Methods to Determine the Critical Damage Criterion of the Kachanov-Rabotnov Law

2012 ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Damage Mechanics ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Considerable Effort ◽  
Damage Criterion ◽  
High Temperature Components ◽  
Life Fraction ◽  
Life Strain ◽  
Critical Damage

Considerable effort has gone towards the implementation of continuum damage mechanics (CDM) laws for the creep damage assessment of high temperature components. Often critical damage is considered to be reached when damage is equal to unity. Analytical methods have demonstrated that for various alloys critical damage is much less than unity and is dependent on stress and temperature. Few studies have been conducted to evaluate and correct this problem. In this paper, an examination of the theory of critical damage is conducted. Based on theory, a new critical damage criterion is introduced. A comparison between Penny and the new critical damage criterion will be conducted to determine the most viable criterion. Damage is introduced into life, strain, and mixed life fraction rules to demonstrate the influence damage has on rupture under thermo-mechanical loading.

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.

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.

scholarly journals Review of Creep Cavitation and Rupture of Low Cr Alloy and its Weldment

2013 ◽  
Vol 744 ◽  
pp. 407-411
Author(s):  
Qi Hua Xu ◽  
Qiang Xu ◽  
Yong Xin Pan ◽  
Michael Short
Keyword(s):  
High Temperature ◽  
Constitutive Equation ◽  
Damage Mechanics ◽  
Experimental Approach ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Safe Operation ◽  
Computational Approaches ◽  
Creep Cavitation

This paper presents a review of creep cavitation and rupture of low Cr alloy and its weldment, particular in the heat-affected zone (HAZ). Creep damage is one of the serious problems for the high temperature industry. One of the computational approaches is continuum damage mechanics which has been developed and applied complementary to the experimental approach and assists in the safe operation. However, the existing creep damage constitutive equations are not developed specifically for low stress. Therefore, in order to form the physical bases for the development of creep damage constitutive equation, it is necessary to critically review the creep cavitation and rupture characteristics of low Cr alloy and its weldment.

Creep Behaviors Calculated by Varying Material Constants Obtained from Different Stress Regions for a Closed-End P91 Pipe

2016 ◽  
Vol 35 (5) ◽  
pp. 441-447
Author(s):  
Zhao Yanping ◽  
Gong Jianming ◽  
Wang Xiaowei ◽  
Li Qingnan
Keyword(s):  
Damage Mechanics ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Creep Tests ◽  
Material Constants ◽  
Mechanics Model ◽  
Stress Region ◽  
Wide Range ◽  
Tertiary Stage

AbstractIn order to predict the creep life of a component at high temperature both accurately and economically, continuum damage mechanics approach is used based on experimental creep data. However, material constants used in the models have a great relationship with the performed stress range of creep tests. In this paper, several sets of material constants were obtained from a wide range of stresses on P91 steel. The creep damage tolerance parameter was used to classify these sets, and the modified continuum damage mechanics model was used to investigate a pipe under closed-end condition. Results have illustrated the main difference lies on the tertiary stage while slight difference on the primary and secondary stages, and the contribution of the tertiary stage to the total damage decreased when using material constants from higher stress region.

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.

Continuum Damage Mechanics and the Life-Fraction Rule

2005 ◽  
Vol 73 (4) ◽  
pp. 702-704 ◽  
Author(s):  
U. Stigh
Keyword(s):  
High Temperature ◽  
Life Prediction ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Short Review ◽  
Necessary Condition ◽  
Continuum Damage ◽  
Evolution Law ◽  
Open Question ◽  
Life Fraction

This paper gives a short review of two different methods for life prediction at high temperature; namely continuum damage mechanics (CDM) and the linear life-fraction rule (LFR). It is well known that the class of CDM theories with a separable evolution law gives a life prediction in accordance with the LFR. However, it appears to be an open question if this is a necessary condition. It is here shown that in order for a CDM theory to comply with the LFR it must have a separable evolution law. That is, if we can assume that a material follows the LFR, it is necessary to chose a separable evolution law for this material. The reverse is also true, to get a life-fraction different from unity, we must chose a nonseparable evolution law.

scholarly journals Analyzing the Characteristics of the Cavity Nucleation, Growth and Coalescence Mechanism of 9Cr-1Mo-VNb Steel (P91) Steel

2013 ◽  
Vol 744 ◽  
pp. 412-416 ◽  
Author(s):  
Li Li An ◽  
Qiang Xu ◽  
Zhong Yu Lu ◽  
Dong Lai Xu
Keyword(s):  
Damage Mechanics ◽  
Experimental Approach ◽  
Axial Stress ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Computational Approach ◽  
Continuum Damage ◽  
Safe Operation ◽  
Cavity Nucleation ◽  
Nucleation Growth

Creep damage is one of the serious problems for the high temperature industries and computational approach (such as continuum damage mechanics) has been developed and used, complementary to the experimental approach, to assist safe operation. However, there are no ready creep damage constitutive equations to be used for predicting the lifetime for this type of alloy, particularly for low stress. This paper presents an analysis of the cavity nucleation, growth and coalescence mechanism of 9Cr-1Mo-VNb steel (P91 type) under high and low stress levels and multi-axial stress state.

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