Using Damage Delocalization to Model Localization Phenomena in Bammann-Chiesa-Johnson Metals

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Koffi Enakoutsa ◽  
Fazle R. Ahad ◽  
Kiran N. Solanki ◽  
Yustianto Tjiptowidjojo ◽  
Douglas J. Bammann
Keyword(s):  
Velocity Gradient ◽  
Adiabatic Shear Band ◽  
Shear Banding ◽  
Finite Size ◽  
Material Model ◽  
Dissipation Energy ◽  
Plane Strain Tension ◽  
Nonlocal Evolution Equation ◽  
Damage Theory ◽  
Spatial Discontinuity

The Bammann, Chiesa, and Johnson (BCJ) material model predicts unlimited localization of strain and damage, resulting in a zero dissipation energy at failure. This difficulty resolves when the BCJ model is modified to incorporate a nonlocal evolution equation for the damage, as proposed by Pijaudier-Cabot and Bazant (1987, “Nonlocal Damage Theory,” ASCE J. Eng. Mech., 113, pp. 1512–1533.). In this work, we theoretically assess the ability of such a modified BCJ model to prevent unlimited localization of strain and damage. To that end, we investigate two localization problems in nonlocal BCJ metals: appearance of a spatial discontinuity of the velocity gradient in any finite, inhomogeneous body, and localization of the dissipation energy into finite bands. We show that in spite of the softening arising from the damage, no spatial discontinuity occurs in the velocity gradient. Also, we find that the dissipation energy is continuously distributed in nonlocal BCJ metals and therefore cannot localize into zones of vanishing volume. As a result, the appearance of any vanishing width adiabatic shear band is impossible in a nonlocal BCJ metal. Finally, we study the finite element (FE) solution of shear banding in a rectangular plate, deformed in plane strain tension and containing an imperfection, thereby illustrating the effects of imperfections and finite size on the localization of strain and damage.

Localization Effects in Bammann-Chiesa-Johnson Metals With Damage Delocalization

2011 ◽  
Author(s):  
Koffi Enakoutsa ◽  
Fazle R. Ahad ◽  
Kiran N. Solanki ◽  
Yustianto Tjiptowidjojo ◽  
Douglas J. Bammann
Keyword(s):  
Velocity Gradient ◽  
Adiabatic Shear Band ◽  
Shear Banding ◽  
Material Model ◽  
Dissipated Energy ◽  
Dissipation Energy ◽  
Plane Strain Tension ◽  
Nonlocal Evolution Equation ◽  
Rectangular Mesh ◽  
Spatial Discontinuity

The presence of softening in the Bammann-Chiesa-Johnson (BCJ) material model presents a major physical drawback: the unlimited localization of strain which results in spurious zero dissipated energy at failure. This difficulty resolves when the BCJ model is modified to incorporate a nonlocal evolution equation for the damage, as proposed by Pijaudier-Cabot and Bazant (1987). The objective of this work is to theoretically assess the ability of such a modified BCJ model to prevent unlimited localization of the strain. To that end, we investigate two localization problems in nonlocal BCJ metals: appearance of a spatial discontinuity of the velocity gradient in a finite, inhomogeneous body, and localization into finite bands. We show that in spite of the softening arising from the damage, no spatial discontinuity occurs in the velocity gradient. Also, we find that the dissipation energy is continuously distributed in nonlocal BCJ metals and therefore can not localize into zones of vanishing volume. As a result, the appearance of any vanishing width adiabatic shear band is impossible in a nonlocal BCJ metal. Finally, we study the finite element (FE) solution of shear banding in a rectangular mesh, deformed in plane strain tension and containing an imperfection, thereby illustrating the effects of imperfections on the localization of the strain.

Bifurcation Effects in Ductile Metals With Nonlocal Damage

1994 ◽  
Vol 61 (2) ◽  
pp. 236-242 ◽  
Author(s):  
J. B. Leblond ◽  
G. Perrin ◽  
J. Devaux
Keyword(s):  
Shear Banding ◽  
Homogeneous Medium ◽  
The Body ◽  
Ductile Material ◽  
Ductile Metals ◽  
Plane Strain Tension ◽  
Bifurcation Phenomena ◽  
Nonlocal Evolution Equation ◽  
Rectangular Mesh ◽  
First Occurrence

The purpose of this paper is to investigate some bifurcation phenomena in a porous ductile material described by the classical Gurson (1977) model, but with a modified, nonlocal evolution equation for the porosity. Two distinct problems are analyzed theoretically: appearance of a discontinuous velocity gradient in a finite, inhomogeneous body, and arbitrary loss of uniqueness of the velocity field in an infinite, homogeneous medium. It is shown that no bifurcation of the first type can occur provided that the hardening slope of the sound (void-free) matrix is positive. In contrast, bifurcations of the second type are possible; nonlocality does not modify the conditions of first occurrence of bifurcation but does change the corresponding bifurcation mode, the wavelength of the latter being no longer arbitrary but necessarily infinite. A FE study of shear banding in a rectangular mesh deformed in plane strain tension is finally presented in order to qualitatively illustrate the effect of finiteness of the body; numerical results do evidence notable differences with respect to the case of an infinite, homogeneous medium envisaged theoretically.

Ship Collision Simulations Using Different Fracture Criteria and Mesh Size

2014 ◽  
Author(s):  
Mihkel Kõrgesaar ◽  
Kristjan Tabri ◽  
Hendrik Naar ◽  
Edvin Reinhold
Keyword(s):  
Mesh Size ◽  
Material Model ◽  
Fracture Criteria ◽  
Dissipation Energy ◽  
Advantages And Disadvantages ◽  
Large Structures ◽  
Plastic Dissipation ◽  
Wide Range ◽  
Ship Collision ◽  
Almost All

There is a wide range of fracture criteria available in the literature to simulate the ductile fracture in large structures. Almost all criteria depend in some form on the mesh size and some criteria also account the effect of the stress state on the fracture ductility. Furthermore, a material model employed could considerably influence the analysis results. Therefore, in this study, four different fracture criteria, three different mesh densities and two different material models are used to simulate ship collision with a rigid bulb. Thereby, plastic dissipation energy, force-displacement curves and structural failure mechanism is compared between different fracture criteria. Advantages and disadvantages of each criterion are discussed.

Prediction of Chip Morphology and Formation in High Speed Milling of Hardened Steels

2015 ◽  
Vol 1120-1121 ◽  
pp. 1145-1152
Author(s):  
Jun Zhong Pang ◽  
Xiao Bin Huang ◽  
Dou Dou Chang ◽  
Jie Pan
Keyword(s):  
Chip Formation ◽  
High Speed ◽  
Shear Banding ◽  
Chip Morphology ◽  
Material Model ◽  
Adiabatic Shear ◽  
Serrated Chip ◽  
Adiabatic Shear Banding ◽  
Serrated Chip Formation ◽  
Material Constitutive Equation

A P20 steel are machined in the milling speed range of 200 to 942m/min. The morphology and formation of the chips are investigated at various speeds. The serrated chips with adiabatic shear band are observed at a high milling speed. The transition from continuous to serrated chip formation is favored by the increase in work material hardness and milling speed. The study assumes that the chip segmentation is only induced by adiabatic shear banding, without material failure in the primary shear zone. Based on adiabatic shear theory, using the JC and the power material constitutive equation, the modified material model which takes into a strain softening is developed for prediction of the serrated chip formation. Experimental measurements are compared with the simulation results.

Analytical solution for shear bands in cold-rolled 1018 steel

2012 ◽  
Vol 20 (4-6) ◽  
pp. 89-102 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Amin H. Almasri ◽  
Danial Faghihi ◽  
Anthony N. Palazotto
Keyword(s):  
Constitutive Model ◽  
Shear Banding ◽  
Shear Bands ◽  
Material Model ◽  
Adiabatic Shear ◽  
Adiabatic Shear Banding ◽  
Softening Behavior ◽  
Dynamic Loadings ◽  
Cold Rolled ◽  
Selection Of

AbstractCold-rolled 1018 (CR-1018) carbon steel has been well known for its susceptibility to adiabatic shear banding under dynamic loadings. Analysis of these localizations highly depends on the selection of the constitutive model. To deal with this issue, a constitutive model that takes temperature and strain rate effect into account is proposed. The model is motivated by two physical-based models: the Zerilli and Armstrong and the Voyiadjis and Abed models. This material model, however, incorporates a simple softening term that is capable of simulating the softening behavior of CR-1018 steel. Instability, localization, and evolution of adiabatic shear bands are discussed and presented graphically. In addition, the effect of hydrostatic pressure is illustrated.

The partial realization theory of finite size two-dimensional arrays

1981 ◽  
Vol 64 (10) ◽  
pp. 1-8
Author(s):  
Tsuyoshi Matsuo ◽  
Yasumichi Hasegawa ◽  
Yoshikuni Okada
Keyword(s):  
Finite Size ◽  
Two Dimensional ◽  
Realization Theory

Effect of Temperature, Velocity Gradient and I.V. Heparin on in Vitro Blood Coagulation and Platelet Aggregation

1967 ◽  
Vol 17 (01/02) ◽  
pp. 112-119 ◽  
Author(s):  
L Dintenfass ◽  
M. C Rozenberg
Keyword(s):  
Blood Coagulation ◽  
Velocity Gradient ◽  
Elevated Temperatures ◽  
Morphological Changes ◽  
Effect Of Temperature ◽  
Clotting Time ◽  
Progressive Change ◽  
Aggregation Of Platelets ◽  
Microscopic Techniques

SummaryA study of blood coagulation was carried out by observing changes in the blood viscosity of blood coagulating in the cone-in-cone viscometer. The clots were investigated by microscopic techniques.Immediately after blood is obtained by venepuncture, viscosity of blood remains constant for a certain “latent” period. The duration of this period depends not only on the intrinsic properties of the blood sample, but also on temperature and rate of shear used during blood storage. An increase of temperature decreases the clotting time ; also, an increase in the rate of shear decreases the clotting time.It is confirmed that morphological changes take place in blood coagula as a function of the velocity gradient at which such coagulation takes place. There is a progressive change from the red clot to white thrombus as the rates of shear increase. Aggregation of platelets increases as the rate of shear increases.This pattern is maintained with changes of temperature, although aggregation of platelets appears to be increased at elevated temperatures.Intravenously added heparin affects the clotting time and the aggregation of platelets in in vitro coagulation.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

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