A Thermodynamic Theory Of The Fracture Of Metals

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-