A Mesh Independent GTN Damage Model and Its Application in Simulation of Ductile Fracture Behaviour

2008 ◽  
Author(s):  
M. K. Samal ◽  
M. Seidenfuss ◽  
E. Roos ◽  
B. K. Dutta ◽  
H. S. Kushwaha
Keyword(s):  
Ductile Fracture ◽  
Fracture Resistance ◽  
Damage Mechanics ◽  
Wide Spectrum ◽  
Weighted Average ◽  
Damage Parameter ◽  
Nonlocal Model ◽  
Fe Method ◽  
Diffusion Type ◽  
Damage Models

Ductile fracture process involves the typical stages of nucleation, growth and coalescence of voids in the micro-scale. In order to take the effects of these voids on the stress carrying capability of a mechanical continuum during simulation, damage mechanics models, such as those of Rousselier and Gurson-Tvergaard-Needleman (GTN) are widely used. These have been highly successful in simulating the fracture resistance behaviour of different specimens and components made of a wide spectrum of engineering steels. However, apart from the material parameters, a characteristic length parameter has to be used as a measure of the size of the discretisation in the zone of crack propagation. This inherent limitation of these local damage models prevents them from simulating the stress distribution near the sharp stress gradients satisfactorily, especially at transition temperature regime. There have been efforts in literature to overcome the effect of mesh-dependency by development of nonlocal and gradient damage models. A nonlocal measure (weighted average of a quantity over a characteristics volume) of damage is usually used in the material constitutive equation. In this paper, the authors have extended the GTN model to its nonlocal form using damage parameter ‘d’ as a degree of freedom in the finite element (FE) formulation. The evolution of the nonlocal damage is related to the actual void volume faction ‘f’ in ductile fracture using a diffusion type equation. The coupled mechanical equilibrium and damage diffusion equations have been discretised using FE method. In order to demonstrate the mesh independent nature of the new formulation, a standard fracture mechanics specimen (i.e., 1T compact tension) has been analysed using different mesh sizes near the crack tip and the results have been compared with those of experiment. The results of the nonlocal model have also been compared with those of the local model. The effect of different GTN parameters on the fracture resistance behaviour of this specimen has been studied for the nonlocal model and these results have been compared with those of experiment.

A mesh-independent Gurson—Tvergaard—Needleman damage model and its application in simulating ductile fracture behaviour

2009 ◽  
Vol 223 (2) ◽  
pp. 283-292 ◽  
Author(s):  
M K Samal ◽  
M Seidenfuss ◽  
E Roos ◽  
B K Dutta ◽  
H S Kushwaha
Keyword(s):  
Finite Element ◽  
Ductile Fracture ◽  
Volume Fraction ◽  
Damage Model ◽  
Type Equation ◽  
Damage Parameter ◽  
Local Form ◽  
Fe Method ◽  
Diffusion Type ◽  
Non Local

In this study, the classical Gurson—Tvergaard—Needleman (GTN) model has been extended to a non-local form using damage parameter ‘ d’ as a degree of freedom in the finite-element (FE) formulation. The evolution of the non-local damage is related to the actual void volume fraction ‘ f’ in ductile fracture using a diffusion type equation. The coupled mechanical equilibrium and damage diffusion equations have been discretized using the finite-element (FE) method. In order to demonstrate the mesh-independent nature of the new formulation, a standard fracture mechanics specimen (i.e. 1T compact tension) has been analysed using different mesh sizes near the crack tip and the results have been compared with those of the experiment. The effect of different GTN parameters on the fracture resistance behaviour of this specimen has been studied for the non-local model and these results have also been compared with those of the experiment.

Prediction of Fracture Resistance Behaviour Using Nonlocal Damage Model

2007 ◽  
Author(s):  
M. K. Samal ◽  
M. Seidenfuss ◽  
E. Roos ◽  
B. K. Dutta ◽  
H. S. Kushwaha
Keyword(s):  
Crack Initiation ◽  
Fracture Resistance ◽  
Damage Mechanics ◽  
Damage Model ◽  
Mesh Size ◽  
Continuum Damage Mechanics ◽  
Nonlocal Model ◽  
Continuum Damage ◽  
Local Damage ◽  
Spatial Discretisation

Prevention of failure of pressurised and high-energy components and systems has been an important issue in design of all types of power and process plants. Each individual component of these systems must be dimensioned such that it can resist the forces or moments to which it will be subjected during normal service and upset conditions. Design by analysis is an important philosophy of modern design. The ability of now-a-days computers to numerically handle complex mathematical problems has inspired the use highly nonlinear material behaviour (including material softening) instead of classical linear constitutive theory for the materials. Under the influence of these developments, a fundamentally different type of modelling has emerged, in which fracture is considered as the ultimate consequence of a material degradation process. Crack initiation and growth then follow naturally from the standard continuum mechanics theory (called continuum damage mechanics). Numerical analyses based on these so-called local damage models, however, are often found to depend on the spatial discretisation (i.e., mesh size of the numerical method used). The growth of damage tends to localise in the smallest band that can be captured by the spatial discretisation. As a consequence, increasingly finer discretisation grids can lead to crack initiation earlier in the loading history and to faster crack growth. This non-physical behaviour is caused by the fact that the localisation of damage in a vanishing volume is no longer consistent with the concept of a continuous damage field, which forms the basis of the continuum damage mechanics approach. In this work, the Rousellier’s damage model has been extended to its nonlocal form using damage parameter ‘d’ as a degree of freedom. The finite element (FE) equations have been derived using the weak form of the governing equations for both mechanical force equilibrium and the damage equilibrium. As an example, a standard fracture mechanics specimen [SE(B)] made up of a German low alloy steel has been analysed in 2D plane strain condition using different mesh sizes near the crack tip. The results of the nonlocal model has been compared with experimental results as well as with those predicted by the local model. It was observed that the fracture resistance predicted by the local damage model goes on decreasing when the mesh size near the crack tip is refined whereas the nonlocal model predicts a converged fracture resistance behaviour which compares well with the experimentally determined behaviour.

Validation of the ductile fracture modeling of CGI at quasi-static loading conditions

2021 ◽  
pp. 105678952199754
Author(s):  
Senad Razanica ◽  
Lennart B Josefson ◽  
Ragnar Larsson ◽  
Torsten Sjögren
Keyword(s):  
Ductile Fracture ◽  
Damage Mechanics ◽  
Damage Model ◽  
Stress Triaxiality ◽  
Image Correlation ◽  
Damage Initiation ◽  
Damage Models ◽  
Fracture Modeling ◽  
Static Conditions ◽  
Force Displacement

Fracture modeling and experimental validation of Compacted Graphite Iron (CGI) specimens loaded under quasi-static conditions at room temperature are considered. Continuum damage mechanics coupled to plasticity is adopted to describe the evolution of damage. The damage production is based on a recently developed rate dependent damage evolution law, where the damage–plasticity coupling is modeled based on a damage driving energy that involves both stored energy and plasticity contributions. To describe ductile fracture accounting for stress triaxiality on the damage initiation, the inelastic contribution to the damage driving energy is controlled by the Johnson-Cook failure criterion. Three different damage models are defined based on elastic/inelastic damage driving energies. The damage models are validated against experiments on a set of notched specimens made of CGI with different notch geometries, where the global force-displacement curves and corresponding strain fields are obtained using digital image correlation technology. It is shown from the testing and the simulations that plastic strains generally need to be accounted for in order to properly describe the different failure processes of the CGI specimens. In addition, the ductile damage model is shown to more accurately predict the experimental force-displacement response as compared to the more simplistic stress drop, element deletion technique.

Cumulative Damage Mechanics: Characterization, Modeling, and Interpretation of Progressive Failure in Ceramics and Composites

2004 ◽  
Author(s):  
Michael G. Jenkins ◽  
Paul E. Labossie`re ◽  
Jonathan A. Salem
Keyword(s):  
Damage Mechanics ◽  
Progressive Failure ◽  
Ceramic Matrix Composites ◽  
Test Methods ◽  
Cumulative Damage ◽  
Material Behavior ◽  
Matrix Composites ◽  
Damage Models ◽  
Novel Design ◽  
Nonlinear Energy

Ceramic matrix composites (CMCs) have evolved to exhibit inherent damage tolerance through nonlinear energy absorption mechanisms while retaining the desirable attributes of their monolithic structural ceramic counterparts. Mathematical (analytic and numeric) models together with experimental measurements of this damage absorption have aided in understanding the thermomechanical behavior of CMCs. This understanding has led to improved test methods, better predictive modeling of material behavior, appropriate processing methods, and finally novel design methodologies for implementing CMCs. In this paper, background on CMC damage is presented, damage measurement and damage models are discussed and finally probabilistic aspects of constituent materials that can be used to illustrate the cumulative damage behavior of CMCs are described.

scholarly journals Localization due to Damage in Two-Direction Fiber-Reinforced Composites

1996 ◽  
Vol 63 (2) ◽  
pp. 321-326 ◽  
Author(s):  
F. Hild ◽  
P.-L. Larsson ◽  
F. A. Leckie
Keyword(s):  
Damage Mechanics ◽  
Ceramic Matrix Composites ◽  
Continuum Damage Mechanics ◽  
General Criterion ◽  
Matrix Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Damage Models ◽  
Pull Out ◽  
Fracture Features

Fiber pull-out is one of the fracture features of fiber-reinforced ceramic matrix composites. The onset of this mechanism is predicted by using continuum damage mechanics, and corresponds to a localization of deformation. After deriving two damage models from a uniaxial bundle approach, different configurations are analyzed through numerical methods. For one model some very simple criteria can be derived, whereas for the second one none of these criteria can be derived and the general criterion of localization must be used.

Comparison of Two Damage Models for Prediction of Failure in Stress Corrosion Cracking

2018 ◽  
Author(s):  
Sorabh Singhal ◽  
Yogeshwar Jasra ◽  
Ravindra K. Saxena
Keyword(s):  
Crack Initiation ◽  
Stress Corrosion ◽  
Stress Corrosion Cracking ◽  
Driving Force ◽  
Damage Mechanics ◽  
Damage Model ◽  
Corrosion Cracking ◽  
Force Model ◽  
Initiation Time ◽  
Damage Models

In the present work, Stress corrosion cracking (SCC) and its mechanical behavior are presented. SCC represents complex behavior due to electrochemical and mechanical interaction. Damage models are proposed to predict crack initiation time for stainless steel under constant load using the concept of continuum damage mechanics to show incremental damage accumulation which finally leads to failure of the material. Two damage models applicable to prediction of damage in SCC, Lemaitre damage model and damage driving force model proposed by Kamaya are compared. The comparative study of the results obtained by these damage models shows that in Lemaitre damage law cracks initiate randomly while in damage driving force model the stress concentration occurs around the periphery of damaged element results in increased damage force. The study can be used to estimate the crack initiation time in SCC under corrosive atmosphere.

Unilateral Damage in Reinforced Concrete Frames

2015 ◽  
pp. 445-502
Keyword(s):  
Cyclic Loading ◽  
Damage Mechanics ◽  
Industrial Applications ◽  
Concrete Frames ◽  
Dual Systems ◽  
Rc Structures ◽  
Damage Models ◽  
Rc Frames ◽  
Earthquake Vulnerability ◽  
Inertia Forces

One of the main applications of the lumped damage mechanics or the damage mechanics of dual systems is the earthquake vulnerability assessment of structures. This means not only the consideration of the inertia forces but, mainly, the adequate description of crack propagation under general cyclic loading. Chapter 9 described the concept of unilateral damage (i.e. the appearance of distinct and independent sets of cracks after loading reversals). This phenomenon can also be observed in RC structures, and the models presented in Chapters 10 and 11 do not describe it; thus, they should be used only in the cases of mono sign loadings. The first goal of this chapter is the generalization of the damage models, including unilateral effects; the next one consists of the development of lumped damage models for tridimensional analysis of RC frames. Finally, some guidelines for the use of the damage models in industrial applications are presented.

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