Neue Ansätze zur Analyse der Lastübertragung und Initiierung finiter Risse in Klebverbindungen

In dieser Arbeit werden neue Analysemethoden für Klebverbindungen vorgeschlagen. Nach einer Darstellung der theoretischen Grundlagen, insbesondere der Hintergründe der finiten Bruchmechanik, wird eine Übersicht über den Stand der Forschung gegeben und die Defizite derzeitiger Analysezugänge diskutiert. Für die Analyse der Lastübertragung in einschnittigen Klebverbindungen wird ein semi-analytisches Berechnungsverfahren entwickelt. Die Ergebnisse dieser effizienten Analyse zeigen eine sehr gute Konvergenz und Übereinstimmung mit Referenzrechnungen. Für die Analyse der Rissinitiierung in einschnittigen Klebverbindungen werden zwei Umsetzungen der finiten Bruchmechanik vorgestellt: eine detaillierte numerische Umsetzung und eine hocheffiziente Umsetzung auf Basis klassischer geschlossen-analytischer Lösungen. Die Versagenslastvorhersagen zeigen gute Übereinstimmung mit experimentellen Ergebnissen

Neue Ansätze zur Analyse der Lastübertragung und Initiierung finiter Risse in Klebverbindungen

In dieser Arbeit werden neue Analysemethoden für Klebverbindungen vorgeschlagen. Nach einer Darstellung der theoretischen Grundlagen, insbesondere der Hintergründe der finiten Bruchmechanik, wird eine Übersicht über den Stand der Forschung gegeben und die Defizite derzeitiger Analysezugänge diskutiert. Für die Analyse der Lastübertragung in einschnittigen Klebverbindungen wird ein semi-analytisches Berechnungsverfahren entwickelt. Die Ergebnisse dieser effizienten Analyse zeigen eine sehr gute Konvergenz und Übereinstimmung mit Referenzrechnungen. Für die Analyse der Rissinitiierung in einschnittigen Klebverbindungen werden zwei Umsetzungen der finiten Bruchmechanik vorgestellt: eine detaillierte numerische Umsetzung und eine hocheffiziente Umsetzung auf Basis klassischer geschlossen-analytischer Lösungen. Die Versagenslastvorhersagen zeigen gute Übereinstimmung mit experimentellen Ergebnissen

Modeling snow slab avalanches caused by weak-layer failure – Part 1: Slabs on compliant and collapsible weak layers

Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak-layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this two-part work we propose a novel closed-form analytical model for a snowpack under skier loading and a mixed-mode failure criterion for the nucleation of weak-layer failure. In the first part of this two-part series we introduce a closed-form analytical model of a snowpack accounting for the deformable layer. Despite the importance of persistent weak layers for slab avalanche release, no simple analytical model considering weak-layer deformations is available. The proposed model provides deformations of the snow slab, weak-layer stresses and energy release rates of cracks within the weak layer. It generally applies to skier-loaded slopes as well as stability tests such as the propagation saw test. A validation with a numerical reference model shows very good agreement of the stress and energy release rate results in several parametric studies including analyses of the bridging effect and slope angle dependence. The proposed model is used to analyze 93 propagation saw tests. Computed weak-layer fracture toughness values are physically meaningful and in excellent agreement with finite element analyses

Modeling snow slab avalanches caused by weak-layer failure – Part 2: Coupled mixed-mode criterion forskier-triggered anticracks

Using the analytical model presented in Part 1 ofthis two-part paper, a new conceptual understanding of an-ticrack nucleation in weak layers is proposed. To obtain asufficient condition for onset of failure, two necessary con-ditions must be satisfied simultaneously: (i) the weak layermust be overloaded in terms of stress and (ii) the initiatingcrack must release enough energy for the formation of newsurfaces. This so-called coupled criterion was proposed byLeguillon (2002). No assumptions on initial defects withinthe weak layer are needed. Instead, the failure criterion pro-vides both critical loading and the size of initiating cracks.It only requires the fundamental material properties strengthand fracture toughness as inputs. Crack initiation and sub-sequent propagation are covered by a single criterion con-taining both a strength-of-materials and a fracture mechanicscondition.Analyses of skier-loaded snowpacks show the impact ofslab thickness and slope angle on critical loading and crackinitiation length. In the limit cases of very thick slabs andvery steep slopes, we obtain natural avalanche release. A dis-cussion of different mixed-mode stress and energy criteriareveals that a wrong choice of mixed-mode hypotheses canyield unphysical results. The effect of material parameterssuch as density and compliance on weak-layer collapse is il-lustrated.The framework presented in this two-part series harnessesthe efficiency of closed-form solutions to provide fast andphysically sound predictions of critical snowpack loads us-ing a new conceptual understanding of mixed-mode weak-layer failure. It emphasized the importance of both stress andenergy in avalanche release

Modeling snow slab avalanches caused by weak-layer failure – Part 1: Slabs on compliant and collapsible weak layers

Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this two-part work we propose a novel closed-form analytical model for a snowpack under skier loading and a mixed-mode failure criterion for nucleation of weak layer failure. In the first part of this two-part series we introduce a closed-form analytical model of a snowpack accounting for the deformable layer. Despite the importance of persistent weak layers for slab avalanche release, no simple analytical model accounting for weak layer deformations is available. The proposed model provides deformations of the snow slab, weak layer stresses and energy release rates of cracks within the weak layer. It generally applies to skier-loaded slopes as well as stability tests such as the propagation saw test. A validation with a numerical reference model shows very good agreement of the stress and energy release rates results in several parametric studies including analyses of the bridging effect and slope angle dependence. The proposed model is used to analyze 93 propagation saw tests. Computed weak layer fracture toughness values are physically meaningful and in excellent agreement with finite element analyses. In the second part of the series we make use of the present mechanical model to establish a novel failure criterion crack nucleation in weak layers. The code used for the analyses in both parts is publicly available

Modeling snow slab avalanches caused by weak-layer failure – Part 2: Coupled mixed-mode criterion for skier-triggered anticracks

Using the analytical model presented in part I of this two-part paper, a new conceptual understanding of anticrack nucleation in weak layers is proposed. To obtain a sufficient condition for onset of failure two necessary conditions must be satisfied simultaneously: i) The weak layer must be overloaded in terms of stress and ii) the initiating crack must release enough energy for the formation of new surfaces. This so-called coupled criterion was proposed by Leguillon (2002) Eur J Mech-A Solid, 21(1), 61{\&}ndash;72, 2002. No assumptions on initial defects within the weak layer are needed. Instead, the failure criterion provides both critical loading and the size of initiating cracks. It only requires the fundamental material properties strength and fracture toughness as inputs. Crack initiation and subsequent propagation are covered by a single criterion containing both a strength-of-materials and a fracture mechanics condition. Analyses of skier-loaded snowpacks show the impact of slab thickness and slope angle on critical loading and crack initiation length. In the limit cases of very thick slabs and and very steep slopes we obtain natural avalanche release. A discussion of different mixed-mode stress and energy criteria reveals that a wrong choice of mixed-mode hypotheses can yield unphysical results. The effect of material parameters such as density and compliance on weak layer collapse is illustrated. The framework presented in this two-part series harnesses the efficiency of closed-form solutions to provide fast and physically sound predictions of critical snowpack loads using a new conceptual understanding of mixed-mode weak layer failure. It emphasized the importance of both stress and energy in avalanche release