Lifetime simulation of thermo-mechanically loaded components

The estimation of the lifetime of thermo-mechanically loaded components by testing is very costly and time-consuming, since the high temperature cycle time in practical application dominates the test duration. Common frequencies for TMF (thermo-mechanical fatigue) tests are at about 0.01 Hz compared to 10–100 Hz at HCF (high cycle fatigue) and about 0.1–1 Hz at isothermal LCF (low cycle fatigue) tests. Therefore, the simulation of fatigue life is an important design step in the fast moving and competitive automotive industry, where the steady rise of engine power and the demand for lightweight construction concurrent with enhanced reliability require an optimised dimensioning process. Methods and models are usually derived from results made on tests with specimens, since it is possible to systematically and exactly define loading parameters and measurement categories. After an extensive test programme (tensile tests, creep tests, low cycle fatigue tests and thermo-mechanical fatigue tests with different influences on specimens) it was possible to develop material models for the simulation of the time- and temperature dependent stress–strain hystereses and damage models for the simulation of the TMF lifetime. Based on this knowledge the whole simulation chain to determine the TMF life of a component is introduced: thermal calculation, mechanical calculation and lifetime calculation. Furthermore the transferability of specimen based simulation models to real components (an alternative test piece and a cylinder head) is investigated.     

Hypersingularities in three-dimensional crack configurations in composite laminates

Three-dimensional crack configurations in composite laminates are studied by means of the Scaled Boundary Finite Element Method (SBFEM) particularly regarding stress singularities and their associated deformation modes. The SBFEM is an efficient semi-analytical method that permits solving linear elastic mechanical problems. Only the boundary needs to be discretized while the problem is considered analytically in the direction of the dimensionless radial coordinate pointing from the scaling center to the boundary . An important advantage is that it requires no additional effort for the characterization of existing stress singularities. The situation of two meeting inter-fiber cracks is investigated in detail, considering different materials and fiber / crack orientations. It is shown that in three-dimensional crack configurations in composite laminates so-called hypersingularities can occur, i.e. stress singularities which are even stronger than the classical crack singularity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Induktive Definitionen und Dilatoren

Summary In this paper we give a new and comparatively simple proof of the following theorem by Girard [1]:If x y (x,y) (where the relation is arithmetic and positive in Kleene's ), then there exists a recursive DilatorD such that x ^<y ^{(x, y).The essential feature of our proof is its very direct definition of the dilatorD. Within a certain infinitary cutfree system of inductive logic (which in fact is a modification of Girard's system in [1]) we construct in a uniform way for each ordinal a derivation T of the formula x <y (x, y), and then defineD immediately from the family (T)_On. Especially we set D():=Kleene-Brouwer length of (T).}     

Local Algorithms for the Prime Factorization of Strong Product Graphs

The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant “approximate” prime factorization, is the development of local approaches that cover the graph by factorizable patches and then use this information to derive global factors. We present here a local, quasi-linear algorithm for the prime factorization of “locally unrefined” graphs with respect to the strong product. To this end we introduce the backbone \mathbbB (G)\mathbb{B} (G) for a given graph G and show that the neighborhoods of the backbone vertices provide enough information to determine the global prime factors.     

On the Strong Product of a k-Extendable and an l-Extendable Graph

 Let G ₁⊗G ₂ be the strong product of a k-extendable graph G ₁ and an l-extendable graph G ₂, and X an arbitrary set of vertices of G ₁⊗G ₂ with cardinality 2[(k+1)(l+1)/2]. We show that G ₁⊗G ₂−X contains a perfect matching. It implies that G ₁⊗G ₂ is [(k+1)(l+1)/2]-extendable, whereas the Cartesian product of G ₁ and G ₂ is only (k+l+1)-extendable. As in the case of the Cartesian product, the proof is based on a lemma on the product of a k-extendable graph G and K ₂. We prove that G⊗K ₂ is (k+1)-extendable, and, a bit surprisingly, it even remains (k+1)-extendable if we add edges to it. Received: February 17, 1997 Final version received: June 14, 2000     

Über ein Problem von Fenyő

Ohne Zusammenfassung

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How Many Bits have to be Changed to Decrease the Linear Complexity?

The k-error linear complexity of periodic binary sequences is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits of the sequence per period. For the period length p ⁿ, where p is an odd prime and 2 is a primitive root modulo p ², we show a relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. Moreover, we describe an algorithm to determine the k-error linear complexity of a given p ⁿ-periodic binary sequence.     

Thermal Analysis of Free‐Corner Effects in Cross‐Ply Plates by a Higher‐Order Theory Approach

Stresses in the vicinity of free edges and corners of composite laminates exhibit a distinct localized three‐dimensional behaviour [1] and thus represent an important technical situation. Since numerical analyses of stress concentration phenomena in layered structures are computationally expensive, the present contribution is devoted to a simple closed‐form higher‐order theory approach for the calculation of displacements, strains and stresses in the vicinity of a rectangular corner of symmetric cross‐ply laminates under uniform thermal load ΔT. An appropriate representation for the displacement field in the form of a single‐layer theory with unknown inplane components and appropriately assumed functions through the plate thickness yields closed‐form expressions for the strains and stresses throughout the whole laminate. Equilibrium and boundary conditions are fulfilled in an integral sense. The present approach is easily applied, is of a completely closed‐form analytic nature and requires only little computational effort. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inplane Stress Singularities at the Corner of an Anisotropic Material Discontinuity

In the mechanics of composite laminates the local mechanical inplane fields at corners of anisotropic material discontinuities are of particular interest since they can have singular behavior. In the present study, the stress and strain fields in the local near field of such corners are investigated by an asymptotic analysis. The order of the singularity of these mechanical inplane fields are determined in closed‐form manner by use of the complex potential method based on Lekhnitskii's approach. Various different geometrical setups and material combinations of corners with material discontinuities are investigated with regard to their effect on the singular behavior of the mechanical fields present. These examples show that the order of singularity considered is clearly weaker than the typical crack tip singularity in fracture mechanics. Nevertheless, it may render the corner a critical location for the onset of failure. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exponential nonnegativity

Let be a Banach algebra, , the spectrum of and the spectral abscissa of . If , then we show that there exists an algebra cone such that is exponentially nonnegative with respect to and the spectral radius is increasing on .