Crystal Plasticity Finite Element Method Research Articles

Exploring the role of Type-II residual stresses in a laser powder bed fusion nickel-based superalloy using measurement and modeling

Far-field high-energy X-ray diffraction microscopy (ff-HEDM) and the crystal plasticity finite element method (CPFEM) are used to investigate the role of grain-scale (Type-II) residual stresses on the fatigue life of additively manufactured (AM) Inconel alloy 625 (IN-625). Grain-averaged orientations, centroids, and residual elastic strain tensors from ff-HEDM data are used to instantiate a crystal plasticity model to simulate the effect of residual stresses at the grain scale. Simulation results indicate that the presence of tensile residual strains increase stress localization and heterogeneity within grains, triggering an earlier onset of plasticity. A microscale fatigue indicator parameter (FIP) is computed to model the impact of these residual strains on the cycles to fatigue crack nucleation. The crack nucleation model, based on the computed FIPs, predicts a significant reduction in the number of cycles for fatigue crack nucleation for mid- and high-cycle fatigue due to the residual strain induced localization, while the residual strains have minimal impact on low-cycle fatigue life.

Modelling of grain size effects in progressive microforming using CPFEM

Progressive microforming is widely recognized as one of the most efficient and desirable methods of mass production in micromanufacturing arena. To predict the deformation behaviour and size effects of materials induced in progressive microforming, the finite element method (FEM) employed for modelling the microforming process needs to account for microstructure details and deformation/failure mechanisms of the materials. This led to the development of the novel crystal plasticity finite element method (CPFEM) and cohesive zone model (CZM). Previous research and application of CPFEM have been mainly limited to simple deformations such as uniaxial tension and compression, whereas the new method can provide physical insights into how the grain size affects the interplay between crystallographic slip and mechanical twinning in complex microforming, and further material deformation during sheet blanking. A case study was conducted to manufacture a hexagonal socket part using a three-step progressive microforming system, with the comparison between experiments and CPFEM simulations focusing on microstructure evolution, deformation load, and product quality. The CPFEM was found to be more reliable than the conventional FEM in predicting complex deformation, particularly in microstructure and texture evolution, dimensional accuracy and irregular geometries. Results showed that the total height of the part increases with the decreasing grain size, while the head diameter rises with grain size. Simulations successfully anticipated the distributions of dead metal zones and shear bands and identified hole and rollover geometries and corresponding grain size effects. In conclusion, this research facilitates the understanding of grain size effects on the deformation behaviour in progressive microforming and presents a novel approach and strategy for modelling, prediction, and product quality assurance in complex micro deformation and forming processes.

Finite difference based stress integration algorithm for crystal plasticity finite element method

In this study, we present a Finite Difference Method (FDM)-based stress integration algorithm for Crystal Plasticity Finite Element Method (CPFEM). It addresses the complexity of computing the first derivative of resolved shear stress in the Euler backward stress integration algorithm with Newton-Raphson method. The proposed FDM-based model was verified by evaluating its accuracy, convergence and computational efficiency through single-element simulations. The developed FDM-based model can be easily applied to various constitutive models for CPFEM, overcoming the problem of deriving complex derivative regardless of constitutive models. Additionally, the proposed FDM-based model was validated with the reduced texture approach using AA 2090-T3. Specific parameters including crystallographic orientations were calibrated and the plastic anisotropy was successfully described. In addition, the earing profiles were compared using various stress integration methods. As a result, the proposed FDM-based model can be used as an alternative to the Euler backward method using analytic derivatives with the compatible accuracy, convergence, computational efficiency along with easy implementation within the CPFEM framework.

Analysis of Thermal Expansion Behavior and Interface Evolution of TSV Under Thermal Cycle Loading Based on Crystal Plastic Finite Element Method

Analysis of Thermal Expansion Behavior and Interface Evolution of TSV Under Thermal Cycle Loading Based on Crystal Plastic Finite Element Method

Revealing the effects of martensitic transformation and dislocation slip in austenite on the micromechanical behaviors of a 9Ni steel using crystal plasticity finite element method

Austenite is an extremely important phase that significantly influence the mechanical properties of (austenite + martensite) duplex steels. Two different deformation mechanisms, i.e., dislocation slip and martensitic transformation, can be activated in the austenite upon plastic deformation. However, these two deformation mechanisms make different contributions to the work hardening and flow stress of the austenite which are hardly separated by experimental methods, making it difficult to clarify the effect of austenite on the micromechanical behavior of (austenite + martensite) duplex steels. In this work, the influence of martensitic transformation and dislocation slip in austenite on the micromechanical behaviors is investigated in a model 9Ni steel consisting of austenite and tempered martensite (TM) using the crystal plasticity finite element method (CPFEM). The austenite and fresh martensite (FM) formed within the austenite grain upon deformation process are regarded as a whole named as FM/A island in the CPFEM. To accurately model the rate of martensitic transformation, the martensitic transformation kinetics law used in the CPFEM is developed by relating the number of possible nucleation sites for fresh martensite to the mechanical driving force originating from the resolved shear stress on each transformation system. The material parameters for the TM were determined by micropillar compression tests. Besides, the method for separating and determining the material parameters accounting for dislocation slip in austenite and martensitic transformation by a combination of neutron diffraction and measurements of stress-strain curves and austenite volume fractions is developed and exemplified. The CPFEM simulation results show that the local concentration of equivalent plastic strain and stress triaxiality in the FM/A island can be enhanced by the dislocation slip in austenite but suppressed by the martensitic transformation. In addition, the martensitic transformation has a remarkable effect on strengthening the local concentration of maximum principal stress in the FM/A island.

A computational study on efficient yield surface calibrations using a crystal plasticity spectral solver

A computational framework is presented, capable of calculating virtual loads using the spectral solver in the DAMASK software for crystal plasticity simulations in desired stress directions. Calculations are used for the calibration of yield surfaces. The required spatial resolution is assessed based on a comparison with the previously published crystal plasticity finite-element method (CPFEM) and experimental results for three different aluminum alloys (AA1050, AA3103O, and AA3103H18) with 1000 and 2500 grains in a representative volume element. The results of the crystal plasticity fast Fourier transform (CPFFT) method agree well with CPFEM. The elongated grain morphology of the AA3103H18 alloy was found to have a small effect on predicted anisotropy. An analysis was made of how many tests are required for proper calibration of the Yld2004-18p orthotropic yield surface. It was found that 32 virtual tests, along either uniformly distributed strain rate or stress directions but obeying the orthotropic symmetry of the Yld2004-18p yield surface, make a good compromise between accuracy and computation time. Randomly chosen directions have a significantly larger error and require more virtual tests for a similarly good calibration of the yield surface. Since a preselected set of strain–rate directions does not require extra iterations, it is the preferred choice for the calibration of the full stress-based Yld2004-18p.

On the importance of Crystal Plasticity Finite Element discretisation for the identification of crack initiation in RCF using energy-based criteria

Material microstructure plays a key role in crack initiation under rolling contact fatigue. When studying microstructure with crystal plasticity finite element method (CPFE), mesh sensitivity study is of great importance, as the surface-near region is under high uniaxial stresses. In this paper, a new structured mesh strategy is purposed and compared with the classical unstructured mesh strategy. Modelling tests on a bi-grain and a polycrystal model show the calculation of geometrically necessary dislocation (GND) density, recently proposed as a suitable fatigue damage indicator, is highly dependent on mesh morphology, when GND hotspots tend to appear near distorted elements even in homogeneous materials. With uniform mesh size and shape, structured mesh elements can provide physically more acceptable GND calculations, which is particularly important in loading scenarios with complex stresses, such as rolling contact fatigue. Computational efficiency is also improved compared to unstructured models because a smaller number of elements are required in a structured mesh model and pre-processing of the mesh is not required.

LCF life prediction of turbine disc alloy using crystal plasticity and 3D representative volume element containing twin boundaries

The traditional LCF life prediction method based on macroscopic behavior is difficult to reveal the microscopic fatigue failure mechanism. Therefore, the crystal plasticity finite element method and the representative volume elements considering the real microstructure were used to simulate the cyclic deformation of a nickel-based superalloy FGH4098, and a fatigue failure criterion is established to predict the LCF life. The influence of twin boundary on the prediction accuracy is particularly discussed. Meanwhile, the hotspots which are potential sites for fatigue crack initiation were analyzed. The results show that the consideration of twin boundary can improve the accuracy of life prediction, with a scatter factor of ±1.3 only.

Micromechanical properties and deformation behavior of the constituent phases in 3rd generation complex phase AHSS: In-situ neutron experiment and crystal plasticity simulation

This paper investigated the micromechanical properties and deformation behavior of the constituent phases in 3rd generation (GEN) complex phase advanced high-strength steel (AHSS). The hybrid method was a comprehensive combination of uniaxial tensile test with digital image correlation (DIC), electron backscatter diffraction (EBSD), in-situ neutron diffraction (NED) and crystal plasticity finite element method (CPFEM). Results reveal that the microstructure of 3rd GEN AHSS exhibits a complex phase of ferrite (46.2 %), bainite (36.1 %), martensite (9.4 %) and austenite (8.3 %), which would be promising microstructure in the development of new-generation complex phase AHSS. The significant findings are: (1) excellent ductility is obtained while high strength is preserved despite small martensite volume fraction, which can reduce the tendency of martensite cracking; (2) macroscopic stress-strain relationships and microscopic hardening properties of constituent phases are successfully determined, which are very important for predicting the overall performance of complex phase AHSS; (3) presence of bainite with high volume fraction plays a critical role in inducing plastic strain localization in ferrite, resulting in the heterogeneous stress/strain distribution. It is disclosed that pronounced strain localization is mostly initiated in ferrite grains while the deformation bands are mainly located in ferrite/bainite grain boundaries. Furthermore, strain partitioning between ferrite and bainite results in the high-stress concentration in bainite grains. As a result, these “hot zones”, i.e., ferrite grains, ferrite/bainite grain boundaries and bainite grains, experience high strain, strain gradient and stress, respectively, which can be a primary origin of ductile fracture initiation in the 3rd GEN complex phase AHSS. The findings reported in the present investigation would be of great interest in the development of new-generation complex phase automotive steels.

A Yield Stress and Work Hardening Model of Al-Mg-Si Alloy Considering the Strengthening Effect of β" and β' Precipitates.

Precipitates are the primary source of strength for the Al-Mg-Si alloy. Aluminum alloy in the peak-aged state mainly contains β" and β' precipitates. Most of the literature has only considered the strengthening effect of β". Here, we develop a single-crystal intensity model including both precipitate enhancement effects for the first time. This model was subsequently implemented into a crystal plastic finite-element method to model the uniaxial tensile process of a polycrystalline aggregate model of Al-Mg-Si alloy. The simulation results for uniaxial stretching are in good agreement with the experimental results, confirming that the constitutive parameters used for the single-crystal strength model with two precipitates are based on realistic physical implications. Furthermore, by comparing the uniaxial tensile simulation results of a peak-aged alloy considering the actual precipitated phase composition of the alloy with those assuming that the precipitated phase is only the β" phase, the predicted tensile strength of the former is around 5.65% lower than that of the latter, suggesting that the two kinds of precipitation should be separately considered when simulating the mechanical response of Al-Mg-Si alloy. It is highly expected that the present simulation strategy is not limited to Al-Mg-Si alloys, and it can be equally applied to the other age-enhanced alloys.

Study on deformation characteristics of multi-pass continuous drawing of micro copper wire based on crystal plasticity finite element method

Abstract Copper-based wire has excellent comprehensive performance and is widely used in integrated circuit packaging, electronic communication, connectors, audio and video transmission, and other fields. Based on the crystal plasticity finite element method, the crystal plasticity finite element model of multi-pass continuous drawing deformation of pure copper micro wires was established, and the reliability of the model was proved. The continuous drawing deformation behavior of micro wires under high-speed deformation and micro wire diameter scale effect was studied. The research shows that there is a fracture risk zone under the alternating action of positive and negative stress values in the deformation zone of the drawn wire. The changing drawing force and contact stress during the continuous drawing process of the wire will also reduce the stability and surface quality of the wire during the drawing process. The shear deformation and slip degree of the surface grain of the drawn wire are greater than those of the core grain, and the drawing die has a greater impact on the slip system state of the surface of the wire. With the increase in drawing passes, the mechanical characteristics inside the wire increase accordingly, and the deformation uniformity inside the grains is improved. The established model can demonstrate the deformation history characteristics and structure inheritance of the continuous wire drawing process.

Metamorphic layer properties with gradient microstructure distribution of 8Cr4Mo4V steel by grinding

In the grinding process, the metamorphic layer difference from the workpiece material is created on the grinding top surface, and its properties can greatly affect the bearing surface yield strength. In this study, the phase content and grain size distribution of 8Cr4Mo4V with the metamorphic layer were detected using advanced surface observation tools, and the influence of grinding process parameters on the microstructure of the metamorphic layer was considered at the same time. In addition, based on the modeling of the observed metamorphic layer with gradient microstructure distribution, tensile simulations of the metamorphic layer were performed by the crystal plasticity finite element method to investigate the effects of different grain size, phase content, and surface texture strength on its mechanical property like yield strength. Furthermore, the yield strength of the metamorphic layer was characterized by the nanoindentation technique. Finally, it was found that the grinding process parameters affected the microstructure and distribution of the metamorphic layer and thus changed its yield strength, and this study which combines the experiment and simulation aimed to quantitatively analyze the influence of different microstructures on the metamorphic layer.

Evolutions of Cube ({001}) and {115} Orientations in Cold-Rolled Ultra-Thin Non-Oriented Silicon Steel.

In this study, the evolutions of Cube and {115}<161> orientations of a cold-rolled ultra-thin non-oriented silicon steel were investigated using a combination of experimental investigation and the crystal plasticity finite element method (CPFEM). The results show that Cube orientations remain relatively stable when their initial deviation angles from the ideal Cube orientation are less than 12°, even after a 60% cold rolling reduction. However, larger deviations occur due to higher strain near grain boundaries. Furthermore, the {115}<161> orientations, with an initial deviation of ~18° from the ideal Cube orientation, become separated into different orientation regions during cold rolling. Some regions gradually approach the ideal Cube orientation as cold rolling progresses and reach ~12.5° deviation from the ideal Cube at a 40% reduction. This study demonstrates good agreement between simulation and experimental results, highlights the micro-deformation mechanisms during rolling, and offers insights for optimizing the ultra-thin strip rolling process.

Nanoindentation behaviour simulation of a polycrystalline NiTi shape memory alloy using the crystal plastic finite element method

Polycrystalline NiTi shape memory alloys (SMAs) are inevitably involved in plastic deformation under the action of an external force, thus significantly affecting the mechanical behaviour of materials. To deeply understand the plastic deformation mechanism of the NiTi SMA at 400 ℃, the representative volume element (RVE) model combined with the crystal plastic finite element method and the improved Voronoi algorithm were used to construct a three-dimensional polycrystalline spherical nanoindentation model for studying the contribution of different slip systems to the plastic deformation. The calculation results show that the constructed polycrystalline model can well match the experimental curve of the macroscopic stressstrain response curve of the polycrystalline NiTi SMA; the nanoindentation curve also confirms this result. Based on the constructed 3D polycrystalline nanoindentation model, three slip systems ({110}<100>, {010}<100>and {110}<111>) were introduced at the same time. According to the average cumulative shear strain calculated during the indentation process, the results show that the {110}<111> slip system provides the largest contribution to plastic deformation, and the {010}<100>slip mode provides the smallest contribution. The elastic modulus of the model was calculated using the Oliver-Pharr method, and the calculated results are consistent with the experimental results, which proves the validity of the model.

Mechanical Properties of Fine-Grained Low Alloy Steel Investigated by Crystal Plasticity Finite Element Method

Mechanical Properties of Fine-Grained Low Alloy Steel Investigated by Crystal Plasticity Finite Element Method

Quantitatively assessing the contributions of temperature-dependent deformation-induced martensitic transformation to uniform elongation and work hardening of TRIP-assisted duplex stainless steel via crystal plasticity

The martensitic transformation produced by transformation-induced plasticity (TRIP) assisted duplex stainless steels (TDSSs) can significantly enhance plasticity and strength of the material under deformation. At different deformation temperatures, the stability of austenite varies, which further affects the varied kinetics of deformation-induced martensitic transformation (DIMT). In the work, The mechanical response during tensile deformation of TDSS in a temperature range of 20 °C–60 °C was investigated. Especially, the quantitative determination of strength- and elongation-contributions of DIMT was characterized by employing crystal plasticity finite element method (CPFEM) considering thermal softening of temperature effect. The higher the temperature is, the weaker the DIMT and resultant TRIP effect are, and hence the contributions of TRIP to work hardening and uniform elongation are correspondingly reduced. The local strain increment is limited after martensitic transformation due to the significant deformation resistance of martensite, and the strain concentration phenomenon has slowed down at martensitic transformation positions. As a result, the maximum value of strain drops, leading to a decrease in the coefficient of variation (CV) of the strain distribution. Providing improvement of the homogeneity of strain, the material exhibits substantial enhanced plasticity characteristics. The global stress increment is lower than the ideal linear law calculated based on stress mixing that the global stress increment is proportional to the volume fraction of martensite. The stress increment caused by martensitic transformation has a certain degree of postponed effect and transformation rate dependence.

A data-driven yield criterion for porous ductile single crystals containing spherical voids via physics-informed neural networks

Yield criteria for porous material have been widely used to model the decrease of yield strength caused by porosity during ductile failure which deserves long-term efforts in modelling to remedy the current drawbacks. To improve their accuracy, a method of building yield criteria for porous single crystals based on physics-informed neural networks (PINNs) has been developed, and the newly well-trained yield functions are capable of predicting the yield stress of porous single crystals with different porosity, stress states and crystal orientations. The reliability of the yield functions is guaranteed by the precise datasets generated by the crystal plasticity finite-element method. In particular, through embedding the associated flow rule into the training process, the PINN-based yield function not only achieves higher accuracy in comparison with the analytical methods (e.g. variational nonlinear homogenization or limit analysis) but also avoids the improper appearance of grooves that happens in feed-forward neural networks. The proposed framework enjoys an excellent portability as the yield functions can be rebuilt in the similar non-trivial procedure when new influencing factors must be introduced, which makes us believe in its potential to be extended.

A crystal plasticity model of Dynamic Strain Aging for a near-[formula omitted] Ti-alloy

Timetal-834, a near-α Ti-alloy, finds use in aeroengines due to its favorable properties. However, the alloy exhibits Dynamic Strain Aging (DSA) in the temperature range of 375-475 °C, that can cause it to fail early during service. As DSA is due to the micro-scale interaction between the diffusing solutes and mobile dislocations, a crystal plasticity model is developed in this work to capture this phenomenon. Additionally, the influence of the α (HCP) and β (BCC) laths of the transformed-β colony of this alloy on the DSA behavior is captured by using an equivalent model based on Taylor’s assumption. The effect of slip system dependent lath and colony size effect due to Burger’s Orientation Relation is also incorporated. Crystal plasticity finite element method simulations of polycrystalline domains, representative of Timetal-834, are performed for calibration and validation of the model using the available temperature dependent experimental data, and successfully capture the flow stress and DSA behavior. The strain rate dependency of DSA predicted by the model also shows an excellent agreement when compared with experimental data. Microstructural analysis of the simulations show that the orientation of grains/colonies have a strong influence on the aging time and hence the DSA response. Also, the initiation of DSA and frequency of serrated slip on the aligned systems of laths show differences due to dissimilar resistances and constraints on plastic flow. Overall, the model developed in this work can capture the microstructure dependent DSA and can be utilized for engineering of Timetal-834.

Managing the inevitable microstructural and property heterogeneity in powder bed fusion Ti-6Al-4V parts via heat treatment

This study investigates the effects of the commonly-observed microstructure heterogeneity from the metal electron beam powder bed fusion (PBF-EB) processes and how it evolves following the associated heat treatment (HT), on the tensile behaviour of Ti-6Al-4V alloy. A strain gradient crystal plasticity finite element (CPFE) method is employed using physically-based dislocation mechanics to capture the microstructure-sensitive size effect. Microstructural characterization is performed using electron backscatter diffraction (EBSD) of the as-built and post-HT specimens, with measurements of grain morphology, phase, and texture extracted from the bottom and top regions of specimens, used to construct the CPFE models. The dual-phase CPFE model represents α (hcp) and β (bcc) basket-weave morphology, typical in Ti-6Al-4V, with accurate PBF-induced texture definitions defined directly from the measured EBSD data. Key microstructural features exhibiting a gradient include lath width and phase fraction. The effects of as-built microstructural gradient in a single component include an increase of lath width by 43 %, and the beta phase fraction, from bottom to top. The CPFE models successfully predict the effect of HT and microstructural gradient on tensile response, specifically yield stress and initial hardening rate. The role of dislocation density and the associated influence of lath width on yield stress are empirically correlated for the structure-property design of PBF-EB metals. This study also demonstrates the homogenising effect of the heat treatment; effectively eradicating the microstructural gradient observed in as-built specimens.

Investigation on the crystal plasticity of α phase Ti-6Al-4V based on nano-indentation simulation and experiment

Ti-6Al-4V parts are usually hypothesized as isotropic mechanical properties during micro-machining operation. However, the crystal anisotropic mechanical property is an influential factor in the machining of crystals with different sizes and orientations. The hypothesis causes distinct variation in predicting machining force, and consequently the surface integrity cannot be exactly predicted in the micro-machining. Actually, Ti-6Al-4V parts are pseudo isotropy composed of grains with different orientations, elastic modulus, and hardness. Simultaneously, the initiation mode of plastic slip system varies with the grain orientation when the crystal is subjected to an applied load. It is challengeable to evaluate the effect of crystal orientation on its macroscopic properties, either by traditional experimental methods or macroscopic finite element analysis. Nano-indentation provides one novel method to investigate the plastic deformation of selected grains with specific orientations to characterize their mechanical response properties. This research aims to investigate the plastic behavior of α phase Ti-6Al-4V with different orientation grains by means of nano-indentation experiment and crystal plastic finite element method. In the study, single crystals of α phase are classified into “hard grains” (θ < 30°), “soft grains” (θ > 60°) and “normal grains” (30° < θ < 60°) by defining the crystal inclination angle (θ). The elastic modulus and hardness of hard grains are 9% and 28% larger than those of soft grains, respectively. This difference in mechanical properties depends on the slip system that dominates the plastic deformation behavior. The plastic deformation of soft grains is dominated by prismatic slip (48%), while hard grains are accommodated to plastic deformation by basal slip (51%). The average total cumulative shear strain of the soft grains is double that of the hard grains at a maximum load of 10 mN. Meanwhile, the sensitivity analysis is performed to evaluate the effects of the three sets of < a > slip systems and the two sets of < c + a > slip systems on plastic deformation with different grain orientations. The research contributes to the understanding of the plastic deformation mechanism in micro-machining and the exactly predicting the surface integrity generated from micro-machining.