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.

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.

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.

scholarly journals Energy Dissipation-Based Method for Strength Determination of Rock under Uniaxial Compression

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
M. M. He ◽  
F. Pang ◽  
H. T. Wang ◽  
J. W. Zhu ◽  
Y. S. Chen
Keyword(s):  
Yield Strength ◽  
Uniaxial Compression ◽  
Peak Strength ◽  
Dissipated Energy ◽  
Compression Tests ◽  
Dissipation Energy ◽  
Evolution Characteristics ◽  
Deformation Properties ◽  
Energy Coefficient ◽  
The Stability

The energy conversion in rocks has an important significance for evaluation of the stability and safety of rock engineering. In this paper, some uniaxial compression tests for fifteen different rocks were performed. The evolution characteristics of the total energy, elastic energy, and dissipated energy for the fifteen rocks were studied. The dissipation energy coefficient was introduced to study the evolution characteristics of rock. The evolution of the dissipation energy coefficient for different rocks was investigated. The linear interrelations of the dissipation energy coefficients and the yield strength and peak strength were explored. The method was proposed to determine the strength of rock using the dissipation energy coefficients. The results show that the evolution of the dissipation energy coefficient exhibits significant deformation properties of rock. The dissipation energy coefficients linearly increase with the compaction strength, but decrease with the yield strength and peak strength. Moreover, the dissipation energy coefficient can be used to determine the rock burst proneness and crack propagation in rocks.

scholarly journals Correlational Analytical Characterization of Energy Dissipation-Liberation and Acoustic Emission during Coal and Rock Fracture Inducing by Underground Coal Excavation

Energies ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2382 ◽  
Author(s):  
Pengfei Shan ◽  
Xingping Lai ◽  
Xiaoming Liu
Keyword(s):  
Acoustic Emission ◽  
Energy Dissipation ◽  
Axial Stress ◽  
Rock Fracture ◽  
Quantitative Relationship ◽  
Dissipated Energy ◽  
Release Mechanism ◽  
Rock Fracturing ◽  
Dissipation Energy ◽  
Energy Parameters

This paper uses an acoustic emission (AE) test to examine the energy dissipation and liberation of coal and rock fracture due to underground coal excavation. Many dynamic failure events are frequently observed due to underground coal excavation. To establish the quantitative relationship between the dissipated energy and AE energy parameters, the coal and rock fracturing characteristics were clearly observed. A testing method to analyze the stage traits and energy release mechanism from damage to fracture of the unloading coal and rock under uniaxial compressive loading is presented. The research results showed that the relevant mechanical parameter discreteness was too large because the internal structures of the coal and rock were divided into multiple structural units (MSU) by a few main cracks. The AE test was categorized into four stages based on both the axial stress and AE event parameters: initial loading stage, elastic stage, micro-fracturing stage, and post-peak fracturing stage. The coal and rock samples exhibited minimum (maximum) U values of 60.44 J (106.41 J) and 321.19 J (820.87 J), respectively. A theoretical model of the dissipation energy during sample fracturing based on the AE event energy parameters was offered. The U decreased following an increase in ΣEAE-II/ΣEAE.

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.

scholarly journals Identification of thermal material parameters for thermo-mechanically coupled material models

Meccanica ◽  
2021 ◽  
Vol 56 (2) ◽  
pp. 393-416
Author(s):  
L. Rose ◽  
A. Menzel
Keyword(s):  
Evolution Equations ◽  
Constitutive Relations ◽  
Material Model ◽  
Basic Material ◽  
Dissipated Energy ◽  
Model Formulation ◽  
Material Models ◽  
Material Parameters ◽  
Simple Tension ◽  
The Impact

AbstractThe possibility of accurately identifying thermal material parameters on the basis of a simple tension test is presented, using a parameter identification framework for thermo-mechanically coupled material models on the basis of full field displacement and temperature field measurements. Main objective is to show the impact of the material model formulation on the results of such an identification with respect to accuracy and uniqueness of the result. To do so, and as a proof of concept, the data of two different experiments is used. One experiment including cooling of the specimen, due to ambient temperature, and one without specimen cooling. The main constitutive relations of two basic material models are summarised (associated and non-associated plasticity), whereas both models are extended so as to introduce an additional material parameter for the thermodynamically consistent scaling of dissipated energy. The chosen models are subjected to two parameter identifications each, using the data of either experiment and focusing on the determination of thermal material parameters. The influence of the predicted dissipated energy of the models on the identification process is investigated showing that a specific material model formulation must be chosen carefully. The material model with associated evolution equations used within this work does neither allow a unique identification result, nor is any of the solutions for the underlying material parameters close to literature values. In contrast to that, a stable, that is locally unique, re-identification of the literature values is possible for the boundary problem at hand if the model with non-associated evolution equation is used and if cooling is included in the experimental data.

scholarly journals Simulation of the Uniaxial Mechanical Properties and Crack Evolution of Coal Pillar-artificial Dam in Abandoned Mines

2021 ◽  
Author(s):  
Xin Lyu ◽  
Ke Yang ◽  
Juejing Fang ◽  
Zhainan Zhang ◽  
Yu Wang ◽  
...  
Keyword(s):  
Early Stage ◽  
Coal Pillar ◽  
Abandoned Mines ◽  
Dissipated Energy ◽  
Energy Curve ◽  
Uniaxial Compression Test ◽  
Peak Strain ◽  
Crack Evolution ◽  
Dissipation Energy ◽  
Coal Pillars

Abstract The key to the construction of underground reservoirs in abandoned mines is the construction of coal pillar-artificial dams, and the choice of bonding parameters between the coal pillars and artificial dams is the deciding factor that determines the engineering stability. Based on the analysis of the force state of coal pillar-artificial dams, the influence of the interface angle was analyzed. Seven sets of coal pillar-artificial dam specimens were prepared and a PFC3D numerical model was constructed to carry out the uniaxial compression test without lateral pressure. Based on the strength, deformation, and energy evolution characteristics of the coal pillar-artificial dam, the influence of the angle of the coal pillar-artificial dam interface on the performance of the specimen was analyzed. The PFC3D model was used to investigate crack evolution, particle displacement, and spatial distribution. The research results showed that the force state of the coal pillar-artificial dam can be divided into three types: split bearing, shared bearing, and coordinated bearing, corresponding to three different constitutive models. The composite simulation curve showed obvious post-peak viscosity. The compressive strength, peak strain, and average dissipated energy curves of the coal pillar-artificial dam showed a unimodal trend that first increased and then decreased. The total energy and elastic energy of the coal pillar-artificial dam showed an increasing trend during loading. The dissipation energy curve increased obviously in the early stage, then flattened, and finally, decayed. The simulated initiation stress and damage stress of the coal pillar-artificial dam specimens were intermediate to that of the coal pillars and the artificial dams, which first increased and then decreased with the increase in inclination, reaching the peak at 70°. The failures of the single and combined models were both dominated by monoclinic splitting. As the inclination increased, the position of the main cracks gradually shifted downwards and then upwards.

scholarly journals Experimental Study on Mechanical Properties and Energy Dissipation of Gas Coal under Dynamic and Static Loads

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Xiang Cheng ◽  
Guangming Zhao ◽  
Yingming Li ◽  
Xiangrui Meng ◽  
Qingyi Tu ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Energy Dissipation ◽  
Strain Rate ◽  
Dynamic Load ◽  
Coal Sample ◽  
Static Load ◽  
Dissipated Energy ◽  
Dissipation Energy ◽  
Static Loads ◽  
Gas Coal

In order to study the mechanical properties and energy dissipation of gas coal under dynamic and static loads, the static loading and impact tests of different strain rates were carried out by the testing systems of SZW-1000 microcomputer servo pressure tester and separated Hopkinson pressure bar (SHPB) for gas coal in the Panxie Coal Field in Huainan City. In the test, the influence laws of various loading patterns on mechanical properties, failure characteristics, and energy dissipation of gas coal sample were analyzed. The results showed that the stress-strain curve of coal gas under dynamic load had no micropore compaction stage compared with that under static load. Dynamic compressive strength, dynamic strength growth factor, mixed dynamic elasticity modulus, and dissipation energy were all highly correlated with strain rate, whereas energy dissipation rate was uncorrelated with strain rate. In addition, the gas coal sample with lower strain had small dissipated energy, and it developed a splitting failure mode. With the increase of strain rate, the dissipation energy increased and the crushing degree of gas coal intensified, finally presenting a compressive failure mode. Based on the comparison of dissipated energy densities of different gas coal samples, given the same dissipated energy density, the failure degree of sample under dynamic load was higher than that under static load.

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.

Sign in / Sign up

Export Citation Format

Share Document