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Stress based design guidelines for hydrogen induced stress cracking (HISC) avoidance in duplex materials (May 2009)

   
Pedro M. Vargas

Chevron ETC
Houston, Texas, USA

Stig Wästberg
Det Norske Veritas (DNV)
Høvik, Norway

Paul Woollin
TWI
Granta Park, Cambridge UK

Paper presented at 28th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2009), Honolulu, Hawaii, 31 May - 5 June 2009.

Abstract

Following the failure of several subsea components made of duplex steel, two JIPs were formed, one by TWI and another by DNV and Sintef to address the failure mechanism and to formulate design guidance for the industry. (TWI: The effects of notches and welds on hydrogen embrittlement stress cracking of duplex stainless steels, Sintef/DNV: HISC) Hydrogen charging from the cathodic protection system in the presence of creep strains embrittles the duplex steel, making the duplex susceptible to cracking (hydrogen-induced-stress-cracking, HISC). Creep effects focused on strain measurements in the test specimens from early work at TWI, favoring a strain based approach in the development of early versions of the design guidance for the industry. This paper summarizes the relevant content from the two JIPs to formulate a stress based design criteria, and provides new FEA assessment of the Foinhaven Hubs to better quantify the effect of residual stresses. The basis for the stress-based design guidelines in DNV-RP-F112 is presented that promises to be easier to apply and equally robust as the strain-based approach.

Introduction

Duplex subsea equipment failures to date have been studied extensively and they can be categorized into two types: 1) Failures in large forgings due to excessive loading, at times combined with unfavorable coarse austenitic spacing, and 2) fillet/socket welds that are under-designed and/or with high ferritic content.

For the forgings, the failure did not typically occur at the weld toe, but instead at a stress concentration location removed but in proximity of a girth weld. The fracture surface showed signs of hydrogen embrittlement in the form of transgranular brittle features. The areas of failure were not coated.

For the fillet/socket welds, due to undersized welds or high loading, overloading was found to be a culprit, and coatings were either not present or damaged.

These HISC failures have initiated from the outer surface which is exposed to cathodic protection.

The experience base suggests that there have been no failures where all the requirements set by the design codes have been fulfilled for the material, fabrication or loading at all times before HISC occured. The reported failures have been in fillet welds not in accordance with code (high ferrite content and/or lack of fusion) and external forces that exceeded design loads.

The level of reliability of these duplex components has been shown to be little less than what industry expects, i.e., most designs can tolerate a little overload/bad design, and still function adequately. Conservatisms built into the codes generally help make this happen. DNV-RP-F112 focuses on providing limits against stress and strain that directly address HISC.

Nomenclature

σm : through wall membrane stress.
σb : through wall bending stress.
σm+b : through wall membrane+bending stress.
R : outside radius
t : wall thickness
γHISC : material factor for coarse grain duplex material
σyield : 0.2% offset yield stress, also called proof stress
SMYS : Specified minimum yield stress, also σ yield
Lres : Critical distance for residual stress effects, 2.5√Rt.

HISC mechanism

Although the interaction between hydrogen, microstructure, stress and strain is not well understood, phenomenologically HISC has been found to occur when cathodic hydrogen charging occurs while the duplex matrix undergoes creep. It is postulated that as the duplex matrix undergoes creep, hydrogen diffuses through the ferrite, recombining and locking itself into vacancies produced, embrittling the ferrite phase. Cracks occur in the ferrite phase, and link up across austenitic phases as the creep progresses (Figure 1).

Fig.1. HISC mechanism
Fig.1. HISC mechanism

The HISC mechanism, although local due to the surface hydrogen concentration, requires the potential for creep strains to occur in the presence of hydrogen diffusion. For smooth axially loaded specimens, since the entire cross-section is at the same nominal stress state, the local stress is equal to the nominal stress state. Then the amplitude of this stress state gives the potential of the entire cross-section for creep, including the local surface with hydrogen, making it a valid parameter for the assessment of HISC. For a more complex stress state (a notched bar for example), however, the local stresses may be high but if the nominal cross-section stresses are low enough that sufficient accumulation of creep strains at the surface is not possible, then HISC will not occur.

Therefore the stress based HISC avoidance criteria focuses on through-wall structural stresses such as that used in ASME codes for pressure vessels: σm for the through-wall membrane stress and, σm+b for the through-wall membrane + bending stresses. These structural stresses give more information on the gross creep potential of the wall than the local peak stresses. This has been validated through a significant amount of testing using notched round bars, single edge notched tensile specimens and full scale girth welds.

Figure 2 shows the separation of these stresses from an arbitrary stress gradient. Since the stress based criteria addresses the notch acuity effects separately, and conventional design practices limit any significant effect on the through-wall structural stresses, linear elastic finite element analyses is sufficient to obtain the stresses needed.

Fig.2. Membrane and bending stresses
Fig.2. Membrane and bending stresses

Stress criteria for HISC avoidance

The stress criteria focuses on providing limits to the through-wall membrane and membrane+bending stresses to avoid loadings that can impose gross membrane-stretching creep or gross through-wall bending creep. Then a penalty is placed: 1) on the presence of stress risers, and 2) on locations that are in the vicinity of girth welds. In addition a material quality factor is applied that reduces the allowable limits for coarse austenite spacing. All through wall sections for a subsea duplex component must satisfy both stress checks:

Membrane stress check:

σm <80%σ yield all through-wall sections, everywhere. (TWI, HISC1, HISC2)
Membrane+bending stress check:
σm+b <100%σ yield smooth sections without stress raisers or welds, outside of Lres, (HISC1, HISC2)
σm+b <90%σ yield smooth sections within Lres = 2.5√Rt of a girth weld (Foinhaven Hub FEA)
σm+b <90%σ yield Weld toes, attachments, and stress risers outside of Lres = 2.5√Rt of a girth weld (HISC2)
σm+b <80%σ yield Weld toes, attachments, and stress risers within Lres = 2.5√Rt of a girth weld (Foinhaven Hub FEA)
Material Penalty: For materials with coarse grain austenite spacing, the stress limits above are multiplied by γ HISC = 0.85. (TWI, HISC2, Foinhaven Hub FEA)

The italics in the parenthesis highlight the JIP data that supports the limit. The Foinhaven FEA is presented in a later section.

The DNV RP-F112 also requires the same checks with the von-Mises (equivalent stresses) for these stresses and provides guidance.

TWI JIP summary

TWI performed a comprehensive study of the HISC performance of smooth tensile coupons (3.75mm diameter) with 18 different materials that included forgings, bars plates and pipes. Over 200 specimens were tested. Different austenitic spacing, weld materials and simulated HAZ were also part of this matrix. Each sample was kept under tension in a small polymer vessel containing natural seawater and polarized by potentiostat. Different temperatures, charging potentials, hydrostatic pressures and test durations were also examined. The test results found important trends with respect to cathodic charging levels and austenitic spacing, but also found that proximity of the nominal stress state to yield was the most prominent indicator of the propensity for HISC. The JIP indicated that:

  • Regardless of material, as long as the applied nominal stress was less than 87% of 0.2% offset yield, HISC did not occur.
  • Regardless of material, as long as the applied initial nominal strain was less than 0.5%, HISC did not occur.

These two observations held for all of the materials tested: coarse and fine austenite spacing, welds and the HAZ simulated specimens. The study also found that pre-straining up to 3% provided resistance to creep and HISC. Figure 3 shows some selected results for materials tested at TWI.

Subsequent extension of the JIP focused on the notch acuity and full scale performance of girth welds. The results from this study indicated that the notch acuity did not affect the HISC performance of the test specimens. A full scale girth weld test also showed that membrane stresses in the pipe in excess of yield was needed for HISC to occur.

These results form the basis for:

  1. The 80%σyield limit on the average membrane stresses.
  2. The use of structural stresses instead of notch stresses for HISC assessment.
  3. The need for a material degradation factor to account for austenite spacing.
  4. Local-self-equilibrated residual stresses have little or no effect on HISC resistance.
Fig.3. HISC stresses for Garn West and Foinhaven
Fig.3. HISC stresses for Garn West and Foinhaven

HISC1 and HISC2

HISC1 and HISC2 did a significant amount of testing using three specimen geometries: 1) Smooth, 2) Single edge notch with a V-notch, and 3) Single edge notch with a U-notch. These specimens were tested under constant load. The V-notch specimen was designed to incur the notch stress concentration equivalent to a typical weld toe in the duplex structure. Due to the one-sided notch, a cross sectional moment is created in the specimen even though loaded axially.

Figure 4 shows the specimens and Figure 5 shows the notch dimensions and the 2-D finite element meshes used to compute the stresses and strains in the specimens. The specimens are 12mm height by 9mm in thickness.

Fig.4. SENT specimens from HISC
Fig.4. SENT specimens from HISC
Fig.5. SENT specimens from HISC
Fig.5. SENT specimens from HISC

The loading frame provides significant flexibility, and for the small deformations leading to HISC cracking, pin-ended boundary conditions were used in the analyses. Using the creep constants derived in HISC, a strain hardening creep law implemented in ABAQUS[7] was used. The stresses across the U-notch and V-notch specimens are shown in Figures 6 and 7. Note that a significant amount of bending is present.

Fig.6. Longitudinal stresses in U-notch specimen @ 80% proof load
Fig.6. Longitudinal stresses in U-notch specimen @ 80% proof load

These figures show the stress distribution immediately after load application, and the stresses after one month worth of creep has occurred. Note that the peak stresses drop significantly due to creep and that due to plasticity and creep, the stress at the notch is not the maximum stress; the maximum longitudinal stress occurs at a small distance into the specimen. Even though there is significant change in the peak stress due to creep, most of the cross section is at stresses less than 60% of the proof stress both immediately after load application and after 1 month worth of creep. Locally the creep strains relax the peak stresses but overall the elastic stress state of over 90% of the cross section will restrain deformation and therefore accumulation of additional creep.

Fig.7. Longitudinal stresses in V-notch specimen @ 80% proof load
Fig.7. Longitudinal stresses in V-notch specimen @ 80% proof load

Table 1 summarizes the computed results. The 0.2% offset yield stress was used as the proof stress, 600 MPa. Four columns are reported for each specimen: 80%, 90%, 100%, and 110% proof load average membrane loading. HISC finite element studies report the elastic SCF, defined as the ratio of the peak stress at the notch to the average membrane stress across the cross section at the notch, to be 6.4 for the V-notch and 3.2 for the U-notch. Figures 6 and 7 attest to the futility in using elastic stress concentration factors in the quantification of HISC; the potential for creep is not reflected in the local stress state at the notch.

The structural stress definition of SCF = σm+bm, ratio of the membrane+bending stresses to the applied nominal membrane stress at the notch cross section, is also reported in Table 1. The average membrane stress is in the plane of the notch, not the nominal remote stresses in the un-notched body of the specimen. These confirm that the SENT specimens are undergoing significant bending: approximately 40% for the V=notch and 50% for the U-notch specimens. The U-notch specimens have more bending due to the larger notch; the applied eccentricity of the loading is higher.

Table 1: Stresses in HISC Specimens

U-notch80% Proof90% Proof100% Proof110% Proof
(MPa)% Proof(MPa)% Proof(MPa)% Proof(MPa)% Proof
Load m 480.122 80.0% 540.288 90.0% 603.32 100.6% 661.028 110.2%
b 276.158 46.0% 308.169 51.4% 334.731 55.8% 358.528 59.8%
m+b 756.28 126.0% 848.457 141.4% 938.051 156.3% 1019.56 169.9%
p 2.51204 0.4% -74.9184 -12.5% -144.919 -24.2% -198.579 -33.1%
  SCF 1.58 1.57 1.55 1.54
Creep m 480.293 80.0% 540.762 90.1% 601.482 100.2% 665.999 111.0%
b 271.498 45.2% 294.2 49.0% 306.393 51.1% 306.202 51.0%
m+b 751.792 125.3% 834.962 139.2% 907.875 151.3% 972.201 162.0%
p -141.719 -23.6% -192.16 -32.0% -226.674 -37.8% -232.687 -38.8%
  SCF 1.57 1.54 1.51 1.46


V-notch80% Proof90% Proof100% Proof110% Proof
(MPa)% Proof(MPa)% Proof(MPa)% Proof(MPa)% Proof
Load m 480.269 80.0% 540.463 90.1% 600.675 100.1% 661.077 110.2%
b 200 33.3% 223.963 37.3% 246.427 41.1% 264.654 44.1%
m+b 680.269 113.4% 764.426 127.4% 847.102 141.2% 925.731 154.3%
p 169.608 28.3% 108.537 18.1% 55.2359 9.2% 23.3327 3.9%
  SCF 1.42 1.41 1.41 1.40
Creep m 480.435 80.1% 540.788 90.1% 599.755 100.0% 665.014 110.8%
b 197.737 33.0% 216.429 36.1% 227.365 37.9% 236.833 39.5%
m+b 678.172 113.0% 757.217 126.2% 827.12 137.9% 901.847 150.3%
p -16.7974 -2.8% -57.496 -9.6% 55.0239 9.2% -91.9798 -15.3%
  SCF 1.41 1.40 1.38 1.36

m: σm, average membrane stress
b: σb, linearized bending stress
m+b: σm+b : σm + σb
p: σp, peak stress such that σm + σb + σp = σnotch

Figure 8 shows the normalized net section stress (again at the notch cross section) as a function of time to HISC failure in hours. Note that the net section average membrane stress limit of 80% is validated, although one V-notch specimen fails at 78% average membrane loading of the proof load.

Fig.8. Normalized net stress vs. time to HISC failure
Fig.8. Normalized net stress vs. time to HISC failure

Figure 9 shows the normalized net section membrane+bending stress (again at the notch cross section) as a function of time to HISC failure in hours. The normalized net section stress is multiplied by 1.4 for the V-notch and 1.5 for the U-notch specimens. This forms the basis for the structural stress limit proposed for HISC assessment. For the membrane+bending stresses, the HISC limit is significantly higher. A membrane+bending stress limit of 100% of the proof load is validated in this plot. Note that the single violation point is that of a smooth specimen (i.e. no bending), and would violate the 80% membrane criteria.

Fig.9. Normalized net membrane+bending stress vs. time to HISC failure
Fig.9. Normalized net membrane+bending stress vs. time to HISC failure

Figure 8 also shows that approximately 10% of proof loading separates the U-notch from the V-notch when comparing the structural stress state in the HISC specimens. This forms the basis for accounting for the notch effects at the weld toes of duplex materials.

Other relevant observations regarding residual stresses and pre-straining:

  1. Residual stresses were introduced into a V-notch specimen through plastic deformation. The resulting specimen showed no difference in HISC resistance than a virgin specimen (HISC2).
  2. Prestraining was found to mitigate HISC, the streses needed to cause HISC increased with the strain-hardening (TWI).
  3. Coarse austenite spacing was found to decrease HISC resistance by approximately 15% (TWI/HISC2).

These results form the basis for:

  1. The 80%σyield limit on the structural membrane stresses.
  2. The 100%σyield limit on the structural membrane+bending stresses.
  3. The use of structural stresses instead of notch stresses for HISC assessment.
  4. A 10% proof load penalty due to notch effects at weld toes.
  5. Local-self-equilibrated residual stresses have little or no effect on HISC resistance.
  6. The material degradation factor to account for austenite spacing, γHISC=0.85.

Foinhaven hub full scale tests

TWI performed full scale testing of the Foinhaven Duplex hubs. These tests proved to be controversial in that a significant penalty was implied to account for residual stresses in the initial strain based HISC assessment. Figure 10 shows the testing arrangement. The duplex material had a coarse grain structure with austenitic spacing measuring 53µm transverse to the grain orientation and 128µm along the grain orientation. The proof loading is reported as 570 MPa. The strain hardening creep model from the HISC2 JIP was modified to give similar creep behavior at the same applied stress-to-yield ratio (Figure 11).

Residual stress measurements showed that the outside was in tension both axially and circumferentially, while the inside of the nib and tube was in compression. Axial residual stresses on the outside surface were in the range of 368-468 MPa on the nib and 112 to 369 MPA on the tube. Axial stresses measured on the inside surface were in the range of -264 to -546 MPa.

Fig.10. Foinhaven hub testing at TWI
Fig.10. Foinhaven hub testing at TWI
Fig.10. Foinhaven hub testing at TWI
Fig.11. Foinhaven hub strain hardening creep model
Fig.11. Foinhaven hub strain hardening creep model

Two full scale tests of the Foinhaven hubs were performed identified as P16 and P15. Cathodic polarization to -1100mV was applied in seawater, with a one week precharging prior to load application. P16 was tested first, and 13 increments of increased step loading were applied to finally fail at critical strain of 0.24%. Bending on the nib and tube was applied through tightening of the nut on the tension bar in Figure 10. Strain was monitored at gage#10 in P16, and gage#1 in P15, and then related to the critical cracking location through calibration loadings and validated through FEA analyses. The critical strain was found to be 2.03 times the gage strain. P15 failed after 2 increments of increased load at a critical strain of 0.22%.

Both failed at similar load levels. Using 20-noded bricks, the hub was modeled as shown in Figure 12. Strain monitoring gage locations and the critical strain location is shown. Proper boundary conditions were applied to correctly apply the tension bolt loading. The multistep loading was simplified to a single step. Three cases were run:

  1. Residual stresses are assumed to be negligible. The bolt tensile loading is applied, and then creep is allowed for one month.
  2. Residual stresses are approximated through shrinkage of 0.003 strain in the weld. The bolt tensile loading is applied, and then creep is allowed for one month.
  3. Upper bound residual stresses are approximated through shrinkage of 0.0045 strain in the weld. The bolt tensile loading is applied, and then creep is allowed for one month.
Fig.12. Foinhaven hub FEA model
Fig.12. Foinhaven hub FEA model

The contour plot in Figure 13 shows the longitudinal stresses at load application for Case 1. In case 1, the residual stresses of the weld is neglected, and only the applied loading via the bolt is applied. Note that the normalized longitudinal stresses approach 0.9 at the critical location on the surface. However, since most of the cross section remains elastic no creep occurs, and the stress state remains the same after 1 month of creep.

Fig.13. Foinhaven hub case 1 longitudinal stresses: no residual stresses
Fig.13. Foinhaven hub case 1 longitudinal stresses: no residual stresses
Fig.13. Foinhaven hub case 1 longitudinal stresses: no residual stresses

The contour plot in Figure 14 shows the longitudinal stresses at the end of the one month worth of creep for Case 2. The blue curve shows the residual stresses due to the 'rubber-band' effect that the weld shrinkage (0.003 strain) has upon cooling. Note that the normalized longitudinal stresses exceed 1.2 at the critical location on the surface once the load is applied. In this case, the residual stress together with the applied stress is sufficient to cause creep near the surface where the hydrogen charging occurs. After 1 month worth of creep, the normalized longitudinal stress drop to 1.0 at the critical location on the surface.

Fig.14. Foinhaven hub case 2 longitudinal stresses: residual stresses due to 0.003 shrinkage
Fig.14. Foinhaven hub case 2 longitudinal stresses: residual stresses due to 0.003 shrinkage
Fig.14. Foinhaven hub case 2 longitudinal stresses: residual stresses due to 0.003 shrinkage

The contour plot in Figure 15 shows the longitudinal stresses at the end of the one month worth of creep for Case 3. The blue curve shows the residual stresses due to the 'rubber-band' effect that the weld shrinkage (0.0045 strain) has upon cooling. Note that the normalized longitudinal stresses approach 1.3 at the critical location on the surface once the load is applied. As in Case 2, the residual stress together with the applied stress is sufficient to cause creep near the surface where the hydrogen charging occurs. After 1 month worth of creep, the normalized longitudinal stress drop to 1.0, identical to Case 2, at the critical location on the surface. The stress distribution for Case 2 and Case 3 are nearly identical after creep has taken place.

Table 2 summarizes the computed results. The 0.2% offset yield stress was used as the proof stress, 570 MPa. The three columns are for each case analyzed. The three rows cover the loading conditions imposed, residual stresses, bending load, and then creep.

The average membrane stress is in the plane of the critical section, shown in Figures 13-15 as the stress path. As expected, the residual stresses are nearly all in through-thickness bending. Case 1 also serves to illustrate the computations that would results for a linear-elastic FEA with out residual stresses. Ideally, a linear-elastic analyses (without the need for creep assessment) would be sufficient for the HISC assessment. Since our focus is on providing a limit to the structural stresses with the objective of limiting creep deformation, the numbers of interest is in column 1 (Case 1) of Table 2. Thus, for Foinhaven full scale tests to be properly reflected in the stress-based criteria, the membrane+bending stresses will have to be limited to 74.3% of the proof loading.

Fig.15. Foinhaven hub case 3 longitudinal stresses: residual stresses due to 0.0045 shrinkage
Fig.15. Foinhaven hub case 3 longitudinal stresses: residual stresses due to 0.0045 shrinkage
Fig.15. Foinhaven hub case 3 longitudinal stresses: residual stresses due to 0.0045 shrinkage

The effect of the weld residual stress is the rubber-band-like squeezing of the tube and nib, causing tension on the outside surface and compression on the inside. This stress decays with distance. A conservative length parameter for curved shell local bending is 2.5√Rt. This residual stress effect is accounted for through a 10% penalty on locations that are within 2.5√Rt of a girth weld.

Table 2: Stresses in Foinhaven FEA

 

 Case 1Case 2Case 3
(MPa)% Proof(MPa)% Proof(MPa)% Proof
Residual m 0 0.0% -4.49568 -0.8% -6.07091 -1.1%
b 0 0.0% 126.986 22.3% 170.041 29.8%
m+b 0 0.0% 122.49 21.5% 163.97 28.8%
p 0 0.0% 44.2328 7.8% 57.6584 10.1%
Load m 186.169 32.7% 181.025 31.8% 177.734 31.2%
b 237.145 41.6% 357.894 62.8% 392.397 68.8%
m+b 423.313 74.3% 538.919 94.5% 570.132 100.0%
p 109.601 19.2% 151.733 26.6% 161.77 28.4%
Creep m 186.083 32.6% 177.221 31.1% 173.02 30.4%
b 236.57 41.5% 335.574 58.9% 354.828 62.3%
m+b 422.653 74.1% 512.795 90.0% 527.848 92.6%
p 101.921 17.9% 58.4945 10.3% 42.4237 7.4%

m: σm, average membrane stress
b: σb, linearized bending stress
m+b: σm+b : σm + σb
p: σp, peak stress such that σm + σb + σp = σnotch

The critical location for the Foinhaven hubs is a stress riser (14mm from weld edge) within 2.5√Rt of a girth weld (R=84.25mm, t=11.25mm, 2.5√Rt=77.0mm). The structural stress state from the linear-elastic FEA would be (Case 1):

  1. σm = 32.7%σyield
  2. σm+b = 74.3%σyield

The stress limits are:

  1. σm <80% γHISCσyield = 68%HISCσyield
  2. σm+b <80% γHISCσyield = 68%HISCσyield

γHISC=0.85 due to the large austenite spacing, and the σm+b <80%σyield is chosen for the stress riser within 2.5√Rt of a girth weld. The stress criteria fits the failure data for the TWI Foinhaven full scale tests.

Summary

The stress criteria focuses on providing limits to the through-wall membrane and membrane+bending stresses to avoid loadings that can impose gross membrane-stretching creep or gross through-wall bending creep. Then a penalty is placed: 1) on the presence of stress risers, and 2) on locations that are in the vicinity of girth welds. In addition a material quality factor is applied that reduces the allowable limits for coarse austenite spacing. Figure 16 summarizes the stress-based criteria.

Fig.16. HISC stress criteria summary
Fig.16. HISC stress criteria summary

References

  1. Stig Wästberg, Morten Solnørdal, Gustav Heiberg, Tikard Törnqvist and Pedro Vargas, Hydrogen Induced Stess Cracking, (HISC) in duplex stainless steels - DNV-RP-F112, Design of duplex stainless steel subsea equipment exposed to cathodic protection, OMAE2009-79655.
  2. DNV recommended practice, DNV-RP-F112, Design of duplex stainless steel subsea equipment exposed to cathodic protection, October 2008.
  3. T. S. Taylor, T. Pendlington, and R. Bird, Foinhaven super duplex BP materials cracking investigation, OTC May 1999.
  4. P. Woollin and A. Gregori, Avoiding hydrogen embrittlement stress cracking of ferritic austenetic stainless steels under cathodic protection, OMAE2004-51203
  5. FEM analyses of notched tension and bend specimens used in the HISC II and the Ormen Lange HISC projects, DNV technical report no. 2006-3259, revision no. 02, January 10, 2007.
  6. Roy Johnsen, Andre Mikkelsen, Bård Nyhus, Stig Wästberg, Hydrogen Induced Stress Cracking of stainless steels final report for HISC2. SINTEF report STFMKF07029, 2007-09-26.
  7. ABAQUS/Standard User's Manual, Volume III, Version 6.4, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI 12860, www.abaqus.com.

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