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In this paper, the J-integral is derived for temperature-dependent elastic–plastic materials described by incremental plasticity. It is implemented using the equivalent domain integral method for assessment of three-dimensional cracks based on results of finite-element calculations. The J-integral considers contributions from inhomogeneous temperature fields and temperature-dependent elastic and plastic material properties as well as from gradients in the plastic strains and the hardening variables. Different energy densities are considered, the Helmholtz free energy and the stress-working density, providing a physical meaning of the J-integral as a fracture criteria for crack growth. Results obtained for a plate with two different crack configurations each loaded by a cool-down thermal shock show domain-independence of the incremental J-integral for different energy densities even for high temperature gradients and significant temperature-dependence of the yield stress and the hardening exponent in the presence of large scale yielding. Hence, the derived J-integral is an appropriate parameter for the assessment of cracks in thermomechanically loaded components.
Ein tiefgreifendes Verständnis des zyklischen Plastizitätsverhaltens metallischer Werkstoffe ist sowohl für die Optimierung der Materialeigenschaften als auch für die industrielle Auslegung und Fertigung von Bauteilen von hoher Relevanz. Insbesondere moderne Legierungen wie Duplex-Stähle zeigen unter Lastumkehr aufgrund des komplexen mehrphasigen Gefüges sowie der Neigung zu verschiedenen Ausscheidungsreaktionen einen ausgeprägten Bauschinger-Effekt, welcher bei technischen Umformvorgängen berücksichtigt werden muss. Der Bauschinger-Effekt begründet sich maßgeblich in der Entstehung von Rückspannungen, welche aus dem unterschiedlichen Plastizitätsverhalten der austenitischen und ferritischen Phase resultieren. Instrumentierte Mikroindenter-Versuche in ausgewählten Ferrit- und Austenitkörnern haben gezeigt, dass austenitische Gefügebestandteile durch einen deutlich früheren Fließbeginn sowie eine stärkere Rückplastifizierung während der Entlastung charakterisiert sind. Zudem wurde nachgewiesen, dass Ausscheidungen im Rahmen einer 475°C-Versprödung diesen Phasenunterschied verstärken und somit in einem höheren Bauschinger-Effekt resultieren.
Turbocharger housings in internal combustion engines are subjected to severe mechanical and thermal cyclic loads throughout their life-time or during engine testing. The combination of thermal transients and mechanical load cycling results in a complex evolution of damage, leading to thermo-mechanical fatigue (TMF) of the material. For the computational TMF life assessment of high temperature components, the DTMF model can provide reliable TMF life predictions. The model is based on a short fatigue crack growth law and uses local finite-element (FE) results to predict the number of cycles to failure for a technical crack. In engine applications, it is nowadays often acceptable to have short cracks as long as they do not propagate and cause loss of function of the component. Thus, it is necessary to predict not only potential crack locations and the corresponding number of cycles for a technical crack, but also to determine subsequent crack growth or even a possible crack arrest. In this work, a method is proposed that allows the simulation of TMF crack growth in high temperature components using FE simulations and non-linear fracture mechanics (NLFM).
A NLFM based crack growth simulation method is described. This method starts with the FE analysis of a component. In this paper, the method is demonstrated for an automotive turbocharger housing subjected to TMF loading. A transient elastic-viscoplastic FE analysis is used to simulate four heating and cooling cycles of an engine test. The stresses, inelastic strains, and temperature histories from the FEA are then used to perform TMF life predictions using the standard DTMF model. The crack position and the crack plane of critical hotspots are then identified. Simulated cracks are inserted at the hotspots. For the model demonstrated, cracks were inserted at two hotspot locations. The ΔJ integral is computed as a fracture mechanics parameter at each point along the crack-front, and the crack extension of each point is then evaluated, allowing the crack to grow iteratively. The paper concludes with a comparison of the crack growth curves for both hotspots with experimental results.
Für langfaserverstärkte Thermoplaste (LFT) wird ein repräsentatives Volumenelement (RVE) für FEM-Simulationen generiert. Dies geschieht unter Berücksichtigung von mikrostrukturellen Kenngrößen wie Faserorientierungsverteilung, -volumengehalt und -längenverteilung, die für einen charakteristischen Werkstoffzustand experimentell ermittelt wurden. Mittels Mikrostruktursimulationen wird das Kriechverhalten von LFT untersucht. Das viskoelastische Verhalten der Matrix wird experimentell an Substanzproben aus Polypropylen ermittelt und in die RVE-Simulationen mit einem modifizierten Burgers-Modell implementiert. Schließlich werden die Rechnungen mit verschiedenen, fiktiven sowie experimentell ermittelten Faserlängenverteilungen mit Kriechversuchen am LFT verglichen. Es zeigt sich eine starke Abhängigkeit des Kriechverhaltens von der Faserlänge und eine hohe Prognosegüte der Simulationen, die die experimentell ermittelte Längenverteilung berücksichtigen.
Cast aluminum cylinder blocks are frequently used in gasoline and diesel internal combustion engines because of their light-weight advantage. However, the disadvantage of aluminum alloys is their relatively low strength and fatigue resistance which make aluminum blocks prone to fatigue cracking. Engine blocks must withstand a combination of low-cycle fatigue (LCF) thermal loads and high-cycle fatigue (HCF) combustion and dynamic loads. Reliable computational methods are needed that allow for accurate fatigue assessment of cylinder blocks under this combined loading. In several publications, the mechanism-based thermomechanical fatigue (TMF) damage model DTMF describing the growth of short fatigue cracks has been extended to include the effect of both LCF thermal loads and superimposed HCF loadings. This approach is applied to the finite life fatigue assessment of an aluminum cylinder block. The required material properties related to LCF are determined from uniaxial LCF tests. The additional material properties required for the assessment of superimposed HCF are obtained from the literature for similar materials. The predictions of the model agree well with engine dyno test results. Finally, some improvements to the current process are discussed.
In this paper, the initial multiaxial yield behavior of three different gray cast iron materials with lamellar shaped graphite inclusions is numerically investigated by means of the finite-element method. Therefore, volume elements including the real microstructure of the materials are loaded bi- and triaxially beyond macroscopic yield. The shape of the obtained yield surfaces are compared to the surfaces of four continuum models which, amongst others, are proposed in literature to describe the inelastic behavior of gray cast iron with lamellar shaped graphite inclusions. It is found that the presented continuum models and the macroscopic yield surfaces obtained with microstructure-based finite-element models deviate. Furthermore, the initial inelastic flow direction is computed at the onset of macroscopic yielding. The analysis show that the inelastic flow is normal to the yield surface.
A new yield function for lamellar gray cast iron materials is proposed. The new model is able to describe the results of recently performed microstructure-based finite-element computations that resolve the three dimensional yield surface of three different gray cast irons. The yield function requires only the yield stress in tension and compression of the respective material as model parameters. Furthermore, the algorithmic formulation of the new model is assessed for numerical robustness and efficiency.