Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-09 GTBL042-Callister-v3 October 4, 2007 11:53

2nd Revised Pages

316 • Chapter 9 / Failure

minimum compressive stress (σmin) of equal magnitude; this is referred to as are-

versed stress cycle. Another type, termedrepeated stress cycle, is illustrated in Figure

9.23b; the maxima and minima are asymmetrical relative to the zero stress level. Fi-

nally, the stress level may vary randomly in amplitude and frequency, as exemplified

in Figure 9.23c.

Also indicated in Figure 9.23bare several parameters used to characterize the

fluctuating stress cycle. The stress amplitude alternates about amean stressσm, defined

as the average of the maximum and minimum stresses in the cycle, or

σm=

σmax+σmin

2

(9.15)

Mean stress for cyclic

loading—

dependence on

maximum and

minimum stress

levels Furthermore, therange of stressσris just the difference betweenσmaxandσmin—

namely,

σr=σmax−σmin (9.16)

Computation of

range of stress for

cyclic loading

Stress amplitudeσais just one half of this range of stress, or

σa=

σr

2

=

σmax−σmin

2

(9.17)

Computation of

stress amplitude for

cyclic loading

Finally, thestress ratio Ris just the ratio of minimum and maximum stress amplitudes:

R=

σmin

σmax

(9.18)

Computation of

stress ratio

By convention, tensile stresses are positive and compressive stresses are negative.

For example, for the reversed stress cycle, the value ofRis –1.

Concept Check 9.2

Make a schematic sketch of a stress-versus-time plot for the situation when the stress

ratioRhas a value of+1.

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]

Concept Check 9.3

Using Equations 9.17 and 9.18, demonstrate that increasing the value of the stress

ratioRproduces a decrease in stress amplitudeσa.

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]