5.5 Materialmodellierung
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- CALPHAD (4)
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- Environmental stress cracking (ESC) (2)
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- 5 Werkstofftechnik (44)
- 5.5 Materialmodellierung (44)
- 5.2 Metallische Hochtemperaturwerkstoffe (29)
- 7 Bauwerkssicherheit (5)
- 5.1 Mikrostruktur Design und Degradation (4)
- 9 Komponentensicherheit (3)
- 5.3 Polymere Verbundwerkstoffe (2)
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- 7.7 Modellierung und Simulation (2)
- 8 Zerstörungsfreie Prüfung (2)
Paper des Monats
- ja (3)
A widespread recovery of waste heat requires a cost‐effective production of thermoelectric generators. Thermoelectric oxides are predestined for use at high temperatures. For manufacturing reasons, a multilayer generator design will be easily scalable and cost‐effective. To evaluate the potential of ceramic multilayer technology for that purpose, a multilayer of the promising thermoelectric oxides calcium cobaltite (Ca3Co4O9), calcium manganate (CMO, CaMnO3), and glass–ceramic insulation layers is fabricated. Cracks and reaction layers at the interfaces are observed in the microstructure. The compositions of these reaction layers are identified by energy‐dispersive X‐ray spectroscopy and X‐ray diffraction. Mechanical and thermal properties of all layers are compiled from literature or determined by purposeful sample preparation and testing. Based on this data set, the internal stresses in the multilayer after co‐firing are calculated numerically. It is shown that tensile stresses in the range of 50 MPa occur in the CMO layers. The reaction layers have only a minor influence on the level of these residual stresses. Herein, it is proven that the material system is basically suitable for multilayer generator production, but that the co‐firing process and the layer structure must be adapted to improve densification and reduce the tensile stresses in the CMO.
Relation of craze to crack length during slow crack growth phenomena in high‐density polyethylene
(2024)
The craze‐crack mechanism occurring in high‐density polyethylene (HDPE) causing slow crack growth and environmental stress cracking is investigated in detail with respect to the relation of crack length and the related craze zone. This is essential for the understanding of the resulting features of the formed fracture surface and their interpretation in the context of the transition from crack propagation to ductile shear deformation. It turns out that an already formed craze zone does not inevitably result in formation of a propagating crack, but could also undergo ductile failure. For the examination, the full notch creep test (FNCT) was employed with a subsequent advanced fracture surface analysis that was performed using various imaging techniques: light microscopy, laser scanning microscopy, scanning electron microscopy, and X‐ray micro computed tomography scan. FNCT specimens were progressively damaged for increasing durations under standard test conditions applying Arkopal, the standard surfactant solution, and biodiesel as test media were used to analyze the stepwise growth of cracks and crazes. From considerations based on well‐established fracture mechanics approaches, a theoretical correlation between the length of the actual crack and the length of the preceding craze zone was established that could be evidenced and affirmed by FNCT fracture surface analysis. Moreover, the yield strength of a HDPE material exposed to a certain medium as detected by a classic tensile test was found to be the crucial value of true stress to induce the transition from crack propagation due to the craze‐crack mechanism to shear deformation during FNCT measurements.
Highlights
- Progress of crack formation in high‐density polyethylene is analyzed by different imaging techniques
- Determined growth rates depend on distinction between craze zone and crack
- The ratio of the present crack to the anteceding craze zone is validated theoretically
- The transition from crack propagation to ductile shear deformation is identified
- An already formed craze zone may still fail by ductile mechanisms
A phenomenological criterion for an optical assessment of PE-HD fracture surfaces obtained from FNCT
(2021)
The full-notch creep test (FNCT) is a common test method to evaluate the environmental stress cracking (ESC) behavior of high-density polyethylene (PE-HD), e.g. for container materials. The test procedure as specified in ISO 16770 provides a comparative measure of the resistance against ESC using the time to failure of PE-HD specimens under constant mechanical load in a well-defined liquid test environment. Since the craze-crack damage mechanism underlying the ESC phenomenon is associated with brittle failure, the occurrence of a predominantly brittle fracture surface is a prerequisite to consider an FNCT measurement as representative for ESC, i.e. a time to failure dominated by craze-crack propagation.
The craze-crack propagation continuously reduces the effective residual cross-sectional area of the specimen during the test, which results in a corresponding increase of the effective mechanical stress. Thus, a transition to ductile shear deformation is inevitable at later stages of the test, leading usually to a pronounced central ligament.
Therefore, an optical evaluation of FNCT fracture surfaces concerning their brittleness is essential. An enhanced imaging analysis of FNCT fracture surfaces enables a detailed assessment of craze-crack Propagation during ESC. In this study, laser scanning microscopy (LSM) was employed to evaluate whether FNCT fracture surfaces are representative with respect to craze-crack propagation and ESC. Based on LSM height data, a phenomenological criterion is proposed to assess the validity of distinct FNCT measurements. This criterion is
supposed to facilitate a quick evaluation of FNCT results in practical routine testing. Its applicability is verified on a sample basis for seven different commercial PE-HD container materials.
The formation of pores in CMSX-4 nickel based superalloys is detrimental to the service life of the material. A way to avoid the problem is to treat the superalloys under Hot Isostatic Pressing (HIP), which enables a large volume fraction of pores to be annihilated. This paper aims to understand the contribution of plastic activity related to the gliding of dislocations on the pore annihilation. Simulations based on a phase-field model of dislocation are performed and make it possible to consider the strong anisotropy of the CMSX-4 under HIP conditions in conjunction to the strong elastic heterogeneity introduced by the pore. For pores with a radius of few micrometers, it is shown that edge parts of dislocation lines that present an extra half atomic plane oriented towards the pore are stacked above and under it in the direction which is perpendicular to their slip-planes, causing an increase of the number of dislocation along the four octahedral directions of the FCC single crystal which intersect the pore center. Results are streamlined within the isotropic elastic theory of dislocations. Effects of elastic anisotropy and dislocation reactions are also investigated in order to specify what would be the dislocation configuration around a pore in CMSX-4 under HIP conditions. Notably, the elastic anisotropy is shown to significantly modify the arrangement of dislocations close to the pore equator. Simulations also allow for the characterization of pore/dislocation interactions when dislocations are involved in Low Angle Boundaries as experimentally observed.
The aluminum alloy 2618A is applied for engine components such as radial compressor wheels which operate for long time at elevated temperatures. This results in coarsening of the hardening precipitates and degradation in mechanical properties during the long-term operation, which is not taken into account in the current lifetime prediction models due to the lack of quantitative microstructural and mechanical data. To address this issue, a quantitative investigation on the evolution of precipitates during long-term aging at 190 °C for up to 25,000 h was conducted. Detailed transmission electron microscopy (TEM) was combined with Brinell hardness measurements and thorough differential scanning calorimetry (DSC) experiments. The results showthat GPB zones and S-phase Al2CuMg grow up to < 1,000 h during which the GPB zones dissolve and S-phase precipitates form. For longer aging times, only S-phase precipitates coarsen, which can be well described using the Lifshitz–Slyozov Wagner theory of ripening. A thorough understanding of the underlying microstructural processes is a prerequisite to enable the integration of aging behavior into the established lifetime models for components manufactured from alloy 2618A.
Hydrogen is an attractive energy carrier that requires high effort for safe storage. For ensuring safety, storage cylinders must undergo a challenging approval process. Relevant standards and regulations for composite cylinders used for the transport of hydrogen and for its onboard storage are currently based on deterministic (e.g. ISO 11119-3) or to some respect semi-probabilistic criteria (UN GTR No. 13; with respect to burst strength).
This paper provides a systematic analysis of the load cycle properties resulting from these regulations and standards. Their characteristics are compared with the probabilistic approach of the Federal Institute for Materials Research and Testing BAM. The most important aspect of comparing different concepts is the rate for accepting designs with potentially unsafe or critical safety properties. This acceptance rate is analysed by operating Monte-Carlo simulations over the available range of production properties.
The effectiveness of the mechanism of precipitation strengthening in metallic alloys depends on the shapes of the precipitates. Two different material systems are considered: tetragonal γ′′ precipitates in Ni-based alloys and tetragonal θ′ precipitates in Al-Cu-alloys. The shape formation and evolution of the tetragonally misfitting precipitates was investigated by means of experiments and phase-field simulations. We employed the method of invariant moments for the consistent shape quantification of precipitates obtained from the simulation as well as those obtained from the experiment. Two well-defined shape-quantities are proposed: (i) a generalized measure for the particles aspect ratio and (ii) the normalized λ2, as a measure for shape deviations from an ideal ellipse of the given aspect ratio. Considering the size dependence of the aspect ratio of γ′′ precipitates, we find good agreement between the simulation results and the experiment. Further, the precipitates’ in-plane shape is defined as the central 2D cut through the 3D particle in a plane normal to the tetragonal c-axes of the precipitate. The experimentally observed in-plane shapes of γ′′-precipitates can be quantitatively reproduced by the phase-field model.
Grain boundary energy effect on grain boundary segregation in an equiatomic high-entropy alloy
(2020)
Grain boundary (GB) Segregation has a substantial effect on the microstructure evolution and properties of polycrystalline alloys. The mechanism of nanoscale segregation at the various GBs in multicomponent alloys is of great challenge to reveal and remains elusive so far. To address this issue, we studied the GB segregation in a representative equiatomic FeMnNiCoCr high-entropy alloy (HEA) aged at 450 °C. By combining transmission Kikuchi diffraction, atom probe tomography analysis and a density-based thermodynamics modeling, we uncover the nanoscale segregation behavior at a series of well-characterized GBs of different characters. No segregation occurs at coherent twin boundaries; only slight nanoscale segregation of Ni takes place at the low-angle GBs and vicinal \Sigma 29b coincidence site lattice GBs. Ni and Mn show cosegregation of high levels at the general high-angle GBs with a strong depletion in Fe, Cr, and Co. Our density-based thermodynamic model reveals that the highly negative energy of mixing Ni and Mn is the main driving force for nanoscale cosegregation to the GBs. This is further assisted by the opposite segregation of Ni and Cr atoms with a positive enthalpy of mixing. It is also found that GBs of higher interfacial energy, possessing lower atomic densities (higher disorder and free volume), show higher segregation levels. By clarifying the origins of GB segregations in the FeMnNiCoCr HEA, the current work provides fundamental ideas on nanoscale segregation at crystal defects in multicomponent alloys.
A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
[1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015
[2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017