Solid State Phenomena Vol. 390

Abstract: Accurate modeling of the real material behavior is fundamental to improve the accuracy of the finite element analysis (FEA) of sheet metal forming processes. Classical material models such as Hill’48 or Barlat Yld2000-2d do not consider the material behavior under plane strain and shear, even though these states are the primary cause of failures observed in sheet metal forming. Moreover, yield criteria are conventionally calibrated at the onset of plastic deformation to determine the initial yield locus. Isotropic hardening is subsequently assumed, based on the flow curve under uniaxial tension. However, some modern sheet metals exhibit a pronounced distortional hardening behavior, which cannot be sufficiently mapped by the conventional modeling strategy. Hence, this contribution aims to improve the mapping of the yield locus distortion by considering the plane strain and shear stress states and by performing the parameter calibration at higher plastic strains. Hereby, the yield locus exponent of the Barlat Yld2000-2d is adapted in order to accurately map the material behavior under plane strain or shear. Moreover, the influence of a strain-dependent calibration of the yield locus on the mapping accuracy is investigated. Two materials, AA5182 and DP600, are being investigated. It is observed that the consideration of the plane strain state leads to a reduction of the yield locus exponent while the consideration of the shear stress state is accompanied with an increase of the yield locus exponent.

Abstract: In order to reliably predict a material’s behavior during the forming process, robust calculations with precisely calibrated material models are required. Especially when it comes to mapping phenomena depending on complex interactions of different effects, sophisticated measuring techniques have to be used in order to capture them sufficiently. Springback of sheet metal components is governed by elastic behavior, determined by geometry and current material properties. While well understood for most materials, dual-phase steels are exceptional due to their non-linear elasticity and pronounced kinematic hardening, which strongly affect elastic response. Kinematic hardening is characterized via the Bauschinger coefficient from tension–compression tests. As the Bauschinger effect depends on pre-strain and strain rate, precise crosshead control is essential. Therefore, state-of-the art characterization techniques control the process speed by calculating the crosshead velocity from the pre-set clamping length and strain rate. This method, however, does not account for setup-related influences such as machine stiffness or specimen slippage. Therefore, to improve the characterization accuracy of the Bauschinger effect, an alternative method for crosshead control during the tensile-compression test is introduced and analyzed in this study. To compare this innovative approach with the conventional one, both methods are used to capture the effect of relaxation on the Bauschinger effect with different dual-phase and mild steel. The mentioned novel method is based on the optical strain rate control during tensile tests by Naumann, using Digital Image Correlation with an Aramis setup by ZEISS. The intended pre-strain before load reversal is actively controlled by measuring the strain in situ. After characterizing the material cards for each setup, the resulting Chaboche-Rousselier curves are compared to the experimental ones. The results demonstrate that the applied method provides a reliable proof of concept and achieves precision comparable to, as well as exceeding, the conventional displacement strain rate control method.

Abstract: Understanding the relationships between microstructure and (mechanical) properties is inevitable for the design of modern structural metallic materials. A crucial property for most high-strength steels is ductile damage tolerance, since ductile damage can accumulate during cold forming, which either leads to failure in the forming process or subsequently affects the performance. Structure-property relations are often investigated using numerical methods, e.g. crystal plasticity (CP) modeling with representative volume elements (RVE). In a previous study, CP-simulations on 3D-RVE were coupled with surrogate modeling techniques performing a variance-based sensitivity analysis. This analysis enables quantitative descriptions of the relationships between microstructure features with the damage tolerance, quantified by individual indicators for individual damage mechanisms. To investigate the effect of the material model and the corresponding phase properties, 500 sRVE simulations were carried out with different CPparameter sets and the damage tolerance is investigated. All sets stem from the same DP800 but were calibrated with different approaches. Surrogate models were trained on the simulative database to calculate Sobol Indices (SI), which are a measure of how strong damage tolerance is affected by a particular microstructure feature. The SI are compared for the individual material models and damage indicators. The structure-property quantification is heavily influenced by the different material models, resulting in different values for the SI and a different order for the individual microstructure features. The main factor for the pronounced differences is the differently evolving mechanical phase contrast between ferrite and martensite.

Abstract: Polylactic acid (PLA) has emerged as a promising alternative to conventional petroleum –based plastics due to its biodegradability, renewable sourcing, and lower environmental impact. However, PLA exhibits a slow crystallization kinetics compared to other semi-crystalline polymers, such as polyethylene (PE) or polypropylene (PP), resulting in an amorphous structure after processing. This amorphous morphology can adversely influence the mechanical properties and overall performance of PLA components. The present study investigates the cold crystallization behavior of PLA using Differential Scanning Calorimetry (DSC) with the objective of developing an empirical model capable of describing crystallinity as joint function of holding temperature and time. The resulting model is intended to serve as a practical reference for industrial applications, facilitating improved control of PLA’s microstructure and mechanical performance.

Abstract: The present work proposes a novel strategy that significantly shortens Solid-State Foaming (SSF) times, delivering a substantial improvement in process efficiency and paving the way for faster production of customized and functionalized prosthetic components. In particular, the evolution of porosity was evaluated in terms of both volume fraction and mean pore diameter and its subsequent effect on microhardness in a Ti6Al4V-ELI alloy that was initially densified via Hot Isostatic Pressing (HIP) and then subjected to Laser-Induced Solid-State Foaming (LISSF). This acronym was introduced by the authors to underline the originality of this approach, which is not reported in the existing literature. Localized heat treatments were performed using a CO₂ laser source at a target temperature of 1020°C, with three distinct dwell times (120, 240, and 360 seconds). To predict density variations and the resulting mechanical properties, two analytical models were implemented and validated: (i) the Johnson–Mehl–Avrami–Kolmogorov (JMAK) kinetic model, which effectively described the time-dependent evolution of porosity and pore growth under different thermal regimes (based on conduction phenomena vs. direct laser exposure) and (ii) the Ryshkewitch-Duckworth (RD) model, which was used to correlate the exponential decay of microhardness with increasing porosity. The experimental results and regression analyses confirm the high predictive accuracy of both models (R² greater than 0.95), demonstrating the feasibility of the LISSF process for fabricating titanium components with locally controlled porosity for biomedical applications with reference to the manufacturing of customized and functionalized prosthetic components, ensuring both structural reliability and enhanced performance. On the other side, experimental results demonstrated that process parameters play a critical role in the microstructural evolution: specifically, increasing the dwell time to 360 s under direct laser exposure (1020°C) led to a maximum porosity fraction of approximately 30% and a growth in mean pore diameter up to about 35 µm.

Abstract: Accurate modeling of elastoplastic behavior is crucial for forming simulations, yet conventional constitutive laws require extensive calibration and often fail to generalize across diverse loading paths. To address this limitation, a thermodynamically informed neural-network framework is proposed for predicting one-dimensional stress evolution. The model integrates physical consistency into a data-driven formulation by coupling two neural components: one learns the state evolution, predicting increments of the internal variable, while the other approximates the Helmholtz free-energy potential, from which stresses are obtained via automatic differentiation. Synthetic datasets generated from randomized strain paths with power-law hardening were used for training, ensuring broad coverage of nonlinear responses. The model successfully reproduces monotonic, unloading, reverse, and random loading behaviors with minimal error accumulation and stable recursive inference. Owing to its incremental formulation, the framework maintains predictive accuracy beyond the trained strain range, offering a physically interpretable and data-efficient alternative to conventional constitutive models.

Abstract: Macroscopic damage models can describe the toughness behavior and formability of metals in terms of limit strains. However, it requires time-, cost-, and material-intensive calibration. In this work, a simulation framework is proposed to derive macroscopic damage model parameters and related properties directly from the microstructure. For this purpose, statistically Representative Volume Elements of the investigated DP1000 steel were generated utilizing the Python framework DRAGen. This was based on quantitative characterization of EBSD measurements of the present microstructure. Mechanical properties were assigned to the geometrical microstructure model by calibrating a phenomenological Crystal Plasticity model for distinct phases. Martensite cracking was identified as the predominant damage mechanism. This behavior on the microscale was represented by an isotropic brittle damage model in DAMASK, using a fracture mechanical literature value as the critical energy release rate parameter. The presented modeling approach enables stress state-dependent prediction of macroscopic damage properties out of the present microstructure.

Abstract: Predicting the deformation behavior of rolled and extruded light metal alloys is a challenging task. Due to the high cost of experimental analysis, finite element simulations are often required. A variety of material models at different scales are available for practical use. In this work, the viscoplastic self-consistent (VPSC) approach is employed to consider microstructural effects. These can be incorporated by using measured crystal sizes and orientations - called texture - of the alloy under consideration. For each integration point in the FE mesh, a corresponding texture is assigned and individually deformed in LS-Dyna^®, where VPSC is implemented as a user-defined material model - referred to as FE-VPSC. This study focuses on preprocessing of texture data as well as their compression for accurate and faster FE simulations. For verifying the simulations, a comparison with digital image correlation (DIC) of experimental puncture tests was conducted.

Abstract: Industrial hot forming of nickel-based superalloys is typically carried out under non-isothermal conditions, where rapid temperature changes between forming steps not only affect the thermo-mechanical response but also the microstructural evolution, including processes such as recrystallization. Most microstructure models are developed and calibrated for idealized isothermal conditions, and their applicability to realistic transient temperature paths is still unclear. Therefore, this study investigates the microstructure evolution of Inconel 718 under non-isothermal hot deformation by combining dilatometer tests with full-field simulations using DIGIMU® in order to provide detailed insight into the underlying microstructural mechanisms and to assess the capability of a Full-Field approach for modelling such non-isothermal forming conditions. For this aim, compression tests with temperature increases (1020 °C to 1070 °C) and decreases (1120 °C to 1070 °C) were performed, with the temperature change applied at different strains. The results reveal a path dependence, heating at low strain to 1070 °C leads to higher DRX-fractions and finer, more homogeneous grain structures, whereas later heating at higher strains produces coarser, partially recrystallized microstructures due to reduced strain at the higher temperature. For the temperature decrease, DRX occurs predominantly at 1120 °C, after a late temperature change, no additional DRX takes place at 1070 °C. While an earlier change still allows additional DRX. The Full-Field simulations reproduce these trends in dislocation density, recrystallized fraction and grain size distributions with good qualitative agreement and moderate quantitative deviations. Overall, the study demonstrates that the timing and direction of temperature changes affect the final microstructural state, and that DIGIMU®, a Full-Field approach, can capture path-dependent microstructure evolution in Inconel 718 and provides a useful digital tool for analyzing and designing transient temperature hot forming processes.