PSI - Issue 2_B

K.K. Tang et al. / Procedia Structural Integrity 2 (2016) 1878–1885 K. K. Tang, F. Berto and H. Wu / Structural Integrity Procedia 00 (2016) 000–000

1881

4

= ma/mi ma mi μ μ μ μ =

,

/ = ma mi = σ σ σ σ ma mi

,

/ = ma mi ma mi d d d = d

(3)

Subscript notations ma and mi stand for macro and micro scales, respectively. ma μ is macro stiffness and mi μ stands for micro stiffness. The combination of two parameters set up the material transitional function. ma σ is the macro stress while mi σ refers to the local restraining stress, which completes the loading transitional function. ma d is macro length and mi is micro length or micro feature scale. Material properties at micro scale are assumed to be appreciably larger than macro parameters. The macro stiffness as well as macro stress degrades over the fatigue cycles. The micro effects stand out as a result. Therefore, curves of and are defined to be monotonically decreasing. Curve of ma/mi is different from the aforementioned ma/mi and ma/mi . It is assumed to be monotonically increasing. This is due to the irreversible macro crack propagation. There results: d ma/mi μ μ ma/ σ σ mi d (4) in which ζ η and λ refer to the transitional coefficients for material, loading and geometry functions. Their values vary over the fatigue cycle life of material degradation. Thus they have to be adjusted according to the estimated fatigue life cycles. This shall be elaborated in the following section. 2 =1 , ma/mi N μ μ = ζ − 2 / =1 , ma mi = N σ σ η − / =1 ma mi d d N + = λ

b

50

a

2024-T3 Al sheet Reference test data

2024-T3 Al sheet Reference test data

40

6

117.6MPa 24.5MPa

a σ σ

=

117.6MPa 24.5MPa

a σ σ

=

=

=

m

m

30

3

20

Crack propagation a(mm)

Crack growth rate (mm/kc)

10

0

0

0

50

100

150

200

250

300

0

10

20

30

40

50

Cycles N(kc)

Crack length (mm)

Fig. 2. (a) Fatigue crack growth of 2024-T3 Al sheets; (b) Crack growth rate history (Broek and Schijive, 1963).

1.2 a

b

40

=

1 ζ ζ ζ

5

0.45 10 0.50 10 0.55 10 × × ×

−

η 1 =0.2 η 2 =0.4 η 3 =0.6

1.0

35

= =

5

−

2

30

5

−

0.8

3

5 Transitional function d geometry 10 15 20 25

0.2 Transitional function μ material 0.4 0.6

0

0.0

0

50

100 150 200 250 300 350 400

0

50 100 150 200 250 300 350 400

Cycles N (kc)

Cycles N (kc)

Fig. 3. (a) Depiction of transitional function material; (b) Depiction of transitional function geometry