Mechanical Modeling of Material Damage

1988 ◽  
Vol 55 (2) ◽  
pp. 280-286 ◽  
Author(s):  
S. Murakami
Keyword(s):  
Effective Stress ◽  
Path Dependence ◽  
Damage Mechanics ◽  
Creep Damage ◽  
Stress Path ◽  
Elastic Behavior ◽  
Material Damage ◽  
Damage State ◽  
Effective Stresses ◽  
Definition Of

A systematic theory to describe the anisotropic damage states of materials and a consistent definition of effective stress tensors are developed within the framework of continuum damage mechanics. By introducing a fictitious undamaged configuration, mechanically equivalent to the real damaged configuration, the classical creep damage theory is extended to the general three-dimensional states of material damage; it is shown that the damage state can be described in terms of a symmetric second rank tensor. The physical implications, mathematical restrictions, and the limitations of this damage tensor, as well as the effects of finite deformation on the damage state, are discussed in some detail. The notion of the fictitious undamaged configuration is then applied also to the definition of effective stresses. Finally, the extension of the effective stresses incorporating the effects of crack closure is discussed. The resulting effective stress tensor is employed to analyze the stress-path dependence of the elastic behavior of a cracked elastic-brittle material.

Life Estimation and Creep Damage Quantification of Service Exposed Reformer Tube

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Raj ◽  
N. Roy ◽  
B.N. Roy ◽  
A.K. Ray
Keyword(s):  
Creep Deformation ◽  
Damage Mechanics ◽  
Residual Life ◽  
Deformation Behaviour ◽  
True Strain ◽  
Creep Damage ◽  
Damage State ◽  
Statistical Point ◽  
Reformer Tube ◽  
Bottom Portion

AbstractThis paper deals with evaluation of creep damage of ~11 years service exposed primary hydrogen reformer tube made of HP-40 grade of steel in a petrochemical industry, which has been carried out in terms of Kachanav’s continuum damage mechanics (CDM) model (K-model) and Bogdanoff model (B-model) based on Markov process. Residual life of the tubes was estimated based on hot tensile, conventional creep deformation under identical test conditions, optical microscopy and fractography. Accumulation of damage due to creep has been quantified through microstructural studies. The as received tubes did not reveal any degradation in the material like creep cavitation or voids, but there was indeed loss of tensile strength from room temperature to 870°C for the bottom portion of the tube due to ageing and overheating. Scatter in creep deformation behaviour of the material is probably due to variation in mode of fracture and scatter in voids. From statistical point of view, Weibull distribution pattern for analysing probability of rupture due to void area shifts with increase in true strain towards the higher population of void. The estimation of mean time to reach a specific damage state from K- model and B-model is in close agreement with that of experimental data and can describe the sudden changes of the creep damage in the tertiary region as well. A remnant life of >10 years is estimated at the operating stress–temperature conditions of the top as well as bottom portion of the tube.

Simplified Computation of Creep Damage Propagation

2016 ◽  
Author(s):  
Douglas L. Marriott ◽  
Herbert E. Stumph ◽  
Arun Sreeranganathan ◽  
Christopher J. Matice
Keyword(s):  
Damage Mechanics ◽  
Creep Damage ◽  
Limit Load ◽  
Continuum Damage Mechanics ◽  
Structural Failure ◽  
Element Analysis ◽  
Damage Propagation ◽  
Standard Design ◽  
Definition Of ◽  
Computational Difficulty

The commonly accepted approach to dealing with material damage as the cause of structural failure is to treat the most highly distressed location in the structure as an equivalent simple test and to define failure of the structure as a whole as being failure at that point location. The exception to this rule is plastic deformation. Yielding at a point was recognized several decades ago as being an excessively conservative definition of component failure and it is now standard design practice to accept failure as being the limit load, which is only reached, sometimes after extensive propagation of a plastic zone. Other material failure mechanisms also occur after a finite period of damage propagation, but this additional strength, or life, is not usually taken into account, partly because the damage mechanisms themselves are not always well defined, and partly because of the computational difficulty involved in assessing the propagation of damage. Creep rupture falls into the category of a mechanism which can enjoy an extensive period of damage propagation before structural failure occurs, but the difficulty of evaluating it quantitatively has meant that it continues to be dealt with as essentially a point failure phenomenon. Relatively recently, many of the problems associated with assessing creep damage have been resolved, on the material side by increased use of so-called “continuum damage mechanics” based models such as Kachanov and Omega and, on the computational side, by the exponential growth in the capabilities of advanced Finite Element Analysis. It is now possible in principle to trace the entire life of a complex component, down to final disintegration. However, this capability still comes at a significant cost, and there is still room for simplification in order to bring this capability to a wider range of potential users. This paper describes a process for evaluating the propagation of creep damage, down to the point of total disintegration, using approximations which exist within the standard capabilities of a typical FE design package. This innovation does not do anything that cannot be done today using the full repertoire of computational tools that exist, notably user subroutines, but provides a simpler platform which can be used to push damage evaluation further into the activities of day-to-day design with a significant reduction in the resource allocation currently required to do the job. Results are compared with creep experiments on notched bars.

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.

A comparative study on methods for determining the hydraulic properties of a clay shale

2020 ◽  
Vol 224 (3) ◽  
pp. 1523-1539
Author(s):  
Lisa Winhausen ◽  
Alexandra Amann-Hildenbrand ◽  
Reinhard Fink ◽  
Mohammadreza Jalali ◽  
Kavan Khaledi ◽  
...  
Keyword(s):  
Pore Pressure ◽  
Effective Stress ◽  
Ion Beam ◽  
Applied Pressure ◽  
Pressure Oscillation ◽  
Stress Conditions ◽  
Data Set ◽  
Clay Shale ◽  
Permeability Coefficients ◽  
Effective Stresses

SUMMARY A comprehensive characterization of clay shale behavior requires quantifying both geomechanical and hydromechanical characteristics. This paper presents a comparative laboratory study of different methods to determine the water permeability of saturated Opalinus Clay: (i) pore pressure oscillation, (ii) pressure pulse decay and (iii) pore pressure equilibration. Based on a comprehensive data set obtained on one sample under well-defined temperature and isostatic effective stress conditions, we discuss the sensitivity of permeability and storativity on the experimental boundary conditions (oscillation frequency, pore pressure amplitudes and effective stress). The results show that permeability coefficients obtained by all three methods differ less than 15 per cent at a constant effective stress of 24 MPa (kmean = 6.6E-21 to 7.5E-21 m2). The pore pressure transmission technique tends towards lower permeability coefficients, whereas the pulse decay and pressure oscillation techniques result in slightly higher values. The discrepancies are considered minor and experimental times of the techniques are similar in the range of 1–2 d for this sample. We found that permeability coefficients determined by the pore pressure oscillation technique increase with higher frequencies, that is oscillation periods shorter than 2 hr. No dependence is found for the applied pressure amplitudes (5, 10 and 25 per cent of the mean pore pressure). By means of experimental handling and data density, the pore pressure oscillation technique appears to be the most efficient. Data can be recorded continuously over a user-defined period of time and yield information on both, permeability and storativity. Furthermore, effective stress conditions can be held constant during the test and pressure equilibration prior to testing is not necessary. Electron microscopic imaging of ion-beam polished surfaces before and after testing suggests that testing at effective stresses higher than in situ did not lead to pore significant collapse or other irreversible damage in the samples. The study also shows that unloading during the experiment did not result in a permeability increase, which is associated to the persistent closure of microcracks at effective stresses between 24 and 6 MPa.

scholarly journals Stress sensitivity of porosity and permeability under varying hydrostatic stress conditions for different carbonate rock types of the geothermal Malm reservoir in Southern Germany

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Daniel Bohnsack ◽  
Martin Potten ◽  
Simon Freitag ◽  
Florian Einsiedl ◽  
Kai Zosseder
Keyword(s):  
Effective Stress ◽  
Hydraulic Properties ◽  
Rock Strength ◽  
Pore Network ◽  
Stress Sensitivity ◽  
Stress Conditions ◽  
Rock Matrix ◽  
Effective Stresses ◽  
Rock Types ◽  
Porosity And Permeability

AbstractIn geothermal reservoir systems, changes in pore pressure due to production (depletion), injection or temperature changes result in a displacement of the effective stresses acting on the rock matrix of the aquifer. To compensate for these intrinsic stress changes, the rock matrix is subjected to poroelastic deformation through changes in rock and pore volume. This in turn may induce changes in the effective pore network and thus in the hydraulic properties of the aquifer. Therefore, for the conception of precise reservoir models and for long-term simulations, stress sensitivity of porosity and permeability is required for parametrization. Stress sensitivity was measured in hydrostatic compression tests on 14 samples of rock cores stemming from two boreholes of the Upper Jurassic Malm aquifer of the Bavarian Molasse Basin. To account for the heterogeneity of this carbonate sequence, typical rock and facies types representing the productive zones within the thermal reservoir were used. Prior to hydrostatic investigations, the hydraulic (effective porosity, permeability) and geomechanical (rock strength, dynamic, and static moduli) parameters as well as the microstructure (pore and pore throat size) of each rock sample were studied for thorough sample characterization. Subsequently, the samples were tested in a triaxial test setup with effective stresses of up to 28 MPa (hydrostatic) to simulate in-situ stress conditions for depths up to 2000 m. It was shown that stress sensitivity of the porosity was comparably low, resulting in a relative reduction of 0.7–2.1% at maximum effective stress. In contrast, relative permeability losses were observed in the range of 17.3–56.7% compared to the initial permeability at low effective stresses. Stress sensitivity coefficients for porosity and permeability were derived for characterization of each sample and the different rock types. For the stress sensitivity of porosity, a negative correlation with rock strength and a positive correlation with initial porosity was observed. The stress sensitivity of permeability is probably controlled by more complex processes than that of porosity, where the latter is mainly controlled by the compressibility of the pore space. It may depend more on the compaction of precedented flow paths and the geometry of pores and pore throats controlling the connectivity within the rock matrix. In general, limestone samples showed a higher stress sensitivity than dolomitic limestone or dolostones, because dolomitization of the rock matrix may lead to an increasing stiffness of the rock. Furthermore, the stress sensitivity is related to the history of burial diagenesis, during which changes in the pore network (dissolution, precipitation, and replacement of minerals and cements) as well as compaction and microcrack formation may occur. This study, in addition to improving the quality of input parameters for hydraulic–mechanical modeling, shows that hydraulic properties in flow zones largely characterized by less stiff, porous limestones can deteriorate significantly with increasing effective stress.

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.

scholarly journals Effective stress regime around a jacked steel pile during installation ageing and load testing in chalk

2018 ◽  
Vol 55 (11) ◽  
pp. 1577-1591 ◽  
Author(s):  
R.M. Buckley ◽  
R.J. Jardine ◽  
S. Kontoe ◽  
B.M. Lehane
Keyword(s):  
Cyclic Loading ◽  
Effective Stress ◽  
Test Site ◽  
Static Tension ◽  
Load Testing ◽  
Stress Regime ◽  
Effective Stresses ◽  
Axial Cyclic Loading ◽  
Tension Testing ◽  
Static And Cyclic Loading

This paper reports experiments with 102 mm diameter closed-ended instrumented Imperial College piles (ICPs) jacked into low- to medium-density chalk at a well-characterized UK test site. The “ICP” instruments allowed the effective stress regime surrounding the pile shaft to be tracked during pile installation, equalization periods of up to 2.5 months, and load testing under static tension and one-way axial cyclic loading. Installation resistances are shown to be dominated by the pile tip loads. Low installation shaft stresses and radial effective stresses were measured that correlated with local cone penetration test (CPT) tip resistances. Marked shaft total stress reductions and steep stress gradients are demonstrated in the vicinity of the pile tip. The local interface shaft effective stress paths developed during static and cyclic loading displayed trends that resemble those seen in comparable tests in sands. Shaft failure followed the Coulomb law and constrained interface dilation was apparent as the pile experienced drained loading to failure, although with a lesser degree of radial expansion than with sands. Radial effective stresses were also found to fall with time after installation, leading to reductions in shaft capacity as proven by subsequent static tension testing. The jacked, closed-ended, piles’ ageing trends contrast sharply with those found with open piles driven at the same site, indicating that ageing is affected by pile tip geometry and (or) installation method.

scholarly journals On continuum damage mechanics

2019 ◽  
Vol 52 (3) ◽  
pp. 125-147
Author(s):  
Kari Juhani Santaoja
Keyword(s):  
Stress Tensor ◽  
Effective Stress ◽  
Elastic Strain ◽  
Damage Mechanics ◽  
Volume Fraction ◽  
Strain Tensor ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
The Matrix ◽  
Elastic Strain Tensor

A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fraction f , which has a clear physical meaning, and the elastic strain tensor \Bold {ε}^e with the damage-elastic strain tensor \Bold {ε}^{de}. The postulate of strain equivalence with the effective stress concept was reformulated and applied to a case where the response of the matrix obeys Hooke’s law. In contrast to many other studies, in the derived relation between the effective stress tensor \Bold {\Tilde{σ}} and the stress tensor \Bold {σ}, the tensor \Bold {\Tilde{σ}} is symmetric. A uniaxial bar model was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.

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