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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