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Failure analysis of an exploded gas cylinder
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Engineering Failure Analysis 15 (2008) 820–834 www.elsevier.com/locate/engfailanal
Failure analysis of an exploded gas cylinder Majid Mirzaei * Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran Received 14 November 2007; accepted 17 November 2007 Available online 3 December 2007
Abstract This paper reports the major activities carried out during the failure analysis of an exploded cylinder containing hydrogen. The general cracking pattern of the cylinder, the fractographic features, and the stress analysis results were all indicative of an internal gaseous detonation. Accordingly, several specific characteristics of detonation-driven fracture of closed-end cylindrical tubes were identified. These characteristics were analyzed through detailed examinations of the fracture surfaces, cracking patterns, and dynamic stress analysis of the cylinder using a transient analytical model. Based on the size and location of special markings found on the shear lips, and using the time duration of flexural waves, the crack growth increments and speed were computed. Consequently, the basic features of the gaseous detonation and the composition of the original gas mixture were identified. The results indicated that the detonation of a low-pressure oxygen-rich mixture of hydrogen and oxygen was the cause of this failure. The presence of oxygen was attributed to an improper usage of an oxygen cylinder for hydrogen storage. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Crack growth; Fractography; Dynamic stress analysis; Hydrogen; Explosion
1. Introduction Commercial gas cylinders are ordinary pressure vessels which their proper design, manufacture, quality control, transportation, and implementation are specified by various standards and regulations [1]. Hence, they are generally considered to be safe to such an extent that divers strap them to their bodies, some patients or even elderly adults regularly use them for medical oxygen supply, and many people carry them in their car trunk as fuel storage. Nevertheless, accidental burst or even explosion of these cylinders is possible and can be devastating. These accidents are quite rare but the price we pay for what we learn from them can be quite high. Thus, a thorough investigation of each and every accident is necessary and the results should be lucidly presented to raise the public awareness. In 2006, a commercial gas cylinder containing hydrogen exploded in a laboratory in Iran. As a result, the cylinder fractured into seven pieces and caused the death of a lab resident and partial destruction of the lab. *
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Nomenclature a C D d h H Kc KI KIc L M1 M2 M3 P1 P2 P3 Patm Q ry R t T Vcj x U r ru rys v
half crack length, m half major axis of semielliptical crack, m shear lip depth, m penetration depth of semielliptical crack, m thickness, m step function pffiffiffiffi plane stress fracture toughness, MPa pm ffiffiffiffi stress intensity factor (mode I), MPa pm ffiffiffiffi plane strain fracture toughness, MPa m cylinder length, m dimensionless parameter dimensionless parameter dimensionless parameter pre-detonation pressure, MPa maximum-detonation pressure, MPa post-shock pressure, MPa atmospheric pressure, MPa dimensionless parameter crack tip plastic zone radius, m mean tube radius, m time variable, s exponential decay factor, s Chapman–Jouguet velocity, m/s distance variable, m dynamic amplification factor far field stress, MPa ultimate strength, MPa yield strength, MPa dimensionless parameter
Fig. 1 shows the schematic of the cylinder along with the pictures of the fragments collected from the accident scene. This paper reports the major activities carried out to determine the cause of this incident. It should be emphasized that this is an independent scientific investigation and is not related to any judicial process. As will be discussed in the sequel, the cracking pattern of the cylinder (along with other evidences) was indicative of an internal gaseous detonation. Detonations are combustion events in which the speed of the combustion wave front is supersonic. A detonation explosion is more severe than a deflagration explosion (with subsonic wave front) since the pressure waves are much stronger. A deflagration of hydrogen can result in a detonation depending on the hydrogen concentration, the degree of space confinement, the conditions that promote turbulence in the gas, and the strength of the ignition source. However, the occurrence of internal detonation in an ordinary gas cylinder seems peculiar because, (a) such detonation needs a proper mixture of hydrogen and oxygen, and (b) some sort of ignition is required to trigger the process. Moreover, in this particular case, the initial reports indicated that the cylinder was nearly empty and the operator was trying to replace it with a new one before the accident happened. Another complex issue in these types of failure analysis is the nature of the fracture itself. Detonation-driven fracture of cylindrical tubes is distinguished from quasi-statically loaded tube fracture because of two main characteristics. First, the structural waves caused by detonation loading can result in oscillatory strains whose amplitudes are dependent on the speed of the traveling load and can be
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Fig. 1. Left: schematic of the cylinder. Right: remains of the exploded cylinder.
significantly higher than those predicted by static formulas. Second, dynamic fracture parameters can be quite different from equivalent static forms. There have been several studies concerning the structural response of tubes to shock or detonation loading [2–10]. These studies were carried out on flawless tubes, so the results can only be used for stress analysis and determination of the critical locations for crack initiation in the tube. In contrast, there was no report in the open literature about the fracture of tubes caused by gaseous detonations, prior to the experimental study reported by Chao and Shepherd [11,12]. Their study was primarily motivated by accidents like those occurred in the nuclear power plants in Japan and Germany in 2001 [12,13]. In both incidents, sections of steel steam pipes were fragmented due to combustion of hydrogen–oxygen mixtures created by radiolysis. One of the most important questions that arose during the accident investigation was whether the type of accidental combustion can be deduced from the fracture patterns. At that time, it seemed that the state of knowledge on detonation-driven fracture was not adequate to answer this question [13]. Mirzaei and Karimi carried out finite element simulations of detonation-driven fracture of a thin aluminum tube using the crack tip opening angle (CTOA) [14] and cohesive element methods and compared the results with the experimental work of Chao and Shepherd [11,12]. These studies showed that an important characteristic of the detonation-driven fracture of tubes is that the crack propagation phase can be mostly or entirely driven by the structural waves. Thus, the whole cracking process and fragmentation can occur after the passage of detonation front. Among other features of detonation-driven fracture are a specific flap bulging process and the resultant crack curving and branching. In the current study, it will be shown that some special markings may also be found on the fracture surface which can be used to quantify the crack growth increments and calculate the crack speed. As mentioned above, reports on incidents involving gaseous detonation are quite rare. Although the prospective usage of hydrogen as a clean fuel and the safety concerns has lead to several investigations [15,16], the lack of substantial data on hydrogen-related accidents, tests, and simulations has so far prevented detailed assessments of hydrogen safety in specific realistic conditions [16]. In a recent hydrogen accident, an unauthorized installation of an adapter for connecting a hydrogen tube trailer manifold to an oxygen manifold at a facility for filling compressed-gas cylinders led into a detonation that ruptured the tube [17]. It was reported that the far end of the tube was folded out like the petals of a flower. The analysis of the cause of the explosion of an acetylene cylinder, which occurred in 1993 in Sydney, was reported by Price [18]. In his paper, Price also
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referred to two other incidents, one was related to an acetylene cylinder where oxygen was present in Munich (1992), and another was the explosion of an oxygen cylinder in Texas (1963) [18]. The Sydney incident caused severe fragmentation of the cylinder and a fatality and property damage. This failure was also attributed to internal gaseous detonation and was announced as outstanding in two respects, (a) the violence of the failure, and (b) the fact that the explosion occurred where there were no apparent ignition sources present [18]. Hence, the only possible cause of initiation seemed to be impacts on the cylinder caused by handling the cylinder on a truck, but the energy available from such an initiator is very low. However, it was suggested that in acetylene gas, there appears to be the possibility of a direct initiation, where the deflagration step is either very small or is omitted [19]. Price also suggested that the pressure transient in the fluid must travel faster than the speed of sound in the metal to cause very small fragments. However, the analyses carried out by Mirzaei and Karimi [14] and the evidences presented in the current study show that the crack propagation phase can be essentially governed by the structural waves. Thus, the traveling of high-pressure detonations at much lower speeds (1000–3000 m/s) can cause fragmentation of tubes. In the following sections, the above mentioned aspects are treated in detail. 2. Examination of deformation pattern and fracture surfaces of fragments The visual inspection and measurements of the periphery of the unbroken part of the cylindrical portion indicated a uniform permanent radial expansion with no bulging. This was in contrast to the bulging of closed-end cylindrical pressure vessels under static internal pressures. This particular type of radial expansion was attributed to a moving local pressure. This was the first clue for the hypothesis of occurrence of an internal gaseous detonation in the cylinder. In the next step, the very well-developed chevron markings on the fracture surfaces were followed and two separate sites of crack initiation were identified. The first one was in the upper portion of the cylindrical part and the second one was at the center of the bottom cap. In continuation, the cracking pattern of the cylinder and the original locations of all the fragments were specified as depicted in Fig. 2. 2.1. Examination of the fracture surfaces of the upper cracking zone In this zone, the chevron markings clearly showed that the location of crack initiation was at the border of the cylindrical and conical portions, 100 mm below the neck (see Fig. 3). The examination of the initial crack showed no evidence of pre-cracking caused by fatigue, stress corrosion, material defects, or manufacturing flaws. In fact, the appearance of this 6-mm through-thickness crack was indicative of a local rupture caused
Fig. 2. Schematic of the cylinder showing the original location of the collected fragments. The sketch is not to scale.
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Fig. 3. The overall cracking pattern of the upper portion of the cylinder. The sketch is not to scale.
by excessive shear (see Fig. 4). The direction of chevron markings indicated that this crack grew in a self-similar fashion in both directions towards the head and the bottom of the cylinder. The upper growing front branched into two new fronts by curving towards right and left. The lower growing front in turn branched into two new fronts at a distance of 292 mm below the neck. The growth of the upper-left and the lower-left branches towards each other caused the formation of the fragment No. 5. Similarly, the growth of the upperright and the lower-right branches towards each other and the final rupture of the ligament by bending led to the formation of the fragment No. 6, from which the fragment No. 7 was already separated. In fact, the fragment No. 7 was formed as a result of a second branching and the final rejoin of this branch with the lower part of the main crack path. At first, this fragment was not considered as a part of the cylinder because it had been
Fig. 4. The upper crack initiation site and special markings on conjugate fracture surfaces of fragments Nos. 5 and 7.
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discolored by chemicals. However, this was one of the most important fragments as it contained on of the two surfaces of the initial crack. By further examination of the fracture surfaces, special markings were found on the very well developed shear lips in this region (see Fig. 4). In fact, the existence of these markings was a clear indication of a periodic crack growth caused by flexural waves. On the one hand, these markings are like ‘‘fatigue striations”, since they represent the increments of crack growth caused by vibrational strains. On the other hand, they can be considered as ‘‘arrest markings”, since they represent the arrest locations of a growing crack under displacement control. Nevertheless, these markings have some special features, like being visible to the naked eye or by a magnifying glass, and they only exist on the shear lips. In order to distinguish them from similar markings and because of their unique appearance, they will be referred to as ‘‘staircase markings” in this article. 2.2. Analysis of deformation and fracture of the upper cracking zone The most important effect of internal gaseous detonation on cylindrical tubes is the development of flexural structural waves [7–14]. According to the schematic depicted in Fig. 5, the passage of detonation front (as a local narrow overpressure) results in local radial displacements. Because of the dynamic effects of this highspeed moving load, these displacements are oscillatory. The result is a pattern of fluctuating circumferential (hoop) strains which exist even after the detonation loading dies out. In presence of an axial trough-thickness crack, the points on the crack surface can continue to oscillate radially. However, because the crack surface is traction free, these points also tend to displace circumferentially under the influence of stresses imposed by the
Fig. 5. Formation of flexural waves by a moving detonation front and the resulting flap bulging. The picture of the finite element simulation [14] is for an aluminum tube.
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neighboring material. The outcome is that the points on the crack surface are forced to displace in the resultant direction. The continuation of this effect, which is maximum at the crack center and minimum at the crack tips, results in the bulging of crack flaps. Note that the crack growth by flexural waves is in fact controlled by the far-field displacements, so the growth is stable and incremental. In fact, the development of the staircase markings is indicative of this type of growth. Of course the amplitude of oscillating displacements in the far-field area decreases as a result of crack growth. This effect if more pronounced for tubes with smaller diameters and thinner wall thicknesses. However, the effect is partially counterbalanced by the increase of the crack driving force with the crack length. With the extension of the bulged area, large tensile stresses (equivalent to yield stress) develop in the bulged region in the axial direction of the tube. Since cracks usually tend to grow perpendicular to the largest principal stress directions, the initial self-similar growth changes into a circumferential growth by curving around the bulged region. The occurrence of branching at this point is also possible for the cases that the energy release rate of the crack is high enough to support two crack fronts. 2.3. Fracture of the bottom cap A number of important issues should be considered in the fracture analysis of the bottom cap. The first one is that the central region of the cap is a unique location. Since the membrane stresses are all equal in this region, every meridional direction is a principal direction. The observed multiple cracking in this region is in fact the result of this state of stress (see Fig. 6). However, for locations further from the center point, the direction of the first principal stress is the hoop direction. The first principal stress at these points is in fact caused by the flexural waves transmitted into the cap and formation of circumferential wrinkles. The directions of cracking of the paint on the convex side of the cap are clear indications of the above argument. In this area, the white paint acted like a brittle coating. The latter is often used in experimental stress analysis for determination of the direction of principal stresses.
Fig. 6. Top: principal directions on the bottom cap. Bottom: multiple cracking at the center point of the bottom cap.
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Fig. 7. Cracking pattern of fragments Nos. 3 and 4.
Fig. 8. Chevron markings, radiating from the crack initiation site, point back towards the initial semielliptical crack (fragment No. 4). The colors of this picture have been changed to increase the contrast of the crack surface features.
The chevron markings showed that the locations of the two major initial cracks, that caused the fracture of the cap, were 10 mm further from the center point. From these two initiation sites, three cracks grew in different directions towards the periphery of the cap. Thereby, the cab was divided into three fragments which where still clinging to the main cylinder through their curved edges. Next, each radial crack branched and created two new fronts which grew circumferentially in opposite directions. As a result, the curved edge of each fragment was cut from both sides and reduced into a ligament. Fig. 7 shows the cracking pattern of the fragments Nos. 3 and 4 (No. 2 behaved similarly). Another important issue is that the final separation of each fragment occurred through its rotation that caused the rupture of the ligament. Thus, the bottom of the cylinder folded out like the petals of a flower. The driving force required for the cracking and folding was maintained solely by the structural waves. It should be noted that this cracking pattern is specific to internal gaseous detonation. Fig. 8 shows the magnified image of one of the initiation sites at the center of the bottom cap. The initial crack was in the form of a semielliptical surface crack with the dimensions of d = 2.5 mm and 2C = 6 mm, slanted with respect to both the fracture surface and the cap outer surface. There was no sign of corrosion products, fatigue markings, or material defects on the surface of the initial crack and it was clear that it initiated naturally as a result of an intense local shear stress. 3. Dynamic stress analysis of the gas cylinder Having determined the type of the pressure loading, the next step was the calculation of the stress levels which caused the deformation and fracture of various parts of the cylinder. The aim was to use the results of the stress analysis to find the two major characteristics of the detonation front, i.e., the peak pressure and the velocity.
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Table 1 Measured mechanical properties for the cylinder material (carbon steel) Yield strength (MPa)
Ultimate strength (MPa)
Elongation (%)
598
700
23
First, the tensile properties of the material (carbon steel) were measured using testing coupons extracted from the cylinder. Table 1 shows the average tensile properties of the cylinder obtained from different samples. It should be mentioned that properties like yield strength are rate-sensitive and their application to a high strain rate of 102 s1 usually requires a correction factor of 1.28 [20]. However, since the measured values were obtained by testing a plastically deformed material that had actually yielded and work hardened under the same strain rate, the above correction was not necessary. 3.1. Determination of the fracture toughness An accurate estimation of the fracture resistance of the material was required to calculate the amplitudes of the stress waves that drove the crack at different locations along the cylinder. Since the facture resistance is sensitive to the strain rate and the state of stress, an indirect approach was implemented to estimate the dynamic fracture toughness as follows. The staircase markings indicated that the initial crack of the cylindrical portion had been able to propagate under the first stress cycle with the magnitude of 700 MPa. The initial estimation of the length of the flexural stress cycle was 200 mm. Since this value was quite larger than the initial crack length (2a = 6 mm), the stress intensity expression for a through-thickness axial crack in a cylinder under internal pressure [21] was used and the value of fracture toughness was calculated as pffiffiffiffi pffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a K I ¼ r pa 1 þ 0:52v þ 1:29v2 0:074v3 ; v ¼ pffiffiffiffiffiffi ) K c ¼ 72 MPa m ð1Þ Rh in which, KI is the mode I stress intensity factor, r is the hoop stress, a is half the crack length, R is the mean radius, h is the thickness, and Kc is the fracture toughness. Another estimation of the fracture toughness was made based on the size of the shear lips [22]. The average amount of the shear lip depth, measured at different locations, was 1.75 mm. The average thickness along the main crack path was measured as 5 mm (due to the thinning caused by flap bulging). Thus, the shear lip depth value was multiplied by 6/5 and Kc was calculated as 2 pffiffiffiffi 1 K ) K c 69 MPa m ð2Þ D ry 2p rys in which, D is the shear lip depth, ry is the crack tip plastic zone pffiffiffiffi radius, and rys is the yield strength. The estimated value was quite consistent with the value of 72 MPa m calculated using Eq. (1). In fact, these values represent the plane stress fracture toughness for the thickness of 6 mm. Nevertheless, the situation was quite different for the initial crack at the bottom cap for which the crack front was predominantly in a state of plane strain. Using the stress intensity calibration for a semi-elliptical surface crack under remote tensile stress [23], the value of plane strain fracture toughness was calculated as follows: sffiffiffiffiffiffi pd H KI ¼ r Q 2 4 1:65 d d d H ¼ M1 þ M2 þ M3 ; Q ¼ 1 þ 1:464 h h C ð3Þ d 0:89 d 0:54 M 1 ¼ 1:13 0:09 ; M2 ¼ C 0:2 þ C 24 1:0 d d þ 14 1:0 M 3 ¼ 0:5 C 0:65 þ C pffiffiffiffi ) K Ic ¼ 46 MPa m
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In the above expressions, d is the deepest point of crack penetration and C is half the major axis of the ellipse. In order to compare the obtained values for the two cracking locations, the expression proposed by Irwin [24] was used to calculate the plane stress fracture toughness for the thickness of 6 mm based on the value of KIc calculated above. " 4 #0:5 1:4 K Ic K c ¼ K Ic 1 þ 2 rys ð4Þ h pffiffiffiffi K c ¼ 70 MPa m pffiffiffiffi The obtained value agreed very well with the value of 72 MPa m for the upper crack. It should be noted that all the values calculated above in fact represent the fracture resistance of the material under dynamic loading with a strain rate of 102 s1. 3.2. Specification of the characteristics of detonation loading One of the essential steps towards determination of the cause of this incident was the specification of the characteristics of the detonation loading. The pressure history for gaseous detonation loading may be represented by an exponential approximation to the Taylor–Zeldovich model and can be characterized by the initial pressure of the gas mixture p1, the peak pressure p2, the final pressure p3, the exponential decay factor T, and the Chapman–Jouguet velocity Vcj as follows [7,8]: t
ð5Þ pðx; tÞ ¼ ðp1 patm Þ þ ðp3 p1 Þ þ ðp2 p3 ÞeT ½1 H ðx V cj tÞ In the above equation, patm is the atmospheric pressure, x is the distance variable, t is the time variable, and H is the step function. In practice, the peak pressure (p2) had to be large enough to cause fracture at the higher portion and yielding at the lower portion of the cylinder. As there was no initial clue to the characteristics of the gas mixture, a number of choices had to be examined. Since the initial reports indicated that the cylinder was nearly empty, naturally the first choice was a load moving at the first critical speed to cause maximum dynamic amplification (the ratio of dynamic strains to equivalent static strains) [7,8,10]. The computed value for the first critical speed was 1165 m/s and a value of 3.7 was considered for the dynamic amplification factor [10]. Using the simple formula for the hoop stress in thin cylinders, the peak pressure was estimated as 1 ru h p2 ¼ ¼ 19 MPa ð6Þ U R In the above expression, ru is the ultimate tensile strength, h is the thickness, R is the mean radius, and U is the dynamic amplification factor. Since the pressure ratio (p2/p1) for a gaseous detonation is usually between 15 and 20, the initial pressure (p1) was estimated as 1.1 MPa, and because of a relative low value of Vcj (1165 m/s), the value of T was set as T = 4.34 104 s [7,8]. Next, an analytical solution for the transient elastodynamic response of cylindrical tubes to gaseous detonation [10] was used to determine the time-dependent distribution of stress in the cylinder. As depicted in Fig. 9, the detonation loading can cause a spectrum of stress fluctuations whose amplitudes are dependent on the speed of the traveling load. It is clear that the stress distribution caused by the assumed loading (Vcj = 1165 m/s) creates elastic deformation at the upper half, plastic deformation at the lower half, and fracture near the bottom cap at a distance of 700 mm from the upper neck. Obviously, this pattern does not agree at all with the actual pattern of deformation and fracture of the cylinder. It should be emphasized that the speeds of detonable mixtures of hydrogen and oxygen are much higher than the critical speed of 1165 m/s. In fact, the latter is possible only in presence of an inert diluting gas (like nitrogen). Thus, the search for the correct loading profile was directed towards examination of various mixtures of hydrogen with pure oxygen. The software CEA2 [25] was used for determination of the features of the burned gas for each mixture. In practice, it was found that the loading profiles caused by hydrogen-rich mixtures were not able to cause the expected damage because of their relative high velocities. Finally, a narrow range of loading profiles that matched all of the specified requirements was found for the mixtures with 35–45 vol% hydrogen, and the initial pressure of p1 2 MPa. The detonation of these mixtures is able to produce a peak pressure of p2 37 MPa, traveling at the speed of 2100–2300 m/s [25]. For these speeds the value of T was
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Fig. 9. Time-dependent distributions of stress in the cylinder caused by gaseous detonation loading: (a) speed of 1165 m/s and (b) speed of 2300 m/s.
set as T = 1.5 104 s [12]. Fig. 9b shows the time-dependent distribution of stress caused by the upper bound of this loading range and indicates that the amount of the hoop stress at the location of the initial crack (100 mm below the neck) was 715 MPa. The results showed that the amount of the hoop stress from 50 mm to 100 mm was slightly higher. However, it should be noted that in this region, the cylinder has a conical shape which means that the diameters are lower and the thicknesses are higher. Beyond the 100 mm-point, the computed values for the maximum fluctuations of the hoop stress remained above the yield and below the ultimate strengths. Measurements of the periphery of the cylinder showed the same pattern of permanent radial expansion. The conclusion was that the ability of the detonation loading to initiate an axial crack in the cylinder was quite marginal. In fact, the calculations indicated that, had the initial pressure of the mixture been slightly (0.2 MPa) lower, at least the cylindrical portion could have survived the blast. Fig. 10 shows the variation of the hoop stress with time at three different locations, during a time period of 3.1 ms after the start of detonation. The amplification of the stresses due to the interference between the forward traveling waves and the waves reflected at both ends of the cylinder are clearly visible in the results for the middle part of the cylinder. 3.3. Determination of the crack speed Having found the pattern of fluctuating stresses, the stress wave characteristics like frequency and wave length were calculated and the time period for each loading cycle was determined as 8.2 102 ms. Accordingly, the crack speed during each increment of growth was calculated. Also the average crack speed for the
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Fig. 10. Variation of hoop stress with time at three different locations. The distances are measured from the upper neck: (a) 100 mm, (b) 400 mm and (c) 700 mm.
fast non-incremental growth periods after branching points was computed as 210 m/s. This result was in agreement with the speed range of 100–300 m/s which was obtained from full-scale testing of rapid ductile crack propagation in pressurized pipelines [26]. Fig. 11 shows the directions of crack growth and the computed speeds for the part No. 5.
Fig. 11. Crack growth directions and speeds for the fragment No. 5.
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4. The overall scenario In this section, the sequence of events which occurred during this incident is briefly reviewed. The intention is to present a unified picture of the various aspects of this investigation. The operator of an experimental apparatus borrowed a hydrogen cylinder to run a test which involved producing a candle flame with a mixture of hydrogen and air (9.1 vol% hydrogen). Although the color of the cylinder indicted that it was originally used for medical oxygen supply, the operator trusted a H2 marking painted by ink on the cylinder. The results of this investigation showed that the content of the cylinder was in fact a mixture of hydrogen and oxygen (35–45 vol% hydrogen) with an approximate initial pressure of 2 MPa. As a result of diluting the initial mixture with air (90.9 vol% air), the content of hydrogen fell below the lower flammability limit of hydrogen (4 vol%). Thus, the operator was not able to get the candle flame. This was later confirmed by the reports issued by the lab authorities. As the operator attempted to replace the cylinder with a new one, the initial mixture was somehow detonated at the top of the cylinder. The exact nature of the triggering process is not clear. There are many literature accounts of accidental hydrogen leaks igniting for no apparent reason [27]. It is usually assumed that these were caused by small static electricity discharges. A weak electrostatic spark from the human body releases about 10 mJ of energy, which is capable of setting fire to a majority of common fuels [16]. As the detonation started, a shock wave with an approximate peak pressure of 37 MPa traveled down the cylinder with a velocity between 2100–2300 m/s, resulting in a dynamic amplification factor of 1.9 on the hoop stress. At a distance of 100 mm below the neck, the hoop stress slightly exceeded the ultimate tensile strength of the material. Consequently, a small through-thickness crack was created in the axial direction by shear. The stress intensity factor caused by the same stress cycle that created the crack was enough to advance it still further (13 mm in the forward direction and 7 mm in the backward direction). About 1.7 ms after the creation of the initial crack, the backward crack tip reached a point (40 mm below the neck) where the tensile axial stresses caused by flap bulging were significant enough to divert the crack and cause branching. The speed of crack growth after the branching point was estimated as 210 m/s. It took 3 ms before the forward tip reached the lower branching point. The axial growth of the initial crack and the circumferential growth of the branches were totally in mode I. The final separation of the fragments was caused by the growth of branches in axial directions towards each other with a combination of bending and tearing (mixed mode I and III). During the separation of the fragments from the main body of the cylinder, the elastic energies stored during the flap
Fig. 12. Various stages of deformation and fracture of the gas cylinder. Double-head arrows represent tensile stresses and curved arrows represent bending. The sketch is not to scale.
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bulging were suddenly released. As a result, these thin fragments suffered severe plastic deformation by twisting and folding. On the other hand, the traveling of the detonation front down the cylinder caused a uniform permanent radial expansion. Upon reaching the bottom, the ensuing impact on the cap drastically pushed it through the cylinder stand. The resulting friction heated the lower segment of the cylinder and blackened a length of about 50 mm and left visible longitudinal scars on the surface of this region. At the same time, several small cracks initiated at central region of the cap due to the stress waves created by detonation impact. Consequently, three cracks grew from two distinct semielliptical initial cracks. The growth, branching, and rejoining of these cracks divided the cap into three fragments. The time that was required for the cap to collide with the floor was estimated as 15 ms. This was quite longer than the cracking events that took place at the top and the bottom of the cylinder. Fig. 12 schematically shows the various stages of deformation and fracture of the cylinder. The striking fact is that the initial pressure of the gas mixture that caused all this damage was only 9% of the working pressure of the cylinder. The reason for the existence of an oxygen-rich mixture in a cylinder which was supposed to have ‘‘pure” hydrogen is not clear. One possibility is that, during the last filling, the cylinder was mistakenly filled with oxygen because of its color. 5. Conclusions The aim of this investigation was the determination of the cause of the explosion of a commercial gas cylinder containing hydrogen. The general cracking pattern of the cylinder, the fractographic features, and the stress analysis results were all indicative of an internal gaseous detonation. Consequently, a number of specific features of the detonation-driven fracture of cylindrical tubes with closed ends were identified. These features included: flap bulging, crack curving and branching adjacent to the bulged area, formation of staircase markings on shear lips, and multiple cracking at the cap center. The investigations indicated that the initial cracks were created by local excessive shear and the crack propagations were almost entirely governed by structural waves. Based on the above observations and using the results of the dynamic stress analysis of the cylinder, the main characteristics of the gaseous detonation such as the initial and peak pressures and the traveling speed were estimated and the composition of the initial gas mixture was specified. The results showed that the content of the cylinder was a detonable mixture of hydrogen and oxygen (35-45 vol% hydrogen) with an approximate pressure of 2 MPa (9% of the working pressure of the cylinder). The reason for the existence of an oxygen-rich mixture in the cylinder is not known. However, a plausible scenario is that during the last filling, the cylinder with some remaining hydrogen was mistakenly filled with oxygen because of its color. Acknowledgements The author wishes to express his appreciation to his colleagues, Professor Mazaheri, Professor Malek, and his graduate student, Mr. Amir Harandi, for their valuable and continuous help during the course of this investigation. References [1] Guide to gas cylinders. Explosive and Dangerous Goods Division, Department of Labour, New Zealand, Revision 1992. [2] Tang S. Dynamic response of a tube under moving pressure. In: Proceedings of the American Society of Civil Engineers, vol. 5. Engineering Mechanics Division; 1965. p. 97–122. [3] Reismann H. Response of a pre-stressed cylindrical shell to moving pressure load. In: Ostrach S, Scanlon R, editors. Eighth midwest mechanics conference. Pergamon Press; 1965. p. 349–63. [4] de Malherbe M, Wing R, Laderman A, Oppenheim A. Response of a cylindrical shell to internal blast loading. J Mech Eng Sci 1966;8(1):91–8. [5] Simkins T. Resonance of flexural waves in gun tubes. Tech. Rep. ARCCB–TR–87008, US Army Armament Research, Development and Engineering Center, Watervliet, NY 12189–4050, July 1987, PVT-03-1045 18.
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[6] Thomas G. The response of pipes and supports generated by gaseous detonations. J Pressure Vessel Technol 2002;124:66–73. [7] Beltman W, Burcsu E, Shepherd J, Zuhal L. The structural response of cylindrical shells to internal shock loading. J Pressure Vessel Technol 1999;121:315–22. [8] Beltman W, Shepherd J. Linear elastic response of tubes to internal detonation loading. J Sound Vib 2002;252(4):617–55. [9] Mirzaei M, Mazaheri K, Biglari H. Analytical modeling of the elastic response of tubes to internal detonation loading. Int J Pressure Vessels Piping 2005;82(12):883–95. [10] Mirzaei M, Biglari H, Salavatian M. Analytical and numerical modeling of the elastodynamic response of a cylindrical tube to internal gaseous detonation. Int J Pressure Vessels Piping 2006;83(7):531–9. [11] Chao TW, Shepherd JE. Fracture response of externally flawed aluminum cylindrical shells under internal gaseous detonation loading. Int J Fracture 2005;134(1):59–90. July. [12] Tong Wa Chao. Gaseous detonation-driven fracture of tubes. PhD thesis, Pasadena, California: California Institute of Technology; 2004 [March]. [13] Naitoh M, Kasahara F, Kubota R, Ohshima I. Analysis of pipe rupture of steam condensation line at Hamoaka-1, (I) accumulation of non-condensable gas in a pipe. J Nuclear Sci Technol 2003;40(12):1032. [14] Mirzaei M, Karimi R. Crack growth analysis for a cylindrical shell under dynamic loading. In: Proceedings of ASME PVP 2006/11th international conference on pressure vessel technology, ICPVT-11, Canada: Vancouver; 2006. [15] Failure modes and effects analysis for hydrogen fueling options, Report to California Energy Commission, Prepared by TIAX LLC, November 2004. [16] Ricci M. Experts’ assessments and representations of risks associated with hydrogen. Institute for Social, Cultural and Policy Research, University of Salford; 2005, UKSHEC Social Science Working Paper No. 12 [July]. [17] Hydrogen Incidents reports at www.h2incidents.org. [18] Price WH. An acetylene cylinder explosion: a most probable cause analysis. Eng Failure Anal 2006;13:705–15. [19] Baker WE, Tang J. Gas, dust, and hybrid explosions. Amsterdam: Elsevier; 1991. [20] Alder JF, Phillips KA. The effect of strain rate and temperature on the resistance of aluminum, copper, and steel to compression. J Inst Met 1954;83:80. [21] Zahoor A. Closed form expressions for fracture mechanics analysis of cracked pipes. J Pressure Vessel Technol 1985;107:203–5. [22] Hertzberg WH. Deformation and fracture mechanics of engineering materials. 4th ed. John Wiley & Sons, Inc.; 1996. p. 702–3. [23] Newman Jr JC, Raju IS. An empirical stress-intensity factor equation for the surface crack. Eng Fracture Mech 1981;15(1–2):185–92. 52, 54. [24] Irwin GR. Fracture mode transition for a crack traversing a plate. J Basic Eng 1960;82:417–25. [25] CEA2, Chemical equilibrium with applications, version 2. NASA Glenn’s computer program. [26] Kanninen MF, Popelar CH. Advanced fracture mechanics. Oxford University Press, Inc.; 1985. p. 250–3. [27] Zalosh R, Short T. Compilation and analysis of hydrogen accident reports. Factory Mutual Research Corp Final Report C00-4492-4 for DOE; 1978 [October].
Engineering Failure Analysis 15 (2008) 820–834 www.elsevier.com/locate/engfailanal
Failure analysis of an exploded gas cylinder Majid Mirzaei * Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran Received 14 November 2007; accepted 17 November 2007 Available online 3 December 2007
Abstract This paper reports the major activities carried out during the failure analysis of an exploded cylinder containing hydrogen. The general cracking pattern of the cylinder, the fractographic features, and the stress analysis results were all indicative of an internal gaseous detonation. Accordingly, several specific characteristics of detonation-driven fracture of closed-end cylindrical tubes were identified. These characteristics were analyzed through detailed examinations of the fracture surfaces, cracking patterns, and dynamic stress analysis of the cylinder using a transient analytical model. Based on the size and location of special markings found on the shear lips, and using the time duration of flexural waves, the crack growth increments and speed were computed. Consequently, the basic features of the gaseous detonation and the composition of the original gas mixture were identified. The results indicated that the detonation of a low-pressure oxygen-rich mixture of hydrogen and oxygen was the cause of this failure. The presence of oxygen was attributed to an improper usage of an oxygen cylinder for hydrogen storage. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Crack growth; Fractography; Dynamic stress analysis; Hydrogen; Explosion
1. Introduction Commercial gas cylinders are ordinary pressure vessels which their proper design, manufacture, quality control, transportation, and implementation are specified by various standards and regulations [1]. Hence, they are generally considered to be safe to such an extent that divers strap them to their bodies, some patients or even elderly adults regularly use them for medical oxygen supply, and many people carry them in their car trunk as fuel storage. Nevertheless, accidental burst or even explosion of these cylinders is possible and can be devastating. These accidents are quite rare but the price we pay for what we learn from them can be quite high. Thus, a thorough investigation of each and every accident is necessary and the results should be lucidly presented to raise the public awareness. In 2006, a commercial gas cylinder containing hydrogen exploded in a laboratory in Iran. As a result, the cylinder fractured into seven pieces and caused the death of a lab resident and partial destruction of the lab. *
Fax: +98 21 88005040. E-mail address: [email protected]
1350-6307/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2007.11.005
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Nomenclature a C D d h H Kc KI KIc L M1 M2 M3 P1 P2 P3 Patm Q ry R t T Vcj x U r ru rys v
half crack length, m half major axis of semielliptical crack, m shear lip depth, m penetration depth of semielliptical crack, m thickness, m step function pffiffiffiffi plane stress fracture toughness, MPa pm ffiffiffiffi stress intensity factor (mode I), MPa pm ffiffiffiffi plane strain fracture toughness, MPa m cylinder length, m dimensionless parameter dimensionless parameter dimensionless parameter pre-detonation pressure, MPa maximum-detonation pressure, MPa post-shock pressure, MPa atmospheric pressure, MPa dimensionless parameter crack tip plastic zone radius, m mean tube radius, m time variable, s exponential decay factor, s Chapman–Jouguet velocity, m/s distance variable, m dynamic amplification factor far field stress, MPa ultimate strength, MPa yield strength, MPa dimensionless parameter
Fig. 1 shows the schematic of the cylinder along with the pictures of the fragments collected from the accident scene. This paper reports the major activities carried out to determine the cause of this incident. It should be emphasized that this is an independent scientific investigation and is not related to any judicial process. As will be discussed in the sequel, the cracking pattern of the cylinder (along with other evidences) was indicative of an internal gaseous detonation. Detonations are combustion events in which the speed of the combustion wave front is supersonic. A detonation explosion is more severe than a deflagration explosion (with subsonic wave front) since the pressure waves are much stronger. A deflagration of hydrogen can result in a detonation depending on the hydrogen concentration, the degree of space confinement, the conditions that promote turbulence in the gas, and the strength of the ignition source. However, the occurrence of internal detonation in an ordinary gas cylinder seems peculiar because, (a) such detonation needs a proper mixture of hydrogen and oxygen, and (b) some sort of ignition is required to trigger the process. Moreover, in this particular case, the initial reports indicated that the cylinder was nearly empty and the operator was trying to replace it with a new one before the accident happened. Another complex issue in these types of failure analysis is the nature of the fracture itself. Detonation-driven fracture of cylindrical tubes is distinguished from quasi-statically loaded tube fracture because of two main characteristics. First, the structural waves caused by detonation loading can result in oscillatory strains whose amplitudes are dependent on the speed of the traveling load and can be
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Fig. 1. Left: schematic of the cylinder. Right: remains of the exploded cylinder.
significantly higher than those predicted by static formulas. Second, dynamic fracture parameters can be quite different from equivalent static forms. There have been several studies concerning the structural response of tubes to shock or detonation loading [2–10]. These studies were carried out on flawless tubes, so the results can only be used for stress analysis and determination of the critical locations for crack initiation in the tube. In contrast, there was no report in the open literature about the fracture of tubes caused by gaseous detonations, prior to the experimental study reported by Chao and Shepherd [11,12]. Their study was primarily motivated by accidents like those occurred in the nuclear power plants in Japan and Germany in 2001 [12,13]. In both incidents, sections of steel steam pipes were fragmented due to combustion of hydrogen–oxygen mixtures created by radiolysis. One of the most important questions that arose during the accident investigation was whether the type of accidental combustion can be deduced from the fracture patterns. At that time, it seemed that the state of knowledge on detonation-driven fracture was not adequate to answer this question [13]. Mirzaei and Karimi carried out finite element simulations of detonation-driven fracture of a thin aluminum tube using the crack tip opening angle (CTOA) [14] and cohesive element methods and compared the results with the experimental work of Chao and Shepherd [11,12]. These studies showed that an important characteristic of the detonation-driven fracture of tubes is that the crack propagation phase can be mostly or entirely driven by the structural waves. Thus, the whole cracking process and fragmentation can occur after the passage of detonation front. Among other features of detonation-driven fracture are a specific flap bulging process and the resultant crack curving and branching. In the current study, it will be shown that some special markings may also be found on the fracture surface which can be used to quantify the crack growth increments and calculate the crack speed. As mentioned above, reports on incidents involving gaseous detonation are quite rare. Although the prospective usage of hydrogen as a clean fuel and the safety concerns has lead to several investigations [15,16], the lack of substantial data on hydrogen-related accidents, tests, and simulations has so far prevented detailed assessments of hydrogen safety in specific realistic conditions [16]. In a recent hydrogen accident, an unauthorized installation of an adapter for connecting a hydrogen tube trailer manifold to an oxygen manifold at a facility for filling compressed-gas cylinders led into a detonation that ruptured the tube [17]. It was reported that the far end of the tube was folded out like the petals of a flower. The analysis of the cause of the explosion of an acetylene cylinder, which occurred in 1993 in Sydney, was reported by Price [18]. In his paper, Price also
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referred to two other incidents, one was related to an acetylene cylinder where oxygen was present in Munich (1992), and another was the explosion of an oxygen cylinder in Texas (1963) [18]. The Sydney incident caused severe fragmentation of the cylinder and a fatality and property damage. This failure was also attributed to internal gaseous detonation and was announced as outstanding in two respects, (a) the violence of the failure, and (b) the fact that the explosion occurred where there were no apparent ignition sources present [18]. Hence, the only possible cause of initiation seemed to be impacts on the cylinder caused by handling the cylinder on a truck, but the energy available from such an initiator is very low. However, it was suggested that in acetylene gas, there appears to be the possibility of a direct initiation, where the deflagration step is either very small or is omitted [19]. Price also suggested that the pressure transient in the fluid must travel faster than the speed of sound in the metal to cause very small fragments. However, the analyses carried out by Mirzaei and Karimi [14] and the evidences presented in the current study show that the crack propagation phase can be essentially governed by the structural waves. Thus, the traveling of high-pressure detonations at much lower speeds (1000–3000 m/s) can cause fragmentation of tubes. In the following sections, the above mentioned aspects are treated in detail. 2. Examination of deformation pattern and fracture surfaces of fragments The visual inspection and measurements of the periphery of the unbroken part of the cylindrical portion indicated a uniform permanent radial expansion with no bulging. This was in contrast to the bulging of closed-end cylindrical pressure vessels under static internal pressures. This particular type of radial expansion was attributed to a moving local pressure. This was the first clue for the hypothesis of occurrence of an internal gaseous detonation in the cylinder. In the next step, the very well-developed chevron markings on the fracture surfaces were followed and two separate sites of crack initiation were identified. The first one was in the upper portion of the cylindrical part and the second one was at the center of the bottom cap. In continuation, the cracking pattern of the cylinder and the original locations of all the fragments were specified as depicted in Fig. 2. 2.1. Examination of the fracture surfaces of the upper cracking zone In this zone, the chevron markings clearly showed that the location of crack initiation was at the border of the cylindrical and conical portions, 100 mm below the neck (see Fig. 3). The examination of the initial crack showed no evidence of pre-cracking caused by fatigue, stress corrosion, material defects, or manufacturing flaws. In fact, the appearance of this 6-mm through-thickness crack was indicative of a local rupture caused
Fig. 2. Schematic of the cylinder showing the original location of the collected fragments. The sketch is not to scale.
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Fig. 3. The overall cracking pattern of the upper portion of the cylinder. The sketch is not to scale.
by excessive shear (see Fig. 4). The direction of chevron markings indicated that this crack grew in a self-similar fashion in both directions towards the head and the bottom of the cylinder. The upper growing front branched into two new fronts by curving towards right and left. The lower growing front in turn branched into two new fronts at a distance of 292 mm below the neck. The growth of the upper-left and the lower-left branches towards each other caused the formation of the fragment No. 5. Similarly, the growth of the upperright and the lower-right branches towards each other and the final rupture of the ligament by bending led to the formation of the fragment No. 6, from which the fragment No. 7 was already separated. In fact, the fragment No. 7 was formed as a result of a second branching and the final rejoin of this branch with the lower part of the main crack path. At first, this fragment was not considered as a part of the cylinder because it had been
Fig. 4. The upper crack initiation site and special markings on conjugate fracture surfaces of fragments Nos. 5 and 7.
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discolored by chemicals. However, this was one of the most important fragments as it contained on of the two surfaces of the initial crack. By further examination of the fracture surfaces, special markings were found on the very well developed shear lips in this region (see Fig. 4). In fact, the existence of these markings was a clear indication of a periodic crack growth caused by flexural waves. On the one hand, these markings are like ‘‘fatigue striations”, since they represent the increments of crack growth caused by vibrational strains. On the other hand, they can be considered as ‘‘arrest markings”, since they represent the arrest locations of a growing crack under displacement control. Nevertheless, these markings have some special features, like being visible to the naked eye or by a magnifying glass, and they only exist on the shear lips. In order to distinguish them from similar markings and because of their unique appearance, they will be referred to as ‘‘staircase markings” in this article. 2.2. Analysis of deformation and fracture of the upper cracking zone The most important effect of internal gaseous detonation on cylindrical tubes is the development of flexural structural waves [7–14]. According to the schematic depicted in Fig. 5, the passage of detonation front (as a local narrow overpressure) results in local radial displacements. Because of the dynamic effects of this highspeed moving load, these displacements are oscillatory. The result is a pattern of fluctuating circumferential (hoop) strains which exist even after the detonation loading dies out. In presence of an axial trough-thickness crack, the points on the crack surface can continue to oscillate radially. However, because the crack surface is traction free, these points also tend to displace circumferentially under the influence of stresses imposed by the
Fig. 5. Formation of flexural waves by a moving detonation front and the resulting flap bulging. The picture of the finite element simulation [14] is for an aluminum tube.
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neighboring material. The outcome is that the points on the crack surface are forced to displace in the resultant direction. The continuation of this effect, which is maximum at the crack center and minimum at the crack tips, results in the bulging of crack flaps. Note that the crack growth by flexural waves is in fact controlled by the far-field displacements, so the growth is stable and incremental. In fact, the development of the staircase markings is indicative of this type of growth. Of course the amplitude of oscillating displacements in the far-field area decreases as a result of crack growth. This effect if more pronounced for tubes with smaller diameters and thinner wall thicknesses. However, the effect is partially counterbalanced by the increase of the crack driving force with the crack length. With the extension of the bulged area, large tensile stresses (equivalent to yield stress) develop in the bulged region in the axial direction of the tube. Since cracks usually tend to grow perpendicular to the largest principal stress directions, the initial self-similar growth changes into a circumferential growth by curving around the bulged region. The occurrence of branching at this point is also possible for the cases that the energy release rate of the crack is high enough to support two crack fronts. 2.3. Fracture of the bottom cap A number of important issues should be considered in the fracture analysis of the bottom cap. The first one is that the central region of the cap is a unique location. Since the membrane stresses are all equal in this region, every meridional direction is a principal direction. The observed multiple cracking in this region is in fact the result of this state of stress (see Fig. 6). However, for locations further from the center point, the direction of the first principal stress is the hoop direction. The first principal stress at these points is in fact caused by the flexural waves transmitted into the cap and formation of circumferential wrinkles. The directions of cracking of the paint on the convex side of the cap are clear indications of the above argument. In this area, the white paint acted like a brittle coating. The latter is often used in experimental stress analysis for determination of the direction of principal stresses.
Fig. 6. Top: principal directions on the bottom cap. Bottom: multiple cracking at the center point of the bottom cap.
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Fig. 7. Cracking pattern of fragments Nos. 3 and 4.
Fig. 8. Chevron markings, radiating from the crack initiation site, point back towards the initial semielliptical crack (fragment No. 4). The colors of this picture have been changed to increase the contrast of the crack surface features.
The chevron markings showed that the locations of the two major initial cracks, that caused the fracture of the cap, were 10 mm further from the center point. From these two initiation sites, three cracks grew in different directions towards the periphery of the cap. Thereby, the cab was divided into three fragments which where still clinging to the main cylinder through their curved edges. Next, each radial crack branched and created two new fronts which grew circumferentially in opposite directions. As a result, the curved edge of each fragment was cut from both sides and reduced into a ligament. Fig. 7 shows the cracking pattern of the fragments Nos. 3 and 4 (No. 2 behaved similarly). Another important issue is that the final separation of each fragment occurred through its rotation that caused the rupture of the ligament. Thus, the bottom of the cylinder folded out like the petals of a flower. The driving force required for the cracking and folding was maintained solely by the structural waves. It should be noted that this cracking pattern is specific to internal gaseous detonation. Fig. 8 shows the magnified image of one of the initiation sites at the center of the bottom cap. The initial crack was in the form of a semielliptical surface crack with the dimensions of d = 2.5 mm and 2C = 6 mm, slanted with respect to both the fracture surface and the cap outer surface. There was no sign of corrosion products, fatigue markings, or material defects on the surface of the initial crack and it was clear that it initiated naturally as a result of an intense local shear stress. 3. Dynamic stress analysis of the gas cylinder Having determined the type of the pressure loading, the next step was the calculation of the stress levels which caused the deformation and fracture of various parts of the cylinder. The aim was to use the results of the stress analysis to find the two major characteristics of the detonation front, i.e., the peak pressure and the velocity.
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Table 1 Measured mechanical properties for the cylinder material (carbon steel) Yield strength (MPa)
Ultimate strength (MPa)
Elongation (%)
598
700
23
First, the tensile properties of the material (carbon steel) were measured using testing coupons extracted from the cylinder. Table 1 shows the average tensile properties of the cylinder obtained from different samples. It should be mentioned that properties like yield strength are rate-sensitive and their application to a high strain rate of 102 s1 usually requires a correction factor of 1.28 [20]. However, since the measured values were obtained by testing a plastically deformed material that had actually yielded and work hardened under the same strain rate, the above correction was not necessary. 3.1. Determination of the fracture toughness An accurate estimation of the fracture resistance of the material was required to calculate the amplitudes of the stress waves that drove the crack at different locations along the cylinder. Since the facture resistance is sensitive to the strain rate and the state of stress, an indirect approach was implemented to estimate the dynamic fracture toughness as follows. The staircase markings indicated that the initial crack of the cylindrical portion had been able to propagate under the first stress cycle with the magnitude of 700 MPa. The initial estimation of the length of the flexural stress cycle was 200 mm. Since this value was quite larger than the initial crack length (2a = 6 mm), the stress intensity expression for a through-thickness axial crack in a cylinder under internal pressure [21] was used and the value of fracture toughness was calculated as pffiffiffiffi pffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a K I ¼ r pa 1 þ 0:52v þ 1:29v2 0:074v3 ; v ¼ pffiffiffiffiffiffi ) K c ¼ 72 MPa m ð1Þ Rh in which, KI is the mode I stress intensity factor, r is the hoop stress, a is half the crack length, R is the mean radius, h is the thickness, and Kc is the fracture toughness. Another estimation of the fracture toughness was made based on the size of the shear lips [22]. The average amount of the shear lip depth, measured at different locations, was 1.75 mm. The average thickness along the main crack path was measured as 5 mm (due to the thinning caused by flap bulging). Thus, the shear lip depth value was multiplied by 6/5 and Kc was calculated as 2 pffiffiffiffi 1 K ) K c 69 MPa m ð2Þ D ry 2p rys in which, D is the shear lip depth, ry is the crack tip plastic zone pffiffiffiffi radius, and rys is the yield strength. The estimated value was quite consistent with the value of 72 MPa m calculated using Eq. (1). In fact, these values represent the plane stress fracture toughness for the thickness of 6 mm. Nevertheless, the situation was quite different for the initial crack at the bottom cap for which the crack front was predominantly in a state of plane strain. Using the stress intensity calibration for a semi-elliptical surface crack under remote tensile stress [23], the value of plane strain fracture toughness was calculated as follows: sffiffiffiffiffiffi pd H KI ¼ r Q 2 4 1:65 d d d H ¼ M1 þ M2 þ M3 ; Q ¼ 1 þ 1:464 h h C ð3Þ d 0:89 d 0:54 M 1 ¼ 1:13 0:09 ; M2 ¼ C 0:2 þ C 24 1:0 d d þ 14 1:0 M 3 ¼ 0:5 C 0:65 þ C pffiffiffiffi ) K Ic ¼ 46 MPa m
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In the above expressions, d is the deepest point of crack penetration and C is half the major axis of the ellipse. In order to compare the obtained values for the two cracking locations, the expression proposed by Irwin [24] was used to calculate the plane stress fracture toughness for the thickness of 6 mm based on the value of KIc calculated above. " 4 #0:5 1:4 K Ic K c ¼ K Ic 1 þ 2 rys ð4Þ h pffiffiffiffi K c ¼ 70 MPa m pffiffiffiffi The obtained value agreed very well with the value of 72 MPa m for the upper crack. It should be noted that all the values calculated above in fact represent the fracture resistance of the material under dynamic loading with a strain rate of 102 s1. 3.2. Specification of the characteristics of detonation loading One of the essential steps towards determination of the cause of this incident was the specification of the characteristics of the detonation loading. The pressure history for gaseous detonation loading may be represented by an exponential approximation to the Taylor–Zeldovich model and can be characterized by the initial pressure of the gas mixture p1, the peak pressure p2, the final pressure p3, the exponential decay factor T, and the Chapman–Jouguet velocity Vcj as follows [7,8]: t
ð5Þ pðx; tÞ ¼ ðp1 patm Þ þ ðp3 p1 Þ þ ðp2 p3 ÞeT ½1 H ðx V cj tÞ In the above equation, patm is the atmospheric pressure, x is the distance variable, t is the time variable, and H is the step function. In practice, the peak pressure (p2) had to be large enough to cause fracture at the higher portion and yielding at the lower portion of the cylinder. As there was no initial clue to the characteristics of the gas mixture, a number of choices had to be examined. Since the initial reports indicated that the cylinder was nearly empty, naturally the first choice was a load moving at the first critical speed to cause maximum dynamic amplification (the ratio of dynamic strains to equivalent static strains) [7,8,10]. The computed value for the first critical speed was 1165 m/s and a value of 3.7 was considered for the dynamic amplification factor [10]. Using the simple formula for the hoop stress in thin cylinders, the peak pressure was estimated as 1 ru h p2 ¼ ¼ 19 MPa ð6Þ U R In the above expression, ru is the ultimate tensile strength, h is the thickness, R is the mean radius, and U is the dynamic amplification factor. Since the pressure ratio (p2/p1) for a gaseous detonation is usually between 15 and 20, the initial pressure (p1) was estimated as 1.1 MPa, and because of a relative low value of Vcj (1165 m/s), the value of T was set as T = 4.34 104 s [7,8]. Next, an analytical solution for the transient elastodynamic response of cylindrical tubes to gaseous detonation [10] was used to determine the time-dependent distribution of stress in the cylinder. As depicted in Fig. 9, the detonation loading can cause a spectrum of stress fluctuations whose amplitudes are dependent on the speed of the traveling load. It is clear that the stress distribution caused by the assumed loading (Vcj = 1165 m/s) creates elastic deformation at the upper half, plastic deformation at the lower half, and fracture near the bottom cap at a distance of 700 mm from the upper neck. Obviously, this pattern does not agree at all with the actual pattern of deformation and fracture of the cylinder. It should be emphasized that the speeds of detonable mixtures of hydrogen and oxygen are much higher than the critical speed of 1165 m/s. In fact, the latter is possible only in presence of an inert diluting gas (like nitrogen). Thus, the search for the correct loading profile was directed towards examination of various mixtures of hydrogen with pure oxygen. The software CEA2 [25] was used for determination of the features of the burned gas for each mixture. In practice, it was found that the loading profiles caused by hydrogen-rich mixtures were not able to cause the expected damage because of their relative high velocities. Finally, a narrow range of loading profiles that matched all of the specified requirements was found for the mixtures with 35–45 vol% hydrogen, and the initial pressure of p1 2 MPa. The detonation of these mixtures is able to produce a peak pressure of p2 37 MPa, traveling at the speed of 2100–2300 m/s [25]. For these speeds the value of T was
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Fig. 9. Time-dependent distributions of stress in the cylinder caused by gaseous detonation loading: (a) speed of 1165 m/s and (b) speed of 2300 m/s.
set as T = 1.5 104 s [12]. Fig. 9b shows the time-dependent distribution of stress caused by the upper bound of this loading range and indicates that the amount of the hoop stress at the location of the initial crack (100 mm below the neck) was 715 MPa. The results showed that the amount of the hoop stress from 50 mm to 100 mm was slightly higher. However, it should be noted that in this region, the cylinder has a conical shape which means that the diameters are lower and the thicknesses are higher. Beyond the 100 mm-point, the computed values for the maximum fluctuations of the hoop stress remained above the yield and below the ultimate strengths. Measurements of the periphery of the cylinder showed the same pattern of permanent radial expansion. The conclusion was that the ability of the detonation loading to initiate an axial crack in the cylinder was quite marginal. In fact, the calculations indicated that, had the initial pressure of the mixture been slightly (0.2 MPa) lower, at least the cylindrical portion could have survived the blast. Fig. 10 shows the variation of the hoop stress with time at three different locations, during a time period of 3.1 ms after the start of detonation. The amplification of the stresses due to the interference between the forward traveling waves and the waves reflected at both ends of the cylinder are clearly visible in the results for the middle part of the cylinder. 3.3. Determination of the crack speed Having found the pattern of fluctuating stresses, the stress wave characteristics like frequency and wave length were calculated and the time period for each loading cycle was determined as 8.2 102 ms. Accordingly, the crack speed during each increment of growth was calculated. Also the average crack speed for the
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Fig. 10. Variation of hoop stress with time at three different locations. The distances are measured from the upper neck: (a) 100 mm, (b) 400 mm and (c) 700 mm.
fast non-incremental growth periods after branching points was computed as 210 m/s. This result was in agreement with the speed range of 100–300 m/s which was obtained from full-scale testing of rapid ductile crack propagation in pressurized pipelines [26]. Fig. 11 shows the directions of crack growth and the computed speeds for the part No. 5.
Fig. 11. Crack growth directions and speeds for the fragment No. 5.
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4. The overall scenario In this section, the sequence of events which occurred during this incident is briefly reviewed. The intention is to present a unified picture of the various aspects of this investigation. The operator of an experimental apparatus borrowed a hydrogen cylinder to run a test which involved producing a candle flame with a mixture of hydrogen and air (9.1 vol% hydrogen). Although the color of the cylinder indicted that it was originally used for medical oxygen supply, the operator trusted a H2 marking painted by ink on the cylinder. The results of this investigation showed that the content of the cylinder was in fact a mixture of hydrogen and oxygen (35–45 vol% hydrogen) with an approximate initial pressure of 2 MPa. As a result of diluting the initial mixture with air (90.9 vol% air), the content of hydrogen fell below the lower flammability limit of hydrogen (4 vol%). Thus, the operator was not able to get the candle flame. This was later confirmed by the reports issued by the lab authorities. As the operator attempted to replace the cylinder with a new one, the initial mixture was somehow detonated at the top of the cylinder. The exact nature of the triggering process is not clear. There are many literature accounts of accidental hydrogen leaks igniting for no apparent reason [27]. It is usually assumed that these were caused by small static electricity discharges. A weak electrostatic spark from the human body releases about 10 mJ of energy, which is capable of setting fire to a majority of common fuels [16]. As the detonation started, a shock wave with an approximate peak pressure of 37 MPa traveled down the cylinder with a velocity between 2100–2300 m/s, resulting in a dynamic amplification factor of 1.9 on the hoop stress. At a distance of 100 mm below the neck, the hoop stress slightly exceeded the ultimate tensile strength of the material. Consequently, a small through-thickness crack was created in the axial direction by shear. The stress intensity factor caused by the same stress cycle that created the crack was enough to advance it still further (13 mm in the forward direction and 7 mm in the backward direction). About 1.7 ms after the creation of the initial crack, the backward crack tip reached a point (40 mm below the neck) where the tensile axial stresses caused by flap bulging were significant enough to divert the crack and cause branching. The speed of crack growth after the branching point was estimated as 210 m/s. It took 3 ms before the forward tip reached the lower branching point. The axial growth of the initial crack and the circumferential growth of the branches were totally in mode I. The final separation of the fragments was caused by the growth of branches in axial directions towards each other with a combination of bending and tearing (mixed mode I and III). During the separation of the fragments from the main body of the cylinder, the elastic energies stored during the flap
Fig. 12. Various stages of deformation and fracture of the gas cylinder. Double-head arrows represent tensile stresses and curved arrows represent bending. The sketch is not to scale.
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bulging were suddenly released. As a result, these thin fragments suffered severe plastic deformation by twisting and folding. On the other hand, the traveling of the detonation front down the cylinder caused a uniform permanent radial expansion. Upon reaching the bottom, the ensuing impact on the cap drastically pushed it through the cylinder stand. The resulting friction heated the lower segment of the cylinder and blackened a length of about 50 mm and left visible longitudinal scars on the surface of this region. At the same time, several small cracks initiated at central region of the cap due to the stress waves created by detonation impact. Consequently, three cracks grew from two distinct semielliptical initial cracks. The growth, branching, and rejoining of these cracks divided the cap into three fragments. The time that was required for the cap to collide with the floor was estimated as 15 ms. This was quite longer than the cracking events that took place at the top and the bottom of the cylinder. Fig. 12 schematically shows the various stages of deformation and fracture of the cylinder. The striking fact is that the initial pressure of the gas mixture that caused all this damage was only 9% of the working pressure of the cylinder. The reason for the existence of an oxygen-rich mixture in a cylinder which was supposed to have ‘‘pure” hydrogen is not clear. One possibility is that, during the last filling, the cylinder was mistakenly filled with oxygen because of its color. 5. Conclusions The aim of this investigation was the determination of the cause of the explosion of a commercial gas cylinder containing hydrogen. The general cracking pattern of the cylinder, the fractographic features, and the stress analysis results were all indicative of an internal gaseous detonation. Consequently, a number of specific features of the detonation-driven fracture of cylindrical tubes with closed ends were identified. These features included: flap bulging, crack curving and branching adjacent to the bulged area, formation of staircase markings on shear lips, and multiple cracking at the cap center. The investigations indicated that the initial cracks were created by local excessive shear and the crack propagations were almost entirely governed by structural waves. Based on the above observations and using the results of the dynamic stress analysis of the cylinder, the main characteristics of the gaseous detonation such as the initial and peak pressures and the traveling speed were estimated and the composition of the initial gas mixture was specified. The results showed that the content of the cylinder was a detonable mixture of hydrogen and oxygen (35-45 vol% hydrogen) with an approximate pressure of 2 MPa (9% of the working pressure of the cylinder). The reason for the existence of an oxygen-rich mixture in the cylinder is not known. However, a plausible scenario is that during the last filling, the cylinder with some remaining hydrogen was mistakenly filled with oxygen because of its color. Acknowledgements The author wishes to express his appreciation to his colleagues, Professor Mazaheri, Professor Malek, and his graduate student, Mr. Amir Harandi, for their valuable and continuous help during the course of this investigation. References [1] Guide to gas cylinders. Explosive and Dangerous Goods Division, Department of Labour, New Zealand, Revision 1992. [2] Tang S. Dynamic response of a tube under moving pressure. In: Proceedings of the American Society of Civil Engineers, vol. 5. Engineering Mechanics Division; 1965. p. 97–122. [3] Reismann H. Response of a pre-stressed cylindrical shell to moving pressure load. In: Ostrach S, Scanlon R, editors. Eighth midwest mechanics conference. Pergamon Press; 1965. p. 349–63. [4] de Malherbe M, Wing R, Laderman A, Oppenheim A. Response of a cylindrical shell to internal blast loading. J Mech Eng Sci 1966;8(1):91–8. [5] Simkins T. Resonance of flexural waves in gun tubes. Tech. Rep. ARCCB–TR–87008, US Army Armament Research, Development and Engineering Center, Watervliet, NY 12189–4050, July 1987, PVT-03-1045 18.
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