IFMASS10

This formula allows an appreciation of the combined influence of stress and crack

length. Stress intensity depends directly, but not singularly, on stress, and it depends on

crack length. In a more general format, stress intensities might be expressed as:

a Y

= ⋅

⋅ ⋅

(2)

where

is a geometric factor allowing the representation of other geometries.

In fact, a stress can never be applied, but a load can. Stress is a resultant and determi-

ned quantity; it is not measurable. It is a mathematical tool of useful characteristics and

provides interpretations and insights, especially in reflecting an areal rationalized force

(load) path through the structure. Structures and materials, however, only experience

loads (mechanical, thermal, chemical) and respond with displacements and strains.

In some cases, however, where complexity precludes a simple "stress" approach,

analytical techniques do allow the calculation of stress intensity factors under the

imposed loads. The connection of stress intensity,

, as a controlling quantity for fracture

is a direct consequence of a physical model for LEFM under plane-strain conditions. Its

limit is

, the critical plane-strain fracture toughness. The use of the stress intensity

range, Δ

, as a controlling quantity for crack extension under cyclic loading is simply by

correlation. The ability of the stress intensity to reflect crack-tip conditions remains

mathematically correct, but the correlation of Δ

to crack growth is successfully

demonstrated. By altering Eq. (1) using

Δσ

instead of

, Δ

results in:

Δ = Δ ⋅

⋅

(3)

The stress intensity factor range to a certain extent simply reflects an extension of the

stress-based practices. However, the testing to support fracture mechanics-based fatigue

data is done differently than in the

or -

methods because of the necessity to monitor

crack growth. Crack growth testing is performed on samples with established

vs.

relation. Under the controlled load specified using two dynamic variables, the crack

length is measured at successive intervals to determine the extension over the last incre-

ment of cycles. Crack length measurement can be done visually or by mechanical or

electronic devices using established techniques that allow for automation of the process.

The result from the testing is not crack growth rate,

, but

versus

. Next nume-

rical differentiation of the

data set using provides

versus

. Coupling this latter

data with a stress intensity factor expression (

as a function of load and crack length)

for the specific sample results in the final desired plot of

versus

ΔK

. This process

is shown schematically in Fig. 7. The

versus

ΔK

curve has a sigmoidal shape, and

a full data set covers crack growth rates that range from fatigue crack threshold to frac-

ture. It is to note that this data represents only "long crack" behaviour; that is, the cracks

are substantially greater in size than any controlling microstructural unit (e.g. grain size)

and typically exceed several millimeters in length. A second important assumption is that

of a plane-strain stress state; therefore, a plane-stress descriptor is not required.

A real test of modelled

vs.

ΔK

expressions is whether, under reintegration, the

original

data will be reproduced. The generation of

vs.

ΔK

data is obviously

more involved than either

or ε-

testing. It does have the advantage, however, of

producing multiple data points from a given test. Figure 8 reflects interesting features at

each extreme of the

vs.

ΔK

curve. First, at the upper limit of

ΔK

, it reaches the

point of instability and the crack growth rate become very large as fracture is approached.