ABSTRACTThe process of producing residualstresses in thick_walled cylinder beforeit is putin to usage is called Autofretage, which it means; a suitable largeenough pressureto cause yielding within the wall, is applied toinner surface ofa sylinder and then removed. So thatacompressive residual stresses are generated to acertain radial depth at a sylinder wall.The objectiveofpresent study, is to investigate the influenceof autofretage treatment ontheradial, circumferential andtotal stresses using von._mises yieldcriteria.
Num.simulationcarried outon ABAQUS software to investigate thestresses distribution andcalculate the autofretage radius. The results revealthat, the autofretage treatmentofthick_wall sylinder lead to decrease thehoob and max.
von._mises stresses and relocate them from the inner surface ofthe sylinder to somewhere along it’sthickness. The reduction in max.stresses is strongly depending on autofretagepressure, it wasvarying from ( 3.6% at Pautofretage = 105 M.
Pa. to 19.2% at Pautofretage =130 M.Pa. ) Also, ithas been found, there is no influenceof autofretage stages number on each of max.von._misesstressand autofretage radius.
Key words: autofretage, radial, hoob andaxial stresses, von._mises yield criteria, autofretage radius, optimum autofretagepressure. 1. INTRODUCTIONThe wide applications ofpressurized sylinder in chemical,nuclear, armaments, fluid transmitting plants,power plants and military equipment, in addition to the increasing scarcity andhigh cost of materials lead the designers toconcentrate their attentions to the elastic – plastic approach which offersmore efficient use of materials 1, 2.
The treatment of producing residualstresses in the wall of thick_walled sylinder before it is put in to usage is called autofretage, which it means; asuitable large enoughpressure to cause yielding within thewall, is applied to the inner surface ofthe sylinder and then removed.So that a compressive residual stresses are generated to a certain radial depthat the sylinder wall. Then, duringthesubsequent application of an operating pressure, the residual stresses willreduce the tensile stresses generated asa result of applying operating pressure1,3.The influenceofresidual stresses onload-carry capacity of thick_walled sylinders have beeninvestigate by Ayob and Albasheer 4, using each analytical andNum.techniques.
The results of the study reveal three scenarios in the design of thick_walled sylinders.Ayob and Elbasheer 5, used von._mises and Tresca yieldcriteria to develop aprocedure in whichthe autofretage pressure determined analytically resulting ina reduced stress concentration. Then they coM.
Pa.red the analytical resultswith F.E.A. results.
They concluded that, the autofretage treatment increasethe max.allowable internal pressure but it cannot increase the max.internalpressure to case whole thickness of the sylinder to yield. Noraziah et al. 6 presented ananalytical autofretage procedure topredict the required autofretage pressure ofdifferent levels of allowable pressure andthey validate their results with F.E.A.
results. They found three cases of autofretage in design of pressurized thick_walled sylinders.Zhu and Yang 7, usingeach yield criteria von.
_mises and Tresca, presented an analytical equation foroptimum radius of elastic-plastic junction in autofretage sylinder , alsotheystudied the influence of autofretage on distribution of stress and load bearingcapacity. They concluded, to achieve optimum radius ofelastic – plasticjunction, an autofretage pressure a bit larger than operating pressure shouldbe applied before a pressure vessel is put in to use. Hu and Puttagunta 8investigate the residual stresses in thick_ walled sylinder induced by internal autofretage pressure, alsothey found the optimum autofretage pressure andthe max.reduction percentage ofthe von._mises stress under elastic-limit working pressure. Md.
Amin et al. 9determined the optimum elasto_plasticradius and optimum autofretage pressure usingvon._mises yield criteria , then they have been coM.
Pa.red with Zhu and Yang’smodel 8. Also they observed that the percentage of max.
von._mises stressreduction increases as value of radius ratio (K) and working pressureincreases. F. Trieb et al.
10 discussed practical application of autofretageon components for waterjet cutting. They reported that the life time of highpressure components is improved by increasing autofretage depth due toreduction of tangential stress at inner diameter, on other hand too highpressure on outside diameter should be avoided to prevent cracks generate. Inaddition to determine the optimum autofretage pressure and the optimum radiusof elastic-plastic junction , Abu Rayhan Md. et al.11 evaluated the influenceofautofretage treatment in strain hardened thick_ walled pressure vessels usingequivalent von._mises stress as yield criteria. They found, the number of autofretagestages has no influenceon max.von.
_mises stress and pressure capacity. Also,they concluded that, optimum autofretage pressure depends on the workingpressure and on the ratio of outer to inner radius.II. Limits of pressureand Distributionof stress in non – autofretaged sylinder 2.1.
Limits of pressureof non – autofretagesylinder According to Von._Mises yield criteria,Each of the internal pressure requires to yield the inner surface of the sylinder ( i.e. partial autofretage ), PYi, and that to yield the whole wall of the sylinder ( i.
e. completely autofretage ), PYo, can be calculated from equations ( 1& 2 )4, 7PYi= ……………………. ( 1 )PYo= …………………….( 2 ) 2.2. Distribution of stress of non – autofretage sylinder The radial stress ?r, circumferential stress ?? and axial stress ?z, distributions in non _autofretage sylinder subjected to an operating pressure, Pi, are given by Lame’s formulations which is available in 3, 4, 5, 6, 7 . As shown in Fig. ( 1 ), it is obvious that the tensile hoob, ??, compressive radial , ?r, and max.
Von._Mises stresses have their max. values at the inner surface of the sylinder . The hoop stress has always positive value which represents as tensile stress while the stress in the radial direction is always compressive. Also the hoop tensile stress’s value is greater than radial compressive stress’s value.
Fig. 1: Distribution of stress on non-autofretage thick-walled sylinder subjected to operating pressure. Fig. 2: Geometry of inspectedmodel.