Solid State Phenomena Vol. 390

Abstract: The plastic deformation behavior of polycrystalline copper is strongly governed by microstructural attributes such as grain boundaries and crystallographic orientation. In this study, the individual and coupled effects of grain size and orientation distribution on the mechanical response of copper are systematically investigated using the crystal plasticity finite element method (CPFEM). Uniaxial compression simulations are performed employing an Abaqus UMAT subroutine, and the resulting stress–strain response, slip system activity, and strain localization are examined. Polycrystalline representative volume elements (RVEs) with varying grain sizes and textures are generated to quantify their influence on flow behavior and dislocation density. The results indicate that grain refinement diminishes orientation sensitivity and the influence of individual grains, while enhancing material strength. Moreover, grain boundaries promote heterogeneous slip, localized deformation near grain edges, and increased stress–strain heterogeneity.

Abstract: The dendritic microstructure formed during solidification plays a critical role in determining the mechanical properties of aluminum castings. In particular, secondary dendrite arm spacing (SDAS) is strongly influenced by the cooling rate and is closely related to yield strength, ultimate tensile strength, and elongation. However, experimental validation of these relationships requires a consistent methodology for defining cooling rate and linking it to microstructural and mechanical measurements. In this study, an experimental framework was established to investigate the relationships among cooling rate, SDAS, and mechanical properties in aluminum castings. Casting blocks with different thicknesses were fabricated to obtain a wide range of cooling rates. Cooling curves were measured during solidification, and cooling rates were determined using the second derivatives of the cooling curves. SDAS measurements and tensile tests were conducted on specimens extracted from symmetric positions within the casting blocks to ensure equivalent thermal histories. The results showed that the cooling rate–SDAS relationship exhibited a linear trend on a logarithmic scale, consistent with previously reported correlations. Smaller SDAS values were associated with increased yield strength, ultimate tensile strength, and elongation. The agreement between the present results and literature data confirms the validity of the proposed experimental framework for correlating solidification conditions, microstructure, and mechanical properties of aluminum castings.

Abstract: During a heat treatment, a material undergoes microstructural changes that result in an alterationof its hardness. In a two-step heat treatment, the material is first adjusted to an initial hardness viaa specified cooling rate. Subsequently, the hardness is reduced through a tempering process, whileits ductility is increased. Depending on the tempering duration, tempering temperature, and initialhardness, different resulting hardness values are obtained. The resulting hardness after a chosen heattreatment has thus far been difficult to predict. This work employs symbolic regression to develop amodel that predicts the hardness evolution of 42CrMo4 steel as a function of cooling rate, temperingduration, and tempering temperature. By describing the model with few parameters, it has alsobeen demonstrated that cooling rates and tempering temperatures leading to a target hardness canbe determined. The overall model achieves a coefficient of determination of R2 = 98.50 % for knownexperimental data and a combined coefficient of determination of R2 = 93.13 % for previouslyunknown cooling rates (forward) and previously unattained resulting hardness values (inverse).Our work shows that the resulting hardness of 42CrMo4 can be predicted using a small numberof parameters. This work is anticipated to establish a foundation for further research endeavors.For instance, the approach using symbolic regression can be further adapted to identify physicallyinterpretable constants. Furthermore, the model description offers the possibility of coupling witha simulation model to accurately predict the hardness of a component.

Abstract: Some steels exhibit the Lüders effect. This phenomenon depends on the material and structure (test piece geometry, loading speed, etc.). Most work hardening laws do not take this phenomenon into account. The objective of this work is to define the most appropriate hardening law to highlight the characteristics of Lüders effects. First, the various aspects of the Lüders effect are presented. Several local hardening laws are proposed to describe the plateau or not, some of which are taken from the bibliography. Simulations of uniaxial tensile testing and forming of stamped parts are performed to compare these different hardening laws in predicting the Lüders effect. The Exp_Swift hardening law is recommended for forming cards because it is fully compatible with all software dedicated to steel sheet formability analysis and does not require inverse calibration during identification to accurately predict the plateau length.

Abstract: The superplastic performance of the dual-phase Ti-6242S titanium alloy makes it a good material for aerospace application to produce structural components using the advanced superplastic forming (SPF) process. The need to optimize the SPF process demands the understanding and quantifications of the influence of the different phase constituents - α and β on the global superplastic behavior. Numerical modelling has been useful to predict mechanical behavior for both one-level and multiscale approach. Multiscale approach: bottom-up (microscale to macroscale) has enabled to understand how the different microstructural parameters influence global material/structural mechanical response; which by large means the modelling approach depends on the material local properties. The identification of these local properties is non-trivial in polycrystal materials, particularly at superplastic (elevated) temperatures. We have developed a methodology that permit us to quantify the microstructural parameters of each of the constitutive phases of a polycrystal at a superplastic temperature using genetic algorithm optimization method on the data from in-situ high energy X-ray diffraction (synchrotron radiation), coupled with SEM (scanning electron microscope) and EBSD (electron backscattered diffraction). These identified local microstructural parameters were directly used in the finite strain crystal plasticity model to simulate the material global response. This approach enabled the quantification of the phase influences on global behavior with much accuracy. It was found that α phase planes have high critical resolved shearing stress (CRSS) at 730°C which is similar to its behaviours at room temperatures, while β phase slip planes have low CRSS that encourage slip shearing at low stress. However, more applied load is partitioned in β phase than in α phase, despite that β phase fraction is about 15% at 730°C. Keyword: Multiscale modelling, CPFE, optimization, HEXRD, dual-phase titanium alloy, superplasticity

Abstract: Crystal plasticity finite element (CPFE) simulations of three-dimensional representative volume elements (RVEs) enable the prediction of polycrystalline material behavior under complex loading conditions. Plastic deformation is modeled through crystallographic slip on lattice slip systems, subject to the Schmid yield criterion based on the maximum resolved shear stress (CRSS). In this work, an efficient rate-independent crystal plasticity (CP) and gradient enhanced crystal plasticity (GECP) formulation is used to investigate the influence of microstructural characteristics on the mechanical performance of FCC materials. Three-dimensional periodic RVEs with irregular grain morphologies are simulated within Abaqus/Standard to study the effects of grain size, grain size distribution, and grain shape under uniaxial loading. Comparative analyses between the CP and GECP frameworks are performed to assess the predictive capabilities and applicability for increasingly heterogeneous microstructures. The results demonstrate that GECP accurately captures grain size dependent work hardening and grain size distribution effects through the intrinsic length scale introduced by strain gradient calculations. In contrast, grain shape variations result in only minor changes in the macroscopic response for both frameworks.

Abstract: During sheet metal forming (for example, deep drawing), the desired geometry is typically produced under large plastic deformations. However, in order to characterize the material behavior in this deformation range as accurately as possible, experimental investigation of the material is indispensable. Such investigations are necessary, among other reasons, to determine material properties that may later serve as input parameters for finite element (FEM) simulations. By defining appropriate material properties, the design and optimization of the forming technology become more efficient. One such property is the material’s flow curve; for determining it in the large deformation range, a particularly promising method is the stack compression test (SCT). At the same time, the method also has certain drawbacks. One is that the test is not standardized, and therefore there is no exact methodology for its execution. Another difficulty arises from the fact that the friction conditions present during the test are not clearly defined. In this paper, we seek to determine whether the friction conditions in the case of the SCT can be inferred by a comparative analysis of experimental force–displacement curves and force–displacement curves obtained from FEM simulations.

Abstract: Interpenetrating Phase Composites (IPCs) with biomimetic properties are promising materials for strengthening orthopaedic implants while also increasing their biocompatibility. Thanks to additive manufacturing techniques, lattice structures can be employed to develop biomaterials with controlled architectures, enabling the replication of human bone structures and offering advantages in terms of strength-to-weight ratio. This study investigates the behaviour of a bi-material steel-polymer lattice structure, observing that the epoxy resin increases the mechanical strength of gyroid, leaving the lightweight properties unchanged. Moreover, an equivalent constitutive model was calibrated, and a homogenization procedure based on the Representative Volume Element theory was applied. The effect on mechanical strength due to the 316L powder dispersed within the epoxy resin was investigated as well.

Abstract: An associated plasticity theory of combining Hill's 1948 quadratic and Gotoh's 1977 quartic stress functions [1,2] has recently been developed for modeling orthotropic steel sheet metals in plane stress [3]. Some further developments of the theory with a higher-order non-homogenous polynomial yield stress function are described in this study. Numerical examples are given to illustrate the expanded capabilities for modeling thin steel sheet metals in plane stress by the enhanced Hill-Gotoh anisotropic plasticity theory.

Abstract: Despite the growing use of biopolymers in automotive, packaging and structural applications, predictive modelling of their elastic–viscoplastic deformation remains limited. In this work, a micromechanically based constitutive model is proposed to describe the micro‑ to macroscopic behaviour of a semi‑crystalline PLA matrix reinforced with short hemp fibers. The formulation relies on a multiplicative split of the deformation gradient into elastic and viscoelastic–plastic parts, with elasticity governed by fiber and crystalline phases and time‑dependent deformation localized in the amorphous phase. High fiber content and strong fiber–matrix bonding enable the suppression of lattice crystalline anisotropy, leading to a compact model with a reduced number of internal variables. The model is calibrated and validated using uniaxial tensile tests on pellet‑extrusion 3D‑printed specimens with controlled porosity and plasticiser content, and reproduces nonlinear loading, unloading, creep and stress relaxation. In a second step, synthetic data generated by the constitutive model are used to train surrogate machine‑learning models, which are discussed as a perspective for accelerating long‑term simulations and parametric studies in forming applications.