A comment on “fracture mechanism maps”

Scripta

METALLURCICA

V o l . 14, pp. 5 5 5 - 5 5 7 , 1980 Printed in t h e U . S . A .

Pergamon Press Ltd. All rights reserved.

A COMMENT ON "FRACTURE MECHANISM MAPS"

D.G. Brandon Dept. of Materials Engineering Technion, Israel Institute of Technology Haifa, Israel (Received

December

ii,

1980)

The fertile mind that gave us "Deformation Mechanism Maps" has now given us an 'overview' of fracture in the form of "Fracture Mechanism Maps" (1,2,3). However, whereas Deformation Mechanism Maps have proved themselves to be an excellent expository tool and a major teaching asset (to me, at least), some doubts could be raised concerning the usefulness of these new maps as an aid to understanding fracture. While most deformation mechanisms have been modeled reasonably satisfactorily in terms of accepted extrinsic and intrinsic parameters (yield stress, dislocation density, grainsize...), the same cannot be said for fracture mechanisms. In partic111ar there is no way I know of in which the dominant fracture mechanism for a given material under known conditions of stress and temperature can be predicted from existing models. Fracture Mechanism Maps are based on empirical observations and the results have about them a distinct air of "Gardening Hints". A basic problem is that neither the mechanism of fracture nor the fracture stress are independent of specimen size and geometry. This is not true for plastic shear, as characterised by the yield stress, which, in practically all engineering situations, is neither size nor shape dependent. Indeed, at least one of the fracture mechanisms considered in the Fracture Mechanism Maps, rupture, does not involve crack propagation at all (the only new surface created is at the external specimen surface). Rupture can only occur in specimens of finite dimensions. Does this mean that fracture is not a process amenable to analysis using the concept of "Mechanism Maps"? Well, perhaps yes, but it is probably worth trying. For a start, let us agree that the process of primary interest is the growth of a crack and so concentrate on this one aspect of fracture. After all, nucleation of a macrocrack is usually a poorly defined event, and in most engineering situations we have crack nuclei galore! Let us also limit the discussion to conditions of plane strain, thus eliminating at one blow all problems of specimen size and shape. Now, one step further, let us differentiate between the various mechanisms contributing to crack growth, the geometrical form of the fracture damage and, finally, the actual site of the damage in relation to the microstructure (Fig.l). In the simplest possible terms, for any polycrystalline material containing just one continuous phase there are only two sites for crack growth - either within the grains of the continuous phase or at the grain boundaries. That is, the fracture is either transgranular or intergranular. Similarly, on the microstructural scale, there are only two possible forms of fracture damage. Either the crack propagates by microcrack formation or it propagates by microvoid formation. All macroscopic crack propagation involves the generation, growth and linking-up of either of these two forms of damage. Finally, and in the crudest terms, there are only three possible mechanisms contributing to crack growth. These are, firstly, diffusionless-decohesion (corresponding to physical separation of the crystals by a Griffith strain-energy relaxation process, either across a cleavage plane or at a boundary), secondly irreversible shear (dislocation glide or viscous flow with varying degrees of thermal activation), or diffusion (either in the bulk or at a boundary, and suitably complicated by point-defect interactions, dislocation climb etc.). If we accept

* I ignore deformation twinning and stress-induced martensitic phase-transformations which can, of course, either increase or decrease fracture toughness.

555 0036-9748/80/050555-03502.00/0 Copyright (c) 1 9 8 0 P e r g a m o n Press

Ltd.

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COMMENT

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"FRACTURE

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this very simple breakdown, there is one corollary of major significance: while slip in plane strain tends to inhibit microcracking (by relaxing the stress at the tip of an existing crack), the same slip process promotes the growth and linking up of microvoids (by plastic thinning of the ligaments between microvoids). Another step towards rationalizing fracture mechanisms can be made by dropping tensile stress ~ as a critical parameter and substituting the stress intensity factor, K = ~ , where C is the half-length of an existing internal macrocrack. After all, fracture mechanics has been with us for some years now, and is clearly an improvement over previous theoretical attempts to understand fracture. Of course, the stress intensity factor must be normalized with respect to an "ideal" fracture toughness, K o = 2 ~ , where E is Young's modulus and y is the surface energy. We are now in a position to sketch the outline of a tentative Fracture Mechanism Map in which crack propagation rates are shown as a function of the normalized stress intensity factor, K/K o and the homologous temperature, T/Tm, where Tm is the absolute melting point (Fig.2). Below some arbitrary crack propagation rate (10 -8 m.sec.-l?) fracture does not occur under conditions of engineering interest and a flawed material retains its integrity "indefinitely". Above a somewhat less arbitrary rate the material disintegrates (that is, ballistic fragmentation is observed, involving the propagation of shock waves and strong adiabatic effects). At sufficiently low temperatures decohesion dominates and the fracture toughness is low because decohesion is not inhibited by significant plastic relaxation (by slip) at the tip of a growing crack. If the temperature is sufficiently high, and the crack growth rate sufficiently low, diffusion processes dominate. Crack propagation can then occur by void growth at low stress intensities without the need for dislocation generation and multiplication. Indeed, the more slip that is involved in fracture, the higher the critical stress intensity irrespective of the mode of fracture. In Fig. 3 I have made an attempt to "map" observed ~ a c t u r e modes onto the coordinates of Fig.2 for a hypothetical material. The cleavage modes correspond to diffusionless decohesion with increasing plastic relaxation at the tip of the propagating crack (and hence increasing toughness). Ductile fracture occurs by diffusionless void nucleation and coalescence. Transgranular creep failure is controlled by diffusion-assisted void growth within the grains, while intergranular creep failure may be controlled by a combination of void growth at boundaries and grain-boundary junctions together with grain-boundary sliding. The analysis of fracture mechanisms within this proposed framework would have several solid advantages. No size effects need be considered (plane-strain fracture only), crack propagation can be isolated from hypothetical nucleation processes, and, finally, crack mechanisms are clearly distinguished from the site or form of the fracture damage. I hope it is not too late to persuade Messrs. Ashby et.al, to change just one of their coordinates? References i. 2. 3.

M.F. Ashby, C. Gandhi and D.M.R. Taplin, Acta Met., 27, 699, C. Gandhi and M.F. Ashby, Scripta Met., i_~3, 371, (1979). C. Gandhi and M.F. Ashby, Acta Met., 2_~7, 1565, (Sept. 1979).

(1979).

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COMMENT

DAMAGE SITE

ON "FRACTURE M E C H A N I S M ~,~PS"

FORM OF DAMAGE

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CRACK GROWTH MECHANISM

DECOHESION

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Classification

of fracture modes.

MICROVO~

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BALLISTIC FRAGMENTATION

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