 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| << Previous article | Volume 44, Issue 4 / 2009 | Next article >> |
| A. V. Khokhlov, "Fracture Criteria under Creep with Strain History Taken into Account, and Long-Term Strength Modelling," Mech. Solids. 44 (4), 596-607 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
4 |
Pages |
596-607 |
| DOI |
10.3103/S0025654409040104 |
| Title |
Fracture Criteria under Creep with Strain History Taken into Account, and Long-Term Strength Modelling |
| Author(s) |
A. V. Khokhlov (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192 Russia, andrey-khokhlov@yandex.ru) |
| Abstract |
In the present paper, we continue to study the nonlinear
constitutive relation (CR) between the stress and strain proposed in [1] to describe one-dimensional isothermal rheological processes in the case of monotone variation of the strain (in particular, relaxation, creep, plasticity, and superplasticity).
We show that this CR together with the strain fracture criterion (FC) leads to theoretical long-term strength curves (LSC) with the same qualitative properties as the typical experimental LSC of viscoelastoplastic materials. We propose two parametric families of fracture criteria in the case of monotone uniaxial strain, which are related to the strain fracture criterion (SFC) but take into account the strain increase history and the dependence of the critical strain on the stress. Instead of the current strain, they use other measures of damage related to the strain history by time-dependent integral operators. For any values of the material parameters, analytic studies of these criteria allowed us to find several useful properties, which confirm that they can be used to describe the creep fracture of different materials. In particular, we prove that, together with the proposed constitutive relations, these FC lead to theoretical long-term strength curves (TLSC) with the same qualitative properties as the experimental LSC. It is important that each of the constructed families of FC forms a monotone and continuous scale of criteria (monotonously and continuously depending on a real parameter) that contains the SFC as the limit case. Moreover, the criteria in the first family always provide the fracture time greater than that given by the SFC, the criteria in the second family always provide a smaller fracture time, and the difference can be made arbitrarily small by choosing the values of the control parameter near the scale end. This property is very useful in finding a more accurate adjustment of the model to the existing experimental data describing the fracture time dependence on the stress, temperature, radiation, and other factors: if these data are poorly described by the SFC, then one can choose a more appropriate criterion from the constructed families by varying the value of the control parameter smoothly and monotonously.
For any admissible values of the model determining parameters, we derive the TLSC corresponding to the proposed fracture criteria. Studying the dependence of their properties on the material function and on the material parameters of the CR and FC, we can state the requirements on the TLSC that follow from the general qualitative properties of experimental LSC of different viscoelastoplastic materials and obtain the corresponding restrictions on the material parameters and the model function. |
| Keywords |
creep, rheology, long-term strength, fracture criterion |
| References |
| 1. | V. N. Kuznetsov, A. V. Khokhlov, and S. A. Shesterikov,
"Constitutive Relations for Rheological Processes,"
Electronic Journal "Investigated in Russia"
6, 152-160 (2003),
http://zhurnal.ape.relarn.ru/articles/2003/016.pdf. |
| 2. | A. V. Khokhlov,
"Constitutive Relation for Rheological Processes: Properties of Theoretic Creep Curves and Simulation of Memory Decay,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 147-166 (2007)
[Mech. Solids (Engl. Transl.)
42 (2), 291-306 (2007)]. |
| 3. | A. V. Khokhlov,
"An Extension of the Constitutive Equation for Rheological Processes and New Properties of the Theoretic Creep Curves,"
in Advanced Methods in Validation and Identification
of Nonlinear Constitutive Equations in Solid Mechanics (EUROMECH Colloquium 458)
(Moscow, 2004),
pp. 44-46. |
| 4. | W. A. Day,
The Thermodynamics of Simple Materials with Fading Memory
(Springer, Berlin, Heidelberg, New York, 1972; Mir, Moscow, 1974). |
| 5. | V. D. Klyushnikov,
Physical-Mathematical Foundations of Strength and Plasticity
(Isd-vo MGU, Moscow, 1994)
[in Russian]. |
| 6. | Yu. G. Basalov, V. N. Kuznetsov, and S. A. Shesterikov,
"Constitutive Relations for a Rheonomous Material,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 69-81 (2000)
[Mech. Solids. (Engl. Transl.)
35 (6), 55-66 (2000)]. |
| 7. | J. E. Fitzgerald and J. Vakili,
"Nonlinear Characterization of Sand-Asphalt Concrete
by Means of Permanent-Memory Norms,"
Proc. SESA
30 (2), 504-510 (1960). |
| 8. | Yu. N. Rabotnov,
Mechanics of Deformable Solids
(Nauka, Moscow, 1979)
[in Russian]. |
| 9. | Yu. N. Rabotnov,
Creep of Construction Elements
(Nauka, Moscow, 1966)
[in Russian]. |
| 10. | A. M. Lokoshchenko,
Creeping and Long-Term Strength of Metals in Aggressive Media
(Isd-vo MGU, Moscow, 2000)
[in Russian]. |
| 11. | A. V. Khokhlov,
"Constitutive Relation for Rheological Processes with Known Loading History,"
Electronic Journal "Investigated in Russia"
8, 355-365 (2005),
http://zhurnal.ape.relarn.ru/articles/2005/032.pdf. |
| 12. | A. V. Khokhlov,
"Constitutive Relation for Rheological Processes with Known Loading History. Creep and Long-Term Strength Curves,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 140-160 (2008)
[Mech. Solids (Engl. Transl.)
43 (2), 283-299 (2008)]. |
|
| Received |
05 December 2006 |
| Link to Fulltext |
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