Fatigue strength of vibration-welded unreinforced nylon butt joints.
Vibration welding welding, process for joining separate pieces of metal in a continuous metallic bond. Cold-pressure welding is accomplished by the application of high pressure at room temperature; forge welding (forging) is done by means of hammering, with the addition of heat. (VW) is a widely used process for joining components made of thermoplastics, with advantages that include short manufacturing cycle times, relatively simple equipment, no surface preparation prior to joining, no additional substances introduced in the weld zone, quick cleanups, and simple recycling [1, 2]. However, the part size and geometry are limited, and currently this joining technique is used to manufacture automotive interior, exterior, and under-hood parts, as well as household appliances, lawn and garden equipment, and power tools [3, 4].
The VW process has been described in the literature. Stokes [1, 5] has identified four significant phases in the process, which are solid friction, transient flow, steady-state flow and solidification. The variables in the vibration welding process that can affect the strength of the resulting joint include welding frequency, amplitude, weld penetration, and weld pressure [1, 2, 5-7]. The effects of amplitude, weld penetration, and pressure on the tensile strength tensile strength
Ratio of the maximum load a material can support without fracture when being stretched to the original area of a cross section of the material. When stresses less than the tensile strength are removed, a material completely or partially returns to its of unreinforced nylon 6 and 6,6 were studied by MacDonald  at a weld frequency of 212 Hz. He concluded that amplitude and penetration had no significant effect on weld strength for the range of values studied. However, he observed that the most influential factor is the weld pressure. It was found that the tensile strength of nylon welded at a relatively low pressure (e.g., 0.8 MPa) was stronger than the ones welded at a relatively high pressure (e.g., 4.0 MPa).
Previously, most of the research [1-7] on vibration welding was focused on short-term mechanical properties with little attention paid to the long-term properties, including fatigue behavior. In general, this body of literature shows that, under optimized welding pressures, the static weld strength of unreinforced nylons can attain that of the unwelded nylon. In a previous study , the authors reported stress-life fatigue data for VW nylon butt welds in the high cycle fatigue regime. It was observed that the fatigue strength of VW nylon butt joints was lower than the static tensile strength; the endurance limit stress was found to be approximately one-third of the static strength of the welded material.
Stokes  studied the fatigue properties of vibration welded polycarbonate A category of plastic materials used to make a myriad of products, including CDs and CD-ROMs. (PC), poly(butylene bu·tyl·ene
Any of three gaseous isomeric ethylene hydrocarbons, C4H8, used principally in making synthetic rubbers. terephthalate Ter`eph´tha`late
n. 1. (Chem.) A salt of terephthalic acid. ) (PBT PBT Provider Backbone Transport (networking technology adding determinism to ethernet)
PBT Polybutylene Terephthalate
PBT Profit Before Tax
PBT Paper Based Test (education) ), polyetherimide (PEI), and modified polyphenylene oxide resin (M-PPO) under tension-tension loading at R = 0.1. He observed that fatigue failure in dog bone specimens tended to occur away from the weld at high stress levels, and at the weld at low stress levels near the fatigue limit Fatigue limit is a property of ferrous alloys and titanium alloys. It is the constant amplitude (or range) of cyclic stress that can be applied to a material without causing fatigue failure. , and found that the ratio of endurance limit stress to the tensile strength was approximately 0.3.
This work focuses on the fatigue properties of vibration welded nylon 6 and 6,6 under tension-tension loading at R = 0.1. Fatigue data are presented for the welded and unwelded materials in the low cycle, high cycle and transition fatigue life regions. The effect of cyclic frequency on the fatigue life and the fatigue mechanisms in the various fatigue life regimes are discussed.
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All nylon pellets were dried in an oven at 80[degrees]C for approximately 24 hours prior to molding. Plaques of unreinforced nylon 6 (Zytel 7301 NC010) and nylon 6,6 (Zytel 101L NC010) were injection molded with dimensions of 100 X 100 X 3.2 mm. The plaques were then cut to 60 X 100 mm and the cut edges were milled to increase the accuracy of alignment in the thickness dimension for butt-welding. The direction of preferential flow during molding was along the 100-mm axis of the the diameter of the sphere which is perpendicular to the plane of the circle.
See also: Axis milled plaques. The milled plaques were securely clamped to the welding fixture mounted on a Branson Mini II Linear Vibration Welder and were then joined by vibration welding with the milled edges in contact. Details of the setup can be found in Ref. 7. This plaque preparation process is illustrated schematically in Fig. 1.
In this study, low and high weld pressures of 0.8 and 4.0 MPa, respectively, were used. These conditions were chosen to allow for an evaluation of the fatigue performance of welds made at high and low pressures, similar to that done for the static tensile properties by MacDonald  and Mah . Weld pressures were set and controlled by regulating air pressure in a pneumatic cylinder The term air cylinder can also refer to a gas cylinder used to store compressed air, including those used for scuba diving.
Pneumatic cylinders (sometimes known as air cylinders monitored through an electronic pressure transducer Pressure transducer
An instrument component which detects a fluid pressure and produces an electrical, mechanical, or pneumatic signal related to the pressure. linked to the data acquisition system. The estimated precision of the VW pressure is [+ or -]10% of the target value. The process began with the top plaque oscillating os·cil·late
intr.v. os·cil·lat·ed, os·cil·lat·ing, os·cil·lates
1. To swing back and forth with a steady, uninterrupted rhythm.
2. with respect to the stationary one, located directly below by a spring-mass system vibrating vibrating,
v using quivering hand motions made across the client's body for therapeutic purposes. at 212 Hz with a peak-to-peak amplitude of 1.8 mm. The weld penetration was set at 1.5 mm and, once the desired penetration was reached, the vibration was stopped and the weld solidified under constant weld pressure.
Two types of mechanical tests were performed in this study: tensile tests and tension-tension fatigue tests. For the tensile tests, the nonwelded and welded plaques were machined into rectangular specimens that resembled a standard ASTM ASTM
American Society for Testing and Materials D638 tensile specimen with the weld in the center and the flash still intact. The "dog bone" specimen shape was not used for tension tests since it has been shown  that failure would occur at or near the weld even for a rectangular specimen. Each plaque produced two specimens that were obtained at the locations shown in Fig. 1. The specimens with a gauge cross-section of 3.2 X 28.5 mm were produced in a numerical control numerical control: see computer-aided manufacturing.
Control of a system or device by direct input of data in the form of numbers, letters, symbols, words, or a combination of these forms. milling machine milling machine
Machine tool that rotates a circular tool with numerous cutting edges arranged symmetrically about its axis, called a milling cutter. The metal workpiece is usually held in a vise clamped to a table that can move in three perpendicular directions. that gave a smooth finish on all edges as shown in Fig. 1. This procedure was followed to minimize edge effects in the specimens cut from the molded plaques. Tensile tests were performed on the specimens at a constant displacement rate of 5 mm/minute until fracture, following the ASTM D638 standard. At least four specimens were tested to measure the average the standard deviation of the stress at fracture for each material and weld condition.
[FIGURE 2 OMITTED]
The remainder of the nonwelded and welded plaques were machined into standard ASTM D638 dog-bone fatigue specimens with the weld flash still attached. The fatigue specimens had a gauge length of 50.8 mm and a cross-section of 19.0 X 3.2 mm, as shown in Fig. 1. It is necessary to have excellent alignment of the plaques since misalignment mis·a·ligned
misa·lignment n. can increase the "notch effects," which would adversely affect the fatigue life of the welded joints and cause scatter in the data. Each specimen was closely examined visually; the few observed to exhibit poor alignment were rejected.
Closely following ASTM D3479, fatigue tests were performed under sinusoidal sinusoidal /si·nus·oi·dal/ (si?nu-soi´dal)
1. located in a sinusoid or affecting the circulation in the region of a sinusoid.
2. shaped like or pertaining to a sine wave. constant amplitude tension-tension loading at R = 0.1 with frequency ranging from 3 to 10 Hz for the welded specimens and 1 to 10 Hz for the nonwelded specimens, with the lower frequency used at high stress levels. Several maximum stress levels below the measured tensile strength were examined. The maximum cyclic load frequency of 10 Hz was chosen to prevent hysteretic hys·ter·e·sis
n. pl. hys·ter·e·ses
The lagging of an effect behind its cause, as when the change in magnetism of a body lags behind changes in the magnetic field. heating of the specimen, which could lead to thermal fatigue. Three trials were conducted at each stress level. The endurance limit stresses were determined with the condition that two specimens endured at least 5 X [10.sup.6] cycles without failure. During testing, each specimen was bagged with dry desiccant desiccant /des·ic·cant/ (des´i-kant)
1. promoting dryness.
2. an agent that promotes dryness.
n. sealed in plastic wrap surrounding the gauge section to ensure that the material was tested in the dry-as-molded (DAM) condition. The temperature of the weld was monitored during testing with a thermocouple placed in the weld zone inside the desiccant wrap (Fig. 2). The fatigue tests were performed in the DAM condition to ensure the fatigue mechanisms were not affected by moisture pickup from the uncontrolled laboratory air environment, especially for the long-life tests, which lasted for up to 2 weeks. The DAM conditions may not be representative of the service environment for all VW nylon components, but it should be applicable to under-hood automotive components, which is the application of primary interest to the authors.
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Tensile tests were performed to determine the standard deviation of the weld tensile strength throughout the plaque, since large dispersion in tensile strengths would likely result in large scattering of the fatigue data. The tensile test results for unreinforced nylon 6 and 6,6 welded at low and high pressures and nonwelded are presented in Fig. 3.
In Fig. 3, the nylon 6 and 6,6 nonwelded specimens clearly had higher tensile strengths than the welded ones. This is expected since vibration welding creates notches (stress concentrations) on the specimens. As well, from Fig. 3, the tensile strength of nylon 6 welded at low pressure was higher than nylon 6 welded at high pressure. This was expected and is consistent with previously published results . However, although the average tensile strength of nylon 6,6 at low weld pressure was higher than at high weld pressure, the measured values were not significantly different at a 95% confidence level.
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Figures 4 and 5 show the S-N (stress-life) curves for the unreinforced nylon 6 and 6,6, welded at low (0.8 MPa) and high (4.0 MPa) pressures, respectively. Nonwelded specimen data corresponding to each nylon are shown on the graphs for reference and the shaded area represents the transition range from high cycle fatigue to low cycle fatigue Low-Cycle Fatigue is cycle conditions that result in
1.) fatigue (material) in less than 105 cycles (some sources say 103cycles).
2.) macroplastic deformation in every cycle. regions. To complete the fatigue profile, the curves are extrapolated to their static tensile strengths (shown as dashed lines in Figs. 4 and 5).
A Basquin equation of the form [S.sub.max] = A [N.sub.f.sup.b] was fit to the high cycle data for each of the welded specimen conditions. Table 1 lists the Basquin coefficients A and b, the endurance limit, transition range, and the correlation coefficients ([R.sup.2]) determined for each set of data. The coefficients listed in Table 1 are strictly fitting parameters valid within the testing range and do not necessarily have a physical meaning.
The S-N curves presented in Figs. 4 and 5 reveal several important trends in the data. In these figures, the fatigue lives of the nonwelded nylon 6 and 6,6 specimens were longer compared to all welded specimens by at least an order of magnitude A change in quantity or volume as measured by the decimal point. For example, from tens to hundreds is one order of magnitude. Tens to thousands is two orders of magnitude; tens to millions is three orders of magnitude, etc. . The fatigue data collected is consistent with the nylons' short-term properties in which the nonwelded specimens have higher tensile strength than the welded ones. The "strength-life equal rank assumption" [11, 12], which proposes that a material with greater tensile strength will have longer fatigue life, appears to be valid as well.
The reduced fatigue lives of the welded specimens were probably caused in part by notches created during vibration welding. The weld itself can be considered to be like a notch inherent in the welding process (Fig. 6). These notches are ideal sites for cracks to initiate, because they have the highest stress concentration. With the presence of notches, the number of loading cycles needed for crack initiation can be ignored because the total fatigue life is dominated by crack propagation .
[FIGURE 6 OMITTED]
For nonwelded nylon 6, only four valid mechanical fatigue data points were collected due to thermal damage in the rest of the specimens. Thermal fatigue occurs when the internal temperature of the specimen passes the glass transition temperature The glass transition temperature is the temperature below which the physical properties of amorphous materials vary in a manner similar to those of a solid phase (glassy state), and above which amorphous materials behave like liquids (rubbery state). , [T.sub.g], of the polymer causing a reduction in the yield stress. Thermal fatigue specimens failed due to excessive permanent deformation, rather than fracture. Figure 7 shows a thermal fatigue specimen where the gauge area is stretched.
This phenomenon was observed in nylon 6 due to its lower dry as molded glass transition temperature, [T.sub.g] (50[degrees]C for nylon 6 and 60[degrees]C for nylon 6,6) and its tendency to absorb more moisture from air (3% water absorption for nylon 6 and 2.7% for nylon 6,6) . In spite of experimental efforts to minimize water pickup, water still may have plasticized the nylon 6 specimens, lowered the [T.sub.g] (nylon 6 [T.sub.g] at 50% relative humidity relative humidity
The ratio of the amount of water vapor in the air at a specific temperature to the maximum amount that the air could hold at that temperature, expressed as a percentage. is 20[degrees]C), and subsequently reduced its yield strength . Thermal fatigue is beyond the scope of this article, but more information can be found in Hertzberg and Manson . The endurance limit for nonwelded nylon 6 can still be extrapolated conservatively to be 35 MPa. A sufficient number of data points were obtained for nonwelded nylon 6,6.
[FIGURE 7 OMITTED]
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Effect of Weld Pressure
Through statistical analysis, it was confirmed that weld pressure plays a significant role in the fatigue properties of nylon 6. In Fig. 6, the fatigue life of nylon 6 welded at low pressure was longer than at high pressure by four orders of magnitude at the stress level of 50 MPa. Furthermore, at a stress level of 40 MPa, the fatigue life of nylon 6 specimens welded at low pressure was an order of magnitude greater than at high pressure. This is expected and agrees with the findings on the tensile strength of the welded specimens and followed the "strength-life equal rank assumption." The reason for high strength and better fatigue life at low welding pressure may be linked to the differences in crystal structure and thickness of the weld heat-affected zone The heat-affected zone (HAZ) is the area of base material, either a metal or a thermoplastic, which has had its microstructure and properties altered by welding or heat intensive cutting operations. between low and high pressures .
A different trend is seen in nylon 6,6. Figure 5 shows that the two weld pressure curves for nylon 6,6 are statistically the same at the 95% confidence interval confidence interval,
n a statistical device used to determine the range within which an acceptable datum would fall. Confidence intervals are usually expressed in percentages, typically 95% or 99%. . The fatigue result was consistent with the tensile strength of welded nylon 6,6 obtained earlier. The reason why weld pressure had no effect on both tensile and fatigue properties is unclear. It may be that the thermal and viscous viscous /vis·cous/ (vis´kus) sticky or gummy; having a high degree of viscosity.
1. Having relatively high resistance to flow.
2. Viscid. properties of nylon 6,6 make it less sensitive to weld pressure.
As can be seen in Fig. 6, the data scatter in nylon 6 welded at high pressure is significantly larger than that of nylon 6 welded at low pressure and nylon 6,6 welded at low and high pressures. This scatter may result from the vibration welding procedure itself. Nylon 6 has the lowest tensile modulus of the two unreinforced polymers tested (3,000 vs. 3,100 MPa) . When the plaques were welded at high pressure, the applied force caused the thin plaques to flex. Misalignments would be more severe in the plaques that were welded at high pressure and with thermoplastics that were less rigid.
Taking a closer look at the S-N curves in Figs. 4 and 5, two distinctive slopes are observed. Starting at 1,000-10,000 cycles, the slope of the S-N curves gets steeper. The exact location for the transition from high to low cycle fatigue regions for the two materials is difficult to pinpoint. However, it is estimated that the transition point lies within the range of 1,000 to 10,000 cycles. The transition point is affected by the testing conditions and the applied stress; this is illustrated in a study conducted by Lesser .
Effect of Materials
The effect of material on the fatigue lives of the specimens is examined in this section. Figure 8 shows the fatigue curves of nylon 6 and 6,6 welded at both pressures, along with the data from nonwelded specimens.
Figure 8 shows that the fatigue data for nonwelded nylon 6 and nylon 6,6 are similar. Also, data for nylon 6 welded at low pressure and all welded nylon 6,6 data are indistinguishable; they all have similar endurance limits (approximately 20 MPa) while nylon 6 welded at high pressure has a poorer fatigue performance for reasons outlined earlier.
FATIGUE ENDURANCE RATIO
In this study, fatigue endurance ratio ([[sigma].sub.e]/[[sigma].sub.u]) is the ratio of fatigue strength at 5 million cycles over the static tensile strength. The fatigue endurance ratio relates the endurance limit ([[sigma].sub.e]) to the ultimate tensile strength ([[sigma].sub.u]). Table 2 shows the [[sigma].sub.e]/[[sigma].sub.u] ratio for different materials and weld pressures.
From the data in Table 2, the average fatigue limit stress of the unreinforced nylon butt-welds is 0.3 of the tensile strength, with the lowest value being 0.27. Hence, the following rule of thumb is suggested: the maximum stress at the fatigue limit for R = 0.1 loading can be estimated as 0.3 of the tensile strength of the unwelded nylon. It is noted that the suggested rule also works conservatively for the unwelded materials.
[FIGURE 9 OMITTED]
These observations are consistent with those made for other thermoplastics. Stokes  studied the fatigue properties of vibration welded PC, PBT, PEI, and M-PPO welded at 120 Hz and tested at 10 Hz with R = 0.1. He found that the [[sigma].sub.e]/[[sigma].sub.u] ratio of these thermoplastics is of the order of 0.3. Therefore, the [[sigma].sub.e]/[[sigma].sub.u] ratio calculated for the unreinforced nylons with low and high weld pressures is within the range of the [[sigma].sub.e]/[[sigma].sub.u] ratio obtained by Stokes  for various butt-welded thermoplastics in similar testing conditions. The testing conditions, materials, and [[sigma].sub.e]/[[sigma].sub.u] ratio from Stoke  are listed in Table 3.
Similar rules of thumb are well known for other fatigue conditions in metals. At R = -1, steel and aluminum alloys typically have [[sigma].sub.e]/[[sigma].sub.u] ratios of 0.5 and 0.3, respectively; this ratio is known to decrease with increasing R ratio. When the R ratio is increased to 0.1, the [[sigma].sub.e]/[[sigma].sub.u] ratio is reduced to about 0.33 and 0.2 for steel and aluminum alloys, respectively. Both nonwelded and butt-welded unreinforced nylons have a [[sigma].sub.e]/[[sigma].sub.u] ratio superior to that of aluminum at R = 0.1. This clearly indicates that welded thermoplastics' fatigue performance at temperatures below [T.sub.g] is relatively good compared with metals.
[FIGURE 10 OMITTED]
Thermocouples were placed on the specimens to monitor the surface temperature in the gauge section during fatigue testing. This procedure was performed to ensure that all specimens failed by mechanical fatigue at a temperature below the [T.sub.g] of the material. The maximum temperatures of selected specimens are shown in Fig. 9.
As mentioned earlier, thermal fatigue was observed in some of the nonwelded nylon 6 specimens. The maximum temperatures for the thermal fatigue specimens (represented by open diamond symbol) approached or exceeded the [T.sub.g] of nylon 6 (50[degrees]C). The high specimen temperatures were caused by hysteretic heating due to a combination of high frequency and high strains. It is unclear why this occurred; perhaps some moisture pick up may have been responsible. These data were not included in the S-N curves presented earlier.
Figure 10 presents typical temperature profiles recorded for the specimens that failed mechanically. There is a larger temperature fluctuation in nylon 6 than in nylon 6,6. In general, the temperature rise was slight and tended to increase with number of cycles and with the stress level. Consequently, thermal fatigue was avoided by reducing the cyclic frequency at higher stress levels.
[FIGURE 11 OMITTED]
Some of the unreinforced specimens within the low cycle fatigue region shattered catastrophically along the gauge section while those beyond the low cycle fatigue region generally failed at the weld. The shattering may be due to the high strain that is experienced by the unreinforced specimens due to their low tensile modulus resulting in more crack opening and a high elastic energy released at failure. Figure 11 shows the fracture surfaces observed from both unreinforced nylons welded at high and low pressure tested at various stress levels.
Similar to a metal fatigue fracture fatigue fracture
A fracture, usually transverse in orientation, that occurs as a result of repeated or unusual endogenous stress.
fatigue fracture surface, the thumbnail fatigue pattern originating from the edge of the fracture surfaces can be seen in Fig. 11. The thumbnails are outlined and the arrows indicated the radial direction of crack growth. As well, the pictures show the full specimens' fracture surfaces. The stress intensity is highest at the edge of the specimen due to the notch effect, where it is the ideal site for cracks to initiate. The cracks initiated at the center of the thumbnail and propagated inward (indicated by the arrows in Fig. 11) in a semicircular pattern and finally, the specimen failed. The fracture surfaces from various weld pressures, stress levels, and material all look similar. This suggests that the fatigue cracking mechanism for vibration-welded unreinforced nylon is the same for both high and low pressure welds over the range of stress levels examined in this study.
From this study, the fatigue strength of both nylon 6 and nylon 6,6 welded at 0.8 (low pressure) and 4.0 (high pressure) MPa all have similar S-N curves, and a maximum stress at the fatigue limit (5 million cycles) of approximately 20 MPa, with the exception of nylon 6 welded at 4.0 MPa (high pressure), which has a fatigue limit of 15 MPa. A rule of thumb is suggested for nylon: the fatigue limit stress at R = 0.1 is 0.3 of the tensile strength. Vibration welding of these materials appears to be viable for structural applications requiring fatigue resistance.
TABLE 1. Fatigue S-N curve data for unreinforced nylon 6 and 6,6 welded at low and high welding pressure. Welding Endurance limit pressure Coefficient, A Exponent, (MPa) based on Material (MPa) (MPa) b 5 X [10.sup.6] cycles Nylon 6 0.8 (low) 124 -0.108 20 Nylon 6 4.0 (high) 211 -0.162 15 Nylon 6 Nonwelded N/A N/A ~35 Nylon 6,6 0.8 (low) 124 -0.108 20 Nylon 6,6 4.0 (high) 124 -0.108 20 Nylon 6,6 Nonwelded 409 -0.154 30 Transition range Material (cycles) [R.sup.2] Nylon 6 1000-10000 0.80 Nylon 6 1000-10000 0.49 Nylon 6 N/A N/A Nylon 6,6 1000-10000 0.80 Nylon 6,6 1000-10000 0.80 Nylon 6,6 N/A 0.92 TABLE 2. [[sigma].sub.e]/[[sigma].sub.u] ratio for nonwelded and welded unreinforced and reinforced nylon 6 and 6,6 welded at low and high pressures. Material Pressure (MPa) [[sigma].sub.e]/[[sigma].sub.u] Nylon 6 Nonwelded 0.42 Nylon 6 0.8 (low) 0.32 Nylon 6 4.0 (high) 0.29 Nylon 6,6 Nonwelded 0.36 Nylon 6,6 0.8 (low) 0.27 Nylon 6,6 4.0 (high) 0.27 TABLE 3. [[sigma].sub.e]/[[sigma].sub.u] ratio for butt-welded thermoplastics . Plaque Weld Weld thickness frequency Amplitude pressure Material (mm) (Hz) (mm) (MPa) PC 5.8 120 1.59 0.9 PBT 6.35 120 1.59 0.9 PEI 6.35 120 1.59 6.9 PEI 6.35 250 0.44 6.9 M-PPO 5.08 120 1.59 0.52 Weld penetration Material (mm) [[sigma].sub.e]/[[sigma].sub.u] PC 0.61 0.29 PBT 0.61 0.31 PEI 0.56 0.34 PEI 0.58 0.17 M-PPO 0.57 0.22
We thank Alcan International, Kingston Research and Development Centre, and DuPont Canada Research and Development for their in-kind support of testing facilities and materials.
Contract grant sponsors: NSERC NSERC Natural Sciences and Engineering Research Council (Canada)
NSERC Naval Systems Engineering Resource Center Auto21 NCE NCE Networks of Centres of Excellence
NCE New Chemical Entity (pharmaceutical research)
NCE Normal Curve Equivalent
NCE New Civil Engineer (UK Journal)
NCE Non-Commercial Educational
NCE New Century Energies , Centre for Automotive Materials and Manufacturing.
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New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of (1995).
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K.Y. Tsang, D.L. DuQuesnay
Department of Mechanical Engineering, Royal Military College of Canada, Kingston, Ontario K7K 7B4, Canada
Department of Chemical Engineering, Royal Military College of Canada, Kingston, Ontario K7K 7B4, Canada
Correspondence to: D.L. DuQuesnay; e-mail: firstname.lastname@example.org