Plasticity Simulations Research Articles

Martensite plasticity and damage competition in dual-phase steel: A micromechanical experimental–numerical study

Martensite damage in Dual-Phase (DP) steel has been studied extensively, yet, the exact deformation mechanisms that trigger or inhibit damage initiation remain mostly unexplored. Whereas generally assumed to be hard and brittle, lath martensite in fact deforms in a highly anisotropic manner, showing large strains under favorable habit plane orientations, which is attributed both to the lath morphology and to so-called ’substructure boundary sliding’. Yet, the correlation (or interplay) between plasticity and damage in lath martensite has not received much attention. Therefore, we raise the question whether these soft martensite plasticity mechanisms can delay or even inhibit damage initiation. We analyze several ’damage-sensitive’ martensite notches, i.e. thin contractions of two martensite islands, by combining several state-of-the-art experimental and analysis methods. Deformations are tracked in-situ at the nanoscale, aligned to detailed microstructure maps, and categorized, for each martensite variant, into habit plane or out-of-habit-plane slip. In these experiments, strong plasticity (>70%) is observed in martensite notches, enabled by slip along a favorably oriented habit plane, whereas damaged notches have unfavorably oriented habit planes, showing limited pre-damage strains (<10%), carried by out-of-habit-plane slip. Additionally, one-to-one experimentally based Crystal Plasticity (CP) simulations are performed in parallel, employing a recently introduced Enriched CP approach which models a soft plasticity mechanism on the variants’ habit plane. The Enriched CP simulations show considerably lower hydrostatic stresses in non-damaged and plastically deforming notches, thereby revealing that the soft habit plane mechanism is key for introducing the high plastic anisotropy that can lead to the inhibition of martensite damage in highly strained martensite notches. Finally, recommendations for improved damage inhibiting steels are proposed.

Integrated experimental–numerical investigation of strain partitioning and damage initiation in a low-carbon lath martensitic steel

Lath martensite is a key constituent of advanced high strength steels (AHSS). Its deformation behavior is intrinsically related to its hierarchical structure composed of packets, blocks and laths exhibiting specific topological and orientation relationships. To improve the ductility of lath martensite, it is therefore important not only to clarify the deformation mechanisms but to also gain a better understanding of the damage initiation mechanisms and their connections with local micro-mechanical features. To this end, an integrated experimental–numerical investigation of a low-carbon lath martensitic steel combining large field-of-view high-resolution digital image correlation (HR-DIC) analyses and crystal plasticity (CP) simulations with different modeling assumptions is proposed. The global and local plastic strain field distributions are first comparatively and quantitatively analyzed to clarify the predictive capabilities and limitations of the CP models within the continuum mechanics approximation. The results confirm that plasticity is predominantly carried out by interface sliding so that a model discriminating bulk and boundary elements with respect to their initial in-lath and out-of-lath slip strengths can reasonably reproduce the plastic deformation in terms of spatial distribution and intensity. Severe strain localization is observed along block boundaries with high in-lath Schmid factor, at packet interfaces but also at prior austenite grain boundaries and probably at an annealing twin boundary. The relationship between the strain localization sites and local micro-mechanical fields, in particular the stress triaxiality is discussed.

Machine learning-enabled identification of micromechanical stress and strain hotspots predicted via dislocation density-based crystal plasticity simulations

The present work uses a full-field crystal plasticity model with a first principles-informed dislocation density (DD) hardening law to identify the key microstructural features correlated with micromechanical fields localization, or hotspots, in polycrystalline Ni. An ensemble learning approach to machine learning interpreted with Shapley additive explanation was implemented to predict nonlinear correlations between microstructural features and micromechanical stress and strain hotspots. Results reveal that regions within the microstructure in the vicinity of grain boundaries, higher Schmid factors, low slip transmissions and high intergranular misorientations, are more prone to being micromechanical hotspots. Additionally, under combined loading and large plastic deformations, slip transmissions take precedence over intergranular misorientations in formation of both strain and stress hotspots. The present work demonstrates a successful integration of physics-based crystal plasticity with DD-based hardening into machine learning models to reveal the microscale features responsible for the formation of local stress and strain hotspots within the grains and near the grain boundaries, as function of applied deformation states, grain morphology/size distribution, and microstructural texture, providing insights into micromechanical damage initiation zones in polycrystalline metals.

Neighborhood spatial correlations and machine learning classification of fatigue hot-spots in Ti–6Al–4V

The identification of grains with a higher propensity to form a fatigue crack in polycrystalline microstructures is crucial to the design and deployment of materials with increased fatigue resilience. The probability of fatigue crack formation within a grain has typically been quantified with the help of extreme value analyses of Fatigue Indicator Parameters (FIPs). Due to the immense computational cost associated with performing the cyclic crystal plasticity simulations necessary to compute these FIPs, a more efficient strategy to identify the fatigue critical neighborhoods in a microstructure is desirable. In this work, we present a novel surrogate modeling approach to isolate the grains that are likely to exhibit extreme values of the FIPs. This approach significantly extends the previously established Materials Knowledge Systems (MKS) framework to compute neighborhood statistics that capture the salient information about the grain and its neighbors. Variational Bayesian Inference along with Feedforward Neural Networks are utilized to build robust, uncertainty quantified linkages between the local neighborhood statistics and the probability of fatigue crack formation. In doing so, we refine the experimental observations pertaining to the identification of grains that are likely to form a fatigue crack. The approach presented herein is shown to generalize well for both the High Cycle and Transition Fatigue regimes, thereby providing a versatile protocol for multiscale materials design efforts.

A mechanism-based multisurface plasticity model for hexagonal close-packed materials with detailed validation and assessment

We present a multi-surface model (MSM) of plasticity to simulate the anisotropic and asymmetric yield responses often observed in hexagonal close-packed (HCP) materials such as magnesium and its alloys. Motivated by the salient outcomes from high-resolution polycrystal plasticity simulations and experimental insights on magnesium alloys, we propose a three-surface representation incorporating two separate anisotropic, symmetric yield surfaces for the soft (basal) and hard (non-basal) glide, and an anisotropic, asymmetric yield surface for extension twinning. This reduced representation of the high-resolution crystal plasticity offers computational attractiveness to analyze large-scale engineering simulations while maintaining key micromechanical details of soft versus hard glide. The model is calibrated to a particular three-dimensional dataset for polycrystal magnesium alloy and is validated against a range of crystal plasticity results for different loading conditions. The capability of the model is then assessed for complex boundary-value problems at the macroscale (round notched bars) and at the microscale (void growth and coalescence). The validation and assessment demonstrate the ability of the proposed MSM to capture finer details of deformation such as identifying regions where soft and hard glide may occur around the void or in other heterogeneous loading states.

Effect of hydrogen on plasticity of [formula omitted]-Fe: A multi-scale assessment

A multi-scale study was carried out to quantify the effect of interstitial hydrogen concentration on plasticity in α-Fe. In this work, the influence of hydrogen on the screw dislocation glide behavior was examined across several length-scales. The insights obtained were integrated to provide an accurate continuum description for the effect of hydrogen on the dislocation based plasticity in polycrystalline α-Fe. At the outset of this work, a new FeH interatomic potential was formulated that enhanced the atomistic estimation of the variation in dislocation glide behavior in presence of hydrogen. Next, the dislocation core reconstruction observed due to the addition of hydrogen using atomistic simulations was validated with the help of large-scale DFT calculations based on the DFT-FE framework. Several atomistic simulations were carried out to comprehensively quantify the effect of hydrogen on the non-Schmid behavior exhibited during the dislocation glide in α-Fe. Finally, crystal plasticity simulations were carried out to understand the effect of hydrogen on the meso-scale deformation behavior of polycrystalline α-Fe.

Physics-informed machine-learning model of temperature evolution under solid phase processes

We model temperature dynamics during Shear Assisted Proccess Extrusion (ShAPE), a solid phase process that plasticizes feedstock with a rotating tool and subsequently extrudes it into a consolidated tube, rod, or wire. Control of temperature is critical during ShAPE processing to avoid liquefaction, ensure smooth extrusion, and develop desired material properties in the extruded products. Accurate modeling of the complicated thermo-mechanical feedbacks between process inputs, material temperature, and heat generation presents a significant barrier to predictive modeling and process design. In particular, connecting micro-structural scale mechanisms of heat generation to macro-scale predictions of temperature can become computationally intractable. In this work we use a neural network (NN) model of heat generation to bridge this gap, by combining it with a simplified model of the temperature dynamics due to conduction and convection to capture the macro scale evolution of temperature. We inform the construction of the NN heat generation model using crystal plasticity simulations at the micro-structural scale to model the effects of process inputs on generation of heat. We achieved close fits of the temperature dynamics model to a diverse experimental data-set. Further, the relationships learned by the NN model between process inputs and heat generation showed qualitative agreement with those predicted by crystal plasticity simulations.

Modeling Bainite Dual-Phase Steels: A High-Resolution Crystal Plasticity Simulation Study

A bainite dual-phase (FB) steel containing polygonal ferrite and granular bainite is thermo-mechanically rolled, followed by an accelerated cooling. Two different cooling rates are applied to obtain two different materials. The aim of the study is to explore the reasons for the differences in the mechanical response experimentally observed for these two materials which are modeled by means of high-resolution crystal plasticity simulations with a phenomenological constitutive description. First, the CP parameters of the individual constituents are determined. Second, different three-dimensional (3D) representative volume elements (RVEs)—one of which includes the substructure of bainite—are used to study the mechanical properties of both FB microstructures. It is shown that, in contrast to the macroscopic response, the microscopic response differs among the RVEs. Third, a comparison of both materials is performed by analyzing their stress–strain response. The onset of plasticity in granular bainite is found to be different for both materials in addition to the strain partitioning, although they both obeyed the iso-work assumption. Finally, a parameter study is carried out in order to investigate the correlation between different microstructures and damage initiation that can be seen experimentally in this steel. It is shown that the difference in ultimate elongation may depend on whether the first voids appear within polygonal ferrite or at the phase boundary.

Study on the crack nucleation mechanism of Ti-2Al-2.5Zr alloy in low cycle fatigue: Quasi in-situ experiments and crystal plasticity simulation

The fatigue crack nucleation mechanism of Ti-2Al-2.5Zr alloy was investigated using the coupling method of quasi in-situ tests with crystal plasticity (CP) simulation. The constitutive parameters in the CP model were validated by digital image correlation based on scanning electron microscope (SEM-DIC). It was found that the transgranular and intergranular cracks nucleated inside grains and at grain boundaries (GBs), respectively, due to slip intrusions/extrusions along prismatic planes with highest SFpris. values, while quasi transgranular cracks were induced by the adjacent microstructure or cracks. The angle Ω between the sample surface and the slip direction of slip planes where the transgranular cracks nucleated was within the range of 20–55°. Three factors for predicting intergranular cracks were identified, and the slip shearing mechanism of GBs was proposed. The CP results revealed that a significant plastic strain difference was generated at GBs where intergranular cracks nucleated. The band averaging method showed better prediction ability than the grain averaging method, and a unified fatigue indicator parameter (FIP) combining the accumulated plastic strain, the strain incompatibility parameter (SIP), and the abovementioned crack prediction factors, was proposed, which improved the unified prediction ability for both transgranular and intergranular cracks.

Nano-structuring of a high entropy alloy by severe plastic deformation: Experiments and crystal plasticity simulations

The evolution of microstructure, texture, and mechanical properties of an induction melted non-equiatomic Al6Co23.5Fe23.5Mn23.5Ni23.5 (at.%) high entropy alloy subjected to severe plastic deformation was investigated experimentally and by simulations. Analyses using electron backscatter diffraction and transmission Kikuchi diffraction images revealed the evolution of the microstructures. The coarse-grained initial structure was deformed down to an average grain size of 50 nm after a shear strain of 11 by employing the high-pressure compressive shearing process, at room temperature. Transmission electron microscopy analysis showed the presence of nano-twins. The high deformation led to a significant increase in the strength, up to ≈ 1.0 GPa. X-ray diffraction macro-texture analysis revealed a shear texture with the dominance of the B/B¯{112}110-type component whose intensity varied with strain. A two-step Taylor-type polycrystal plasticity simulation approach reproduced the texture by a correlation value of 91%. In the first part of the modeling, grain fragmentation was simulated, while in the second part, grain boundary shearing and deformation twinning were considered together with the operation of {111}112-type partial slip. The effect of twinning was also examined in the texture modeling and the simulations estimated that its fraction was less than 2%.

Parameter identification and pileup behavior of TiAl alloy through nanoindentation and crystal plasticity simulation

In this work, the load-displacement curves of γ and B2 phases in Ti-43.5Al-4 Nb-1Mo-0.1B (TNM) alloy were obtained from nanoindentation experiments and corresponding crystal plasticity finite element (CPFE) simulations. The good consistency of constitutive curves and the small error of hardness between experiments and simulation results confirmed that the constitutive parameters of γ and B2 phase in TiAl alloy could be well verified by nanoindentation. Based on nanoindentation tests and CPFE simulation, the pileup morphology of each grain around the indents has been systematically discussed. The pileup morphology is closely related to the slip behavior around the indents, which could be analyzed by the calculation of Schmid factors, including surface Schmid factor (SSF) and interior Schmid factor (ISF). Results show that a large SSF and a small ISF will promote the accumulation of cumulative shear strain at the surface of the materials, further facilitating the pileup profile. Besides, the pileup morphology is closely related with the movement of dislocation, which greatly influences the flow ability of the material, further altering the height of pileup profiles.

Life Prediction for Directed Energy Deposition‐Manufactured 316L Stainless Steel using a Coupled Crystal Plasticity–Machine Learning Framework

Additively manufactured stainless steels have become increasingly popular due to their desirable properties, but their mechanical behavior in structural parts is not yet fully understood. Specifically, the impact of columnar microstructures on fatigue behavior is still unclear. A typical directed energy deposition (DED)‐fabricated 316L stainless steel microstructure consists of distinct zones with equiaxed and columnar grains. To answer the question of how these zones of a DED‐fabricated 316L stainless steel microstructure affect the local mechanical behavior individually, such as the fatigue strength, stress/strain distribution, and fatigue life, crystal plasticity simulations are conducted to investigate the influence of microstructure on local mechanical behavior such as fatigue strength, stress/strain distribution, and fatigue life. The simulations find that columnar microstructures exhibit better fatigue strength than equiaxed structures when the load is parallel to the major axis of the columnar grains, but the strength decreases when the load is perpendicular. This study also uses machine learning to predict fatigue life, which shows good agreement with crystal plasticity modeling. The study suggests that the combined crystal plasticity–machine learning approach is an effective way to predict the fatigue behavior of additively manufactured components.

A numerical case study on the long-term seismic assessment of reinforced concrete tunnels in corrosive environments

The paper investigates the long-term seismic behaviour of an underground reinforced concrete (RC) metro tunnel in Santiago, Chile, considering the combined effects of chloride-induced corrosion and cumulative, low-amplitude seismic shaking on the structure's performance. The soil-tunnel response is evaluated with the aid of transient, nonlinear finite element analysis using a two-dimensional (2D) plane strain numerical model that adopts advanced nonlinear models for the simulation of soil and concrete plasticity and the dynamic stiffness behaviour. The effects of corrosion deterioration are demonstrated in terms of time-dependent loss of rebar area and cover concrete stiffness and strength. The study illustrates the influence of ageing and repeated seismic shaking on lining deformation, crack development, and the modal characteristics of the intact and degrading systems. The results indicate that multiple low-amplitude events drive the non-degrading RC tunnel beyond its elastic regime without significant structural response consequences. A noticeable impact of corrosion deterioration on the structure's seismic performance is revealed, increasing with the number and intensity of earthquake events. Two different tunnel embedment depths are comparatively assessed. The analyses demonstrate larger co-seismic section convergence in the case of the deeper tunnel, yet a less pronounced effect of ageing and successive seismic loading compared to the shallow section, which is evident in the RC lining cracks at the end of shaking.

Mesoscale slip behavior in single crystal and bicrystal tantalum

Single-crystal and bicrystal tensile specimens of various orientations were prepared from coarse-grained, pure Ta to investigate fundamental BCC slip behavior at the mesoscale, that is, without considering discrete dislocation mechanisms. Single crystal yield behavior was well-represented by concurrent {110} and {112} slip modes with the initial CRSS for {110} 6% lower than for {112}. A new metric quantitatively representing slip multiplicity in a crystal visco-plastic context was introduced. Initial strain hardening correlates positively with this “activity index” tending to confirm the dominant role of latent hardening in single crystals. Anelastic hysteresis at least as significant as in polycrystal/polyphase alloys was observed, with loop width increasing with pre-strain rather than solely with flow stress as previously supposed. Tensile tests of “triplets” consisting of a bicrystal specimen and its two constituent single crystal specimens revealed the differential effects of grain boundaries (GB) on strength and anelastic hysteresis. Two triplets followed the rule-of-mixtures (ROM); two triplets showed synergistic strength and anelasticity. Crystal plasticity (CP) simulations with two slip modes having different hardening behaviors predicted the single crystal stress-strain curves reasonably for various orientations. Plastic deformation incompatibility was identified as the likely source of deviation from rule-of-mixture behavior. CP simulations predicted the appearance of additional slip systems near the GBs in the synergistic triplets, but did not predict the observed strength and anelastic hysteresis.

Understanding the anisotropic tensile deformation behavior of commercially pure titanium by experiments and crystal plasticity simulations

Current work reveals the anisotropic tensile deformation mechanisms of commercially pure titanium (CP-Ti) along rolling direction (RD) and transverse direction (TD) by the statistical analysis of electron back scattered diffraction (EBSD) data and crystal plasticity (CP) simulations. The analysis of texture evolution, misorientation angle distribution, in-grain misorientation axis (IGMA) and Schmid factor indicates that the anisotropic tensile deformation behavior is originating from the anisotropic slip modes. Further CP simulation results confirm this conjecture and reveal that the higher fraction of basal slip accommodates the deformation and leads to the lower strain hardening behavior along TD. The lower uniform elongation along TD is caused by the heterogeneous strain distribution in the microstructure as deduced from digital image correlation (DIC) results and kernel average misorientation (KAM) maps.

Ductile fracture simulation using phase field method with various damage models based on different degradation and geometric crack functions

For simulation of ductile fracture, plasticity and damage are two essential aspects. The phase field method emerged as an efficient mathematical tool to address the fracture processes involving crack initiation, merging, and branching. From the wide literature, it has been observed that the information on the suitability of the existing phase field models for simulation of ductile fracture is scanty. This paper proposes a phase field methodologies for simulation of ductile fracture considering the aspects like different degradation and crack geometric functions. The proposed formulation couples the damage model, constitutive behaviour of elasto-plastic solid and J2 plasticity. Numerical simulations are carried out using ABAQUS with user-defined element (UEL) subroutine codes, defining the displacement field and phase field variable. Several benchmark problems were analysed to investigate the (i) behaviour of the specimen (ii) the performance of various phase field damage models (PFDM) and (iii) the effect of non-dimensional parameters considered in the damage models. The maximum percentage difference between the numerically predicted maximum load and its corresponding displacement is in good agreement w.r.t experimental value under PFDM4 (±10% range). The output of the study provides an insight on the use of various damage models and other parameters for the simulation of ductile crack propagation. This proposed model can be further extended to the prediction of remaining life or residual strength of the structural component.

Prediction of Fatigue Crack Initiation of 7075 Aluminum Alloy by Crystal Plasticity Simulation.

The 7075 aluminum alloy is a promising material for the aerospace industry due to its combination of light weight and high strength. This study proposed a method for predicting fatigue crack initiation of the 7075 aluminum alloy by crystal plasticity finite element analysis considering microstructures. In order to accurately predict the total fatigue life, it is necessary to calculate the number of cycles for fatigue crack initiation, small crack growth, and long crack growth. The long crack growth life can be estimated by the Paris law, but fatigue crack initiation and small crack growth are sensitive to the microstructures and have been difficult to predict. In this work, the microstructure of 7075 aluminum alloy was reconstructed based on experimental observations in the literature and crystal plasticity simulations were performed to calculate the elasto-plastic deformation behavior in the reconstructed polycrystalline model under cyclic deformation. The calculated local plastic strain was introduced into the crack initiation criterion (Tanaka and Mura, 1981) to predict fatigue crack initiation life. The predicted crack initiation life and crack morphology were in good agreement with the experimental results, indicating that the proposed method is effective in predicting fatigue crack initiation in aluminum alloys. From the obtained results, future issues regarding the prediction of fatigue crack initiation were discussed.

Dislocation structures formation induced by thermal stress in additive manufacturing: Multiscale crystal plasticity modeling of dislocation transport

The motion of dislocations governs the plastic deformation of crystalline materials, which in turn determines the mechanical properties. The complex thermal history, large temperature gradients and high cooling rates during the process of additive manufacturing (AM) can induce high dislocation density and unique dislocation structures in the material. The origin of these dislocation structures and their stability during mechanical loading are debated. A novel temperature dependent continuum dislocation dynamics (CDD) model is developed, in which four state variables are used for each slip system representing the total dislocation density, edge and screw geometrically necessary dislocation densities and dislocation curvature. The CDD model is fully coupled with a crystal plasticity solver, which captures the plastic deformation induced by the dislocation motion. A hybrid continuous and discontinuous Galerkin formulation is developed to accurately reproduce the dynamics of highly discontinuous dislocation density fields that are typical of dislocation structures. A multiscale modeling approach is used, in which the thermally induced deformation in specific grains of a polycrystal is extracted from larger scale crystal plasticity simulations of the laser powder-bed fusion process, and is then used for single crystal scale dislocation dynamics simulations. Simulation results reveal the dynamics of dislocation structure formation in grains at different positions during laser scanning and cooling stages. The effect of the cyclic thermal stress during multi-layer AM fabrication is also investigated. The simulations provide a new perspective on the specific conditions that should be satisfied during AM process for the formation of stable dislocation structures.

An experimental and crystal plasticity investigation of anisotropic compression behaviour of Mg-Sn-Ca alloy

The ductility of Magnesium alloys is often limited due to the strong basal texture. Initial attempts were made to reduce the intensity of the basal textures by adding rare earth(RE) elements. However, owing to the cost and scarcity of RE elements, alloys with calcium and tin were recently introduced. Among them, Mg-2Sn-2Ca alloys are the most promising, with high strength reported in the extruded condition. In this work, we report, for the first time, the mechanical properties of the alloy in the sheet form. In plane mechanical anisotropy in compressive behaviour is studied along with the detailed characterisation of texture, microstructure and the deformation twins in the material. Unlike strongly basal textured Mg alloys, deformation twinning was also observed in samples loaded along the normal direction. Crystal plasticity simulations were performed to confirm the slip and twin activity. Furthermore, a detailed analysis of deformation twins revealed that the so called Schmid twins accommodate strain by both twin growth and slip, whereas the non-Schmid twins accommodate the strain exclusively by crystallographic slip.

Mechanisms of the preferential cleavage of Ti2AlNb-based alloy: The influence of grain size and local plasticity

An in-depth understanding on the preferential cleavage of the matrix B2 phase, with an ordered body-centered cubic (BCC) structure, is pivotal to improve the processability of Ti2AlNb-based alloys. This research employed in-situ micro tensile tests, multiscale microstructure characterizations, and crystal plasticity simulations to study the grain-size dependent cleavage of the alloy with a full B2 phase. The material was intentionally prepared with two grain sizes differing by order of magnitude, i.e., the millimeter-level coarse grain (CG) and the micron-level fine grain (FG). The experimental results showed that the cleavage of CGs always occurred on the {100} planes, even when the loading direction was much less favorable for the cleavage of these planes, whereas the cleavage of FGs took place on both {100} and {110} planes. The investigation demonstrated that the plastic deformation takes a critical role in selecting cleavage planes. Full-field crystal plasticity simulations demonstrated that, for the CGs, the plastic deformation associated with cleavage on {100} planes is less than that associated with cleavage on {110} planes, indicating a less plastic deformation-induced blunting effect with cleavage on {100} planes. For the FG material, however, the existence of plentiful grain boundaries (GBs) leads to significantly heterogeneous plastic deformation, local stress distribution deviating from the imposed global stress, and hot spots of stress and strain concentration at GB triple junctions. These local plasticity heterogeneities enable the possibility for cleavage on both the {100} and {110} planes.