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At least 37 records · Page 2

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗

An uncoupled viscoplastic constitutive model for metals at elevated temperature

An uncoupled constitutive model for predicting the transient response of thermal and rate dependent, inelastic material behavior is presented. The uncoupled model assumes that there is a temperature below which the total strain consists essentially of elastic and rate insensitive inelastic strains only. Above this temperature, the rate dependent inelastic strain (creep) dominates. The rate insensitive inelastic strain component is modeled in an incremental form with a yield function, flow rule and hardening law. Revisions to the hardening rule permit the model to predict temperature-dependent kinematic-isotropic hardening behavior, cyclic saturation, asymmetric stress-strain response upon stress reversal, and variable Bauschinger effect. The rate dependent inelastic strain component is modeled using a rate equation in terms of back stress, drag stress and exponent n as functions of temperature and strain. A sequence of hysteresis loops and relaxation tests are utilized to define the rate dependent inelastic strain rate. Evaluation of the model is performed by comparison with experiments involving various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy-X.

Haisler, W. E.↗

Development of constitutive models for cyclic plasticity and creep behavior of super alloys at high temperature

An uncoupled constitutive model for predicting the transient response of thermal and rate dependent, inelastic material behavior was developed. The uncoupled model assumes that there is a temperature below which the total strain consists essentially of elastic and rate insensitive inelastic strains only. Above this temperature, the rate dependent inelastic strain (creep) dominates. The rate insensitive inelastic strain component is modelled in an incremental form with a yield function, blow rule and hardening law. Revisions to the hardening rule permit the model to predict temperature-dependent kinematic-isotropic hardening behavior, cyclic saturation, asymmetric stress-strain response upon stress reversal, and variable Bauschinger effect. The rate dependent inelastic strain component is modelled using a rate equation in terms of back stress, drag stress and exponent n as functions of temperature and strain. A sequence of hysteresis loops and relaxation tests are utilized to define the rate dependent inelastic strain rate. Evaluation of the model has been performed by comparison with experiments involving various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy X.

Haisler, W. E.↗

Twin nucleation and growth in hexagonal close-packed metals: The role of slip-mediated plasticity on twin embryo formation and evolution

Twinning is a key deformation mechanism in hexagonal close-packed (hcp) metals, which are typified by a lack of easily activated slip systems that can accommodate a general state of loading. Pragmatically, the nucleation and evolution of twin domains occurs concomitantly with slip, such that the eventual twin network is conditioned by both external and internal stresses resulting, among others, from the evolution of dislocations. However our understanding of the interplay between dislocations, and twin nucleation and stability remains limited. This work focuses on elucidating the influence of dislocation-mediated plasticity on the formation, growth, and stability of twin embryos. First, a new mesoscale spectral crystal plasticity-twinning framework is developed and used to quantify the change in the free energy landscape following the nucleation {$10\bar{1}2$} of twins in Mg. Representative twin morphologies are modeled under conditions of limited and profuse slip activity, which are emulative of small- and bulk-scale samples, respectively. Then, the driving traction profiles around twin embryos are investigated via a sharp interface approach to obtain insights into how concurrent slip-mediated plasticity can influence the growth/stabilization of nanometric twins. The driving traction profiles are further utilized to determine the stability of twin embryos post loading. The initial dislocation density in the samples, and within the different domains (i.e., twin vs. parent), is seen to have a significant effect on the twin nucleation stress. Namely, the activation of high levels of concomitant plasticity in the parent grain is seen to significantly drive the formation of nanometric twin nuclei at stresses as low as 250 MPa. Further, the sharp interface analysis reveals that profuse plasticity in the parent grain simultaneously alters the forward and back stresses, such that the magnitude/polarity of the driving tractions become increasingly favorable for nanometric twin growth when slip is active. Finally, prior plasticity in the parent grain is seen to result in favorable driving tractions for nanometric twin growth, even at applied stresses as low as ~ 100 MPa. In conclusion, these results are in stark contrast to a case without any dislocations, wherein applied stresses as high as ~ 500 MPa are necessary to grow the twin domains.

36 MATERIALS SCIENCE↗

Criteria for Yielding of Dispersion-Strengthened Alloys

A dislocation model is presented in order to account for the yield behavior of alloys with a finely dispersed second-phase. The criteria for yielding used in the model, is that appreciable yielding occurs in these alloys when the shear stress due to piled-up groups of dislocations is sufficient to fracture or plastically deform the dispersed second-phase particles, relieving the back stress on the dislocation sources. Equations derived on the basis of this model, predict that the yield stress of the alloys varies as the reciprocal square root of the mean free path between dispersed particles. Experimental data is presented for several SAP-Type alloys, precipitation-hardened alloys and steels which are in good agreement with the yield strength variation as a function of dispersion spacing predicted by this theoretical treatment.

Ansell, G. S.↗

Low Temperature Creep of Hot-Extruded Near-Stoichiometric NiTi Shape Memory Alloy: Effect of Thermal Cycling - Part 2

This paper is the first report on the effect prior low temperature creep on the thermal cycling behavior of NiTi. The isothermal low temperature creep behavior of near-stoichiometric NiTi between 300 and 473 K was discussed in Part I. The effect of temperature cycling on its creep behavior is reported in the present paper (Part II). Temperature cycling tests were conducted between either 300 or 373 K and 473 K under a constant applied stress of either 250 or 350 MPa with hold times lasting at each temperature varying between 300 and 700 h. Each specimen was pre-crept either at 300 or at 473 K for several months under an identical applied stress as that used in the subsequent thermal cycling tests. Irrespective of the initial pre-crept microstructures, the specimens exhibited a considerable increase in strain with each thermal cycle so that the total strain continued to build-up to 15 to 20 percent after only 5 cycles. Creep strains were immeasurably small during the hold periods. It is demonstrated that the strains in the austenite and martensite are linearly correlated. Interestingly, the differential irrecoverable strain, in the material measured in either phase decreases with increasing number of cycles, similar to the well-known Manson-Coffin relation in low cycle fatigue. Both phases are shown to undergo strain hardening due to the development of residual stresses. Plots of true creep rate against absolute temperature showed distinct peaks and valleys during the cool-down and heat-up portions of the thermal cycles, respectively. Transformation temperatures determined from the creep data revealed that the austenitic start and finish temperatures were more sensitive to the pre-crept martensitic phase than to the pre-crept austenitic phase. The results are discussed in terms of a phenomenological model, where it is suggested that thermal cycling between the austenitic and martensitic phase temperatures or vice versa results in the deformation of the austenite and a corresponding development of a back stress due to a significant increase in the dislocation density during thermal cycling.

Raj, S. V.↗

Identification of crystal plasticity model parameters by multi-objective optimization integrating microstructural evolution and mechanical data

Crystal plasticity models evolve a polycrystalline yield surface using meso-scale descriptions of deformation mechanisms. The activation of deformation mechanisms is governed by crystallography and a set of model parameters, which are typically calibrated through the fitting of mechanical data such as stress–strain curves and elastic lattice strains. Microstructural data such as phase fractions and texture evolution are used for verifying crystal plasticity parameters. In this study, we use a multi-objective genetic algorithm to identify hardening parameters from flow stress curves with an option to incorporate texture into the optimization approach. Robust, generalized objective functions are developed and used to identify sets of parameters pertaining to dislocation density-based hardening laws in visco-plastic and elasto-plastic self-consistent (VPSC and EPSC) homogenization models. First, the parameters are identified for pure Nb directly from texture using an objective function based on generalized spherical harmonics. Since texture evolution is driven by the relative contribution of active slip systems, the parameters governing the evolution of slip resistance ratios can be recovered from fitting discrete textures at a series of strains. Next, a comprehensive set of load reversal data for dual phase (DP) 780 steel is used to fit a hardening law and a back-stress law in EPSC. Finally, parameters pertaining to a complex hardening law for the evolution of slip and twinning in pure α-Ti are identified. Remarkably, using texture as an objective in combination with stress–strain objectives constrains the model of Ti to fully reproduce not only stress–strain and texture evolution but also hierarchical twinning measurements as a function of initial grain size and texture. Furthermore, given an appropriate model fit to representative experimental texture evolution, underlying twin volume fractions contributing to texture evolution can be predicted.

42 ENGINEERING↗

The hierarchical energy landscape of screw dislocation motion in refractory high-entropy alloys

High-entropy alloys (HEAs) with concentrated solid solutions are conceived to possess a rugged atomic and energy landscape in which dislocation motion necessarily proceeds to accommodate mechanical deformation. Fundamental questions remain as to how rough the energy landscape is and to what extent it can be influenced by the local ordering of their constituent elements. Here, we construct and report the potential energy landscape (PEL) governing screw dislocation motion in refractory HEAs that reveals a hierarchical and multilevel structure with a collection of small basins nested in large metabasin. This striking feature pertaining to HEAs exerts a trapping force and back stress on saddle point activations, retarding dislocation movement. Further, by introducing chemical short-range order, the energy landscape is smoothed but skewed to different degrees that shifts the rate-liming process from kink-glide to kink-pair nucleation. The chemical disorder-roughened PEL in HEAs, analogous to structural disorder induced in metallic glasses, signifies the role of various barrier-hopping processes underlying the extraordinary mechanical behaviors of the two distinct groups of materials.

36 MATERIALS SCIENCE↗

Tailoring mechanical properties of a multi-principal element alloy through a multi-length-scale approach

In this study, a multi-length-scale strengthening approach was used to tailor the microstructure and the mechanical properties of a NiCoCr-based multi-principal element alloy (MPEA). Grain size refinement, severe lattice distortion, and stacking fault energy (SFE) reduction with Mo addition (up to 10 at.%) enhance yield strength by 85% with only 10% reduction in ductility in as-annealed MPEAs. A pronounced increase in the strain hardening rate was observed with the addition of Mo, which is ascribed to the promotion of complex stacking fault (SF) interaction and intersection, accompanied by Lomer-Cottrell (L-C) and Hirth locks inhibiting dislocation motion and substantial increase in the accumulation of back stress. To push the limit of the yield strength further, the Suzuki segregation phenomenon was manipulated by a careful control of SF density by pre-straining and a subsequent 500 °C heat treatment. The stress-strain responses of the pre-strained and heat treated MPEAs showed an obvious SF density and Mo concentration dependence. Furthermore, the yield strength of the pre-strained Mo-added MPEAs with subsequent heat treatment was increased up to true stress of 2.3 GPa with a corresponding fracture elongation of 12% true strain. SFs formed during pre-straining served as Cr segregation sites during subsequent heat treatment, which substantially varies the local SFE within the SF, presenting a roughened landscape and frustrating the dislocation dynamics.

mechanical properties↗

Deformation behavior of CP-titanium under strain path changes: Experiment and crystal plasticity modeling

The deformation behavior of commercially pure rolled titanium subjected to strain path changes is studied using experiments and a crystal plasticity model. Four different loading combinations are performed at room temperature to study the activation of slip, twinning, de-twinning and double-twinning in hexagonal closed packed titanium. The strain paths considered are: rolling direction compression (RDC) followed by normal direction compression (NDC), RDC followed by transverse direction compression (TDC), NDC followed by RDC, and NDC followed by TDC. An EBSD-based analysis of the distribution of boundary misorientation angles before and after reload was developed to analyze the evolution of {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twins. This analysis supports the model results concerning the treatment of twin reorientation. A de-twinning and double-twinning model accounting for back stress effects, an important feature of strain path changes, is implemented within the framework of the visco-plastic self-consistent (VPSC) model along with a dislocation density (DD) based hardening scheme. In the model, plasticity is accommodated by prismatic $\langle$a$\rangle$, basal $\langle$a$\rangle$ and pyramidal $\langle$c+a$\rangle$ slip modes, and {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twinning modes. The VPSC model predicts the evolution of twinning, de-twinning and double-twinning processes for both tensile and compression twinning modes under strain path change. The model predicts macroscopic stress-strain response, texture evolution, and twin volume fraction that are in agreement with experimental observations. The evolution of texture is investigated in detail by separately analyzing the twinned domains, rather than the evolution of the global texture.

36 MATERIALS SCIENCE↗

Additive manufacturing of an ultrastrong, deformable Al alloy with nanoscale intermetallics

Abstract Light-weight, high-strength, aluminum (Al) alloys have widespread industrial applications. However, most commercially available high-strength Al alloys, like AA 7075, are not suitable for additive manufacturing due to their high susceptibility to solidification cracking. In this work, a custom Al alloy Al 92 Ti 2 Fe 2 Co 2 Ni 2 is fabricated by selective laser melting. Heterogeneous nanoscale medium-entropy intermetallic lamella form in the as-printed Al alloy. Macroscale compression tests reveal a combination of high strength, over 700 MPa, and prominent plastic deformability. Micropillar compression tests display significant back stress in all regions, and certain regions have flow stresses exceeding 900 MPa. Post-deformation analyses reveal that, in addition to abundant dislocation activities in Al matrix, complex dislocation structures and stacking faults form in monoclinic Al 9 Co 2 type brittle intermetallics. This study shows that proper introduction of heterogeneous microstructures and nanoscale medium entropy intermetallics offer an alternative solution to the design of ultrastrong, deformable Al alloys via additive manufacturing.

Science & Technology - Other Topics↗

DiscoFluxM version 1.x

DiscoFluxM is software for modeling the deformation behavior of crystalline materials within the third-party finite-element based software, MOOSE. The software enables full-field crystal plasticity finite element simulations of deformation processes of metals and other crystalline materials. DiscoFluxM is an implementation of the DiscoFlux theoretical and algorithmic framework for coupling single-crystal plasticity with dislocation transport. The continuum mesoscale modeling framework is founded upon a nonlocal dislocation-density based crystal plasticity theory. The nonlocal theory couples continuum dislocation transport with an otherwise spatially-local single-crystal model employing nonlinear thermoelasticity and crystallographic plasticity. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. The configuration of geometrically necessary dislocation density gives rise to a back-stress that inhibits or accentuates the flow of dislocations.

Luscher, Darby↗

Constitutive modeling and computational implementation for finite strain plasticity

This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-tpe constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the 'back-stress,' in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.

Reed, K. W.↗

Structure of a viscoplastic theory

The general structure of a viscoplastic theory is developed from physical and thermodynamical considerations. The flow equation is of classical form. The dynamic recovery approach is shown to be superior to the hardening function approach for incorporating nonlinear strain hardening into the material response through the evolutionary equation for back stress. A novel approach for introducing isotropic strain hardening into the theory is presented, which results in a useful simplification. In particular, the limiting stress for the kinematic saturation of state (not the drag stress) is the chosen scalar-valued state variable. The resulting simplification is that there is no coupling between dynamic and thermal recovery terms in each evolutionary equation. The derived theory of viscoplasticity has the structure of a two-surface plasticity theory when the response is plasticlike, and the structure of a Bailey-Orowan creep theory when the response is creeplike.

Freed, Alan D.↗

Refinements in a viscoplastic model

A thermodynamically admissible theory of viscoplasticity with two internal variables (a back stress and a drag strength) is presented. Six material functions characterize a specific viscoplastic model. In the pursuit of compromise between accuracy and simplicity, a model is developed that is a hybrid of two existing viscoplastic models. A limited number of applications of the model to Al, Cu, and Ni are presented. A novel implicit integration method is also discussed. Applications are made to obtain solutions using this viscoplastic model.

Freed, A. D.↗

Viscoplasticity: A thermodynamic formulation

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity, as it applies to initially isotropic materials. Three fundamental internal state variables are admitted. They are: a tensor valued back stress for kinematic effects, and the scalar valued drag and yield strengths for isotropic effects. All three are considered to phenomenologically evolve according to competitive processes between strain hardening, strain induced dynamic recovery, and time induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is put forth. This theory allows each of the three fundamental internal variables to be composed as a sum of independently evolving constituents.

Freed, A. D.↗

A viscoplastic theory with thermodynamic considerations

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation-induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.

Freed, A. D.↗

A viscoplastic theory with thermodynamic considerations

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three, fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.

Freed, A. D.↗