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Asymptotic homogenisation technique and two-scale convergence is used for analysis of macro-strength and fatigue durability of composites with a periodic structure under cyclic loading. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic loading. Both local and non-local strength and durability conditions are analysed. The strong convergence of the strength and fatigue damage measure as the structure period tends to zero is proved and their limiting values are estimated.

This paper is devoted to the mathematica l description of the solution of the so-called rainflow reconstruction problem, i.e. the problem of constructing a time series with an a priori given rainflow m atrix. The algorithm we present is mathematically exact in the sense that no app roximations or heuristics are involved. Furthermore it generates a uniform distr ibution of all possible reconstructions and thus an optimal randomization of the reconstructed series. The algorithm is a genuine on-line scheme. It is easy adj ustable to all variants of rainflow such as sysmmetric and asymmetric versions a nd different residue techniques.

Test rig optimization
(2014)

Designing good test rigs for fatigue life tests is a common task in the auto-
motive industry. The problem to find an optimal test rig configuration and
actuator load signals can be formulated as a mathematical program. We in-
troduce a new optimization model that includes multi-criteria, discrete and
continuous aspects. At the same time we manage to avoid the necessity to
deal with the rainflow-counting (RFC) method. RFC is an algorithm, which
extracts load cycles from an irregular time signal. As a mathematical func-
tion it is non-convex and non-differentiable and, hence, makes optimization
of the test rig intractable.
The block structure of the load signals is assumed from the beginning.
It highly reduces complexity of the problem without decreasing the feasible
set. Also, we optimize with respect to the actuators’ positions, which makes
it possible to take torques into account and thus extend the feasible set. As
a result, the new model gives significantly better results, compared with the
other approaches in the test rig optimization.
Under certain conditions, the non-convex test rig problem is a union of
convex problems on cones. Numerical methods for optimization usually need
constraints and a starting point. We describe an algorithm that detects each
cone and its interior point in a polynomial time.
The test rig problem belongs to the class of bilevel programs. For every
instance of the state vector, the sum of functions has to be maximized. We
propose a new branch and bound technique that uses local maxima of every
summand.

Liquid Composite Molding (LCM) processes, like Resin Transfer Molding (RTM) and Vacuum Assisted Resin Infusion (VARI), are gaining increasing interest for the cost-efficient production of fiber reinforced polymer matrix composites, e. g. Airbus A380 rear bulkhead. Meanwhile, purpose-built thermoset resin systems with adequately low processing viscosities are available. Although showing a better fatigue resistance composites from epoxy resins (EP) tend to be expensive while vinylester resin (VE) composites are more brittle and, hence, less fatigue resistant but attract due to their lower material costs. Following research on the toughness improvement of vinylester based resin systems, one subject of this thesis was the broad experimental characterization of the static and cyclic behavior of carbon fiber reinforced composites from resin systems which were toughened by either the generation of interpenetrating networks with aliphatic (Al-EP) and cyclo-aliphatic epoxy resins (Cal-EP) or by addition of a liquid, epoxy-terminated butadiene-nitrile rubber (ETBN). While quasi-static in-plane tension, compression and shear testing of [0°]8 and [±45°]3S laminates resulted in an unclear picture with regard to the mechanical performance of the investigated resin systems, R = -1 cyclic step loading provided a definite indication of the considerably higher cyclic fatigue strength of the modified carbon fiber reinforced vinylester-urethane (CF/VEUH:ETBN) composite which, consequently, was selected for detailed mechanical testing. To provide experimental input for subsequent fatigue life simulations applying the Critical Element Concept of Reifsnider et al. [76] the study included the determination of ultimate in-plane tension, compression and shear properties as well as the characterization of the cyclic fatigue behavior under constant amplitude loading. Different descriptions of S-N curves of the [0°]8-, [0°/90°]2S- and [+45°/0°/-45°/90°]S-laminates for R = +0.1, -1 and +10 were determined to derive constant fatigue life diagrams applying methods of Goodman or Harris et al. Furthermore the residual strength degradation model for the critical element (0° ply) and the residual stiffness degradation models for the sub-critical elements have been derived by experimental determination on [0°]8-, [0°/90°]2S- and [+45°/0°/-45°/90°]S-(CF/VEUH:ETBN)-laminates. Deficiencies in current fatigue life time prediction modeling for carbon fiber reinforced materials nowadays results in large factors of safety to be adopted. As a consequence composite structures are often overdesigned and expensive proto-type testing is required for life time prediction. Therefore, in this thesis standardized random-ordered miniTWIST (minimized transport wing standard) spectrum loading was used to understand improvements in fatigue life modeling so that fatigue life prediction results in a more efficient use of these materials. In particular the influence of constant amplitude cyclic fatigue modeling as well as constant fatigue life modeling itself on the results of the fatigue life analysis of random loading sequences have been investigated. Finally the bearing of residual strength or residual stiffness degradation modeling and the effect of filtering and counting methods on the fatigue life time prediction was determined in a sensitivity analysis. The fatigue life models were validated by experimental results using the random miniTWIST-loading on [0°]8-, [0°/90°]2S- and [+45°/0°/-45°/90°]S-(CF/VEUH:ETBN)-laminates.