Effects of Hydro Static Pressure on Mechanical

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

Effects of hydrostatic pressure on mechanicalbehaviour and deformation processing of materialsJJ Lewandowski and P Lowhaphandu

The processing and subsequent mechanicalbehaviour of a variety of commercially importantmaterials are affected by the imposed stress stateIn this review the experimentally documentedeffects of superimposed pressure on deformationunder quasistatic conditions are summarisedfollowed by a presentation of the effects ofsuperimposed pressure on the fracture behaviourof a variety of materials including both ductile andbrittle systems It is shown that the pressureresponses of a variety of materials show distinctdifferences and the potential reasons for thesedifferences are presented Finally in the light of allof these observations the effects of changes instress state on deformation processing arereviewed In particular the evolution of hydrostaticstresses during various forming operations iscovered followed by a review of published workand the potential benefits of superimposingpressure during processing of a variety ofmaterials IMR328

copy 1998 The Institute of Materials and ASM InternationalThe authors are Professor and Research Assistant respect-ively in the Department of Materials Science andEngineering The Case School of Engineering CaseWestern Reserve University Cleveland OH 41106 USA

List of symbolsa minimum specimen radius

Gm shear modulus of matrixk linear compressibility

ka linear compressibility in a directionkc linear compressibility in c directionkr linear compressibility in any directionky macroscopic shear yield stressK material constant

KIc fracture toughness11K stress intensity rangeKm bulk modulus of matrixKp bulk modulus of particle

n work hardening exponentP applied or superimposed hydrostatic

pressurePex extrusion pressure

r reductionrn distance from centre of specimen along

plane of neckrp particle radiusR radius of curvature at neck or notch

Rex extrusion ratiosij elastic complianceVf volume fraction of microvoidsa extrusion die angler direction cosineE[ fracture strain

Gn critical strain for microvoid nucleation

fl coefficient of friction(J true tensile stress

(J B yield strength of billet material(Jc critical interfacial cohesive strength of

interface(J[ brittle fracture stress in tension

(J flow flow stress(Jm mean normal stress

(Jmeff effective mean normal stress(In critical mean stress required to initiate

plastic flow or internal necking inintervoid matrix

(JT hydrostatic tension(J y uniaxial yield strength in tensionif effective stress

(J 1 (J 2 (J3 principal stressestmax maximum shear stress

IntroductionOver past decades extensive studies have been con-ducted by a variety of researchers on the effects ofsuperimposed hydrostatic pressure on the deforma-tion and fracture behaviour of materials tested underquasistatic conditions including related topics suchas hydrostatic extrusion1-312 The pioneering workconducted by Bridgman2-44 documented the effectsof superimposed hydrostatic pressure (at levels up to3 GPa) on a variety of properties including the flowand fracture behaviour (eg ductility) of a variety ofmonolithic metals Subsequent experimental work bya variety of researchers focused on the source(s) ofthe improved ductility45-201 Concurrent with theseexperimental investigations was the developmentof a number of theoretical models focusing onaddressingpredicting the effects of changes instress state on the deformation and fracture ofmetals808296116117136151313314metallic compos-ites315-320metallic glasses321-324 and geologic mater-ials267 Bridgmans work2-44 and other more recentwork also investigated the effects of superimposedpressure on the mechanical behaviour of non-metallic materials including intermetallics154-170 cer-amics171-181 composites182-201 and polymeric202-235based systems There is also an extensive body ofliterature236-28o on the effects of superimposed press-ure on geologic materials

In many of the materials systems studied significantpressure induced changes to the flow stress andductility have been observed Such observations mayhave important implications on their service perform-ance as the stress state encountered in the service ofmany structural materials is often not uniaxial Thisis clearly true in various applications where pressureis present whether it is in a pressure vessel atsignificant depths in the ocean or the earth in thevicinity of a shock wave propagating through asolid325 or due to the triaxial stresses developed

International Materials Reviews 1998 Vol 43 No4 145

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

146 Lewandowski and Lowhaphandu Effects of hydrostatic pressure on materials

from differences in the thermal expansion coefficientbetween the matrix and the reinforcement in a com-posite In addition to providing experimental inputto various modelling efforts focusing on the funda-mentals of flow and fracture such information is alsorelevant to the formability of a material In this casethe broadest definition of formability relates to theability of the material to sustainaccommodate plasticflow often to very high levels of strain This caninclude such operations as rolling forging extrusionsheet metal forming etc While the formability deformability depends on a combination of factorsincluding the chemical composition microstructuretemperature and deformation velocity critical para-meters include the stress state and the superpositionof any residual stresses Since the stress state experi-mentally obtained where testing is conducted withsuperimposed hydrostatic pressure is closely relatedto that achieved (or desired) in many of the form-ing operations described above the data obtained(eg flow stress ductility etc) from such testing arevery relevant to the formability In addition many ofthe models for deformation processing require asinput the flow stress at very high values of strain Astesting with superimposed pressure typically increasesthe strain to fracture of many industrially importantmaterials to levels well beyond that obtained inuniaxial tension such large strain data can also beused as input for the various modelling efforts aimedat the forming operations described above

This review summarises the published experimentalobservations of the effects of superimposed hydro-static pressure on the mechanical behaviour obtainedunder quasistatic conditions for a variety of inorganicmaterials including recently obtained data on inter-metallics and metallic composites Although there isa body of similar literature on organic materials andceramic based systems this is beyond the scope ofthe present review However some relevant referenceshave been provided for the behaviour of organicmaterials202-235 which exhibit highly pressure sensitivebehaviour as well as for ceramic and geologic mater-ialsl71-181236-280tested with superimposed pressureThis review is divided into separate summaries andbegins with the testing techniques typically utilised instudies where quasi static loading conditions aredesired The effects of superimposed pressure on theflow fracture and deformation processing of a varietyof inorganic materials including intermetallics andcomposites follows The data summaries were pre-pared from published work on the various systemslisted while references to the original published worksare provided in the text as well as in each of theindividual data summaries The primary factors con-trolling flow and fracture will precede the presentationof the data summaries while the data summariesconclude with a short discussion of the major obser-vations Details of the various observations and issuesmay be found in the references cited

Experimental test techniques utilisedin high pressure testingHigh pressure mechanical testing13336 of struc-tural materials under quasistatic conditions has

International Materials Reviews 1998 Vol 43 NO4

Top plunger

Pressure gauge

Load cell

Specimen

Window

Support

Extension rod

High pressurecontainer

Bottom plunger

25mm

Schematic diagram of oil based high pressuredeformation apparatus3672 122 126269326-329

been conducted using a variety of high pressuremedia including solid171-174179249251273277326327liquids36122126269326-329and gases271273330The lasttwo groups are typically preferred as non-hydrostaticconditions may exist with solid media Typical liquidmedia include a variety of oils as well as kerosenepentane and naphtha while gas media include inertgases (eg Ar He) and hydrogen Pressure levels inexcess of 3 GPa have been obtained with such sys-tems High pressure tests well in excess of 3 GPa havebeen conducted using diamond anvil cells326327331and other test systems where the volume of materialtested in such studies is typically too small to sampleenough of the material to be of use to the structuralmaterials community where size effects on materialproperties have been observed Significantly higherpressure (eg gt 10 GPa) may be present in variousshock loading experiments conducted under impactor high velocity experiments as reviewed elsewhere325and not covered in this review The liquid mediasystems utilised in quasistatic testing are typicallylimited to use below 300degC because of the potentialdecompositioncracking of the oil while the solid-and gas-based systems have been utilised at gt 1000degCThis review focuses primarily on data obtained oneither oil- or gas-based systems and those opera-ted at relatively modest (eg lt 300degC) temperaturesthough references to tests conducted at high pressureand high temperature are provided (Refs 171-181236-244 246 247 251-253 255 258 260-262 264

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

Lewandowski and Lowhaphandu Effects of hydrostatic pressure on materials 147

pressure vessel mantle

7y 6_10_m_m f-pressure vessel liner

servohydraulicactuator bull

argon gas line

a internal load cellb specimen

2 Schematic diagram of gas based high pressure deformation apparatus271273330334

265 268 269 271-273 276-278) References to theeffects of superimposed pressure on creep265281-286have also been provided though this aspect is notcovered in this review

Pressure generation in the oil based systems ofteninvolves compression of the fluid in a pressure vesselvia pressing a plunger in to the bore of a pressurevessel as shown in Fig 1 Pressure is typically moni-tored via the use of a manganin coil pressure gaugethat is exposed to the high pressure environmentManganin coils are used in this case because of thehighly reproducible and linear manner with whichthe resistance of the coil varies with changes inpressure22332 Simple pressurisation experiments canbe conducted with such systems whereby a materialis placed into the pressure vessel and the fluid (ieoil) is compressed to produce a measurable level ofhydrostatic pressure In such simple pressurisationstudies the pressure is subsequently reducedremovedin order to measure the resulting behaviour of thematerial at atmospheric pressure Typically both thepressurisation rate and depressurisation rate aremonitored and kept at a constant low value becauseof the possibility of significant specimen heating (orcooling) during the pressurisation (depressurisation)cycles

Mechanical testing with superimposed hydrostaticpressure has also been conducted on similar devicesto that shown in Fig 1 In these cases the specimenis typically inserted into the load train assemblypresent in the pressure vessel shown in Fig 1 followedby pressurisation of the fluid and the subsequenttension (or compression) testing of the specimen atthe desired level of superimposed hydrostatic pressureIn such tests the high pressure fluid has access to allsurfaces of the specimen It is important to monitorcontinuously (and keep constant) the pressure dur-ing the test in addition to having the capabilityto monitor accurately the load and displacementrequired to deform the specimen under pressure aspointed out elsewhere33o In oil based pressure systemssuch as that shown in Fig 1 the confining (iehydrostatic) pressure is kept constant via either using

an intensifier or retracting the bottom hydraulicpiston while inserting the top plunger In such testingthe use of external load cells (ie positioned on theload train but outside of the pressure vessel) mayproduce erroneous data for the load required todeform the specimen because of the variable amountof seal friction which results during the generation ofpressure in the chamber In an attempt to determinethe load on the specimen inside the vessel moreaccurately pressure compensated load cells consistingof a measuring load cell and a compensating loadcell were developed330333 as shown schematicallyin Fig 1 Displacement andor strain measurementin such studies has typically relied on monitor-ing piston displacement though more recentstudies103 155-157161-163189190192-195197have utilisedpressure compensated strain gauges affixed to thespecimen surfaces In some studies195197213the press-ure vessel was fitted with machined cross-bores andtransparent quartz windows as shown in Fig 1 whichenabled in situ monitoring of deformation and thedevelopment of necks under pressure

Gas based systems like that shown schematicallyin Fig 2 typically utilise a pressure intensifier togenerate pressure that is contained within a multi-walled pressure vessel where the volume of gas pre-sent at high pressure in the vessel is kept as low aspossible because of the danger associated with thestored energy Such systems often utilise many of thesame types of diagnostic techniques as that describedabove though direct visual monitoring of the speci-men during deformation has not been conductedbecause of the inherently higher danger associatedwith gas based systems Pressure fluctuations duringmechanical testing in gas based systems are typicallymuch less than those of the oil based systems wherethe pressure generation techniquedevice is directlylinked to the piston which controls displacement ofthe specimen

Tables 1 and 2 summarise many of the variousinvestigators that have utilised high pressure testingto evaluate the mechanical behaviour of materialsTable 1 summarises the maximum pressure utilised

International Materials Reviews 1998 Vol 43 NO4