Back calculation method COMPRESSED - WEB.pdf

MTS3000: Automatic system for determining residual stresses by the strain-gage method

SINT Technology srl Via Giusti, 229 50041 Calenzano (Florence) – ItalyTel: +39.055.8826-302 – Fax: -303Web: www.sintechnology.come-mail: [email protected]

RESIDUAL STRESS CALCULATION USING MTS3000 – RESTAN

Automatic system for determining residual stresses by the strain-gage method

Development of MTS3000 – RESTAN system

Calculation method

The main calculation method for hole drilling measurementsimplemented in SINT EVAL software vers. 5 are:

ANALYSIS METHODS

UNIFORM STRESSES OVER THE DEPTH

NOT UNIFORM STRESSES OVER THE

DRILLING DEPTH

• ASTM E837-08

• ASTM E837-08

• Integral Method

• Kockelmann method

• ASTM E837-08 for uniform stress field

• ASTM E837-08 for not uniform stress field

• Integral method

• Schwarz-Kochelmann method.


Measurement of the strains

The first operation to carry out for obtaining agood calculation of residual stress is the correctacquisition of the strains.

MTS3000 system allows to automatically configurethe measurement chain using all the HBM rosettesand using the HBM strain gage amplifiers Spider8.30 and MGCPlus.

SINT Eval software allows torealize an optimized polinomialinterpolation of the input strains.

Hole drilling strain gage method to ASTM E837-08


The hole-drilling strain-gage method is the only method for calculating residualstress that is STANDARDIZED at world level (standard ASTM E837-08).

The first version of this standard dates back to 1995.

Standard ASTM E837-08 specifies:

• the number of drilling increments required

• the numerical coefficients for determining the value of residual stresses

• the data processing method

• the measurement-related uncertainty.



THROUGH HOLE

• Workpiece thickness < 0.4·DGAGE (std. 2.0 mm)

INTERMEDIATE HOLE

• Workpiece thickness between 0.4·DGAGE

e 1.2·DGAGE (std. between 2.0 mm and 6.1 mm)

THROUGH HOLE INTERMEDIATE HOLE

• Drilling depth: entire thicknessof the specimen

• Stresses are assumed uniformover the drilling depth

• Acquisition of a set of threestrains once the through holeis completed.

• Drilling depth: 2 mm

• Uniform stress value over 2mm of thickness

• 8 drilling steps of 0.05 · DGAGE

(standard 0.25 mm)

• Approximate results.

STRESSES ARE CONSIDERED UNIFORM OVER THE DRILLING DEPTH



UNIFORMITY TEST

• Stresses are considered uniform over thedrilling depth provided strains do not deviatefrom the curves provided by ± 3%.

BLIND HOLE

• Workpiece thickness > 1.2·DGAGE (std. 6.1 mm)

UNIFORM STRESSES

NOT UNIFORM STRESSES


• Uniform stress value over 2mm of thickness

• 8 drilling steps of 0.05 · DGAGE

(standard 0.25 mm).


• Residual stress pattern in 1 mmof depth

• 40 drilling steps of 0.05 mm

• Evolution of the Integralmethod.


Calculation of a, b coefficients for HBM rosettes

SINT Technology has realized the calculation of a, b coefficients for all the typesof HBM rosettes.

The standard ASTM E837-08 tales into account hole drilling rosettes with differentsizes (like average grid radius, length and height).

Using the EVAL software,you can automaticallydetect the strain gagerosettes that you areusing and perform acorrect back-calculationof residual stress.

1-RY61-1.5/120S - Coefficient a 1-RY61-1.5/120S - Coefficient b


Integral method

Integral method for residual stress analysis wasproposed by G. S. Schajer in 1988 in order toovercome the limits of ASTM standard regardingthe constant stress field.

The system’s software allows you to select numberand distribution of the depth increments, while inthe Non-Uniform Stress Method these parametersare fixed by the ASTM standard.

The maximum calculation depth is 0.5 times themean radius of the strain rosettes used for thetest.

The integral method should be chosen when residualstresses are expected to vary significantly with depth;however, it also has the highest sensitivity to testerrors.


Integral method

Point 1

Point 2

Axial direction

Tangential direction

15 mm

40 mm

Integral method: computation of non-uniform stress

Depth σMIN σMAX β σx (AXIAL) σy (TANGENTIAL) τxy σVonMises

[mm] [MPa] [MPa] [°] [MPa] [MPa] [MPa] [MPa]

0.005 -130.5 21.6 74.2 -14.7 -94.2 -74.0 142.6

0.015 -471.0 -138.5 68.0 -189.4 -420.1 -166.2 419.3

0.025 -699.3 -283.4 63.5 -325.2 -657.5 -205.9 609.2

0.035 -877.1 -396.4 61.1 -433.4 -840.1 -234.4 760.8

0.045 -1011.4 -484.3 59.7 -518.2 -977.4 -253.9 876.1

0.055 -1109.2 -551.8 58.8 -583.4 -1077.5 -265.9 960.6

0.065 -1176.8 -602.6 58.1 -632.2 -1147.2 -271.9 1019.3

0.075 -1219.7 -639.6 57.6 -667.3 -1192.0 -272.9 1056.7

0.085 -1242.0 -665.2 57.2 -690.9 -1216.3 -269.9 1076.5

0.095 -1247.6 -681.4 56.8 -705.0 -1223.9 -263.6 1082.0

0.105 -1239.3 -689.7 56.4 -711.2 -1217.8 -254.5 1075.6

0.115 -1219.6 -691.4 56.0 -710.7 -1200.4 -243.2 1059.4

0.125 -1190.5 -687.7 55.6 -704.6 -1173.5 -230.0 1035.1

0.135 -1153.4 -679.2 55.1 -693.8 -1138.9 -215.2 1004.1

0.145 -1109.8 -666.7 54.5 -678.9 -1097.6 -199.2 967.6

0.155 -1060.5 -650.7 53.9 -660.5 -1050.7 -182.3 926.3

0.165 -1006.6 -631.4 53.1 -639.0 -999.1 -164.5 881.1

0.175 -948.8 -609.2 52.2 -614.6 -943.4 -146.3 832.7

0.185 -887.8 -584.3 51.1 -587.8 -884.3 -127.7 781.6

0.195 -824.2 -556.8 49.8 -558.7 -822.3 -108.9 728.3

0.205 -758.6 -526.8 48.1 -527.4 -757.9 -90.2 673.3

0.215 -691.7 -494.2 45.8 -494.2 -691.6 -71.8 617.1

0.225 -624.2 -459.0 42.8 -459.2 -623.9 -53.7 560.2

0.235 -557.0 -420.8 38.6 -422.5 -555.3 -36.2 502.9

0.245 -491.3 -379.2 32.6 -384.4 -486.2 -19.4 446.0

0.263 -426.2 -336.6 16.3 -357.3 -405.6 9.6 389.2

0.287 -371.3 -273.4 5.1 -313.7 -331.0 27.9 333.3

0.312 -263.7 -139.6 -6.7 -216.0 -187.3 52.8 228.5

0.338 -157.1 -8.8 -11.3 -111.4 -54.5 68.5 152.9

0.362 -52.1 107.2 -12.1 -5.1 60.2 74.5 140.7

0.388 24.3 170.1 -7.8 77.7 116.8 63.5 159.4

0.412 106.5 252.4 -2.4 173.3 185.5 55.7 219.4

0.437 176.8 320.9 6.5 265.0 232.7 38.3 278.4

0.463 221.1 379.2 16.9 344.1 256.3 15.4 329.9

0.487 238.6 429.1 25.7 408.3 259.5 -10.5 372.4

0.525 213.5 480.2 34.6 471.4 222.2 -54.5 416.7

0.575 227.2 571.6 39.5 568.4 230.4 -96.2 498.5

0.625 223.5 599.7 43.0 599.2 224.0 -123.2 524.9

0.675 288.2 677.5 45.8 677.4 288.2 -141.3 588.9

0.725 347.5 725.4 47.7 724.6 348.4 -145.7 628.4

0.775 338.3 719.0 48.3 717.8 339.5 -149.0 623.1

0.825 321.4 749.2 47.6 748.3 322.2 -164.1 651.0

0.875 247.7 744.3 46.3 744.1 247.9 -183.4 656.5

0.925 205.0 816.7 46.1 816.4 205.2 -224.5 735.9

0.975 207.7 951.9 46.0 951.7 207.9 -272.1 866.9

Head of residual stresses area Test Owner

Ing. Alessio Benincasa Ing. Lorenzo Bertelli

-1300.0

-900.0

-500.0

-100.0

300.0

700.0

1100.0

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Re

sid

ual

str

ess

es

[MP

a]

Depth [mm] σMIN σMAX σVonMises

-1300.0

-900.0

-500.0

-100.0

300.0

700.0

1100.0

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Re

sid

ual

str

ess

es

[MP

a]

Depth [mm] σx (AXIAL) σy (TANGENTIAL) τxy

Integral method: computation of non-uniform stress

Depth σMIN σMAX β σx (AXIAL) σy (TANGENTIAL) τxy σVonMises

[mm] [MPa] [MPa] [°] [MPa] [MPa] [MPa] [MPa]

0.005 -287.7 -142.7 -57.2 -281.2 -149.2 25.4 249.1

0.015 -597.7 -378.0 -73.8 -546.7 -429.0 -24.0 523.7

0.025 -786.2 -497.9 -81.1 -686.2 -597.9 -65.8 688.9

0.035 -931.7 -587.0 -84.7 -790.9 -727.7 -97.5 815.9

0.045 -1040.6 -653.9 -86.9 -868.1 -826.4 -121.2 911.0

0.055 -1120.0 -703.8 -88.4 -923.3 -900.5 -138.9 980.6

0.065 -1176.1 -740.1 -89.6 -961.1 -955.2 -152.1 1029.9

0.075 -1213.9 -765.5 89.4 -984.8 -994.5 -162.0 1063.2

0.085 -1237.2 -781.8 88.5 -997.2 -1021.8 -169.5 1083.8

0.095 -1249.0 -790.4 87.6 -1000.2 -1039.2 -175.3 1094.3

0.105 -1251.5 -792.5 86.7 -995.3 -1048.7 -180.0 1096.6

0.115 -1246.3 -788.8 85.8 -983.8 -1051.3 -183.9 1092.0

0.125 -1234.7 -779.8 84.8 -966.4 -1048.0 -187.1 1081.5

0.135 -1217.2 -765.9 83.9 -943.8 -1039.3 -189.7 1065.8

0.145 -1194.5 -747.6 83.0 -916.6 -1025.5 -191.7 1045.3

0.155 -1166.8 -725.0 82.0 -885.1 -1006.7 -193.1 1020.4

0.165 -1134.4 -698.5 81.1 -849.8 -983.1 -193.8 991.1

0.175 -1097.3 -668.4 80.2 -811.0 -954.7 -193.7 957.8

0.185 -1055.6 -634.8 79.4 -768.9 -921.5 -192.6 920.4

0.195 -1009.4 -598.1 78.6 -724.0 -883.5 -190.4 879.2

0.205 -958.9 -558.7 77.9 -676.6 -841.0 -187.1 834.2

0.215 -904.2 -516.8 77.2 -626.9 -794.1 -182.6 785.7

0.225 -845.5 -472.9 76.6 -575.4 -743.0 -176.9 734.0

0.235 -783.2 -427.2 76.2 -522.5 -688.0 -170.0 679.2

0.245 -717.7 -380.2 75.8 -468.4 -629.5 -161.8 621.9

0.263 -662.5 -348.7 75.6 -430.1 -581.0 -150.6 574.0

0.287 -573.7 -292.2 76.5 -369.1 -496.9 -133.9 496.9

0.312 -404.0 -182.9 77.9 -247.9 -338.9 -103.4 350.4

0.338 -231.0 -71.8 81.0 -126.8 -176.0 -70.9 204.8

0.362 -66.6 37.3 87.7 -10.5 -18.9 -39.6 91.2

0.388 39.1 117.1 -77.3 61.4 94.9 -13.1 103.3

0.412 149.0 214.8 -66.3 157.7 206.1 1.3 190.6

0.437 247.0 309.4 -52.6 248.1 308.3 15.6 283.4

0.463 324.9 385.7 -42.5 325.0 385.6 23.3 359.2

0.487 384.6 440.3 -34.1 386.6 438.3 25.6 415.3

0.525 431.2 468.4 -26.2 435.1 464.6 18.5 451.0

0.575 516.6 546.8 -12.5 525.3 538.1 14.2 532.3

0.625 543.1 558.6 -45.4 543.1 558.6 5.4 551.0

0.675 610.7 675.0 -74.5 626.4 659.4 -7.8 645.3

0.725 661.8 811.8 -85.8 725.8 747.8 -44.7 748.2

0.775 657.6 911.0 86.6 799.4 769.2 -99.6 814.4

0.825 674.0 999.6 81.5 884.5 789.1 -143.8 883.0

0.875 555.1 842.0 79.9 748.1 649.1 -130.2 741.4

0.925 360.4 538.9 84.8 465.9 433.4 -73.6 475.5

0.975 165.7 273.4 88.9 221.6 217.5 -39.5 238.6

Head of residual stresses area Test Owner

Ing. Alessio Benincasa Ing. Lorenzo Bertelli

-1300.0

-900.0

-500.0

-100.0

300.0

700.0

1100.0

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Re

sid

ual

str

ess

es

[MP

a]

Depth [mm] σMIN σMAX σVonMises

-1300.0

-900.0

-500.0

-100.0

300.0

700.0

1100.0

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Re

sid

ual

str

ess

es

[MP

a]

Depth [mm] σx (AXIAL) σy (TANGENTIAL) τxy


Tikhonov regularization

SINT EVAL software allows to use the Tikhonov regularization of calculatedresidual stresses for ASTM E837-08 (not uniform) and for the integral method.

The regularization can be useful to reduce the influence of the input data errorsin the calculation.

290.0

295.0

300.0

305.0

310.0

315.0

320.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Stre

ss [M

Pa]

Depth [mm]

Benchmark integral method - ASTM E837-08 for not uniform stress filed

Integral method with Tikhonov regolaritation

Integral method

True stress

ASTM E837-08

ASTM E837-08 with Tickonov


Schwarz-Kockelmann method

This method, proposed by H. Kockelmann in 1993 is based on the strain ratiomeasured during the hole drilling.

Schwartz – Kochelmann calculation method is centered on theexperimental/numerical evaluation of calibration functions Kx and Ky.

This method uses the numerical coefficients calculated by Kockelmann and allowsyou to reach a calculation depth equal to the hole diameter. It is a method whichhas little sensitivity to the effects of test errors but it is valid only in a veryparticular case of rosette diameter and hole diameter (dm/d0 = 3).

Recently, also coefficients for different values of D/D0 have been provided andincluded in the SINT EVAL software.

MTS3000: Automatic system for determining residual stresses by the strain-gage method

SINT Technology srl Via Giusti, 229 50041 Calenzano (Florence) – ItalyTel: +39.055.8826-302 – Fax: -303Web: www.sintechnology.come-mail: [email protected]

RESIDUAL STRESS CALCULATION USING MTS3000 – RESTAN

Automatic system for determining residual stresses by the strain-gage method

Back calculation method COMPRESSED - WEB.pdf

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