Creep tests were conducted by means of a closed loop servocontrolled materials test system. The strain history prior to creep is carefully monitored. Tests were performed for aluminum alloy 6061-O at 150 C and were monitored by a PDP 11/04 minicomputer at a preset constant plastic strain rate prehistory. The results show that the plastic strain rate prior to creep plays a significant role in creep behavior. The endochronic theory of viscoplasticity was applied to describe the observed creep curves. Intrinsic time and strain rate sensitivity function concepts are employed and modified according to the present observation

Wu, H. C.

English

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https://ntrs.nasa.gov/search.jsp?R=19820007293 2020-03-21T09:39:01+00:00Z
F MISALIGNMENT ON
VIOR OF METALS IN CKEEH
nal Report
by
an C. Wu
G 302-2"-003
Prepared for
NASA-La:-gley Research Center
Grant No. NSG 1499
Division of Materials Engineering
The University of Iowa
Iowa City, Iowa	 52242
Uecember 20, 1981
IIn this project, under Grant No. N5G 1499, we have investigated the
effects of misalignment on the mechanical testing of metals. The primary
objective is to assess the errors caused by test system misalignment in a
creep test. Due to the importance of the prehistory of a creep test, which
has been shown in this study to seriousl, p affect the subseq!ient creep
behavior, the effect of misalignment in a tension test has also been studied.
The latter investigation included the strain-rate effect.
In connection with the misalignment analysis, we have developed the
endochronic creep equation. The development was based on the endochronic
theory of viscoplasticity. We have carried out cearp tests for bobl-U
aluminum alloy at 150% using a closed loop servo-hydraulic test system.
Parameters of the theory have been determined based on these test results.
We believe that the project has been successful. The effect of system
misalignment has been thoroughly analyzed. In this comprehensive analysis,
several assumptions made by other investigators have been relaxed. They arc::
1. the constant relationship between the axial load P and the bending
moment M applied at the ends of the creep specimen;
2. the condition that dM - U when dP - U;
dt	 lit
3. the fixed neutral ,axis of the specimen;
4. the absence of pull-rod effect.
In addition, the endochronicc creep equatioti, which tin y been shown to
sati g facturily describe the experimental data for some aluminum alloys )uts
been used in the analysts.
Due to the relaxation of the above assumptions, some ut the results of
this analysis are different than those found in the literature. We will now
summarize our findings in the following paral*raphs. These findings are
2presented in three parts. The first part is for misalignment analysis of a
tension test under static loading condition. The second part is for analysis
of a tension test under dyLiamic loading condition and the third part is for
misalignment analysis of a creep test. Although these findings are based on
1100-0 aluminum specimens, it is anticipated that they are also valid for
other metallic materials as long as the shape of their stress-strain
cu:'ves is similar to 1100-0 aluminum.
I. TENSION TEST UNDER STATIC LOAD
The following conclusions have been drawn from this investigation of
1100-0 aluminum specimens:
(1) The stress-strain curve is not significantly affected
by misalignment at strain levels greater than 0.003.
(2) The strain at the outermost fibers of the specimen is
strongly affected by misalignment.
(3) The misalignment effects are smaller for load trains
with longer pull rods.
(4) The symmetric case is the most severe case of all the
cases considered.
(5) pent pull rods do not affect strain errucs due to
symmetrical misalignuents.
The second conclusion mentioned above has important implici.tions when
properties sensitive to local strain concentrations are being investigated.
Fatigue strength in a strain-controlled test is such a property. In this
test, an error band in the strain will induce an even larger error band in the
fatigue life. This is due to the small slope of the fatigue curve. Fatigue
data usually have been known to have a large scatter. It is conceivable that
a major factor causing this scatter is testing system misalignment.
f3
II. DYNAMIC TENSION TEST
The following conclusions have been drawn from the study of 1100-0
aluminum specimens:
(1) Based on the endochronic constitutive equation, the formulation of
the misalignment problem in the dynamic tension test has been developed. Two
assumptions have been madet (a) plane cross-sections remain plane during
defotma*_ion; and (b) the srr_^iZ rate history effect is negligible in the
computation of stress. The second assumption is justifiable due to the
extremely small variation in the strain rate throughout the tension test for
each element of the discrete model.
(2) The lower the strain rate is at the tension test, the more
significant the misalignment errors become. Three levels of strain rate,
i.e., 1.30 x 10-5 , 1.24 x 10-2 , and 7.63 x 10-1 sec l have been investigated.
In this strain rate range, the misalignment error at the geometrical
centerline of the specimen is within 2% and vanishes mostly as the plastic
strain increases beyond 2%. At the extreme fibers of the specimen, the
misalignment errors approach to 50% at the very small plastic strain range.
Therefore, any investigation related to the local deformation of the extreme
fibers will have to account for the misalignment effect.
(3) In the range of plastic deformation, the error introduced by
misalignment decreases with the magnitude of plastic strain. Hence, it is
conjectured that the most significant effect of misalignment occurs at the
interface between the elastic and the plastic range. This conjecture is in
agreement with the finding of the investigation reported in part I, in which
it has been found that the most significant error occurs at the knee portion
of the stress-strain curve.
(4) At the midspan of the specimen, the variation of strain rate between
4extreme fibers decreases with increasing plastic strain. The strain rate
reaches a uniform value at plastic strain equal to 0.8%.
(5) The neutral axis (N.A.) will shift toward the geometrical centerline
of the specimen as the plastic strain increases. But, it will reach a limit
and will not move back to the geometrical centerline at large plastic strain
as anticipated by the uniform strain rate formulation.
(6) The misalignment errors and the shifting of the N.A. predicted by
the uniform strain rate formulation in which the strain rate is constant for
the whole specimen are always overestimated at the small plastic strain range
and underestimated at the larger plastic strain range.
(7) The formulation of the work reported in part I belongs to the case
of uniform strain rate formulation.
III. CREEP TEST
The formulation of a misaligned specimen subjected to the creep test has
been presented. The investigation is restricted to the symmetric case of test
system misalignment. The specimens used in the calculation are the sheet type
rectangular specimens of 1100-0 aluminum. Three cases have h,-en investigated
in detail which correspond to different pull rod lengths and different initial
strains. The following results have been obtained from this investigation:
(1) During the creep test, the stress is quite constant for all fibers.
The total change in stress for the 8-hour creep period for the top and bottom
fibers is w.'.thin 2% for all cases considered.
(2) The difference between the creep strains at the geometric centerline
and the the F.A. decreases with the creep time in spite of the test system
misalignment.
(3) The center error and the errors at the extreme fibers are always
decreasing during creep.
IL-
5(4) For the same pull rod lergth but with different amounts of
prestrain, the smaller the prestrain is (in the plastic range) the greater is
the misalignment error at the onset of creep and the longer creep time it
takes for the misalignment effect to vanish. For the same prestrain but with
different pull rod lengths, the error is greater for the shorter pull rod than
for the longer.
(5) in order to effectively reduce the misalignment error in a creep
test, long pull rod should be used and the test should be conducted with a
large prestrain.
In addition to the misalignment analysis we have carried out an
investigation on the creep behavior of metallic materials. This investibatioli
consists of two aspects which are the theoretical and the experimental
studies.
Theoretically, the endochronic creep equa--ion has been developed. The
development was based on the endochronic theory of viscoplasticity. The
following results have been obtained:
(1) The governing equations for constant-strain rate stress strain
behavior, creep, creep recovery, and stress relaxation have been derived by
imposing appropriate constraints on the general endochronic constitutive
equation.
(2) A set of material constants has been fou 3 which correlate
strain-hardening, creep, creep recovery, and stress relaxation for 1100-0
aluminum at 150%.
i3) The theory predicts with reasonable accuracy the creep and creep
recovery behaviors at short time.
6(4) The strain-rate history at prestraining stage affects the subsequent
creep.
(5) A critical stress is established which distinguishes forward creep
from normal strain recovery.
(6) It has been found that a logarithmic function is a reasonably good
form for the strain-rate sensitivity function for 1100-0 aluminum, and an
archyperbolic sine function is for 6061-0 aluminum.
(7) A nonlinear intrinsic time scale function has been proposed which
will achieve a steady state at large intrinsic time.
Although the conventional time-hardening or strain-hardening (or their
combination) models have been employed in the literature to describe creep and
the effect of stress variation during creep, the approach is valid only for
the description of creep and may not be applicable to describing stress
variation arising from other loading histories. At the service load, it is
likely that several types of loading histories may be present (possibly
including creep and cyclic loading, etc.) either simultaneously or in
sequence. The description of this complex behavior calls for a unified
approach which is the objective of this theoretical investigation.
The experiments have been conducted by use of a servo-controlled
-materials test system, and we used a PUP-11/04 mini-computer to control the
tes . The specimens were made of 6061-0 aluminum and were tested in an
env i ronmental chamber at a temperature of 150 * C. We have performed the
constant-strain-rare tension test, the creep test, the creep recovery test,
and the stress relaxation test.
The difference between this series of experiments and the conventional
creep or stress relaxation test is that the loading prehistory of the creep or
stress relaxtion test may be programmed and recorded.
Investigation of Creep by Use of
Closed Loop Servo-Hydraulic Test System
by	 Han C. Wu and J. C. Yao
ABSTRACT
Creep tests have been conducted by means of a closed
loop servo-controlled materials test system. These tests
are different from the conventional creep tests in that the
strain history prior to creep may be ca,.efully monitored.
Tests have been performed for aluminum alloy 6061-0 at 150 1C
and have been monitored by a PDP 11/04 minicomputer at a
preset constant plastic-strain rate prehistory. The results
show that the plastic-strain rate prior to creep plays a
significant role in creep behavior.
The endochronic theory of viscoplasticity has been
applied to describe the observed creep curves. The concepts
of intrinsic time and strain rate sensitivity function are
employed and modified according to the present observation.
8The following publications are related to this project. Abstracts of
some of these publications are attached.
(1) Wu, H.C. and Rummler, D.R., "Analysis of Misalignment in the Tensile
Test", Lighth U.S. National Congress of Applied Mechanics, Abstracts,
P. 48, University of California, Los Angeles, June 26-30, 1978.
(2) Wu, H.C. and Rummler, D.R., "Analysis of Misalignment in the Tension
Test", The ASME Journal of Engineering Materials_ and Technology, Vol. 101
pp. 68-74, January 1979.
(3) Wu, H.C. and Chen, L., "Endochronic Theory of Transient Creep and Creep
Reovery", Report G302-79-001, Division of Materials Engineering, the
University of Iowa, April 1979.
(4) Wu, H.C., Wang, T.Y. and Yip, M.C., "The Effect of Test System
Misalignment in the Dynamic Tension Test", Report G302-80-001, Division
of Materials Engineering, The University of Iowa, March 1980.
(5) Wu, H.C., Wang, T.P. and Yip, M.C., "The Effect of Test System
Misalignment in the Creep Test", Report G302-80-002, Division of
Materials Engineering, The University of Iowa, April 1980.
(6) Wu, H.C., "An Endochronic Description of Creep and Recovery", Develop-
ments in Mechanics, Vol. 11, pg. 225 (Abstract), Proceedings of the 17th
Midwestern Mechanics Conference, The University of Michigan, Ann Arbor,
May 6-8, 1981.
(7) Wu, H.C. and Yao, J. C., "Investigation of Creep by Use of Closed Loop
Servo-Hydraulic Test System", Report G302-81-001, Divisopm of Materials
Engineering, The University of Iowa, November 1981.
(8) Wu, H.C. and Yao, J.C., "Creep Recovery and Stress Relaxation Tests of
6061-0 Aluminum", Report G302-81-002, Division of Materials Engineering.
The University of Iowa, December 1981.
(9) Wu, H.C., "Effects of Misalignment on Mechanical Behavior of Metals in
Creep - Final Report", Report G302-81-003, Division of Materials
Engineering, The University of Iowa, December 1981.
Analysis of Misalignment in the TenRion Test
by Man C. Wu and D. R. Rummler
Abs. tracV
Many experimEnters fail }o appreciate the significance of test system
alignment during a tensile tes:. Poor alignment can increase data scatter
and significantly influence some of the 'Lest results. In this paper a
comprehensive analytical study of the misalignment problem in the plastic,
strain range is pres^nted and errors caused by misalignment estimateA.
The results show that the stress-strain curve is not significantly
affected by misalignment. However, the strains at the outermost fibers
of the specimen cross-section are strongly affected by misalignment.
Therefore, the effect of misalignment is most important when properties
sensitive to local strain coxicentrations are being investigated.
The Effect of Test System Misalignment
in the Dynamic Tension Test
by Dian C. Wu, T. P. Warp and M. C. Yip
ABSTRACT
An analysis of test system misalignment is presented for dynamic tension
test. Sheet type rectangular 1100-0 aluminum specimens are used for discuss.ott
For a constant strain rate tension test, the strain rate is constant only
on the neutral axis of the specimen. The following results have been obtained:
(a) The lower the strain rate is,the more significant the misalignment errors
become. (b) Misalignment errors of 50% have biull found at the extreme fibers
of the specimen. (c) 11ie strain rate variation io the cruss-section decreases
with increasing plastic strain and vanishes at plastic strain equal to 0.8% at
the midspan of the spe.A men. (d) The neutral axis will shift toward the
centerline of the specimen as the plastic str.,to increases. But, it will
reach a limit and will not complet4iy move back to the centerline.
A more restricted uniform strain rate formulation is also presented.
The result is compared with that of the nonuniform strain rate formulation.
The Effect of Test System Nisrli=nment
in the Creep To-t
by Tian C. Wu and T. P. Wang
Abstract
An analysis of teat system misalignment Is presented for the creep
test. Sheet type rectangular 1100-0 alumin °a specimens are used for dircu:-
sion. It is fou:.d that the creep strain at the gemetric centerline of the
specimen it different than that at the neutral axis. However, this differ-
eace in the creep strain decreases with time. Gene;:ally, the effect of mis-
altgnm.mt decreases with creep time.
Creep tests conducted with long pullrods and large initial strain level
(high creep stress) will tend to minimise tht ±ffect of misalignment.
ORIGINAL PACE 11.
Cyr pOOR QUALITY
AN ENDOCHRONIC DESCRIPTION
OF CREEP AND KECOVERY
Han-Chin Wu
Division of Materials Engineering
Univetiii y of Iowa
Iowa City, Iowa 52242
Short time creep and creep recovery have been investigated by means of the
modified endochronic theory of viscoplasticity. The intrinsic time is defined
in terms of the plastic strain and is further modified `,y making it depend on
plastic strain rate in this ii,veStigat inn.	 Therrfor( , , thc material behavior
is linearly elastic before yi.-Id and vi ,;coplasfic if l cr yield.
The first. part of the paper discusses the rrerp bch ;tvior of Aluminum 1100-0
at 150 U C (300 0F) . The strain rate pl;tvs a significant role in this considera-
tion and it is shown how the strain rata is ;iccountcd for in the present
approach.
Creep recovery is treated using equation dVrived from the same general consti-
tutive equation by imposing appropriate constraint.
	 A critical stress is
established which distinguishes forward crvv p from norm;;l strain recovery.
Investigation of Creep by Use of
Closed Loop Servo-Hydraulic Test System
by	 Han C. Wu and J. C. Yao
ABSTRACT
Creep tests have been conducted by means of a closed
loop servo-controlled materials test system. These tests
are different from the conventional creep tests in that the
strain history prior to creep may be ca,.efully monitored.
Tests have been performed for aluminum alloy 6061-0 at 150 1C
and have been monitored by a PDP 11/04 minicomputer at a
preset constant plastic-strain rate prehistory. The results
show that the plastic-strain rate prior to creep plays a
significant role in creep behavior.
The endochronic theory of viscoplasticity has been
applied to describe the observed creep curves. The concepts
of intrinsic time and strain rate sensitivity function are
employed and modified according to the present observation.


Effects of misalignment on mechanical behavior of metals in creep

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