Rate-dependent Plasticity Model Research Articles

A macro-micro approach for identifying crystal plasticity parameters for necking and failure in nickel-based alloy haynes 282

This work develops a two-scales macro-micro approach to address the challenge in calibrating crystal plasticity microstructural models when samples undergo necking prior to fracture. The crystal plasticity models are crucial for predicting the materials’ plastic deformation and failure at the microstructure level, identifying the materials’ intrinsic properties as well as investigating the microstructure-properties relationships. However, after necking occurs, the experimentally measured stress-strain curves fail to reflect the materials ‘true’ stress-strain behavior and cannot be directly fitted into crystal plasticity models. The proposed macro-micro approach employs a top-down strategy to address this challenge, which has been studied with experimental tests on precipitation-strengthened Ni-based superalloy Haynes® 282®. In this approach, a macro rate-dependent anisotropic plasticity model with Voce-type hardening and Rice-Tracey damage law is first utilized to model the deformation and failure of the tensile bar, and calibrated by matching the stress-strain curves, necking strain, and reduction of area. Especially, to match the testing results under different applied strain rates, the rate-sensitivity parameter m and saturation stress in the elasticity model are modified to incorporate dependence on the local strain rate. Then, the ‘true’ stress-strain behaviors are extracted from the necking zone of the macro-model, which are used to calibrate a micro-model with explicit microstructures and governed by an extended crystal plasticity law. The consistency between the micro-model and macro-model are enforced during calibration. The calibration outcomes from the crystal plasticity model elucidate the materials intrinsic properties for slip, hardening, and failure, which is vital for further investigations into the microstructure-properties relationship and for accurate prediction of the material behavior under various test and service conditions.

Dynamic response optimization of the multistage sandwich structures imperiled to explosive loading

Explosive attacks are increasing day by day in the present era, and the design optimization of protective structures without increasing their weight is mainly a critical task for vehicles. Assessment of the dynamic response of the structures under explosive loading through experimentation is costly, with many restrictions, and highly harmful for both people and the environment. Hence, the present study deals with an explicit numerical investigation of the protective sandwich structures’ blast performance. The influence of the number of stages of honeycomb on the sandwich structures’ blast mitigation capacity was evaluated with the effective utilization of face sheets’ material as their intermediate sheets while maintaining the total volumes as well as masses of the structure's constant. The explosive loads of 1 to 3 kg of trinitrotoluene were used for the stand-off distance of 100 mm. The rate-dependent Johnson-Cook plasticity model was implemented on the designed sandwich models to discover their damage behaviors. The sandwiches’ face deflection, energy absorption, kinetic energy variation, and crushing behaviors were considered to characterize their blast mitigation capacity. The obtained results showed that increasing the number of stages of core in the sandwich structure by using a fraction of the back face sheet materials for intermediate sheets significantly improved their blast performance without increasing their volume occupancies and masses. For the two-stage and three-stage sandwich designs, 50% and 20%, respectively, utilization of their back face material for their intermediate sheet was found to be optimal.

New aspects of a single-crystal gradient plasticity model: Rate-dependency of size-dependent response

Gradient crystal plasticity and rate-dependent plasticity models have been widely developed. However, describing the rate-dependency of the size-dependent behavior remains a long-term challenge and is of great interest in the field. This study investigates the interaction between the rate and size dependency of single crystals. The main contribution is to determine whether the size dependency of the stress–strain responses increases or decreases with increasing deformation rates. A thermodynamically consistent model based on the finite-deformation single-crystal gradient plasticity framework proposed by Gurtin is presented. In the current formulation, the particular features are a rate-dependent function and a rate-sensitivity parameter incorporated into the dissipative gradient strengthening term. These features allowed us to observe the disparate rate-dependencies induced by the dissipative conventional and dissipative gradient terms. From an experimental perspective, few studies have investigated the interaction between the size- and rate-dependence of single crystals. Interestingly, these studies reported different modes of interaction. Here, we categorize existing experimental stress–strain data into two distinct groups: first, the stress data obtained at fixed overall strains, and second, those captured at offset strains, that is, at the yield or post-yield strains. The numerical results obtained through a two-dimensional framework and based on a common set of material and modeling parameters were qualitatively compared with existing experimental data reported for different materials. Trends in the interactions were numerically captured and discussed. The results indicate the promising potential of the model for describing the rate-dependency of the size-dependent yield stress and subsequent behaviors.

The physics of desiccation cracks 1: Ductile fracturing and dependence on relative humidity

Ductile deformation is ubiquitously found in the shrinkage of geomaterials. The existence of ductility requires elastoplastic mechanics when analyzing the structure deformation under external stress. In this work, we explore the physics of ductile fracturing based on the results from desiccation experiments and triaxial tests. By using the digital image correlation (DIC) method to generate the strain maps of samples undergoing desiccation cracking under different relative humidities, we obtain results showing the previously postulated Cnoidal Wave ductile failure patterns propagating under atmospheric condition-controlled crack velocities. We then correlate these observations with rate-dependent plasticity models calibrated through triaxial tests undergoing several unloading–reloading cycles and velocity stepping. This work demonstrates the necessity to consider ductility in soil cracking, indicating that the formation of crack patterns in soil desiccation is a slow and predictable process.

Efficient computational framework for image-based micromechanical analysis of additively manufactured Ti-6Al-4V alloy

The increase in additively manufactured (AM) Ti-6Al-4V alloys in high-performance industrial applications has necessitated the development of robust computational models that can aid in their qualification and certification. Physics-based micromechanical models, relating the AM-processed material microstructure and defect state with the overall material response and life, can play an important role in reducing uncertainty in component behavior and increasing acceptance. Motivated by this need, the present paper develops a novel image-based crystal plasticity finite element model (CPFEM) for efficient micromechanical simulation of the additively manufactured Ti-6Al-4V alloy, whose Widmanstätten microstructure is characterized by 12 HCP α lath variants in the parent β grain. A unique feature of this work is the creation of an efficient crystal plasticity framework for the parent β grain polycrystalline ensembles with parametric representation of the α lath statistics of size, shape, orientation, and crystallography. This statistical representation is expected to significantly enhance its efficiency over models that represent each α lath explicitly in the microstructure. Defects in the form of voids are represented at two scales. The smaller voids in the microstructure are manifested as porosity or void volume fraction distribution in the crystal plasticity model. Larger voids are represented explicitly in the statistically equivalent microstructural volume element (SEMVE) model. The models are built from experimentally acquired electron back scatter diffraction (EBSD) and micro-focus X-ray computed tomography (XCT) images and calibrated and validated with mechanical testing data. This paper extends the developments in Pinz et al. (2022) through the development of a special self-consistent boundary condition in the context of a concurrent model to overcome limitations of periodicity boundary conditions. The concurrent model embeds the SEMVE in a homogenized exterior domain represented by a rate-dependent isotropic plasticity model. Parametric studies are conducted to comprehend the effect of void size, shape and orientation on the overall material response.

Comparative numerical study of rate-dependent continuum-based plasticity models for high-velocity impacts of copper particles against a substrate

The problem of high-rate elastic-plastic deformation of micro-sized copper particles impacting against a copper substrate was investigated by applying the continuum-based formulation and finite element thermomechanical analysis. Comparative study of selected plasticity models was performed. The aim of the paper was to study strain rate-dependant plasticity for a wide range of strain rates. The strain-rate-dependant Johnson-Cook and Cowper-Symonds models were studied by comparing displacements, velocities, strains, strain rates, stresses, contact forces, and temperatures and their contribution to material yield stress. The study shows the importance of the high-strain rate yielding model and its adequacy for experimental data. Both models complement each other and may be regarded as soft and hard bounds of the solution. A new, combined, two-function model, containing two independent functions for each of the two ranges, is suggested. The proposed model describes a low strain rate sensitivity range using the Johnson-Cook expression, while allows fitting of the model for experimental results in a high strain rate sensitivity range, using a modified Cowper-Symonds expression. This combination is capable of describing both low and high strain rate regimes, giving the minimum deviation from experimental results.

Strain Rate Dependent Plasticity Model for Precipitate Hardened Aerospace Aluminum Alloy Produced with Solid-State Additive Manufacturing

Strain Rate Dependent Plasticity Model for Precipitate Hardened Aerospace Aluminum Alloy Produced with Solid-State Additive Manufacturing

Numerical Investigation of Penetration Characteristics of Preformed Spherical Fragments at Hyper Velocity

Numerical investigation of penetration characteristics of 6mm SS304 preformed spherical fragments released from a Fragment Generator Warhead (FGW) impacting on Steel 1006 target plate of 1 mm, 3 mm and 6 mm thick in velocity range 1000 m/s to 5000 m/s and impact angle between 0° and 75°, has been carried out using the explicit code LS-Dyna which is predominantly used for solving impact problems. The simulation model employs a strain rate dependent plasticity model viz. Johnson-Cook model supplemented by Gruneisen Equation of State (EoS), to capture the large strain encountered in target plate due to impact of a spherical fragment at high velocities. The simulation model results are presented in terms of crater diameter on the target plate normalised over original fragment diameter. Empirical equations are available in literature to estimate the normalised crater diameter under the same impact conditions employed in simulation models. The simulation model results have been validated with experimental data available in literature and also found to be in good agreement with the results obtained from empirical equations. The effectiveness of the erosion contact algorithm over Smoothed Particle Hydrodynamics (SPH) method in LS-Dyna to reasonably predict the behaviour of the target material at high velocities of impact is demonstrated in the current study.

Component-based machine learning paradigm for discovering rate-dependent and pressure-sensitive level-set plasticity models

Abstract Conventionally, neural network constitutive laws for path-dependent elasto-plastic solids are trained via supervised learning performed on recurrent neural network, with the time history of strain as input and the stress as input. However, training neural network to replicate path-dependent constitutive responses require significant more amount of data due to the path dependence. This demand on diverse and abundance of accurate data, as well as the lack of interpretability to guide the data generation process, could become major roadblocks for engineering applications. In this work, we attempt to simplify these training processes and improve the interpretability of the trained models by breaking down the training of material models into multiple supervised machine learning programs for elasticity, initial yielding and hardening laws that can be conducted sequentially. To predict pressure-sensitivity and rate dependence of the plastic responses, we reformulate the Hamliton-Jacobi equation such that the yield function is parametrized in the product space spanned by the principle stress, the accumulated plastic strain and time. To test the versatility of the neural network meta-modeling framework, we conduct multiple numerical experiments where neural networks are trained and validated against (1) data generated from known benchmark models, (2) data obtained from physical experiments and (3) data inferred from homogenizing sub-scale direct numerical simulations of microstructures. The neural network model is also incorporated into an offline FFT-FEM model to improve the efficiency of the multiscale calculations.

Examination of Dynamic Strain Ageing Effects during Rapid Quenching of Inconel 718 Superalloy Disc

In this work, an experimental measurement, contour method, is implemented for an after quenching IN718 forging specimen to obtain the distribution of residual stress field. A sequentially coupled thermal mechanical finite element model is developed with the similar 3D geometry of the experimental specimen and implemented the same heat transfer boundary of the rapid quenching with the experimental condition. A thermal mechanical rate dependent continuum plasticity model for IN718 alloy, with the dynamic strain ageing (DSA) effect incorporated, is developed to study the impact of DAS effect on the evolution of residual stress during rapid quenching. The modelling predictions of residual stress are in good agreement with the contour method measurements. The impact of DSA effect is further quantified, indicating that an annular high plastic strain rate region in the core part of the disc is captured during the simulation of the quenching process.

Mechanics of shock induced pore collapse in poly(methyl methacrylate) (PMMA): Comparison of simulations and experiments

Head-to-head comparisons are made between calculations and experimental data on shock-driven pore collapse in the transparent material, poly(methyl methacrylate) (PMMA). Simulations are performed using SCIMITAR3D, an Eulerian sharp-interface multi-material code, while plate impact experiments are visualized using ultra-high speed x-ray imaging. The experiments and simulations are conducted over a wide range of loading conditions; from low strength loading regimes where adiabatic shear banding predominates all the way up to the regime where hydrodynamic pore collapse is expected. PMMA is modeled using an isotropic rate-dependent plasticity model for the deviatoric stress response and a Tillotson equation of state for the pressure. Calculations are primarily done in 2D, to save computational effort, but a limited number of 3D calculations are also performed to assess the differences entailed by the dimensionality. The 2D calculations are in fairly good agreement with the experimental results, for the evolution of pore shape. 3D calculations, while quite computationally intense, indeed produce better agreement with experimental data. The computations also agree well with the experiments in delineating the loading strength at which a transition from the strength-dominated to hydrodynamics-dominated pore collapse occurs. This work provides confidence in the ability of Eulerian, sharp interface computational techniques to correctly represent and understand the mechanics of shock-loaded porous condensed phase materials over a range of loading conditions.

Finite element analysis of synergetic deformation in precision cutting of polymer bonded explosive

Synergetic deformation behavior between crystal particles and polymeric binders dominates the machinability of energetic materials. In the present work, we elucidate cutting mechanisms of HMX-based polymer bonded explosive (PBX) in orthogonal cutting by numerical simulations based on a cohesive finite element framework. The polygonal HMX crystals with a particle volume fraction of 90% are modeled by a linear elasticity model, while the HTPB binders are described by a rate-independent hyperelastic model coupled with a rate-dependent plasticity model. Furthermore, cohesive elements are implemented in both crystal particles and binders to describe thermal-mechanical coupling-induced material failure behavior in the cutting process of PBX. Simulation results reveal different deformation modes of PBX, as well as their correlations with machining results. Furthermore, it is found that depth of cut has a strong impact on the cutting processes of PBX, in terms of material failure mode, subsurface damage and energy dissipation. These findings provide important guidelines for the design and synthesis of energetic materials with high machinability.

A Numerical Study on Ductile Failure of Porous Ductile Solids With Rate-Dependent Matrix Behavior

Abstract This work examines the effects of loading rate on the plastic flow and ductile failure of porous solids exhibiting rate-dependent behavior relevant to many structural metals. Two different modeling approaches for ductile failure are employed and numerical analyses are performed over a wide range of strain rates. Finite element unit cell simulations are carried out to evaluate the macroscopic mechanical response and ductile failure by void coalescence for various macroscopic strain rates. The unit cell results are then used to assess the accuracy of a rate-dependent porous plasticity model, which is subsequently used in strain localization analyses based on the imperfection band approach. Strain localization analyses are conducted for (i) proportional loading paths and (ii) non-proportional loading paths obtained from finite element simulations of axisymmetric and flat tensile specimens. The effects of strain rate are most apparent on the stress–strain response, whereas the effects of strain rate on ductile failure is found to be small for the adopted rate-dependent constitutive model. However, the rate-dependent constitutive formulation tends to regularize the plastic strain field when the strain rate increases. In the unit cell simulations, this slightly increases the strain at coalescence with increasing strain rate compared to a rate-independent constitutive formulation. When the strain rate is sufficiently high, the strain at coalescence becomes constant. The strain localization analyses show a negligible effect of strain rate under proportional loading, while the effect of strain rate is more pronounced when non-proportional loading paths are assigned.

Sandia Fracture Challenge 3: detailing the Sandia Team Q failure prediction strategy

The third Sandia Fracture Challenge highlighted the geometric and material uncertainties introduced by modern additive manufacturing techniques. Tasked with the challenge of predicting failure of a complex additively-manufactured geometry made of 316L stainless steel, we combined a rigorous material calibration scheme with a number of statistical assessments of problem uncertainties. Specifically, we used optimization techniques to calibrate a rate-dependent and anisotropic Hill plasticity model to represent material deformation coupled with a damage model driven by void growth and nucleation. Through targeted simulation studies we assessed the influence of internal voids and surface flaws on the specimens of interest in the challenge which guided our material modeling choices. Employing the Kolmogorov–Smirnov test statistic, we developed a representative suite of simulations to account for the geometric variability of test specimens and the variability introduced by material parameter uncertainty. This approach allowed the team to successfully predict the failure mode of the experimental test population as well as the global response with a high degree of accuracy.

Machine-learning based temperature- and rate-dependent plasticity model: Application to analysis of fracture experiments on DP steel

Slow, intermediate and high strain rate experiments are carried out on flat smooth and notched tensile specimens extracted from dual phase steel sheets. A split Hopkinson pressure bar testing system with load inversion device is utilized to achieve high strain rates. Temperature dependent experiments ranging from 20 °C to 300 °C are performed at quasi-static strain rates. The experimental results reveal a non-monotonic effect of the temperature on the stress-strain curve for DP800 steel. For the temperatures considered, the lowest and highest curves are obtained for 120 °C and 300 °C, respectively. A modified Johnson-Cook plasticity model is developed to capture the observed unconventional effect of the strain rate- and temperature on the hardening response. It includes a von Mises yield surface, a non-associated Hill’48 flow rule, a Swift-Voce reference stress-strain curve describing the rate-independent behavior at room temperature, and a neural network function depending on the plastic strain, strain rate and temperature. This model is implemented into a material user subroutine and identified using a combination of analytical formulas along with a resilient back propagation algorithm. It is found that the obtained machine-learning based Johnson-Cook plasticity model can describe all experimental data with high accuracy, including both force-displacement and local surface strain measurements. Using a hybrid experimental-numerical approach, the loading paths to fracture are determined. It is found that the temperature not only affects the plasticity of the DP800 steel in a non-monotonic manner, but also its strain to fracture, with ductility loss of up to 30% when increasing the temperature from 20 to 120 °C, followed by a gain in ductility when increasing the temperature further to 300 °C.

A model for decoding the life cycle of granular avalanches in a rotating drum

Granular materials can behave as harmless sand dunes or as devastating landslides. A granular avalanche marks the transition between these distinct solid-like and fluid-like states. The solid-like state is typically described using plasticity models from critical state theory. In the fluid regime, granular flow is commonly captured using a visco-plastic model. However, due to our limited understanding of the mechanism governing the solid–fluid-like transition, characterizing the material behavior throughout the life cycle of an avalanche remains an open challenge. Here, we employ laboratory experiments of transient avalanches spontaneously generated by a rotating drum. We report measurements of dilatancy and grain kinematics before, during, and after each avalanche. Those measurements are directly incorporated into a rate-dependent plasticity model that quantitatively predicts the granular flow measured in experiments. Furthermore, we find that dilatancy in the solid-like state controls the triggering of granular avalanches and therefore plays a key role in the solid–fluid-like transition. With the proposed approach, we demonstrate that the life cycle of a laboratory avalanche, from triggering to run out, can be fully explained. Our results represent an important step toward a unified understanding of the physical phenomena associated with transitional behavior in granular media.

Global Existence Results for Viscoplasticity at Finite Strain

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate and thus, depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance (EDB) and energy-dissipation-inequality (EDI) solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

A Phase Field Model for Rate-Dependent Ductile Fracture

In this study, a phase field viscoplastic model is proposed to model the influence of the loading rate on the ductile fracture, as one of the main causes of metallic alloys’ failure. To this aim, the effects of the phase field are incorporated in the Peric’s viscoplastic model; the model can efficiently be converted to a standard rate-independent model. The novel aspects of this work include: Describing a coupling between rate-dependent plasticity and phase field formulation by defining an energy function that contains the energy dissipation caused by plastic deformation as well as the fracture process and elastic energy. In addition, the equations required to develop the numerical solution are presented. The governing equations are determined by a minimization principle that results in balance laws for the coupled displacement-phase field problem. Furthermore, an implicit integration algorithm for a viscoplasticity model coupled with a phase field is presented for a three-dimensional stress state. The proposed algorithm can be utilized for different constitutive models of rate-dependent and rate-independent plasticity models coupled with fracture by changing the definition of the plastic multiplier. In addition, to control the influence of the plastic deformation and its work on the crack propagation, a threshold variable is defined in the model. Finally, using the proposed model, the influence of the loading rate on the responses of the different specimens in one-dimensional and multi-dimensional cases is investigated and the accuracy of the results was verified by comparing them with existing experimental and numerical results. The obtained result proves that the model can simulate the impact of the loading rate on the material response, and the gradual change of the fracture phase from ductile to brittle, caused by increasing the loading rate.

A model for the strain rate dependent plasticity of a metastable austenitic stainless steel

A continuum material model is developed for the dynamic plastic deformation behavior of metastable austenitic stainless steel EN 1.4318-2B. An incremental approach in both experimental testing and in the model is used to distinguish between the direct effects of strain rate and the macroscopic adiabatic heating effects. In the model a set of evolution equations is integrated over the deformation path, which makes the model flexible in terms of changes in the strain rate and material temperature. The strain-induced phase transformation from austenite to α′-martensite is accounted for with evolution equations based on the Olson-Cohen transformation model. In order to describe the phase transformation accurately during dynamic loading, the original model is modified by adding instantaneous strain rate sensitivity to the α′-transformation rate. Comparison with experimental results shows that the model can be used to describe the strain rate and temperature dependent behavior of a metastable austenitic alloy with a reasonable number of material parameters. Finally, the model gives realistic results in a set of validation experiments.

Attaining the rate-independent limit of a rate-dependent strain gradient plasticity theory

The existence of characteristic strain rates in rate-dependent material models, corresponding to rate-independent model behavior, is studied within a back stress based rate-dependent higher order strain gradient crystal plasticity model. Such characteristic rates have recently been observed for steady-state processes, and the present study aims to demonstrate that the observations in fact unearth a more widespread phenomenon. In this work, two newly proposed back stress formulations are adopted to account for the strain gradient effects in the single slip simple shear case, and characteristic rates for a selected quantity are identified through numerical analysis. Evidently, the concept of a characteristic rate, within the rate-dependent material models, may help unlock an otherwise inaccessible parameter space.