@ Pergamon B R S M V 1 1 E S C 4 A M I P m U r r 1 $ + PIIS1359-6462(97)00386-2 I C O B L Dov Sherman DepartmentofMaterialsEngineering Technion-Israel Instituteof Technology Haifa32000,Israel (ReceivedFebruary21, 1997) (AcceptedAugust26, 1997) Introduction Griftlh [1] establishedthe criterionfor unstablecrackadvanceunderconditionof constantstress,and the role of the surfaceenergy in controllingthe initiationof such a crack. Irwin [2] generalizedGrif- fith’stheory by introducingthe critical strain ener~ release rate (SERR), r, which controls crack initiationthroughtherelation g- r (1) where Gis the strain energy release rate. Neither consideredthe dynamicbehavior associatedwith crack advance in brittle materials,e.g. the velocityof the crack tip, the responseof the mechanical loadingsystem, increasingenergy,etc. The inabilityof the systemto reduce the strain energy of the advancingcrack in brittlesolidsis explainedby the following:while r does not change significantly, the strain energy term, @rapidly increases,and the energybalanceis violated.In an attemptto cm- siderdynamiceffects,Mott[3]addeda kineticenergytermto the energybalance: g -&. (2) The unbalancedenergy is translatedintokineticenergy, UK, which is responsiblefor the accelera- tion of the crack tip to a certainterminalvelocity[4]. Brittlesolidsexhibitfour stageswhen unstable ffactureoccurs:mirror, mist, hackle, and finally,branchingoccurs,as a more efficientway to absorb the increasingkinetic energyof the system[5,6].The branchingmechanismin glass as a fi.mctionof the initial flaw length was demonstratedby Field [7] and the same behavior was observed in thin monolithic,polycrystallinealuminalayers[8,9]. The aboveobservationsrelateto unconstrainedbrittleplates.Thispaper addressesthe questionsof whetherbranchingoccursin constrainedceramiclayersand if it does,what is itsextent. 1939