Fatigue crack propagation assisted bygaseous hydrogen: experimental

and numerical approaches

G. Bilotta, C. Moriconi, G. Hénaff, M. Arzaghi, D. Halm

Experimental study of Fatigue Crack Growth in a 15-5PH martensitic stainless steel

•Material: commercial 15-5PH steel (UNS number S15500)

precipitation-hardened chromium-nickel-copper martensitic

stainless steel aged at 550 ºC for 4h.

•Testing: CT W=40mm B=8mm specimens; constant amplitude

loading; R=0.7; P=0.09, 0.9 and 9 MPa; f=0.2 and 20Hz

Objective: Comparison of simulated and experimental fatigue

crack propagation rates in gaseous hydrogen at different

pressures, levels of ∆K, and for two loading frequencies

Influence of hydrogen pressure

10-9

10-8

10-7

10-6

10-5

10-4

4 5 6 7 8 9 10 20 30 40

15-5 PHR=0.7, 20Hz

room temperature

air LT

air TL

H2 0.09 MPa

H2 9MPa

da

/dN

(m

/cy

cle

)

∆∆∆∆K (MPa x m1/2

)

10-10

10-9

10-8

10-7

10-6

10-5

10-4

4 5 6 7 8 9 10 20 30 40

0.9 MPa / 20Hz

0.9 MPa / 0.2Hz

da

/dN

(m

/cy

cle

)

∆∆∆∆K (MPa x m1/2

)

mean curve 9MPa/20Hz

mean curve 0.09MPa/20Hz

15-5PHR=0.7

Development of a specific traction-separation law

Objective: Development of a cohesive zone model that can accountfor cyclic damage and hydrogen embrittlement to describe fatiguecrack growth under high pressure of gaseous hydrogen.

The TSL is implemented in ABAQUS using a UEL subrou tine

2

0

2

0

2

0 21

21

)1(21

δδ

δδ

δδϕ t

tn

compn kkDk +−+−=

Influence of loading frequency

Future works

HYCOMAT

Pmax : 40 MPa

Tmax : 150 °C

Metrology techniques: monitoring of crack length variation, measuring crack

closure…

Automated control and data acquisition

Low frequency -> High time for diffusion

Intergranular fracture is more pronounced

Competition between HELP and HEDE mechanisms: dominance

related to several parameters such as frequency, H2 pressure

and ∆K level.

Hydrogen concentration profile in the thickness of the specimen.It is observed that the hydrogen diffusion in the

thickness is low for a test duration of 24h (average

duration of a test at 20Hz), but it should be taken

into account for a 0.2Hz frequency

� Moderate effect of

hydrogen relative to air

(few intergranular facets)

� Fracture mechanisms

changes depending on

hydrogen pressure

(secondary microcracks)

(a) – Air, ∆K=10 MPa m1/2(b) – H2, P=0.09MPa ∆K=10 MPa m1/2

(c) – H2, P = 9MPa∆K=10 MPa m1/2

(c)

(b)

(a)

H2, P=9MPa, f=20Hz H2, P=9MPa, f=0.2Hz

Cohesive elements with a specific Traction-Separation Law

1 – Framework of the Thermodynamics of Irreversible Processes

2 – TSL influenced by cyclic loading and presence of hydrogen2.1 – Decrease of cohesive strength2.2 – Stiffness degradation

hHLL

LLmRT

VCDCDJ σ∇+∇−=

rrr

Hydrogen diffusion controlled by: • Gradient of hydrogen concentration ( Fick’s law )• Gradient of hydrostatic stress

( DL = 10-12 m2/s )

1,E-09

1,E-08

1,E-07

1,E-06

1,E-05

1,E-04

1 10 100∆K (MPa√m)

Cra

ck p

ropa

gatio

n ra

te d

a/dN

(m

/cyc

le)

Sim. P=9 MPa Exp. Air Sim. No H2 Exp. P=9 MPa Exp. P=0,09 MPa

•The cohesive zone model with the TSL developed predicts qualitatively

the detrimental influence of hydrogen on fatigue crack propagation rate.

•It underestimates the drastic loss of resistance observed at high pressure.

Further studies will seek to provide a better knowledge about the

hydrogen diffusion within the specimen and its interaction with the

plasticity.

Possible approaches are:

1. Development of the model taking into account other

mechanisms of hydrogen transport.

2. Add the hydrogen influence on the plasticity of bulk.

3. Include the possibility of transporting hydrogen by mobile

dislocations.0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x [mm]

C(x

,t)/C

s.

1 day5 days

Tension Compression Shear

Damage variable : D (t) = max( Dm (t) , DC (t) )

Cyclic damage can only evolve if the opening is positive and increasing.

Accumulation of cyclic damage.

Consistency equation:Threshold: