Fatigue Crack Paths 2003

dissipated in each hysteresis loop and the inelastic increment of εv in the same cycle.

ii)The ultimate contraction in the direction of loading characterizes the material

performance: independently of the load-history, failure occurs when such a parameter,

sometimes denoted “strain capacity”, reaches a certain limit, characteristic of each rock

type. iii) Maintaining fixed the loading intervals, the inelastic part of the deformation

exhibits a “steady trend”, characterized by a pseudo-linear dependence upon the

logarithm of the number of cycles n undergone by the specimen.

-120

[M P a]

a) vertical gauge response

b) horizontal gauge response

S t r e s s

-100

-80

-60

σ

-40

-20

0

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

Strain

ε v

εh

Figure 1. Typical σ-ε relations for cyclic-compression tests on a Carrara Marble.

9,E-04

10200

678,E-04

Phase1

i n e l a s c s t r a i n t i

Phase2

800

5,E-04

600

4,E-04

3,E-04

400

2,E-04

200

1,E-04

0

0,E+00

1

10

100

1,0E+01 1,0E+02 1,0E+03 1,0E+04 1,0E+05 1,0E+06

1,0E+07

Numberof cycles [n ]

number of cycles n

(b)

(a)

Figure 2. (a) Pseudo-linear relationship between inelastic strain and Log(n) and (b)

detail of the final stage, immediately prior to specimen failure. Both graphs

are in semi-logarithmic scale.