- Email: [email protected]
Effect of Lüders front number on the yield point of iron
ACTA
258
METALLURGICA,
3. A. R. ROSENFIELDand B. L. AVERBACH, Acta Met. 8, 624 (1960). 4. J. M. COWLEY, Ph.D. Thesis, Massachusetts Institute of Technology (1949). 5. D. T. KEATING and B. E. WARREN, J. Appl. Phys. 22, 286 (1951). * Received September 20, 1961.
Effect The
of Liiders front number yield point of iron*
inhomogeneous
nature
requires that consideration number
of
on the
yielding
in
iron
be given to the type and
present when measuring Lamer(l) recognized that the nature
of the boundaries separating the yielded and unyielded portions
of the specimen
was an important
influencing the lower yield stress.
10,
1962
nearly equal and constant speeds and at a nearly constant stress, the lower yield stress. load-extension
factor in
This note will show
Fig. I(a) shows a
curve which is characteristic
the specimens,
those
each propagating
containing
of most of
two Liiders
fronts
from a grip.
In some specimens with larger grain sizes pulled at relatively high strain rates, Liiders front formation was not limited to regions of the specimen
of inhomogeneities
the yield stress.
VOL.
continued reached.
adjacent
to the grips.
Liiders
to form after the upper yield With the nucleation of these
bands
point was additional
Liiders bands along the gauge length, the lower yield stress dropped and the speed of the individual Liiders fronts
decreased.
The characteristic
load-extension
curve for this specimen type is shown in Fig. l(b). Eventually a minimum stress was reached where no new Liiders
fronts
were nucleated.
With
increased
as the number
of Liiders
that the number of fronts separating the yielded and
strain, the stress increased
unyielded
fronts decreased through the junction and annihilation
portions
of the specimen
(which are com-
monly referred to as Liiders fronts) is also important in determining
The experimental work was carried out on lowcarbon steel wires 0.030 in. in diameter and sheets 0.004 in. thick having
of Liiders fronts propagating
in opposite directions.
The reason for the formation
the lower yield stress.
a 5-in. gauge length between
of additional
high strain rates and was most prominent
grips of the Instron tensile machine. The length to gauge ratios were large enough to allow the formation
grained
of simple planar Liiders fronts only.
larger than average grains are potential
the Liiders front in the specimen function lacquer
of time through from the surface
The position
was observed
the cracking
of
as a
of a brittle
of the specimen
upon
the
passage of a Liiders front.c2) Upon tensile straining, Liiders fronts first appeared in the specimen
at the upper yield point.
Bending
stresses at the grips caused by specimen misalignment caused these Liiders fronts to nucleate
at each grip The
and also helped to minimize the upper yield point. two Liiders fronts propagated
away from each grip at
Liiders
bands in spite of the decreasing stress is not apparent; however, this phenomenon occurred most readily at samples
large grains.
which
contained
some
A possible explanation
in large
abnormally
may be that the sites for local
yielding and nuclei for Liiders band formation. However, these grains require larger delay times for yielding because of the stress drop resulting from earlier Liiders band formation near the grips. Therefore, after sufficiently large delay times, additional local yielding and Liiders band f ormation could occur even at lower stresses(3) in this type of microstructure. In specimens with a uniform grain size, the effect of the number of Liiders fronts on the stress for Liiders front propagation can best be illustrated by straining samples
with a constant
Liiders fronts.
in sheet specimens Upon
number
of
by bending the specimen through
the yield point at uniform length.
and controlled
Liiders bands were purposely nucleated
tensile
intervals
straining
two
along the gauge Liiders
fronts
propagated from each bend and travelled in opposite directions at nearly equal speeds. The effect of Liiders
2
s
front number upon the yield stress is shown in Fig. 2 for two grain sizes.
The drop in stress caused by in-
creasing the number of Liiders fronts also resulted in a decreased yield point elongation, Ed, and hence in an increased total Liiders front speed, C 1~~1,according to the relationship: ELONGATION
Fro. 1. Typical load-extension plot of yielding (a) for a specimen containing two Liiders fronts; (b) for a specimen containing multiple Liiders fronts which form during deformation.
where i is the strain rate and I, is the original gauge
LETTERS
TO THE
EDITOR
259
TABLE 1
Grain size
q, yield stress (lb/in*)
= Iv,1 total Liiders front speed (mm/set)
sL yield point elongation
10
28,000-28,800 26,300-27,400 25,500-25,800
1.89 2.30 2.99
4.5 3.7 2.8
2 4 10 20
37,800-39,800 36,900-37,100 35,200-35,400 33,900-34,100
1.10 1.33 1.48 1.76
7.7 6.4 5.7 4.8
Number of Liiders fronts
-__
True stress during homogeneous deformation (lb/ins) .__._
0.020 mm
2
0.007 mm
44,700 44,800 44,500 44,400
Strain rate, E = 0.04 min-‘(0.0066 set-I). Gauge length, 1, = 5in.(127 mm).
length. These data are listed in Table 1. The flow stress curves for homogeneous deformation were very similar for samples of comparable grain size even though the yield stress was changed considerably by varying the number of Liiders fronts. This point is illustrated in Table 1 by the similarity of the true stresses on the specimens at two values of uniform strain. The data have their significance in the interpretation of the lower yield stress for the discontinuous yielding of iron and other body-centered cubic metals. Lower yield stresses or the stresses necessary to propagate Liiders bands can be compared only among specimens which show a fixed number of simple Liiders fronts. For example, in plotting the dependence of the lower yield stress on the grain size in the manner of Petchc4), all samples should contain the same number of Liiders fronts. The yield stress for large grain sizes with multiple Liiders fronts can be considerably lower than the stress predicted by the extrapolation of the
yield stress-grain size relationship from fine grain sizes where only two Liiders fronts are p&sent. The slope of the yield stress versus the reciprocal square root of grain size plotted from the data of the present study for specimens with two Liiders fronts is approximately 10 per cent lower than the slope reported by Codd and Petch(5) for a similar steel. A qualitative explanation of the stress drop which results from the nucleation of additional Liiders bands may lie in the increased number of dislocations which can participate in the deformation. With an increased number of active dislocations located at the new Liiders fronts, the same specimen strain rate can be maintained by the motion of dislocations at lower velocity which in turn requires a smaller applied stress.‘@ Graham Research Laboratory & Laughlin Steel Corp.
J. F. BUTLER
Jones
Pittsburgh, Pa.
References 1. W. M. LOMER,J. Me&. Phys. S&da 1, 64 (1952). 2. J. C. FISHERand H. C. ROGERS,Acta Met. 4, 180 (1966). 3. D. S. CLARKand D. S. WOOD, Proc. Amer. Sm. Test. Mat. 49, 717 (1949). 4. N. J. PETCR,J. Iron St. Inat. 173, 25 (1953). 5. I. CODD and N. J. PETCH, Phil Mag. 5, 30 (1960). 6. W. G. JOHNSONand J. J. GILMAN, J. Appl. Phys. 80, 129 (1969). * Received September 29, 1961; revised October 20, 1961.
x
z
30-
b’
25-
GRAIN
SIZE
0.020 mm.
Bemerkung zur Eindeutigkeit der Boltzmannschen Liisung der eindimensionalen Diffusionsgleichung* Fiir die Differentialgleichung der eindimensionelen Diffusion
20
t
151
’ 2
I
I
4 NUMBER
IO OF
LijDERS
I
20 FRONTS
FIG. 2. The dependence of the lower yield stress on the number of Liiders fronts present in the sample. 6
au a Da” -=at
axf ax
1
(1)
mit konzentrationssbh&ngigem Diffusionskoeffizienten
258
METALLURGICA,
3. A. R. ROSENFIELDand B. L. AVERBACH, Acta Met. 8, 624 (1960). 4. J. M. COWLEY, Ph.D. Thesis, Massachusetts Institute of Technology (1949). 5. D. T. KEATING and B. E. WARREN, J. Appl. Phys. 22, 286 (1951). * Received September 20, 1961.
Effect The
of Liiders front number yield point of iron*
inhomogeneous
nature
requires that consideration number
of
on the
yielding
in
iron
be given to the type and
present when measuring Lamer(l) recognized that the nature
of the boundaries separating the yielded and unyielded portions
of the specimen
was an important
influencing the lower yield stress.
10,
1962
nearly equal and constant speeds and at a nearly constant stress, the lower yield stress. load-extension
factor in
This note will show
Fig. I(a) shows a
curve which is characteristic
the specimens,
those
each propagating
containing
of most of
two Liiders
fronts
from a grip.
In some specimens with larger grain sizes pulled at relatively high strain rates, Liiders front formation was not limited to regions of the specimen
of inhomogeneities
the yield stress.
VOL.
continued reached.
adjacent
to the grips.
Liiders
to form after the upper yield With the nucleation of these
bands
point was additional
Liiders bands along the gauge length, the lower yield stress dropped and the speed of the individual Liiders fronts
decreased.
The characteristic
load-extension
curve for this specimen type is shown in Fig. l(b). Eventually a minimum stress was reached where no new Liiders
fronts
were nucleated.
With
increased
as the number
of Liiders
that the number of fronts separating the yielded and
strain, the stress increased
unyielded
fronts decreased through the junction and annihilation
portions
of the specimen
(which are com-
monly referred to as Liiders fronts) is also important in determining
The experimental work was carried out on lowcarbon steel wires 0.030 in. in diameter and sheets 0.004 in. thick having
of Liiders fronts propagating
in opposite directions.
The reason for the formation
the lower yield stress.
a 5-in. gauge length between
of additional
high strain rates and was most prominent
grips of the Instron tensile machine. The length to gauge ratios were large enough to allow the formation
grained
of simple planar Liiders fronts only.
larger than average grains are potential
the Liiders front in the specimen function lacquer
of time through from the surface
The position
was observed
the cracking
of
as a
of a brittle
of the specimen
upon
the
passage of a Liiders front.c2) Upon tensile straining, Liiders fronts first appeared in the specimen
at the upper yield point.
Bending
stresses at the grips caused by specimen misalignment caused these Liiders fronts to nucleate
at each grip The
and also helped to minimize the upper yield point. two Liiders fronts propagated
away from each grip at
Liiders
bands in spite of the decreasing stress is not apparent; however, this phenomenon occurred most readily at samples
large grains.
which
contained
some
A possible explanation
in large
abnormally
may be that the sites for local
yielding and nuclei for Liiders band formation. However, these grains require larger delay times for yielding because of the stress drop resulting from earlier Liiders band formation near the grips. Therefore, after sufficiently large delay times, additional local yielding and Liiders band f ormation could occur even at lower stresses(3) in this type of microstructure. In specimens with a uniform grain size, the effect of the number of Liiders fronts on the stress for Liiders front propagation can best be illustrated by straining samples
with a constant
Liiders fronts.
in sheet specimens Upon
number
of
by bending the specimen through
the yield point at uniform length.
and controlled
Liiders bands were purposely nucleated
tensile
intervals
straining
two
along the gauge Liiders
fronts
propagated from each bend and travelled in opposite directions at nearly equal speeds. The effect of Liiders
2
s
front number upon the yield stress is shown in Fig. 2 for two grain sizes.
The drop in stress caused by in-
creasing the number of Liiders fronts also resulted in a decreased yield point elongation, Ed, and hence in an increased total Liiders front speed, C 1~~1,according to the relationship: ELONGATION
Fro. 1. Typical load-extension plot of yielding (a) for a specimen containing two Liiders fronts; (b) for a specimen containing multiple Liiders fronts which form during deformation.
where i is the strain rate and I, is the original gauge
LETTERS
TO THE
EDITOR
259
TABLE 1
Grain size
q, yield stress (lb/in*)
= Iv,1 total Liiders front speed (mm/set)
sL yield point elongation
10
28,000-28,800 26,300-27,400 25,500-25,800
1.89 2.30 2.99
4.5 3.7 2.8
2 4 10 20
37,800-39,800 36,900-37,100 35,200-35,400 33,900-34,100
1.10 1.33 1.48 1.76
7.7 6.4 5.7 4.8
Number of Liiders fronts
-__
True stress during homogeneous deformation (lb/ins) .__._
0.020 mm
2
0.007 mm
44,700 44,800 44,500 44,400
Strain rate, E = 0.04 min-‘(0.0066 set-I). Gauge length, 1, = 5in.(127 mm).
length. These data are listed in Table 1. The flow stress curves for homogeneous deformation were very similar for samples of comparable grain size even though the yield stress was changed considerably by varying the number of Liiders fronts. This point is illustrated in Table 1 by the similarity of the true stresses on the specimens at two values of uniform strain. The data have their significance in the interpretation of the lower yield stress for the discontinuous yielding of iron and other body-centered cubic metals. Lower yield stresses or the stresses necessary to propagate Liiders bands can be compared only among specimens which show a fixed number of simple Liiders fronts. For example, in plotting the dependence of the lower yield stress on the grain size in the manner of Petchc4), all samples should contain the same number of Liiders fronts. The yield stress for large grain sizes with multiple Liiders fronts can be considerably lower than the stress predicted by the extrapolation of the
yield stress-grain size relationship from fine grain sizes where only two Liiders fronts are p&sent. The slope of the yield stress versus the reciprocal square root of grain size plotted from the data of the present study for specimens with two Liiders fronts is approximately 10 per cent lower than the slope reported by Codd and Petch(5) for a similar steel. A qualitative explanation of the stress drop which results from the nucleation of additional Liiders bands may lie in the increased number of dislocations which can participate in the deformation. With an increased number of active dislocations located at the new Liiders fronts, the same specimen strain rate can be maintained by the motion of dislocations at lower velocity which in turn requires a smaller applied stress.‘@ Graham Research Laboratory & Laughlin Steel Corp.
J. F. BUTLER
Jones
Pittsburgh, Pa.
References 1. W. M. LOMER,J. Me&. Phys. S&da 1, 64 (1952). 2. J. C. FISHERand H. C. ROGERS,Acta Met. 4, 180 (1966). 3. D. S. CLARKand D. S. WOOD, Proc. Amer. Sm. Test. Mat. 49, 717 (1949). 4. N. J. PETCR,J. Iron St. Inat. 173, 25 (1953). 5. I. CODD and N. J. PETCH, Phil Mag. 5, 30 (1960). 6. W. G. JOHNSONand J. J. GILMAN, J. Appl. Phys. 80, 129 (1969). * Received September 29, 1961; revised October 20, 1961.
x
z
30-
b’
25-
GRAIN
SIZE
0.020 mm.
Bemerkung zur Eindeutigkeit der Boltzmannschen Liisung der eindimensionalen Diffusionsgleichung* Fiir die Differentialgleichung der eindimensionelen Diffusion
20
t
151
’ 2
I
I
4 NUMBER
IO OF
LijDERS
I
20 FRONTS
FIG. 2. The dependence of the lower yield stress on the number of Liiders fronts present in the sample. 6
au a Da” -=at
axf ax
1
(1)
mit konzentrationssbh&ngigem Diffusionskoeffizienten