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Experimental study of the effect of the type of stress state on plastic strain in structural materials at low temperatures
. , ~ c m ~ Vol. 11. No. 7-8.1~. 483--48& I~14 P n a ~ m a'- U.S.A.
0094-57f3.S,g4 $ 3 0 0 + 0 0 PesBsmoa Press l.zd.
E X P E R I M E N T A L STUDY OF THE EFFECT OF THE TYPE OF STRESS STATE ON PLASTIC STRAIN IN S T R U C T U R A L MATERIALS AT LOW T E M P E R A T U R E S G. S. PLS~'tENKO,? A. A. LEBEDEV and B. I. KOVALCHUK Institute for Problems of Strength of the Academy of Sciences of the Ukr. SSR, Timiryazevskaya str. 2, Kiev 14, 252014, U.S.S.R.
(Received 13 December 1983) Abstract--The analysis is made of modern methods and equipment for testing materials at cryogenic temperatures. The authors describe an automated complex developed at the Institute for Problems of Strength of the Academy of Sciences of the Ukr. SSR for low-temperature tests of structural materials under conditions of controlled biaxial loading which imitates the operation of cryogenic vessels and pipe-lines. Analyzed are the results of experimental investigations into the laws of elasto-plastic deformation which were carried out on the materials of different grades loaded in accordance with complex programs over a wide temperature range. Main attention is given to new effects which are associated with the influence of cooling on the process of deformation under conditions of stress state variation. Variants are presented of analytical description within the framework of the elasto-plasticdeformation theory of the experimentally established laws.
The published data on the effect of temperature on
mechanical propertiesof structuralmaterials used in cryogenic rocket and space engineering are obtained, as a rule, in uniaxial tension tests of specimens. However, an overwhelming majority of actual structures components operate under complex conditions of mechanical and thermal effects.Their strength is determined not only by the level of operating temperatures, but also by the type of stress state. Therefore, to assess and predict the load carrying capacity of the components it is important to study the mechanical behaviour o f materials under a variety of combinations of stress tensor components. Systematic studies of deformation mechanism and strength criteria for structural materials at low temperatures in complex stress state are conducted at the Institute for Problems o f Strength of the Academy of Sciences of the Ukrainian SSR. A complex of experimental equipment has been developed at the Institute which allows one to investigate the laws o f elastoplastic deformation and strength of materials under these conditions within the temperature range from 20 to 1200 K.
onto the specimen, working chamber, specimen heating and cooling system and strain measuring system (Fig. I). The working chambers of the testing unit make it possible to conduct measurements in inert gas or in vacuum.
The set-ups employ a unique temperature-control system incorporating a thermal element placed inside the specimen (a flow-through cooler for lowtemperature tests and an electric heater for hightemperature tests) and the monitoring equipment unit.
For measuring strains in the specimen working section the electromechanical extensometers of various design employing the resistancestraingauges are used.
This complex includes set-ups for testingthin-wall tubular specimens by axial force,torque and internal pressure, cross-shaped specimens in biaxial tension, as well as flat specimens of membrane type and pressure vesselscomponents by hydrostatic buckling technique[I]. Set-ups for testing tubular specimens at the temperature from I00 to 1200 K comprise a hydraulic testing machine, pressure unit for creating pressure fAcademy Member (Secuon I).
483
Mechanical propertiesof sheet materials in biaxial tension are studied using 2-8 m m thick round and cross-shaped specimens within the temperature range from 30 to 293 K[2]. The set-up for testingmembranes of up to 300 m m in diameter by the hydrostatic buckling technique (Fig. 2) incorporates a cryostat with a device for fixingspecimens, pressure generating system, vacuum system, cooling system, extensometers for measuring strains and the monitoring equipment. Precooling of the specimen down to 97 K and of the fixing device is realized by liquid nitrogen. Further cooling of the specimen working section to 2 0 K is realized by helium vapours with the aid of an atomizer. The specimen fixing device incorporates a set of special fiat springs made as rings with notches ensuring smooth bending of the specimen and preventing its fracture at the point of fastening.
G, S. Ft~J~)~o
4~,M
tt d.
¢ Fig. I. Tubular specimen tcst ~t: (I) tcsting machine; (2) pressure unit; (3) vacuum working chamber; (4) specimcn cooling system; (5) sFm.imcn heating systcm; (6) strain measuring system; (7) pumps; (8, 9) monitoring and distributing hydraulic equipment. ?
5
8
9
4
12
3 2
,
• ~
114
_13
l--
Fig. 2. Membrane test set: (I) vacuum chamber; (2) nitrogen shield; (3) cryostat housing; (4) fixing device; (5) cover; (6) pipe ~cket; (7, 8) strain measuring system; (9) atomizer; (10) specimen: (I I) washer; (12) matrix; (13) compressed gas cylinder; (14) vacuum pump. The set-up for testing cross-shaped specimens (Fig. 3) comprises hydraulic loading system consisting of four cylinders, a cryostat, specimen cooling system, vacuum system and strain measuring system. To reduce heat input to the specimen, the nitrogen
shields arc employed along with a system of flexible coolant ducts which serve to supply coolant to the machine grips. The specimen ends are cooled with the aid of special bellows contact coolers into which liquid helium is supplied. Strains in the working section of the specimen are measured visually with the help of grids, as well as by electro-mechanical extensometers. The experimental set-ups are provided with the test automatic control system (Fig. 4) which automatically follows the preset program of multicomponent loading of specimens, outputs and processes the experimental data in real time and prints out the calculation results[3]. The system incorporates the stress and strain gauges, extensometer measurements amplifier, switch, analog-to-digital converter, servomotors of load controllers, electric drive control unit and computer. The system provides the mode of automatic loading following the preset trajectory in the coordinates of real stresses or strains. The experimental equipment made it possible to carry out thorough investigation into the laws of elasto-plastic deformation and of the criteria of ultimate state for materials of various classes. Our work deals with the results of testing chromium-nickel steel HI8NIOT, aluminium alloys DI6T, AMg3, AMg6, AMnS and titanium alloy VTS-I which found their widespread application in cryogenic engineering. The experiments were carried
Stress state on plastic strain in structural materials at low temperatures
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Fig. 3. Cross-shaped specimen test set: (I) hydraulic cylinder; (2) vessel for nitrogen; (3) flexible coolant ducts; (4) specimen: (5) sylphon chamber; (6) optical system for strain measuring; (7) temperature registering system; (g)joint; (9) cryostat; (10) grips: (I I, 12) reducing valves; (13) electrohydraulic system: (14) vacuum pump.
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Fig. 4. Experiment automatic control system. out using tubular specimens made of 4 0 - 5 0 mm diameter bars. Steli H iSN 10T was hardened (heated to 1370 K with subsequent cooling in water). The rest of the materials were in as-delivered-state. The testing of specimens in uniaxial tension in the axial and tangential directions has shown that steel H 18N 10T, by its yield strength and tensile strength, is virtually isotropic. The aluminium and titanium alloys arc fairly anisotropic and offer a considerable resistance to plastic deformation as well as possess a significant plasticity in axial tension. The moduli of elasticity of the alloys in the axial and tangential directions differ by 10% on the average. Here, in DI6T, AMg6 and VT5-1 alloys the directions corresponding to the maximum values of the elasticity
moduli and to the maximum values of strength characteristics do not coincide. A reduction in the test temperature is accompanied by an increase in the strength of materials. The palsticity of the aluminium alloys during cooling becomes somewhat greater, while that of the chromium nickel steel and titanium alloys slightly drops. Here, it is necessary to mention that reduction in temperature entails a reduction in anisotropy of the alloys. The investigations performed with the initially anisottopic alloys proved that the generalized stress-strain curves in the coordinate axes of stress intensity and strain intensity corresponding to different ratios of principal stresses do not coincide
G.S. PISARENICOet
480 r
I
al.
I
T,293 K
,b
~---'-
~
7S.- =
/,,...~..
°'1
-
..--3
L
°
2 -
4 .-
---
--o°
~00
r.l,o
K ~
/
~'" ~
Z FI
300 i / ~
"
~3
20O 0
J
2
3 ~j
\4
4
5
(*/.)
Fig. 5. Slress-strain curves of aluminium alloy AMg6 at various ratios of principal stres~s: (I) k = o,/o 2 - ~:; (2) k = I; (3) k =0.5; (4) k =0.
either at room or at low temperatures (Fig. 5). As the temperature drops a fan of curves does not spread: absolute deviations remain the same. However. at low temperatures the values of current stresses are considerably highcr, and therefore, as the tcmperaturc drops the relative value of deviations becomes smaller. In the region of minor deformation in initially anisotropic media rectilinear trajectories of plastic swains correspond to proportional loading, but the guide stress and swain tensors do not coincide. The angle between the trajectories of loading and of plastic deformation depends on the orientation of the loading trajectory in the stress space. Under proportional loading plastic strain trajectories are normal to the smooth portion on the yield surface which is described by the following equation[4] 'I ~ / [ a , 2 + ~2(a22 + o) z) - a,o5 - o , a j
GIS
-(2~-
Io,-,,,I =
l)(r.,(rj] + ~
where k = I; 1 = 3: at (o t -
I,
Gj)/(O2-oj)
(1)
t> (~; k = 2; ~<(at - 0 2 ) / ( 0 2 - o~); k = I; / = 2 : at ( a t - o 2 ) / ( o 2 - o j ) - . < ~ ; ~.=otslo,s; a~s. o,.s are the yield strength in the axial and tangential directions. in the stress space, condition ( ! ) is interpreted as a singular cylindrical surface parallel to the hydrostatic axis with the deviatoric cross section as an irregular curvilinear hexagon (Fig. 6). I = 3: a t
Fig. 6. Deviatoric cross-sections of yield surfaces, corresponding to different yield conditions. Curves obtained with: I: yon Mises-Hill condition; 2: Coulomb--Tresca condition; 3: condition (I).
( a t - 0 3 ) / ( 0 2 - 03) ~< ~
in the case of loading via angular point the loading and plastic strain trajectories coincide. The obtained results allowed the authors to write the relation between the stresses and plastic strains in the orthotropic media for the smooth portion of the yield surface[5] ~,P(o',) e~=(~
;If
aS,,Of " aS,~/afl "Z aS"'
(2)
(k, Lm.n,
=1,2,3). where S,,, are the stress deviator components; a, = a,(~,e) is the function invariant to the type of stress state; stress o, is determined by the yield criterion, i.e. a, = cf(S,). The stress-strain relationship for the trajectory running via the angular point is as follows
3 ~,r(a,) _ '' = 5
(3)
The investigations carried out with austenitic chromium-nickel steel H l g N I 0 T proved that a reduction in temperature effects considerably the nature of strain hardening of the steel in complex stress state. When some level of plastic deformation is reached, a zone of intensive hardening appears which is related to phase transformations. A nonmonotonous dependence of the lateral strain factor on the degree of deformation is observed: at ~, > 5--6%, a significant reduction in this factor takes place, thus indicating a residual change in the steel volume (Fig. 7). Here, as the transition from uniaxial to uniform biaxial tension proceeds, the intensity of residual volume ~ increase in the process of deformarion declines. A reduction in temperature upsets the invariance of curves (r, = cr,(¢,) to the type of stress
Stress state on plastic strain m structural materials at
•
~" 400
/
K
~.,.®
;,,o~
3 (, (*' = 2 (pC(,, T,
f
200
"*,05
k,i
T,293
4
8
487
temperatures
state, while a similarity between stress and strain deviators is retained. The obtained results made it possible to determine the stress-strain relationship for structurally unstable media in the case of proportional loading in the following form
.ltO K 600
low
- 6,#'0)
xJ (~,a
¢0
(%)
(
(4)
+6,1 ~K + m
04 -
:d
OZ
0
I0
5
where x,, are some o f the structural parameters; K is the bulk m o d u l u s o f elasticity; ~o is the mean stress, oo = ~6,#.,t, 6,~ is the Kronecher's symbol.
The functions of hardening ~ ¢~((,, 7", K,.) and of the residual change in volume ~ J = ( J ( ( , , K J are =
,~o
15
% /
Fig. 7. Results of nickel-chromium steel tests at various ratios
o" ~ ( M P a ) e
r,293
of pnncipal stres~s.
K
I
.,~
L~2
o', (MPo) r,93 K
~oo T,293 K ,/~----"u" / 400 /
HISNIOT
/
|
)
t20o
_/ /
-300
I00
0" i
2000
/
•
200
300
400
(MPo)
] t
16OO
I I I
f200
i
0
|
400
,u
T.II3 K
0" 2 ( M P o )
(a)
1200
1600 ' '
2[0' 0 0
~
t
VTS-I
ottoy
o.//"
I
t
000
I
o
I I I
..oo
-400
0
o
'
-800
-I00
0"2 (MPo)
/
/
-200
L~.2
I I
K
/
"1
,
I I
•800
/
-,,
-;-
"
/
T,II3
DI6T oU.oy ~ --
o
T.I?3 K
/
L-dOO
L'--
/--I'--
[
;/
/
steel
-1200
-800
-400
0
,
,
J!
400
800
1200
O*2 ( M P o }
(b)
Fig. 8. Yield and ultimatc stn:ngth limiting curves of HI8NIOT steel (a). DI6T alloy and V'['5-1 alloy (b): h yon Mises condition, 2: Coulomb--Tn~a condition; 3: condition (I),
488
G. S. ~ . ' ~ o
04
l
/o °°t
_ Io,l
05L
I
l
04
o6
I
0,.. ~ 0._ ~ _.,.. ,.0
~
oa
t
_(cl
Or
I
l
(d)
0
3 -200
I
~ -~00
el 0
T ('C) Fig. 9. Temperature relationships of the ratio of yield strength to ultimate strength: (at carbon steel (0.37"/,C); (b) DI6T alloy; (el VTS-I alloy; (d) AMg6 alloy; (¢l chromium nickel steel !-I18N I0T. specified on the basis of combined mechanical and structural studies of steel. The investigations of the ultimate state of chromium-nickel steel, aluminium and titanium alloys[rJ showed that with a decrease in temperature the region bounded on the limiting yield and strength curves extends without noticeable change in its shape (Fig. 8). Both at room and low temperatures the onset of HI8NIOT steel yielding under conditions of plane stress state corresponds to yon Mises condition for isotropic bodies. Transition of aluminium and titanium alloys into plastic state can be well described by criterion (I) which generalizes the yon Mises-Hill and St. Venant-Tresca condition. The strength of steel and alloys at room and low temperatures is in satisfactory agreement with the St. Venant-Tresca condition for the anisotropic and isotropic bodies, respectively. Brittle state of a metal is usually associated with some critical temperature (or temperature range) corresponding to a sharp reduction in paisticity, i.e. to such a state of the metal when the ultimate plastic strain e e l 0 , or as~Ok-, I. The use of the offset yield strength to the ultimate strength ratio as a parameter characterizing the plasticity available in the material under preset temperature and loading conditions offers ready assessment of the effect of the type of
et al.
stress state on the brittleness critical temperature. For the materials studied temperature dependences of the Os/(7b ratio were determined for the uniaxial and biaxial tension (Fig. 9). With allowance made for anisotropy and inevitable scatter of the experimentally determined characteristics, the yield strength and the ultimate strength axe assumed to be equal in uniaxial tension to the mean values of the respective magnitudes for the axial and tangential directions, while in biaxial tension these are the mean values obtained for ot/o 2 = 0.5 and o~ a, = 1. it is found out that the plasticity available in the materials considered can decrease (DI6T), remain at the same level (AMg6, V"l'5-1) or even increase (H 18NIOT). However, for all the materials the Os/a ~ ratio in biaxial tension is higher than that in the uniaxial tension within the whole temperature range. Therefore, in more severe stress states (for example, under triaxial tension in the stress concentrator zone where the deformation is constrained) conditions may be created favourable for brittle fracture. Thus, one can reasonably assume that in practical work one of possible reasons for brittle fracture or for the loss in load carrying capacity of structures manufitctured of materials sufficiently plastic at room and low temperatures is the exhaustion of plasticity and fracture at the regions where severe stress state is induced at rather high stress levels. The results of the investigations carried out at the Institute for Problems of Strength of the Academy of Sciences of the Ukrainian SSR point to the need in further broadening of the experimental studies aimed at rational accumulation of data on the physical and mechanical properties of cryogenic materials in complex stress state with subsequent simulation of the respective phenomenological patterns of deformation and fracture applicable for practical calculations.
REFERENCES
I. N, V. Novikov, A. A. l.~bcdcv and B. i. Kovalchuk, Mechanical Testing of Structural Materials at Low Temperatures. Naukova Dumka, Kiev (1974).
2. A. A. Lcbedev, B. [. Kovalchuk and N R. Muzika, Methods and equipment for experimcnt-,d investigation of deformation and strength of materials under complex stress state over a wide temperature range, in 5th All-Union Congress on Theoretical and Applied Mechan-
ics (Abstracts), pp. 193--194. Alma-Ata (1981). 3. V. N. Bilan, V. G. Grishko, B. [. Kovalchuk and A. A.
Lcbcdev, Automatic experiment control system for studying mechanical properties of materials under complex stress conditions. ProbL Prochn. 5, 109-112 (t977). 4. A. A. I.,¢bcdcv, V. V. Kosarchuk and B. |. Kovalchuk, Study of the scalar and vector properties of anisotropic materials under complex loading. Report N I. Yield condition of anisotropic materials. Probl. Prochn 3, 23--31 (1982). 5. B. !. Kovalchuk, Y. V. Kosarchuk and A. A. Lebedev, Scalar and vector propcrtics of anisotropic materials in a complex stress state. Report 2. Plastic deformation of anisotropic matcrials under simple loading. Probl Prochn. 8, 114-121 (1982). 6. A. A. Lcbedev, N. V. Novikov, B. !. Kovalchuk and V. P. Lamashevsky, Plasticity and fracture of ductile structural alloys under plane stress at low temperatures. Adt,. Cry. Engng 22, 102-108 (1976).
0094-57f3.S,g4 $ 3 0 0 + 0 0 PesBsmoa Press l.zd.
E X P E R I M E N T A L STUDY OF THE EFFECT OF THE TYPE OF STRESS STATE ON PLASTIC STRAIN IN S T R U C T U R A L MATERIALS AT LOW T E M P E R A T U R E S G. S. PLS~'tENKO,? A. A. LEBEDEV and B. I. KOVALCHUK Institute for Problems of Strength of the Academy of Sciences of the Ukr. SSR, Timiryazevskaya str. 2, Kiev 14, 252014, U.S.S.R.
(Received 13 December 1983) Abstract--The analysis is made of modern methods and equipment for testing materials at cryogenic temperatures. The authors describe an automated complex developed at the Institute for Problems of Strength of the Academy of Sciences of the Ukr. SSR for low-temperature tests of structural materials under conditions of controlled biaxial loading which imitates the operation of cryogenic vessels and pipe-lines. Analyzed are the results of experimental investigations into the laws of elasto-plastic deformation which were carried out on the materials of different grades loaded in accordance with complex programs over a wide temperature range. Main attention is given to new effects which are associated with the influence of cooling on the process of deformation under conditions of stress state variation. Variants are presented of analytical description within the framework of the elasto-plasticdeformation theory of the experimentally established laws.
The published data on the effect of temperature on
mechanical propertiesof structuralmaterials used in cryogenic rocket and space engineering are obtained, as a rule, in uniaxial tension tests of specimens. However, an overwhelming majority of actual structures components operate under complex conditions of mechanical and thermal effects.Their strength is determined not only by the level of operating temperatures, but also by the type of stress state. Therefore, to assess and predict the load carrying capacity of the components it is important to study the mechanical behaviour o f materials under a variety of combinations of stress tensor components. Systematic studies of deformation mechanism and strength criteria for structural materials at low temperatures in complex stress state are conducted at the Institute for Problems o f Strength of the Academy of Sciences of the Ukrainian SSR. A complex of experimental equipment has been developed at the Institute which allows one to investigate the laws o f elastoplastic deformation and strength of materials under these conditions within the temperature range from 20 to 1200 K.
onto the specimen, working chamber, specimen heating and cooling system and strain measuring system (Fig. I). The working chambers of the testing unit make it possible to conduct measurements in inert gas or in vacuum.
The set-ups employ a unique temperature-control system incorporating a thermal element placed inside the specimen (a flow-through cooler for lowtemperature tests and an electric heater for hightemperature tests) and the monitoring equipment unit.
For measuring strains in the specimen working section the electromechanical extensometers of various design employing the resistancestraingauges are used.
This complex includes set-ups for testingthin-wall tubular specimens by axial force,torque and internal pressure, cross-shaped specimens in biaxial tension, as well as flat specimens of membrane type and pressure vesselscomponents by hydrostatic buckling technique[I]. Set-ups for testing tubular specimens at the temperature from I00 to 1200 K comprise a hydraulic testing machine, pressure unit for creating pressure fAcademy Member (Secuon I).
483
Mechanical propertiesof sheet materials in biaxial tension are studied using 2-8 m m thick round and cross-shaped specimens within the temperature range from 30 to 293 K[2]. The set-up for testingmembranes of up to 300 m m in diameter by the hydrostatic buckling technique (Fig. 2) incorporates a cryostat with a device for fixingspecimens, pressure generating system, vacuum system, cooling system, extensometers for measuring strains and the monitoring equipment. Precooling of the specimen down to 97 K and of the fixing device is realized by liquid nitrogen. Further cooling of the specimen working section to 2 0 K is realized by helium vapours with the aid of an atomizer. The specimen fixing device incorporates a set of special fiat springs made as rings with notches ensuring smooth bending of the specimen and preventing its fracture at the point of fastening.
G, S. Ft~J~)~o
4~,M
tt d.
¢ Fig. I. Tubular specimen tcst ~t: (I) tcsting machine; (2) pressure unit; (3) vacuum working chamber; (4) specimcn cooling system; (5) sFm.imcn heating systcm; (6) strain measuring system; (7) pumps; (8, 9) monitoring and distributing hydraulic equipment. ?
5
8
9
4
12
3 2
,
• ~
114
_13
l--
Fig. 2. Membrane test set: (I) vacuum chamber; (2) nitrogen shield; (3) cryostat housing; (4) fixing device; (5) cover; (6) pipe ~cket; (7, 8) strain measuring system; (9) atomizer; (10) specimen: (I I) washer; (12) matrix; (13) compressed gas cylinder; (14) vacuum pump. The set-up for testing cross-shaped specimens (Fig. 3) comprises hydraulic loading system consisting of four cylinders, a cryostat, specimen cooling system, vacuum system and strain measuring system. To reduce heat input to the specimen, the nitrogen
shields arc employed along with a system of flexible coolant ducts which serve to supply coolant to the machine grips. The specimen ends are cooled with the aid of special bellows contact coolers into which liquid helium is supplied. Strains in the working section of the specimen are measured visually with the help of grids, as well as by electro-mechanical extensometers. The experimental set-ups are provided with the test automatic control system (Fig. 4) which automatically follows the preset program of multicomponent loading of specimens, outputs and processes the experimental data in real time and prints out the calculation results[3]. The system incorporates the stress and strain gauges, extensometer measurements amplifier, switch, analog-to-digital converter, servomotors of load controllers, electric drive control unit and computer. The system provides the mode of automatic loading following the preset trajectory in the coordinates of real stresses or strains. The experimental equipment made it possible to carry out thorough investigation into the laws of elasto-plastic deformation and of the criteria of ultimate state for materials of various classes. Our work deals with the results of testing chromium-nickel steel HI8NIOT, aluminium alloys DI6T, AMg3, AMg6, AMnS and titanium alloy VTS-I which found their widespread application in cryogenic engineering. The experiments were carried
Stress state on plastic strain in structural materials at low temperatures
2
3
4
5
B7-23 r-'-'l
6
MCP60 r"-I
KM-8
tlr
485
M 244
toY9
I
Y
• #
"~
1:5
14
Fig. 3. Cross-shaped specimen test set: (I) hydraulic cylinder; (2) vessel for nitrogen; (3) flexible coolant ducts; (4) specimen: (5) sylphon chamber; (6) optical system for strain measuring; (7) temperature registering system; (g)joint; (9) cryostat; (10) grips: (I I, 12) reducing valves; (13) electrohydraulic system: (14) vacuum pump.
SNT-~PM I converterdiqtolAnat°g-to"
I.
I
1
t,, . I Scanner
Computer
AmpLifier I
t
Printer
l
}
J
Looa control ~n,t
121 I~t
Fig. 4. Experiment automatic control system. out using tubular specimens made of 4 0 - 5 0 mm diameter bars. Steli H iSN 10T was hardened (heated to 1370 K with subsequent cooling in water). The rest of the materials were in as-delivered-state. The testing of specimens in uniaxial tension in the axial and tangential directions has shown that steel H 18N 10T, by its yield strength and tensile strength, is virtually isotropic. The aluminium and titanium alloys arc fairly anisotropic and offer a considerable resistance to plastic deformation as well as possess a significant plasticity in axial tension. The moduli of elasticity of the alloys in the axial and tangential directions differ by 10% on the average. Here, in DI6T, AMg6 and VT5-1 alloys the directions corresponding to the maximum values of the elasticity
moduli and to the maximum values of strength characteristics do not coincide. A reduction in the test temperature is accompanied by an increase in the strength of materials. The palsticity of the aluminium alloys during cooling becomes somewhat greater, while that of the chromium nickel steel and titanium alloys slightly drops. Here, it is necessary to mention that reduction in temperature entails a reduction in anisotropy of the alloys. The investigations performed with the initially anisottopic alloys proved that the generalized stress-strain curves in the coordinate axes of stress intensity and strain intensity corresponding to different ratios of principal stresses do not coincide
G.S. PISARENICOet
480 r
I
al.
I
T,293 K
,b
~---'-
~
7S.- =
/,,...~..
°'1
-
..--3
L
°
2 -
4 .-
---
--o°
~00
r.l,o
K ~
/
~'" ~
Z FI
300 i / ~
"
~3
20O 0
J
2
3 ~j
\4
4
5
(*/.)
Fig. 5. Slress-strain curves of aluminium alloy AMg6 at various ratios of principal stres~s: (I) k = o,/o 2 - ~:; (2) k = I; (3) k =0.5; (4) k =0.
either at room or at low temperatures (Fig. 5). As the temperature drops a fan of curves does not spread: absolute deviations remain the same. However. at low temperatures the values of current stresses are considerably highcr, and therefore, as the tcmperaturc drops the relative value of deviations becomes smaller. In the region of minor deformation in initially anisotropic media rectilinear trajectories of plastic swains correspond to proportional loading, but the guide stress and swain tensors do not coincide. The angle between the trajectories of loading and of plastic deformation depends on the orientation of the loading trajectory in the stress space. Under proportional loading plastic strain trajectories are normal to the smooth portion on the yield surface which is described by the following equation[4] 'I ~ / [ a , 2 + ~2(a22 + o) z) - a,o5 - o , a j
GIS
-(2~-
Io,-,,,I =
l)(r.,(rj] + ~
where k = I; 1 = 3: at (o t -
I,
Gj)/(O2-oj)
(1)
t> (~; k = 2; ~<(at - 0 2 ) / ( 0 2 - o~); k = I; / = 2 : at ( a t - o 2 ) / ( o 2 - o j ) - . < ~ ; ~.=otslo,s; a~s. o,.s are the yield strength in the axial and tangential directions. in the stress space, condition ( ! ) is interpreted as a singular cylindrical surface parallel to the hydrostatic axis with the deviatoric cross section as an irregular curvilinear hexagon (Fig. 6). I = 3: a t
Fig. 6. Deviatoric cross-sections of yield surfaces, corresponding to different yield conditions. Curves obtained with: I: yon Mises-Hill condition; 2: Coulomb--Tresca condition; 3: condition (I).
( a t - 0 3 ) / ( 0 2 - 03) ~< ~
in the case of loading via angular point the loading and plastic strain trajectories coincide. The obtained results allowed the authors to write the relation between the stresses and plastic strains in the orthotropic media for the smooth portion of the yield surface[5] ~,P(o',) e~=(~
;If
aS,,Of " aS,~/afl "Z aS"'
(2)
(k, Lm.n,
=1,2,3). where S,,, are the stress deviator components; a, = a,(~,e) is the function invariant to the type of stress state; stress o, is determined by the yield criterion, i.e. a, = cf(S,). The stress-strain relationship for the trajectory running via the angular point is as follows
3 ~,r(a,) _ '' = 5
(3)
The investigations carried out with austenitic chromium-nickel steel H l g N I 0 T proved that a reduction in temperature effects considerably the nature of strain hardening of the steel in complex stress state. When some level of plastic deformation is reached, a zone of intensive hardening appears which is related to phase transformations. A nonmonotonous dependence of the lateral strain factor on the degree of deformation is observed: at ~, > 5--6%, a significant reduction in this factor takes place, thus indicating a residual change in the steel volume (Fig. 7). Here, as the transition from uniaxial to uniform biaxial tension proceeds, the intensity of residual volume ~ increase in the process of deformarion declines. A reduction in temperature upsets the invariance of curves (r, = cr,(¢,) to the type of stress
Stress state on plastic strain m structural materials at
•
~" 400
/
K
~.,.®
;,,o~
3 (, (*' = 2 (pC(,, T,
f
200
"*,05
k,i
T,293
4
8
487
temperatures
state, while a similarity between stress and strain deviators is retained. The obtained results made it possible to determine the stress-strain relationship for structurally unstable media in the case of proportional loading in the following form
.ltO K 600
low
- 6,#'0)
xJ (~,a
¢0
(%)
(
(4)
+6,1 ~K + m
04 -
:d
OZ
0
I0
5
where x,, are some o f the structural parameters; K is the bulk m o d u l u s o f elasticity; ~o is the mean stress, oo = ~6,#.,t, 6,~ is the Kronecher's symbol.
The functions of hardening ~ ¢~((,, 7", K,.) and of the residual change in volume ~ J = ( J ( ( , , K J are =
,~o
15
% /
Fig. 7. Results of nickel-chromium steel tests at various ratios
o" ~ ( M P a ) e
r,293
of pnncipal stres~s.
K
I
.,~
L~2
o', (MPo) r,93 K
~oo T,293 K ,/~----"u" / 400 /
HISNIOT
/
|
)
t20o
_/ /
-300
I00
0" i
2000
/
•
200
300
400
(MPo)
] t
16OO
I I I
f200
i
0
|
400
,u
T.II3 K
0" 2 ( M P o )
(a)
1200
1600 ' '
2[0' 0 0
~
t
VTS-I
ottoy
o.//"
I
t
000
I
o
I I I
..oo
-400
0
o
'
-800
-I00
0"2 (MPo)
/
/
-200
L~.2
I I
K
/
"1
,
I I
•800
/
-,,
-;-
"
/
T,II3
DI6T oU.oy ~ --
o
T.I?3 K
/
L-dOO
L'--
/--I'--
[
;/
/
steel
-1200
-800
-400
0
,
,
J!
400
800
1200
O*2 ( M P o }
(b)
Fig. 8. Yield and ultimatc stn:ngth limiting curves of HI8NIOT steel (a). DI6T alloy and V'['5-1 alloy (b): h yon Mises condition, 2: Coulomb--Tn~a condition; 3: condition (I),
488
G. S. ~ . ' ~ o
04
l
/o °°t
_ Io,l
05L
I
l
04
o6
I
0,.. ~ 0._ ~ _.,.. ,.0
~
oa
t
_(cl
Or
I
l
(d)
0
3 -200
I
~ -~00
el 0
T ('C) Fig. 9. Temperature relationships of the ratio of yield strength to ultimate strength: (at carbon steel (0.37"/,C); (b) DI6T alloy; (el VTS-I alloy; (d) AMg6 alloy; (¢l chromium nickel steel !-I18N I0T. specified on the basis of combined mechanical and structural studies of steel. The investigations of the ultimate state of chromium-nickel steel, aluminium and titanium alloys[rJ showed that with a decrease in temperature the region bounded on the limiting yield and strength curves extends without noticeable change in its shape (Fig. 8). Both at room and low temperatures the onset of HI8NIOT steel yielding under conditions of plane stress state corresponds to yon Mises condition for isotropic bodies. Transition of aluminium and titanium alloys into plastic state can be well described by criterion (I) which generalizes the yon Mises-Hill and St. Venant-Tresca condition. The strength of steel and alloys at room and low temperatures is in satisfactory agreement with the St. Venant-Tresca condition for the anisotropic and isotropic bodies, respectively. Brittle state of a metal is usually associated with some critical temperature (or temperature range) corresponding to a sharp reduction in paisticity, i.e. to such a state of the metal when the ultimate plastic strain e e l 0 , or as~Ok-, I. The use of the offset yield strength to the ultimate strength ratio as a parameter characterizing the plasticity available in the material under preset temperature and loading conditions offers ready assessment of the effect of the type of
et al.
stress state on the brittleness critical temperature. For the materials studied temperature dependences of the Os/(7b ratio were determined for the uniaxial and biaxial tension (Fig. 9). With allowance made for anisotropy and inevitable scatter of the experimentally determined characteristics, the yield strength and the ultimate strength axe assumed to be equal in uniaxial tension to the mean values of the respective magnitudes for the axial and tangential directions, while in biaxial tension these are the mean values obtained for ot/o 2 = 0.5 and o~ a, = 1. it is found out that the plasticity available in the materials considered can decrease (DI6T), remain at the same level (AMg6, V"l'5-1) or even increase (H 18NIOT). However, for all the materials the Os/a ~ ratio in biaxial tension is higher than that in the uniaxial tension within the whole temperature range. Therefore, in more severe stress states (for example, under triaxial tension in the stress concentrator zone where the deformation is constrained) conditions may be created favourable for brittle fracture. Thus, one can reasonably assume that in practical work one of possible reasons for brittle fracture or for the loss in load carrying capacity of structures manufitctured of materials sufficiently plastic at room and low temperatures is the exhaustion of plasticity and fracture at the regions where severe stress state is induced at rather high stress levels. The results of the investigations carried out at the Institute for Problems of Strength of the Academy of Sciences of the Ukrainian SSR point to the need in further broadening of the experimental studies aimed at rational accumulation of data on the physical and mechanical properties of cryogenic materials in complex stress state with subsequent simulation of the respective phenomenological patterns of deformation and fracture applicable for practical calculations.
REFERENCES
I. N, V. Novikov, A. A. l.~bcdcv and B. i. Kovalchuk, Mechanical Testing of Structural Materials at Low Temperatures. Naukova Dumka, Kiev (1974).
2. A. A. Lcbedev, B. [. Kovalchuk and N R. Muzika, Methods and equipment for experimcnt-,d investigation of deformation and strength of materials under complex stress state over a wide temperature range, in 5th All-Union Congress on Theoretical and Applied Mechan-
ics (Abstracts), pp. 193--194. Alma-Ata (1981). 3. V. N. Bilan, V. G. Grishko, B. [. Kovalchuk and A. A.
Lcbcdev, Automatic experiment control system for studying mechanical properties of materials under complex stress conditions. ProbL Prochn. 5, 109-112 (t977). 4. A. A. I.,¢bcdcv, V. V. Kosarchuk and B. |. Kovalchuk, Study of the scalar and vector properties of anisotropic materials under complex loading. Report N I. Yield condition of anisotropic materials. Probl. Prochn 3, 23--31 (1982). 5. B. !. Kovalchuk, Y. V. Kosarchuk and A. A. Lebedev, Scalar and vector propcrtics of anisotropic materials in a complex stress state. Report 2. Plastic deformation of anisotropic matcrials under simple loading. Probl Prochn. 8, 114-121 (1982). 6. A. A. Lcbedev, N. V. Novikov, B. !. Kovalchuk and V. P. Lamashevsky, Plasticity and fracture of ductile structural alloys under plane stress at low temperatures. Adt,. Cry. Engng 22, 102-108 (1976).