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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References
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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.
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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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Online ISBN: 978-1-4614-4226-4
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