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A Deformation History-Based Approach for Ultra-Low Cycle Fatigue Damage Evaluation of Steel Structures

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Abstract

Ultra-low cycle fatigue (ULCF) damage is one of the main failure modes of steel structures when subjected to intense earthquake action, such as near-field action. However, existing ULCF evaluation methods are based on the plastic strain history of structures, which requires fine numerical simulation and causes high calculation cost. In order to improve and simplify the ULCF evaluation process for steel structures, a new damage index based on the structure deformation history was proposed in this paper, with the application of structure life curve and Miner’s rule. Two types of steel components, notched round steel bar and steel pier, were employed as the research objectives to verify the accuracy of proposed damage index. The predicted ULCF life was compared with the results of tests and finite element simulations, which showed that the application of damage index was of acceptable accuracy. Compared with the traditional plastic strain history-based ULCF evaluation methods, the advantage of proposed damage index is that ULCF life of a given steel structure can be determined quickly according to the loading condition once its life curve is realized, thus eliminating the cumbersome numerical simulation process.

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Abbreviations

ULCF:

Ultra-low cycle fatigue

SHS:

Square hollow section

LCF:

Low cycle fatigue

CDM:

Continuous damage mechanics

CVGM:

Cyclic void growth model

FE:

Finite element

F:

The group code of round bar specimens used to establish the life curve

V:

The group code of round bar specimens used to verify the accuracy of proposed index D

PTF:

Loading mode: pull to failure

CA:

Constant amplitude cyclic loading

C1:

One-cycle cyclic loading with a stable increment per cycle

C3:

Three-cycle cyclic loading with a stable increment per three cycles

C-PTF:

Loading mode: cycle and pull to failure

S4R:

4-Node reduced integration shell element

B31:

Linear interpolation, three-dimensional beam element

C3D8R:

Three dimensional, 8-node reduced integration solid element

ε pD :

The damage strain threshold in pure tension for Tateishi model

Δεp :

Plastic strain range

N fL :

LCF initiation life (unit: cycle)

Cp, kp :

Two constants related to Coffin–Manson’s relationship

Δε :

Strain range

Δεe :

Elastic strain range

l*:

Material characteristic length (unit: m)

Δδ :

Deformation range of steel structure (unit: mm)

N f :

ULCF life (unit: cycle)

Cδ, k :

Two constants related to Eq. (2)

N hf :

Half of Nf (unit: half cycle)

k1, k2 :

Two constants related to life curve

D i :

The cumulative damage of structures at ith load cycle

N hf,i :

The ULCF life of steel structure under constant amplitude cyclic loading with the imposed deformation Δδ at ith cycle

D :

The proposed damage index

Δδi :

The deformation range at the ith cycle (unit: mm)

n :

The total number of the load cycle (unit: half cycle)

E :

Elastic modulus (unit: MPa)

σ y :

Yield strength (unit: MPa)

σ u :

Ultimate strength (unit: MPa)

A l :

Elongation ratio (unit: %)

N hc :

The number of half cycles (unit: half cycle)

ε :

The strain of extensometer

R 2 :

Correlation coefficient

N hfe :

The ULCF life obtained by tests (unit: half cycle)

N hfp :

The ULCF life predicted by proposed method (unit: half cycle)

N hfC :

The ULCF life predicted by CVGM (unit: half cycle)

δ e :

The fractured deformation obtained by tests (unit: mm)

δ p :

The fractured deformation predicted by proposed method (unit: mm)

δ C :

The fractured deformation predicted by CVGM (unit: mm)

VGI cyclic :

The void growth index

\(VGI_{\text{cyclic}}^{\text{critical}}\) :

The critical void growth index

ε 1 :

The equivalent plastic strain at the beginning of each tension or compression cycle

ε 2 :

The equivalent plastic strain at the end of each tension or compression cycle

T :

The stress triaxiality

σ m :

The hydrostatic pressure (unit: MPa)

σ eq :

The Mises stress (unit: MPa)

dεp :

The equivalent plastic strain increment

η :

The toughness parameter of materials

\(\varepsilon_{\text{p}}^{\text{critical}}\) :

The fracture strain

λ :

The degradation parameter of materials

\(\varepsilon_{\text{p}}^{\text{accumulated}}\) :

The cumulative equivalent plastic strain at the beginning of each tension cycle

f :

The material damage ratio

λ B :

The slenderness ratio

R R :

The width-to-thickness ratio

h :

The height of piers (unit: mm)

r :

The radius of gyration (unit: mm)

B :

The width of the compression flange (unit: mm)

t :

The thickness of flange and web (unit: mm)

ν :

The Poisson’s ratio

n r :

The number of regions divided by stiffeners in a flange or web

W :

The width of the web (unit: mm)

P/Py :

The axial compression ratio

a :

The spacing of transverse partitions (unit: mm)

γ/γ*:

The relative stiffness of longitudinal stiffeners

t s :

The thickness of vertical stiffener (unit: mm)

b s :

The width of vertical stiffener (unit: mm)

δ :

The imposed deformation (unit: mm)

P :

The axial force applied on the top of piers (unit: N)

L d :

The length of effective damage zone (unit: mm)

α :

The ratio of a to B

h f :

The fillet size (unit: mm)

σ|0 :

Initial yield stress

Q ∞ :

The maximum value of yield surface

b :

The change ratio of yield surface with increasing plastic strain

C1, C2, C3 :

Three initial values of kinematic hardening modulus

γ1, γ2, γ3 :

Three reduction ratios of kinematic hardening modulus with increasing plastic strain

δ y :

The yield displacement (unit: mm)

δ y1 :

The bending yield displacement (unit: mm)

δ y2 :

The shear yield displacement (unit: mm)

H y :

The yield lateral load (unit: N)

I :

The moment of inertia (unit: mm4)

κ :

The shear unevenness coefficient of cross section

G :

The shear modulus (unit: MPa)

A S :

The sectional area (unit: mm2)

M y :

The yield bending moment (unit: N·mm)

P E :

The Euler’s buckling axial load (unit: N)

P u :

The ultimate axial strength (unit: N)

P y :

The yield axial force (unit: N)

δ yI :

The yield displacement of steel pier No. S20-30P15

δ yII :

The yield displacement of steel pier No. S20-40P15

δ yIII :

The yield displacement of steel pier No. S30-30P15

A, C :

Two constants in life curve of steel piers

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Acknowledgements

The study described in this paper was supported by the grant from the Natural Science Foundation of China (51878606). Besides, further appreciation is given to Dassault Systèmes Simulia Corporation for the FE simulation of the powerful commercial FE software ABAQUS 6.14.

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  1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, 310058, Zhejiang Province, China

    Xu Xie, Cheng Cheng & Shuailing Li

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  1. Xu Xie
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  2. Cheng Cheng
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  3. Shuailing Li
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Correspondence to Xu Xie.

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Xie, X., Cheng, C. & Li, S. A Deformation History-Based Approach for Ultra-Low Cycle Fatigue Damage Evaluation of Steel Structures. Int J Steel Struct 20, 1378–1392 (2020). https://doi.org/10.1007/s13296-020-00369-7

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