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2 Phenomenology, a Clue, and Methodology

2 Phenomenology, a Clue, and Methodology

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122



Subcritical Crack Growth



CRACK GROWTH RATE



da

inch/minute

dt



Ti – 5AI –2.5Sn ALLOY

HYDROGEN AT 0.9 ATMOSPHERE

74C

23C

−9C

−46C

−70C



100



74C



10 −1



23C

−9C



10 −2



−46C



Figure 8.2. Influence of temperature on crack growth response for a Ti-5Al-2.5Sn alloy

under sustained load in hydrogen at 0.9 atmosphere [2].



−70C

10 −3



10 −4

0



20



40



60



KI ksi



80



100



120



inch



Crack Growth Rate (m/s)



10 −3



10 −4



AISI 4340 Steel in 0.6N NaCl Solution

−700 mV (SCE) pH = 6.4

[O2] < 0.3 ppm



Figure 8.3. Influence of temperature on crack growth response for an AISI 4340 steel

under sustained load in a 0.6

N NaCl solution (pH = 6.4) at

276 to 358 K [3].



10 −5



276K

294K

318K

345K

358K



10 −6



10 −7

20



30



40



50



60



70



80



Stress Intensity Factor, K (MPa-m1/2)



Crack Growth Rate (m/s)



10 −4



10 −5



Pure Water

0.6N NaCl Solution

0.6N NaCl Solution

1N Na2 CO3 + 1N NaHCO3 Solution



Figure 8.4. Influence of solution chemistry on crack growth

response for an AISI 4130

steel under sustained load [3].



10 −6



10 −7



AISI 4130 Steel

10 −8

20



30



40



50



60



Stress Intensity Factor, KI (MPa-m1/2)



70



80



8.3 Processes that Control Crack Growth



123



room temperature [3]. The indicated near-independence of crack growth rate on the

mechanical crack-driving force K, and its dependence on thermal and chemical environments, provide a link for examining the process(s)/mechanism(s) that control

crack growth, and for the development of tools for their mitigation and for design.

The essential methodology for understanding and developing effective tools for

design and sustainment of engineered systems involves the development of understanding of the damage evolution processes and of tools for their mitigation and

control. It involves the use of well designed experiments to probe the underlying

mechanisms and rate-controlling processes for crack growth through:

r

r

r

r



influence of temperature, frequency, etc.

partial pressure and gaseous species (for gaseous environments)

ionic species, concentration, pH, etc. (for aqueous environments)

supporting microstructural and chemical investigations.



8.3 Processes that Control Crack Growth

The processes that are involved in the enhancement of crack growth in high-strength

alloys by gaseous environments (e.g., hydrogen and hydrogenous gases (such as

H2 O and H2 S), or oxygen), are illustrated schematically in Fig. 8.5 and are as

follows [1]:

1. Transport of the gas or gases to the crack tip.

2. Reactions of the gas or gases with newly produced crack surfaces to evolve

hydrogen, or surface oxygen (namely, physical and chemical adsorption).

3. Hydrogen or oxygen entry (or absorption).

4. Diffusion of hydrogen or oxygen to the fracture (or embrittlement) sites.

5. Partition of hydrogen or oxygen among the various microstructural sites.

6. Hydrogen-metal or oxygen-metal interactions leading to embrittlement (i.e.,

the embrittlement reaction) at the fracture site.



Local Stress

Fracture

Zone



Crack-Tip Region



Figure 8.5. Schematic diagram of

processes involved in the enhancement of crack growth in gaseous

environments [1].



1

2



3



5

4



M

I

H

I

M



Transport Processes

1. Gas Phase Transport

2. Physical Adsorption

3. Dissociative Chemical Adsorption Embrittlement

Reaction

4. Hydrogen Entry

5. Diffusion



124



Subcritical Crack Growth

Local Stress

Fracture

Zone



Crack-Tip Region

Oxidized (Cathode)

Base

(Anode)



[me+,

Bulk

Solution



me++,....H+





+

OH , CL ....] me ne

H+









3 R



H



Transport Processes

1. Ion Transport

2. Electrochemical Reaction

3. Hydrogen Entry

4. Diffusion



Me

I

H

I

Me



Figure 8.6. Schematic diagram

of processes involved in the

enhancement of crack growth

in aqueous environments [1].



Embrittlement



For crack growth in aqueous solutions, the corresponding processes are as follows, and are schematically shown in Fig. 8.6 [1]:

1. Liquid phase transport along the crack

r Convection (pressure gradient)

r Diffusion (concentration gradient)

r Electromigration (potential gradient)

2. Coupled electrochemical reaction at the crack tip/dissolution (go no further for

dissolution mechanism).

3. Hydrogen entry (or absorption).

4. Diffusion and partitioning of hydrogen to the fracture (or embrittlement) sites.

5. Hydrogen-metal interactions leading to embrittlement (i.e., the embrittlement

reaction) at the fracture site. (Although metal dissolution has been considered

as the mechanism for stress corrosion crack growth, fractographic evidence to

date does not support it as a viable mechanism.)

The various processes, and their inter-relationships, are depicted in the schematic diagrams in Fig. 8.7. Figure 8.8, on the other hand, represents the more traditional empirical or phenomenological approach in which empiricism resides. More

recent studies of hydrogen-enhanced crack growth in steels [3], moisture-induced

crack growth in ceramics [4], and oxygen-enhanced crack growth in nickel-base

superalloys at high temperatures [5], for example, broaden the understanding and

quantification of material response.



8.4 Modeling of Environmentally Enhanced (Sustained-Load)

Crack Growth Response

The basic approach to the understanding and “prediction” of crack growth response

resides in the following: (a) postulate and (b) corollary, i.e.,

(a) “Environmentally enhanced crack growth results from a sequence of processes

and is controlled by the slowest process in the sequence.”



8.4 Modeling of Environmentally Enhanced (Sustained-Load)



External



Proverbial Black Box



BULK

ENVIRONMENT



CYCLIC LOADING



CRACK OPENING



MASS

TRANSPORT

OF

SPECIES



125



MECHANICAL

FATIGUE



CHEMICAL

OR

ELECTROCHEMICAL

REACTIONS



da

dN



⋅ (1− φ)

r



FRESH

SURFACE

GENERATION



da

dN



e



Internal

HYDROGEN

ABSORPTION



HYDROGEN

DIFFUSION

and

PARTITIONING



HYDROGEN

EMBRITTLEMENT

da

dN



c



⋅φ



CYCLIC LOADING



Figure 8.7. Block diagram showing the various processes that are involved, and their relationships, in the environmental enhancement of crack growth.



(b) Crack growth response reflects the dependence of the rate-controlling process on

the environmental, microstructural, and loading variables.

This fundamental hypothesis reflects the existence of a region (i.e., stage II) in crack

growth response over which the growth rate is essentially constant (i.e., independent of the mechanical crack-driving force). The existence of this rate-limited region



External

BULK

ENVIRONMENT



Proverbial Black Box

CYCLIC LOADING



da

dN



e



CYCLIC LOADING



Figure 8.8. Illustration of a more empirical approach in which the controlling processes

(Fig. 8.7) are by-and-large hidden.



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