A constitutive model for the high-temperature creep of particle-hardened alloys based on the ? projection method

The θ projection method is a procedure for the interpolation and extrapolation of creep properties. It works by describing the shape of conventional creep curves by suitable mathematical functions and then by projecting those curves to different stresses and temperatures. It involves techniques for the collection of data that enable large amounts of information to be summarized and this paper explores the possibility that this information–rich method can be extended to give a constitutive creep relationship for component analysis. A general framework involving a variety of hardening, recovery and damage mechanisms is evolved and the relationships between the required experimental parameters and the θ values are derived. The collection of data is illustrated with respect to a wrought superalloy (Waspaloy), creep tested in uniaxial and multiaxial stress conditions. The material is shown to be isotropic with a creep potential function equal to the second deviatoric stress invariant and the resulting flow rule, together with the constitutive relationship, is applied to the creep of notched bars by a finite–element procedure. The analysis incorporates a stress–dependent failure criterion and is shown to predict the experimentally observed notch hardening successfully. In addition, it correctly describes the failure paths in this quasi–static situation. The implications of the relationships with regard to design methods which use skeletal stresses are discussed.

[1]  J. Boyle,et al.  Chapter 5 – Stress analysis for steady creep , 1983 .

[2]  B. F. Dyson,et al.  Continuous cavity nucleation and creep fracture , 1983 .

[3]  Steve Brown,et al.  New approach to creep of pure metals with special reference to polycrystalline copper , 1987 .

[4]  E. Krempl,et al.  Models of viscoplasticity some comments on equilibrium (back) stress and drag stress , 1987 .

[5]  J. Weertman.  Theory of internal stress for class I high temperature creep alloys , 1977 .

[6]  Steve Brown,et al.  Creep strain and creep life prediction for the cast nickel-based superalloy IN-100 , 1986 .

[7]  R. Evans,et al.  A re-interpretation of r and h measurements during creep , 1985 .

[8]  David R Hayhurst,et al.  Creep stress redistribution in notched bars , 1977 .

[9]  O. C. Zienkiewicz,et al.  VISCO-PLASTICITY--PLASTICITY AND CREEP IN ELASTIC SOLIDS--A UNIFIED NUMERICAL SOLUTION APPROACH , 1974 .

[10]  B. Dyson.  Constraints on diffusional cavity growth rates , 1976 .

[11]  Yuri Estrin,et al.  A unified phenomenological description of work hardening and creep based on one-parameter models , 1984 .

[12]  D. R. J. Owen,et al.  Engineering approaches to high temperature design , 1983 .

[13]  I. M. How,et al.  Techniques for multiaxial creep testing , 1987 .

[14]  R. T. Fenner,et al.  Steady-State stress distributions in circumferentially notched bars subjected to creep , 1982 .

[15]  M. F. Ashby,et al.  CREEP DAMAGE MECHANICS AND MICROMECHANISMS , 2013 .

[16]  D. Mclean.  REVIEW ARTICLES: The physics of high temperature creep in metals , 1966 .

[17]  D. Owen,et al.  Recent Advances in Creep and Fracture of Engineering Materials and Structures , 1982 .

[18]  Yiu-Wing Mai,et al.  Advances in Fracture Research , 1997 .

[19]  M. Manjoine.  Size Effect on Notched Rupture Time , 1962 .

[20]  M. Loveday,et al.  Practical Aspects of Testing Circumferential Notch Specimens at High Temperature , 1986 .

[21]  A. Johnson.  COMPLEX-STRESS CREEP OF METALS , 1960 .

[22]  J. Chaboche.  Constitutive equations for cyclic plasticity and cyclic viscoplasticity , 1989 .

[23]  J. Spence,et al.  Chapter 11 – Design for creep , 1983 .

[24]  I. Cormeau,et al.  Numerical stability in quasi‐static elasto/visco‐plasticity , 1975 .

[25]  J. Hancock.  Creep cavitation without a vacancy flux , 1976 .

[26]  D. R. Hayhurst,et al.  Skeletal point stresses in circumferentially notched tension bars undergoing tertiary creep modelled with physically based constitutive equations , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[27]  R. Evans,et al.  Creep behaviour of crystalline solids , 1985 .

[28]  B. Ule,et al.  Modification of θ projection creep law by introducing mean stress term , 1997 .