Dynamic nonlinear crack growth at interfaces in multi-layered materials

Size: px

Start display at page:

Download "Dynamic nonlinear crack growth at interfaces in multi-layered materials"

Edwin Barker
5 years ago
Views:

$- B14 Dynamic fracture - Dynamic nonlinear crack rowth at interfaces in$ Structural, Geotechnical and Buildin Enineerin mauro.corrado@polito.

1 - B14 Dynamic fracture - Dynamic nonlinear crack rowth at interfaces in multi-layered materials Mauro Corrado POLITECNICO DI TORINO Department of Structural, Geotechnical and Buildin Enineerin mauro.corrado@polito.it Marco Pai INSTITUTE FOR ADVANCED STUDIES LUCCA MUSAM Multi-scale Analysis of Materials marco.pai@imtlucca.it

2 Outline Finite thickness interfaces in material microstructures and in composite laminates Modellin fracture in finite thickness interfaces Dynamic crack propaation in systems with finite thickness interfaces

Finite thickness interfaces Finite thickness interfaces in material microstructures Polycrystalline Copper Two-phase hard metal WC-Co/PCD

19, 453-459. Finite thickness interfaces in composites to control structural dampin A. Arikolu, I. Ozkol (2010) Comp Struct, 92, 3031-3039.

3 Finite thickness interfaces Finite thickness interfaces in material microstructures Polycrystalline Copper Two-phase hard metal WC-Co/PCD material D.J. Benson et al. (2001) Mater Sci En A, Vol , Z.K. Fan et al. (2001) Int J Refr Metals & Hard Mat, Vol. 19, Finite thickness interfaces in composites to control structural dampin A. Arikolu, I. Ozkol (2010) Comp Struct, 92, Truss-like interfaces with specific inertial properties to filter elastic waves D. Bioni, A.B. Movchan (2002) Int J Solids Struct, 39,

4 Delamination Glass-silicon cell delamination in photovoltaic modules F. Novo et al. (2012) 2012 PV Module Reliability Workshop. ERC Startin Grant IDEAS 2012: Multi-field and Multi-scale Computational Approach to Desin and Durability of PhotoVoltaic Modules Principal investiator: Prof. Marco Pai

5 Modellin interfaces Interfaces are usually modelled by means of the Cohesive Zone Model - A detailed finite element discretization of the interface microstructure is very often too expensive from the computational point of view. - The available CZMs apply to zero-thickness interfaces As simple as possible for numerical reasons rather than bein physical meaninful Inverse methods Molecular dynamics simulations (Yamakov et al. (2006), JMPS, Vol. 54, ) Multiscale approaches (C.B. Hirschberer et al. (2009), EFM, Vol. 76, ; M.G. Kulkarni et al. (2009), MOM, Vol. 41, ) - Definition of a CZM that accounts for the finite thickness properties of the interfaces

6 Nonlocal CZM based on damae mechanics l 2 +d 2 N M. Pai, P. Wriers (2011) Computational Mater Sci, Vol. 50,

7 Nonlocal CZM based on damae mechanics No need of meshin the interface reion with continuum elements (computational ain) The shape of the CZM depends on the damae evolution law (physically motivated) Damae vs. crack openin Shape of the nonlocal CZM

8 The DCB test Composite laminates with adhesive N s S. Li, M.D. Thouless, A.M. Waas, J.A. Schroeder, P.D. Zavattieri (2005) Comp Sci Tech, Vol. 65,

9 Interface fracture: Mode I CZM Mode I: irreversible cohesive law s Elastic branch: Softenin curve: σ = σ max e l 0 T rms σ = σ max e N T rms N l 0 s peak K Compression response overned by a penalty stiffness. p n l 0 N K = E i t i t (mm) l 0 (mm) K p n (N/m 3 ) x x x x 10 11

S S G S S d, d N T T int s d d d p The nonlinear dependency between the vector p and the ap vector has to be linearized for the application of the Newton-Raphson method: Interface contribution to the

10 S S G S S d, d N T T int s d d d p The nonlinear dependency between the vector p and the ap vector has to be linearized for the application of the Newton-Raphson method: Interface contribution to the weak form: S G S d, N T N T int C d d Tanent interface constitutive matrix C: N T N T s s C M. Ortiz, A. Pandolfi (1999) Int J Num Meth En, Vol. 44, M. Pai, P. Wriers (2011) Comp Mat Sci, Vol. 50, FE implementation Body 1 Body 2

Mass of the interface defined as a function of the interface thickness and density: Implicit solution

11 Dynamics Discretized equation of dynamic equilibrium: Ma R int ext ( x) R ( t) Mass matrix, M, lumped, both for elastic continuum and interfaces. Mass of the interface defined as a function of the interface thickness and density: Implicit solution scheme in space and time: - Interation over time: Newmark constant-averae-acceleration scheme (=0.5, =0.25) - Solution of the equilibrium equations: Newton-Raphson method

Case study Specimen eometry FE model t = 0.5, 1.0, 2.

4-node isoparametric FEs Finite element size: 75 x 100 m

5 s Displacement-controlled loadin Laminae E = 70 GPa =

12 Case study Specimen eometry FE model t = 0.5, 1.0, 2.0, 3.0 mm Mechanical properties 2D plane strain model 4-node isoparametric FEs Finite element size: 75 x 100 m Time step: t = 0.5 s Displacement-controlled loadin Laminae E = 70 GPa = 0.3 = 2700 k/m 3 Interface E i = 0.42 GPa s peak = 8.5 MPa Nc = 3 x 10 4 m G F = 600 N/m = 2700 k/m 3

13 t = 0.5 mm The loadin rate

14 The adhesive thickness Quasi-static v=10 m/s v=10 m/s

15 The adhesive mass density t = 2 mm; v = 20 m/s

16 The crack velocity In both cases the interface mass is varied by a factor of 4 times The combined effect of varyin both interface stiffness and mass has a larer effect on the crack velocity as compared to the case when only the mass is modified

17 Conclusions Dynamics of finite thickness interfaces: (1) Nonlinear fracture dynamics of laminates with finite thickness adhesives is investiated (2) Both mass and stiffness of the adhesive layer are considered in the dynamic equilibrium equations (3) Inertia of the interface has a non-neliible effect on the dynamic strenth increase factor (4) Inertia of the adhesive has a remarkable effect on crack rowth kinetics

18 Acknowledements FIRB Future in Research 2010 Structural Mechanics Models for Renewable Enery Applications RBFR107AKG Principal investiator: Prof. Marco Pai

Emergent properties in interface mechanical problems:

IMT Institute for Advanced Studies March 5, 2013, Lucca, Italy Emergent properties in interface mechanical problems: A paradigm of organized complexity Dr. Ing. Marco Paggi Politecnico di Torino Centre