Mechanical Threshold Stress 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.

Rate controlling deformation mechanisms in SS316L stainless steel manufactured using laser powder bed fusion technique

We conducted uniaxial tensile strain rate jump tests to account for the strain rate controlling mechanisms in the additively manufactured SS316L stainless steel. Special emphasis is placed on the role of high dislocation density and chemical segregation on dictating the rate sensitive behavior. Lowest strain rate sensitivity is found, despite the highest dislocation density in the as build state, which signified the role of solute segregation at cell walls in increasing the activation volume and forms the strong basis for rejecting dislocation forest as the strain rate controlling obstacles. Consistent increase in the strain rate sensitivity with annealing is found consistent with the chemical homogenisation of the solutes causing smaller inter-obstacle spacing causing decreasing activation volume. Experimental findings are supported by CALPHAD simulations and mechanical threshold stress (MTS) modelling framework. Significant difference between the instantaneous and steady state rate sensitivity is understood using the dynamic pileup dislocation density readjustment mechanism causing considerable flow transient while adjusting the mobile dislocation density on strain rate change in the presence of solute decorated dislocation cells. Present investigation helps in gaining newer insights into the deformation mechanisms of the additively manufactured alloys featuring cellular microstructures.

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.

Identification of the Constitutive Parameters of Viscosity and the Prediction of the Cutting Force of S32760 Duplex Stainless Steel under a High Strain Rate

The mechanical properties of S32760 duplex stainless steel under dynamic loading conditions at high strain rates are significantly different from those under quasi-static conditions. As a result of large strain, high strain rate, and high temperature, the analysis of the cutting process needs to factor in the influence of the viscous behavior of the material on the plastic deformation process. Based on the viscous effect of the two phases and the mixing rule, a mechanical threshold stress (MTS) constitutive model of S32760 duplex stainless steel considering the viscous effect is established to analyze the effect of strain rate on flow stress. An inverse identification method of the constitutive parameters based on Oxley's theory is proposed. The constitutive parameters of S32760 duplex stainless steel were reversely modified using an equal shear zone model and an orthogonal cutting experiment. The results show that the viscosity of the austenite phase was greater than that of the ferrite phase, and the strain rate had the greatest influence on the viscosity effect in the constitutive model. The prediction error of the constitutive model constructed in this manuscript was less than 4%, which had high accuracy.

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

MTS Model Application to Materials Not Starting in the Annealed Condition.

Application of the Mechanical Threshold Stress constitutive model becomes challenging when the material of interest is not supplied in the annealed condition with a low initial dislocation density. When the material has some existing warm or cold work, the evaluation of the internal state variables, specification of the activation energies, and analysis of strain hardening can be affected. This paper gives an example of this in molybdenum and presents options for proceeding with the model development. A hypothetical Body-Centered Cubic (BCC) alloy with known model variables is used to demonstrate the issues and solution options.

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.

Physical modelling with experimental validation of high ductility metal cutting chip formation illustrated by copper machining

This paper addresses problems of predicting chip formation in high strain machining conditions. A complete physical model of chip formation requires both plasticity and chip/tool friction models. Friction models are commonly partly phenomenological, with friction coefficients measured from the conditions in which the models are applied. This paper's thesis is that friction emerges from the plastic response of the chip material in contact with the cutting tool. Extremely large strains are generated in the contact region. In the case of machining highly ductile metals large strains also occur in the bulk of the chip. This paper applies a Mechanical Threshold Stress plasticity model extended to high strains (equivalent strains >5) to simulating chip formation in copper machining, without assuming measured values of friction coefficients. In the case of copper machining there is not a unified source of experimental knowledge against which to validate simulations. There is a need to provide such a source. This paper reports extensive results from machining three coppers in general engineering conditions. At all cutting speeds there remains a systematic difference between the simulated and experimental chip thicknesses. In addition, at low cutting speeds an experimental observation is that chip formation cycles between low and high thicknesses. The simulations do not predict this. The experiments show the cycling to occur when the chip thickness rises to 10 or more times the uncut thickness. It is speculated with some evidence that the cycling is associated with plastic failure rather than with strain hardening, as is currently commonly given as the explanation. Modelling large strain plasticity and failure of highly ductile metals, for metal machining simulations, remains incomplete.

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.

Constitutive modelling and formability prediction of Inconel-718 sheet at elevated temperatures for space applications

ABSTRACT In this work, uniaxial tensile tests of Inconel-718 (IN718) sheets were performed at elevated temperature domain of 773-1023K and a deformation rate between 0.001-1s-1. A substantial reduction in maximum stress was observed at 923K indicating a decrease in peak load by approximately 75.6% and 8.5% in contrast to room temperature (303K) and 773K respectively. Further, different constitutive models, namely Cowper-Symonds (CS), Mechanical Threshold Stress (MTS), and Johnson-Cook (JC), were established to envisage the stress-strain behaviour. The CS model predicted flow stress response better with the correlation coefficient, average absolute error, and standard deviation of 0.98, 4.09% and 6.14% respectively. Also, formability experiments were performed at higher temperatures of 773K and 923K using stretch forming test facility. The highest dome height was noted at 923K signifying an improvement in limiting dome height (LDH) by 32% with respect to 303K. Further, thermo-mechanical numerical simulations of the process were successfully carried out, integrating established constitutive models independently. The predicted formability parameters, such as maximum attained load and surface strain distribution, were validated with the experimental data. The CS constitutive equation predicted the deformation behaviour close to the experimental results and, therefore, was considered as the appropriate model.

Simulation of laser shock peening on X12Cr steel using an alternate computational mechanical threshold stress plasticity model

The ever-increasing relationship between energy consumption and economic growth continues to reinforce functional power generation infrastructure as the centerpiece of development. However, downtimes from in-service failure of power plant components, such as turbine blades, portend dire consequences in the form of huge financial and safety concerns. This challenge is now being progressively overcome through intensive research in the development of laser shock peening (LSP) models, which simulate the induction of compressive layers around and beneath the surface of the blades. This paper presents an alternate experimentally validated computational modelling approach of the LSP process, grounded on a physics-based plasticity model which describes a mechanical threshold for compressive residual stress induction irrespective of increasing laser shock intensities. This is a phenomenon which hitherto has previously been overlooked by many researches. The results of this work show considerable promise when compared to experimental results.

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.

Modelling high temperature deformation of lamellar TiAl crystal using strain-rate enhanced crystal plasticity

Multi-phase lamellar γ-TiAl alloys are highly anisotropic and rate sensitive. At high temperature, the strain rate sensitivity (SRS) increases, which eventually influences the yield behaviour of the alloy. With increasing temperature, the onset of yield changes anomalously showing an increasing or sometimes a decreasing trend. This anomalous behaviour depends on alloy chemistry, lamellar microstructure and anisotropy due to lamellar orientations. To capture the strain rate sensitive deformation behaviour over a wide temperature range and to understand distinct nature of yield anisotropy, a new formulation of the strain rate sensitivity (SRS) expressed by a temperature dependent exponent has been proposed within the framework of the classical power-law based visco-plastic Crystal Plasticity Finite Element Method (CPFEM). In the presented formulation, the evolution of SRS parameter was deduced from laws of thermally activated dislocation motion to obtain temperature-enhanced strain rate sensitivity. Moreover, a dislocation pile-up assisted mechanical threshold stress was incorporated to obtain an “anomalous yield” response. The model was validated for a lamellar PST-TiAl, which is a single crystal consisting of γ-TiAl and α2-Ti3Al lamellar phases. Detailed predictive numerical analysis was performed for an in-depth understanding of temperature enhanced strain-rate sensitivity during local deformation behaviour of TiAl alloy based on slip activities.

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.