CRITERION FOR THE ACTION OF APPLIED STRESS IN THE
`MARTENSITIC TRANSFORMATION*
`
`J. R. PATEL and M. COHENt
`
`The martensitic reaction is treated as a strain transformation with shear and dilatational displace(cid:173)
`ment~, respectively parallel and normal to the habit plane. vVhen external forces are acting, the
`resnlting effect on the lvI, temperature is calculated from the mechanical work done on or by the
`transforming region as the resolved shear and normal components of the applied stress are carried
`through the corresponding transformation strains. This energy term is added algebraically to the
`chemical free energy change of the reaction, to compute the alteration in temperature at which the
`critical value of the thermodynamic driving force is attained to initiate the transformation. The
`transformation is aided by shear stresses, but may be aided or opposed by the normal stress com(cid:173)
`ponent depending on whether the latter is tensile or compressive.
`The above criterion for the action of applied stress has successfully predicted the quantitative
`chang;e in the lv!, temperature of iron-nickel anc! iron-nickel-carbon alloys under uniaxial tension,
`uniaxial compression and hydrostatic pressure. }'Is is raised by tension, less so by compression, and is
`lowered by hydrostatic pressure.
`
`UN CRITERIUM DE L'ACTION D'UNE TENSION APPLIQUEE SUR LA
`TRANSFO RMA TI ON MAR TENSITI QU E
`La reaction martensitique est consideree comme une transformation de deformation avec efes
`deplacements induits par un cisaillement et une dilatation, respectivement parallele et normale au
`plan limite. Quand des efforts exterieurs agissent, leur effet sur la temperature lvis est calcule d'apres
`Ie travail effectue sur ou par la region en transformation quandles deux composantes, de cisaillement
`et norma Ie, de la tension appliquee sont reliees aux deformations correspondantes de la transforma(cid:173)
`tion. Cette energie est ajoutee algebriquement au changement de l'energie libre de la reaction, ce qui
`permet de calculer la modification de la temperature pour laquelle on atteint la valeur critique de la
`"force motrice" thermodynamique, pour initier la transformation. La transformation est aidee par
`les tensions de cisaillement, mais peut etre aidee ou contrariee par la composante normale de la
`tension, suivant que c'est une composante d'extension ou de compression.
`Ce criterium de l'action d'une tension appliquee a predit quantitativement, d'une maniere satis(cid:173)
`faisante, Ie changement de la temperature Ms des alliages fer-nickel et fer-nickel-carbone sous
`extension et compression uniaxiales et so us une pression hydrostatique. j118 est elevee par l'extension,
`un peu moins par la compression, et est abaissee par la pression hydrostatique.
`
`KRITERION FUR DIE WIRKUNG AUSSERER SPA~NUNGEN ACF DIE
`MARTENSITBILDUNG
`Die Martensitreaktion wird als eine Verzernmgsumwandlung mit Scherungs- und Dehnungsver(cid:173)
`schiebungen parallel und senkrecht zur Habitusebene behandelt. 1m Faile der Einwirkung ausserer
`Krafte wird der Gesamteffekt auf die M8 -Temperatur aus der geleisteten mechanischen Arbeit auf
`oder durch die transformierten Bereiche berechnet; dabei werden die Scherungs- und Normal(cid:173)
`komponenten der ausseren Spannung mit den entsprechenden Umwandlungsverzerrungen zusammen(cid:173)
`gefasst. Dieser Energ!~faktor wird algebraisch zu der Anderung der freien chemischen Reaktionsen(cid:173)
`ergie addiert urn die Anderung der Temperatur, bei der der kritische Wert der thermodynamischen
`Kraft die die Transformation auslbst erreicht ist, zu berechnen. Scherspannungen kbnnen die
`Transformation unterstiitzen; jedoch kann die Normalkomponente entweder eine unterstiitzende
`oder eine hindernde Wirkung haben, je nachdem ob es sich urn eine Zug- oder Druckkomponente
`handelt.
`Dies Kriteri~n fUr die \Virkung der ausseren Spannungen hat zu einer richtigen Voraussage der
`quantitativen Anderung der 1118 Temperatur in Eisen-Nickel- und Eisen-Nickel-Kohlenstoff Legier(cid:173)
`ungen unter einachsigem Zug, einachsiger Kompression und hydrostatischem Druck gefUhrt. lvIs
`wird durch Zug erhoht, in geringerm Masse auch durch Kompression und durch hydrostatischen
`Druck vermindert.
`
`1. Martensite Formation as a Strain
`Transformation
`The martensitic transformation is characterized
`by its displacive shear-like nature. Consequently, it
`may be regarded as a strain transformation or as a
`mode of deformation which competes with slip when
`external stresses are applied to the parent phase.
`According to Scheil [1], the shear stress required to
`activate the martensitic transformation decreases
`
`*Received April 1, 1953.
`tDepartment of Metallurgy, Massachusetts Institute of
`Technology, Cambridge, Massachusetts, U.S.A.
`
`ACTA METALLURGICA, VOL. I, SEPT. 1953
`
`with decreasing temperature (becoming nil at the
`Ms temperature where the reaction starts spontan(cid:173)
`eously on cooling), whereas the shear stress required
`to initiate yielding by slip increases with decreasing
`temperature. Thus, at temperatures near M" applied
`stresses should induce plastic deformation by the
`martensitic mode rather than by slip. On the other
`hand, when stresses are applied at temperatures
`.M." the slip mechanism
`sufficiently high above
`should supersede the transformation in the deforma(cid:173)
`tion process. In a general way, these postulated
`trends have been confirmed by experiment.
`Scheil's concept leads to a shear-stress criterion for
`
`Lombard Exhibit 1030, p. 1
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`538
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`ACTA :VIETALLCRGICA, \'OL. I, ID53
`
`References
`
`1. SCHElL, E. Z, anorg. Chern., 207 (1!l32) 21.
`2. MACHLIN, E. S. and COHEN, M. Trans. A.I.M.E., 191
`(ID51) 1019.
`3. GRENINGER, A. B. and TROIANO, A. R. Trans. A.I.M.E.,
`140 (1940) 307; 185 (1949) 590.
`4. BOWLES, J. S. Acta Cryst., 4 (1951) 162.
`5. FRANK, F. C. Acta Met., 1 (1953) 15.
`6. KULIN, S. A., COHEN, M., and AVERBACH, B. L.
`Metals, 4 (1952) 661.
`
`j.
`
`7. ZENER, C. Trans. A.1..'\1.E., 167 (I~I.H)) 513.
`8. COHEN, M., MACHLIN, E. S., and I'ARA);JPE, V. G.
`Thermodynamics
`in Physical Metallurgy
`(American
`Society for Metals, 1950) p. 242.
`9. JONES, F. W. and PUMPHREY, W. I.
`163 (1949), Part 2, 121.
`10. FISHER, j. C. Trans. A.I.M.E., 185 (l!J49) 688.
`11. FISHER, J. c., HOLLOMON, j. H., and TURNBULL, D.
`Trans. A.I.M.E., 185 (1949) 691.
`12. MACHLIN, E. S. and COHEN, M. j. Metals, 4 (1952) 489.
`13. AUSTIN, j. B. J. lndustr. Engng Chem., 24 (1932) 1225.
`
`j. Iron Steel lnst.,
`
`Lombard Exhibit 1030, p. 8
`
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