Conceptual theory proposes that cyclic hardening due to non-uniform strain and stress amplitudes during testing, especially during the initial application of stress to a specimen, may correlate positively with the ultimate strength of the specimen under test

Kettunen, P. O.

Kocks, U. F.

English

NASA Technical Reports Server

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September 1969	 Brief 69-10414 
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AEC-NASA TECH BRIEF 
TES
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Cumulative Plastic Strain 
Fig. 1. "Fatigue hardening" (schematic): at constant prescribed plastic-strain amplitude, the observed 
shear-stress amplitude increases with increasing number of cycles (solid line). The flow stress, 
as measured in an interposed tensile test, may rise even more (dashed line), T, Tension; 
C, Compression. 
A conceptual theory for the correlation of strain-
hardening with fatigue-failure has been presented 
(1). It is proposed that cyclic hardening due to non-
uniform strain and stress amplitudes during testing, 
especially during the initial application of stress to a 
specimen, may correlate positively with the ultimate 
strength of the specimen under test. The work is a 
logical treatment of the problems involved in fatigue-
failure analyses.
Fatigue tests can be done at constant stress ampli-
tude or at constant strain (or plastic-strain) amplitude. 
Schematic diagrams of stress versus cumulative 
plastic strain for these two cases are shown (Figs. 
1 and 2). The stress, needed for maintenance of a 
constant plastic-strain amplitude, increases as the 
number of cycles increases ("fatigue hardening") 
until, after some hundreds or thousands of cycles, 
it reaches a saturation value (Fig. 1).
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Conversely, in a test done at constant stress 
amplitude, the plastic strain per half-cycle decreases 
as the number of cycles increases until, after some 
hundreds or thousands of cycles, it reaches an ap-
proximately constant value (Fig. 2). 
During the stage of saturation, both strain and 
stress amplitudes are thus constant, no matter which 
is prescribed. During the initial hardening period, 
however, there are substantial differences in the be-
havior of the material for the two different boundary 
conditions. These differences may have a profound 
effect upon whether or not fatigue-failure eventuates 
(1). 
It is shown that, while the structural changes 
leading to eventual fatigue-failure occur throughout 
the entire test, the very possibility of structural 
changes, during the long stage of saturation, depends 
on the mean free-slip area of individual dislocation 
segments during this stage; this in turn depends on 
the degree of cyclic hardening during the first few 
hundred cycles. This hardening depends sensitively 
on the exact boundary conditions. 
If the cyclic hardening is related to the work-
hardening coefficient in a monotonic test to the same 
stress level, the endurance level correlates with the 
beginning of low work-hardening. This fact may ex-
plain the phenomenological correlation between 
endurance limit and ultimate tensile strength. The 
latter, like the former, is determined by a critically 
low work-hardening rate and not by a crack-nucleation 
or crack-propagation stress.
Reference: 
1. P. 0. Kettunen and U. F. Kocks, "On a possible 
relation between work hardening and fatigue 
failure" (Argonne National Laboratory, May 1967). 
Notes: 
1. This problem is currently of significant interest; 
any work toward its solution will interest the steel 
and aluminum industries, as well as manufacturers 
of almost all nonstatic systems—the aircraft, 
marine, construction, power, and machine-tools 
industries. 
2. Inquiries may be directed to: 
Office of Industrial Cooperation 
Argonne National Laboratory 
9700 South Cass Avenue 
Argonne, Illinois 60439 
Reference: B69-10414 
Source: P. 0. Kettunen and, U. F. Kocks

Metallurgy Division

(ARG- 1037 1) 
Patent status: 
Inquiries concerning rights for commercial use of 
this innovation may be made to: 
Mr. George H. Lee, Chief 
Chicago Patent Group 
U.S. Atomic Energy Commission 
Chicago Operations Office 
9800 South Cass Avenue 
Argonne, Illinois 60439 
Cumulative Plastic Strain 
Fig. 2. 'Cyclic hardening (schematic): at constant prescribed shear-stress amplitude, the observed plastic-
strain amplitude decreases with increasing number of cycles (solid line); the flow stress as 
measured in an interposed tensile test rises above the applied stress amplitude (dashed lines). 
T. Tension; C. Compression. 
Brief 69-10414
	
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Possible correlation between work-hardening and fatigue-failure

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