Presentation on theme: "Buckling Delamination with Application to Films and Laminates"— Presentation transcript:
1 Buckling Delamination with Application to Films and Laminates Thermal gradient withinterruption of heat transferacross crack.No crack driving forcedue to film stress; UnlessMixed modeinterface crackCompression in filmproducing bucklingBucklingdelaminationShow Volinsky movie
2 Mechanics of thin films and multilayers Application areas electronics, coatings of all kinds.Example: Buckle DelaminationsGood Delaminations onPatterned substrates
3 Thermal Barrier Coatings (TBCs) Application to jet and power generating turbinesCeramic(Zirconia)Ceramic(Alumina)Metalbond coatBlades taken from an engineshowing areas of spalled-offTBC
4 Buckle Delaminations: Interface cracking driven by buckling Three Morphologies: Straight-sided, Varicose and Telephone CordComputer simulationsExperimental observations200nm DLC film on siliconStraight-sidedPropagation of a buckle delamination along a pre-patterned tapered region of low adhesion betweenfilm and substrate. In the wider regions the telephonecord morphology is observed. It transitions to thestraight-sided morphology in the more narrow regionand finally arrests when the energy release rate dropsbelow the level needed to separate the interface.
5 A Model Problem—Mode I Buckling Delamination of Symmetric Bi-layer buckled stateunbuckled stateThis neglects the very slightincrease of P as the bucklingamplitude increasesBuckling stress of clamped beam length 2b.w is the width perpendicular to the plane.Overall buckling of the entire laminate (withthickness 2h) will not occur if b>L/4.unbuckledbuckledFixed btwo crack tips
6 Mode I Buckling Delamination of Symmetric Bi-layer: continued The energy release rate G can be re-written in the following non-dimensional form:unbuckled
7 Abbreviated Analysis of the Straight-Sided Buckle Delamination A 1D analysis based on vonKarman plate theory (Derived in Class)Propagation directionFilm pre-stresshAverage stress in buckled film:In-plane compatibility conditionBuckle deflection:Buckle amplitude:At edge of buckle:Energy release rate alongpropagating frontEnergy release rate and mode mix along sides from basic solution:Energy-release rate can also be obtained fromdirect energy change calculationMode mix depends on the amplitude ofThe bucklePlots are given on next overhead
8 if you can. It makes life easier! BASIC ELASTICITY SOLUTION FOR INFINITE ELASTIC BILAYER WITH SEMI-INFINITE CRACK(Covered in earlier lecture)Equilibrated loads. General solution for energyrelease rate and stress intensity factors availablein Suo and Hutchinson (1990)Infinitely thick substrate--Primary case of interest for thin filmsand coatings on thick substratesmoment/lengthDundurs’ mismatch parameters for plane strain:force/lengthdelamination crackinterfaceFor homogeneous case:If both materials incompressible:is the more important of the two parameters for most bilayer crack problemsTakeif you can. It makes life easier!
9 Basic solution continued: Energy release ratedelamination crackinterfaceStress intensity factors:(see Hutchinson & Suo (1992) if secondDundurs’ parameter cannot be taken to be zero)whereis shown as a plot and is tabulated in Suo & Hutch.Note: For any interface crack between two isotropic materials,no mismatch
10 Interface toughness—the role of mode mix Experimental finding: The energy release rate required to propagatea crack along an interface generally depends on the mode mix, often withlarger toughness the larger the mode II component.A phenomenological interface toughness lawLiechti & Chai (1992) data for an epoxy/glassinterface.
11 Half-width of straight-sided delamination Energy release rate and mode mix on sides of Straight-sided buckle delaminationStress atonset ofbucklingHalf-width atonset ofbucklingEnergy/areaavailable forrelease inplanes strainHalf-width of straight-sided delaminationImpose:Stable configurations(half-widths, b) of1D delaminationsSee earlier slide for interface toughness functionMode IICaution! This plot is difficult to interpret becauseeach axis depends on
12 Inverse determination of interface toughness, stress (or modulus) by measuring buckling deflection and delamination widthStraight-sided delamination without ridge crack on flat substratefront (SS)The basic results can be written as:sideApplies to any multilayer film with arbitrarystress distributionIf bending and stretching stiffness of the film are known, then the energy release rates and theresultant pre-stress can be determined by measurement of the deflection and the delamination width.If resultant pre-stress is known, then the equations can be used to determine film modulus andrelease rates in terms of deflection and delamination width– see Faulhaber, et al (2006) for an example.