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Anisotropic and Pressure-Dependent Plasticity Modeling for Residual Stress Prediction

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Experimental and Applied Mechanics, Volume 4

Abstract

In order to provide well characterized residual stress specimens, 10-mm thick, 60-mm diameter disks of 2024-T351 Aluminum were plastically indented by opposing 15-mm diameter indenters of hardened steel. The residual stresses in the disk specimen were measured using neutron diffraction, the contour method, and the slitting method. A finite element model of the indentation process was constructed, but matching the measured residual stresses proved unexpectedly challenging. An attempt was made to improve the agreement honestly (without any unjustified parameter changes) by improving the constitutive model for 2024. Cyclic stress–strain curves were measured in multiple directions in the source plate of 2024-T351 which showed plastic anisotropy on the order of 15% in the flow strength. Recent literature has also shown a pressure dependence in 2024-T351 which would increase the flow strength in the triaxial stress region under the indenter. Combining anisotropy, cyclic loading, and pressure dependence effects in Abaqus has significantly improved agreement with the data, but a completely accurate prediction remains elusive.

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Acknowledgements

This work was performed at Los Alamos National Laboratory, operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.

Author information

Authors and Affiliations

  1. Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Michael B. Prime

Authors
  1. Michael B. Prime
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Corresponding author

Correspondence to Michael B. Prime .

Editor information

Editors and Affiliations

  1. University of British Columbia, Vancouver, V6T-1Z4, Canada

    Carlos E. Ventura

  2. University of Wisconsin–Madison, Madison, 53706, USA

    Wendy C. Crone

  3. Worcester Polytechnic Institute, Worcester, 01609, USA

    Cosme Furlong

Appendix

Appendix

For reference, the information to reproduce the constitutive behaviour of this paper is given below in two parts: (1) the information for the input file and (2) the user subroutine for the triaxiality user defined field.

49.1.1 Input File Text

*USER DEFINED FIELD

*DEPVAR

1

*INITIAL CONDITIONS, TYPE=FIELD, VARIABLE=1

,0

*Material, name=Al2024_cyclic

*Density

2.7e-09,

*Elastic

73200., 0.33

*Plastic, hardening=isotropic, dependencies=1

80.55, 0.0000e+000, 0.0, -3.000

131.58, 2.5000e-004, 0.0, -3.000

207.90, 5.0000e-004, 0.0, -3.000

252.85, 7.5000e-004, 0.0, -3.000

294.90, 1.0000e-003, 0.0, -3.000

322.78, 1.2500e-003, 0.0, -3.000

341.79, 1.5000e-003, 0.0, -3.000

358.45, 1.7500e-003, 0.0, -3.000

369.07, 2.0000e-003, 0.0, -3.000

377.69, 2.2500e-003, 0.0, -3.000

384.92, 2.5000e-003, 0.0, -3.000

391.61, 2.7500e-003, 0.0, -3.000

397.88, 3.0000e-003, 0.0, -3.000

402.24, 3.2500e-003, 0.0, -3.000

406.36, 3.5000e-003, 0.0, -3.000

410.22, 3.7500e-003, 0.0, -3.000

413.93, 4.0000e-003, 0.0, -3.000

416.46, 4.2500e-003, 0.0, -3.000

419.62, 4.5000e-003, 0.0, -3.000

422.66, 4.7500e-003, 0.0, -3.000

425.34, 5.0000e-003, 0.0, -3.000

427.84, 5.2500e-003, 0.0, -3.000

429.73, 5.5000e-003, 0.0, -3.000

432.32, 5.7500e-003, 0.0, -3.000

434.48, 6.0000e-003, 0.0, -3.000

436.50, 6.2500e-003, 0.0, -3.000

438.19, 6.5000e-003, 0.0, -3.000

440.25, 6.7500e-003, 0.0, -3.000

442.01, 7.0000e-003, 0.0, -3.000

443.77, 7.2500e-003, 0.0, -3.000

445.70, 7.5000e-003, 0.0, -3.000

447.06, 7.7500e-003, 0.0, -3.000

448.54, 8.0000e-003, 0.0, -3.000

450.01, 8.2500e-003, 0.0, -3.000

451.31, 8.5000e-003, 0.0, -3.000

452.60, 8.7500e-003, 0.0, -3.000

454.08, 9.0000e-003, 0.0, -3.000

455.52, 9.2500e-003, 0.0, -3.000

457.04, 9.5000e-003, 0.0, -3.000

458.35, 9.7500e-003, 0.0, -3.000

459.51, 1.0000e-002, 0.0, -3.000

461.23, 1.0375e-002, 0.0, -3.000

463.95, 1.0938e-002, 0.0, -3.000

467.77, 1.1781e-002, 0.0, -3.000

492.94, 1.3047e-002, 0.0, -3.000

480.53, 1.4945e-002, 0.0, -3.000

490.26, 1.7793e-002, 0.0, -3.000

503.44, 2.2064e-002, 0.0, -3.000

520.75, 2.8472e-002, 0.0, -3.000

542.84, 3.8083e-002, 0.0, -3.000

562.77, 4.8083e-002, 0.0, -3.000

580.89, 5.8083e-002, 0.0, -3.000

597.08, 6.8083e-002, 0.0, -3.000

611.45, 7.8083e-002, 0.0, -3.000

624.45, 8.8083e-002, 0.0, -3.000

636.16, 9.8083e-002, 0.0, -3.000

646.78, 1.0808e-001, 0.0, -3.000

656.68, 1.1808e-001, 0.0, -3.000

665.60, 1.2808e-001, 0.0, -3.000

673.75, 1.3808e-001, 0.0, -3.000

681.30, 1.4808e-001, 0.0, -3.000

688.23, 1.5808e-001, 0.0, -3.000

694.57, 1.6808e-001, 0.0, -3.000

700.46, 1.7808e-001, 0.0, -3.000

705.87, 1.8808e-001, 0.0, -3.000

710.90, 1.9808e-001, 0.0, -3.000

715.59, 2.0808e-001, 0.0, -3.000

51.32, 0.0000e+000, 0.0, 2.000

83.83, 2.5000e-004, 0.0, 2.000

132.45, 5.0000e-004, 0.0, 2.000

161.09, 7.5000e-004, 0.0, 2.000

187.88, 1.0000e-003, 0.0, 2.000

205.64, 1.2500e-003, 0.0, 2.000

217.75, 1.5000e-003, 0.0, 2.000

228.37, 1.7500e-003, 0.0, 2.000

235.14, 2.0000e-003, 0.0, 2.000

240.62, 2.2500e-003, 0.0, 2.000

245.23, 2.5000e-003, 0.0, 2.000

249.50, 2.7500e-003, 0.0, 2.000

253.49, 3.0000e-003, 0.0, 2.000

256.26, 3.2500e-003, 0.0, 2.000

258.89, 3.5000e-003, 0.0, 2.000

261.35, 3.7500e-003, 0.0, 2.000

263.71, 4.0000e-003, 0.0, 2.000

265.33, 4.2500e-003, 0.0, 2.000

267.34, 4.5000e-003, 0.0, 2.000

269.28, 4.7500e-003, 0.0, 2.000

270.99, 5.0000e-003, 0.0, 2.000

272.57, 5.2500e-003, 0.0, 2.000

273.78, 5.5000e-003, 0.0, 2.000

275.43, 5.7500e-003, 0.0, 2.000

276.80, 6.0000e-003, 0.0, 2.000

278.09, 6.2500e-003, 0.0, 2.000

279.17, 6.5000e-003, 0.0, 2.000

280.48, 6.7500e-003, 0.0, 2.000

281.60, 7.0000e-003, 0.0, 2.000

282.72, 7.2500e-003, 0.0, 2.000

283.95, 7.5000e-003, 0.0, 2.000

284.82, 7.7500e-003, 0.0, 2.000

285.77, 8.0000e-003, 0.0, 2.000

286.70, 8.2500e-003, 0.0, 2.000

287.53, 8.5000e-003, 0.0, 2.000

288.35, 8.7500e-003, 0.0, 2.000

289.29, 9.0000e-003, 0.0, 2.000

290.21, 9.2500e-003, 0.0, 2.000

291.18, 9.5000e-003, 0.0, 2.000

292.01, 9.7500e-003, 0.0, 2.000

292.75, 1.0000e-002, 0.0, 2.000

293.85, 1.0375e-002, 0.0, 2.000

295.58, 1.0938e-002, 0.0, 2.000

298.02, 1.1781e-002, 0.0, 2.000

301.31, 1.3047e-002, 0.0, 2.000

306.15, 1.4945e-002, 0.0, 2.000

312.34, 1.7793e-002, 0.0, 2.000

320.74, 2.2064e-002, 0.0, 2.000

331.77, 2.8472e-002, 0.0, 2.000

345.84, 3.8083e-002, 0.0, 2.000

358.54, 4.8083e-002, 0.0, 2.000

370.08, 5.8083e-002, 0.0, 2.000

380.40, 6.8083e-002, 0.0, 2.000

389.55, 7.8083e-002, 0.0, 2.000

397.83, 8.8083e-002, 0.0, 2.000

405.30, 9.8083e-002, 0.0, 2.000

412.06, 1.0808e-001, 0.0, 2.000

418.37, 1.1808e-001, 0.0, 2.000

424.05, 1.2808e-001, 0.0, 2.000

429.24, 1.3808e-001, 0.0, 2.000

434.05, 1.4808e-001, 0.0, 2.000

438.47, 1.5808e-001, 0.0, 2.000

442.51, 1.6808e-001, 0.0, 2.000

446.26, 1.7808e-001, 0.0, 2.000

449.71, 1.8808e-001, 0.0, 2.000

452.91, 1.9808e-001, 0.0, 2.000

455.90, 2.0808e-001, 0.0, 2.000

**

*Potential

1.162, 1.162, 1., 1.2364, 1.1, 1.1

**

49.1.2 User Subroutine to Give Triaxiality as User Defined Field

SUBROUTINE USDFLD(FIELD,STATEV,PNEWDT,DIRECT,T,CELENT,

1 TIME,DTIME,CMNAME,ORNAME,NFIELD,NSTATV,NOEL,NPT,LAYER,

2 KSPT,KSTEP,KINC,NDI,NSHR,COORD,JMAC,JMATYP,MATLAYO,

3 LACCFLA)

C

INCLUDE 'ABA_PARAM.INC'

C

CHARACTER*80 CMNAME,ORNAME

CHARACTER*3 FLGRAY(15)

DIMENSION FIELD(NFIELD),STATEV(NSTATV),DIRECT(3,3),

1 T(3,3),TIME(2)

DIMENSION ARRAY(15),JARRAY(15),JMAC(*),JMATYP(*),

1 COORD(*)

C

C Cet Pressure from stress invariants output

CALL GETVRM('SINV',ARRAY,JARRAY,FLGRAY,JRCD,JMAC,JMATYP,MATLAYO,LACCFLA)

PRESS = ARRAY(3)

SMISES = ARRAY(1)

C Calculate triaxiality

IF (SMISES.ne. 0) THEN

TRIAX = -PRESS / SMISES

ELSE

TRIAX = 0

END IF

FIELD(1) = TRIAX

STATEV(1) = FIELD(1)

C If error, write comment to.DAT file:

IF(JRCD.NE.0)THEN

WRITE(6,*) 'REQUEST ERROR IN USDFLD FOR ELEMENT NUMBER ',

1 NOEL,'INTEGRATION POINT NUMBER ',NPT

ENDIF

C

RETURN

END

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Prime, M.B. (2013). Anisotropic and Pressure-Dependent Plasticity Modeling for Residual Stress Prediction. In: Ventura, C., Crone, W., Furlong, C. (eds) Experimental and Applied Mechanics, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4226-4_49

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  • DOI: https://doi.org/10.1007/978-1-4614-4226-4_49

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-4225-7

  • Online ISBN: 978-1-4614-4226-4

  • eBook Packages: EngineeringEngineering (R0)

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