Crystal Plasticity Finite Element Model Research Articles

Exploring the hydride-slip interaction in zirconium alloys

Hydrogen pick-up and hydride precipitation can lead to embrittlement and fracture strength reduction of nuclear fuel cladding tubes made of Zircaloy. Plastic deformation of hydride packets and its interaction with local plasticity in the zirconium matrix is a key linkage of microstructure feature to structural integrity of hydrided polycrystalline bulk Zircaloy. This work focuses on explicit representation of hydride packets from high spatial resolution electron backscatter diffraction onto a crystal plasticity finite element model for capturing and understanding slip localisation near hydride-matrix phase boundaries, based on the extracted material property of hydrides. The mechanisms behind slip evolution including slip nucleation, slip transfer, and slip inhibition are studied by combined high-resolution digital image correlation and crystal plasticity results. Through assessing various slip transfer parameters, new slip transfer criterion is proposed for α/δ phase boundaries. Prior to slip transfer criterion, local micromechanical quantities, specifically shear stress and stored energy density, are necessary to drive and provide pathway for subsequent slip transfer at α/δ phase boundaries.

On the effects of transformation strain induced by hydride precipitation

One of the main degradation mechanisms of the zirconium alloys used in nuclear reactors is hydrogen embrittlement and hydride formation. The formation of zirconium hydrides is accompanied by a transformation strain, the effects of which on the development of localized deformation zones are not well-understood. This study uses a crystal plasticity finite element model that is coupled with diffusion subroutines to quantify such effects. For this purpose, a zirconium specimen was hydrided in the absence of any external mechanical loads. With the use of electron backscatter diffraction, the rotation fields around interacting intragranular hydrides as well as those located at grain boundaries or triple points were measured at a high spatial resolution. The as-measured zirconium and hydride morphologies were mapped to the model for numerical simulation. Both numerical and experimental results show that hydride precipitation induces large rotation fields within the zirconium matrix, where such rotations are at their maximum in the vicinity of hydride tips. While the crystallographic orientations and shapes of hydrides affect the magnitude of rotation fields, both experimental and modeling results revealed the development of discrete and parallel geometrically necessary dislocation fields and a strong interaction among neighboring hydrides. It is shown that the stress field resulting from hydride precipitation affects the patterning of hydrogen distribution, which in return affects further hydride interlinking.

An energy-CP-combined model for predicting the fatigue life of polycrystalline materials under high cycle and very high cycle fatigue

A fatigue life prediction model in the high to very high cycle fatigue (VHCF) regime of as-received 7075-T6 Al alloy material is proposed. The relative parameters in the life prediction model are obtained by crystal plasticity finite element (CPFE) framework. The modified Ohno-Wang constitutive model is embedded into the CPFE model considering the evolution of back stress during the cyclic loading. In the life prediction model, the range of energy efficiency factors is validated by verifying the plastic strain energy density (PSED) with fatigue experimental data. The fatigue experiments are performed using an ultrasonic fatigue system to validate the fatigue life prediction model. The predicted life is estimated using the maximum and minimum energy efficiency factors, it is found that the life prediction model can accurately predict the VHCF life. It is found that 72.8%–81.3% of the experimental fatigue life can be captured using the proposed model. Moreover, the localized deformation in the grain scale can be well-captured considering the heterogeneity of mechanical properties.

A sensitivity analysis of twinning crystal plasticity finite element model using single crystal and poly crystal Zircaloy

The popularity of crystal plasticity finite element method (CPFEM) models is increasing due to their ability to predict the mechanical response of crystalline materials such as metals and metal alloys more accurately than traditional continuum mechanics models. This is since the crystal plasticity models consider the effect of atomic structure, microstructural morphology, and properties of individual grains. These CPFEM models use a large number of material parameters in order to capture the mesoscale physics which comes with the downside of the tedious calibration process. In this paper, a CPFEM code was developed to include the twinning induced grain reorientation and subsequent crystallographic slip for HPC material. The developed code is incorporated in a large-scale, parallelized nonlinear solver WARP3D. A sensitivity analysis with respect to 22 material parameters was then conducted using single crystal and polycrystal representative volume element (RVE) of Zircaloy material. Loading was applied along five different crystallographic orientations for single crystal RVE and along three directions namely, rolling (RD), transverse (TD), and normal (ND) direction for polycrystal RVE. Results obtained from the sensitivity analysis were used for the calibration of material parameters for Zircaloy. Finally, developed code along with calibrated material parameters was used to investigate the effect of the hydride phase formation in Zircaloy which is a typical case observed for nuclear applications. It was found that the volume fraction of the hydride phase has a significant impact on the mechanical properties of Zircaloy.

Geometrical and crystal plasticity modelling: Towards the establishment of a process-structure-property relationship for additively manufactured 316L struts

This paper presents a methodology to establish a process structure property (PSP) relationship for the additive manufacturing (AM) of thin AISI 316L struts, as might be used in coronary stent applications. The methodology is based on a new geometrically based process-structure method for AM process variables, and crystal plasticity finite element (CPFE) modelling that includes the representation of melt pool microstructure morphology and texture. The effects of AM process variables are characterised with respect to ductility, yield strength and UTS across a range of process variables, including hatch spacing, layer thickness and build orientation (two orientations are considered: horizontal and vertical). The CPFE-predicted effect of build orientation is shown to be consistent with experimental test results. The present methodology has allowed identification of optimal hatch spacing and layer thickness for a given laser spot size, power and scanning speed. CPFE modelling of AM melt pool texture is shown to be key to successful prediction of the effects of process variables on mechanical behaviour.

Deformation-Induced Surface Roughening of an Aluminum-Magnesium Alloy: Experimental Characterization and Crystal Plasticity Modeling.

The deformation-induced surface roughening of an Al-Mg alloy is analyzed using a combination of experiments and modeling. A mesoscale oligocrystal of AA5052-O, obtained by recrystallization annealing and subsequent thickness reduction by machining, that contains approx. 40 grains is subjected to uniaxial tension. The specimen contains one layer of grains through the thickness. A laser confocal microscope is used to measure the surface topography of the deformed specimen. A finite element model with realistic (non-columnar) shapes of the grains based on a pair of Electron Back-Scatter Diffraction (EBSD) scans of a given specimen is constructed using a custom-developed shape interpolation procedure. A Crystal Plasticity Finite Element (CPFE) framework is then applied to the voxel model of the tension test of the oligocrystal. The unknown material parameters are determined inversely using an efficient, custom-built optimizer. Predictions of the deformed shape of the specimen, surface topography, evolution of the average roughness with straining and texture evolution are compared to experiments. The model reproduces the averaged features of the problem, while missing some local details. As an additional verification of the CPFE model, the statistics of surface roughening are analyzed by simulating uniaxial tension of an AA5052-O polycrystal and comparing it to experiments. The averaged predictions are found to be in good agreement with the experimentally observed trends. Finally, using the same polycrystalline specimen, texture-morphology relations are discovered, using a symbolic Monte Carlo approach. Simple relations between the Schmid factor and roughness can be inferred purely from the experiments. Novelties of this work include: realistic 3D shapes of the grains; efficient and accurate identification of material parameters instead of manual tuning; a fully analytical Jacobian for the crystal plasticity model with quadratic convergence; novel texture-morphology relations for polycrystal.

Microstructure sensitivity of the low cycle fatigue crack initiation mechanisms for the Al0.3CoCrFeNi high entropy alloy: in-situ SEM study and crystal plasticity simulation

In this study, in-situ fatigue tests under scanning electron microscopy (SEM) were performed to reveal the relationship between grain slip deformation and fatigue crack initiation of Al0.3CoCrFeNi high entropy alloy (HEA). It was found that the fine grains (FG) exhibited a higher fatigue crack initiation life than that of the coarse grains (CG), which is related to the inhibition effects of twins and grain boundaries on fatigue crack initiation. The initiation of fatigue cracks in both the CG and FG specimens occurred in the area of high density of slip lines. The fatigue cracks were observed to deviate from the single slip line, which is related to the activation of multiple slip systems inside the grain, leading to the alternation of fatigue crack propagation path. In addition, the intersection of different slip planes can be another preferential crack initiation site if two or more slip planes are activated inside one grain. By combining EBSD analysis and crystal plasticity finite element modeling (CPFEM), the influence of microstructures, such as grain orientation and grain boundaries, on the fatigue crack initiation mechanism was further analyzed. The CPFEM results confirmed that the CG specimen resulted in a higher cumulative shear strain (CSS) than that of the FG specimen under the same stress level, which led to higher fatigue damage.

A Computationally Efficient Multiscale, Multi-Phase Modeling Approach Based on CPFEM to Assess the Effect of Second Phase Particles on Mechanical Properties

Crystal plasticity finite element (CPFEM) modeling of metals that can be age hardened consisting of second phase particles is extensively performed based on representative volume element (RVE) models. The RVE model is generated for ferritic low-carbon steel using the data obtained from microstructural observation through optical microscopy (OM) and electron backscatter diffraction (EBSD). The generated RVE is required to statistically represent the original material in terms of grain topology and texture in microscale, as well as the configuration of second phase particles in submicron scale. The multiscale, multi-phase nature of the generated RVE leads to a computationally expensive modeling procedure. To overcome this issue, an alternative multiscale modeling approach based on a homogenization scheme is proposed, in which the effect of second phase particles on deformation behavior is accounted for with no need for the explicit presence of particles in RVE. Lastly, a thorough parametric analysis is performed to investigate the sensitivity of the mechanical properties to the second phase particles in terms of size, volume fraction, geometrical distribution, and deformable or non-deformable properties of precipitates in the investigated material. The results show that the proposed multiscale modeling approach successfully accounts for the effect of second phase particles on deformation behavior, while the computational cost is reduced by more than 99%. In addition, the simulations show that the configuration of second phase particles at a microscale plays an important role in defining the mechanical behavior of the material.

In-situ EBSD observation and simulation of free surface roughening and ductile failure in the ultra-thin ferritic stainless steel sheet

Surface roughening is one of the most fundamental issues which greatly affects the plastic deformation and ductile fracture behavior of ultra-thin sheet materials. The present study investigated the influence of free surface roughening on the micromechanical failure in the ultra-thin ferritic stainless steel (FSS) sheet for bipolar plate in proton exchange membrane (PEM) fuel cell under in-situ tensile deformation. The microstructural evolution during uniaxial tension was monitored using in-situ electron backscatter diffraction (EBSD) technique. Then the initial microstructure was directly mapped onto the finite element mesh of representative volume element (RVE) in the crystal plasticity finite element (CPFE) simulation. The CPFE model was incorporated with the microscopic ductile fracture criterion in terms of plastic energy dissipation in order to simulate the initiation of ductile fracture caused by the free surface roughening. The in-situ EBSD observations reveal that the microstructure of the ultra-thin FSS sheet exhibits heterogeneous plastic deformation and strain localization on the surface at the large deformation owing to the considerable free surface roughening. The CPFE simulations well reproduce the stress/strain heterogeneity and the local hotspots of the ductile fracture initiation. It reveals that the increase of surface roughness with the deformation results in the increased inhomogeneity of thickness which accelerates the strain localization, consequently the premature necking and failure in the ultra-thin steel sheet. Due to the free surface roughening which can facilitate strain localization, the initiation of ductile fracture is obviously observed in both the ridges and valleys in the free surface and its propagation along the pronounced localization band through the thickness, leading to material failure. The good correlation of free surface roughening to the onset of plastic instability and ductile fracture further advances the insight into the micromechanical failure during plastic deformation of the ultra-thin FSS sheet for bipolar plate in PEM fuel cell.

Role of δ-phase on Mechanical Behaviors of Additive Manufactured Inconel 718: Detailed Microstructure Analysis and Crystal Plasticity Modelling

In this work, a multi-scale approach was applied to reveal the evolution mechanisms of the δ (Ni3Nb) phase and the resultant mechanical responses in wire-arc additive manufactured (WAAM) Inconel (IN) 718. Several heat treatment strategies, consist of homogenization, intermediate heat treatment and aging process, were firstly conducted to produce δ phases with different characteristics. The early evolution of the δ phase was then analyzed in detail via transmission electron microscopy. The nanoindentation and tensile tests were also used to verify the strengthen response of δ phase. Moreover, a crystal plasticity finite element (CPFE) model, taking into account the different configurations of δ phase, was developed to study and predict the micro deformation behavior. Results revealed that when the intermediate heat treatment time exceeded 1 h, the formation of the main strengthening phase γ" was constrained by the δ phase, accompanied by the coarsening of γ". The decrease of γ" phase and the destruction of coherent γ"/γ interface are the main causes of strength loss in the WAAMed IN718. The intergranular dislocation transmission was hindered by the δ phase, thereby increasing the grain boundary strength. However, the needle-like δ phase within the grain may cause premature fracture due to strain localization, thereby reducing the material properties. The evolution mechanisms of the δ phase obtained in this study provides theoretical guidance for the optimization of the microstructures and mechanical properties of WAAM Inconel 718.

Deterministic approach on microstructurally small crack definition based on a crystalline plasticity finite element method incorporating strain localization

AbstractThe transition point of the crack length to a microstructurally small crack is necessary for predicting crack extension behavior. The conventional criterion is the crack length smaller than the grain size and is a probabilistic criterion. This criterion does not consider the metal's crystallite plasticity property discrepancy (CPPD). However, CPPD determines crack extension behavior for recently developed advanced materials with complex microstructures. Therefore, the authors propose a deterministic judgment method for microstructurally small cracks considering crystallite plasticity based on a physics‐based crystal plasticity finite element model with strain localization. The proposed method is based on the difference value of the crack tip opening displacement varying with the ratio between the crack length and grain size with the change in the grain orientation ahead of the crack tip. A case study for copper is performed, and the results show that the novel method can be applied to define the microstructurally small crack.

Experimental investigation and crystal plasticity simulation for the fatigue crack initiation of the equiaxed Ti-6Al-4V alloy in the very high cycle regime

This work investigated the fatigue crack initiation mechanism of the equiaxed Ti-6Al-4V alloy in the very high cycle fatigue (VCHF) regime. Ultrasonic fatigue experiments were carried out on Ti-6Al-4V specimens and a detailed analysis of the failure mechanism was conducted by means of scanning electron microscopy (SEM). The localized cyclic plastic response of the alloy was investigated using the crystal plasticity finite element (CPFE) method to further clarify the fatigue crack initiation process in the VHCF regime, and the CPFE models with varying transformed β(βt) phase volume fractions were presented to investigate the impact of βt phase on the VHCF behavior. The simulation results indicate that the proposed CPFE model can effectively captures the microstructural plastic deformation mechanisms, such as stress concentration near the phase boundaries and plastic accumulation. And the βt phase significantly affects the VHCF behavior of the alloy.

On the mechanistic driving force for short fatigue crack path

The growth of fatigue cracks at the microstructural level is significant for many engineering industries. The multifarious nature of crack propagation at microstructure length scales necessitates the use of advanced modelling techniques to predict fatigue life accurately. A key contributor to this is the path of the crack, which also remains challenging to predict; the maximum slip criterion has been used widely in the literature but is not fully adequate. This paper tests the hypothesis that for short crystallographic cracks, there is some other factor responsible for guiding their extension on a particular plane. With this, using a crystal plasticity finite element modelling framework, two new energy-based methods are developed: a microstructure-sensitive maximum energy release rate criterion, and a maximum normal stored energy density criterion. Results demonstrate, for the two cases studied, both methods offer a significant improvement over the maximum slip criterion when applied to real microstructures. In particular, the maximum normal stored energy method gives closest agreement with experiments, while maximum energy release rate offers new insights into a mechanism for crack bifurcation.

Analysis of the mechanism of orientations evolution during hot rolling and mechanical properties of TiBw/TA15 composites based on crystal plasticity finite element model

An in-depth understanding of the crystal orientation evolution during hot rolling of TiB whisker (TiBw) /TA15 composites and the anisotropy of the as-rolled plates can help fully utilize the material properties. In this paper, the crystal plasticity finite element models of high-temperature (HT) β-phase and room-temperature (RT) α-phase were constructed from electron backscattering diffraction data. Based on this, the orientation evolution during hot rolling in the single-phase region and the effects of the matrix texture on the mechanical properties of the as-rolled plates were analyzed. The effect of TiBw on the anisotropy was studied by the composites finite element model. Results showed that the α-fiber texture of the β-phase was formed during HT rolling. This texture was converted to the T-texture of the α-phase at RT during cooling according to the Burgers orientation relationships. The TiBw had little effect on the matrix texture composition. The TiBw and matrix texture caused the matrix to have higher strength along the rolling direction and the transverse direction, respectively. The matrix texture dominated the difference in mechanical properties because its effect exceeded that of TiBw. The effect of the matrix on the mechanical properties was caused by the Schmid factors (SFs) and the critical resolved shear stress (CRSS) of the slip system together. The slip mode was influenced by SFs determined by the angular relationship between the crystal orientation and the loading direction. The CRSS of the activated slip system determined the yield strength.

Imparted benefits on mechanical properties by achieving grain boundary migration across voids

Understanding the interaction of micro-voids and grain boundaries is critical to achieving superior mechanical properties for safety-critical parts. Micro-voids and grain boundaries may interact during advanced manufacturing processes such as sintering, additive manufacturing and diffusion bonding. Here, we show imparted benefits on mechanical properties by achieving grain boundary migration across voids. The micro-mechanisms and quantitative analysis of grain boundary migration on local deformation were studied by integrated in-situ EBSD/FSE and crystal plasticity finite element modelling. It is revealed that a migrated grain boundary does not alter the activated slip systems but precludes grain boundary-multislip interaction around interfacial voids to alleviate stress concentrations. The stress mitigation caused by grain boundary migration is almost the same as that caused by void closure under the example diffusion bonding thermal-mechanical process used in this study. This new understanding sheds light on the mechanistic link between GND hardening, grain boundary migration and the corresponding material tensile behaviour. It opens a new avenue for achieving superior mechanical properties for metallic parts with micro-defects such as those generated in diffusion-bonded, sintered and additive manufactured components.

Nanoindentation study of δ-phase zirconium hydride using the crystal plasticity model

Zirconium hydride precipitation degrades the fracture toughness of nuclear reactor fuel cladding tube. Due to the difficulty of experiment, deep understanding on mechanical properties of zirconium hydride via numerical approaches is in a great need. To study the mechanical properties of zirconium hydride, the crystal plasticity finite element model considering geometrically necessary dislocations evolution is used to simulate the nanoindentation deformation behavior of single-crystal δ-hydride. The parameters in the crystal plasticity model are calibrated by Young's modulus along different crystallographic orientations and experimental stress-strain data at different strain rates. The predicted polycrystalline Young's modulus, Poisson's ratio, and nanoindentation hardness are in good agreement with the experimental results. The simulation results show that the nanoindentation hardness strongly depends on the indentation depth when it is smaller than 500 nm. Furthermore, the effects of crystallographic orientation and zirconium matrix on the indentation results are also studied. We find that the nanoindentation hardness of δ-hydride is slightly orientation dependent. For smaller hydride size or larger indentation depth, the surrounding zirconium matrix undergoes plastic deformation, which leads to a significant underestimate of the nanoindentation hardness of the hydride.

Grain size and shape dependent crystal plasticity finite element model and its application to electron beam welded SS316L

Electron beam welding is an autogenous welding process that leads to microstructural heterogeneities; crystallographic texture, elongated and larger grain size relative to the surrounding parent material. The goal of this study is to predict the changes in mechanical response of the weld fusion zone as a function of grain morphology and texture by using the parent material properties to avoid extensive and costly experimental campaigns. For this reason, a crystal plasticity solver, “University of BRIstol cryStal plasTicity sOLver” (BRISTOL), is implemented in a finite element framework with new constitutive laws to account for the length-scale dependence considering the size and shape of the grains. It is found that the crystallographic texture governs the orientation specific elastic stiffness and yield stress having the most dominant effect on the macroscopic response of the weldment at the grain size scales considered. Crucially the length-scale dependent model allows accurate prediction of the yield strength of the weldment over a range of microstructures, also highlighting the presence of other factors such as prior strain hardening during the welding process and residual stresses.

Research on the evolving yielding behaviour and micro-mechanism in biaxial deformation of DP1180 sheet based on crystal plasticity finite element model

Dual-phase steels (DP steels) consist of ferrite and hard martensitic phase. For the high strength and good formability, they are widely used in automotive applications. Compared with the DP steels with lower strength, DP1180 is more special for the volume fraction of martensite is higher than that of ferrite. In this paper, the evolving plastic yielding behaviours and insight into their microscale mechanisms of DP1180 were studied by biaxial tension experiments and crystal plasticity finite element method. The representative volume element (RVE) model of DP1180 taking the dual phase fraction, grain size and texture into consideration is established and the relevant parameters of crystal plasticity are reverse calibrated by the uniaxial tensile test stress strain curve. The simulated biaxial tension tests were conducted by the established RVE model to investigate the yielding micro-mechanisms of DP1180 steel, and the obtained yield loci matches well with the test results. The simulation results show that the texture has a significant effect on the contours of the yield loci. The soft ferrite grains weaken the kinetic constraints to the polycrystalline matrix and further free the rotation and plastic deformation of the neighbouring grains. This study thus provides a comprehensive understanding of the effect of the microstructure (crystal structure, texture and dual phase fraction) on the yielding behaviour of DP1180 steel as well as a method of virtual experiment to get the yield loci of metallic materials.

The effect of phase distribution of constituent-fiber structure on the deformation heterogeneity of TRIP-assisted lean duplex stainless steel

The cold-rolled TRIP-assisted lean duplex stainless steel (TLDX) showed the directional distribution of constituent-fiber structure. The effect of phase distribution of constituent-fiber structure on the deformation heterogeneity during tensile tests and deep drawing of cylindrical cup was investigated through crystal plasticity finite element model (CPFEM) involved in the martensitic transformation. The results showed that the strain for the plastic instability was lower in the transverse direction (TD)-loaded case (true strain εT ∼0.408) compared with the rolling direction (RD)-loaded case (εT ∼0.485). Also, the strain localization bands formed at a lower strain (engineering strain εE ∼40%) in the TD-loaded case than that in the RD-loaded case (εE ∼55%). At the same strain, the volume fraction of transformed martensite of the TD-loaded case was relatively less than that of the RD-loaded case. For the transformed martensite, it only accommodated a low proportion (<5%) of global strain in the two cases. The proportion of partitioned strain into austenite (Pεγ) in the RD-loaded case was always higher than that in the TD-loaded case, while the partitioned strain into ferrite (Pεα) showed a converse law, which indicated that the deformation heterogeneity in the TD-loaded case is more pronounced. Similarly, the high risk of cracking of deep-drawn cylindrical cups with different sizes also always formed at the specific zones corresponding to the TD-loaded case.

Experimental investigation and micromechanical modeling of load partitioning behavior of duplex stainless steel 2205 during cyclic hardening

This paper aims to understand the load partitioning behavior between austenite and ferrite of duplex stainless steel 2205 under cyclic loading by experiments, including a series of low cycle fatigue tests and electron back scattered diffraction observation. Meanwhile, a crystal plasticity finite element model was developed to predict the cyclic micromechanical response of two constituent phases. The results show that more slip bands were found within the austenite. The cyclic plasticity of 2205 started within the austenite, and gradually translated into the ferrite with the elevation of applied cyclic amplitude. The plastic deformation within the austenite was inclined to form at the phase boundaries, while it promoted at grain boundaries in the ferrite. The micromechanical elasto-viscoplastic parameters of two constituent phases were calibrated accurately. The proposed crystal plasticity finite element model has a great ability of predicting not only the time- and amplitude- macroscopic cyclic hardening behavior but also the micro-deformation within two constituent phases, even the cyclic hardening of 2205 with different phase ratios can also be reproduced accurately. The prediction error on cyclic stress amplitude of 2205 during cyclic hardening can be controlled within 3.2%.