Fundamental Strength Sciences:

First Explaining

Bridgman's Effect

© Lev Gelimson

P. W. Bridgman, Nobel Prize Winner, discovered essentially increasing strength of materials in uniform triaxial compression, e.g., for isotropic ductile materials with equal strength in tension and compression. But the well-known critical state criteria ignore Bridgman's effect completely, consider strength of materials to be independent of uniform triaxial compression at all, and, in spherical tension, give infinite limiting stresses physically impossible. All the more, those criteria are separate for diverse materials types, have nothing in common with simple and universal fundamental laws of nature, and possess evident defects.

In the simplest case, the structure of a critical state criterion is as follows.

The equidangerous uniaxial tensile stress that is equivalent to the triaxial stress state under consideration by the degree of the danger of the closest critical state (by yield, failure, etc.) and represented by a certain function of the principal stresses by vanishing the shear stresses and possibly of some material constants is equal to the uniaxial limiting stress in a corresponding critical state such as yield or failure of a solid's material, e.g., the yield stress or the ultimate strength. 

That function is specified by diverse criteria. For example, according to the theory of maximum shearing stresses, it is the difference of the ultimate principal stresses. By the theory of potential energy of distortion, it is the intensity of stresses. They both are not sensitive at all to uniform triaxial tensions or compressions, the third one additionally to the intermediate principal stress also important.

The cardinal idea and physical sense of correcting a critical state criterion in fundamental mechanical and strength sciences is using variable values of critical state (process) criteria functions in critical states (processes). In the simplest case, it is the hypothesis on a linear influence of the principal stresses on reaching a limiting state. Namely, in limiting states, suppose the equivalent stress be no constant as in an initial criterion but a linear function of the principal stresses. Taking the data on uniaxial tension and compression into account gives the criterion with an additional constant of the material. In the case of the theory of maximum shearing stresses, use the more specific hypothesis on the linear influence of the intermediate principal stress on reaching a limiting state.

The introduction of the pure (dimensionless) constant of a material additional to the unique constant of a material, is justified as follows. The limiting stress is not sufficient to take into account the influence of the intermediate principal stress and of uniform triaxial tensions and compressions on reaching a limiting state.

The physical sense of this additional constant: It is the uniaxial limiting stress divided by the limiting stress in uniform triaxial tension. The last can be hardly determined directly but may be obtained by using the data on a third experiment with a nonzero intermediate principal stress, e.g., biaxial compression or triaxial tension and compression (but pure shear is not suitable).

Fundamental mechanical and strength sciences also foresee further generalizing the above linear correction method to extend strength laws hierarchies using equations including different functions of the reduced (relative) principal normal stresses and possibly of some pure constants of a solid's material. It is desirable to choose those functions having obvious physical sense and possibly least numbers of material's parameters. Their values may be selected from experimental data on uniaxial critical states and other simple ones.

It can happen that the reduced experimental data on the strength of some material under consideration essentially differs from the data given by corresponding critical state criteria under similar conditions of loading. The least possible increase of the number of parameters in such a criterion is then necessary according to the principle of tolerable simplicity as a milestone of fundamental mechanical and strength sciences.

The results obtained in this way fit experimental data, e.g., for steel, gray iron, aluminum alloys, ceramic metal, graphite, glass, crystalline glass, and polystyrene.

Such a correction of critical state criteria allows to take into account the influence of uniform triaxial tension and compression on reaching a critical state and to except corresponding methodical errors typical for all well-known criteria. Thus it first explains Bridgman's effect.

For formulae and details, see the scientific website of the author and especially his works under "Strength".