scholarly journals Application of a Microstructure-Based ISV Plasticity Damage Model to Study Penetration Mechanics of Metals and Validation through Penetration Study of Aluminum

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yangqing Dou ◽  
Yucheng Liu ◽  
Youssef Hammi ◽  
Wilburn Whittington
Keyword(s):  
Internal State ◽  
Void Nucleation ◽  
Damage Model ◽  
Rate Equations ◽  
Modeling Framework ◽  
Experimental Calibration ◽  
Model Compression ◽  
Penetration Mechanics ◽  
Stress States ◽  
First Time

A developed microstructure-based internal state variable (ISV) plasticity damage model is for the first time used for simulating penetration mechanics of aluminum to find out its penetration properties. The ISV damage model tries to explain the interplay between physics at different length scales that governs the failure and damage mechanisms of materials by linking the macroscopic failure and damage behavior of the materials with their micromechanical performance, such as void nucleation, growth, and coalescence. Within the continuum modeling framework, microstructural features of materials are represented using a set of ISVs, and rate equations are employed to depict damage history and evolution of the materials. For experimental calibration of this damage model, compression, tension, and torsion straining conditions are considered to distinguish damage evolutions under different stress states. To demonstrate the reliability of the presented ISV model, that model is applied for studying penetration mechanics of aluminum and the numerical results are validated by comparing with simulation results yielded from the Johnson-Cook model as well as analytical results calculated from an existing theoretical model.

Comparison of Johnson-Cook Model and an ISV Plasticity Damage Model in Penetration Simulation

2016 ◽  
Author(s):  
Yangqing Dou ◽  
Yucheng Liu ◽  
Youssef Hammi
Keyword(s):  
High Speed ◽  
Internal State ◽  
Damage Model ◽  
Rate Equations ◽  
State Variables ◽  
High Speed Impact ◽  
Internal States ◽  
Penetration Mechanics ◽  
History Of ◽  
Cook Model

This paper compares Johnson-Cook model and an internal state variable (ISV) damage model developed by Bammann and Horstemeyer in simulating damage behavior of materials during penetration process. Bammann and Horstemeyer’s ISV damage model employs internal state variables and their rate equations to capture the evolution of internal states of materials during high speed impact and penetration. From the calculated internal states, observable states or global penetration and perforation response of materials can be decided. Compared to the JC model, the ISV damage model closely reflect history of materials’ mechanical behavior during the penetration and perforation process. Moreover, the damage model links the global impact and penetration performance of the materials to their microstructural evolution, such as the nucleation, growth, and coalescence of micro voids and cracks. Therefore, it possesses an enhanced predicative capability for high speed impact, penetration, and perforation problems. To demonstrate the reliability of the presented ISV model, that model is applied for studying penetration mechanics of aluminum and the numerical results are validated by comparing with simulation results yielded from the Johnson-Cook model as well as analytical results calculated from an existing theoretical model.

Experimental Calibration of ISV Damage Model Constants for Pure Copper for High-Speed Impact Simulation

2016 ◽  
Author(s):  
Yangqing Dou ◽  
Yucheng Liu ◽  
Wilburn Whittington ◽  
Jonathan Miller
Keyword(s):  
High Speed ◽  
Impact Analysis ◽  
Split Hopkinson Pressure Bar ◽  
Internal State ◽  
Pure Copper ◽  
Damage Model ◽  
Hopkinson Pressure Bar ◽  
Experimental Calibration ◽  
High Speed Impact ◽  
The Impact

Coefficients and constants of a microstructure-based internal state variable (ISV) plasticity damage model for pure copper have been calibrated and used for damage modeling and simulation. Experimental stress-strain curves obtained from Cu samples at different strain rate and temperature levels provide a benchmark for the calibration work. Instron quasi-static tester and split-Hopkinson pressure bar are used to obtain low-to-high strain rates. Calibration process and techniques are described in this paper. The calibrated material model is used for high-speed impact analysis to predict the impact properties of Cu. In the numerical impact scenario, a 100 mm by 100 mm Cu plate with a thickness of 10 mm will be penetrated by a 50 mm-long Ni rod with a diameter of 10mm. The thickness of 10 mm was selected for the Cu plate so that the Ni-Cu penetration through the thickness can be well observed through the simulations and the effects of the ductility of Cu on its plasticity deformation during the penetration can be displayed. Also, that thickness had been used by some researchers when investigating penetration mechanics of other materials. Therefore the penetration resistance of Cu can be compared to that of other metallic materials based on the simulation results obtained from this study. Through this study, the efficiency of this ISV model in simulating high-speed impact process is verified. Functions and roles of each of material constant in that model are also demonstrated.

A Thermo-Electro-Elasto-Viscoplastic Damage Internal State Variable (ISV) Model for Ductile Metals

2018 ◽  
Author(s):  
Nikolay Dimitrov ◽  
Yucheng Liu ◽  
M. F. Horstemeyer
Keyword(s):  
Internal State ◽  
Deformation Gradient ◽  
Damage Model ◽  
Rate Equations ◽  
Thermodynamic Force ◽  
Practical Implementation ◽  
Internal State Variable ◽  
State Variable ◽  
Simplifying Assumptions ◽  
Future Work

A multiphysics Internal State Variable (ISV) theory that couples the thermoelastoviscoplastic damage model of Bammann-Horstemeyer with electricity-related electromagnetic phenomena is presented in which the kinematics, thermodynamics, and kinetics are internally consistent. An extended multiplicative decomposition of the deformation gradient that accounts for elasticity, plasticity, damage, thermal expansion, electricity, and magnetism is introduced. The different geometrically-affected rate equations are given for each phenomenon after the ISV formalism and have a thermodynamic force pair that acts as an internal stress-like quantity. Guidelines for practical implementation, recommendations for simplifying assumptions, and suggestions for future work supplement the theoretical model. The abstraction of the model can capture the full multi-physics described above; however, the robustness of the model is realized when any of the listed phenomena are not included in the boundary value problem, the model reduces to the previous form — the model will revert to the Bammann-Horstemeyer plasticity-damage ISV model.

Plasticity and Fracture Modeling/Experimental Study of a Porous Metal Under Various Strain Rates, Temperatures, and Stress States

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
P. G. Allison ◽  
H. Grewal ◽  
Y. Hammi ◽  
H. R. Brown ◽  
W. R. Whittington ◽  
...  
Keyword(s):  
Model Calibration ◽  
Nearest Neighbor ◽  
Internal State ◽  
Damage Model ◽  
Porous Metal ◽  
Local Stress ◽  
Porous Powder ◽  
Tension Tests ◽  
Stress States ◽  
Bearing Cap

A microstructure-based internal state variable (ISV) plasticity-damage model was used to model the mechanical behavior of a porous FC-0205 steel alloy that was procured via a powder metal (PM) process. Because the porosity was very high and the nearest neighbor distance (NND) for the pores was close, a new pore coalescence ISV equation was introduced that allows for enhanced pore growth from the concentrated pores. This coalescence equation effectively includes the local stress interaction within the interpore ligament distance between pores and is physically motivated with these highly porous powder metals. Monotonic tension, compression, and torsion tests were performed at various porosity levels and temperatures to obtain the set of plasticity and damage constants required for model calibration. Once the model calibration was achieved, then tension tests on two different notch radii Bridgman specimens were undertaken to study the damage-triaxiality dependence for model validation. Fracture surface analysis was performed using scanning electron microscopy (SEM) to quantify the pore sizes of the different specimens. The validated model was then used to predict the component performance of an automotive PM bearing cap. Although the microstructure-sensitive ISV model has been employed for this particular FC-0205 steel, the model is general enough to be applied to other metal alloys as well.

A Multiphase Internal State Variable Model With Rate Equations for Predicting Elastothermoviscoplasticity and Damage of Fiber Reinforced Polymer Composites

2017 ◽  
Author(s):  
Ge He ◽  
Yucheng Liu ◽  
D. J. Bammann ◽  
M. F. Horstemeyer
Keyword(s):  
Internal State ◽  
Damage Model ◽  
Matrix Cracking ◽  
Fiber Reinforced Polymer ◽  
Rate Equations ◽  
Internal State Variable ◽  
Fiber Reinforced ◽  
Variable Model ◽  
State Variable ◽  
Reinforced Polymer

This paper agglomerates an Internal State Variable (ISV) model for polymers (Bouvard et al., 2010, 2013) with damage evolution (Horstemeyer and Gokhale, 1999: Horstemeyer et al., 2000; Francis et al., 2014) into a multiphase ISV framework (Rajagopal and Tao, 1995; Bammann et al., 1996) that features a finite strain theoretical framework for Fiber Reinforced Polymer (FRP) composites under various stress states, temperatures, strain rates, and history dependencies. In addition to the inelastic ISVs for the polymer matrix and interphase, new ISVs associated with the interaction between phases are introduced. A scalar damage variable is employed to capture the damage history of such material, which is a result of three damage modes: matrix cracking, fiber breakage, and deterioration of the fiber-matrix interface, and each damage model was well calibrated to the experimental data from Rolland et al., (2016). The constitutive model developed herein arises employing standard postulates of continuum mechanics with the kinematics, thermodynamics, and kinetics being internally consistent.

scholarly journals Analysis of Bifurcation and Chaos of the Size-dependent Micro–plate Considering Damage

2019 ◽  
Vol 8 (1) ◽  
pp. 461-469 ◽  
Author(s):  
Xiumei Wang ◽  
Jihai Yuan ◽  
Haorui Zhai
Keyword(s):  
Internal State ◽  
Couple Stress Theory ◽  
Damage Model ◽  
Modified Couple Stress Theory ◽  
Damage Effect ◽  
Bifurcation And Chaos ◽  
Stress Theory ◽  
Size Dependent ◽  
Material Length Scale ◽  
Plate System

Abstract In this research, nonlinear dynamics and characteristics of a micro–plate system under electrostatic forces on both sides are studied. A novel model, which takes micro-scale effect and damage effect into account, is established on the basis of the Talreja’s tensor valued internal state damage model and modified couple stress theory. According to Hamilton principle, the dynamic governing equations of the size-dependent micro–plate are derived by variational method and solved via Galerkin method and the fourth order Runge-Kutta method. The effects of damage variable and material length scale parameter on bifurcation and chaos of the micro–plate system are presented with numerical simulations using the bifurcation diagram, Poincare map. Results provide a theoretical basis for the design of dynamic stability of electrically actuated micro- structures.

Uncertainty Quantification in Metallic Additive Manufacturing Through Data-Driven Modelling Based on Multi-Scale Multi-Physics Models and Limited Experiment Data

2020 ◽  
Author(s):  
Zhuo Wang ◽  
Chen Jiang ◽  
Mark F. Horstemeyer ◽  
Zhen Hu ◽  
Lei Chen
Keyword(s):  
Temperature Field ◽  
Additive Manufacturing ◽  
Uncertainty Quantification ◽  
Surrogate Modeling ◽  
Data Driven ◽  
Modeling Framework ◽  
High Quality ◽  
Experimental Calibration ◽  
Multi Scale ◽  
Metallic Additive

Abstract One of significant challenges in the metallic additive manufacturing (AM) is the presence of many sources of uncertainty that leads to variability in microstructure and properties of AM parts. Consequently, it is extremely challenging to repeat the manufacturing of a high-quality product in mass production. A trial-and-error approach usually needs to be employed to attain a product with high quality. To achieve a comprehensive uncertainty quantification (UQ) study of AM processes, we present a physics-informed data-driven modeling framework, in which multi-level data-driven surrogate models are constructed based on extensive computational data obtained by multi-scale multi-physical AM models. It starts with computationally inexpensive metamodels, followed by experimental calibration of as-built metamodels and then efficient UQ analysis of AM process. For illustration purpose, this study specifically uses the thermal level of AM process as an example, by choosing the temperature field and melt pool as quantity of interest. We have clearly showed the surrogate modeling in the presence of high-dimensional response (e.g. temperature field) during AM process, and illustrated the parameter calibration and model correction of an as-built surrogate model for reliable uncertainty quantification. The experimental calibration especially takes advantage of the high-quality AM benchmark data from National Institute of Standards and Technology (NIST). This study demonstrates the potential of the proposed data-driven UQ framework for efficiently investigating uncertainty propagation from process parameters to material microstructures, and then to macro-level mechanical properties through a combination of advanced AM multi-physics simulations, data-driven surrogate modeling and experimental calibration.

Further Development of the Nonlocal Damage Model of Rousselier for the Transition Regime of Fracture Toughness and Different Stress States

2014 ◽  
Author(s):  
Sarah Gehrlicher ◽  
Michael Seidenfuss ◽  
Xaver Schuler
Keyword(s):  
Fracture Toughness ◽  
Damage Mechanics ◽  
Damage Model ◽  
Nonlocal Damage ◽  
Brittle Transition ◽  
Mechanics Model ◽  
Element Size ◽  
Transition Area ◽  
Ductile To Brittle Transition ◽  
Stress States

In nuclear power engineering failure has to be excluded for components with high safety relevance. Currently, safety assessments mainly use fracture mechanics concepts. Especially in the transition region of fracture toughness where limited stable crack extension may appear before cleavage fracture the currently applied methods are limited. This Paper deals with the development and verification of a closed concept for safety assessment of components over the whole range from the lower shelf to the upper shelf of fracture toughness. The results of classical used local damage mechanics models depend on the element size of the numerical model. This disadvantage can be avoided using an element size depending on microstructure. With high stress gradients and small crack growth rates usually smaller elements are required. This is in conflict with an element size depending on microstructure. By including the damage gradient as an additional degree of freedom in the damage mechanics model the results depend no longer at the element size. In the paper damage mechanics computations with a nonlocal formulation of the Rousselier model are carried out for the evaluation of the upper transition area. For the prediction of fracture toughness from the ductile to brittle transition area the nonlocal Rousselier model is coupled with the Beremin model. Thus ductile crack growth and failure by brittle fracture can be described in parallel. The numerical prediction of the behaviour of fracture toughness specimens (C(T)-specimens and SE(B)-specimens with and without side grooves) and the experimental results are highly concordant. The load displacement behavior of the specimens and the developed crack front from the ductile to brittle transition area can be well calculated with the nonlocal damage model. The instability in relation to temperature calculated with the coupled damage mechanics model predicts the variations of the experimental results very well. For further application of the nonlocal Rousselier model experiments and numerical calculations of specimens with different stress states and multi-axiality are carried out. Modified fracture toughness specimens like CTS-specimens (compact tension shear specimens) are taken to investigate the applicability of the nonlocal damage model of Rousselier to mixed mode fracture.

Jump Relaxation: Simple Equations, Relevant Functions, and Kohlrausch-Williams-Watts Behavior

1990 ◽  
Vol 210 ◽  
Author(s):  
Klaus Funke
Keyword(s):  
Solid Electrolytes ◽  
Structural Disorder ◽  
Time Correlation ◽  
Standard Theory ◽  
Rate Equations ◽  
Analytic Expressions ◽  
Repulsive Coulomb ◽  
Simple Equations ◽  
Mobile Ions ◽  
First Time

AbstractSolid electrolytes with structural disorder generally exhibit characteristic deviations from standard-theory spectra. The effect is known as “universal” dynamic response. In the jump-relaxation model, the phenomena are consistently explained in terms of the non-random hopping resulting from the repulsive Coulomb interaction among the mobile ions. In previous stages of the development of the model, the treatment required either crude approximations or extensive numerical calculations. Now. however, we are able to present, for the first time. simple analytic expressions for the relevant time correlation functions, derived from the rate equations of the model. In particular, the dependence of the ionic conductivity on frequency and temperature is now expressed by a simple equation. Furthermore, we recover the Kohlrausch-Williams- Watts behavior and find the KWW exponent. β. and the mismatch parameter of our model, α. to be identical. The validity of the KWW law is shown to be limited to the dispersive regime on the frequency and time scales.

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