Residual stress influence on material properties and column behaviour of stainless steel SHS

Michal Jandera

Josef Macháček

Czech Technical University in Prague

residual stresses:

– austenitic steel grade 1.4301

– cold-rolled SHS

– previous residual stress measurement

– numerical study:

– FE model

– influence of residual stresses on column behaviour including different degree of non-linearity

– Analytical model

– residual stress influence on material behaviour

introduction column behaviour material behaviour conclusions

residual stresses:

– X-ray diffraction method for through thickness stress pattern

– rectangular block-like distribution of bending residual stresses

– sectioning method for residual stress pattern along sections membrane component

introduction column behaviour material behaviour conclusions

longitudinal bending component

σm = (-0,253+1,483(x-x2)) σ0.2 σb.pl = (0,833+1,866(x-x2)) σ0.2

σb.pl.t = -0,376 σ0.2

column behaviour:

FE model in software Abaqus validated on experiments

1. parametric study of influence of residual stresses based on tested section SHS 120x120x4

– measured material properties for flat and corner area

– influence of residual stresses on global and local buckling separately

2. parametric study for material described by Ramberg-Osgood formula with varying hardening exponent n

introduction column behaviour material behaviour conclusions

parametric study:

residual stresses introduced in five steps

– Membrane: longitudinal membrane stresses only

– Longitudinal: longitudinal membrane and bending stresses

– Max. longitudinal: longitudinal membrane and bending stresses (by the upper

bound of the 95% predictive interval)

– All: longitudinal membrane and bending as well as transverse bending stresses

– Max. all: longitudinal membrane and bending stresses as well as transverse

bending stresses, the longitudinal bending residual stresses (by the upper bound of the 95% predictive interval)

introduction column behaviour material behaviour conclusions

parametric study: based on measured material properties - global stability

-24%

-16%

-8%

0%

8%

16%

0.4 0.8 1.2 1.6 2 2.4

influence o

f re

sid

ual str

esses o

n

the

load

capcity [

%]

non-dimensional column slenderness λ [-]

all max. all longitudinal max. longitudinal membrane

positive influence of residual stresses (up to 10 %) for middle slenderness

negative influence (up to -16 %) for very slender columns

membrane residual stresses not significant

introduction column behaviour material behaviour conclusions

parametric study: based on measured material properties - local stability

-3%

0%

3%

6%

9%

12%

0.40 0.80 1.20 1.60 2.00 2.40

influence o

f re

sid

ual str

esses o

n

the

load

capcity [

%]

plate slenderness λp [-]

all max. all longitudinal max. longitudinal membrane

introduction column behaviour material behaviour conclusions

always positive influence of residual stresses (up to 9 %)

parametric study: influence of bending residual stresses on the stress-strain diagram

introduction column behaviour material behaviour conclusions

change of the material non-linearity due to the presence of bending residual stress

tangential modulus of elasticity increased for some region

parametric study: local buckling – the collapse strain

0

125

250

375

500

0.00% 0.05% 0.10% 0.15% 0.20%

load [kN

]

strain [%]

0.94 1.05 1.28 1.40

1.63 1.86 2.32

non-dimensional slenderness λ:

0

250

500

750

1000

0.00% 0.15% 0.30% 0.45% 0.60%lo

ad [kN

]

strain [%]

0.75 1.00 1.12 1.24

1.37 1.49 1.73

plate slenderness λp:

introduction column behaviour material behaviour conclusions

global buckling local buckling

parametric study: based on Ramberg-Osgood formula - four different diagrams

n = 4, n = 6, n = 16, bilinear

0

75

150

225

300

0 0.001 0.002 0.003 0.004 0.005

str

ess [M

Pa]

strain [-]

n=4 n=6 n=16 bilinear

introduction column behaviour material behaviour conclusions

parametric study: global stability, varying Ramberg-Osgood parameter

non-dimensional column slenderness 1.0

-30%

-20%

-10%

0%

10%

20%

4 8 16 32 64

influence o

f re

sid

ual str

esses o

n

the load c

apacity o

f colu

mns [%

]

Ramberg-Ogood nonlinearity parameter n [-]

all max. all longitudinal max. longitudinal membrane

introduction column behaviour material behaviour conclusions

parametric study: local buckling, varying Ramberg-Osgood parameter

non-dimensional plate slenderness 1.0

-20%

-10%

0%

10%

20%

30%

4 8 16 32 64

influence o

f re

sid

ual str

esses o

n the

lo

ad c

apacity o

f stu

b c

olu

mns [%

]

Ramberg-Osgood strain hardening parameter n [-]

all max. all longitudinal max. longitudinal membrane

introduction column behaviour material behaviour conclusions

material behaviour:

analytical model of tensile coupon test

– calibrated on tests of coupons taken form web centre of SHS 100x100x3 and SHS 120x120x4 / as delivered and stress relieved (annealed) material tested

– measured longitudinal bending stress included for SHS 100x100x3: σb.pl = 0.354 * σ0.2 = 0.354 * 416.5= 147.4 MPa for SHS 120x120x4: σb.pl = 0.380 * σ0.2 = 0.380 * 429.0 = 163.0 MPa

introduction column behaviour material behaviour conclusions

Specimen E0 u n n0.2,1.0

[GPa] [MPa] [MPa] [MPa] [-] [-]

100×100×3-F 205.8 417 457 753 7.1 2.3

100×100×3-FA* 211.5 429 456 753 13.4 1.5

120×120×4-F 192.0 429 479 783 4.3 2.7

120×120×4-FA* 205.5 405 441 762 8.1 2.1 * Stress relieved specimen

analytical model:

analytical model of tensile coupon test

presence of residual stress:

– increase in non-linearity

– slight decrease in the initial modulus of elasticity

introduction column behaviour material behaviour conclusions

conclusions:

– membrane residual stresses may be generally neglected

– bending residual stresses have a significant influence on material nonlinearity (resp. tangential modulus)

– for cold-worked stainless steels the influence of residual stresses on the load capacity ranges: +10 to -16 % for elements subjected to global buckling up to +9 % for elements subjected to local buckling

– in material behaviour approximated by bilinear stress-strain diagram the same residual stress pattern has a negative influence on the load capacity

– bending residual stress may be considered by increased non-linearity

introduction column behaviour material behaviour conclusions

Michal Jandera

Josef Macháček

Czech Technical University in Prague

Residual stress influence on material properties and column behaviour of stainless steel SHS