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
Top Related