The laws of similitude and crack propagation

The mechanics of cracking follow the laws of similitude in an odd sense. As a result, crack load-external displacement-crack extension data are not usually non-dimensionalized. It follows that a new "group" should be used (analogous to the Reynolds, Froude or Cauchy numbers) when scaling ship ice-breaking resistance from tests of models in ice-towing-tanks.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22303/1/0000747.pd

Contribution on "Stability of cracking" by C. Gurney and Y. W. Mai

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22399/1/0000849.pd

The incorporation of work hardening and redundant work in rod-drawing analyses

With few exceptions, metal deformation analyses employ a constant yield stress (rigid, perfectly plastic metal) which ignores strain hardening, or a "mean" yield stress which attempts to accommodate strain hardening in a simplified manner. Since strain hardening is of interest here, little reference will be made to a rigid, plastic type of behavior.The first part of this paper demonstrates that the use of a mean yield stress underestimates the working loads (or stresses) needed to draw metal through conical dies as compared to those loads predicted by more "exact" analyses. In this context "exact" refers to those solutions obtained by incorporating the strain hardening relationship in the governing "force balance" differential equations prior to the integration of the said equations. It is shown, however, that the error introduced by the use of a mean yield stress is no more than some 8 per cent for conditions that typify actual practice. Since analyses of other metal-working processes, such as rolling and extrusion, employ the same sort of differential equation, it is felt that these results are applicable there also.The second part of this paper shows that redundant work in rod drawing may be approached either from considerations of the mechanical properties that result after the metal is drawn or from considerations of the stress necessary to draw down the rod. Contrary to what is implied in the literature, it is shown that these two approaches lead to different interpretations of the "redundant work factor". Relationships are given between the two for metals that are assumed to strain harden in certain simple ways.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33226/1/0000616.pd

Determination of valid R -curves for materials with large fracture toughness to yield strength ratios

Crack growth resistance curves are derived from a generalised theory of quasi-static crack propagation due to Gurney and Hunt. Both the subcritical and continuous cracking regions are investigated, where the fracture toughness of the material may depend on the cracking rate, the reacting environment at the crack tip and the mode of fracture. Precise conditions for stability of the spreading crack relative to chosen constraints of either a displacement- or load-controlled machine are formulated. Cracking of sheet materials with high fracture toughness and low yield stress, (e.g. ( K /σ y ) 2 > 200 mm), which do not satisfy certain size requirements, is often complicated by generalised yielding at regions remote from the crack tip. Complete R -curves for such materials cannot be established with conventional testpieces in the laboratory. The present paper adopts a new experimental technique [1] where a laboratory size reinforcement rig attached to the testpiece eliminates all irreversibilities caused by generalised yielding. Valid fracture toughness values and crack growth resistance curves are thereby determined, irrespective of the amount of elastic and plastic deformations occurring at the crack tip. Successful R -curve experiments are described for fracture in a few ductile and tough materials such as 7075-T3. and 1100-0 aluminium alloys, and a low carbon steel. Comparison is made with other published R -curves, and the influence of sheet thickness and ( K 1 c /σ y ) ratio on the geometry of R -curves is investigated. A simple relationship for R -curves is suggested, viz. : R = R 0 + (Δ L ) p , where, it seems, R 0 can be identified with the plane strain toughness (i.e. R 0 = G 1c = K 1c 2 / E (1 - v 2 )1/2). A possible reason for this unexpected result is given in the paper. Useful estimates of K lc may thus be available from thin sheet tests.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42760/1/10704_2004_Article_BF00032834.pd

On the stability of cracking in tapered DCB testpieces

The conventional tapered DCB specimen loaded at the apex is shown to exhibit less stability than parallel DCB testpieces cracking under stiff testing conditions. A modified test with loadings applied at the thick base instead of near the apex is suggested. Experiments agree with theory that this provides better cracking stability and easier control of the crack path, along with a wider range of crack velocities in one test. On montre que les éprouvettes doubles Cantilever conventionelles à bords convergents et chargées à leur extrémité présentent une stabilité moindre que les éprouvettes à bords parallèles, lors de la fissuration sous des conditions d'essai rigides. On suggère un essai modifié, où les charges sont appliquées du côté le plus épais au lieu du voisinage de la pointe de l'éprouvette.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42754/1/10704_2004_Article_BF00033840.pd

A yield criterion for anisotropic and pressure dependent solids such as oriented polymers

The anisotropic yield criterion first posed by Hill has been modified to account for differences in tensile and compressive yield strengths in a given direction; additionally, the influence of hydrostatic pressure on yielding is also considered. Predictions using this new criterion are compared with published experimental results involving oriented polymers and excellent agreement is found. It is suggested that this criterion is more correct on fundamental grounds than those put forth in earlier publications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44783/1/10853_2004_Article_BF00754900.pd

Crack tip effective strain rates in rate sensitive materials

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42755/1/10704_2004_Article_BF00033853.pd

Macroscopic yielding of oriented polymers

Uniaxial and biaxial stress states were employed to compare the measured macroscopic yield behaviour of oriented polycarbonate, polyethylene, and polypropylene with a proposed anisotropic and pressure-dependent yield criterion. A good correlation between theory and experiment was found for each material.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44674/1/10853_2004_Article_BF00561975.pd

The macroscopic yield behaviour of polymers

A yield criterion, not previously compared with the actual macroscopic behaviour of polymers, is herein compared with the pressure-modified octahedral shear stress criterion earlier suggested by others. This new relation, which is a version of the von Mises criterion, accommodates differences in tensile and compressive yield strengths and accounts for any dependence of yielding on the hydrostatic component of the applied stress state.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44784/1/10853_2004_Article_BF00550671.pd