Effect of lateral impact loads on failure of pressurized pip(8)

200CSNgandWQShen

criterionforthecurrentmodel,wherethenon-linearhardeningwasspeci edinsteadoftheyieldstress.Linearelasticisotropicmaterialpropertieswereassignedtothefoundationsinthepresentmodelling.Datawereobtaineddirectlyfromtheplateloadingtestandthetriaxialcompressiontestforthesandandkaolinfoundations,respectively.

Thefoundation,indenter,andpipewerecon-structedusingthethree-dimensionalSolidConti-nuumExplicitDynamicsElements(HX8E)[20].Asuitabletimestepautomaticallycalculatedbytheprogramwasusedtoeliminatetheunconvergenterror,asthistimeintegrationschemewascon-ditionallystable.

Thefullyclampedpipeswithandwithoutafoun-dationsupportweresubjectedtoanimpactloadingatthemid-span,whereitwasfreetomovealongthelongitudinalaxis.Inordertostartadynamicanalysis,theknowledgeoftheinitialconditionsoftheproblemwascompulsory,i.e.theinitialvelocityoftheindenterinthepresentstudy.Theinitialvel-ocityshouldonlybeappliedtothe rstloadcase.Asthecompressednitrogengaswasusedtopres-surizethepipespecimensintheimpacttests,thepressureinsidethepipeswasalmostunchangedaftertheimpact,forthepipelinesremainingintact.Inordertomodeltheimpactloadactingonthepressurizedpipe,aninternalconstantpressurewasassignedperpendiculartothelocalfaceoftheelementsattheinnersurfaceofthepipebyusingtheelementfaceload[20].Thefaceloadsforexplicitdynamicselementsbeingconstantshouldbe

highlighted,i.e.theaverageoftheinputnodalpress-ures.Astheinitialvelocityshouldonlybeappliedtothe rstloadcase,boththeinitialvelocityandtheinternalpressureactedsimultaneouslyinthepipes,i.e.attime¼0s.

Slidelinewasusedtomodelthenon-linearcontactandseparationbetweenthestructures[20].Forsim-pli cation,three-dimensionalgeneralslidingwith-outfrictionslidelinewasusedinordertoignorethefrictionbetweenthestructuresforalltheFEAmodelsinthepresentnumericalstudy.

Geometricalnon-linearitywasappliedforalltheFEAthroughtheEulerianformulation[20].Themainadvantageofthisformulationwasthatthestressandstrainmeasuresnaturallydescribedthematerialresponse.

3.2FEAresults

Someofthesigni cantFEAresultsarerecordedinTables4to6forthepipessupportedbysandandkaolinfoundationsandwithoutafoundationsup-port,respectively.Theseresultscorrespondtothetotalresponsetimetfwhenthevelocityoftheinden-terreachedorwasnearto0m/s.

ThevaluesofWfandWginTables4to6arethetotalmaximumpermanenttransversedisplacementandtheglobaldeformationofthepipesattheimpactlocation,respectively.ThelocaldeformationofthepipeWlatthesameimpactlocationisthedifferencebetweentheWfandWg[4,8].

Table4FEAresultsforthepipessupportedbyasandfoundation

SpecimencodeA1A2A3A4A5A6A7ALP1ALP2ALP3ALP4ALP5AMP1AMP2AMP3AMP4AMP5AHP1AHP2AHP3AHP4AHP5

tf(ms)15.7215.2213.8814.5614.1314.1214.3212.5512.3812.3712.3712.3711.9011.7111.8111.8111.9111.6411.8211.9411.7511.76

Wf(mm)70.2758.2642.5948.3544.4445.2246.0239.9036.2138.0837.0037.4836.0934.1734.9334.6634.4734.7536.5335.1834.6833.77

Wg(mm)45.7834.7721.5926.2523.0323.6424.3022.1219.1220.5919.7820.1320.0318.4719.0818.8518.6919.6621.1620.0119.6518.86

Wl(mm)24.4923.4821.0022.1021.4221.5821.7217.7817.0917.4917.2317.3516.0615.7015.8415.8115.7715.1015.3715.1715.0214.91

Cf(mm)19.3215.9710.0612.2910.9811.5311.2616.1913.6014.9514.1814.7215.3713.9914.5114.7414.3715.7817.2116.3815.8315.36

1max(%)9.637.324.345.524.744.835.084.944.514.704.614.785.054.594.824.674.755.415.955.555.355.03

lA(mm)12.939.135.296.605.735.905.996.255.295.725.415.595.765.195.415.365.325.756.315.915.775.51

lB(mm)11.167.624.225.354.614.764.824.834.034.404.174.304.403.944.124.104.044.434.914.624.454.25

lp(mm)23.1723.0620.6221.5521.7121.7321.3411.9411.1011.4111.4111.5110.7810.5110.6910.6010.6310.3310.3510.3410.4410.19

Proc.IMechEVol.220PartE:J.ProcessMechanicalEngineering

JPME97#IMechE2006