共查询到20条相似文献,搜索用时 31 毫秒
1.
Summary This paper discusses the nature of an approximate solution for the hollow circular cylinder whose fixed ends are given a uniform relative axial displacement and whose cylindrical surfaces are free from traction. We shall take the solution of this problem to be given by a super-position of the following two problems: problem I considers a finite length cylinder whose ends are given a relative axial displacement, but are no longer fixed; problem II removes the radial displacement at the end of the cylinder obtained in problem I.Nomenclature a
mid-surface radius of cylinder
- c
half-height of cylinder
- E,
in-plane elastic moduli
- Et,
t, Gt
transverse elastic moduli
- z, , r
axial, circumferential, and normal strain
-
rz
transverse shear strain
- h
cylinder thickness
- z, , r
axial, circumferential, and normal stress
-
rz
transverse shear stress
- z, r
axial and radial coordinates
- uz, ur
axial and normal displacements 相似文献
2.
Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.
Nomenclature yy longitudinal tensile stress in the notch tip plastic zone - xx transverse stress in the x-direction - zz transverse stress in the z-direction - k yield stress in shear - 0 yield stress in tension - 0 * strain hardened yield stress (flow stress) - 0/* c flow stress at notch tip - total total strain pl plastic strain l principal strain - 1 c maximum principal strain at notch tip - 1pl plastic strain in they-direction - 1 cp1 E1 pl at notch tip - eff effective plastic strain - c eff eff at notch tip - 0 yield strainC Stress decay constant in the notch tip region - /epl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k I applied stress intensity for Mode I loading - E Young's modulus - V c crack tip opening displacement 相似文献
Résumé En utilisant les résultats d'analyses de contrainte élastoplastique dans le cas de barres entaillées, on montre qu'il est possible d'utiliser une forme simplifiée de solution du champ des lignes de glissement pour expliquer de façon satisfaisante la variation des contraintes longitudinales en avant d'extrémités d'entaille dans des matériaux susceptibles d'un écrouissage.
Nomenclature yy longitudinal tensile stress in the notch tip plastic zone - xx transverse stress in the x-direction - zz transverse stress in the z-direction - k yield stress in shear - 0 yield stress in tension - 0 * strain hardened yield stress (flow stress) - 0/* c flow stress at notch tip - total total strain pl plastic strain l principal strain - 1 c maximum principal strain at notch tip - 1pl plastic strain in they-direction - 1 cp1 E1 pl at notch tip - eff effective plastic strain - c eff eff at notch tip - 0 yield strainC Stress decay constant in the notch tip region - /epl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k I applied stress intensity for Mode I loading - E Young's modulus - V c crack tip opening displacement 相似文献
3.
Dr. inż. M. Rysz 《Acta Mechanica》1987,66(1-4):83-102
Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation
A
cross-sectional area
-
C, ,
creep rupture constants
-
K, n,
C
,
C
creep constants
-
F
dimensionless creep modulus
-
M
bending moment
-
N
axial force
-
a(),b()
internal and external radii of the cross-section
-
j
creep modulus
-
p
internal pressure
-
r, ,z
cylindrical coordinates
-
s
r
,s
,s
z
,t
r
dimensionless stresses
-
t
R
time to rupture
-
stress function
- , ()
dimensionless internal and external radii
-
e
effective strain rate
-
kl
strain rates
-
rate of curvature
-
rate of elongation of the central axis
-
dimensionless radius
-
e
effective stress
-
I
maximal principal stress
-
S
Sdobyrev's reduced stress
-
r
,
,
z
,
r
components of the stress tensor
-
measure of material continuity
-
measure of deterioration
With 7 Figures 相似文献
4.
Dershin Gan 《Journal of Materials Science》1982,17(1):89-99
A new method was developed to study the Bailey-Orowan equation of creep,
c=r/h, where
c is the creep rate,r is the recovery rate andh is the work-hardening coefficient. The method was to vary the strain rate,, around the creep rate,
c, and to measure the corresponding stress rate,. In a plot of stress rate against strain rate, a straight line was obtained. The slope of the straight line was equal toh, and the intersection of the straight line with the stress axis was equal to –r, as in the equation=–r+h. The creep test under a constant stress is a special case of this equation when the stress rate,, is zero. The above measurement was carried out within a very small stress variation, less than 1% of the total stress, so that the values ofr andh were not disturbed. The creep test was performed on Type 316 stainless steel. The creep rate was shown to be equal to the ratior/h, but the value ofh was approximately equal to Young's modulus at the testing temperature, rather than, as is commonly believed, to the work-hardening coefficient. 相似文献
5.
The dielectric constants and loss factors,, for pure single-crystal MgO and for Fe-and Cr-doped crystals have been measured at frequencies, , from 500 Hz to 500 kHz at room temperature. For pure MgO at 1 kHz the values of and the loss tangent, tan , (9.62 and 2.16×10–3, respectively) agree well with the data of Von Hippel; the conductivity, , varies as
n
withn=0.98±0.02. In Fe-doped crystals increases with Fe-concentration (at any given frequency); for a crystal doped with 12800 ppm Fe, was about four times the value for pure MgO. At all concentrations the variation of log with log was linear andn=0.98±0.02. A decrease in with increasing Fe-concentration was also observed. A similar, although less pronounced, behaviour was found in Cr-doped crystals. The effects are discussed in terms of hopping mechanisms. 相似文献
6.
J. S. Thorp A. B. Ahmad B. L. J. Kulesza S. V. J. Kenmuir 《Journal of Materials Science》1984,19(10):3211-3216
Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-t8)(n–1) and '(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies. 相似文献
7.
The a.c. electrical conductivity (
ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO4 are presented.
ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity =
0 exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)–1 cm–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K. 相似文献
8.
The effect of antimony on the creep behaviour (dislocation creep) of a 25 wt% Cr-20 wt% Ni stainless steel with ~ 0.005 wt% C was studied with a view to assessing the segregation effect. The antimony content of the steel was varied up to 4000 ppm. The test temperature range was 1153 to 1193 K, the stress range, 9.8 to 49.0 MPa, and the grain-size range, 40 to 600m. The steady state creep rate,
, decreases with increasing antimony content, especially in the range of intermediate grain sizes (100 to 300m). Stress drop tests were performed in the secondary creep stages and the results indicate that antimony causes dislocations in the substructure to be immobile, probably by segregating to them, reducing the driving stress for creep.Nomenclature
a
Creep stress in a constant load creep test without stress-drop
-
A
Initial applied stress in stress-drop tests
-
Stress decrement
- (
A-)
Applied stress after a stress decrement,
- t
i
Incubation time after stress drop (by the positive creep)
-
C
Strain-arrest stress
-
i
Internal stress
-
s
s-component (=
i-
c)
-
Steady state creep rate (average value) in a constant load creep test
-
Strain rate at time,t, in a constant load creep test
-
New steady state creep rate (average value) after stress drop from
A to (
A-)
-
Strain rate at time,t, after stress drop. 相似文献
9.
Some fibrous composites exhibit different mechanical properties in tension as compared to those in compression. Proper material modelling is required to enable correct behavioural prediction of components made of such composites. Though the models due to Ambartsumyan, Bert and Jones are often used, there are still many unanswered questions pertaining to material modelling. In Bert's model the strain transverse to the fibres and the shear strain are discontinuous when the fibre strain is zero. In Jones' model, cross compliances in tension-compression zones are assumed to depend on the magnitudes of principal stresses.Here we have proposed a new model for bimodulus orthotropic materials with zonewise symmetric linear constitutive laws valid for biaxial fields and dependent on the signs of both normal stresses and strains, referred to material axes. This model maintains strain continuity in the entire biaxial field and has ten independent elastic constants compared to eight each in Bert's and Jones' model. Applicability of the present model is illustrated by considering limited experimental data available on Aramid cord-rubber and ATJ graphite.List of symbols
L, T
Axes parallel and transverse to fibres
-
S
SS
±
Shear compliance for ±
LT
-
S
Lt
,S
Lc
Compliances inL-direction for uniaxial tension and compression applied inL-direction
-
S
Tt
,S
Tc
Compliances inT-direction for uniaxial tension and compression applied inT-direction
-
S
TL
(t)
Cross compliance corresponding to uniaxial load inL- orT-direction maintaining
L
> 0
-
S
TL
(c)
Cross compliance corresponding to uniaxial load inL- orT-direction maintaining
L
< 0
-
S
LL
+,S
TT
+,S
TL
+
Compliances when
L
> 0 and
T
> 0
-
S
LL
–,S
TT
–,S
TL
–
Compliances when
L
< 0 and
T
< 0
-
S
Lt
–
Compliance inL-direction when
L
< 0 under the combined action of tensile
L
and
T
-
S
Tt
–
Compliance inT-direction when
T
< 0 under the combined action of tensile
L
and
T
-
S
Lc
+
Compliance inL-direction when
L
> 0 under the combined action of compressive
L
and
T
-
S
Tc
Compliance inT-direction when
T
> 0 under the combined action of compressive
L
and
T
- 1 , 2 ; 3, 4
Parameters defined in Eqs. (12); (12)
-
L
,
T
,
LT
Strains with respect toL-,T-axes
-
L
,
T
,
LT
Stresses with respect toL-,T-axes
-
Orientation of fibres with respect toL-axis
-
S
11,S
21
Compliances referred to axes oriented at an angle toL-,T-axes 相似文献
10.
This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols
d
diameter of fibre
-
E
f
elastic modulus of fibre
-
E
m
elastic modulus of epoxy
-
G
m
shear modulus of epoxy
-
k
radius of gyration of fibre section
-
l
length of buckle in fibre
-
P
confining pressure (=
2 =
3)
-
R
radius of bent fibre
-
V
f
volume fraction of fibres in composite
-
t,
c
bending strains in fibres
-
angle between the plane of fracture and
1
-
1
principal stress
-
3
confining pressure
-
c
strength of composite
-
f
strength of fibre in buckling mode
-
n
normal stress on a fracture plane
-
m
strength of epoxy matrix
-
shear stress
-
tangent slope of Mohr envelope
-
slope of pressure versus strength curves in Figs. 3 and 4. 相似文献
11.
Effect of crystalline phase, orientation and temperature on the dielectric properties of poly (vinylidene fluoride) (PVDF) 总被引:1,自引:0,他引:1
The effect of crystalline phase, uniaxial drawing and temperature on the real () and imaginary () parts of the relative complex permittivity of poly (vinylidene fluoride) (PVDF) was studied in the frequency range between 102 and 106 Hz. Samples containing predominantly and phases, or a mixture of these, were obtained by crystallization from a DMF solution at different temperatures. phase samples were also obtained from melt crystallization and from commercial films supplied by Bemberg Folien. Different molecular orientations were obtained by uniaxial drawing of and phase samples. The results showed that the crystalline phase exerts strong influence on the values of and , indicating that the a relaxation process, associated with the glass transition of PVDF, is not exclsively related to the amorphous region of the polymer. An interphase region, which maintains the conformational characteristics of the crystalline regions, should influence the process decisively. The molecular orientation increased the values of for both PVDF phases and modified its dependence with temperature over the whole frequency range studied. The influence of the crystallization and molecular orientation conditions on the dc electric conductivity (dc) were also verified. The value of dc was slightly higher for samples crystallized from solution at the lowest temperature and decreased with draw ratio. 相似文献
12.
The dielectric properties of chemically vapour-deposited (CVD) amorphous and crystalline Si3N4 were measured in the temperature range from room temperature to 800° C. The a.c. conductivity (
a.c.) of the amorphous CVD-Si3N4 was found to be less than that of the crystalline CVD-Si3N4 below 500° C, but became greater than that of the crystalline CVD-Si3N4 over 500° C due to the contribution of d.c. conductivity (
d.c.). The measured loss factor () and dielectric constant () of the amorphous CVD-Si3N4 are smaller than those of the crystalline CVD-Si3N4 in all of the temperature and frequency ranges examined. The relationships of
n-1, (-
)
n-1 and/(-
) = cot (n/2) (were observed for the amorphous and crystalline specimens, where is angular frequency andn is a constant. The values ofn of amorphous and crystalline CVD-Si3N4 were 0.8 to 0.9 and 0.6 to 0.8, respectively. These results may indicate that the a.c. conduction observed for both of the above specimens is caused by hopping carriers. The values of loss tangent (tan) increased with increasing temperature. The relationship of log (tan) T was observed. The value of tan for the amorphous CVD-Si3N4 was smaller than that of the crystalline CVD-Si3N4. 相似文献
13.
Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D
rate of strain tensor
-
L
slit halfheight
-
P
pressure, indeterminate part of the Cauchy stress tensor
- R
the Reynolds number
-
t
time
-
U
average velocity in the slit
- u
velocity vector
-
u,v
velocity components
-
W
the Weissenberg number based on the difference between stress relaxation time and retardation time
-
W
1
the Weissenberg number based on stress relaxation time
-
x,y
rectangular Cartesian coordinates
-
ratio of retardation time to stress relaxation time
-
zero-shear-rate viscosity, 1 + 2
- 1
non-Newtonian contribution to
- 2
Newtonian contribution to
- 1
stress relaxation time
- 2
retardation time
-
density
- (, , )
xx, yy and xy components of 1, respectively
-
determinate part of the Cauchy stress tensor
- 1
non-Newtonian contribution to
- 2
Newtonian contribution to 相似文献
14.
A. G. Shashkov S. Yu. Yanovskii 《Journal of Engineering Physics and Thermophysics》1977,33(5):1363-1369
Using the structural approach, the temperature stresses are examined in a semiinfinite rod, insulated on the lateral faces and rigidly fixed at the end. A comparative analysis is made for three heat-transfer models.Notation k(t)
heat flux relaxation function
-
(t)
internal energy relaxation function
- T
rod temperature
-
ambient temperature
- t
time
- x
coordinate along the rod
- xx(x, t)
stress
- u(x, t)
displacement
- (x, t)
deformation
- c0=(E/)1/2
speed of sound in the rod under isothermal conditions
- E
elasticity modulus
-
density of the material
-
t
coefficient of thermal expansion
-
thermal-conductivity coefficient
-
a
thermal-diffusivity coefficient
- b
thermal-activity coefficient
- cq=(a/r)1/2
velocity of heat propagation
- r
heat flux relaxation time
-
(t)
unique Heaviside function
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 912–921, November, 1977. 相似文献
15.
A new high-order model for analysing distribution of temperature in periodic composites is proposed. The original scalar elliptic problem with Y-periodic coefficients (Y is a cube) is replaced with a vectorial elliptic problem of constant coefficients. The unknown fields are: the averaged distribution of temperature and the vector field which stands for perturbation of the temperature within the cells of periodicity. The recovery of temperature in the original composite is given by the approximation: 0(x)=0(x) +h
a
(x/)
a
(x) analogous with the first terms of the two-scale asymptotic expansion known from the homogenization theory. The functions h
are defined as approximations of the solutions to the basic cell problems. In contrast to the two-scale expansion the expression for satisfies the boundary condition. 相似文献
16.
I. M. Nafikov N. Kh. Zinnatullin 《Journal of Engineering Physics and Thermophysics》1980,39(1):750-754
An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n
rhenological constants
-
density
-
surface tension
- r
current cup radius
- R
maximum cup radius
- rc
critical radius for film breakup
- ¯r=¯r=r/R
dimensionless current radius
- ¯rc=rc/R
dimensionless critical radius
-
0,
c
actual and critical film thicknesses
-
current thickness
- Rr
ridge radius
- h0
ridge height
- h
current ridge height
-
0
limiting wetting angle
-
current angle of tangent to ridge surface
-
angle between axis of rotation and tangent to cup surface
-
angular velocity of rotation
- q
volume liquid flow rate
- v1 and v
meridional and tangential velocities
-
=4vv
lm/r,=4vm/r
dimensionless velocities
- M
moments of surface and centrifugal forces
- Mv
moment from velocity head
- pr
pressure within ridge
- Pvm
pressure from velocity head
- pm, ppm
pressures from centrifugal force components tangent and normal to cup surface
-
deviation range of breakup radius from calculated value
- ¯rmax, ¯rmin
limiting deviations of breakup radius
- c
angle of tangent to curve c/°0=f(¯r) at critical point
- t
random oscillation of ratio c/c
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980. 相似文献
17.
E. I. Marchenkov V. I. Aleinikova 《Journal of Engineering Physics and Thermophysics》1977,33(5):1318-1324
The thermal conductivity of neon and argon-neon mixtures is studied in the temperature range 400–1500°K. This is the first recording of such data above 793°K.Notation Tg
true temperature drop in gas layer °K
- ¯T
temperature, °K, Q, effective thermal flux, W
- Qt, Qr
thermal flux transmitted by thermal conductivity and radiation, respectively, W
-
Tsh
correction for temperature shift, %
-
thermal conductivity of gas mixture, W/m·°K
- xi
a molar concentration of neon
- i, i, ij, ij
potential function parameters for inter molecular interaction of homogeneous and inhomogeneous molecules
-
slope of exponential repulsion term
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 848–856, November, 1977. 相似文献
18.
Z. C. Ou 《International Journal of Fracture》2003,119(2):41-46
Two parameters, and (Suo et al., 1992), are of key importance in fracture mechanics of piezoelectric material interfaces. In this paper, it is shown, for any transversely isotropic piezoelectric (TIP) bimaterial, that one of the two parameters and always vanishes but the other one remains non-zero. Physically, it means that the non-oscillating crack-tip generalized stress field singularity exists for some TIP bimaterials (with vanishing ). Consequently, TIP bimaterials can be classified into two classes: one with vanishing performed crack tip generalized stress field oscillating singularity and the other one with vanishing is independent from the oscillating singularity. Some numerical results for and are given too. 相似文献
19.
A. F. Kugaevskii 《Measurement Techniques》1963,6(11):949-952
Conclusions It is possible by means of the above resonator, according to our analysis and in the absence of air gaps between the sample and the line, to evaluate the real components and of permeability and permittivity respectively in the range of 2 to 100 with an error between ±3% and ±10% in the temperature range from room temperature to +400°C, and the imaginary components and (for tan and tan in the range of 0.001 to 2) with an error of 7 to 20% over the same temperature range. 相似文献
20.
An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF's). Analytical derivations of these SIF's for a multicraked plate can be complex and tedious. Recent advances, however, in intelligent application of symbolic computation can overcome these difficulties and provide the means to rigorously and efficiently analyze this class of problems. Here, the symbolic algorithm required to implement the methodology for the rigorous solution of the system of singular integral equations for SIF's is presented. The special problem-oriented symbolic functions to derive the fundamental kernels are described, and the associated automatically generated FORTRAN subroutines are given. As a result, a symbolic/FORTRAN package named SYMFRAC, capable of providing accurate SIF's at each crack tip, has been developed and validated.Simple illustrative examples using SYMFRAC show the potential of the present approach for predicting the macrocrack propagation path due to existing microcracks in the vicinity of a macrocrack tip, when the influence of the microcracks' location, orientation, size, and interaction are accounted for.List of symbols
offset angle between inner tips of two parallel cracks
- lr, mz
direction cosines between two local coordinate systems
- jl
strain tensor
-
offset of notch-microcracks system with respect to Y axis
- k
four roots of the characteristic equation
-
v
Poisson's ratio
-
jl
o
,
jl
T
far-field and total stress field, respectively
-
XX
o
,
YY
o
,
XY
o
components of stress in global coordinate system
- j
angle defining local frame orientation
- ,
normalized real variable
- (s, y)
Fourier transform of Airy stress function with respect to x variable
-
a
j
half crack length
-
a
11, a12, a22
coefficients of strain-stress relationship
-
d
normalized radial (tip) distance
-
f
nj
auxiliary functions
-
k
1, k2
mode-I and mode-II stress intensity factors
-
ker
inf
sup
Fredholm kernels
-
p
j
normal traction at crack surface
-
q
j
shear traction at crack surface
-
s
Fourier variable
-
r
j, rkX, rkY
position vector and its components, for an origin of local frame
-
u, v
x, y component of displacement, respectively
-
w
weight function
-
x
j yjand X, Y
local and global coordinates
- [A]
matrix of coefficients
-
C'
j, Cj
functions of s in Fourier space (i.e., constrants in x, y-real space)
-
E
Young modulus
-
F
j(xj, yj)
Airy stress function
- Gnj(p)
discrete auxiliary function
- {}
loading function vector 相似文献