Estimating Johnson-Cook Material Parameters using Neural Networks
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Titu, Nesar Ahmed↗
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A combined experimental and numerical approach that eliminates the non-uniqueness associated with the Johnson-Cook parameters obtained using inverse methods
Abstract Johnson-Cook constitutive model is a commonly used material model for machining simulations. The model includes five parameters that capture the initial yield stress, strain-hardening, strain-rate hardening, and thermal softening behavior of the material. These parameters are difficult to determine using experiments since the conditions observed during machining (such as high strain-rates of the order of $$10^5$$ 10 5 /sec - $$10^6$$ 10 6 /sec) are challenging to recreate in the laboratory. To address this problem, several researchers have recently proposed inverse approaches where a combination of experiments and analytical models are used to predict the Johnson-Cook parameters. The errors between the measured cutting forces, chip thicknesses and temperatures and those predicted by analytical models are minimized and the parameters are determined. In this work, it is shown that only two of the five Johnson-Cook parameters can be determined uniquely using inverse approaches. Two different algorithms, namely, Adaptive Memory Programming for Global Optimization (AMPGO) and Particle Swarm Optimization (PSO), are used for this purpose. The extended Oxley’s model is used as the analytical tool for optimization. For determining a parameter’s value, a large range for each parameter is provided as an input to the algorithms. The algorithms converge to several different sets of values for the five Johnson-Cook parameters when all the five parameters are considered as unknown in the optimization algorithm. All of these sets, however, yield the same chip shape and cutting forces in FEM simulations. Further analyses show that only the strain-rate and thermal softening parameters can be determined uniquely and the three parameters present in the strain-hardening term of the Johnson-Cook model cannot be determined uniquely using the inverse method. A combined experimental and numerical approach is proposed to eliminate this determine all parameters uniquely.
42 ENGINEERING↗
An evaluation of the Johnson-Cook model to simulate puncture of 7075 aluminum plates.
The objective of this project was to evaluate the use of the Johnson-Cook strength and failure models in an adiabatic finite element model to simulate the puncture of 7075- T651 aluminum plates that were studied as part of an ASC L2 milestone by Corona et al (2012). The Johnson-Cook model parameters were determined from material test data. The results show a marked improvement, in particular in the calculated threshold velocity between no puncture and puncture, over those obtained in 2012. The threshold velocity calculated using a baseline model is just 4% higher than the mean value determined from experiment, in contrast to 60% in the 2012 predictions. Sensitivity studies showed that the threshold velocity predictions were improved by calibrating the relations between the equivalent plastic strain at failure and stress triaxiality, strain rate and temperature, as well as by the inclusion of adiabatic heating.
Corona, Edmundo↗
Bayesian optimization for inverse calibration of expensive computer models: A case study for Johnson-Cook model in machining
Inverse model calibration for identifying the constitutive model parameters can be computationally demanding for expensive-to-evaluate simulation models. Here, this paper presents a modified Bayesian optimization (BO) method, denoted as BO-bound, that incorporates theoretical bounds on the quantity of interest. A case study for the inverse calibration of the Johnson Cook (J-C) flow stress model parameters is presented using machining (cutting) force data. The results show fast calibration of the five J-C parameters within 25 simulations. In general, the BO-bound method is applicable for inverse calibration of any expensive simulation models as well as optimization problems with known bounds.
Bayesian optimization↗
Transfer Tube Material Properties Obtained from Test Data
A series of tension and compression tests were performed on typical transfer tubes made of 304L corrosion-resistant steel. The results were compiled and converted to true stress and true plastic strain for comparison to numerical models. The parameters of a Johnson-Cook constitutive model and fracture criterion were calibrated to mimic the test data. Comparisons were made between the converted data and the empirical formulas in the Johnson-Cook model. Simulations were performed to evaluate the implementation of the formula in finite element analysis, and the parameters were adjusted to improve the correlation.
36 MATERIALS SCIENCE↗
Constitutive model development of aluminum alloy 1100 for elevated temperature forming process
Commercially pure aluminum alloy, AA1100, presents good electrical and thermal conductivity, high formability, and low cost. Those favorable characteristics have the potential to enable bipolar plates with improved economics and enhanced performance compared to current stainless steel bipolar plates for proton exchange membrane fuel cells. An accurate constitutive model is essential to develop and optimize processing parameters and effectively control the forming process. Here, the objective of this work is to develop a constitutive model of AA1100 that is able to simulate stress-strain relation, formed geometry, and predict the onset of fracture strain to avoid forming failure. Initially, a set of tensile tests at temperature between 300 and 500°C and strain rate between 0.005 and 1.0/s were conducted to examine the deformation behavior. Then, a set of damage-based unified visco-plastic constitutive equations is proposed and calibrated based on the results of stress-strain data. A genetic algorithm optimization method is applied to search for best fitting material constants in constitutive equations. The proposed model shows good predictability of both the stress-strain relation and fracture strain at low strain rate and high temperature conditions. The accuracy of proposed model is also evaluated statistically. A comparison of the proposed model with three popular models (Arrhenius-type mode, Johnson-Cook model and Zerilli-Armstrong model) was made. The proposed model shows the best experimental agreement with correlation coefficient of 0.96 in contrast to 0.25, 0.38 and 0.75 for the popular models, respectively. The proposed model can help to optimize the elevated temperature forming process and guide die design to enable optimal geometric features in the formed components.
08 HYDROGEN↗
A comparison of material flow strength models using Bayesian cross-validation
Predicting material flow strength over a range of conditions, such as temperature and strain rate, is necessary for many engineering applications. In this paper, we consider how to compare the predictiveness of several different strength models using a statistical technique called Bayesian cross-validation. Given a dataset of flow strength measurements obtained from mechanictesting experiments, the procedure consists of performing a Bayesian calibration of each strength model on a subset of the data and evaluating how well the trained models predict the remaining data. The predictiveness of a calibrated strength model is quantifiable probabilistically, which provides an interpretable metric for comparing the different models. As an illustrative example, we compare the Johnson-Cook (JC), Zerilli-Armstrong (ZA), Preston-Tonks-Wallace (PTW), and Mechanical Threshold Stress (MTS) flow strength models for the tantalum stress-strain curve data from Chen and Gray (1996). We show that prediction intervals for the four strength models cover the held-out data at most experimental conditions, but also that prediction interval coverage and prediction uncertainty varies by model and experimental condition. Finally, the analysis further allows us to identify experimental regimes for which one of the strength models predicts better than the other three.
36 MATERIALS SCIENCE↗
Shock compression behavior of stainless steel 316L octet-truss lattice structures
Lattice structures offer desirable mechanical properties for applications of energy absorption and impact mitigation but limited research has been carried out on their shock compression behavior. In this work, the shock compression behavior of stainless steel 316L (SS316L) octet-truss lattice structures was investigated through experimental techniques and numerical simulations. Plate impact experiments with high-speed imaging were conducted at impact velocities of 270 – 390 m/s on lattice specimens with 5x5x10 unit cell geometries additively manufactured (AM) using direct metal laser sintering. High-speed imaging together with digital image correlation was used to extract full-field measurements and define a two-wave structure consisting of an elastic wave and planar compaction (shock) wave which propagated along the impact direction. A linear shock velocity versus particle velocity relation was found to approximate the measurements with a unit slope and a linear fit constant equal to the crushing speed. Furthermore, the shock velocity versus particle velocity relation, full-field measurements, and elastic limit together with the Eulerian form of the Rankine-Hugoniot jump conditions were used to find relations for the stress and internal energy behind the shock. Stress behind the shock increased with relative density and particle velocity, and specific internal energy converged to a single curve similar to that of bulk AM SS316L. Explicit finite element analysis using the Johnson-Cook constitutive model demonstrated similar shock behavior observed in experiments and a linear shock velocity versus particle velocity relation and corresponding Hugoniot calculations were found to be in agreement with experimental results. Numerical simulations confirmed negligible effects of exterior versus interior measurements and further validated the application of one-dimensional shock theory.
42 ENGINEERING↗
A mechanism-based quantitative multi-scale framework for investigating irradiation hardening of tungsten at low temperature
We present the development and validation of a mechanism-based multi-scale modeling framework to quantitatively link the irradiation defect evolution kinetics at the microscopic scale to the macroscopic yield strength and flow stress evolution of tungsten irradiated at low temperature (0.08 < T/T m < 0.18, where T m is the melting point and is equal to 3673 K). The mechanism-based strength model, proposed as the superposition of thermal softening and modified dispersed barrier hardening, is developed to understand the underlying strengthening mechanisms. The thermal softening exponent as defined in the Johnson-Cook model is obtained by fitting unirradiated yield strength at different temperatures. A set of irradiation-induced defect kinetics equations with the thermodynamics parameters derived from the atomic calculations reported in the literature is used to determine the densities and sizes of defect clusters at the meso-scale, and the predicted irradiation damage characteristics are in reasonable quantitative agreement with experimental data from literature. The effects of irradiation condition (temperature and irradiation dose) and test temperature on yield strength are quantitatively predicted and compared with experimental measurements from the literature. Here, the predicted irradiation hardening and strain hardening are compared with experimental data as model validation.
36 MATERIALS SCIENCE↗
Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data
A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.
42 ENGINEERING↗
Material Testing for Shear-Dominated Ductile Failure
An initial foray into the design of specimens that can be used to provide data about the quasistatic ductile failure of metals when subjected to shear-dominated (low triaxiality) states of stress was undertaken. Four specimen geometries made from two materials with different ductility (Al 7075, lower ductility and steel A286, higher ductility) were considered as candidates. Based on results from analysis and experimentation, it seems that two show promise for further consideration. Whereas preliminary results indicate that the Johnson-Cook model fit the failure data for Al 7075 well, it did not fit the data for steel A286. Further work is needed to consolidate the results and evaluate other failure models that may fit the steel data better, as well as to extend the results of this work to the dynamic loading regime.
36 MATERIALS SCIENCE↗
Modular Growth and Nucleation Formulations in Modular Plasticity Models
Recent investigations like the second and third Sandia Fracture Challenges have characterized and demonstrated the performance of a variety of failure techniques and models. These surveys have considered a wide breadth of models encapsulating both general failure criteria as well as those focusing on pore nucleation and growth. Extensive reviews exist on both topics. The former category generally consists of classic models like the Johnson-Cook or Wilkins criteria. These models were recently added to modular plasticity models in the Library of Advanced Materials for Engineering (LAME) as criteria for use with element death capabilities. The latter category was not treated in that effort. There exists a large class of failure models based on predicting the evolution of pores and failure associated with such microstructures. While the exact mechanisms and corresponding impact on the macroscale behavior remain an active area of research, a large suite of formulations have been proposed combining different features of both pore nucleation and subsequent growth. The most famous of these are based on the popular Gurson model of pore growth derived via micromechanical analysis assuming a plastically incompressible matrix. Numerous other models exist for both growth and nucleation and the Cocks-Ashby growth and Horstemeyer-Gokhale nucleation models have been used successfully in recent Sandia Fracture Challenges. This specific combination is colloquially referred to as the "BCJ-failure model as it has been frequently used with the Bammann-Chisea-Johnson plasticity model.
36 MATERIALS SCIENCE↗
Characterization of Tri-lab β-Tin (Sn)
This report documents details of the microstructure and mechanical properties of -tin (Sn), that is used in the Tri-lab (Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), Sandia National Laboratories (SNL)) collaboration project on Multi-phase Tin Strength. We report microstructural features detailing the crystallographic texture and grain morphology of as-received -tin from electron back scatter diffraction (EBSD). Temperature and strain rate dependent mechanical behavior was investigated by multiple compression tests at temperatures of 200K to 400K and strain rates of 0.0001 /s to 100 /s. Tri-lab tin showed significant temperature and strain rate dependent strength with no significant plastic anisotropy. A sample to sample material variation was observed from duplicate compression tests and texture measurements. Compression data was used to calibrate model parameters for temperature and rate dependent strength models, Johnson-Cook (JC), Zerilli-Armstrong (ZA) and Preston-Tonks-Wallace (PTW) strength models.
36 MATERIALS SCIENCE↗
Effects of Model Uncertainties in Underground Chemical Explosions on Far-field Results
We used the CTH shock physics code to simulate the explosion of an 18-t chemical explosive at a depth of 250 m. We used the CTH in the two-dimensional axisymmetric (cylindrical) geometry (2DC) and most simulations included fully tamped explosions in wet tuff. Our study focused on parametric studies of three of the traditional strength models available in CTH, namely, geologic-yield, elastic perfectly-plastic von Mises, and Johnson-Cook strength (flow stress) models. We processed CTH results through a code that generates Reduced Displacement Potential (RDP) histories for each simulation. Since RDP is the solution of the linear wave equation in spherical coordinates, it is mainly valid at far-enough distance from the explosion the elastic radius. Among various parameters examined, we found the yield strength to have the greatest effect on the resulting RDP, where the peak RDP reduces almost linearly in log-log space as the yield strength increases. Moreover, an underground chemical explosion results in a cavity whose final diameter is inversely proportional to the material yield strength, i.e., as the material's yield strength increases the resulting final cavity radius decreases. Additionally, we found the choice of explosive material (COMP-C4 versus COMP-B) has minor effects on the peak RDP, where denser COMP-C4 shows higher peak RDP than the less dense COMP-B by a factor of ~1.1. In addition to wet tuff, we studied explosions in dry tuff, salt, and basalt, for a single strength model and yield strength value. We found wet tuff has the highest peak RDP value, followed by dry tuff, salt, and basalt. 2DC simulations of explosions in 11 m radius spherical, hemispherical, and cylindrical cavities showed the RDP signals have much lower magnitude than tamped explosions, where the cavity explosions mimicked nearly decoupled explosions.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Calibration of Al7075 with Plate-Puncture Predictions
The following details calibration of a material model for Al7075-T6511. This aluminum alloy is commonly used across a host of engineering applications. Owing to its widespread prevalence, there is great benefit in improving simulation predictions for this alloy. In the present effort, a calibration is performed of its elastic-plastic response accounting for both rate and temperature dependence. The calibration is informed by a series of tests that include specimens of different geometries tested at different rates and temperatures. All specimens are derived from the same barstock, 3.5 inches in diameter. The fitted model itself uses an anisotropic, Hill yield surface coupled with a Johnson-Cook hardening model. Failure predictions are had by means of a modified Wilkins failure criterion. Following calibration of the material model, a validation exercise is performed against platepuncture experiments. These experiments include multiple probe shapes, probe diameters, and plate thicknesses. The puncture experiments are replicated in simulation with mesh studies performed to assess uncertainty. Key quantities of interest, notably the absorbed energy up to failure, are compared between simulation and experiment providing a means to assess the suitability of the calibration in puncture simulations.
36 MATERIALS SCIENCE↗
RaDIATE Collaboration Thermal shock studies
As next-generation accelerator target facilities (High Energy Physics, Spallation Sources, ... ) become increasingly more powerful and intense, high power target systems face key technical challenges, such as radiation damage and thermal shock. Those ultimately degrade the performance and lifetime of targets and have been identified as the leading cross-cutting challenges of high-power target facilities. In order to operate reliable beam-intercepting devices in the framework of energy and intensity increase for next generation accelerators, the RaDIATE Collaboration (Radiation Damage In Accelerator Target Environment), established in 2012 and managed by Fermilab, brings together existing expertise in nuclear material and accelerator targets from 20 international institutions, including CERN, to execute a coordinated strategy for high power targetry R&D. In this context, several thermal shock studies were performed at CERN's HiRadMat (High-Radiation to Materials) facility, that took a key step towards improving our knowledge on target damage tolerance. The first experiment HRMT-24, supported by EURCARD2 and completed in 2015, successfully validated the Johnson-Cook strength model developed at SwRI on beryllium S200FH (used for beam window material), providing a better confidence in simulating the thermal shock response of current and future S200FH beryllium components. HRMT-43, supported by ARIES and completed in 2018, tested various materials (Be, C, SiC, Si, Ti and ceramic nanofiber). It was a first and unique test which included pre-irradiated specimens from high energy proton beam irradiation to identify thermal shock response differences between non-irradiated and previously irradiated materials. Real-time measurement of dynamic thermomechanical response of graphite helped to benchmark numerical simulations.
43 PARTICLE ACCELERATORS↗