Mechanical Threshold Stress Model Research Articles

Prediction of flow stress of Ta–W alloys using machine learning

Abstract The primary aim of this article was to predict the flow stress of Ta–W alloys using the eXtreme Gradient Boosting (XGBoost) machine learning model and to explain the outcome using SHapley Additive exPlanations (SHAP). The article details the effect of temperature, strain rate, and alloying content on the deformation behavior. Though grain size, dislocation density, texture and impurities are also important factors affecting the deformation behavior, these have not been considered in this work. Data and constitutive models from the literature were used to find and compare the predictiveness of the flow stress in Ta–W alloys. XGBoost predicted flow stress with a root mean square error of 12 MPa during training and 40 MPa during testing, while constitutive models such as Johnson–Cook (JC), Zerilli–Armstrong (ZA) and mechanical threshold stress (MTS) models showed a root mean square error of 208, 131 and 149 MPa respectively. The linear correlation between the predicted and experimental flow stress at 10% strain was calculated using the Pearson correlation coefficient and found to be 0.64, 0.93, and 0.70 for JC, ZA and MTS models respectively, while XGBoost showed 0.99 during training and 0.98 during testing. The optimized XGBoost model was validated using five-fold and leave-one-group-out cross-validations. The flow stress at 10% strain was predicted using XGBoost at various temperatures, strain rates, and alloying content. The flow stress was low at temperatures above 1000 K and strain rates below 10−2 s−1. From SHAP analysis, it was found that the base flow stress value (at which the SHAP value is zero) was 477 MPa. For temperatures less than 275 K, strain rates greater than 1 s−1, and alloying content greater than 2.5 wt.% W, the flow stress showed an increase from its base value.

Constitutive Modeling of Annealed OFHC with Wide Strain-Rate and Temperature Effects: Incorporating Dislocation Dynamics and Normalized Microstructural Size Evolution.

The flow stress of face-centered cubic (FCC) metals exhibits a rapid increase near a strain rate of 104 s-1 under fixed-strain conditions. However, many existing constitutive models either fail to capture the mechanical characteristics of this plastic deformation or use piecewise strain-rate hardening models to describe this phenomenon. Unfortunately, these piecewise models may suffer from issues such as discontinuity of physical quantities and difficulties in determining segment markers, and struggle to reflect the underlying physical mechanisms that give rise to this mutation phenomenon. In light of this, this paper proposes that the abrupt change in flow stress sensitivity to strain rate in FCC metals can be attributed to microstructural evolution characteristics. To address this, a continuous semiempirical physical constitutive model for FCC metals is established based on the microstructural size evolution proposed by Molinari and Ravichandran and the dislocation motion slip mechanism. This model effectively describes the mutation behavior of strain-rate sensitivity under fixed strain, particularly evident in an annealed OFHC. The predicted results of the model across a wide range of strain rates (10-4-106 s-1) and temperatures (77-1096 K) demonstrate relative errors generally within ±10% of the experimental values. Furthermore, the model is compared with five other models, including the mechanical threshold stress (MTS), Nemat-Nasser-Li (NNL), Preston-Tonks-Wallace (PTW), Johnson-Cook (JC), and Molinari-Ravichandran (MR) models. A comprehensive illustration of errors reveals that the proposed model outperforms the other five models in describing the plastic deformation behavior of OFHC. The error results offer valuable insights for selecting appropriate models for engineering applications and provide significant contributions to the field.

Modification of the MTS model for high strain-rate behavior of TI-6AL-4V

The Mechanical Threshold Stress (MTS) model provides excellent predictive capabilities for the material constitutive response for a wide range of temperatures and strain rates. However, the MTS model fails to capture the rapidly increasing yield stress at high strain rate behavior as the deformation controlling mechanism transitions from thermal activation to drag mechanisms, only capturing the linear behavior. Further, the model typically over predicts the flow stress behavior at yield and post yield due to its use of a constant work hardening rate parameter derived from the stress–strain response at constant saturation stress. An alternative approach to fitting portions of the MTS model is investigated and mathematical models are developed to address these issues. The results show that with appropriate experimental data, the mechanical threshold stress and work hardening rate parameters within the MTS model can quite easily and accurately be modified to extend applicability to high strain rate behavior and more accurately model the initial flow stress behavior at early work hardening rates without modification of the functions core to the MTS model itself.

A Comprehensive Review of Experience with the Application of the Mechanical Threshold Stress Model

A Comprehensive Review of Experience with the Application of the Mechanical Threshold Stress Model

Dynamic strain ageing in an AlMg alloy at different strain rates and temperatures: Experiments and constitutive modelling

Uniaxial tension tests at strain rates from 10−4 to 10−1s−1 and temperatures from 298 to 418 K are performed to study the dynamic strain ageing (DSA) of an AA5182-O sheet. Digital image correlation (DIC) is used to obtain the stress-strain curves and characterize the heterogenous deformations. A constitutive model based on the mechanical threshold stress (MTS) framework is then proposed and used to calculate the stress–strain response at different strain rates and temperatures. The modified MTS model captures the dependence of the strain rate sensitivity (SRS) on strain, temperature and strain rate both inside and outside the Portevin–Le Chatelier (PLC) domain. Special attention is paid to re-interpret the occurrence of stress serrations. It is found that the competition between work hardening and DSA leads to different jerky flow scenarios. The modified MTS model is used to predict the PLC domain as a function of strain rate and temperature. To further test the validity of the model at various temperatures and alloys, it is also approximately calibrated to Ni-based superalloys, for which it captures earlier reported behaviour at elevated temperatures.

Application of the Mechanical Threshold Stress Model to Large Strain Processing

Application of the Mechanical Threshold Stress Model to Large Strain Processing

Comparative studies of the constitutive models for tungsten heavy alloy (95W-3.5Ni-1.5Fe) at high strain rates

The plastic behaviors’ description of a tungsten heavy alloy (95W-3.5Ni-1.5Fe) at temperatures of 298–773 K and strain rates of 0.001–11,000 s−1 is systematically studied based on four constitutive models, that is, Zerilli-Armstrong model, modified Zerilli-Armstrong model, Mechanical Threshold Stress model, and modified Mechanical Threshold Stress model. The quasi-static compression experiments using an electronic universal testing machine and the dynamic compression experiments using a split Hopkinson pressure bar apparatus are employed to obtain the true stress–strain curves at a total of three temperatures (298 K, 573 K, and 773 K) and a wide range of strain rates (0.001–11,000 s−1). The parameters of the four constitutive models are obtained by the above fundamental experimental data and Grey Wolf Optimizer. The correlation coefficient and average absolute relative error are used to evaluate the predicted performance of these models. Modified Mechanical Threshold Stress model is found to have the highest predicted performance in describing the flow stress of the 95W-3.5Ni-1.5Fe alloy. Eventually, two compression experiments whose loading conditions are not in the fundamental experiments are conducted to validate the four models.

Physics-based and phenomenological plasticity models for thermomechanical simulation in laser powder bed fusion additive manufacturing: A comprehensive numerical comparison

The present study investigated the sensitivity of material constitutive models on thermomechanical responses in laser powder bed fusion additive manufacturing of Ti-6Al-4V. Uniform scan strategies with scan lengths of 0.5, 1, and 2 mm were applied so that wide ranges of thermal histories could be generated. The Johnson-Cook (JC) and Mechanical Threshold Stress (MTS) material plasticity models were chosen to capture the influence of strain, strain rate, and temperature. The JC model is a phenomenological model which is known for its easy implementation and excellent agreement with material testing results. On the other hand, the MTS model is a more complex physics-based internal state variable plasticity model that is expected to provide more accurate estimation, particularly for cases involving changes in strain rate and temperature. Numerical results revealed that both JC and MTS models provided a similar stress evolution, however, the plastic strain evolution was more realistic using the MTS model. Moreover, it was found that the maximum strain and the strain rate in the LPBF process are high compared to typical quasi-static testing, i.e., ~ 2% and ~ 4 s−1, respectively. Accordingly, the material models should be calibrated with data obtained under similar deformation conditions. The choice of scan length also strongly affects in-plane stress anisotropy. Ultimately, we show both qualitatively and quantitatively the dependency of mechanical behavior prediction in LPBF on the choice of material models.

Microstructure affected residual stress prediction based on mechanical threshold stress in direct metal deposition of Ti-6Al-4 V

Although the material microstructure attributes play an important role in the mechanical properties of the additively manufactured (AM) part, their impact is largely ignored in the mechanics modeling of AM processes. A physics-based mechanical threshold stress (MTS) model is proposed to consider the material internal attributes, such as grain size and dislocation to dislocation barrier during simulation of the material flow stress and deformation. This model is based on the dislocation dynamics and thermal activation theory with a combination of three main components of athermal stress, thermal stress, and threshold stress. The MTS flow stress model is embedded into a fully coupled thermo-mechanical incremental plasticity model to predict the residual stress during AM processes from the prediction of temperature field and associated thermal stresses. The experimental measurements of residual stress are conducted on additively manufactured Ti-6Al-4 V samples for the model validation. The proposed model provides insight into the impact of microstructure on residual stress prediction in the additive manufacturing process modeling.

Examining material constitutive response under dynamic compression and large plastic strains using in situ imaging of hole closure

For understanding material performance under dynamic loading, there is significant interest in the strain rate dependence of material response and in the degree to which high-rate response depends on initial material state. Experimental tests at high strain rates (>103/s) often use measurement of shape change to infer flow strength behavior. Given stress and strain heterogeneities, inferences about flow strength behavior from those observations are facilitated by comparisons with advanced simulations. A new plate impact-based experimental test is described, consisting of in situ X-ray imaging to observe the closure of a cylindrical hole during the passage of a pressure pulse of controlled amplitude and duration. With the goal of providing unique data regarding plastic response at high strain rates, the closure of the hole is measured through time using multi-frame imaging. A first set of experiments on copper examines the role of starting microstructure on material flow behavior. The experimental observations are compared with predictions from direct numerical simulations using the Preston-Tonks-Wallace (PTW) and the Mechanical Threshold Stress (MTS) flow strength models. The quantitative utility of the overall approach is demonstrated in that the results provide information about MTS model parameters associated with high-rate hardening behavior, with the parameters having been unconstrained by quasi-static experimental data.

Creep deformation behavior of nano oxide dispersion strengthened Fe–18Cr ferritic steel

The objective of present work is to investigate the creep behavior of nano oxide dispersion strengthened Fe–18Cr ferritic steel (Fe–18Cr–3W–0.3Ti–0.35Y2O3) over a range of temperatures 923–1023 K and range of stresses 175–400 MPa. The analysis of creep data according to the power law equation suggests high apparent stress exponents (17–26) and high apparent activation energy (~690 kJ/mol). Microstructural analysis indicated that no change in the grain and nanoprecipitate size occurred in the sample crept at 973 K and 225 MPa after 2600 h. Transmission electron microscopy studies on crept samples revealed substantial dislocation activity in the grains and the interaction between dislocations and nanoprecipitates. Based on the analysis of results, dislocation detachment mechanism is identified as a creep mechanism in the present steel. Accordingly, the creep results are rationalized based on the dislocation detachment model and mechanical threshold stress model.

Prediction of the deformation behavior of a selective laser-melted Ti-6Al-4V alloy as a function of process parameters

Recent studies have shown that the mechanical properties of Ti alloys produced by additive manufacturing (AM) methods are sensitive to AM process parameters. The mechanical threshold stress (MTS) model is capable of predicting the flow stress behavior of materials; however, the parameters needed in the MTS model are affected by the microstructure that originates from the AM process parameters. To find a relationship between the AM process parameters and the MTS parameters, the effect of process parameters on the mechanical properties of selective laser-melted (SLM) Ti-6Al-4V samples was studied. As the MTS model is sensitive to the microstructure, only near fully dense samples were considered.

Taylor impact test revisited: Determination of plasticity parameters for metals at high strain rate

Taylor impact test is the simplest experimental approach for characterizing plastic behaviour of metals under high strain rate (up to 105 s−1). Herein, a cylindrical rod is impacted upon a rigid stationary anvil and the dynamic yield strength is estimated by comparing the experimentally obtained rod deformation with its theoretical counterpart. Despite being simple and potent concept, the lack of a comprehensive theoretical model (which relates the material constitutive with the deformation pattern of the rod) has so far restricted the use of the Taylor impact test in material characterization. In the present study the Taylor impact test is revisited and an attempt is made to formulate an inverse framework for efficient determination of constitutive parameters for metals. The inverse analysis is performed via the Extended Kalman Filter technique where the forward model is constituted based on the derivation given in Chakraborty et al. (2015). Unlike the common practice, for better estimation of material constants, the deformation time histories are also included in the present inverse formulation. For demonstration five different plasticity models viz Johnson–Cook model, Zerilli–Armstrong model, Steinberg–Cochran–Guinan–Lund model, Mechanical Threshold Stress model and Preston-Tonks-Wallace model are considered. The estimated parameters are found to be in good agreement with their reference values. It is shown that the most distinguished feature of the present attempt is that a single Taylor test is sufficient to determine the parameters with reasonable accuracy.

Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities

Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this paper, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over the global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element. The mechanical threshold stress (MTS) model, modified to account for dynamic recrystallization, is adopted as the constitutive model for rate- and temperature-sensitive metallic materials, and the constitutive equations are formulated in a corotational setting. The algorithmic implementation of the integrated finite element framework, including the global tracking strategy, is described in detail. Subsequently, a simple example problem involving shear band formation under uni-axial tension is presented, to illustrate the advantages of the proposed computational framework over conventional finite element techniques, in terms of convergence and mesh insensitivity of their numerical results. In addition, to demonstrate the capabilities of the proposed computational framework in more realistic problems, numerical results are compared to data from split-Hopkinson pressure bar dynamic experiments, conducted on two stainless steel samples with different geometric designs. In each problem presented, we study the effect of the mesh size on the numerical solution, including global results such as the load–displacement response, and local quantities such as material state variables at individual quadrature points. These numerical studies show that the geometry and total volume of the fully-developed embedded shear band are independent of the mesh size.

Physically-based constitutive description of a commercial Al-Mg-Si alloy deformed under cold-warm working conditions

The experimental and numerical modeling of cold forging operations conducted on commercial Al alloys requires a precise knowledge of the functional dependence of both flow stress and work-hardening rate on microstructure and deformation conditions. In order to contribute to the improvement of the finite element computer modeling of forming operations conducted on Al alloys, under cold-warm working conditions, an original and rational constitutive description, able to predict accurately both the flow stress and work-hardening rate of an AA6082-T6 Al alloy is proposed. The constitutive formulation has been developed on the basis of the Mechanical Threshold Stress (MTS) model and its applicability is limited to the deformation of the material under cold-warm working conditions, that is to say, in the temperature range of 298–423 K. A novel differential equation for the description of the continuous change in the work-hardening rate of the alloy has been developed, which allows the prediction of the changes in flow stress and work-hardening rate during deformation either under constant and variable temperature and strain rate conditions. The validation of the developed constitutive description has been accomplished by its implementation into a finite element (FE) model for the accurate prediction of the change in some local contact parameters, such as contact pressure, sliding velocity and interface temperature, during the friction test employed in the evaluation of friction conditions in metalworking, known as the Upsetting Sliding Test (UST).

Grain size sensitive–MTS model for Ti-6Al-4V machining force and residual stress prediction

Material properties are significantly influenced by the parameters of the machining process. The accurate prediction of machining force and residual stress reduces power consumption, enhances material properties, and improves dimensional accuracy of the finished product. Traditional method using the finite element analysis (FEA) costs a significant amount of time, and the archived mechanical threshold stress (MTS) model without consideration of microstructure of the material yields inaccurate result. In this paper, a grain size–sensitive MTS model is introduced for the machining process of Ti-6Al-4V. A grain size–sensitive term is introduced to the modified MTS model to account for evolution of the grain size. The grain size–sensitive MTS model takes the microstructure of the Ti-6Al-4V into consideration for the calculation of machining force and residual stress. The grain size–sensitive term is introduced into the athermal stress component using the initial yield stress, strain hardening coefficient, and the Hall-Petch coefficient. The analytical result is compared with those of experimental studies and the traditional Johnson-Cook model to prove the validity in the prediction of machining force and residual stress. The proposed model explores a new area for calculating cutting forces and residual stress.

Residual stress prediction based on MTS model during machining of Ti-6Al-4V

The material microstructure attributes are largely ignored in the machining community for the machining mechanics modeling. A physical-based mechanical threshold stress (MTS) model is proposed for the orthogonal turning application of Ti-6Al-4V material. The MTS model takes the material internal state variables, such as dislocation to dislocation interaction and dislocation/interstitial resistance, into the flow stress consideration. The MTS model is embedded into an analytical residual stress prediction model for machining induced residual stress prediction. The experimental data are provided for the model validation. The prediction generally captures the trend of the residual stress profile compared with experiments. The proposed model provides a microstructure insight of the workpiece material in the machining process modeling.

Numerical simulation of plastic deformation and mechanical response of strip rolled aluminium alloys

During the optimal design and simulation of machining or forming processes, detailed simulation of structural response is typically required for use in Finite Element Analysis (FEA). In this study, the bulk temperature and rate dependent resistance to deformation of strip formed aluminium alloys is modelled using the Mechanical Threshold Stress model. The model is characterised to AA5182 alloy data and used in the FEA simulation of a strip rolling process. The effects of element choice, dynamic or quasi-static simulations and the use of particular modelling algorithms on the computational cost and overall accuracy associated with each simulation have to be considered. Given the correctly implemented material tangent, an implicit analysis is illustrated to allow larger stable time-steps. Dynamic and quasi-static solutions are very similar for the simulated process meaning inertia effects are negligible. It is further demonstrated that great care be given to the maximum allowable time step size in order to capture the expected interaction between temporal and spatial discretisation in a fully Lagrangian FEA simulation.

Investigating mechanical degradation due to fire exposure of aluminum alloy 5083 using crystal plasticity finite element method

Fire exposure causes significant mechanical property degradation of metallic materials. This paper investigates the influence of fire exposure on mechanical response of AA5083 through in situ neutron diffraction tensile tests and crystal plasticity finite element simulations. The Mechanical Threshold Stress (MTS) model is utilized, with a focus on the lattice strain response under tensile loading before and after exposure. A rigorous material parameter calibration procedure is proposed for this MTS model directly based on yield stress, plastic flow, hardening and rate dependency as a function of temperature, requiring only the macroscopic stress–strain curve. Material parameters of virgin material and fire-exposed material with full recrystallization are calibrated separately using this procedure. To initiate the investigation of mechanical degradation caused by fire exposure, a fire-exposed specimen with partial recrystallization is simulated by assigning material parameters and texture of recrystallized grains to selected grains in the virgin material according to the recrystallization fraction. Experimentally measured stress–strain curves and lattice strain evolution are employed to validate the simulations. For the first time, the local mechanical response of AA5083 is compared between in situ testing and finite element simulations, and the discrepancies of lattice strain evolution between virgin and fire-exposed material are discussed. Finally, the influence of fire-exposure on stress and lattice strain distribution is investigated to provide insight into mechanical property degradation.

Extension of the Mechanical Threshold Stress Model to Static and Dynamic Strain Aging: Application to AA5754-O

Based on the mechanical threshold stress model and the visco-plastic self-consistent algorithm, a modified constitutive model is developed to model static strain aging and dynamic strain aging for application to a non-heat treatable aluminum alloy, AA5754-O. The implementation is based on a combination of the evolution of dislocation density and the effect of solutes on both mobile dislocations and forest dislocations. Using this model, the stress–strain behavior of AA5754-O is simulated in multi-path, multi-temperature, and variable strain rate tensile tests. The low temperature and strain rate sensitivities of the modified mechanical threshold stress model in the dynamic strain aging regime are successfully accounted for. The results show quantitative agreement with experimental data from multiple sources.