Crystal plasticity theory during the 1950s and 1960s

Abstract

In the field of crystal plasticity, the two decades 1950–1969 were a time of great activity, in which the foundations were laid for our present understanding of the work-hardening of face-centred cubic metals in terms of dislocation mechanisms. Decisive developments were the ‘invention’ of the Frank–Read source, the recognition of the importance of the specific energy of stacking faults, and the (at least partial) resolution of the controversy between macroscopic stress–strain measurements, X-ray results, ferromagnetism and the study of slip lines and slip bands on the one hand, and the observation of dislocations by transmission electron microscopy of thin foils prepared from plastically deformed macroscopic specimens on the other hand. The understanding of the dislocation mechanisms dominant at very large plastic strains was and still is limited, however. It is argued that here a holistic approach based on concepts such as energy dissipation and self-organization is more promising than the mechanistic approach based on concepts successfully developed in the two decades covered in the paper.

Keywords:

• plasticity
• dislocations
• metals
• work-hardening

Acknowledgements

The author wishes to express his gratitude to the two anonymous referees, whose reports were of exemplary quality, as well as to Professor Haél Mughrabi for his critical comments. He acknowledges also the assistance of the librarians at the Max Planck campus in Stuttgart–Büsnau, in particular to Daniela Kabinová, Ingrid Schwarz-Remeih and Ingeborg Jaiser, without whose competence and efficiency the present paper could not have been completed within a reasonable time.

Notes

1. For a personal description of the discovery by Frank see [2].

2. Based on a quantitative analysis of the Science Citation Index, the listed authors were either first or only authors of science publications during the 15 year period 1961–1975. During this period, each one of the 250 authors had been cited more than 4000 times. Among the 40 most frequently quoted physics publications (including mathematical physics and spectroscopy) two papers had originated from Germany, namely H.A. Bethe, Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie[14], and Ref. [12]. They were quoted 545 times [14] and 259 times [12], respectively.

3. Emil Heyn (1867–1921, [18]) was the founding director of the Kaiser-Wilhelm-Institut für Metallforschung in Berlin–Dahlem, which owing to the work of Schmid, Sachs, Boas, Wassermann and their associates became the leading institution in the experimental study of crystal plasticity till about 1932 [15], when the economic crisis forced the activities in Berlin–Dahlem to close down. – Heyn’s 1914 May Lecture to the Institute of Metals at Westminster [20] was entitled ‘Internal Strains in Cold-Wrought Metals, and some Troubles Caused thereby’.

4. Taylor [32] translated Dehlinger’s ‘Verhakung’ as ‘hooking’. In Dehlinger’s one-dimensional atomistic model (now usually referred to as Frenkel–Kontorova model [33]), Verhakungen represent sections perpendicular to their line direction through pairs of parallel dislocations of opposite sign. Dehlinger was the first to realize that in bulk what was to become known as dislocations had to be created pair wise. See also W.G. Burgers [29] and a letter of Nabarro to Burgers of 9 July 1946 referred to in Ref. [29].

5. Their paper appeared in the first volume of Acta Metallurgica, a truly international and interdisciplinary journal, launched in 1953 and financially supported by the American Society of Metals. The journal had an independent international board of governors that were nominated by the various national metallurgical societies participating in the project. All papers were accompanied by abstracts in English, French and German. Papers were acceptable in any language (which in practice meant in English, French or German, with Spanish as a rare exception). The journal was a tremendous success; many papers relevant for the present topic appeared in it. Unfortunately, its founders had not realized that there was no internationally accepted proof-marking system. For the Seeger–Schöck paper, this had the consequence that the printed version contained so many printing errors that it appeared impossible to correct them in an erratum. The most important errors were rectified in ref. [9], Sect. 73. Gaps due to the lack of computing capabilities were filled later by Schottky [64].

6. Hence emerging edge dislocations do not produce surface traces. In situations with a dominant slip system, this led to the nomenclature of ‘side surfaces’ (slip direction approximately parallel to the surface normal) and ‘front surfaces’ (slip direction perpendicular to the surface normal).

7. See, e.g. the otherwise excellent book of Zener [89], Sect. VII B II.

8. The active slip line lengths were determined after removing earlier slip traces by polishing, as pioneered by Crussard [118] and Blewitt et al. [72]. Active slip lines are visible only if they were generated by a not too small number n of dislocations with an appreciable screw character moving either on the same slip plane or on a bundle of neighbouring planes.

9. Determinations of this fraction at small plastic strains (in single crystals: Stage I) are difficult.