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In scientific studies, sheet metal is usually considered as a two-dimensional body. Thus, it is accepted that material properties are in most cases regarded homogeneous in thickness direction. However, a gradation of certain properties becomes apparent when going beyond the standard characterization methods for sheet metals, which can for example, influence the springback behavior and the thinning of the sheet after forming. Thus, the aim of this work is to further improve the prediction accuracy of springback after forming in simulations, by implementing several inhomogeneous properties over the sheet thickness in an existing material model. For this purpose, the entire procedure from the identification of the inhomogeneous properties for describing the gradation to the implementation in a numerical model and its validation by comparing experimental and simulated bending operations is carried out on a DC04 cold-forming steel in order to prove its influence on the springback behavior. It is shown that including graded material properties in simulations does indeed have an impact on the prediction quality of springback and that the information about inhomogeneous properties can be provided by existing characterization methods with a high local resolution like electron backscatter diffraction or X-ray stress analysis. In a further step, it was possible to validate the improvement in numerical accuracy by comparing the prediction of the springback angle from both the existing and the extended model with experimental bending results. Both the initial model as well as the model supplemented with the 3D properties provide a good prediction accuracy in the solution heat treated material state. For the predeformed material, however, the initial numerical model predicts a springback angle of about 13°, which deviates remarkably from the experimentally obtained mean value of about 17°. The extended model delivers a significantly improved accuracy in springback prediction in relation to the initial prediction (deviation of 4°) with a minor deviation of only about 0.8°, which proves the importance of considering the gradation of material properties in thickness direction for an overall higher dimensional accuracy of sheet metal products.

The steady laminar stagnation flow flame of NH3-H2-air gas mixture stabilized at a plane wall is numerically investigated. Its interaction with the wall with the consideration of heat loss is the focus of this work. The numerical study of the combustion system is performed by using the full chemical mechanism and detailed transport model including the differential diffusion and Soret effect. The simulation of the solid mechanics is based on the theory of isotropic linear thermo-elasticity. With the numerical simulation, it will be discussed how the wall material would change the flame stability in terms of extinction limit, and how the combustion system such as mixture composition, flame strain rate, and pressure would vary the thermo-mechanical stresses in the solid wall and the corrosive behavior at the surface of the wall.

A three-dimensional CFD–CHT simulation method is presented and validated with a turbocharged single cylinder SI engine. Various ignition time and lambda strategies as well as variations of boost pressure are investigated with regard to cycle averaged component temperatures. This complements existing published works which experimentally studied crank angle resolved heat fluxes or temperature swings rather than averaged temperatures. Cyclical fluctuations in the pressure curves were measured and processed statistically using probability density functions for the heat transfer coefficient and the cylinder gas temperature. The corresponding joint probability density function considers their strong correlation. The interpretation as random variables enables a time-scale separation with a low-pass filter function. The thermomechanical problem of heat transfer is addressed with simplified models according to Woschni, Eichelberg, and Hohenberg. Previous investigations primarily focused on their predictive quality of instantaneous in-cylinder heat fluxes. In this paper, their effect on cycle averaged component temperatures is investigated and the corresponding different sensitivities to specific engine settings are presented and compared with measurements. It is shown that, by choosing the right model, the suggested simulation approach is an alternative to prevailing experimental methods in temperature analysis: all thermodynamic variations examined are in good agreement with theoretical predictions.

While thermomechanical analyses in solid and combustion processes in the gas phase are intensively studied separately, their interaction is less investigated. On one hand, the combustion system can be affected by the solid as a result of, for example, the heat conduction. On the other hand, the high-temperature flame can induce the thermal load in the solid, which significantly affects the mechanical stress field in the material. This work focuses on the coupling between the solid and flame and the combustion-induced mechanical stress in the material. The influence of the solid on the flame structures and properties and also the influence of the flame on the thermomechanical behavior in the solid are investigated. A stagnation flow NH3–H2–air flame to a plane wall is considered as a representative model, which is simple but also realistic in many engineering conditions. It is mainly found that an increase of the flame strain rate leads to an increase of thermomechanical stress in the wall, and the system pressure improves the flame stability against extinction but enlarges the induced thermomechanical stress at the same time. Furthermore, it is observed that the hydrogen content in the gas mixture does not affect the thermomechanical stress in the wall if the flames with different hydrogen additions are imposed with the same strain rate. On the basis of various flame parameters, it is also shown that the solid would also flow plastically under certain conditions, such as high pressures. From the viewpoint of the wall, it is mainly shown that the flame stability against extinction can be improved using wall materials with larger heat conductivities.

The entire simulation process for long fiber reinforced thermoplastics is examined to determine the effective mechanical properties which are influenced by the microstructural fiber orientation state. Therefore, flow and fiber orientation simulations are conducted and the obtained fiber orientation tensors are used in two-scale structural simulations. The fiber orientation distributions as well as the mechanical properties are compared with micro-computed tomography data and results from threepoint bending tests performed by dynamical mechanical analysis (DMA), respectively. The validated results show that prediction of the essential mechanical properties is possible with the applied combinated methods and that the knowledge of the fiber orientation and its gradients is of crucial importance for the entire simulation process.

The use of sheet molding compounds (SMC) in diverse applications requires different specific material properties for each type of finished parts. These material properties have to be assured by a reliable quality control, which does not only have to be performed for the prefabricated SMC itself but also during the production process of the semi-finished material. This is of high importance because quality fluctuations and defects can already occur during the production of the semi-finished SMC. This results in high scrap rates as well as machine failure and can additionally cause further problems in the following process steps. Hence, an inline quality control can help to establish objective quality criteria for semi-finished SMC and can enable controlled and stable production processes.

Aluminum sheets used for beverage cans show a significant anisotropic plastic material behavior in sheet metal forming operations. In a deep drawing process of cups this anisotropy leads to a non-uniform height, i.e., an earing profile. The prediction of this earing profiles is important for the optimization of the forming process. In most cases the earing behavior cannot be predicted precisely based on phenomenological material models. In the presented work a micromechanical, texture-based model is used to simulate the first two steps (cupping and redrawing) of a can forming process. The predictions of the earing profile after each step are compared to experimental data. The mechanical modeling is done with a large strain elastic visco-plastic crystal plasticity material model with Norton type flow rule for each crystal. The response of the polycrystal is approximated by a Taylor type homogenization scheme. The simulations are carried out in the framework of the finite element method. The shape of the earing profile from the finite element simulation is compared to experimental profiles.

This work deals with comparing the prediction of the development of rolling textures by using a homogenization method that is based on a homogeneous reference material. The proposed homogenization scheme, assuming constant stress polarisations in each phase, has in a natural way the potential to model the transition between Taylor- and Sachs-type textures. Therefore, the stiffness ef the hemogeneous reference material has to be varied between infinitely stiff and infinitely compliant. In the present study, texture evolution during rolling is simulated, showing that the application of different comparison materials in the homogenization scheme leads to the development of different main texture characteristics (Cube, Cu, Bs, Goss) in the orientation distribution function. For efficiently carrying out the rolling simulations using the proposed method, the measured texture information of the bulk aluminum sample is representatively reduced by using a partitioning technique of the orientation space.

In this contribution, the prediction of the self-consistent homogenization method with regard to the effective material response of cubic crystal aggregates is analyzed and compared to results from full field simulations. The influence of the crystalline orientation distribution but also the effect of the grain shape on the macroscopic elastic response of sheet metals is especially emphasized.

Polycrystalline microcomponents made of Stabilor®G, a dental alloy mainly consisting of gold, are examined in terms of their elastic properties. Finite element calculations of uniaxial tensile tests are carried out with ABAQUS so as to identify the characteristic parameters of the distribution of Young's modulus. It is shown that the statistics of mechanical properties observed experimentally can be estimated by using the finite element method. The findings are generalized to microcomponents consisting of crystals with a cubic symmetry.

An overview on modeling of high-cycle fatigue is given and experimental findings of the damage accumulation are discussed. Finally we sketch an isotropic constitutive model for the description of the damage accumulation due to high-cycle fatigue.

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Two recently proposed Helmholtz free energy potentials including the full dislocation density tensor as an argument within the framework of strain gradient plasticity are used to predict the cyclic elastoplastic response of periodic laminate microstructures. First, a rank-one defect energy is considered, allowing for a size-effect on the overall yield strength of micro-heterogeneous materials. As a second candidate, a logarithmic defect energy is investigated, which is motivated by the work of Groma et al. (2003) . The properties of the back-stress arising from both energies are investigated in the case of a laminate microstructure for which analytical as well as numerical solutions are derived. In this context, a new regularization technique for the numerical treatment of the rank-one potential is presented based on an incremental potential involving Lagrange multipliers. The results illustrate the effect of the two energies on the macroscopic size-dependent stress–strain response in monotonic and cyclic shear loading, as well as the arising pile-up distributions. Under cyclic loading, stress–strain hysteresis loops with inflections are predicted by both models. The logarithmic potential is shown to provide a continuum formulation of Asaro's type III kinematic hardening model. Experimental evidence in the literature of such loops with inflections in two-phased FFC alloys is provided, showing that the proposed strain gradient models reflect the occurrence of reversible plasticity phenomena under reverse loading. [ABSTRACT FROM AUTHOR]

We investigate deep material networks (DMNs), recently introduced by Liu et al. Comput. Method Appl. M. , vol. 345, pp. 1138–1168, 2019], from the viewpoint of classical micromechanics at small strains. We aim to establish the basic micromechanical principles of deep material networks, shed light on the characteristics of the building blocks and introduce a simple, robust and fast solution technique for inelastic deep material networks. In their original formulation, DMNs are solely trained by linear elastic data, but applied to nonlinear and inelastic problems with astonishing accuracy. We clarify this phenomenon theoretically by showing that, to first order in the strain rate, the effective inelastic behavior of composite materials is determined by linear elastic localization. Our argumentation applies to arbitrary microstructures comprising nonlinear generalized standard materials at small strains. The main technical tool is a Volterra series approximation of the stress of a generalized standard material, which we adapt from nonlinear dynamical systems theory. Next, we establish that deep material networks inherit thermodynamic consistency and stress-strain monotonicity from their phases. These properties root in the definition of the DMN as a tree of hierarchical laminates and contrast with other applications of neural networks to the approximation of material laws, where consistency and monotonicity typically cannot be guaranteed far away from the training set. Last but not least, we introduce rotation-free DMNs with arbitrary directions of lamination and exploit a novel formulation, uniting the implementation of DMNs of arbitrary tree topology and multi-phase laminates, and apply our insights to microstructures of industrial complexity. [ABSTRACT FROM AUTHOR]

In this paper, deterministic stability analyses for soil slopes reinforced with pile of different locations and lengths were conducted firstly to calculate the factor of safety through limit equilibrium method (LEM). Since the effect of inherent uncertainties as well as the spatial variability of soils cannot be reflected via the deterministic factor of safety, probabilistic stability analyses of slopes reinforced with pile in spatially constant soils and spatially variable soils were successively carried out, respectively. The failure probability was determined by random limit equilibrium method (RLEM) considering the influence of different pile locations, pile length and soil statistical parameters. The optimal locations along slope and length of pile were analyzed based on the reliability analyses results in spatially constant soils and spatially variable soils, which were inconsistent with the results via the traditional deterministic methods, with a lower probability of sliding failure. Finally, method was proposed to determine the minimum samples of simulation iterations for investigating the convergence of failure probability of soil slope reinforced with piles. The results revealed that the multiple potential sliding surfaces introduced by the installations of pile would result in the increased uncertainty of slope failures. [ABSTRACT FROM AUTHOR]