uniaxial tension specimen and for an impulsively loaded plane-strain ring/cylinder. In addition, a simple, one-dimensional strain-softening model is developed that investigates the relationship between instabilities associated with displacement-controlled loading and impulsive loading. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells: local and global. Moreover, the local instability, associated with failure under displacement control and impulsive loading, is found to require an imperfection to develop, whereas the global instability does not require an imperfection. The need for experiments to verify these results is discussed.

A 51mm thick plate of high-strength low-alloy (HSLA-100) steel was impacted by 6.4mm diameter tungsten carbide spheres traveling at velocities ranging from 0.8–2.5km/s. The width and depth of the crater for each impact event are provided in tabulated form and graphed as a function of velocity. The impacts were simulated using an explicit Lagrangian finite element model. A residual stress map over a cross-section through the crater was also measured by the Contour Method for the 2.2km/s impact. The predominant feature of the stress map was a peak compressive stress of 1100MPa, which is 1.6 times the yield strength, centered approximately one crater diameter below the crater floor. Residual stresses in the as-received HSLA-100 plate were also measured and were used to evaluate the effect of initial stresses on the model prediction. Good agreement is shown between the numerical simulation of the impact event and the experimental data.

Ductile failure criteria suitable for application to impulsively loaded high pressure vessels that are designed to the rules of the ASME Code Section VIII Division 3 are described and justified. The criteria are based upon prevention of load instability and the associated global failure mechanisms, and on protection against progressive distortion for multiple-use vessels. The criteria are demonstrated by the design and analysis of vessels that contain high explosive charges.

Spherical pressure vessels are used to fully contain the effects of high explosions. In this paper, the vibrations of a spherical containment vessel undergoing elastic response are investigated. Vibration modes of containment vessels are of particular interest, as it is the superposition and interaction of different modes of response with closely spaced frequencies (beating) that has been reported to be the mechanism of ‘strain growth’. The modal frequencies of a complete spherical shell for both axisymmetric and nonaxisymmetric response modes are discussed, based on a sequence of papers that have appeared in the open literature. Analytical predictions are then compared with finite element numerical simulations. It is found that the numerical simulations accurately predict both the axisymmetric and nonaxisymmetric modal frequencies for the complete spherical shell. Next, numerical simulations of modal frequencies for the more complex spherical containment vessel (with nozzles) are compared with the spherical shell results. These simulations for the spherical containment vessel reveal that frequencies are similar to the complete spherical shell, although a splitting of the degenerate frequencies (associated with nonaxisymmetric modes) occurs when progressing from a perfect spherical shell to the containment vessel. As a result, the vibrational response of the spherical containment vessel can be interpreted as a perturbation on the response of a perfect spherical shell. Limited comparisons with experimentally recorded frequencies for participating modes of vessel dynamic response during high explosive containment testing are presented as well. Participating modes potentially capable of beating together to produce ‘strain growth’ are isolated and are found to agree within 4 percent with frequencies determined from beating frequency measurements.

Spherical pressure vessels are used to fully contain the effects of high explosions. In this paper, the vibrations of a spherical containment vessel undergoing elastic response are investigated. Vibration modes of containment vessels are of particular interest, as it is the superposition and interaction of different modes of response with closely spaced frequencies that has been reported to be the mechanism of ‘strain growth’. First, the modal frequencies of a spherical shell for both axisymmetric and nonaxisymmetric response modes are discussed, based on a sequence of papers that have appeared in the open literature. Analytical predictions are then compared with numerical simulations using ABAQUS. It is found that the numerical simulations accurately predict both the axisymmetric and nonaxisymmetric modal frequencies for the complete spherical shell. Next, numerical simulations of modal frequencies for the more complex spherical containment vessel (with nozzles) are compared with the spherical shell results. Numerical simulations for the spherical containment vessel reveal that frequencies are somewhat similar to the complete spherical shell. Limited comparisons with experimentally recorded frequencies for participating modes of vessel dynamic response during high explosive containment testing are presented as well.

A methodology is developed for determining the remaining life of an 8-ft inside diameter (ID) spherical high explosive (HE) containment vessel. The methodology is based upon fatigue crack growth, and specifies the maximum number of HE tests that can be performed without any cracks growing to their critical crack size. An upper bound on crack growth for a single explosive test is determined in closed form by integrating the Paris Law assuming an infinite number of damped vibrations of the vessel with exponentially decreasing amplitude. The procedure is then to use this expression as a recursion relationship one test at a time, determining the new crack size and comparing it to the critical flaw size until the critical flaw size is reached, indicating the number of vessel tests permitted. Results are presented for a variety of initial postulated cracks in the parent vessel material. This method is also used for weld evaluation but is not reported in this paper.

A simplified approach to the dynamic finite element modeling of composite girder-slab bridges is presented using the limiting case of a single beam element to represent the girder-slab cross section. Dynamic properties calculated with this simplified model are compared with experimental results obtained from an in situ composite girder bridge and with more detailed shell element model predictions. The simplified beam element model accurately calculates the mode shapes of the structure. This agreement, however, is dependent on accurate modeling of the piers and kinematic constraints between the bridge and piers and the appropriate representation of the bridge's torsional properties. The calculated resonant frequencies associated with these modes show some discrepancy when compared with the experimental results. This discrepancy is attributed to the inability of the single beam element model to simulate the three-dimensional boundary conditions found in the actual structure. The simple models provide approximations to the dynamic properties that are accurate enough to be useful in preliminary seismic scoping studies and in the simplified modeling of long, multispan bridges.