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Interfacial Fatigue Modelling of Ultrasonic Metal Welded ... - ZARM

Interfacial Fatigue Modelling of Ultrasonic Metal Welded ... - ZARM

Interfacial Fatigue Modelling of Ultrasonic Metal Welded ... -

Proceedings in Applied Mathematics and Mechanics, 27 May 2008Interfacial Fatigue Modelling ofUltrasonic Metal Welded Tensile SpecimensJ. Utzinger 1,∗ 2, ∗∗and P. Steinmann1 Chair of Applied Mechanics, Faculty of Mechanical and Process Engineering, University of Kaiserslautern, P.O. Box 3049,67653 Kaiserslautern, Germany2 Chair of Applied Mechanics, Institute of Mechanical Engineering, University of Erlangen-Nuremberg, Egerlandstr. 5,91058 Erlangen, GermanyFor the sake of weight reduction, new joining technologies are investigated in the field of lightweight design. In this context,tensile fatigue tests of welded metal/fibre-reinforced polymer joints are simulated with finite elements. For the discretisation ofthe very thin welding zone, so-called interface elements are expedient. In this contribution, a fatigue-motivated cohesive-typeconstitutive law is applied to the interface.Copyright line will be provided by the publisher1 MotivationSince fibre-reinforced thermoplastic materials offer a great potential for lightweight design and construction, they are increasingin use. They feature high specific stiffness, strength, and impact resistance as well as an excellent resistance against manychemical agents. However, the limits of today’s composites can be pushed even further by combining their advantages withthe properties of traditional construction materials by means of reliable, strong and easy-to-use methods of joining metal partswith composite structures. Thus, the development of new joining techniques is an active field of research. Certainly, the simulationof such modern engineering structures is economically imperative. In what follows, a fatigue test of an ultrasonic metalwelded specimen is simulated by finite elements. Here, the failure zone is a priori identified with the welding zone, locatedbetween an aluminium and a CF-PA66 substrate. It is discretised by so-called interface elements (Schellekens [8], Utzingeret al. [9,10]). In what follows, a fatigue-motivated geometrically linear traction-separation-law is concisely introduced, to beincorporated in a finite element context. Thereafter, some preliminary results are discussed.2 Modelling and ComputationA free energy Ψ shall depend on the interfacial displacement jump [u] and the Lemaitre-type damage parameter d, reading asΨ([u], d) = 1 2 [1 −d] [u] ·C if,el · [u], τ = [1 −d] C if,el · [u], C if,el = c s s ⊗s+c t t ⊗t+c n n ⊗n (1)Furthermore, equation (1) includes the nominal traction vector τ . In the interface, the displacement jump and the nominaltraction vector are energetically conjugated quantities. Moreover, in equation (1), the interface tangent for linear elasticityC if,el is introduced. The interfacial stiffness parameters are given as c s , c t and c n , and the constitutive behaviour shall bedecoupled with respect to an interfacial orthonormal system {s, t, n}. The fatigue behaviour of the welding zone is expressedby a stiffness reduction due to the Lemaitre-type damage parameter d. The evolution of this parameter shall primarily dependon an effective displacement jump δ. Together with the damage loading function f, δ is given in equation (2), see also Pandolfiand Ortiz [5].√δ = βs 2 [u s ] 2 + βt 2 [u t ] 2 + βn 2 [u n ] 2 , f(δ, κ) = δ − κ (2)If δ exceeds the threshold κ, damage evolution shall be active. Therefore, a damage evolution function and a material law forthe damage rate are introduced as{h(d, δ) = C exp(γ d)δ β , d ˙ h(d, δ) ˙δ if f ≥ 0 and f˙≥ 0 and d < 1=(3)0 elseMaterial parameters are given as C, β, γ. This formulation has first been introduced by Paas et al. [4] and Peerlings et al. [6].It is able to reflect the experimentally observed Basquins law (see Basquin [1]) and has been adopted to the interface contextby e.g. Robinson et al. [7], Muñoz et al. [3], Erinc et al. [2] and Utzinger et al. [10]. At first, the damage rate is integrated over∗ Corresponding author E-mail: utzinger@rhrk.uni-kl.de, Phone: +49 (0) 631 205 3855, Fax: +49 (0) 631 205 2128∗∗ E-mail: paul.steinmann@ltm.uni-erlangen.de, Phone: +49 (0) 9131 85 28501, Fax: +49 (0) 9131 85 28503Copyright line will be provided by the publisher

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