Notion of Continuum Damage Mechanics and its Application to Anisotropic Creep Damage Theory

1983 ◽  
Vol 105 (2) ◽  
pp. 99-105 ◽  
Author(s):  
S. Murakami
Keyword(s):  
Damage Mechanics ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Damage State ◽  
Creep Theory ◽  
Damage Theory ◽  
Damaged Materials ◽  
Damage Tensor ◽  
Anisotropic Creep

After discussing the notion and the practical procedures of continuum damage mechanics, their utility is elucidated by applying them to formulate an anisotropic creep damage theory for nonsteady multiaxial states of stress. By taking account of the mechanisms of microstructural change of materials due to creep, it is shown that the creep damage state can be described by a second rank symmetric damage tensor, while the effects of material damage on creep deformation of damaged materials should be expressed by a fourth rank tensor formed from the damage tensor. Validity of the creep theory formulated in terms of these damage variables is examined by performing model tests. Specialization of the proposed theory is also discussed.

An Anisotropic Creep Damage Model for Anisotropic Weld Metal

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
S. Peravali ◽  
T. H. Hyde ◽  
K. A. Cliffe ◽  
S. B. Leen
Keyword(s):  
Weld Metal ◽  
Test Data ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Material Behavior ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Anisotropic Creep

Past studies from creep tests on uniaxial specimens and Bridgman notch specimens, for a P91 weld metal, showed that anisotropic behavior (more specifically transverse isotropy) occurs in the weld metal, both in terms of creep (steady-state) strain rate behavior and rupture times (viz., damage evolution). This paper describes the development of a finite element (FE) continuum damage mechanics methodology to deal with anisotropic creep and anisotropic damage for weld metal. The method employs a second order damage tensor following the work of Murakami and Ohno (1980, “A Continuum Theory of Creep and Creep Damage,” Creep in Structures, A. R. S. Ponter and D. R. Hayhurst, eds., Springer-Verlag, Berlin, pp. 422–444) along with a novel rupture stress approach to define the evolution of this tensor, taking advantage of the transverse isotropic nature of the weld metal, to achieve a reduction in the number of material constants required from test data (and hence tests) to define the damage evolution. Hill’s anisotropy potential theory is employed to model the secondary creep. The theoretical model is implemented in a material behavior subroutine within the general-purpose nonlinear FE code ABAQUS (ABAQUS User’s Manual, Version 6.6, 6006, Hibbitt, Karlsson and Sorenson, Inc., Providence, RI). The validation of the implementation against established isotropic continuum damage mechanics solutions for the isotropic case is described. A procedure for calibrating the multiaxial damage constants from notched bar test data is described for multiaxial implementations. Also described is a study on the effect of uniaxial specimen orientation on anisotropic damage evolution.

Development of continuum damage in the creep rupture of notched bars

1984 ◽  
Vol 311 (1516) ◽  
pp. 103-129 ◽  
Keyword(s):  
New York ◽  
Damage Mechanics ◽  
Axial Stress ◽  
Numerical Procedure ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Constant Load ◽  
Creep Rupture ◽  
Continuum Damage ◽  
Discrete Crack

The creep rupture of circumferentially notched, circular tension bars which are subjected to constant load for long periods at constant temperature is studied both experimentally and by using a time-iterative numerical procedure which describes the formation and growth of creep damage as a field quantity. The procedure models the development of failed or cracked regions of material due to the growth and linkage of grain boundary defects. Close agreement is shown between experimental and theoretical values of the representative rupture stress, of the zones of creep damage and of the development of cracks for circular (Bridgman, Studies in large plastic flow and fracture , New York: McGraw-Hill (1952)) and British Standard notched specimens (B.S. no. 3500 (1969)). The minimum section of the circular notch is shown to be subjected to relatively uniform states of multi-axial stress and damage while the B.S. notch is shown to be subjected to non-uniform stress and damage fields in which single cracks grow through relatively undamaged material. The latter situation is shown to be analogous to the growth of a discrete crack in a lightly damaged continuum. The continuum damage mechanics theory presented here is shown to be capable of accurately predicting these extreme types of behaviour.

Finite Element Simulation of the Creep Behavior of 2.25Cr-1Mo-0.25V Steel Based on Continuum Damage Mechanics

2015 ◽  
Vol 750 ◽  
pp. 266-271 ◽  
Author(s):  
Yu Zhou ◽  
Xue Dong Chen ◽  
Zhi Chao Fan ◽  
Yi Chun Han
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Creep Behavior ◽  
Constitutive Equations ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Element Simulation

The creep behavior of 2.25Cr-1Mo-0.25V ferritic steel was investigated using a set of physically-based creep damage constitutive equations. The material constants were determined according to the creep experimental data, using an efficient genetic algorithm. The user-defined subroutine for creep damage evolution was developed based on the commercial finite element software ANSYS and its user programmable features (UPFs), and the numerical simulation of the stress distribution and the damage evolution of the semi V-type notched specimen during creep were studied. The results showed that the genetic algorithm is a very efficient optimization approach for the parameter identification of the creep damage constitutive equations, and finite element simulation based on continuum damage mechanics can be used to analyze and predict the creep damage evolution under multi-axial stress states.

Damage Mechanisms Modeling for Ceramic Composites

1994 ◽  
Vol 116 (3) ◽  
pp. 331-336 ◽  
Author(s):  
P. Ladeve`ze ◽  
A. Gasser ◽  
O. Allix
Keyword(s):  
Structural Analysis ◽  
Damage Mechanics ◽  
Constitutive Relations ◽  
Continuum Damage Mechanics ◽  
Ceramic Composites ◽  
Continuum Damage ◽  
Damage State ◽  
Damage Mechanisms ◽  
Final Fracture

For ceramic composites, continuum damage mechanics models are built, which include information coming from both the “micro” and “macro” scales. These models are constitutive relations which, when included in a structural analysis code, are able to predict the damage state of the studied structure at any time and at any point until final fracture.

An Anisotropic Creep Damage Model for Anisotropic Weld Metal

2007 ◽  
Author(s):  
S. Peravali ◽  
T. H. Hyde ◽  
K. A. Cliffe ◽  
S. B. Leen
Keyword(s):  
Weld Metal ◽  
Test Data ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Isotropic Case ◽  
Anisotropic Damage ◽  
Secondary Creep ◽  
Continuum Damage ◽  
Anisotropic Creep

Past studies from creep tests on uniaxial specimens and Bridgman notch specimens, for a P91 weld metal, showed that anisotropic behaviour (more specifically transverse isotropy) occurs in the weld metal, both in terms of creep (steady-state) strain rate behaviour and rupture times (viz. damage evolution). This paper describes the development of a finite element (FE) continuum damage mechanics methodology to deal with anisotropic creep and anisotropic damage for weld metal. The method employs a second order damage tensor following the work of Murakami and Ohno [1] along with a novel rupture stress approach to define the evolution of this tensor, taking advantage of the transverse isotropic nature of the weld metal, to achieve a reduction in the number of material constants required from test data (and hence tests) to define the damage evolution. Hill’s anisotropy potential theory is employed to model the secondary creep. The theoretical model is implemented in a material behaviour subroutine within the general-purpose, non-linear FE code ABAQUS [2]. The validation of the implementation against established isotropic continuum damage mechanics solutions for the isotropic case is described. A procedure for calibrating the multiaxial damage constants from notched bar test data is described for multiaxial implementations. Also described is a study on the effect of uniaxial specimen orientation on anisotropic damage evolution.

Interpretation of damage mechanics behaviour of two-bar structures for the life extension of high-temperature components

2003 ◽  
Vol 38 (2) ◽  
pp. 125-132 ◽  
Author(s):  
S-T Tu ◽  
X Ling
Keyword(s):  
High Temperature ◽  
Damage Mechanics ◽  
Creep Damage ◽  
Life Extension ◽  
Continuum Damage ◽  
Basic Model ◽  
Different Dimensions ◽  
Damage Theory ◽  
High Temperature Components

The creep damage behaviour of two-bar structures of different dimensions and materials is studied in terms of continuum damage theory. The basic model is used to interpret the effectiveness of life extension measures for complicated structures. It is found that replacement of the more damaged component prior to rupture will result in an optimized life extension efficiency, depending on the geometric or material difference between the damaged and less damaged components. This has potential to provide guidance on the effectiveness of life extension repairs in high-temperature plants.

Damage Deactivation

1995 ◽  
Vol 62 (2) ◽  
pp. 450-458 ◽  
Author(s):  
N. R. Hansen ◽  
H. L. Schreyer
Keyword(s):  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Uniaxial Stress ◽  
Projection Operators ◽  
Continuum Damage ◽  
Order Tensor ◽  
Smooth Functions ◽  
One Dimensional ◽  
Opening And Closing ◽  
Damage Tensor

A phenomenological algorithm, motivated by the “mode I” microcrack opening and closing mechanism, is developed for the deactivation and reactivation of the damage effects as modeled by certain continuum damage mechanics theories. One-dimensional formulations with and without coupled plasticity are used to elucidate concepts associated with damage deactivation and to suggest multidimensional deactivation formulations applicable to continuum damage theories that employ a second-order tensor as the damage measure. Strain-based projection operators are used to deactivate the damage effects in the damage tensor. Motivated by observations from one-dimensional coupled formulations, both the total and elastic strains must be compressive for the damage to be rendered inactive. By introducing smooth functions to represent the transition from the active to the inactive state, discontinuities in the response are avoided. To illustrate the aspects associated with deactivation, a consistent set of examples using a strain-controlled one-cycle uniaxial stress loading is given for each formulation.

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