The crystallography of martensite transformations I

Bowles, J.S; Mackenzie, J. K.

doi:10.1016/0001-6160(54)90102-9

Cited by 940 publications

(379 citation statements)

References 3 publications

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“…Furthermore, the Bain strain does not satisfy the minimum requirement of martensitic transformation, that the deformation must leave one line invariant in order to ensure sufficient coherency in the γ/α' interface to enable it to move without diffusion [3,4,[9][10][11]. This can be seen in Figs (Fig.…”

Section: Microstructure and Texture In Steels Andmentioning

confidence: 99%

“…However, it is often assumed in texture analysis that the orientation relationship between the austenite and martensite is that due to Kurdjumov-Sachs (KS) or Nishiyama-Wasserman (NW) [13,[17][18][19], but it has been known for some time that the true relation must be irrational [3,4,9,11]. Although the difference between this irrational and assumed orientation may seem less than a few degrees, it is vital because the assumed orientations do not in general lead to an invariant--line between the parent and product lattices.…”

Section: Microstructure and Texture In Steels Andmentioning

confidence: 99%

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Mathematics of Crystallographic Texture in Martensitic and Related Transformations

Bhadeshia

Kundu

Abreu

2009

Microstructure and Texture in Steels

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This paper is an introduction to the mathematical estimation of the crystallographic texture and microstructure resulting from the displacive transformation of austenite in steels, under the influence of an externally applied system of stresses. It begins with an introduction to the problem, a description of the phenomenological theory of martensite crystallography, and the application of this theory along with a variant selection criterion to determine the texture due to solid-state, displacive transformation. It is demonstrated that there remain difficulties which make a complete closure between theory and experiment unlikely. Progress is needed in relating the chemical and mechanical driving forces for phase transformation to the evolution of overall volume fractions of different crystallographic variants.

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Section: Microstructure and Texture In Steels Andmentioning

confidence: 99%

Section: Microstructure and Texture In Steels Andmentioning

confidence: 99%

Mathematics of Crystallographic Texture in Martensitic and Related Transformations

Bhadeshia

Kundu

Abreu

2009

Microstructure and Texture in Steels

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“…For example, we consider isotropic elasticity, whereas typically, the crystalline lattice of each of the martensite variants has less symmetry than that of the austenite. Further, for sufficiently large grains, the lattices associated with the various martensite variants could be combined, giving rise to twins and/or higher-rank laminates of two or more different variants of martensite within each grain [4,5,14,16,20]-an effect that our model does not allow. We also note that, in general, a stress-free transformation is a time-dependent process that involves energy dissipation.…”

Section: Stress-free Transformationmentioning

confidence: 99%

Rise of Correlations of Transformation Strains in Random Polycrystals

Berlyand¹,

Bruno

Novikov³

2008

SIAM J. Math. Anal.

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Abstract. We investigate the statistics of the transformation-strains that arise in random martensitic polycrystals as boundary conditions cause its component crystallites to undergo martensitic phase transitions. In our one-dimensional polycrystal model the orientation of the n grains is given by an uncorrelated random array of the orientation angles θ i , i = 1, . . . , n. Under imposed boundary conditions the polycrystal grains may undergo a martensitic transformation. The associated transformation strains ε i , i = 1, . . . , n depend on the array of orientation angles, and they can be obtained as a solution to a nonlinear optimization problem. While the random variables θ i , i = 1, . . . , n are uncorrelated, the random variables ε i , i = 1, . . . , n may be correlated. This issue is central in our considerations. We investigate it in following three different scaling limits: (i) Infinitely long grains (L = ∞); (ii) Grains of finite but large height (L = L ≫ 1); and (iii) Chain of short grains (L = l 0 /(2n), l 0 ≪ 1). With references to de Finetti's Theorem, Riesz' rearrangement inequality and near neighbor approximations, our analyses establish that under the scaling limits (i), (ii) and (iii) the arrays of transformation strains arising from given boundary conditions exhibit no correlations, long-range correlations and exponentially decaying short-range correlations, respectively.

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“…There have been extensive studies on the properties of α [3][4][5][6] and the phenomenological theory martensite crystallography (PTMC) [7,8]. Unlike the α martensite transformation, the α martensite transformation which was first found in a Ti-Nb system [9] can be thermoelastic, and the shape memory effect is present [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Martensitic Twinning in Alpha + Beta Ti-3.5Al-4.5Mo Titanium Alloy

Changfu

Yang

et al. 2011

Journal of Metallurgy

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The twinning structure of the orthorhombic α martensite phase in alpha + beta Ti-3.5Al-4.5Mo (wt%) titanium alloy was studied using X-ray diffraction and transmission electron microscopy by water quenching from below transus temperatures. While water quenching from 910 • C induced the formation of {110} • twins, quenching from 840 • C formed the α martensite with {111} • type I twins. The effect of the principle strains on the twinning structure was discussed. As compared to the previous studies, the principle strains play an important role in the formation of the twinning type.

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The crystallography of martensite transformations I

Cited by 940 publications

References 3 publications

Mathematics of Crystallographic Texture in Martensitic and Related Transformations

Mathematics of Crystallographic Texture in Martensitic and Related Transformations

Rise of Correlations of Transformation Strains in Random Polycrystals

Martensitic Twinning in Alpha + Beta Ti-3.5Al-4.5Mo Titanium Alloy

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